L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [OK ] extrinsic_L0_1 (solved pops=2 evals=6 maxopen=3) [OK ] extrinsic_L0_3 (solved pops=5 evals=14 maxopen=10) [OK ] extrinsic_L0_6 (solved pops=5 evals=14 maxopen=10) [OK ] extrinsic_L0_5 (solved pops=9 evals=48 maxopen=40) [OK ] extrinsic_L0_4 (solved pops=11 evals=68 maxopen=58) [OK ] extrinsic_L0_2 (solved pops=14 evals=76 maxopen=63) [OK ] extrinsic_L0_10 (solved pops=4 evals=9 maxopen=6) [OK ] extrinsic_L0_8 (solved pops=13 evals=75 maxopen=63) [OK ] extrinsic_L0_13 (solved pops=4 evals=10 maxopen=7) [OK ] extrinsic_L0_9 (solved pops=11 evals=69 maxopen=43) [OK ] extrinsic_L0_7 (solved pops=17 evals=84 maxopen=68) [OK ] extrinsic_L0_11 (solved pops=15 evals=76 maxopen=62) [OK ] extrinsic_L0_12 (solved pops=14 evals=59 maxopen=29) [OK ] extrinsic_L1_4 (solved pops=4 evals=12 maxopen=7) [OK ] extrinsic_L1_1 (solved pops=16 evals=97 maxopen=64) [OK ] extrinsic_L1_2 (solved pops=26 evals=198 maxopen=154) [OK ] extrinsic_L1_3 (solved pops=25 evals=182 maxopen=139) [OK ] extrinsic_L0_14 (solved pops=44 evals=285 maxopen=242) [OK ] extrinsic_L2_1 (solved pops=66 evals=351 maxopen=286) [OK ] extrinsic_L2_7 (solved pops=32 evals=192 maxopen=161) [OK ] extrinsic_L2_4 (solved pops=86 evals=567 maxopen=482) [OK ] extrinsic_L2_3 (solved pops=104 evals=679 maxopen=576) [OK ] extrinsic_L2_9 (solved pops=47 evals=356 maxopen=310) [OK ] extrinsic_L2_11 (solved pops=5 evals=13 maxopen=7) [OK ] extrinsic_L2_10 (solved pops=46 evals=313 maxopen=268) [OK ] extrinsic_L2_6 (solved pops=148 evals=852 maxopen=705) [OK ] extrinsic_L2_8 (solved pops=100 evals=597 maxopen=498) [OK ] extrinsic_L3_1 (solved pops=61 evals=445 maxopen=385) [OK ] extrinsic_L2_12 (solved pops=109 evals=652 maxopen=544) [OK ] extrinsic_L3_3 (solved pops=40 evals=266 maxopen=227) [OK ] extrinsic_L3_4 (solved pops=82 evals=587 maxopen=485) [OK ] extrinsic_L3_5 (solved pops=83 evals=618 maxopen=515) [OK ] extrinsic_L2_2 (solved pops=410 evals=2108 maxopen=1699) [OK ] extrinsic_L3_2 (solved pops=473 evals=2519 maxopen=2047) [OK ] extrinsic_L2_5 (solved pops=795 evals=4382 maxopen=3588) [OK ] extrinsic_L3_6 (solved pops=740 evals=4100 maxopen=3361) [OK ] extrinsic_L3_11 (solved pops=252 evals=1326 maxopen=1072) [OK ] extrinsic_L3_12 (solved pops=217 evals=1157 maxopen=941) [OK ] extrinsic_L3_13 (solved pops=30 evals=185 maxopen=156) [OK ] extrinsic_L3_14 (solved pops=46 evals=338 maxopen=293) [OK ] extrinsic_L3_15 (solved pops=1663 evals=9917 maxopen=8255) [OK ] extrinsic_L3_16 (solved pops=181 evals=979 maxopen=799) [ ] extrinsic_L2_13 (budget pops=4000 evals=25210 maxopen=21211) [ ] extrinsic_L3_7 (budget pops=4000 evals=24794 maxopen=20795) [OK ] extrinsic_L3_18 (solved pops=592 evals=3428 maxopen=2816) [OK ] extrinsic_L3_17 (solved pops=1359 evals=8178 maxopen=6801) [ ] extrinsic_L3_8 (budget pops=4000 evals=28200 maxopen=24201) [ ] extrinsic_L3_9 (budget pops=4000 evals=25416 maxopen=21417) [ ] extrinsic_L3_10 (budget pops=4000 evals=26882 maxopen=22883) [OK ] extrinsic_L3_23 (solved pops=477 evals=2990 maxopen=2514) [OK ] extrinsic_L3_25 (solved pops=495 evals=2874 maxopen=2360) [ ] extrinsic_L3_19 (budget pops=4000 evals=23887 maxopen=19888) [ ] extrinsic_L3_24 (budget pops=4000 evals=27030 maxopen=23031) [ ] extrinsic_L3_20 (budget pops=4000 evals=25074 maxopen=21075) [ ] extrinsic_L3_21 (budget pops=4000 evals=24618 maxopen=20619) [ ] extrinsic_L3_22 (budget pops=4000 evals=24240 maxopen=20241) [ ] extrinsic_L3_26 (budget pops=4000 evals=28211 maxopen=24212) [OK ] extrinsic_L4_3 (solved pops=989 evals=5608 maxopen=4620) [ ] extrinsic_L4_1 (budget pops=4000 evals=26839 maxopen=22840) [OK ] extrinsic_L4_2 (solved pops=3886 evals=32218 maxopen=28333) [ ] extrinsic_L3_27 (budget pops=4000 evals=26923 maxopen=22924) [ ] extrinsic_L3_28 (budget pops=4000 evals=26199 maxopen=22200) [ ] extrinsic_L4_4 (budget pops=4000 evals=28098 maxopen=24099) [ ] extrinsic_L3_29 (budget pops=4000 evals=33376 maxopen=29377) [ ] extrinsic_L4_5 (budget pops=4000 evals=29691 maxopen=25692) [ ] extrinsic_L4_6 (budget pops=4000 evals=28385 maxopen=24386) [OK ] extrinsic_L4_12 (solved pops=139 evals=808 maxopen=667) [ ] extrinsic_L4_7 (budget pops=4000 evals=24224 maxopen=20225) [ ] extrinsic_L4_8 (budget pops=4000 evals=27966 maxopen=23967) [ ] extrinsic_L4_9 (budget pops=4000 evals=24187 maxopen=20188) [ ] extrinsic_L4_10 (budget pops=4000 evals=28454 maxopen=24455) [ ] extrinsic_L4_13 (budget pops=4000 evals=27712 maxopen=23713) [ ] extrinsic_L4_11 (budget pops=4000 evals=32557 maxopen=28558) [ ] extrinsic_L4_14 (budget pops=4000 evals=27657 maxopen=23658) [ ] extrinsic_L5_1 (budget pops=4000 evals=30373 maxopen=26374) [ ] extrinsic_L5_2 (budget pops=4000 evals=29841 maxopen=25842) [ ] extrinsic_L5_3 (budget pops=4000 evals=30605 maxopen=26606) [ ] extrinsic_L5_6 (budget pops=4000 evals=23774 maxopen=19775) [ ] extrinsic_L5_5 (budget pops=4000 evals=30765 maxopen=26766) [ ] extrinsic_L5_4 (budget pops=4000 evals=30439 maxopen=26440) [OK ] extrinsic_L6_1 (solved pops=344 evals=1958 maxopen=1615) [ ] extrinsic_L5_7 (budget pops=4000 evals=30080 maxopen=26081) [ ] extrinsic_L5_11 (budget pops=4000 evals=30864 maxopen=26865) [ ] extrinsic_L5_8 (budget pops=4000 evals=31602 maxopen=27603) [ ] extrinsic_L5_9 (budget pops=4000 evals=30833 maxopen=26834) [ ] extrinsic_L5_10 (budget pops=4000 evals=33105 maxopen=29106) [ ] extrinsic_L6_2 (budget pops=4000 evals=29263 maxopen=25264) [ ] extrinsic_L6_3 (budget pops=4000 evals=27721 maxopen=23722) [ ] extrinsic_L6_4 (budget pops=4000 evals=27734 maxopen=23735) [ ] extrinsic_L6_5 (budget pops=4000 evals=28157 maxopen=24158) [ ] extrinsic_L6_6 (budget pops=4000 evals=25708 maxopen=21709) [ ] extrinsic_L6_7 (budget pops=4000 evals=24357 maxopen=20358) [ ] extrinsic_L6_9 (budget pops=4000 evals=24500 maxopen=20501) [ ] extrinsic_L6_8 (budget pops=4000 evals=25221 maxopen=21222) L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] L0_1 [('A : prop) -> ['A -> 'A]] L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] L0_9 [('A : prop) -> (not 'A) -> 'A -> false] L0_10 [false -> ('A : prop) -> 'A] L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] L0_12 [('A : prop) -> (or 'A (not 'A))] L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] L1_1 [('A : prop) -> 'A -> (not (not 'A))] L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] L2_9 [('A : prop) -> (iff (and 'A false) false)] L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] L2_11 [('A : prop) -> (iff 'A 'A)] L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not '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_1pt_base_bf_extrinsic-95.json Solved 50/94 in 2150.7s