TSTP Solution File: SYO016^1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO016^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 04:21:07 EDT 2023
% Result : Theorem 4.02s 4.23s
% Output : Proof 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO016^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 05:42:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.02/4.23 SZS status Theorem for theBenchmark.p
% 4.02/4.23 SZS output start Proof for theBenchmark.p
% 4.02/4.23 Clause #0 (by assumption #[]): Eq (Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y) True
% 4.02/4.23 Clause #1 (by assumption #[]): Eq (Not (leibeq (h (leibeq (h True) (h False))) (h False))) True
% 4.02/4.23 Clause #2 (by clausification #[1]): Eq (leibeq (h (leibeq (h True) (h False))) (h False)) False
% 4.02/4.23 Clause #3 (by identity loobHoist #[2]): Or (Eq (leibeq (h (leibeq (h True) (h False))) True) False) (Eq (h False) False)
% 4.02/4.23 Clause #4 (by identity boolHoist #[2]): Or (Eq (leibeq (h (leibeq (h True) (h False))) False) False) (Eq (h False) True)
% 4.02/4.23 Clause #5 (by identity loobHoist #[3]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (h (leibeq (h True) (h False))) False))
% 4.02/4.23 Clause #6 (by identity boolHoist #[3]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Eq (h (leibeq (h True) (h False))) True))
% 4.02/4.23 Clause #7 (by identity loobHoist #[5]): Or (Eq (h False) False)
% 4.02/4.23 (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Eq (leibeq (h True) (h False)) False)))
% 4.02/4.23 Clause #8 (by identity boolHoist #[5]): Or (Eq (h False) False)
% 4.02/4.23 (Or (Eq (leibeq True True) False) (Or (Eq (h False) False) (Eq (leibeq (h True) (h False)) True)))
% 4.02/4.23 Clause #9 (by identity loobHoist #[7]): Or (Eq (h False) False)
% 4.02/4.23 (Or (Eq (leibeq True True) False)
% 4.02/4.23 (Or (Eq (h True) False) (Or (Eq (leibeq (h True) True) False) (Eq (h False) False))))
% 4.02/4.23 Clause #11 (by eliminate duplicate literals #[9]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Eq (leibeq (h True) True) False)))
% 4.02/4.23 Clause #12 (by identity loobHoist #[11]): Or (Eq (h False) False)
% 4.02/4.23 (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Or (Eq (leibeq True True) False) (Eq (h True) False))))
% 4.02/4.23 Clause #14 (by eliminate duplicate literals #[12]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (h True) False))
% 4.02/4.23 Clause #15 (by clausification #[0]): Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y
% 4.02/4.23 Clause #16 (by argument congruence #[15]): ∀ (a : Prop), Eq (leibeq a) ((fun X Y => ∀ (P : Prop → Prop), P X → P Y) a)
% 4.02/4.23 Clause #18 (by betaEtaReduce #[16]): ∀ (a : Prop), Eq (leibeq a) fun Y => ∀ (P : Prop → Prop), P a → P Y
% 4.02/4.23 Clause #19 (by identity loobHoist #[18]): ∀ (a : Prop), Or (Eq (leibeq True) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a False)
% 4.02/4.23 Clause #20 (by identity boolHoist #[18]): ∀ (a : Prop), Or (Eq (leibeq False) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a True)
% 4.02/4.23 Clause #21 (by falseElim #[19]): Eq (leibeq True) fun Y => ∀ (P : Prop → Prop), P True → P Y
% 4.02/4.23 Clause #22 (by argument congruence #[21]): ∀ (a : Prop), Eq (leibeq True a) ((fun Y => ∀ (P : Prop → Prop), P True → P Y) a)
% 4.02/4.23 Clause #23 (by argument congruence #[20]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) ((fun Y => ∀ (P : Prop → Prop), P a_1 → P Y) a)) (Eq a_1 True)
% 4.02/4.23 Clause #26 (by identity loobHoist #[4]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq (h (leibeq (h True) (h False))) False))
% 4.02/4.23 Clause #27 (by identity boolHoist #[4]): Or (Eq (h False) True) (Or (Eq (leibeq False False) False) (Eq (h (leibeq (h True) (h False))) True))
% 4.02/4.23 Clause #28 (by identity loobHoist #[26]): Or (Eq (h False) True)
% 4.02/4.23 (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Eq (leibeq (h True) (h False)) False)))
% 4.02/4.23 Clause #31 (by identity boolHoist #[28]): Or (Eq (h False) True)
% 4.02/4.23 (Or (Eq (leibeq True False) False)
% 4.02/4.23 (Or (Eq (h True) False) (Or (Eq (leibeq (h True) False) False) (Eq (h False) True))))
% 4.02/4.23 Clause #32 (by betaEtaReduce #[22]): ∀ (a : Prop), Eq (leibeq True a) (∀ (P : Prop → Prop), P True → P a)
% 4.02/4.23 Clause #33 (by identity loobHoist #[32]): ∀ (a : Prop), Or (Eq (leibeq True True) (∀ (P : Prop → Prop), P True → P a)) (Eq a False)
% 4.02/4.23 Clause #35 (by falseElim #[33]): Eq (leibeq True True) (∀ (P : Prop → Prop), P True → P True)
% 4.02/4.23 Clause #36 (by bool simp #[35]): Eq (leibeq True True) True
% 4.02/4.23 Clause #46 (by identity loobHoist #[6]): Or (Eq (h False) False)
% 4.02/4.23 (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Eq (leibeq (h True) (h False)) False)))
% 4.02/4.26 Clause #48 (by identity loobHoist #[46]): Or (Eq (h False) False)
% 4.02/4.26 (Or (Eq (leibeq False True) False)
% 4.02/4.26 (Or (Eq (h True) True) (Or (Eq (leibeq (h True) True) False) (Eq (h False) False))))
% 4.02/4.26 Clause #50 (by eliminate duplicate literals #[48]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Eq (leibeq (h True) True) False)))
% 4.02/4.26 Clause #52 (by identity boolHoist #[50]): Or (Eq (h False) False)
% 4.02/4.26 (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Or (Eq (leibeq False True) False) (Eq (h True) True))))
% 4.02/4.26 Clause #59 (by betaEtaReduce #[23]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) (∀ (P : Prop → Prop), P a_1 → P a)) (Eq a_1 True)
% 4.02/4.26 Clause #61 (by identity boolHoist #[59]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a_1)) (Eq a_1 True))
% 4.02/4.26 Clause #71 (by equality factoring #[61]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Ne True True) (Eq a True))
% 4.02/4.26 Clause #75 (by eliminate duplicate literals #[8]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (leibeq (h True) (h False)) True))
% 4.02/4.26 Clause #76 (by forward demodulation #[75, 36]): Or (Eq (h False) False) (Or (Eq True False) (Eq (leibeq (h True) (h False)) True))
% 4.02/4.26 Clause #77 (by clausification #[76]): Or (Eq (h False) False) (Eq (leibeq (h True) (h False)) True)
% 4.02/4.26 Clause #78 (by identity loobHoist #[77]): Or (Eq (h False) False) (Or (Eq (leibeq (h True) True) True) (Eq (h False) False))
% 4.02/4.26 Clause #80 (by eliminate duplicate literals #[78]): Or (Eq (h False) False) (Eq (leibeq (h True) True) True)
% 4.02/4.26 Clause #82 (by identity boolHoist #[80]): Or (Eq (h False) False) (Or (Eq (leibeq False True) True) (Eq (h True) True))
% 4.02/4.26 Clause #143 (by clausification #[71]): ∀ (a : Prop),
% 4.02/4.26 Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Or (Eq True False) (Eq True False)))
% 4.02/4.26 Clause #145 (by clausification #[143]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Eq True False))
% 4.02/4.26 Clause #146 (by clausification #[145]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Eq a True)
% 4.02/4.26 Clause #147 (by bool simp #[146]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True)
% 4.02/4.26 Clause #148 (by equality factoring #[147]): Or (Ne True True) (Eq (leibeq False False) True)
% 4.02/4.26 Clause #150 (by clausification #[148]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False))
% 4.02/4.26 Clause #152 (by clausification #[150]): Or (Eq (leibeq False False) True) (Eq True False)
% 4.02/4.26 Clause #153 (by clausification #[152]): Eq (leibeq False False) True
% 4.02/4.26 Clause #156 (by forward demodulation #[27, 153]): Or (Eq (h False) True) (Or (Eq True False) (Eq (h (leibeq (h True) (h False))) True))
% 4.02/4.26 Clause #157 (by clausification #[156]): Or (Eq (h False) True) (Eq (h (leibeq (h True) (h False))) True)
% 4.02/4.26 Clause #158 (by identity loobHoist #[157]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq (h True) (h False)) False))
% 4.02/4.26 Clause #159 (by identity boolHoist #[157]): Or (Eq (h False) True) (Or (Eq (h False) True) (Eq (leibeq (h True) (h False)) True))
% 4.02/4.26 Clause #161 (by identity boolHoist #[158]): Or (Eq (h False) True) (Or (Eq (h True) True) (Or (Eq (leibeq (h True) False) False) (Eq (h False) True)))
% 4.02/4.26 Clause #178 (by eliminate duplicate literals #[159]): Or (Eq (h False) True) (Eq (leibeq (h True) (h False)) True)
% 4.02/4.26 Clause #180 (by identity boolHoist #[178]): Or (Eq (h False) True) (Or (Eq (leibeq (h True) False) True) (Eq (h False) True))
% 4.02/4.26 Clause #181 (by eliminate duplicate literals #[31]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Eq (leibeq (h True) False) False)))
% 4.02/4.26 Clause #182 (by identity loobHoist #[181]): Or (Eq (h False) True)
% 4.02/4.26 (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Or (Eq (leibeq True False) False) (Eq (h True) False))))
% 4.02/4.26 Clause #184 (by eliminate duplicate literals #[182]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq (h True) False))
% 4.02/4.26 Clause #185 (by eliminate duplicate literals #[180]): Or (Eq (h False) True) (Eq (leibeq (h True) False) True)
% 4.02/4.28 Clause #186 (by identity loobHoist #[185]): Or (Eq (h False) True) (Or (Eq (leibeq True False) True) (Eq (h True) False))
% 4.02/4.28 Clause #223 (by eliminate duplicate literals #[161]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq (h True) False) False))
% 4.02/4.28 Clause #225 (by identity boolHoist #[223]): Or (Eq (h False) True) (Or (Eq (h True) True) (Or (Eq (leibeq False False) False) (Eq (h True) True)))
% 4.02/4.28 Clause #226 (by eliminate duplicate literals #[52]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Eq (h True) True))
% 4.02/4.28 Clause #227 (by eliminate duplicate literals #[225]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq False False) False))
% 4.02/4.28 Clause #228 (by superposition #[227, 153]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq False True))
% 4.02/4.28 Clause #229 (by clausification #[228]): Or (Eq (h False) True) (Eq (h True) True)
% 4.02/4.28 Clause #231 (by superposition #[229, 82]): Or (Eq (h True) True) (Or (Eq True False) (Or (Eq (leibeq False True) True) (Eq (h True) True)))
% 4.02/4.28 Clause #232 (by superposition #[229, 226]): Or (Eq (h True) True) (Or (Eq True False) (Or (Eq (leibeq False True) False) (Eq (h True) True)))
% 4.02/4.28 Clause #233 (by clausification #[231]): Or (Eq (h True) True) (Or (Eq (leibeq False True) True) (Eq (h True) True))
% 4.02/4.28 Clause #234 (by eliminate duplicate literals #[233]): Or (Eq (h True) True) (Eq (leibeq False True) True)
% 4.02/4.28 Clause #236 (by clausification #[232]): Or (Eq (h True) True) (Or (Eq (leibeq False True) False) (Eq (h True) True))
% 4.02/4.28 Clause #237 (by eliminate duplicate literals #[236]): Or (Eq (h True) True) (Eq (leibeq False True) False)
% 4.02/4.28 Clause #238 (by superposition #[237, 234]): Or (Eq (h True) True) (Or (Eq (h True) True) (Eq False True))
% 4.02/4.28 Clause #241 (by clausification #[238]): Or (Eq (h True) True) (Eq (h True) True)
% 4.02/4.28 Clause #242 (by eliminate duplicate literals #[241]): Eq (h True) True
% 4.02/4.28 Clause #243 (by backward demodulation #[242, 14]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq True False))
% 4.02/4.28 Clause #244 (by backward demodulation #[242, 184]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq True False))
% 4.02/4.28 Clause #245 (by backward demodulation #[242, 186]): Or (Eq (h False) True) (Or (Eq (leibeq True False) True) (Eq True False))
% 4.02/4.28 Clause #249 (by clausification #[245]): Or (Eq (h False) True) (Eq (leibeq True False) True)
% 4.02/4.28 Clause #254 (by clausification #[244]): Or (Eq (h False) True) (Eq (leibeq True False) False)
% 4.02/4.28 Clause #255 (by superposition #[254, 249]): Or (Eq (h False) True) (Or (Eq (h False) True) (Eq False True))
% 4.02/4.28 Clause #256 (by clausification #[255]): Or (Eq (h False) True) (Eq (h False) True)
% 4.02/4.28 Clause #257 (by eliminate duplicate literals #[256]): Eq (h False) True
% 4.02/4.28 Clause #260 (by clausification #[243]): Or (Eq (h False) False) (Eq (leibeq True True) False)
% 4.02/4.28 Clause #261 (by forward demodulation #[260, 257]): Or (Eq True False) (Eq (leibeq True True) False)
% 4.02/4.28 Clause #262 (by clausification #[261]): Eq (leibeq True True) False
% 4.02/4.28 Clause #263 (by superposition #[262, 36]): Eq False True
% 4.02/4.28 Clause #264 (by clausification #[263]): False
% 4.02/4.28 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------