diff --git a/experiments/learnability/bestfirst_eval_gold/eval_driver.log b/experiments/learnability/bestfirst_eval_gold/eval_driver.log new file mode 100644 index 0000000000000000000000000000000000000000..59bc6a7abbfc56a3975d4dec5f179fadf1ba0326 --- /dev/null +++ b/experiments/learnability/bestfirst_eval_gold/eval_driver.log @@ -0,0 +1,62 @@ +[2026-06-29 17:15:58] ===== START: 20 gold best-first evals (max_pops=4000 timeout=600s) on GPUs 0 1 2 3 ===== +[2026-06-29 17:15:58] EVAL [0/20] final/gold_0pt/s42/2026-06-29_07-09-16 -> gpu 0 +[2026-06-29 17:15:58] EVAL [1/20] final/gold_0pt/s43/2026-06-29_07-09-16 -> gpu 1 +[2026-06-29 17:15:58] EVAL [2/20] final/gold_0pt/s44/2026-06-29_07-09-16 -> gpu 2 +[2026-06-29 17:15:58] EVAL [3/20] final/gold_0pt/s45/2026-06-29_07-09-27 -> gpu 3 +[2026-06-29 18:01:44] EVAL DONE final/gold_0pt/s44/2026-06-29_07-09-16 +[2026-06-29 18:01:50] EVAL DONE final/gold_0pt/s45/2026-06-29_07-09-27 +[2026-06-29 18:01:56] EVAL DONE final/gold_0pt/s43/2026-06-29_07-09-16 +[2026-06-29 18:02:13] EVAL DONE final/gold_0pt/s42/2026-06-29_07-09-16 +[2026-06-29 18:02:13] EVAL [4/20] final/gold_0pt/s46/2026-06-29_07-09-27 -> gpu 0 +[2026-06-29 18:02:13] EVAL [5/20] final/gold_1pt/s42/2026-06-29_07-09-27 -> gpu 1 +[2026-06-29 18:02:13] EVAL [6/20] final/gold_1pt/s43/2026-06-29_07-09-43 -> gpu 2 +[2026-06-29 18:02:13] EVAL [7/20] final/gold_1pt/s44/2026-06-29_07-09-43 -> gpu 3 +[2026-06-29 18:44:56] EVAL DONE final/gold_1pt/s44/2026-06-29_07-09-43 +[2026-06-29 18:46:19] EVAL DONE final/gold_1pt/s43/2026-06-29_07-09-43 +[2026-06-29 18:47:32] EVAL DONE final/gold_1pt/s42/2026-06-29_07-09-27 +[2026-06-29 18:48:39] EVAL DONE final/gold_0pt/s46/2026-06-29_07-09-27 +[2026-06-29 18:48:39] EVAL [8/20] final/gold_1pt/s45/2026-06-29_07-09-43 -> gpu 0 +[2026-06-29 18:48:39] EVAL [9/20] final/gold_1pt/s46/2026-06-29_07-10-05 -> gpu 1 +[2026-06-29 18:48:39] EVAL [10/20] mid/gold_0pt/s42/2026-06-29_07-09-16 -> gpu 2 +[2026-06-29 18:48:39] EVAL [11/20] mid/gold_0pt/s43/2026-06-29_07-09-16 -> gpu 3 +[2026-06-29 19:32:23] EVAL DONE final/gold_1pt/s45/2026-06-29_07-09-43 +[2026-06-29 19:34:20] EVAL DONE mid/gold_0pt/s42/2026-06-29_07-09-16 +[2026-06-29 19:34:22] EVAL DONE mid/gold_0pt/s43/2026-06-29_07-09-16 +[2026-06-29 19:34:59] EVAL DONE final/gold_1pt/s46/2026-06-29_07-10-05 +[2026-06-29 19:34:59] EVAL [12/20] mid/gold_0pt/s44/2026-06-29_07-09-16 -> gpu 0 +[2026-06-29 19:34:59] EVAL [13/20] mid/gold_0pt/s45/2026-06-29_07-09-27 -> gpu 1 +[2026-06-29 19:34:59] EVAL [14/20] mid/gold_0pt/s46/2026-06-29_07-09-27 -> gpu 2 +[2026-06-29 19:34:59] EVAL [15/20] mid/gold_1pt/s42/2026-06-29_07-09-27 -> gpu 3 +[2026-06-29 20:09:44] EVAL DONE mid/gold_1pt/s42/2026-06-29_07-09-27 +[2026-06-29 20:20:36] EVAL DONE mid/gold_0pt/s46/2026-06-29_07-09-27 +[2026-06-29 20:20:45] EVAL DONE mid/gold_0pt/s45/2026-06-29_07-09-27 +[2026-06-29 20:21:13] EVAL DONE mid/gold_0pt/s44/2026-06-29_07-09-16 +[2026-06-29 20:21:13] EVAL [16/20] mid/gold_1pt/s43/2026-06-29_07-09-43 -> gpu 0 +[2026-06-29 20:21:13] EVAL [17/20] mid/gold_1pt/s44/2026-06-29_07-09-43 -> gpu 1 +[2026-06-29 20:21:13] EVAL [18/20] mid/gold_1pt/s45/2026-06-29_07-09-43 -> gpu 2 +[2026-06-29 20:21:13] EVAL [19/20] mid/gold_1pt/s46/2026-06-29_07-10-05 -> gpu 3 +[2026-06-29 20:55:08] EVAL DONE mid/gold_1pt/s45/2026-06-29_07-09-43 +[2026-06-29 20:56:18] EVAL DONE mid/gold_1pt/s46/2026-06-29_07-10-05 +[2026-06-29 20:56:31] EVAL DONE mid/gold_1pt/s43/2026-06-29_07-09-43 +[2026-06-29 20:56:43] EVAL DONE mid/gold_1pt/s44/2026-06-29_07-09-43 +[2026-06-29 20:56:43] --- All gold best-first evals complete --- +27 / 94 /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/bf_extrinsic-95_final.json +26 / 94 /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/bf_extrinsic-95_mid.json +27 / 94 /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_final.json +26 / 94 /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 +27 / 94 /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 +26 / 94 /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 +27 / 94 /datadrive/ayush/home/minimoX/learning/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 +26 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.json +27 / 94 /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_final.json +26 / 94 /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 +51 / 94 /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/bf_extrinsic-95_final.json +49 / 94 /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/bf_extrinsic-95_mid.json +53 / 94 /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_final.json +49 / 94 /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 +51 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json +49 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +52 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json +49 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +50 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json +51 / 94 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json diff --git a/experiments/learnability/run_bestfirst_eval.sh b/experiments/learnability/run_bestfirst_eval.sh new file mode 100644 index 0000000000000000000000000000000000000000..77072843e4f72fd44126ca3e017d4e1ce9a5be50 --- /dev/null +++ b/experiments/learnability/run_bestfirst_eval.sh @@ -0,0 +1,89 @@ +#!/bin/bash +# ============================================================================= +# Best-first eval driver (value-free, no MCTS). Sibling of run_policy_only_eval.sh. +# +# Evaluates the SAME checkpoints with bestfirst_search.py (priority = cumulative +# log policy prob; budget = --max-pops, mirrors MCTS max_mcts_nodes=4000). +# +# eval set: base minimo_0pt (0.pt), base minimo_1pt (1.pt), and every +# policy-only finetuned epoch_2.pt (final) + epoch_1.pt (mid). +# eval: bestfirst_search.py, extrinsic-95, --max-pops 4000, --timeout 600. +# Action cap OFF (faithful to MCTS). +# +# Uses all 4 GPUs, one eval per GPU at a time. +# ============================================================================= +set -u + +LEARN=/datadrive/ayush/home/minimoX/learning +cd "$LEARN" || exit 1 + +source "$(conda info --base)/etc/profile.d/conda.sh" +conda activate minimo_new +export WANDB_MODE=offline + +CKPT0=/datadrive/ayush/home/minimoX/learning/checkpoints/dnn3_bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +CKPT1=/datadrive/ayush/home/minimoX/learning/checkpoints/dnn3_bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +TRAIN_BASE=$LEARN/experiments/learnability/train_policy_only +BF_EVAL=$LEARN/experiments/learnability/bestfirst_eval +mkdir -p "$BF_EVAL" + +PROBLEMSET=extrinsic-95 +BF_MAXPOPS=4000 +BF_WORKERS=6 +BF_TIMEOUT=600 # per-problem wall-clock budget (s) +GPUS=(0 1 2 3) +NGPU=${#GPUS[@]} + +LOG=$BF_EVAL/eval_driver.log +ts() { date +"%Y-%m-%d %H:%M:%S"; } +log() { echo "[$(ts)] $*" | tee -a "$LOG"; } + +# ---- Build eval job table (parallel arrays) -------------------------------- +E_CKPT=(); E_JSON=(); E_LOG=(); E_LABEL=() +add_eval() { E_CKPT+=("$1"); E_JSON+=("$2"); E_LOG+=("$3"); E_LABEL+=("$4"); } + +add_eval "$CKPT0" "$BF_EVAL/minimo_0pt_base_bf_${PROBLEMSET}.json" \ + "$BF_EVAL/minimo_0pt_base_bf_${PROBLEMSET}.log" "base/minimo_0pt" +add_eval "$CKPT1" "$BF_EVAL/minimo_1pt_base_bf_${PROBLEMSET}.json" \ + "$BF_EVAL/minimo_1pt_base_bf_${PROBLEMSET}.log" "base/minimo_1pt" + +for CKPT_NAME in epoch_2.pt epoch_1.pt; do + TAG=$([[ $CKPT_NAME == epoch_2.pt ]] && echo final || echo mid) + while IFS= read -r ckpt; do + [[ -z "$ckpt" ]] && continue + ckpt=$(realpath "$ckpt") + label=$(echo "$ckpt" | sed "s#.*train_policy_only/##; s#/updates.*##") + add_eval "$ckpt" \ + "$(dirname "$ckpt")/bf_${PROBLEMSET}_${TAG}.json" \ + "$(dirname "$ckpt")/bf_${PROBLEMSET}_${TAG}.log" \ + "$TAG/$label" + done < <(find "$TRAIN_BASE" -name "$CKPT_NAME" -path "*updates_*" 2>/dev/null | sort) +done + +NJOBS=${#E_CKPT[@]} +log "===== START: $NJOBS best-first evals (max_pops=${BF_MAXPOPS} timeout=${BF_TIMEOUT}s) on GPUs ${GPUS[*]} =====" + +k=0 +for ((j=0; j gpu $gpu" + ( + CUDA_VISIBLE_DEVICES=$gpu python -u bestfirst_search.py \ + --agent "${E_CKPT[$j]}" \ + --problemset "$PROBLEMSET" \ + --max-pops "$BF_MAXPOPS" \ + --workers "$BF_WORKERS" \ + --timeout "$BF_TIMEOUT" \ + --output "${E_JSON[$j]}" \ + > "${E_LOG[$j]}" 2>&1 + echo "[$(ts)] EVAL DONE ${E_LABEL[$j]}" >> "$LOG" + ) & + k=$((k + 1)) + if (( k % NGPU == 0 )); then wait; fi +done +wait +log "--- All evals complete ---" + +for f in $(find "$BF_EVAL" "$TRAIN_BASE" -name "bf_${PROBLEMSET}_*.json" -o -name "minimo_*_base_bf_${PROBLEMSET}.json" 2>/dev/null | sort); do + python -c "import json;d=json.load(open('$f'));print(d['num_solved'],'/',d['num_problems'],'$f')" 2>/dev/null | tee -a "$LOG" +done diff --git a/experiments/learnability/run_bestfirst_eval_gold.sh b/experiments/learnability/run_bestfirst_eval_gold.sh new file mode 100644 index 0000000000000000000000000000000000000000..b39eaa10d4a05be5d8be54a0504f4da2006dd111 --- /dev/null +++ b/experiments/learnability/run_bestfirst_eval_gold.sh @@ -0,0 +1,80 @@ +#!/bin/bash +# ============================================================================= +# Best-first eval driver for the POLICY-ONLY GOLD checkpoints. +# Sibling of run_bestfirst_eval.sh; evaluates only the gold finetuned models +# (base 0/1.pt are already covered by run_bestfirst_eval.sh). +# +# eval set: every policy-only-gold epoch_2.pt (final) + epoch_1.pt (mid) +# under train_policy_only_gold/. +# eval: bestfirst_search.py, extrinsic-95, --max-pops 4000, --timeout 600. +# Action cap OFF (faithful to MCTS). +# +# Uses all 4 GPUs, one eval per GPU at a time. +# ============================================================================= +set -u + +LEARN=/datadrive/ayush/home/minimoX/learning +cd "$LEARN" || exit 1 + +source "$(conda info --base)/etc/profile.d/conda.sh" +conda activate minimo_new +export WANDB_MODE=offline + +TRAIN_BASE=$LEARN/experiments/learnability/train_policy_only_gold +BF_EVAL=$LEARN/experiments/learnability/bestfirst_eval_gold +mkdir -p "$BF_EVAL" + +PROBLEMSET=extrinsic-95 +BF_MAXPOPS=4000 +BF_WORKERS=6 +BF_TIMEOUT=600 +GPUS=(0 1 2 3) +NGPU=${#GPUS[@]} + +LOG=$BF_EVAL/eval_driver.log +ts() { date +"%Y-%m-%d %H:%M:%S"; } +log() { echo "[$(ts)] $*" | tee -a "$LOG"; } + +E_CKPT=(); E_JSON=(); E_LOG=(); E_LABEL=() +add_eval() { E_CKPT+=("$1"); E_JSON+=("$2"); E_LOG+=("$3"); E_LABEL+=("$4"); } + +for CKPT_NAME in epoch_2.pt epoch_1.pt; do + TAG=$([[ $CKPT_NAME == epoch_2.pt ]] && echo final || echo mid) + while IFS= read -r ckpt; do + [[ -z "$ckpt" ]] && continue + ckpt=$(realpath "$ckpt") + label=$(echo "$ckpt" | sed "s#.*train_policy_only_gold/##; s#/updates.*##") + add_eval "$ckpt" \ + "$(dirname "$ckpt")/bf_${PROBLEMSET}_${TAG}.json" \ + "$(dirname "$ckpt")/bf_${PROBLEMSET}_${TAG}.log" \ + "$TAG/$label" + done < <(find "$TRAIN_BASE" -name "$CKPT_NAME" -path "*updates_*" 2>/dev/null | sort) +done + +NJOBS=${#E_CKPT[@]} +log "===== START: $NJOBS gold best-first evals (max_pops=${BF_MAXPOPS} timeout=${BF_TIMEOUT}s) on GPUs ${GPUS[*]} =====" + +k=0 +for ((j=0; j gpu $gpu" + ( + CUDA_VISIBLE_DEVICES=$gpu python -u bestfirst_search.py \ + --agent "${E_CKPT[$j]}" \ + --problemset "$PROBLEMSET" \ + --max-pops "$BF_MAXPOPS" \ + --workers "$BF_WORKERS" \ + --timeout "$BF_TIMEOUT" \ + --output "${E_JSON[$j]}" \ + > "${E_LOG[$j]}" 2>&1 + echo "[$(ts)] EVAL DONE ${E_LABEL[$j]}" >> "$LOG" + ) & + k=$((k + 1)) + if (( k % NGPU == 0 )); then wait; fi +done +wait +log "--- All gold best-first evals complete ---" + +for f in $(find "$TRAIN_BASE" -name "bf_${PROBLEMSET}_*.json" 2>/dev/null | sort); do + python -c "import json;d=json.load(open('$f'));print(d['num_solved'],'/',d['num_problems'],'$f')" 2>/dev/null | tee -a "$LOG" +done diff --git a/experiments/learnability/train_policy_only/driver.log b/experiments/learnability/train_policy_only/driver.log new file mode 100644 index 0000000000000000000000000000000000000000..7286999fc307e4d2ac95bcaa8ddd649c2d87852b --- /dev/null +++ b/experiments/learnability/train_policy_only/driver.log @@ -0,0 +1,26 @@ +[2026-06-28 05:29:53] ===== START: 10 policy-only training jobs on GPUs 2 3 ===== +[2026-06-28 05:29:53] --- Phase 1: training (policy-only) --- +[2026-06-28 05:29:53] TRAIN [0/10] minimo_0pt/s42 (seed=42) -> gpu 2 +[2026-06-28 05:29:53] TRAIN [1/10] minimo_0pt/s43 (seed=43) -> gpu 3 +[2026-06-28 05:30:10] TRAIN DONE minimo_0pt/s43 +[2026-06-28 05:30:11] TRAIN DONE minimo_0pt/s42 +[2026-06-28 05:30:11] TRAIN [2/10] minimo_0pt/s44 (seed=44) -> gpu 2 +[2026-06-28 05:30:11] TRAIN [3/10] minimo_0pt/s45 (seed=45) -> gpu 3 +[2026-06-28 05:30:28] TRAIN DONE minimo_0pt/s44 +[2026-06-28 05:30:29] TRAIN DONE minimo_0pt/s45 +[2026-06-28 05:30:29] TRAIN [4/10] minimo_0pt/s46 (seed=46) -> gpu 2 +[2026-06-28 05:30:29] TRAIN [5/10] minimo_1pt/s42 (seed=42) -> gpu 3 +[2026-06-28 05:30:48] TRAIN DONE minimo_0pt/s46 +[2026-06-28 05:30:48] TRAIN DONE minimo_1pt/s42 +[2026-06-28 05:30:48] TRAIN [6/10] minimo_1pt/s43 (seed=43) -> gpu 2 +[2026-06-28 05:30:48] TRAIN [7/10] minimo_1pt/s44 (seed=44) -> gpu 3 +[2026-06-28 05:31:08] TRAIN DONE minimo_1pt/s44 +[2026-06-28 05:31:08] TRAIN DONE minimo_1pt/s43 +[2026-06-28 05:31:08] TRAIN [8/10] minimo_1pt/s45 (seed=45) -> gpu 2 +[2026-06-28 05:31:08] TRAIN [9/10] minimo_1pt/s46 (seed=46) -> gpu 3 +[2026-06-28 05:31:27] TRAIN DONE minimo_1pt/s45 +[2026-06-28 05:31:27] TRAIN DONE minimo_1pt/s46 +[2026-06-28 05:31:28] --- Phase 1 complete --- +[2026-06-28 05:31:28] --- Eval phase (final, epoch_2.pt, value-free rollout) --- +[2026-06-28 05:31:28] EVAL-final [0] minimo_0pt/s42 (epoch_2.pt) -> gpu 2 +[2026-06-28 05:31:28] EVAL-final [1] minimo_0pt/s43 (epoch_2.pt) -> gpu 3 diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/summary.json b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..0ef46a3e0a5b3cef04764ee655102089186c3ad0 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + 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+ "pops_used": 4000, + "evals_used": 31101, + "max_open": 27102, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31006, + "max_open": 27007, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25933, + "max_open": 21934, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26066, + "max_open": 22067, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31380, + "max_open": 27381, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31159, + "max_open": 27160, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..b42a9c8508eeb47e3fec42f918b622dcc72c66ba --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_final.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=5 evals=25 maxopen=19) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_5 (solved pops=56 evals=368 maxopen=313) +[OK ] extrinsic_L0_3 (solved pops=61 evals=368 maxopen=308) +[OK ] extrinsic_L0_6 (solved pops=57 evals=353 maxopen=297) +[OK ] extrinsic_L0_10 (solved pops=7 evals=41 maxopen=35) +[OK ] extrinsic_L0_7 (solved pops=55 evals=353 maxopen=299) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_13 (solved pops=20 evals=152 maxopen=133) +[OK ] extrinsic_L0_8 (solved pops=57 evals=358 maxopen=302) +[OK ] extrinsic_L0_9 (solved pops=50 evals=327 maxopen=278) +[OK ] extrinsic_L0_4 (solved pops=210 evals=1122 maxopen=913) +[OK ] extrinsic_L1_4 (solved pops=15 evals=100 maxopen=84) +[OK ] extrinsic_L0_11 (solved pops=210 evals=1128 maxopen=919) +[OK ] extrinsic_L1_1 (solved pops=220 evals=1197 maxopen=978) +[OK ] extrinsic_L1_2 (solved pops=453 evals=2391 maxopen=1939) +[OK ] extrinsic_L1_3 (solved pops=453 evals=2388 maxopen=1936) +[OK ] extrinsic_L2_1 (solved pops=1258 evals=6879 maxopen=5622) +[OK ] extrinsic_L2_6 (solved pops=1632 evals=9480 maxopen=7849) +[OK ] extrinsic_L2_7 (solved pops=1018 evals=5729 maxopen=4712) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25975 maxopen=21976) +[OK ] extrinsic_L0_14 (solved pops=3961 evals=25978 maxopen=22018) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25929 maxopen=21930) +[OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25924 maxopen=21925) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25762 maxopen=21763) +[OK ] extrinsic_L2_9 (solved pops=982 evals=5486 maxopen=4505) +[OK ] extrinsic_L2_12 (solved pops=1372 evals=7859 maxopen=6488) +[ ] extrinsic_L2_8 (budget pops=4000 evals=25957 maxopen=21958) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26423 maxopen=22424) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25801 maxopen=21802) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25943 maxopen=21944) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25834 maxopen=21835) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25838 maxopen=21839) +[ ] extrinsic_L3_4 (budget pops=4000 evals=26051 maxopen=22052) +[ ] extrinsic_L3_5 (budget pops=4000 evals=26026 maxopen=22027) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25763 maxopen=21764) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25865 maxopen=21866) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26009 maxopen=22010) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26172 maxopen=22173) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25980 maxopen=21981) +[ ] extrinsic_L3_11 (budget pops=4000 evals=26132 maxopen=22133) +[OK ] extrinsic_L3_14 (solved pops=3258 evals=19954 maxopen=16697) +[OK ] extrinsic_L3_13 (solved pops=3540 evals=22824 maxopen=19285) +[ ] extrinsic_L3_12 (budget pops=4000 evals=26150 maxopen=22151) +[ ] extrinsic_L3_15 (budget pops=4000 evals=26074 maxopen=22075) +[ ] extrinsic_L3_16 (budget pops=4000 evals=26067 maxopen=22068) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25715 maxopen=21716) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25421 maxopen=21422) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26015 maxopen=22016) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26112 maxopen=22113) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26108 maxopen=22109) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25824 maxopen=21825) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26312 maxopen=22313) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26026 maxopen=22027) +[ ] extrinsic_L3_25 (budget pops=4000 evals=26895 maxopen=22896) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25928 maxopen=21929) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26273 maxopen=22274) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25782 maxopen=21783) +[ ] extrinsic_L4_1 (budget pops=4000 evals=25492 maxopen=21493) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26809 maxopen=22810) +[ ] extrinsic_L4_3 (budget pops=4000 evals=26063 maxopen=22064) +[ ] extrinsic_L4_2 (budget pops=4000 evals=25825 maxopen=21826) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25916 maxopen=21917) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26129 maxopen=22130) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25949 maxopen=21950) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26691 maxopen=22692) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26648 maxopen=22649) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26170 maxopen=22171) +[OK ] extrinsic_L4_12 (solved pops=1359 evals=7543 maxopen=6182) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25514 maxopen=21515) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26263 maxopen=22264) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26113 maxopen=22114) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26299 maxopen=22300) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25763 maxopen=21764) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26236 maxopen=22237) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26293 maxopen=22294) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25736 maxopen=21737) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26570 maxopen=22571) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26095 maxopen=22096) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26521 maxopen=22522) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26315 maxopen=22316) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26292 maxopen=22293) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26492 maxopen=22493) +[ ] extrinsic_L6_1 (budget pops=4000 evals=26085 maxopen=22086) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31467 maxopen=27468) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31314 maxopen=27315) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31270 maxopen=27271) +[ ] extrinsic_L6_4 (budget pops=4000 evals=31101 maxopen=27102) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31006 maxopen=27007) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25933 maxopen=21934) +[ ] extrinsic_L6_7 (budget pops=4000 evals=26066 maxopen=22067) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31380 maxopen=27381) +[ ] extrinsic_L6_9 (budget pops=4000 evals=31159 maxopen=27160) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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 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"solution_actions": null, + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26340, + "max_open": 22341, + "solution_actions": null, + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25473, + "max_open": 21474, + "solution_actions": null, + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26131, + "max_open": 22132, + "solution_actions": null, + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26205, + "max_open": 22206, + "solution_actions": null, + "problem": "extrinsic_L5_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25443, + "max_open": 21444, + "solution_actions": null, + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26459, + "max_open": 22460, + "solution_actions": null, + "problem": "extrinsic_L5_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26130, + "max_open": 22131, + "solution_actions": null, + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26402, + "max_open": 22403, + "solution_actions": null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26271, + "max_open": 22272, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26532, + "max_open": 22533, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26596, + "max_open": 22597, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31081, + "max_open": 27082, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25735, + "max_open": 21736, + "solution_actions": null, + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31216, + "max_open": 27217, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31181, + "max_open": 27182, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30910, + "max_open": 26911, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30805, + "max_open": 26806, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25755, + "max_open": 21756, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25697, + "max_open": 21698, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31211, + "max_open": 27212, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30989, + "max_open": 26990, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..3114ee896495f921103aa1b62bd4c0f9b2cdbce5 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/bf_extrinsic-95_mid.log @@ -0,0 +1,755 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) +[OK ] extrinsic_L0_2 (solved pops=55 evals=352 maxopen=298) +[OK ] extrinsic_L0_3 (solved pops=79 evals=452 maxopen=374) +[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_6 (solved pops=51 evals=316 maxopen=266) +[OK ] extrinsic_L0_9 (solved pops=49 evals=328 maxopen=264) +[OK ] extrinsic_L0_7 (solved pops=55 evals=354 maxopen=300) +[OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) +[OK ] extrinsic_L0_8 (solved pops=53 evals=349 maxopen=297) +[OK ] extrinsic_L0_13 (solved pops=21 evals=167 maxopen=147) +[OK ] extrinsic_L0_4 (solved pops=223 evals=1221 maxopen=999) +[OK ] extrinsic_L1_4 (solved pops=15 evals=101 maxopen=85) +[OK ] extrinsic_L0_11 (solved pops=224 evals=1214 maxopen=991) +[OK ] extrinsic_L1_1 (solved pops=214 evals=1175 maxopen=944) +[OK ] extrinsic_L1_2 (solved pops=505 evals=2731 maxopen=2227) +[OK ] extrinsic_L1_3 (solved pops=505 evals=2728 maxopen=2224) +[OK ] extrinsic_L2_1 (solved pops=1263 evals=7083 maxopen=5821) +[OK ] extrinsic_L2_6 (solved pops=1678 evals=9802 maxopen=8125) +[OK ] extrinsic_L2_7 (solved pops=1003 evals=5742 maxopen=4740) +[OK ] extrinsic_L0_14 (solved pops=3830 evals=25318 maxopen=21489) +[ ] extrinsic_L2_2 (budget pops=4000 evals=25996 maxopen=21997) +[ ] extrinsic_L2_3 (budget pops=4000 evals=25896 maxopen=21897) +[OK ] extrinsic_L2_11 (solved pops=24 evals=177 maxopen=152) +[ ] extrinsic_L2_4 (budget pops=4000 evals=25891 maxopen=21892) +[ ] extrinsic_L2_5 (budget pops=4000 evals=25724 maxopen=21725) +[OK ] extrinsic_L2_9 (solved pops=971 evals=5490 maxopen=4520) +[OK ] extrinsic_L2_12 (solved pops=1247 evals=6885 maxopen=5639) +[ ] extrinsic_L2_8 (budget pops=4000 evals=26332 maxopen=22333) +[ ] extrinsic_L2_10 (budget pops=4000 evals=26314 maxopen=22315) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25647 maxopen=21648) +[ ] extrinsic_L3_1 (budget pops=4000 evals=25894 maxopen=21895) +[ ] extrinsic_L3_2 (budget pops=4000 evals=25646 maxopen=21647) +[ ] extrinsic_L3_3 (budget pops=4000 evals=25681 maxopen=21682) +[ ] extrinsic_L3_4 (budget pops=4000 evals=25846 maxopen=21847) +[ ] extrinsic_L3_5 (budget pops=4000 evals=25853 maxopen=21854) +[ ] extrinsic_L3_6 (budget pops=4000 evals=25712 maxopen=21713) +[ ] extrinsic_L3_8 (budget pops=4000 evals=26043 maxopen=22044) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25835 maxopen=21836) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26079 maxopen=22080) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26043 maxopen=22044) +[ ] extrinsic_L3_11 (budget pops=4000 evals=25936 maxopen=21937) +[OK ] extrinsic_L3_14 (solved pops=3165 evals=19528 maxopen=16364) +[ ] extrinsic_L3_12 (budget pops=4000 evals=25922 maxopen=21923) +[OK ] extrinsic_L3_13 (solved pops=3648 evals=23484 maxopen=19837) +[ ] extrinsic_L3_15 (budget pops=4000 evals=25968 maxopen=21969) +[ ] extrinsic_L3_16 (budget pops=4000 evals=25945 maxopen=21946) +[ ] extrinsic_L3_17 (budget pops=4000 evals=25674 maxopen=21675) +[ ] extrinsic_L3_18 (budget pops=4000 evals=25094 maxopen=21095) +[ ] extrinsic_L3_20 (budget pops=4000 evals=25985 maxopen=21986) +[ ] extrinsic_L3_19 (budget pops=4000 evals=25871 maxopen=21872) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26016 maxopen=22017) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25824 maxopen=21825) +[ ] extrinsic_L3_23 (budget pops=4000 evals=26115 maxopen=22116) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26224 maxopen=22225) +[ ] extrinsic_L3_25 (budget pops=4000 evals=27031 maxopen=23032) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26110 maxopen=22111) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26197 maxopen=22198) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25838 maxopen=21839) +[ ] extrinsic_L3_29 (budget pops=4000 evals=26689 maxopen=22690) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26020 maxopen=22021) +[ ] extrinsic_L4_3 (budget pops=4000 evals=25859 maxopen=21860) +[ ] extrinsic_L4_2 (budget pops=4000 evals=26972 maxopen=22973) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25794 maxopen=21795) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26119 maxopen=22120) +[ ] extrinsic_L4_6 (budget pops=4000 evals=25770 maxopen=21771) +[ ] extrinsic_L4_7 (budget pops=4000 evals=26812 maxopen=22813) +[ ] extrinsic_L4_9 (budget pops=4000 evals=26349 maxopen=22350) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26020 maxopen=22021) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25854 maxopen=21855) +[OK ] extrinsic_L4_12 (solved pops=1318 evals=7592 maxopen=6272) +[ ] extrinsic_L4_11 (budget pops=4000 evals=26238 maxopen=22239) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25882 maxopen=21883) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26340 maxopen=22341) +[ ] extrinsic_L5_1 (budget pops=4000 evals=25473 maxopen=21474) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26131 maxopen=22132) +[ ] extrinsic_L5_3 (budget pops=4000 evals=26205 maxopen=22206) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25443 maxopen=21444) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26459 maxopen=22460) +[ ] extrinsic_L5_6 (budget pops=4000 evals=26130 maxopen=22131) +[ ] extrinsic_L5_7 (budget pops=4000 evals=26402 maxopen=22403) +[ ] extrinsic_L5_8 (budget pops=4000 evals=26271 maxopen=22272) +[ ] extrinsic_L5_9 (budget pops=4000 evals=26532 maxopen=22533) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26596 maxopen=22597) +[ ] extrinsic_L6_1 (budget pops=4000 evals=25735 maxopen=21736) +[ ] extrinsic_L5_11 (budget pops=4000 evals=31081 maxopen=27082) +[ ] extrinsic_L6_3 (budget pops=4000 evals=31181 maxopen=27182) +[ ] extrinsic_L6_2 (budget pops=4000 evals=31216 maxopen=27217) +[ ] extrinsic_L6_4 (budget pops=4000 evals=30910 maxopen=26911) +[ ] extrinsic_L6_5 (budget pops=4000 evals=30805 maxopen=26806) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25755 maxopen=21756) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25697 maxopen=21698) +[ ] extrinsic_L6_9 (budget pops=4000 evals=30989 maxopen=26990) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31211 maxopen=27212) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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]]] 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exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ['A -> 'A]]); [('A : prop) -> ['A -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : 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-> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 302, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "a exfalso" + ] + }, + { + "mode": "sample", + 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'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]).", + "c x2", + "=> (x2 not_e@type not_i@type p4 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> x]]]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal4).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 494, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> false]].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c em", + "=> (em iff_i@type).", + "c p2", + "=> (p2 not_i).", + "a exfalso", + "=> false.", + "c p3", + "=> (p3 p0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "c p2", + "=> (p2 p5).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_e@type).", + "c x0", + "=> (x0 false).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 653, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a x", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false)].", + "intro.", + "a x0", + "=> (and [('A : prop) -> ['A -> 'A]] (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> 'P]) x); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [x -> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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('Q : prop) -> (and 'P 'Q) -> 'Q])) false)).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]].", + "intro.", + "c em", + "=> (em iff_er@type).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> x]]))) (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 26, + "evals_used": 157, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type)." + ] + } + ], + "problem": "extrinsic_L0_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 13363, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + 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-> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 539, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "intro.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))).", + "a not_i", + "=> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [false -> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]; [(not false) -> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [false -> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [false -> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> 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+ ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1847, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (iff (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)].", + "a x", + "=> (iff [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (iff (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)).", + "a iff_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (iff (or 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1545, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal em@type or_il).", + "c x", + "=> (x iff_i@type p@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type p@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal14 or_il).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 623, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (or x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (or x 'B)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('B : prop) -> x -> (or x 'B)]); [('B : prop) -> x -> (or x 'B)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> 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: prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> false].", + "intro.", + "a x", + "=> (not x0); x0.", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [x0 -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]))].", + "c x1", + "=> (x1 not_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c x1", + "=> (x1 x).", + "c p2", + "=> (p2 p0@type and_i@type and_i).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]].", + "c p2", + "=> (p2 goal9 and_er@type and_er).", + "c p2", + "=> (p2 goal4 em@type em).", + "c p2", + "=> (p2 goal16 p5@type p5).", + "c p1", + "=> (p1 goal19 p@type x2).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2079, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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: prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x not_i@type not_e@type not_e).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x p@type@2 and_er@type and_er).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2094, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) 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false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c x", + "=> (x goal p2@type@2 or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10583, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "c x0", + "=> (x0 not_i@type em@type not_i em).", + "c x0", + "=> (x0 and_i@type or_il@type x0 or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> 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x0", + "=> (x0 p15@type p17@type p15 p17).", + "c x1", + "=> (x1 and_el@type iff_el@type and_el iff_el).", + "c and_er", + "=> (and_er iff_er@type iff_i@type p16)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "intro.", + "c x0", + "=> (x0 goal10).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c not_e", + "=> (not_e p2@type x1 p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 629, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]); false.", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)].", + "intro.", + "a x", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false))).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)))]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]])) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)))].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> (not x)].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]]]; [(not false) -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]; [(not [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]]]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]; [(not [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not x)]] -> false]]]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[[('A : prop) -> 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-> [[false -> ('P : prop) -> 'P] -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1733, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a 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false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('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) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 532, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]; [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]]; [(not false) -> [(not false) -> [('B : prop) -> (iff x 'B) -> [x -> 'B]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]])); (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p8@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2470, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))))).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))))) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p2@type x1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1490, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (not (not [('P : 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-> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a x0", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 655, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + 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not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [x -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [x -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type goal5 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] false); [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [false -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]].", + "c x0", + "=> (x0 not_e@type p3@type@2 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [false -> ('P : prop) -> 'P]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[false -> ('P : prop) -> 'P] -> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R 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[('B : prop) -> (iff x 'B) -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff x 'B) -> ['B -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 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false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not (or [('A : prop) -> (not 'A) -> 'A -> false] (not [('A : prop) -> (not 'A) -> 'A -> false])))).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false]; (not (or [('A : prop) -> (not 'A) -> 'A -> false] (not [('A : prop) -> (not 'A) -> 'A -> false]))).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1423, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> (not 'A) -> 'A -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> (not 'A) -> 'A -> false])].", + "intro.", + "c x", + "=> (x goal or_e@type not_e).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7651, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P 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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] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_ir@type exfalso).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not false) -> [false -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 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['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_ir", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a x1", + "=> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]); [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]].", + "a or_il", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a x1", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))); [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a x1", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e" + ] + }, + { + "mode": "sample", + 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-> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal not_i@type iff_i).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7123, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]].", + "a x", + "=> (or (not [[false -> ('P : prop) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [[false -> ('P : prop) -> 'P] -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not 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(iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 48, + "evals_used": 5174, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em 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[('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 exfalso@type and_i@type exfalso and_i).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il)." + ] + } + ], + "problem": "extrinsic_L0_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 26858, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x or_e@type x3 or_e).", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 p3@type).", + "c x2", + "=> (x2 or_e@type x3 or_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 452, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> (or 'P (not 'P))])).", + "a and_i", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (and (not [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])])]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and (not [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal or_e@type em).", + "c x", + "=> (x iff_i@type and_el@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7445, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (or 'A (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (or 'A (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c x0", + "=> (x0 or_e@type p0@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false] [('P : prop) -> (or 'P (not 'P))]); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or [('A : prop) -> (or 'A (not 'A))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('A : prop) -> (or 'A (not 'A))] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('A : prop) -> (or 'A (not 'A))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('A : prop) -> (or 'A (not 'A))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 446, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (or 'A (not 'A))]); [('A : prop) -> (or 'A (not 'A))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (or 'A (not 'A))]); [('A : prop) -> (or 'A (not 'A))].", + "a or_e", + "=> [false -> (not [('A : prop) -> (or 'A (not 'A))])]; [(not false) -> (not [('A : prop) -> (or 'A (not 'A))])].", + "c x0", + "=> (x0 iff_er@type).", + "c x0", + "=> (x0 goal5).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> (not [('A : prop) -> (or 'A (not 'A))])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> (not [('A : prop) -> (or 'A (not 'A))])]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type).", + "c x0", + "=> (x0 p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 9728, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_ir", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal2).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c and_er", + "=> (and_er not_e@type p2@type p3).", + "c x0", + "=> (x0 p1@type x p1 x2).", + "c x1", + "=> (x1 iff_el@type or_il@type iff_el or_il).", + "c and_er", + "=> (and_er p1@type x p5).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em iff_el@type).", + "c x0", + "=> (x0 iff_i@type p1@type iff_i p1).", + "c x1", + "=> (x1 iff_i@type p9@type iff_i p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 em@type p12@type em p12).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c x1", + "=> (x1 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('A : prop) -> ['A -> false] -> (not 'A)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1457, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x goal or_e@type not_i).", + "c x", + "=> (x iff_i@type or_il@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type or_e@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2111, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x goal goal16 not_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + 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'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P])].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : 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'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6985, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> 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-> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]); [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 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['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> 'A -> (not (not 'A))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> 'A -> (not (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> 'A -> (not (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> 'A -> (not (not 'A))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[('A : prop) -> 'A -> (not (not 'A))] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_il@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 iff_i@type or_il@type iff_i or_il).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c p8", + "=> (p8 not_e@type p10@type not_e p10).", + "c x1", + "=> (x1 and_i@type and_i@type p8 and_i).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso and_i).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 iff_er@type iff_el@type iff_er iff_el).", + "c x1", + "=> (x1 p@type p12@type p p12).", + "c p8", + "=> (p8 p7@type and_i@type p7 p8).", + "c p8", + "=> (p8 p16@type p16@type p16 p16).", + "c x1", + "=> (x1 and_el@type x and_el x2)." + ] + }, + { + "mode": "sample", + 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and_i@type x1 and_i).", + "a exfalso", + "=> .", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p1@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> 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[('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [false -> ('P : prop) -> 'P]))]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> (not (not [false -> ('P : prop) -> 'P]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6765, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> 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-> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))] false); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x and_er@type x1 and_er).", + "a exfalso", + "=> .", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal10).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1610, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> false].", + "c p5", + "=> (p5 not_i).", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false] -> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]) -> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2018, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e em@type x1 em).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8695, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_il@type not_i or_il).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em 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'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [false -> ('P : prop) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 3340, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : 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'P))])))) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 goal9 or_e@type or_e).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L1_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19613, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 540, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> (or 'P (not 'P))] -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> (or 'P (not 'P))] -> false])]].", + "a 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false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "c x0", + "=> (x0 iff_i@type p@type p).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1458, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or x [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [x -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> x.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 549, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "c x0", + "=> (x0 goal10).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('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)])].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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(and 'B x)]]])).", + "a x1", + "=> (and x (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] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x (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] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])))]; [(not [('P : prop) 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'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])))]).", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x (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] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]])))] (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x (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] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]] 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-> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "c x", + "=> (x or_ir@type goal3 or_ir).", + "c x", + "=> (x or_il@type p@type@2 or_il).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c x", + "=> (x p3@type p3@type@2 p3).", + "c x", + "=> (x p0@type p5@type p0).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 392, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x and_el@type p@type@2 p).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x not_e@type goal11 p6).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('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] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('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] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (iff [('P : prop) -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 361, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> 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-> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false)); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not false) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])); [(or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not false) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))]); [(not false) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not false))] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]))]; [(not false) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]))].", + "a or_e", + "=> [false -> [false -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]))]]; [(not false) -> [false -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and x [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> x; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]])]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]]) (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])).", + "a iff_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]])].", + "a x", + "=> (iff (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false]])).", + "a iff_i", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]) -> (not [[('P : prop) -> 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false]]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 515, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> 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-> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 680, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> 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false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]); [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 517, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false].", + "intro.", + "c x1", + "=> (x1 and_er).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1485, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false; (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a x", + "=> (and (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])].", + "intro.", + "c x0", + "=> (x0 p@type@2 p0@type p0).", + "a x", + "=> (and (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))].", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (and (and false [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 448, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e not_i@type x0 not_i).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(or (not [('P : 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-> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 553, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> 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-> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not false) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "intro.", + "c and_er", + "=> (and_er x x x0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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: prop) -> 'P] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "a x1", + "=> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a x1", + "=> (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 408, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> (iff (and 'A 'A) 'A)])).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A 'A) 'A)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> (iff (and 'A 'A) 'A)]))]; [(not [('A : prop) -> (iff (and 'A 'A) 'A)]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> (iff (and 'A 'A) 'A)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 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-> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 311, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(and x x) -> x]); [(and x x) -> x].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(and x x) -> x])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [(and x x) -> x])].", + "a x1", + "=> (iff (not [(and x x) -> x]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [(and x x) -> x]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [(and x x) -> x]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2485, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : 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'P) -> 'P -> false])))); (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))] (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal4).", + "a x1", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]).", + "a and_i", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (or 'A 'A) 'A)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] [('P : prop) -> ['P -> false] -> (not 'P)]) (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or x0 x0)); (or x0 x0).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or x0 x0) -> x0]]).", + "a x1", + "=> (and (and false [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or x0 x0) -> x0]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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('P : prop) -> 'P] -> false]; [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, 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'A)]); [('A : prop) -> (iff (or 'A 'A) 'A)].", + "a not_i", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x goal9 not_e@type not_e).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a x1", + "=> (iff (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 907, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> 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(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 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false].", + "c em", + "=> (em em@type).", + "intro.", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> (or 'P (not 'P))] false)).", + "c em", + "=> (em goal17).", + "a and_i", + "=> (and [('P : prop) -> (or 'P (not 'P))] false).", + "a or_e", + "=> [(and [('P : prop) -> ['P -> false] -> (not 'P)] false) -> (and [('P : prop) -> (or 'P (not 'P))] false)]; [(not (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) -> (and [('P : prop) -> (or 'P (not 'P))] false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 677, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c p8", + "=> (p8 p@type@2 and_i@type and_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 473, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x2", + "=> false.", + "a x2", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a x2", + "=> false.", + "a x", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "a x", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a x2", + "=> false.", + "a x3", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false].", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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+ "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]].", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]] [('P : prop) -> (not 'P) -> 'P -> false]); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (or false (not false))).", + "a exfalso", + "=> false.", + "a or_e", + "=> 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'Q) -> ['P -> 'Q]])))) -> false]].", + "a x1", + "=> (or [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]] -> [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]]); [[[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]] -> [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) -> false]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]] -> [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : 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(iff 'A 'A)]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> x0]; [x0 -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x0 -> x0]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> [[('P : prop) -> 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'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> (not [x0 -> x0])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> (not [x0 -> x0])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> (not [x0 -> x0])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> (not [x0 -> x0])]]].", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]]).", + "a x1", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]]) (iff x0 x0)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A 'A)] -> false]; [(not [('A : prop) -> (iff 'A 'A)]) -> false].", + "a x", + "=> (and [[('A : prop) -> (iff 'A 'A)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> [[('A : prop) -> (iff 'A 'A)] -> false].", + 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-> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", 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['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 306, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a iff_i", + "=> [x -> x]; [x -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> 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'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3283, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 not_i@type and_i@type and_i).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal11 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type and_er@type and_er).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_er@type and_er).", + "a not_i", + "=> [false -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]].", + "a not_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] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (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] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))])).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))])))]]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]]] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [('P : prop) -> (or 'P (not 'P))])))]].", + "intro.", + "c em", + "=> (em not_i@type).", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) 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-> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 331, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", 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-> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] [false -> [false -> false]]).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]; [(not [('P : prop) -> ('Q : 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x", + "=> (x iff_er@type x1 iff_er).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 343, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> (or 'P (not 'P))] -> false] (not [('P : prop) -> (or 'P (not 'P))]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]); [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] -> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]] -> (or (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 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(not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3259, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em 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-> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or false (not false)))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em 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+ "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]).", + "a x0", + "=> (and (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false])).", + "a x0", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] (and (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]))).", + "a exfalso", + "=> 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'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3819, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "c x2", + "=> (x2 goal6 and_el@type and_el).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "a x0", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 goal14 p3@type p3).", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c x2", + "=> (x2 p8@type iff_i@type iff_i).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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"=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 p1@type iff_i@type p1 iff_i).", + "c x3", + "=> (x3 p@type not_e@type p x).", + "c and_er" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])) -> false]; [(not (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]))) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not false))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not false))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1461, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [false -> false] (or false (not false))); [[false -> false] -> [false -> [false -> false]]]; [(or false (not false)) -> [false -> [false -> false]]].", + "a or_il", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> 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em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type@2).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]) -> false].", + "c not_e", + "=> (not_e not_e@type x2 not_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 2045, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + 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'C]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]; false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)].", + "intro.", + "a x0", + "=> (or (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]) (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]))) (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)); [(or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]) (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]))) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)]; [(and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)].", + "a x" + ] + } + ], + "problem": "extrinsic_L3_3" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 26696, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4971, + "actions": [ + "c em", + "=> (em or_e@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em x).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [false -> (not (not false))]; [(not false) -> (not (not false))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false]; [(not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, 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x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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: prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + 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-> (not 'P)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> 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-> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not false) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> false].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 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: prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [false -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 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prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> 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[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 1392, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x or_e@type p3 or_e).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('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) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not false) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not false) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em 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-> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> 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false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]].", + "intro.", + "c x1", + "=> (x1 exfalso).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 523, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "c em", + "=> (em goal8).", + "c em", + "=> (em p2@type@2).", + "intro.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a not_i", + "=> [[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6870, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]])).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]]].", + "a x2", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]))]]]]].", + "a x2", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [false -> ('P : prop) -> 'P]) -> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a x2", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not [false -> ('P : prop) -> 'P]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not [false -> ('P : prop) -> 'P]))].", + "c x1", + "=> (x1 p1@type goal10 p1).", + "a x1", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "intro.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2040, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 44, + "evals_used": 4412, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el 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-> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]))).", + "a or_e", + "=> [false -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)])))]; [(not false) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)])) -> false]]; [(not [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]) -> [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)])) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 299, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a x", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> 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'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "intro.", + "a or_e", 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em iff_i@type).", + "c em", 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-> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 513, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + 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"solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 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'Q) -> ['P -> 'Q]])))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2417, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + 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prop) -> (or 'P (not 'P))])) (not (not (not [('P : prop) -> (or 'P (not 'P))])))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not x); x.", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [x -> false].", + "intro.", + "c x0", + "=> (x0 goal11 x x1).", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))]].", + "c em", + "=> (em goal).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))).", + "a x1", + "=> (and (or (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false]))))).", + "a or_e", + "=> [(or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) -> (and (or (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))))]; [(not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false]))) -> (and (or (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> [(or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) -> (and (or (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])) (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false])))) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (or [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false] (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> 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+ "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1463, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type or_il@type and_el or_il).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 534, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not 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'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 671, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : 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em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 569, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c x1", + "=> (x1 p3@type).", + "c em", + "=> (em goal18).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [false -> ('P : prop) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a x", + "=> (and [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P]))]; [(not [false -> ('P : prop) -> 'P]) -> (and [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false])].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 658, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a 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false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x", + "=> (x exfalso@type p1@type@2 exfalso).", + "c x", + "=> (x em@type not_i@type em).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type p0@type@2 p0).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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'P]) -> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1859, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 361, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 669, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not x2); x2.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or (or false (not false)) (not (or false (not false))))).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p7@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2384, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 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prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", 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-> ['Q -> 'R] -> 'R]))); [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 5848, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]))).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1" + ] + } + ], + "problem": "extrinsic_L3_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 30855, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a 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-> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (not [('A : prop) -> (iff (not 'A) ['A -> false])])).", + "a x0", + "=> (and (and false (not [('A : prop) -> (iff (not 'A) ['A -> false])])) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> (and (and false (not [('A : prop) -> (iff (not 'A) ['A -> false])])) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('A : prop) -> (iff (not 'A) ['A -> false])]) -> (and (and false (not [('A : prop) -> (iff (not 'A) ['A -> false])])) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em goal11)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not x) -> [x -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> [x -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> [x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> [x -> false]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not x) -> [x -> false]]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "c em", + "=> (em goal0@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]])]; [(not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff (not 'A) ['A -> false])]].", + "intro.", + "intro.", + "a iff_i", + "=> [(not x0) -> [x0 -> false]]; [[x0 -> false] -> (not x0)].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x0) -> [x0 -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x0) -> [x0 -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [false -> false]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal9).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [(not x0) -> [x0 -> false]]); [(not x0) -> [x0 -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x0)); (not x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not x0))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not x0))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not x0))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not x0))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not x0))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [(not x0) -> [x0 -> false]])); (not [(not x0) -> [x0 -> false]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [x0 -> false]); [x0 -> false].", + "c x3", + "=> (x3 x1).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]; [(not [('A : prop) -> (iff (not 'A) ['A -> false])]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])])) -> false]; [(not (or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])]))) -> false].", + "c x", + "=> (x or_e@type).", + "intro.", + "c iff_el", + "=> (iff_el p4@type@2 p5@type@2 p5).", + "a or_e", + "=> [(or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])])) -> false]; [(not (or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])]))) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])])) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + 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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] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [false -> false])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [false -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [false -> false]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [false -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])]; [(not false) -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])].", + "a or_e", + "=> [false -> [false -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])]]; [(not false) -> [false -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(or x (and x x2)) -> x]; [x -> (or x (and x x2))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x2); x2.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('B : prop) -> (iff (or x (and x 'B)) x)]); [('B : prop) -> (iff (or x (and x 'B)) x)].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal12).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2407, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(or (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not (or (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))))); (not (or (not (or [('P 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(not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]); [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[[[('P : prop) -> (or 'P (not 'P))] -> false] -> false] -> false].", + "intro.", + "a x1", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 not_e@type).", + "c x0", + "=> (x0 false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 471, + "actions": [ + "a exfalso", + "=> 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-> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])))]].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (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] -> (not [false -> ('P : prop) -> 'P])]]] (not [false -> ('P : prop) -> 'P])))]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c not_e", + "=> (not_e iff_el@type x0 iff_el).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em exfalso@type).", + "a x", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em goal5).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 505, + "actions": [ + "c em", + "=> (em not_e@type).", 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-> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]; [(not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]; [(not [('A : prop) -> 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exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "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].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal5).", + "a x", + "=> (iff (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 iff_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [false -> (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 x", + "=> (iff (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false).", + "c em", + "=> (em goal9).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not (iff (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)) -> (iff (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)]; [(not (not (iff (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))) -> (iff (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 x", + "=> (iff (not (iff (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)) (iff (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 iff_i", + "=> [(not (iff (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)) -> (iff (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)]; [(iff (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false) -> (not (iff (or [('P : prop) 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"a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": 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(or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or (not [false -> ('P : prop) -> 'P]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4274, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal1).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em p@type).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a x", + "=> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or (or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [(or (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> 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false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x1", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false 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prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))])].", + "c em", + "=> (em p1@type).", + "c x2", + "=> (x2 goal14 p1@type p1).", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))])].", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6870, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]].", + "a x2", + "=> (or (not (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(not (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]]].", + "a x2", + "=> (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]])); [(not [false -> ('P : prop) -> 'P]) -> (or (not (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]) -> (or (not (not [false -> ('P : prop) -> 'P])) (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]))]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]]] -> (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]))].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a 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'P])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 43, + "evals_used": 1459, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + 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-> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1736, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> 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(and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])); (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "c em", + "=> (em goal21).", + "c x3", + "=> (x3 p0@type em@type p0 em).", + "c x3", + "=> (x3 iff_er@type p0@type iff_er p0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('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] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 6423, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso", + "=> false.", + "c x0" + ] + } + ], + "problem": "extrinsic_L3_21" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 20569, + "solution_actions": null, + "traces": [ + { + "mode": 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[(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 590, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 533, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 355, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and [('P : prop) -> 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-> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 goal8).", + "c x0", + "=> (x0 x).", + "c x0", + "=> (x0 p8@type).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2).", + "c x0", + "=> (x0 p5@type@2).", + "a not_e", + "=> (not (not (or x (not x)))); (not (or x (not x))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or x (not x)) -> false]; [(not (or x (not x))) -> false].", + "c em", + "=> (em p9@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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"=> (iff [false -> ('P : prop) -> 'P] false).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x1", + "=> (iff (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) false).", + "a iff_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [false -> (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 442, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 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x2", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x not_i@type x3 not_i).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 not_i@type x3 not_i).", + "c x2", + "=> (x2 not_i@type x3 not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 705, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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+ "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, 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-> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : 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prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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-> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not 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-> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> '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) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('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 : 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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] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]] -> [(or [(not [false -> ('P : prop) -> 'P]) -> false] (not [(not [false -> ('P : prop) -> 'P]) -> false])) -> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a 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'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) 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'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) [('P : prop) -> (not 'P) -> 'P -> false])]; [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> (or (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em goal11).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]].", + "intro.", + "c em", + "=> (em goal6).", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (not (not [x0 -> 'B])) -> [(not (not x0)) -> (not (not 'B))]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('B : prop) -> (not (not [x0 -> 'B])) -> [(not (not x0)) -> (not (not 'B))]]].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em 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'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> false]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 629, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P 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"=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and (not false) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> (not false); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 498, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> 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: prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "intro.", + "c x0", + "=> (x0 p3@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 457, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + 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'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])); [(or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [false -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10748, + "actions": [ + "c em", + "=> (em and_i@type).", + "c 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-> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal0).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P '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].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 690, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A (not (not 'A)))]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> (not (not x0))]; [(not (not x0)) -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [x0 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(iff 'A (not (not 'A)))]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> (not (not x0))]]).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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'Q)])]) (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not (not 'A)))]); [('A : prop) -> (iff 'A (not (not 'A)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> (iff 'A (not (not 'A)))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : 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-> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : 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'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal1).", + "a x", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]); [false -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em p@type).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or false [('P : prop) -> (not 'P) -> 'P -> false])); [[false -> ('P : prop) -> 'P] -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(or false [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "intro." 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('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]]]; [(not (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]]].", + "a or_e", + "=> [false -> [(or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) 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prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L4_3" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 25738, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4971, + "actions": [ + "c em", + "=> (em or_e@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em x).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> 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-> 'R] -> 'R]); [[('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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : 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[false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c not_e", + "=> (not_e p0@type x2 p0).", + "c x1", + "=> (x1 and_er@type p0@type@2 and_er).", + "a x0", + "=> .", + "intro.", + "c not_e", + "=> (not_e p0@type x2 p0).", + "c x1", + "=> (x1 or_e@type goal8 or_e).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 709, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x2", + "=> (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false).", + "a x2", + "=> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false)).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))].", + "a x1", + "=> [(not (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])])).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> 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[('P : prop) -> (not 'P) -> 'P -> false]) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]])).", + "a x2", + "=> (and (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and x0 (and [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] false))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]]))).", + "c em", + "=> (em goal19).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 285, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", 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em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P 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false]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]).", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)]; [(not [false -> ('P : prop) -> 'P]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false)].", + "intro.", + "a x0", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] 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[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + 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(and 'P 'Q)]) -> false].", + "c x", + "=> (x goal p2@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", 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p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 6418, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_er@type not_e iff_er).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p10@type p0@type p10 p0).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L4_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 25934, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4971, + "actions": [ + "c em", + "=> (em or_e@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em x).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", 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-> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> '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] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x or_ir@type p3 or_ir).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal5 exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])); [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> (or (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : 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[('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 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-> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(or (or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x0", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 40, + "evals_used": 3067, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a 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: prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] false); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [false -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "c em", + "=> (em 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + 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prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + } + ], + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 30127, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> 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goal24)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 433, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) 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-> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 671, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[x -> 'B] -> (or (not x) 'B)]]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]; [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type p5@type p5).", + "a or_e", + "=> [[(not [false -> ('P : prop) -> 'P]) -> [false -> false]] -> false]; [(not [(not [false -> ('P : prop) -> 'P]) -> [false -> false]]) -> false].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[(not [false -> ('P : prop) -> 'P]) -> [false -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[(not [false -> ('P : prop) -> 'P]) -> [false -> false]] -> false]].", + "c x1", + "=> (x1 p@type@2 exfalso@type exfalso).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1117, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])] [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]).", + "a x1", + "=> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])] [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal12).", + "a x1", + "=> (and (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])] [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])])).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])])) (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]])).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]])]]).", + "c x3", + "=> (x3 iff_i@type p1@type iff_i p1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 321, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])].", + "a x", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])])]).", + "a not_i", + "=> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])])])] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])]; [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 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false]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x", + "=> (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> (not 'P) -> 'P -> false]) [('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] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> ('Q : prop) -> 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x", + "=> (or (or (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false)); [(or (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false)]; [(or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false) -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false)].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false).", 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-> 'P -> false]) -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x0) -> x0] -> x0]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x0) -> x0] -> x0]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))); (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not (not [('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 -> (or 'P 'Q)] -> (not (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))); (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "a x3", + "=> (and (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]) (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 433, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x or_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x", + "=> (x goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 421, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[false -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]; [(not [false -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[false -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]); [false -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]; [false -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + 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false]].", + "a x0", + "=> (iff [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a x", + "=> (not (iff [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] [('P : prop) -> (or 'P (not 'P))])); (iff [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false] [('P : prop) -> (or 'P (not 'P))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not (not [false -> ('P : prop) -> 'P]))])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x iff_i@type p3 iff_i).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1469, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 em@type goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_i@type p8@type not_i p8)." + ] + } + ], + "problem": "extrinsic_L4_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 27561, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 470, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", 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(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "c x", + "=> (x p3@type@2 goal17).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c not_e", + "=> (not_e iff_i@type x0 iff_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + 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-> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 426, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "c x0", + "=> (x0 p4@type p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[[[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> false] -> [[[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p8@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2262, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [false -> false]); [false -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_el@type p4).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c x1", + "=> (x1 not_e@type and_er@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 526, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x3", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a and_i", + "=> false.", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x3", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (not [('P : prop) -> (or 'P (not 'P))])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2865, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x goal iff_er@type).", + "a or_e", + "=> [[(or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])) -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [(or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])) -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (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)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 3386, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el)." + ] + } + ], + "problem": "extrinsic_L4_14" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19484, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1507, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x p3@type@2 goal17).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 830, + "actions": [ + "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 x", + "=> (x or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x exfalso@type).", + "c x", + "=> (x 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'Q]]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 554, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> false]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> 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(and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, 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exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 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-> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]])]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 380, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])); (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1968, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))); (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 659, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x2", + "=> (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))).", + "a x2", + "=> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x2", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x2", + "=> (and false (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x2", + "=> (and false (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x2", + "=> (and (and false (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (and false (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6472, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [('P : prop) -> (or 'P (not 'P))]) -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not 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false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : 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+ "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em x).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : 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not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))))).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))) -> false].", + "intro.", + "c x0", + "=> (x0 goal11 p@type p).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))) -> false]); [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))) -> false].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> (not [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))) -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))) -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 648, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : 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-> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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-> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> (not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 534, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", 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false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))].", + "a or_e", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) 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-> ['P -> false] -> (not 'P)])].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))))].", + "a x", + "=> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); [[('P : prop) -> ('Q : prop) -> 'P -> 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em x0).", + "a x1", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [x0 -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not x0) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x0 -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a x1", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal17).", + "a x", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 437, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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['Q -> 'R] -> 'R] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", 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-> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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"intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> (not 'P) -> 'P -> false]); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not false) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 653, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) 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+ "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not false))]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not false))]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em exfalso@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2373, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 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'Q) -> 'P] -> false]).", + "a and_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [false -> ('P : prop) -> 'P]); [false -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or false (or false [false -> ('P : prop) -> 'P])); [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(or false [false -> ('P : prop) -> 'P]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (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].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 656, + "actions": [ + "c em", + "=> 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(iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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-> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 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(or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em p@type).", + "a x", + "=> (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] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])); [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> false]; [(not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1928, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em", + "=> (em exfalso@type).", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x1", + "=> (x1 not_e@type not_i@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + 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-> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal6).", + "a x1", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_ir", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a 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) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]].", + "c x2", + "=> (x2 goal11).", + "c x2", + "=> (x2 p0@type@2).", + "c x2", + "=> (x2 goal18).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]].", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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+ "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> false]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> false]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; 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-> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [false -> ('P : prop) -> 'P])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a exfalso", + "=> false.", + "a x1", + "=> (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) false).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) false)).", + "c em", + "=> (em p3@type).", + "a and_i", + "=> (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2914, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not false)].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x0", + "=> (x0 p3@type iff_er@type p3 iff_er).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p5@type exfalso@type p5 exfalso).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]].", + "c x0", + "=> (x0 iff_i@type exfalso@type iff_i exfalso).", + "c x0", + "=> (x0 p1@type and_i@type p1 x0).", + "c and_er", + "=> (and_er p1@type and_i@type p8).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a not_i", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]].", + "intro.", + "c x1", + "=> (x1 p0@type p3@type p0 p3).", + "c p9" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2110, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('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) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c p8", + "=> (p8 goal p1@type p1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em 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prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 375, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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+ "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])))); (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> 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-> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 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(em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P 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: prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false])); [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))] -> (or (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not 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])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not false) -> [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])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]].", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2109, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a not_i", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c p8", + "=> (p8 goal p0@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x iff_i@type p3 iff_i).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false] false).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; false.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false]).", + "a or_e", + "=> [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false])]; [(not (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])))) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 35, + "evals_used": 799, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..b138b6fd64bb0f396eb797ecee17e1a3e0186ae5 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,860 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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_4 (traces=1 evals=157) + +thread '' (641608) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_3 (traces=17 evals=13363) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_6 (traces=17 evals=39669) +[ ] - extrinsic_L0_5 (traces=17 evals=19034) +[ ] - extrinsic_L0_2 (traces=16 evals=28619) +[ ] - extrinsic_L0_7 (traces=17 evals=16461) +[ ] - extrinsic_L0_1 (traces=17 evals=20568) +[OK ] - extrinsic_L0_10 (traces=5 evals=12418) +[ ] - extrinsic_L0_8 (traces=17 evals=33606) +[ ] - extrinsic_L0_9 (traces=14 evals=29498) +[ ] - extrinsic_L0_11 (traces=13 evals=30617) +[ ] - extrinsic_L0_13 (traces=13 evals=19180) +[ ] - extrinsic_L0_12 (traces=13 evals=26858) +[ ] - extrinsic_L0_14 (traces=14 evals=19836) +[ ] - extrinsic_L1_1 (traces=17 evals=23815) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641608) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641607) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641608) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641607) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_1 (traces=17 evals=19613) +[ ] - extrinsic_L1_3 (traces=17 evals=25230) +[ ] - extrinsic_L1_2 (traces=15 evals=27942) +[ ] - extrinsic_L1_4 (traces=14 evals=28335) + +thread '' (641604) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641604) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_2 (traces=15 evals=28335) +[ ] - extrinsic_L2_3 (traces=14 evals=25720) +[ ] - extrinsic_L2_4 (traces=17 evals=20171) +[ ] - extrinsic_L2_6 (traces=17 evals=16593) +[ ] - extrinsic_L2_5 (traces=7 evals=14596) +[ ] - extrinsic_L2_7 (traces=14 evals=20837) +[ ] - extrinsic_L2_9 (traces=17 evals=20825) +[ ] - extrinsic_L2_10 (traces=17 evals=28960) +[ ] - extrinsic_L2_8 (traces=14 evals=22102) + +thread '' (641608) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641608) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_11 (traces=14 evals=17432) +[ ] - extrinsic_L2_12 (traces=17 evals=27171) +[ ] - extrinsic_L2_13 (traces=13 evals=20910) +[ ] - extrinsic_L3_1 (traces=17 evals=34124) + +thread '' (641611) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641611) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=11 evals=7855) +[ ] - extrinsic_L3_3 (traces=15 evals=26080) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_4 (traces=17 evals=26696) +[ ] - extrinsic_L3_5 (traces=12 evals=25859) +[ ] - extrinsic_L3_6 (traces=17 evals=19873) +[ ] - extrinsic_L3_7 (traces=13 evals=28622) +[ ] - extrinsic_L3_8 (traces=17 evals=26577) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_9 (traces=17 evals=32833) +[ ] - extrinsic_L3_12 (traces=17 evals=16216) +[ ] - extrinsic_L3_10 (traces=17 evals=22955) +[ ] - extrinsic_L3_11 (traces=17 evals=24714) +[ ] - extrinsic_L3_13 (traces=13 evals=18428) + +thread '' (641609) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (641609) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641609) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_14 (traces=17 evals=30855) +[ ] - extrinsic_L3_15 (traces=16 evals=25111) +[ ] - extrinsic_L3_17 (traces=17 evals=23629) +[ ] - extrinsic_L3_16 (traces=13 evals=20904) +[ ] - extrinsic_L3_18 (traces=17 evals=25080) +[ ] - extrinsic_L3_19 (traces=11 evals=17350) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=11 evals=18780) + +thread '' (641611) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_23 (traces=17 evals=30618) +[ ] - extrinsic_L3_21 (traces=13 evals=26941) +[ ] - extrinsic_L3_22 (traces=17 evals=20569) +[ ] - extrinsic_L3_24 (traces=9 evals=25569) +[ ] - extrinsic_L3_25 (traces=17 evals=11448) + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641610) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_26 (traces=17 evals=17614) +[ ] - extrinsic_L3_27 (traces=14 evals=28104) +[ ] - extrinsic_L3_28 (traces=17 evals=11882) +[ ] - extrinsic_L3_29 (traces=14 evals=28432) +[ ] - extrinsic_L4_1 (traces=14 evals=20370) +[ ] - extrinsic_L4_2 (traces=17 evals=20918) + +thread '' (641609) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641609) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_6 (traces=17 evals=25934) +[ ] - extrinsic_L4_3 (traces=8 evals=25486) + +thread '' (641611) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_5 (traces=13 evals=27705) +[ ] - extrinsic_L4_4 (traces=15 evals=25738) +[ ] - extrinsic_L4_7 (traces=13 evals=20448) +[ ] - extrinsic_L4_8 (traces=13 evals=32357) +[ ] - extrinsic_L4_9 (traces=17 evals=30127) +[ ] - extrinsic_L4_10 (traces=13 evals=24078) +[ ] - extrinsic_L4_11 (traces=14 evals=23992) +[ ] - extrinsic_L4_12 (traces=14 evals=25135) +[ ] - extrinsic_L4_13 (traces=13 evals=41908) +[ ] - extrinsic_L4_14 (traces=13 evals=27561) +[ ] - extrinsic_L5_1 (traces=17 evals=19484) +[ ] - extrinsic_L5_4 (traces=17 evals=13022) +[ ] - extrinsic_L5_2 (traces=3 evals=19680) +[ ] - extrinsic_L5_3 (traces=17 evals=30755) +[ ] - extrinsic_L5_5 (traces=11 evals=27855) +[ ] - extrinsic_L5_6 (traces=17 evals=28951) +[ ] - extrinsic_L5_7 (traces=17 evals=29261) +[ ] - extrinsic_L5_8 (traces=17 evals=26971) + +thread '' (641607) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (641607) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=13 evals=26518) +[ ] - extrinsic_L5_10 (traces=8 evals=30444) +[ ] - extrinsic_L5_11 (traces=12 evals=18475) +[ ] - extrinsic_L6_1 (traces=11 evals=11532) +[ ] - extrinsic_L6_3 (traces=6 evals=21172) +[ ] - extrinsic_L6_2 (traces=15 evals=34885) +[ ] - extrinsic_L6_4 (traces=2 evals=39874) +[ ] - extrinsic_L6_6 (traces=1 evals=166) +[ ] - extrinsic_L6_5 (traces=6 evals=45417) +[ ] - extrinsic_L6_7 (traces=11 evals=16887) +[ ] - extrinsic_L6_8 (traces=6 evals=53697) +[ ] - extrinsic_L6_9 (traces=11 evals=44023) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 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(iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> 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'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 2/94 in 9103.4s diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..0c7344678604b51ede201a56571a3cb1608147e8 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,334 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_2 (traces=17 evals=19642) +[ ] - extrinsic_L0_5 (traces=17 evals=20732) +[ ] - extrinsic_L0_4 (traces=17 evals=21760) +[ ] - extrinsic_L0_3 (traces=17 evals=21603) +[ ] - extrinsic_L0_1 (traces=17 evals=27361) +[ ] - extrinsic_L0_6 (traces=17 evals=33858) +[OK ] - extrinsic_L0_10 (traces=5 evals=12230) +[ ] - extrinsic_L0_8 (traces=17 evals=12521) +[ ] - extrinsic_L0_9 (traces=17 evals=19042) +[ ] - extrinsic_L0_7 (traces=15 evals=28101) + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_11 (traces=10 evals=18491) +[ ] - extrinsic_L0_12 (traces=13 evals=18203) +[ ] - extrinsic_L0_13 (traces=17 evals=33424) + +thread '' (924234) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_2 (traces=17 evals=25381) +[ ] - extrinsic_L1_1 (traces=13 evals=27060) +[ ] - extrinsic_L0_14 (traces=5 evals=21845) +[ ] - extrinsic_L2_1 (traces=17 evals=12326) +[ ] - extrinsic_L1_3 (traces=17 evals=22986) + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_4 (traces=9 evals=19442) +[ ] - extrinsic_L2_2 (traces=17 evals=14009) +[ ] - extrinsic_L2_3 (traces=17 evals=19636) +[ ] - extrinsic_L2_6 (traces=17 evals=16192) +[ ] - extrinsic_L2_4 (traces=17 evals=24776) +[ ] - extrinsic_L2_5 (traces=11 evals=16943) +[ ] - extrinsic_L2_7 (traces=17 evals=26530) +[ ] - extrinsic_L2_9 (traces=17 evals=17255) +[ ] - extrinsic_L2_8 (traces=14 evals=22887) +[ ] - extrinsic_L2_11 (traces=17 evals=22956) +[ ] - extrinsic_L2_13 (traces=17 evals=22915) +[ ] - extrinsic_L2_10 (traces=17 evals=32997) +[ ] - extrinsic_L2_12 (traces=8 evals=25562) +[ ] - extrinsic_L3_1 (traces=17 evals=20553) +[ ] - extrinsic_L3_2 (traces=17 evals=30162) +[ ] - extrinsic_L3_3 (traces=9 evals=10053) +[ ] - extrinsic_L3_4 (traces=14 evals=43202) +[ ] - extrinsic_L3_5 (traces=13 evals=29001) +[ ] - extrinsic_L3_6 (traces=17 evals=18446) +[ ] - extrinsic_L3_7 (traces=12 evals=18240) +[ ] - extrinsic_L3_8 (traces=17 evals=29391) +[ ] - extrinsic_L3_9 (traces=17 evals=18076) +[ ] - extrinsic_L3_10 (traces=17 evals=22273) +[ ] - extrinsic_L3_12 (traces=17 evals=18201) + +thread '' (924233) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_11 (traces=17 evals=26120) +[ ] - extrinsic_L3_13 (traces=13 evals=16010) +[ ] - extrinsic_L3_14 (traces=17 evals=20498) +[ ] - extrinsic_L3_15 (traces=13 evals=20798) +[ ] - extrinsic_L3_16 (traces=17 evals=27943) +[ ] - extrinsic_L3_17 (traces=17 evals=25831) +[ ] - extrinsic_L3_18 (traces=17 evals=17967) +[ ] - extrinsic_L3_19 (traces=11 evals=8232) +[ ] - extrinsic_L3_20 (traces=14 evals=25164) +[ ] - extrinsic_L3_22 (traces=17 evals=21439) +[ ] - extrinsic_L3_21 (traces=11 evals=9918) +[ ] - extrinsic_L3_24 (traces=17 evals=37569) +[ ] - extrinsic_L3_23 (traces=11 evals=16985) +[ ] - extrinsic_L3_26 (traces=17 evals=19119) + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_25 (traces=14 evals=23385) +[ ] - extrinsic_L3_28 (traces=17 evals=15839) + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924232) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_27 (traces=17 evals=20472) +[ ] - extrinsic_L4_2 (traces=17 evals=19878) +[ ] - extrinsic_L4_1 (traces=17 evals=27410) +[ ] - extrinsic_L3_29 (traces=8 evals=11557) +[ ] - extrinsic_L4_4 (traces=17 evals=20998) +[ ] - extrinsic_L4_3 (traces=17 evals=27883) +[ ] - extrinsic_L4_5 (traces=17 evals=26622) +[ ] - extrinsic_L4_6 (traces=17 evals=23860) +[ ] - extrinsic_L4_7 (traces=14 evals=26034) +[ ] - extrinsic_L4_8 (traces=15 evals=23885) +[ ] - extrinsic_L4_9 (traces=17 evals=27019) +[ ] - extrinsic_L4_10 (traces=14 evals=24636) +[ ] - extrinsic_L4_11 (traces=14 evals=27601) +[ ] - extrinsic_L4_12 (traces=14 evals=28420) +[ ] - extrinsic_L4_13 (traces=16 evals=30625) +[ ] - extrinsic_L4_14 (traces=16 evals=32670) +[ ] - extrinsic_L5_1 (traces=13 evals=24552) +[ ] - extrinsic_L5_2 (traces=16 evals=23174) +[ ] - extrinsic_L5_3 (traces=17 evals=18201) +[ ] - extrinsic_L5_4 (traces=17 evals=14427) +[ ] - extrinsic_L5_7 (traces=17 evals=31669) +[ ] - extrinsic_L5_6 (traces=11 evals=23160) +[ ] - extrinsic_L5_5 (traces=15 evals=22233) + +thread '' (924228) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (924228) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (924228) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=15 evals=22522) +[ ] - extrinsic_L5_9 (traces=13 evals=18763) +[ ] - extrinsic_L5_10 (traces=11 evals=21560) +[ ] - extrinsic_L6_1 (traces=15 evals=17141) +[ ] - extrinsic_L6_2 (traces=9 evals=45141) +[ ] - extrinsic_L6_4 (traces=17 evals=19005) +[ ] - extrinsic_L5_11 (traces=7 evals=77505) +[ ] - extrinsic_L6_3 (traces=6 evals=26291) diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..4fcb890a03703ddbe29efbb64641d87f8848dce2 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 50 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s42/train.log b/experiments/learnability/train_policy_only/minimo_0pt/s42/train.log new file mode 100644 index 0000000000000000000000000000000000000000..e9225b72f496d8f1422a1d3ee92be9cc95e8047b --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s42/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_052959-70wbe9fe +[2026-06-28T05:29:55.233022] Seeded RNGs with seed=42 +[2026-06-28T05:29:55.233313] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-28T05:29:58.908114] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json + 1567 training examples loaded. + +============================================================ +[2026-06-28T05:29:58.910140] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 1567 -> 1567 unique examples + Epoch 1/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 50 total steps, 1567 unique examples (batch_size=64) +[2026-06-28T05:30:09.912146] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:09.922251] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s42/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 50} diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/summary.json b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..1c4ca5e226afe3cc1c7c8be6bbb0ec9bd333be75 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_0_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 50 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..b29f0311b244620ff675a52640e8acbf7911f2cf --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..4fcb890a03703ddbe29efbb64641d87f8848dce2 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 50 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only/minimo_0pt/s43/train.log b/experiments/learnability/train_policy_only/minimo_0pt/s43/train.log new file mode 100644 index 0000000000000000000000000000000000000000..674652b55e4559064d35949f218939d3dac44821 --- /dev/null +++ b/experiments/learnability/train_policy_only/minimo_0pt/s43/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260628_052958-svhdp7dy +[2026-06-28T05:29:55.270533] Seeded RNGs with seed=43 +[2026-06-28T05:29:55.270820] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-28T05:29:58.588605] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/minimo_0pt/examples_policy_only.json + 1567 training examples loaded. + +============================================================ +[2026-06-28T05:29:58.590957] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 1567 -> 1567 unique examples + Epoch 1/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/25 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 50 total steps, 1567 unique examples (batch_size=64) +[2026-06-28T05:30:09.268462] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-28T05:30:09.276070] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only/minimo_0pt/s43/2026-06-28_05-29-55/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 50} 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_final.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..7d3edb31846a22b53d959ca0e19174009a4c7e57 --- /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_final.json @@ -0,0 +1,1397 @@ +{ + "agent_path": "/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/epoch_2.pt", + "problemset": "extrinsic-95", + "max_pops": 4000, + "max_actions": 0, + "timeout": 600.0, + "workers": 6, + "num_problems": 94, + "num_solved": 53, + "elapsed_sec": 2642.263150691986, + "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": "solved", + "pops_used": 5, + "evals_used": 14, + "max_open": 10, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "c and_er", + "=> (and_er x x0 x1)." + ], + "problem": "extrinsic_L0_3" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 6, + "evals_used": 16, + "max_open": 11, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a 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"solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25337, + "max_open": 21338, + "solution_actions": null, + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 38276, + "max_open": 34277, + "solution_actions": null, + "problem": "extrinsic_L5_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 28912, + "max_open": 24913, + "solution_actions": null, + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 30194, + "max_open": 26195, + "solution_actions": null, + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 34352, + "max_open": 30353, + "solution_actions": null, + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 24741, + "max_open": 20742, + "solution_actions": null, + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 26859, + "max_open": 22860, + "solution_actions": null, + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 89980, + "max_open": 85981, + "solution_actions": null, + "problem": "extrinsic_L5_11" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 24, + "evals_used": 171, + "max_open": 148, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> x].", + "intro.", + "c x3", + "=> (x3 x5).", + "c x4", + "=> (x4 p)." + ], + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 23934, + "max_open": 19935, + "solution_actions": null, + "problem": "extrinsic_L6_2" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25458, + "max_open": 21459, + "solution_actions": null, + "problem": "extrinsic_L6_3" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 46572, + "max_open": 42573, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 24448, + "max_open": 20449, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": true, + "outcome": "solved", + "pops_used": 495, + "evals_used": 2255, + "max_open": 1761, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "c and_er", + "=> (and_er x x1 x5).", + "c x4", + "=> (x4 p).", + "a and_i", + "=> x0.", + "a x3", + "=> x.", + "c and_el", + "=> (and_el x x1 x5)." + ], + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 22169, + "max_open": 18170, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 76962, + "max_open": 72963, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 60554, + "max_open": 56555, + "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_final.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_final.log new file mode 100644 index 0000000000000000000000000000000000000000..d7dc7011359352f7d6d6f319d194bddeaaf7829d --- /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_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_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_2 (solved pops=7 evals=18 maxopen=12) +[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_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_8 (solved pops=10 evals=29 maxopen=20) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_7 (solved pops=14 evals=39 maxopen=26) +[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=12 evals=64 maxopen=53) +[OK ] extrinsic_L1_2 (solved pops=12 evals=64 maxopen=53) +[OK ] extrinsic_L0_12 (solved pops=22 evals=128 maxopen=90) +[OK ] extrinsic_L0_14 (solved pops=12 evals=36 maxopen=25) +[OK ] extrinsic_L2_1 (solved pops=25 evals=88 maxopen=64) +[OK ] extrinsic_L2_3 (solved pops=16 evals=71 maxopen=56) +[OK ] extrinsic_L2_4 (solved pops=16 evals=71 maxopen=56) +[OK ] extrinsic_L2_7 (solved pops=11 evals=26 maxopen=16) +[OK ] extrinsic_L2_6 (solved pops=33 evals=197 maxopen=165) +[OK ] extrinsic_L2_8 (solved pops=13 evals=35 maxopen=23) +[OK ] extrinsic_L2_9 (solved pops=18 evals=90 maxopen=73) +[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=10 evals=27 maxopen=18) +[OK ] extrinsic_L3_3 (solved pops=10 evals=26 maxopen=17) +[OK ] extrinsic_L2_12 (solved pops=42 evals=192 maxopen=151) +[OK ] extrinsic_L3_4 (solved pops=12 evals=72 maxopen=40) +[OK ] extrinsic_L3_2 (solved pops=44 evals=245 maxopen=202) +[OK ] extrinsic_L3_5 (solved pops=12 evals=71 maxopen=39) +[OK ] extrinsic_L2_5 (solved pops=86 evals=425 maxopen=340) +[OK ] extrinsic_L3_6 (solved pops=71 evals=364 maxopen=294) +[OK ] extrinsic_L2_2 (solved pops=185 evals=948 maxopen=764) +[OK ] extrinsic_L3_11 (solved pops=108 evals=574 maxopen=464) +[OK ] extrinsic_L3_12 (solved pops=115 evals=613 maxopen=499) +[OK ] extrinsic_L3_13 (solved pops=8 evals=24 maxopen=17) +[OK ] extrinsic_L3_14 (solved pops=15 evals=87 maxopen=73) +[OK ] extrinsic_L3_15 (solved pops=85 evals=515 maxopen=431) +[OK ] extrinsic_L3_16 (solved pops=40 evals=207 maxopen=168) +[OK ] extrinsic_L3_17 (solved pops=71 evals=440 maxopen=351) +[OK ] extrinsic_L3_18 (solved pops=44 evals=368 maxopen=304) +[OK ] extrinsic_L3_7 (solved pops=936 evals=4270 maxopen=3335) +[ ] extrinsic_L2_13 (budget pops=4000 evals=22683 maxopen=18684) +[OK ] extrinsic_L3_9 (solved pops=3897 evals=22962 maxopen=19043) +[ ] extrinsic_L3_10 (budget pops=4000 evals=24353 maxopen=20354) +[OK ] extrinsic_L3_23 (solved pops=58 evals=345 maxopen=288) +[ ] extrinsic_L3_19 (budget pops=4000 evals=22609 maxopen=18610) +[ ] extrinsic_L3_8 (budget pops=4000 evals=31207 maxopen=27208) +[OK ] extrinsic_L3_25 (solved pops=461 evals=3507 maxopen=3027) +[ ] extrinsic_L3_20 (budget pops=4000 evals=23608 maxopen=19609) +[ ] extrinsic_L3_24 (budget pops=4000 evals=31353 maxopen=27354) +[ ] extrinsic_L3_21 (budget pops=4000 evals=22464 maxopen=18465) +[ ] extrinsic_L3_22 (budget pops=4000 evals=20890 maxopen=16891) +[ ] extrinsic_L3_27 (budget pops=4000 evals=31865 maxopen=27866) +[ ] extrinsic_L3_26 (budget pops=4000 evals=30877 maxopen=26878) +[OK ] extrinsic_L4_3 (solved pops=257 evals=1333 maxopen=1077) +[ ] extrinsic_L3_28 (budget pops=4000 evals=30149 maxopen=26150) +[ ] extrinsic_L4_1 (budget pops=4000 evals=27643 maxopen=23644) +[OK ] extrinsic_L4_2 (solved pops=3225 evals=32341 maxopen=29117) +[ ] extrinsic_L4_4 (budget pops=4000 evals=41072 maxopen=37073) +[ ] extrinsic_L3_29 (budget pops=4000 evals=31635 maxopen=27636) +[ ] extrinsic_L4_6 (budget pops=4000 evals=41819 maxopen=37820) +[ ] extrinsic_L4_5 (budget pops=4000 evals=47345 maxopen=43346) +[OK ] extrinsic_L4_12 (solved pops=106 evals=599 maxopen=491) +[ ] extrinsic_L4_8 (budget pops=4000 evals=28892 maxopen=24893) +[ ] extrinsic_L4_7 (budget pops=4000 evals=30970 maxopen=26971) +[ ] extrinsic_L4_9 (budget pops=4000 evals=32017 maxopen=28018) +[ ] extrinsic_L4_10 (budget pops=4000 evals=40292 maxopen=36293) +[ ] extrinsic_L4_13 (budget pops=4000 evals=37740 maxopen=33741) +[ ] extrinsic_L4_11 (budget pops=4000 evals=40919 maxopen=36920) +[ ] extrinsic_L4_14 (budget pops=4000 evals=39135 maxopen=35136) +[ ] extrinsic_L5_1 (budget pops=4000 evals=23710 maxopen=19711) +[ ] extrinsic_L5_2 (budget pops=4000 evals=26150 maxopen=22151) +[ ] extrinsic_L5_3 (budget pops=4000 evals=27917 maxopen=23918) +[ ] extrinsic_L5_6 (budget pops=4000 evals=28912 maxopen=24913) +[ ] extrinsic_L5_4 (budget pops=4000 evals=25337 maxopen=21338) +[ ] extrinsic_L5_5 (budget pops=4000 evals=38276 maxopen=34277) +[OK ] extrinsic_L6_1 (solved pops=24 evals=171 maxopen=148) +[ ] extrinsic_L5_7 (budget pops=4000 evals=30194 maxopen=26195) +[ ] extrinsic_L5_8 (budget pops=4000 evals=34352 maxopen=30353) +[ ] extrinsic_L5_9 (budget pops=4000 evals=24741 maxopen=20742) +[ ] extrinsic_L5_10 (budget pops=4000 evals=26859 maxopen=22860) +[OK ] extrinsic_L6_6 (solved pops=495 evals=2255 maxopen=1761) +[ ] extrinsic_L5_11 (budget pops=4000 evals=89980 maxopen=85981) +[ ] extrinsic_L6_2 (budget pops=4000 evals=23934 maxopen=19935) +[ ] extrinsic_L6_3 (budget pops=4000 evals=25458 maxopen=21459) +[ ] extrinsic_L6_4 (budget pops=4000 evals=46572 maxopen=42573) +[ ] extrinsic_L6_7 (budget pops=4000 evals=22169 maxopen=18170) +[ ] extrinsic_L6_5 (budget pops=4000 evals=24448 maxopen=20449) +[ ] extrinsic_L6_9 (budget pops=4000 evals=60554 maxopen=56555) +[ ] extrinsic_L6_8 (budget pops=4000 evals=76962 maxopen=72963) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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 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a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..bbc2450515fb4f51f9167218477bba7b27b486eb --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/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 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prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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_5 (solved pops=8 evals=32 maxopen=25) +[OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_2 (solved pops=9 evals=22 maxopen=14) +[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_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_8 (solved pops=10 evals=54 maxopen=45) +[OK ] extrinsic_L0_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_7 (solved pops=15 evals=80 maxopen=66) +[OK ] extrinsic_L1_1 (solved pops=11 evals=71 maxopen=43) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L0_12 (solved pops=19 evals=102 maxopen=67) +[OK ] extrinsic_L1_2 (solved pops=23 evals=161 maxopen=139) +[OK ] extrinsic_L1_3 (solved pops=23 evals=160 maxopen=138) +[OK ] extrinsic_L0_14 (solved pops=31 evals=197 maxopen=167) +[OK ] extrinsic_L2_1 (solved pops=41 evals=208 maxopen=168) +[OK ] extrinsic_L2_3 (solved pops=41 evals=297 maxopen=257) +[OK ] extrinsic_L2_4 (solved pops=41 evals=297 maxopen=257) +[OK ] extrinsic_L2_7 (solved pops=26 evals=151 maxopen=126) +[OK ] extrinsic_L2_6 (solved pops=45 evals=312 maxopen=268) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=35 evals=233 maxopen=199) +[OK ] extrinsic_L2_10 (solved pops=27 evals=179 maxopen=153) +[OK ] extrinsic_L2_8 (solved pops=41 evals=269 maxopen=229) +[OK ] extrinsic_L2_12 (solved pops=46 evals=228 maxopen=183) +[OK ] extrinsic_L3_1 (solved pops=28 evals=153 maxopen=126) +[OK ] extrinsic_L3_3 (solved pops=19 evals=87 maxopen=69) +[OK ] extrinsic_L3_4 (solved pops=32 evals=272 maxopen=220) +[OK ] extrinsic_L3_2 (solved pops=56 evals=358 maxopen=303) +[OK ] extrinsic_L3_5 (solved pops=32 evals=268 maxopen=216) +[OK ] extrinsic_L2_5 (solved pops=157 evals=835 maxopen=679) +[OK ] extrinsic_L3_6 (solved pops=120 evals=646 maxopen=527) +[OK ] extrinsic_L2_2 (solved pops=480 evals=2168 maxopen=1689) +[OK ] extrinsic_L3_11 (solved pops=183 evals=959 maxopen=774) +[OK ] extrinsic_L3_12 (solved pops=239 evals=1219 maxopen=981) +[OK ] extrinsic_L3_13 (solved pops=16 evals=98 maxopen=83) +[OK ] extrinsic_L3_14 (solved pops=26 evals=189 maxopen=164) +[OK ] extrinsic_L3_15 (solved pops=650 evals=2518 maxopen=1869) +[OK ] extrinsic_L3_16 (solved pops=62 evals=394 maxopen=333) +[OK ] extrinsic_L3_17 (solved pops=314 evals=1423 maxopen=1091) +[OK ] extrinsic_L3_18 (solved pops=61 evals=491 maxopen=410) +[OK ] extrinsic_L3_7 (solved pops=2353 evals=12564 maxopen=10212) +[ ] extrinsic_L2_13 (budget pops=4000 evals=25272 maxopen=21273) +[ ] extrinsic_L3_9 (budget pops=4000 evals=25973 maxopen=21974) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25972 maxopen=21973) +[OK ] extrinsic_L3_23 (solved pops=183 evals=901 maxopen=719) +[ ] extrinsic_L3_8 (budget pops=4000 evals=29381 maxopen=25382) +[OK ] extrinsic_L3_25 (solved pops=647 evals=3796 maxopen=3130) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26356 maxopen=22357) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26594 maxopen=22595) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25770 maxopen=21771) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26946 maxopen=22947) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25642 maxopen=21643) +[ ] extrinsic_L3_27 (budget pops=4000 evals=30293 maxopen=26294) +[ ] extrinsic_L3_26 (budget pops=4000 evals=28198 maxopen=24199) +[OK ] extrinsic_L4_3 (solved pops=507 evals=2226 maxopen=1720) +[ ] extrinsic_L3_28 (budget pops=4000 evals=29395 maxopen=25396) +[ ] extrinsic_L4_1 (budget pops=4000 evals=27959 maxopen=23960) +[ ] extrinsic_L4_2 (budget pops=4000 evals=44965 maxopen=40966) +[ ] extrinsic_L3_29 (budget pops=4000 evals=30901 maxopen=26902) +[ ] extrinsic_L4_4 (budget pops=4000 evals=36290 maxopen=32291) +[ ] extrinsic_L4_5 (budget pops=4000 evals=40776 maxopen=36777) +[ ] extrinsic_L4_6 (budget pops=4000 evals=36726 maxopen=32727) +[OK ] extrinsic_L4_12 (solved pops=108 evals=638 maxopen=528) +[ ] extrinsic_L4_7 (budget pops=4000 evals=27398 maxopen=23399) +[ ] extrinsic_L4_8 (budget pops=4000 evals=28304 maxopen=24305) +[ ] extrinsic_L4_9 (budget pops=4000 evals=28887 maxopen=24888) +[ ] extrinsic_L4_10 (budget pops=4000 evals=36341 maxopen=32342) +[ ] extrinsic_L4_11 (budget pops=4000 evals=42591 maxopen=38592) +[ ] extrinsic_L4_13 (budget pops=4000 evals=33494 maxopen=29495) +[ ] extrinsic_L4_14 (budget pops=4000 evals=35113 maxopen=31114) +[ ] extrinsic_L5_1 (budget pops=4000 evals=29008 maxopen=25009) +[ ] extrinsic_L5_2 (budget pops=4000 evals=31033 maxopen=27034) +[ ] extrinsic_L5_3 (budget pops=4000 evals=31633 maxopen=27634) +[ ] extrinsic_L5_6 (budget pops=4000 evals=25924 maxopen=21925) +[ ] extrinsic_L5_4 (budget pops=4000 evals=29497 maxopen=25498) +[ ] extrinsic_L5_5 (budget pops=4000 evals=34259 maxopen=30260) +[OK ] extrinsic_L6_1 (solved pops=51 evals=408 maxopen=358) +[ ] extrinsic_L5_7 (budget pops=4000 evals=31088 maxopen=27089) +[ ] extrinsic_L5_8 (budget pops=4000 evals=34471 maxopen=30472) +[ ] extrinsic_L5_9 (budget pops=4000 evals=30502 maxopen=26503) +[ ] extrinsic_L5_10 (budget pops=4000 evals=31649 maxopen=27650) +[ ] extrinsic_L5_11 (budget pops=4000 evals=96848 maxopen=92849) +[OK ] extrinsic_L6_6 (solved pops=1253 evals=5425 maxopen=4173) +[ ] extrinsic_L6_2 (budget pops=4000 evals=66149 maxopen=62150) +[ ] extrinsic_L6_4 (budget pops=4000 evals=60860 maxopen=56861) +[ ] extrinsic_L6_3 (budget pops=4000 evals=66812 maxopen=62813) +[ ] extrinsic_L6_5 (budget pops=4000 evals=61326 maxopen=57327) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25868 maxopen=21869) +[ ] extrinsic_L6_9 (budget pops=4000 evals=53212 maxopen=49213) +[ ] extrinsic_L6_8 (budget pops=4000 evals=64757 maxopen=60758) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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 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b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json new file mode 100644 index 0000000000000000000000000000000000000000..e3914d924a05c618ac4f015733c3654601ca9e20 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json @@ -0,0 +1,1331 @@ +{ + "agent_path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_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": 49, + "elapsed_sec": 2126.0108280181885, + "results": [ + { + "solved": true, + "outcome": "solved", + "pops_used": 2, + "evals_used": 6, + "max_open": 3, + "solution_actions": [ + "intro.", + "intro." + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": true, 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"pops_used": 4000, + "evals_used": 35524, + "max_open": 31525, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..68e1a5030374e2dd3a0b9edb9247399b23cb21b2 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_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=13 evals=57 maxopen=45) +[OK ] extrinsic_L0_4 (solved pops=9 evals=35 maxopen=27) +[OK ] extrinsic_L0_7 (solved pops=18 evals=99 maxopen=82) +[OK ] extrinsic_L0_3 (solved pops=8 evals=33 maxopen=26) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=9 evals=65 maxopen=41) +[OK ] extrinsic_L0_6 (solved pops=6 evals=29 maxopen=24) +[OK ] extrinsic_L0_5 (solved pops=9 evals=48 maxopen=40) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_11 (solved pops=9 evals=35 maxopen=27) +[OK ] extrinsic_L0_12 (solved pops=17 evals=81 maxopen=48) +[OK ] extrinsic_L0_8 (solved pops=16 evals=94 maxopen=79) +[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=30 evals=217 maxopen=188) +[OK ] extrinsic_L1_3 (solved pops=30 evals=216 maxopen=187) +[OK ] extrinsic_L0_14 (solved pops=40 evals=260 maxopen=221) +[OK ] extrinsic_L2_1 (solved pops=64 evals=388 maxopen=325) +[OK ] extrinsic_L2_3 (solved pops=71 evals=517 maxopen=447) +[OK ] extrinsic_L2_7 (solved pops=32 evals=193 maxopen=162) +[OK ] extrinsic_L2_4 (solved pops=71 evals=517 maxopen=447) +[OK ] extrinsic_L2_6 (solved pops=88 evals=602 maxopen=515) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_8 (solved pops=54 evals=366 maxopen=313) +[OK ] extrinsic_L2_10 (solved pops=47 evals=340 maxopen=294) +[OK ] extrinsic_L2_9 (solved pops=49 evals=327 maxopen=279) +[OK ] extrinsic_L3_1 (solved pops=52 evals=384 maxopen=333) +[OK ] extrinsic_L2_12 (solved pops=89 evals=518 maxopen=430) +[OK ] extrinsic_L3_3 (solved pops=42 evals=302 maxopen=261) +[OK ] extrinsic_L3_4 (solved pops=67 evals=546 maxopen=459) +[OK ] extrinsic_L3_5 (solved pops=69 evals=547 maxopen=458) +[OK ] extrinsic_L3_2 (solved pops=311 evals=1521 maxopen=1211) +[OK ] extrinsic_L2_2 (solved pops=612 evals=2790 maxopen=2179) +[OK ] extrinsic_L2_5 (solved pops=664 evals=3050 maxopen=2387) +[OK ] extrinsic_L3_6 (solved pops=621 evals=2850 maxopen=2230) +[OK ] extrinsic_L3_11 (solved pops=185 evals=991 maxopen=804) +[OK ] extrinsic_L3_12 (solved pops=345 evals=1670 maxopen=1326) +[OK ] extrinsic_L3_13 (solved pops=33 evals=204 maxopen=172) +[OK ] extrinsic_L3_14 (solved pops=43 evals=326 maxopen=284) +[OK ] extrinsic_L3_15 (solved pops=1156 evals=5211 maxopen=4056) +[OK ] extrinsic_L3_16 (solved pops=130 evals=758 maxopen=629) +[OK ] extrinsic_L3_17 (solved pops=1501 evals=7424 maxopen=5905) +[ ] extrinsic_L2_13 (budget pops=4000 evals=26471 maxopen=22472) +[OK ] extrinsic_L3_18 (solved pops=362 evals=1812 maxopen=1430) +[ ] extrinsic_L3_7 (budget pops=4000 evals=24781 maxopen=20782) +[ ] extrinsic_L3_9 (budget pops=4000 evals=27456 maxopen=23457) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25587 maxopen=21588) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26893 maxopen=22894) +[OK ] extrinsic_L3_23 (solved pops=475 evals=2133 maxopen=1659) +[OK ] extrinsic_L3_25 (solved pops=984 evals=4757 maxopen=3754) +[ ] extrinsic_L3_19 (budget pops=4000 evals=27333 maxopen=23334) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26523 maxopen=22524) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26554 maxopen=22555) +[ ] extrinsic_L3_24 (budget pops=4000 evals=26046 maxopen=22047) +[ ] extrinsic_L3_22 (budget pops=4000 evals=24923 maxopen=20924) +[ ] extrinsic_L3_26 (budget pops=4000 evals=25146 maxopen=21147) +[OK ] extrinsic_L4_3 (solved pops=719 evals=3273 maxopen=2555) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26070 maxopen=22071) +[ ] extrinsic_L3_27 (budget pops=4000 evals=26139 maxopen=22140) +[ ] extrinsic_L4_2 (budget pops=4000 evals=33343 maxopen=29344) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25240 maxopen=21241) +[ ] extrinsic_L3_29 (budget pops=4000 evals=28499 maxopen=24500) +[ ] extrinsic_L4_4 (budget pops=4000 evals=27795 maxopen=23796) +[ ] extrinsic_L4_6 (budget pops=4000 evals=28642 maxopen=24643) +[ ] extrinsic_L4_5 (budget pops=4000 evals=30481 maxopen=26482) +[OK ] extrinsic_L4_12 (solved pops=142 evals=815 maxopen=671) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24931 maxopen=20932) +[ ] extrinsic_L4_8 (budget pops=4000 evals=27543 maxopen=23544) +[ ] extrinsic_L4_9 (budget pops=4000 evals=25205 maxopen=21206) +[ ] extrinsic_L4_10 (budget pops=4000 evals=29146 maxopen=25147) +[ ] extrinsic_L4_13 (budget pops=4000 evals=26654 maxopen=22655) +[ ] extrinsic_L4_11 (budget pops=4000 evals=33104 maxopen=29105) +[ ] extrinsic_L4_14 (budget pops=4000 evals=26789 maxopen=22790) +[ ] extrinsic_L5_1 (budget pops=4000 evals=28513 maxopen=24514) +[ ] extrinsic_L5_2 (budget pops=4000 evals=28801 maxopen=24802) +[ ] extrinsic_L5_3 (budget pops=4000 evals=28411 maxopen=24412) +[ ] extrinsic_L5_6 (budget pops=4000 evals=24197 maxopen=20198) +[ ] extrinsic_L5_5 (budget pops=4000 evals=27605 maxopen=23606) +[ ] extrinsic_L5_4 (budget pops=4000 evals=29467 maxopen=25468) +[OK ] extrinsic_L6_1 (solved pops=297 evals=1578 maxopen=1282) +[ ] extrinsic_L5_7 (budget pops=4000 evals=27474 maxopen=23475) +[ ] extrinsic_L5_8 (budget pops=4000 evals=30137 maxopen=26138) +[ ] extrinsic_L5_9 (budget pops=4000 evals=28944 maxopen=24945) +[ ] extrinsic_L5_11 (budget pops=4000 evals=42055 maxopen=38056) +[ ] extrinsic_L5_10 (budget pops=4000 evals=29398 maxopen=25399) +[ ] extrinsic_L6_2 (budget pops=4000 evals=44601 maxopen=40602) +[ ] extrinsic_L6_3 (budget pops=4000 evals=44762 maxopen=40763) +[ ] extrinsic_L6_4 (budget pops=4000 evals=44861 maxopen=40862) +[ ] extrinsic_L6_5 (budget pops=4000 evals=44610 maxopen=40611) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25647 maxopen=21648) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25236 maxopen=21237) +[ ] extrinsic_L6_9 (budget pops=4000 evals=35524 maxopen=31525) +[ ] extrinsic_L6_8 (budget pops=4000 evals=44294 maxopen=40295) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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 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a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..ab6662194a7e2e7ec92bb7ef820d260bf848f666 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/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 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-> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] 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'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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=7 evals=17 maxopen=11) +[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_8 (solved pops=8 evals=25 maxopen=18) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_7 (solved pops=16 evals=72 maxopen=57) +[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_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_12 (solved pops=23 evals=146 maxopen=107) +[OK ] extrinsic_L1_1 (solved pops=7 evals=36 maxopen=12) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L0_14 (solved pops=17 evals=79 maxopen=63) +[OK ] extrinsic_L1_3 (solved pops=13 evals=82 maxopen=70) +[OK ] extrinsic_L1_2 (solved pops=13 evals=101 maxopen=70) +[OK ] extrinsic_L2_1 (solved pops=37 evals=172 maxopen=136) +[OK ] extrinsic_L2_3 (solved pops=24 evals=126 maxopen=103) +[OK ] extrinsic_L2_7 (solved pops=14 evals=48 maxopen=35) +[OK ] extrinsic_L2_4 (solved pops=23 evals=139 maxopen=117) +[OK ] extrinsic_L2_6 (solved pops=41 evals=278 maxopen=238) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_8 (solved pops=27 evals=160 maxopen=134) +[OK ] extrinsic_L2_10 (solved pops=12 evals=45 maxopen=34) +[OK ] extrinsic_L2_9 (solved pops=29 evals=195 maxopen=167) +[OK ] extrinsic_L3_1 (solved pops=13 evals=50 maxopen=38) +[OK ] extrinsic_L3_3 (solved pops=11 evals=47 maxopen=37) +[OK ] extrinsic_L2_12 (solved pops=44 evals=198 maxopen=155) +[OK ] extrinsic_L3_4 (solved pops=20 evals=182 maxopen=142) +[OK ] extrinsic_L3_2 (solved pops=46 evals=283 maxopen=238) +[OK ] extrinsic_L3_5 (solved pops=20 evals=180 maxopen=140) +[OK ] extrinsic_L2_5 (solved pops=95 evals=515 maxopen=421) +[OK ] extrinsic_L3_6 (solved pops=87 evals=478 maxopen=392) +[OK ] extrinsic_L2_2 (solved pops=201 evals=1051 maxopen=851) +[OK ] extrinsic_L3_11 (solved pops=92 evals=565 maxopen=471) +[OK ] extrinsic_L3_12 (solved pops=99 evals=607 maxopen=509) +[OK ] extrinsic_L3_13 (solved pops=9 evals=42 maxopen=34) +[OK ] extrinsic_L3_14 (solved pops=17 evals=91 maxopen=75) +[OK ] extrinsic_L3_15 (solved pops=277 evals=1322 maxopen=1046) +[OK ] extrinsic_L3_16 (solved pops=44 evals=269 maxopen=226) +[OK ] extrinsic_L3_17 (solved pops=112 evals=600 maxopen=470) +[OK ] extrinsic_L3_18 (solved pops=48 evals=417 maxopen=349) +[OK ] extrinsic_L3_7 (solved pops=1159 evals=5127 maxopen=3969) +[ ] extrinsic_L2_13 (budget pops=4000 evals=23289 maxopen=19290) +[ ] extrinsic_L3_9 (budget pops=4000 evals=24344 maxopen=20345) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25465 maxopen=21466) +[OK ] extrinsic_L3_23 (solved pops=78 evals=443 maxopen=366) +[ ] extrinsic_L3_19 (budget pops=4000 evals=24605 maxopen=20606) +[ ] extrinsic_L3_8 (budget pops=4000 evals=33325 maxopen=29326) +[OK ] extrinsic_L3_25 (solved pops=555 evals=3816 maxopen=3242) +[ ] extrinsic_L3_20 (budget pops=4000 evals=24556 maxopen=20557) +[ ] extrinsic_L3_24 (budget pops=4000 evals=29436 maxopen=25437) +[ ] extrinsic_L3_21 (budget pops=4000 evals=23987 maxopen=19988) +[ ] extrinsic_L3_22 (budget pops=4000 evals=23442 maxopen=19443) +[ ] extrinsic_L3_27 (budget pops=4000 evals=31844 maxopen=27845) +[ ] extrinsic_L3_26 (budget pops=4000 evals=31571 maxopen=27572) +[OK ] extrinsic_L4_3 (solved pops=348 evals=1691 maxopen=1344) +[ ] extrinsic_L3_28 (budget pops=4000 evals=31638 maxopen=27639) +[ ] extrinsic_L4_1 (budget pops=4000 evals=28717 maxopen=24718) +[OK ] extrinsic_L4_2 (solved pops=3329 evals=33867 maxopen=30519) +[ ] extrinsic_L4_4 (budget pops=4000 evals=38810 maxopen=34811) +[ ] extrinsic_L3_29 (budget pops=4000 evals=33670 maxopen=29671) +[ ] extrinsic_L4_5 (budget pops=4000 evals=45728 maxopen=41729) +[ ] extrinsic_L4_6 (budget pops=4000 evals=39972 maxopen=35973) +[OK ] extrinsic_L4_12 (solved pops=88 evals=513 maxopen=423) +[ ] extrinsic_L4_7 (budget pops=4000 evals=30680 maxopen=26681) +[ ] extrinsic_L4_8 (budget pops=4000 evals=27741 maxopen=23742) +[ ] extrinsic_L4_9 (budget pops=4000 evals=31468 maxopen=27469) +[ ] extrinsic_L4_10 (budget pops=4000 evals=37136 maxopen=33137) +[ ] extrinsic_L4_11 (budget pops=4000 evals=38582 maxopen=34583) +[ ] extrinsic_L4_13 (budget pops=4000 evals=37141 maxopen=33142) +[ ] extrinsic_L4_14 (budget pops=4000 evals=37068 maxopen=33069) +[ ] extrinsic_L5_1 (budget pops=4000 evals=27600 maxopen=23601) +[ ] extrinsic_L5_2 (budget pops=4000 evals=28506 maxopen=24507) +[ ] extrinsic_L5_3 (budget pops=4000 evals=32521 maxopen=28522) +[ ] extrinsic_L5_6 (budget pops=4000 evals=28276 maxopen=24277) +[ ] extrinsic_L5_4 (budget pops=4000 evals=28661 maxopen=24662) +[ ] extrinsic_L5_5 (budget pops=4000 evals=36217 maxopen=32218) +[OK ] extrinsic_L6_1 (solved pops=41 evals=295 maxopen=255) +[ ] extrinsic_L5_7 (budget pops=4000 evals=32274 maxopen=28275) +[ ] extrinsic_L5_8 (budget pops=4000 evals=33089 maxopen=29090) +[ ] extrinsic_L5_9 (budget pops=4000 evals=28011 maxopen=24012) +[ ] extrinsic_L5_10 (budget pops=4000 evals=31475 maxopen=27476) +[OK ] extrinsic_L6_6 (solved pops=782 evals=3450 maxopen=2669) +[ ] extrinsic_L5_11 (budget pops=4000 evals=103978 maxopen=99979) +[ ] extrinsic_L6_2 (budget pops=4000 evals=62041 maxopen=58042) +[ ] extrinsic_L6_3 (budget pops=4000 evals=63193 maxopen=59194) +[ ] extrinsic_L6_4 (budget pops=4000 evals=56082 maxopen=52083) +[ ] extrinsic_L6_5 (budget pops=4000 evals=51784 maxopen=47785) +[ ] extrinsic_L6_7 (budget pops=4000 evals=25295 maxopen=21296) +[ ] extrinsic_L6_8 (budget pops=4000 evals=32432 maxopen=28433) +[ ] extrinsic_L6_9 (budget pops=4000 evals=53783 maxopen=49784) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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 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"budget", + "pops_used": 4000, + "evals_used": 37828, + "max_open": 33829, + "solution_actions": null, + "problem": "extrinsic_L6_4" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31602, + "max_open": 27603, + "solution_actions": null, + "problem": "extrinsic_L6_5" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 25872, + "max_open": 21873, + "solution_actions": null, + "problem": "extrinsic_L6_6" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 24792, + "max_open": 20793, + "solution_actions": null, + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 31187, + "max_open": 27188, + "solution_actions": null, + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "outcome": "budget", + "pops_used": 4000, + "evals_used": 29370, + "max_open": 25371, + "solution_actions": null, + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..d126c678a4442167c7d9710aac7cba58827592ab --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_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=16 evals=105 maxopen=90) +[OK ] extrinsic_L0_3 (solved pops=12 evals=70 maxopen=59) +[OK ] extrinsic_L0_4 (solved pops=12 evals=55 maxopen=44) +[OK ] extrinsic_L0_6 (solved pops=11 evals=53 maxopen=43) +[OK ] extrinsic_L0_5 (solved pops=13 evals=56 maxopen=44) +[OK ] extrinsic_L0_10 (solved pops=7 evals=28 maxopen=22) +[OK ] extrinsic_L0_8 (solved pops=21 evals=146 maxopen=126) +[OK ] extrinsic_L0_9 (solved pops=14 evals=88 maxopen=59) +[OK ] extrinsic_L0_13 (solved pops=7 evals=29 maxopen=23) +[OK ] extrinsic_L0_11 (solved pops=14 evals=59 maxopen=46) +[OK ] extrinsic_L0_7 (solved pops=24 evals=170 maxopen=147) +[OK ] extrinsic_L0_12 (solved pops=16 evals=63 maxopen=31) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_1 (solved pops=23 evals=151 maxopen=111) +[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=66 evals=407 maxopen=342) +[OK ] extrinsic_L2_1 (solved pops=97 evals=542 maxopen=446) +[OK ] extrinsic_L2_7 (solved pops=40 evals=267 maxopen=228) +[OK ] extrinsic_L2_3 (solved pops=127 evals=800 maxopen=674) +[OK ] extrinsic_L2_4 (solved pops=128 evals=801 maxopen=674) +[OK ] extrinsic_L2_6 (solved pops=120 evals=741 maxopen=622) +[OK ] extrinsic_L2_11 (solved pops=8 evals=32 maxopen=23) +[OK ] extrinsic_L2_10 (solved pops=79 evals=551 maxopen=473) +[OK ] extrinsic_L2_9 (solved pops=108 evals=652 maxopen=545) +[OK ] extrinsic_L2_8 (solved pops=133 evals=771 maxopen=639) +[OK ] extrinsic_L2_12 (solved pops=113 evals=616 maxopen=504) +[OK ] extrinsic_L3_3 (solved pops=58 evals=402 maxopen=345) +[OK ] extrinsic_L3_1 (solved pops=85 evals=579 maxopen=495) +[OK ] extrinsic_L3_4 (solved pops=103 evals=741 maxopen=618) +[OK ] extrinsic_L3_5 (solved pops=105 evals=741 maxopen=616) +[OK ] extrinsic_L3_2 (solved pops=587 evals=2694 maxopen=2108) +[OK ] extrinsic_L2_2 (solved pops=1065 evals=5018 maxopen=3954) +[OK ] extrinsic_L2_5 (solved pops=1155 evals=5500 maxopen=4346) +[OK ] extrinsic_L3_6 (solved pops=1058 evals=4867 maxopen=3810) +[OK ] extrinsic_L3_11 (solved pops=330 evals=1594 maxopen=1262) +[OK ] extrinsic_L3_12 (solved pops=626 evals=2863 maxopen=2238) +[OK ] extrinsic_L3_13 (solved pops=45 evals=349 maxopen=305) +[OK ] extrinsic_L3_14 (solved pops=81 evals=582 maxopen=502) +[ ] extrinsic_L2_13 (budget pops=4000 evals=26994 maxopen=22995) +[OK ] extrinsic_L3_16 (solved pops=256 evals=1278 maxopen=1023) +[ ] extrinsic_L3_7 (budget pops=4000 evals=25553 maxopen=21554) +[OK ] extrinsic_L3_15 (solved pops=2545 evals=14439 maxopen=11895) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25180 maxopen=21181) +[ ] extrinsic_L3_9 (budget pops=4000 evals=27632 maxopen=23633) +[OK ] extrinsic_L3_18 (solved pops=767 evals=3617 maxopen=2830) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26589 maxopen=22590) +[OK ] extrinsic_L3_23 (solved pops=849 evals=4094 maxopen=3246) +[OK ] extrinsic_L3_17 (solved pops=2633 evals=15760 maxopen=13109) +[OK ] extrinsic_L3_25 (solved pops=1316 evals=6703 maxopen=5368) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26813 maxopen=22814) +[ ] extrinsic_L3_22 (budget pops=4000 evals=25865 maxopen=21866) +[ ] extrinsic_L3_20 (budget pops=4000 evals=26229 maxopen=22230) +[ ] extrinsic_L3_21 (budget pops=4000 evals=26329 maxopen=22330) +[ ] extrinsic_L3_24 (budget pops=4000 evals=25995 maxopen=21996) +[ ] extrinsic_L3_26 (budget pops=4000 evals=26211 maxopen=22212) +[ ] extrinsic_L4_1 (budget pops=4000 evals=26321 maxopen=22322) +[ ] extrinsic_L3_27 (budget pops=4000 evals=25686 maxopen=21687) +[ ] extrinsic_L3_28 (budget pops=4000 evals=25797 maxopen=21798) +[OK ] extrinsic_L4_3 (solved pops=1413 evals=6831 maxopen=5419) +[ ] extrinsic_L4_2 (budget pops=4000 evals=31230 maxopen=27231) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27674 maxopen=23675) +[ ] extrinsic_L4_4 (budget pops=4000 evals=25939 maxopen=21940) +[ ] extrinsic_L4_5 (budget pops=4000 evals=26630 maxopen=22631) +[ ] extrinsic_L4_6 (budget pops=4000 evals=26466 maxopen=22467) +[OK ] extrinsic_L4_12 (solved pops=250 evals=1204 maxopen=952) +[ ] extrinsic_L4_7 (budget pops=4000 evals=24329 maxopen=20330) +[ ] extrinsic_L4_8 (budget pops=4000 evals=27942 maxopen=23943) +[ ] extrinsic_L4_9 (budget pops=4000 evals=25364 maxopen=21365) +[ ] extrinsic_L4_10 (budget pops=4000 evals=25503 maxopen=21504) +[ ] extrinsic_L4_11 (budget pops=4000 evals=30580 maxopen=26581) +[ ] extrinsic_L4_13 (budget pops=4000 evals=25811 maxopen=21812) +[ ] extrinsic_L4_14 (budget pops=4000 evals=25081 maxopen=21082) +[ ] extrinsic_L5_1 (budget pops=4000 evals=28533 maxopen=24534) +[ ] extrinsic_L5_2 (budget pops=4000 evals=28579 maxopen=24580) +[ ] extrinsic_L5_3 (budget pops=4000 evals=27927 maxopen=23928) +[ ] extrinsic_L5_6 (budget pops=4000 evals=24074 maxopen=20075) +[ ] extrinsic_L5_5 (budget pops=4000 evals=26524 maxopen=22525) +[ ] extrinsic_L5_4 (budget pops=4000 evals=28059 maxopen=24060) +[OK ] extrinsic_L6_1 (solved pops=412 evals=2057 maxopen=1646) +[ ] extrinsic_L5_7 (budget pops=4000 evals=28122 maxopen=24123) +[ ] extrinsic_L5_8 (budget pops=4000 evals=29073 maxopen=25074) +[ ] extrinsic_L5_11 (budget pops=4000 evals=28684 maxopen=24685) +[ ] extrinsic_L5_9 (budget pops=4000 evals=27836 maxopen=23837) +[ ] extrinsic_L5_10 (budget pops=4000 evals=29047 maxopen=25048) +[ ] extrinsic_L6_2 (budget pops=4000 evals=30968 maxopen=26969) +[ ] extrinsic_L6_3 (budget pops=4000 evals=30994 maxopen=26995) +[ ] extrinsic_L6_4 (budget pops=4000 evals=37828 maxopen=33829) +[ ] extrinsic_L6_5 (budget pops=4000 evals=31602 maxopen=27603) +[ ] extrinsic_L6_6 (budget pops=4000 evals=25872 maxopen=21873) +[ ] extrinsic_L6_7 (budget pops=4000 evals=24792 maxopen=20793) +[ ] extrinsic_L6_9 (budget pops=4000 evals=29370 maxopen=25371) +[ ] extrinsic_L6_8 (budget pops=4000 evals=31187 maxopen=27188) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 49/94 in 2030.9s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/bf_extrinsic-95_final.json 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-> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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_5 (solved pops=7 evals=17 maxopen=11) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[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_11 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) +[OK ] extrinsic_L0_9 (solved pops=5 evals=30 maxopen=10) +[OK ] extrinsic_L0_8 (solved pops=10 evals=56 maxopen=47) +[OK ] extrinsic_L1_1 (solved pops=8 evals=52 maxopen=27) +[OK ] extrinsic_L0_7 (solved pops=17 evals=84 maxopen=68) +[OK ] extrinsic_L0_12 (solved pops=19 evals=102 maxopen=67) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_2 (solved pops=26 evals=183 maxopen=158) +[OK ] extrinsic_L1_3 (solved pops=26 evals=182 maxopen=157) +[OK ] extrinsic_L0_14 (solved pops=37 evals=227 maxopen=191) +[OK ] extrinsic_L2_1 (solved pops=41 evals=208 maxopen=168) +[OK ] extrinsic_L2_3 (solved pops=41 evals=297 maxopen=257) +[OK ] extrinsic_L2_4 (solved pops=42 evals=319 maxopen=278) +[OK ] extrinsic_L2_7 (solved pops=27 evals=170 maxopen=144) +[OK ] extrinsic_L2_6 (solved pops=51 evals=327 maxopen=277) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_10 (solved pops=29 evals=218 maxopen=190) +[OK ] extrinsic_L2_9 (solved pops=35 evals=233 maxopen=199) +[OK ] extrinsic_L2_8 (solved pops=55 evals=356 maxopen=302) +[OK ] extrinsic_L3_1 (solved pops=29 evals=169 maxopen=141) +[OK ] extrinsic_L2_12 (solved pops=46 evals=239 maxopen=194) +[OK ] extrinsic_L3_3 (solved pops=24 evals=144 maxopen=121) +[OK ] extrinsic_L3_4 (solved pops=31 evals=257 maxopen=206) +[OK ] extrinsic_L3_2 (solved pops=58 evals=383 maxopen=326) +[OK ] extrinsic_L3_5 (solved pops=31 evals=253 maxopen=202) +[OK ] extrinsic_L2_5 (solved pops=177 evals=917 maxopen=741) +[OK ] extrinsic_L3_6 (solved pops=141 evals=753 maxopen=613) +[OK ] extrinsic_L2_2 (solved pops=562 evals=2556 maxopen=1995) +[OK ] extrinsic_L3_11 (solved pops=224 evals=1137 maxopen=911) +[OK ] extrinsic_L3_12 (solved pops=361 evals=1625 maxopen=1265) +[OK ] extrinsic_L3_13 (solved pops=26 evals=181 maxopen=156) +[OK ] extrinsic_L3_14 (solved pops=27 evals=209 maxopen=183) +[OK ] extrinsic_L3_15 (solved pops=1019 evals=4421 maxopen=3403) +[OK ] extrinsic_L3_16 (solved pops=77 evals=479 maxopen=403) +[OK ] extrinsic_L3_17 (solved pops=289 evals=1348 maxopen=1041) +[OK ] extrinsic_L3_18 (solved pops=54 evals=439 maxopen=365) +[ ] extrinsic_L2_13 (budget pops=4000 evals=26945 maxopen=22946) +[ ] extrinsic_L3_7 (budget pops=4000 evals=26092 maxopen=22093) +[ ] extrinsic_L3_9 (budget pops=4000 evals=25917 maxopen=21918) +[ ] extrinsic_L3_10 (budget pops=4000 evals=26634 maxopen=22635) +[OK ] extrinsic_L3_23 (solved pops=348 evals=1507 maxopen=1160) +[ ] extrinsic_L3_8 (budget pops=4000 evals=31803 maxopen=27804) +[OK ] extrinsic_L3_25 (solved pops=662 evals=4545 maxopen=3864) +[ ] extrinsic_L3_19 (budget pops=4000 evals=30235 maxopen=26236) +[ ] extrinsic_L3_20 (budget pops=4000 evals=30285 maxopen=26286) +[ ] extrinsic_L3_21 (budget pops=4000 evals=27102 maxopen=23103) +[ ] extrinsic_L3_24 (budget pops=4000 evals=29369 maxopen=25370) +[ ] extrinsic_L3_22 (budget pops=4000 evals=26272 maxopen=22273) +[ ] extrinsic_L3_26 (budget pops=4000 evals=29737 maxopen=25738) +[OK ] extrinsic_L4_3 (solved pops=680 evals=2910 maxopen=2231) +[ ] extrinsic_L3_27 (budget pops=4000 evals=32556 maxopen=28557) +[ ] extrinsic_L4_1 (budget pops=4000 evals=29389 maxopen=25390) +[ ] extrinsic_L4_2 (budget pops=4000 evals=46561 maxopen=42562) +[ ] extrinsic_L3_28 (budget pops=4000 evals=31236 maxopen=27237) +[ ] extrinsic_L3_29 (budget pops=4000 evals=32475 maxopen=28476) +[ ] extrinsic_L4_4 (budget pops=4000 evals=40082 maxopen=36083) +[ ] extrinsic_L4_5 (budget pops=4000 evals=44174 maxopen=40175) +[ ] extrinsic_L4_6 (budget pops=4000 evals=40276 maxopen=36277) +[OK ] extrinsic_L4_12 (solved pops=156 evals=835 maxopen=677) +[ ] extrinsic_L4_7 (budget pops=4000 evals=29830 maxopen=25831) +[ ] extrinsic_L4_8 (budget pops=4000 evals=29161 maxopen=25162) +[ ] extrinsic_L4_9 (budget pops=4000 evals=29949 maxopen=25950) +[ ] extrinsic_L4_10 (budget pops=4000 evals=39293 maxopen=35294) +[ ] extrinsic_L4_11 (budget pops=4000 evals=43680 maxopen=39681) +[ ] extrinsic_L4_13 (budget pops=4000 evals=36762 maxopen=32763) +[ ] extrinsic_L4_14 (budget pops=4000 evals=37492 maxopen=33493) +[ ] extrinsic_L5_1 (budget pops=4000 evals=30571 maxopen=26572) +[ ] extrinsic_L5_2 (budget pops=4000 evals=33980 maxopen=29981) +[ ] extrinsic_L5_3 (budget pops=4000 evals=34702 maxopen=30703) +[ ] extrinsic_L5_6 (budget pops=4000 evals=27427 maxopen=23428) +[ ] extrinsic_L5_4 (budget pops=4000 evals=31484 maxopen=27485) +[ ] extrinsic_L5_5 (budget pops=4000 evals=36049 maxopen=32050) +[OK ] extrinsic_L6_1 (solved pops=72 evals=543 maxopen=472) +[ ] extrinsic_L5_7 (budget pops=4000 evals=31469 maxopen=27470) +[ ] extrinsic_L5_8 (budget pops=4000 evals=36592 maxopen=32593) +[ ] extrinsic_L5_9 (budget pops=4000 evals=34956 maxopen=30957) +[ ] extrinsic_L5_10 (budget pops=4000 evals=36319 maxopen=32320) +[ ] extrinsic_L5_11 (budget pops=4000 evals=100970 maxopen=96971) +[OK ] extrinsic_L6_6 (solved pops=2048 evals=10209 maxopen=8162) +[ ] extrinsic_L6_2 (timeout pops=3934 evals=68878 maxopen=64945) +[ ] extrinsic_L6_4 (budget pops=4000 evals=64973 maxopen=60974) +[ ] extrinsic_L6_3 (timeout pops=3944 evals=69183 maxopen=65240) +[ ] extrinsic_L6_5 (budget pops=4000 evals=66026 maxopen=62027) +[ ] extrinsic_L6_7 (budget pops=4000 evals=26438 maxopen=22439) +[ ] extrinsic_L6_9 (budget pops=4000 evals=54320 maxopen=50321) +[ ] extrinsic_L6_8 (budget pops=4000 evals=43326 maxopen=39327) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> 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b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..6b0fcae6f0bed4c171266fc944499a1427e95791 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/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_4 (solved pops=6 evals=16 maxopen=11) +[OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) +[OK ] extrinsic_L0_5 (solved pops=7 evals=17 maxopen=11) +[OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) +[OK ] extrinsic_L0_9 (solved pops=7 evals=34 maxopen=12) +[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_7 (solved pops=25 evals=132 maxopen=108) +[OK ] extrinsic_L0_12 (solved pops=17 evals=66 maxopen=33) +[OK ] extrinsic_L0_8 (solved pops=21 evals=95 maxopen=75) +[OK ] extrinsic_L1_1 (solved pops=13 evals=75 maxopen=45) +[OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) +[OK ] extrinsic_L1_2 (solved pops=24 evals=168 maxopen=126) +[OK ] extrinsic_L1_3 (solved pops=24 evals=167 maxopen=125) +[OK ] extrinsic_L0_14 (solved pops=39 evals=239 maxopen=201) +[OK ] extrinsic_L2_1 (solved pops=62 evals=332 maxopen=271) +[OK ] extrinsic_L2_3 (solved pops=50 evals=369 maxopen=320) +[OK ] extrinsic_L2_4 (solved pops=52 evals=374 maxopen=323) +[OK ] extrinsic_L2_7 (solved pops=28 evals=155 maxopen=128) +[OK ] extrinsic_L2_8 (solved pops=37 evals=240 maxopen=204) +[OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) +[OK ] extrinsic_L2_9 (solved pops=37 evals=269 maxopen=233) +[OK ] extrinsic_L2_6 (solved pops=74 evals=518 maxopen=445) +[OK ] extrinsic_L2_10 (solved pops=41 evals=272 maxopen=232) +[OK ] extrinsic_L3_1 (solved pops=39 evals=289 maxopen=251) +[OK ] extrinsic_L3_3 (solved pops=32 evals=187 maxopen=156) +[OK ] extrinsic_L2_12 (solved pops=83 evals=489 maxopen=407) +[OK ] extrinsic_L3_4 (solved pops=46 evals=369 maxopen=303) +[OK ] extrinsic_L3_5 (solved pops=48 evals=367 maxopen=299) +[OK ] extrinsic_L3_2 (solved pops=166 evals=1016 maxopen=851) +[OK ] extrinsic_L2_2 (solved pops=352 evals=1820 maxopen=1469) +[OK ] extrinsic_L2_5 (solved pops=339 evals=1700 maxopen=1362) +[OK ] extrinsic_L3_6 (solved pops=315 evals=1575 maxopen=1261) +[OK ] extrinsic_L3_11 (solved pops=100 evals=613 maxopen=511) +[OK ] extrinsic_L3_12 (solved pops=138 evals=791 maxopen=654) +[OK ] extrinsic_L3_13 (solved pops=29 evals=196 maxopen=168) +[OK ] extrinsic_L3_14 (solved pops=36 evals=275 maxopen=240) +[OK ] extrinsic_L3_15 (solved pops=447 evals=1966 maxopen=1520) +[OK ] extrinsic_L3_16 (solved pops=66 evals=432 maxopen=367) +[OK ] extrinsic_L3_17 (solved pops=541 evals=2290 maxopen=1731) +[OK ] extrinsic_L3_18 (solved pops=169 evals=1066 maxopen=877) +[ ] extrinsic_L2_13 (budget pops=4000 evals=26244 maxopen=22245) +[ ] extrinsic_L3_7 (budget pops=4000 evals=23498 maxopen=19499) +[ ] extrinsic_L3_9 (budget pops=4000 evals=26290 maxopen=22291) +[ ] extrinsic_L3_8 (budget pops=4000 evals=25345 maxopen=21346) +[ ] extrinsic_L3_10 (budget pops=4000 evals=25711 maxopen=21712) +[OK ] extrinsic_L3_23 (solved pops=264 evals=1351 maxopen=1088) +[OK ] extrinsic_L3_25 (solved pops=658 evals=2840 maxopen=2163) +[ ] extrinsic_L3_19 (budget pops=4000 evals=26239 maxopen=22240) +[ ] extrinsic_L3_20 (budget pops=4000 evals=24760 maxopen=20761) +[ ] extrinsic_L3_24 (budget pops=4000 evals=25090 maxopen=21091) +[ ] extrinsic_L3_21 (budget pops=4000 evals=25095 maxopen=21096) +[ ] extrinsic_L3_22 (budget pops=4000 evals=23942 maxopen=19943) +[ ] extrinsic_L3_26 (budget pops=4000 evals=23467 maxopen=19468) +[ ] extrinsic_L3_27 (budget pops=4000 evals=24971 maxopen=20972) +[OK ] extrinsic_L4_3 (solved pops=567 evals=2661 maxopen=2095) +[ ] extrinsic_L4_1 (budget pops=4000 evals=24718 maxopen=20719) +[OK ] extrinsic_L4_2 (solved pops=3998 evals=34153 maxopen=30156) +[ ] extrinsic_L3_28 (budget pops=4000 evals=24936 maxopen=20937) +[ ] extrinsic_L4_4 (budget pops=4000 evals=28861 maxopen=24862) +[ ] extrinsic_L3_29 (budget pops=4000 evals=27678 maxopen=23679) +[ ] extrinsic_L4_5 (budget pops=4000 evals=30810 maxopen=26811) +[ ] extrinsic_L4_6 (budget pops=4000 evals=29504 maxopen=25505) +[OK ] extrinsic_L4_12 (solved pops=147 evals=841 maxopen=692) +[ ] extrinsic_L4_7 (budget pops=4000 evals=22696 maxopen=18697) +[ ] extrinsic_L4_8 (budget pops=4000 evals=26669 maxopen=22670) +[ ] extrinsic_L4_9 (budget pops=4000 evals=23771 maxopen=19772) +[ ] extrinsic_L4_10 (budget pops=4000 evals=28903 maxopen=24904) +[ ] extrinsic_L4_11 (budget pops=4000 evals=35006 maxopen=31007) +[ ] extrinsic_L4_13 (budget pops=4000 evals=28530 maxopen=24531) +[ ] extrinsic_L4_14 (budget pops=4000 evals=27205 maxopen=23206) +[ ] extrinsic_L5_1 (budget pops=4000 evals=27920 maxopen=23921) +[ ] extrinsic_L5_2 (budget pops=4000 evals=28081 maxopen=24082) +[ ] extrinsic_L5_3 (budget pops=4000 evals=27910 maxopen=23911) +[ ] extrinsic_L5_4 (budget pops=4000 evals=28538 maxopen=24539) +[ ] extrinsic_L5_6 (budget pops=4000 evals=23574 maxopen=19575) +[ ] extrinsic_L5_5 (budget pops=4000 evals=29221 maxopen=25222) +[OK ] extrinsic_L6_1 (solved pops=103 evals=767 maxopen=665) +[ ] extrinsic_L5_7 (budget pops=4000 evals=27461 maxopen=23462) +[ ] extrinsic_L5_8 (budget pops=4000 evals=30344 maxopen=26345) +[ ] extrinsic_L5_11 (budget pops=4000 evals=24413 maxopen=20414) +[ ] extrinsic_L5_9 (budget pops=4000 evals=27248 maxopen=23249) +[ ] extrinsic_L5_10 (budget pops=4000 evals=28485 maxopen=24486) +[ ] extrinsic_L6_2 (budget pops=4000 evals=44077 maxopen=40078) +[OK ] extrinsic_L6_6 (solved pops=2782 evals=15232 maxopen=12451) +[ ] extrinsic_L6_4 (budget pops=4000 evals=44548 maxopen=40549) +[ ] extrinsic_L6_3 (budget pops=4000 evals=44494 maxopen=40495) +[ ] extrinsic_L6_5 (budget pops=4000 evals=37350 maxopen=33351) +[ ] extrinsic_L6_7 (budget pops=4000 evals=23964 maxopen=19965) +[ ] extrinsic_L6_9 (budget pops=4000 evals=28356 maxopen=24357) +[ ] extrinsic_L6_8 (budget pops=4000 evals=42104 maxopen=38105) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/bf_extrinsic-95_mid.json +Solved 51/94 in 2101.3s