L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [OK ] extrinsic_L0_1 (solved pops=3 evals=21 maxopen=17) [OK ] extrinsic_L0_6 (solved pops=53 evals=346 maxopen=294) [OK ] extrinsic_L0_2 (solved pops=55 evals=350 maxopen=296) [OK ] extrinsic_L0_5 (solved pops=57 evals=353 maxopen=297) [OK ] extrinsic_L0_3 (solved pops=64 evals=395 maxopen=332) [OK ] extrinsic_L0_10 (solved pops=11 evals=75 maxopen=65) [OK ] extrinsic_L0_7 (solved pops=55 evals=352 maxopen=298) [OK ] extrinsic_L0_12 (solved pops=16 evals=89 maxopen=57) [OK ] extrinsic_L0_8 (solved pops=53 evals=347 maxopen=295) [OK ] extrinsic_L0_13 (solved pops=25 evals=176 maxopen=152) [OK ] extrinsic_L0_9 (solved pops=53 evals=362 maxopen=294) [OK ] extrinsic_L0_4 (solved pops=201 evals=1060 maxopen=860) [OK ] extrinsic_L1_4 (solved pops=18 evals=121 maxopen=102) [OK ] extrinsic_L0_11 (solved pops=210 evals=1157 maxopen=948) [OK ] extrinsic_L1_1 (solved pops=225 evals=1196 maxopen=954) [OK ] extrinsic_L1_2 (solved pops=452 evals=2444 maxopen=1993) [OK ] extrinsic_L1_3 (solved pops=452 evals=2441 maxopen=1990) [OK ] extrinsic_L2_1 (solved pops=1414 evals=7998 maxopen=6585) [OK ] extrinsic_L2_6 (solved pops=1418 evals=8021 maxopen=6604) [OK ] extrinsic_L2_7 (solved pops=898 evals=4947 maxopen=4050) [ ] extrinsic_L2_2 (budget pops=4000 evals=26022 maxopen=22023) [ ] extrinsic_L0_14 (budget pops=4000 evals=26308 maxopen=22309) [ ] extrinsic_L2_3 (budget pops=4000 evals=26017 maxopen=22018) [OK ] extrinsic_L2_11 (solved pops=22 evals=145 maxopen=122) [ ] extrinsic_L2_4 (budget pops=4000 evals=26012 maxopen=22013) [ ] extrinsic_L2_5 (budget pops=4000 evals=25845 maxopen=21846) [OK ] extrinsic_L2_9 (solved pops=995 evals=5535 maxopen=4541) [OK ] extrinsic_L2_12 (solved pops=1322 evals=7487 maxopen=6166) [ ] extrinsic_L2_8 (budget pops=4000 evals=26325 maxopen=22326) [ ] extrinsic_L2_10 (budget pops=4000 evals=26099 maxopen=22100) [ ] extrinsic_L2_13 (budget pops=4000 evals=25708 maxopen=21709) [ ] extrinsic_L3_1 (budget pops=4000 evals=26029 maxopen=22030) [ ] extrinsic_L3_2 (budget pops=4000 evals=25731 maxopen=21732) [ ] extrinsic_L3_3 (budget pops=4000 evals=25729 maxopen=21730) [ ] extrinsic_L3_4 (budget pops=4000 evals=25927 maxopen=21928) [ ] extrinsic_L3_5 (budget pops=4000 evals=25932 maxopen=21933) [ ] extrinsic_L3_6 (budget pops=4000 evals=25833 maxopen=21834) [ ] extrinsic_L3_7 (budget pops=4000 evals=26004 maxopen=22005) [ ] extrinsic_L3_8 (budget pops=4000 evals=26146 maxopen=22147) [ ] extrinsic_L3_9 (budget pops=4000 evals=26098 maxopen=22099) [ ] extrinsic_L3_10 (budget pops=4000 evals=26006 maxopen=22007) [OK ] extrinsic_L3_13 (solved pops=3008 evals=17936 maxopen=14929) [OK ] extrinsic_L3_14 (solved pops=3163 evals=19748 maxopen=16586) [ ] extrinsic_L3_11 (budget pops=4000 evals=25697 maxopen=21698) [ ] extrinsic_L3_12 (budget pops=4000 evals=25704 maxopen=21705) [ ] extrinsic_L3_15 (budget pops=4000 evals=26079 maxopen=22080) [ ] extrinsic_L3_16 (budget pops=4000 evals=26053 maxopen=22054) [ ] extrinsic_L3_17 (budget pops=4000 evals=25822 maxopen=21823) [ ] extrinsic_L3_18 (budget pops=4000 evals=26002 maxopen=22003) [ ] extrinsic_L3_19 (budget pops=4000 evals=25892 maxopen=21893) [ ] extrinsic_L3_20 (budget pops=4000 evals=26009 maxopen=22010) [ ] extrinsic_L3_21 (budget pops=4000 evals=25965 maxopen=21966) [ ] extrinsic_L3_22 (budget pops=4000 evals=26014 maxopen=22015) [ ] extrinsic_L3_23 (budget pops=4000 evals=26021 maxopen=22022) [ ] extrinsic_L3_24 (budget pops=4000 evals=26314 maxopen=22315) [ ] extrinsic_L3_26 (budget pops=4000 evals=26023 maxopen=22024) [ ] extrinsic_L3_25 (budget pops=4000 evals=27014 maxopen=23015) [ ] extrinsic_L3_27 (budget pops=4000 evals=25989 maxopen=21990) [ ] extrinsic_L3_28 (budget pops=4000 evals=25958 maxopen=21959) [ ] extrinsic_L4_1 (budget pops=4000 evals=26683 maxopen=22684) [ ] extrinsic_L3_29 (budget pops=4000 evals=26769 maxopen=22770) [ ] extrinsic_L4_2 (budget pops=4000 evals=25941 maxopen=21942) [ ] extrinsic_L4_3 (budget pops=4000 evals=25895 maxopen=21896) [ ] extrinsic_L4_4 (budget pops=4000 evals=25861 maxopen=21862) [ ] extrinsic_L4_5 (budget pops=4000 evals=25952 maxopen=21953) [ ] extrinsic_L4_6 (budget pops=4000 evals=25879 maxopen=21880) [ ] extrinsic_L4_7 (budget pops=4000 evals=26271 maxopen=22272) [ ] extrinsic_L4_8 (budget pops=4000 evals=25910 maxopen=21911) [ ] extrinsic_L4_9 (budget pops=4000 evals=26151 maxopen=22152) [OK ] extrinsic_L4_12 (solved pops=1261 evals=7127 maxopen=5864) [ ] extrinsic_L4_10 (budget pops=4000 evals=25478 maxopen=21479) [ ] extrinsic_L4_11 (budget pops=4000 evals=26382 maxopen=22383) [ ] extrinsic_L4_13 (budget pops=4000 evals=25817 maxopen=21818) [ ] extrinsic_L4_14 (budget pops=4000 evals=26299 maxopen=22300) [ ] extrinsic_L5_1 (budget pops=4000 evals=26391 maxopen=22392) [ ] extrinsic_L5_2 (budget pops=4000 evals=26218 maxopen=22219) [ ] extrinsic_L5_3 (budget pops=4000 evals=26210 maxopen=22211) [ ] extrinsic_L5_4 (budget pops=4000 evals=26331 maxopen=22332) [ ] extrinsic_L5_5 (budget pops=4000 evals=26028 maxopen=22029) [ ] extrinsic_L5_6 (budget pops=4000 evals=26112 maxopen=22113) [ ] extrinsic_L5_7 (budget pops=4000 evals=26387 maxopen=22388) [ ] extrinsic_L5_8 (budget pops=4000 evals=26480 maxopen=22481) [ ] extrinsic_L5_9 (budget pops=4000 evals=26331 maxopen=22332) [ ] extrinsic_L5_10 (budget pops=4000 evals=26648 maxopen=22649) [ ] extrinsic_L6_1 (budget pops=4000 evals=26031 maxopen=22032) [ ] extrinsic_L5_11 (budget pops=4000 evals=30991 maxopen=26992) [ ] extrinsic_L6_4 (budget pops=4000 evals=30992 maxopen=26993) [ ] extrinsic_L6_2 (budget pops=4000 evals=31039 maxopen=27040) [ ] extrinsic_L6_3 (budget pops=4000 evals=30994 maxopen=26995) [ ] extrinsic_L6_5 (budget pops=4000 evals=31015 maxopen=27016) [ ] extrinsic_L6_6 (budget pops=4000 evals=25918 maxopen=21919) [ ] extrinsic_L6_7 (budget pops=4000 evals=25846 maxopen=21847) [ ] extrinsic_L6_8 (budget pops=4000 evals=31196 maxopen=27197) [ ] extrinsic_L6_9 (budget pops=4000 evals=30994 maxopen=26995) L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/bestfirst_eval/minimo_0pt_base_bf_extrinsic-95.json Solved 26/94 in 2773.7s