TSTP Solution File: SYO007^1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO007^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 04:21:06 EDT 2023
% Result : Theorem 8.56s 8.83s
% Output : Proof 8.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO007^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.11 % Command : duper %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 05:32:26 EDT 2023
% 0.10/0.31 % CPUTime :
% 8.56/8.83 SZS status Theorem for theBenchmark.p
% 8.56/8.83 SZS output start Proof for theBenchmark.p
% 8.56/8.83 Clause #0 (by assumption #[]): Eq (Eq leibeq fun U V => ∀ (Q : Prop → Prop), Q U → Q V) True
% 8.56/8.83 Clause #1 (by assumption #[]): Eq (Not (∀ (A B : Prop), Iff A B → leibeq A B)) True
% 8.56/8.83 Clause #2 (by clausification #[1]): Eq (∀ (A B : Prop), Iff A B → leibeq A B) False
% 8.56/8.83 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (Not (∀ (B : Prop), Iff (skS.0 0 a) B → leibeq (skS.0 0 a) B)) True
% 8.56/8.83 Clause #4 (by clausification #[3]): ∀ (a : Prop), Eq (∀ (B : Prop), Iff (skS.0 0 a) B → leibeq (skS.0 0 a) B) False
% 8.56/8.83 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Not (Iff (skS.0 0 a) (skS.0 1 a a_1) → leibeq (skS.0 0 a) (skS.0 1 a a_1))) True
% 8.56/8.83 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1) → leibeq (skS.0 0 a) (skS.0 1 a a_1)) False
% 8.56/8.83 Clause #7 (by clausification #[6]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1)) True
% 8.56/8.83 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), Eq (leibeq (skS.0 0 a) (skS.0 1 a a_1)) False
% 8.56/8.83 Clause #9 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) False)
% 8.56/8.83 Clause #10 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) True)
% 8.56/8.83 Clause #11 (by identity loobHoist #[9]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 True) True) (Eq a False))
% 8.56/8.83 Clause #13 (by identity loobHoist #[11]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq (skS.0 1 a True) False) (Eq a_1 False)))
% 8.56/8.83 Clause #15 (by identity loobHoist #[13]): ∀ (a a_1 : Prop),
% 8.56/8.83 Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) False) (Eq a False))))
% 8.56/8.83 Clause #17 (by eliminate duplicate literals #[15]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)))
% 8.56/8.83 Clause #18 (by falseElim #[17]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) False))
% 8.56/8.83 Clause #19 (by clausification #[0]): Eq leibeq fun U V => ∀ (Q : Prop → Prop), Q U → Q V
% 8.56/8.83 Clause #20 (by argument congruence #[19]): ∀ (a : Prop), Eq (leibeq a) ((fun U V => ∀ (Q : Prop → Prop), Q U → Q V) a)
% 8.56/8.83 Clause #22 (by betaEtaReduce #[20]): ∀ (a : Prop), Eq (leibeq a) fun V => ∀ (Q : Prop → Prop), Q a → Q V
% 8.56/8.83 Clause #23 (by identity loobHoist #[22]): ∀ (a : Prop), Or (Eq (leibeq True) fun V => ∀ (Q : Prop → Prop), Q a → Q V) (Eq a False)
% 8.56/8.83 Clause #24 (by identity boolHoist #[22]): ∀ (a : Prop), Or (Eq (leibeq False) fun V => ∀ (Q : Prop → Prop), Q a → Q V) (Eq a True)
% 8.56/8.83 Clause #25 (by falseElim #[23]): Eq (leibeq True) fun V => ∀ (Q : Prop → Prop), Q True → Q V
% 8.56/8.83 Clause #26 (by argument congruence #[25]): ∀ (a : Prop), Eq (leibeq True a) ((fun V => ∀ (Q : Prop → Prop), Q True → Q V) a)
% 8.56/8.83 Clause #27 (by betaEtaReduce #[26]): ∀ (a : Prop), Eq (leibeq True a) (∀ (Q : Prop → Prop), Q True → Q a)
% 8.56/8.83 Clause #28 (by identity loobHoist #[27]): ∀ (a : Prop), Or (Eq (leibeq True True) (∀ (Q : Prop → Prop), Q True → Q a)) (Eq a False)
% 8.56/8.83 Clause #30 (by falseElim #[28]): Eq (leibeq True True) (∀ (Q : Prop → Prop), Q True → Q True)
% 8.56/8.83 Clause #31 (by identity loobHoist #[8]): ∀ (a a_1 : Prop), Or (Eq (leibeq (skS.0 0 a) True) False) (Eq (skS.0 1 a a_1) False)
% 8.56/8.83 Clause #32 (by identity boolHoist #[8]): ∀ (a a_1 : Prop), Or (Eq (leibeq (skS.0 0 a) False) False) (Eq (skS.0 1 a a_1) True)
% 8.56/8.83 Clause #33 (by identity loobHoist #[31]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (leibeq True True) False) (Eq (skS.0 0 a) False))
% 8.56/8.83 Clause #36 (by identity boolHoist #[33]): ∀ (a a_1 : Prop),
% 8.56/8.83 Or (Eq (leibeq True True) False) (Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True)))
% 8.56/8.83 Clause #42 (by bool simp #[30]): Eq (leibeq True True) True
% 8.56/8.83 Clause #52 (by argument congruence #[24]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) ((fun V => ∀ (Q : Prop → Prop), Q a_1 → Q V) a)) (Eq a_1 True)
% 8.56/8.83 Clause #56 (by identity loobHoist #[10]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 0 True) False) (Eq a False))
% 8.56/8.86 Clause #59 (by identity boolHoist #[56]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq (skS.0 1 a False) True) (Eq a_1 True)))
% 8.56/8.86 Clause #99 (by betaEtaReduce #[52]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) (∀ (Q : Prop → Prop), Q a_1 → Q a)) (Eq a_1 True)
% 8.56/8.86 Clause #101 (by identity boolHoist #[99]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a_1)) (Eq a_1 True))
% 8.56/8.86 Clause #113 (by equality factoring #[101]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Ne True True) (Eq a True))
% 8.56/8.86 Clause #122 (by clausification #[113]): ∀ (a : Prop),
% 8.56/8.86 Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Eq a True) (Or (Eq True False) (Eq True False)))
% 8.56/8.86 Clause #124 (by clausification #[122]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Eq a True) (Eq True False))
% 8.56/8.86 Clause #125 (by clausification #[124]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Eq a True)
% 8.56/8.86 Clause #126 (by bool simp #[125]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True)
% 8.56/8.86 Clause #128 (by equality factoring #[126]): Or (Ne True True) (Eq (leibeq False False) True)
% 8.56/8.86 Clause #130 (by clausification #[128]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False))
% 8.56/8.86 Clause #132 (by clausification #[130]): Or (Eq (leibeq False False) True) (Eq True False)
% 8.56/8.86 Clause #133 (by clausification #[132]): Eq (leibeq False False) True
% 8.56/8.86 Clause #143 (by falseElim #[18]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) False)
% 8.56/8.86 Clause #164 (by identity boolHoist #[32]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (leibeq False False) False) (Eq (skS.0 0 a) True))
% 8.56/8.86 Clause #195 (by forward demodulation #[36, 42]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True)))
% 8.56/8.86 Clause #196 (by clausification #[195]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True))
% 8.56/8.86 Clause #197 (by identity loobHoist #[196]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a False) False) (Or (Eq a_1 True) (Or (Eq (skS.0 0 True) False) (Eq a False)))
% 8.56/8.86 Clause #199 (by identity loobHoist #[197]): ∀ (a a_1 : Prop),
% 8.56/8.86 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True False) False) (Eq a_1 False))))
% 8.56/8.86 Clause #201 (by eliminate duplicate literals #[199]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False)))
% 8.56/8.86 Clause #253 (by identity loobHoist #[59]): ∀ (a a_1 : Prop),
% 8.56/8.86 Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 True) (Or (Eq (skS.0 1 True False) True) (Eq a False))))
% 8.56/8.86 Clause #255 (by eliminate duplicate literals #[253]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True)))
% 8.56/8.86 Clause #326 (by forward demodulation #[164, 133]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq True False) (Eq (skS.0 0 a) True))
% 8.56/8.86 Clause #327 (by clausification #[326]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (skS.0 0 a) True)
% 8.56/8.86 Clause #328 (by identity loobHoist #[327]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a True) True) (Eq a_1 False))
% 8.56/8.86 Clause #330 (by identity loobHoist #[328]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 0 True) True) (Eq a False)))
% 8.56/8.86 Clause #332 (by identity loobHoist #[330]): ∀ (a a_1 : Prop),
% 8.56/8.86 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False))))
% 8.56/8.86 Clause #334 (by eliminate duplicate literals #[332]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True)))
% 8.56/8.86 Clause #338 (by falseElim #[334]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True))
% 8.56/8.86 Clause #342 (by falseElim #[338]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True)
% 8.56/8.87 Clause #343 (by superposition #[342, 143]): Or (Eq (skS.0 0 True) True) (Or (Eq (skS.0 0 True) True) (Eq True False))
% 8.56/8.87 Clause #349 (by clausification #[343]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 0 True) True)
% 8.56/8.87 Clause #350 (by eliminate duplicate literals #[349]): Eq (skS.0 0 True) True
% 8.56/8.87 Clause #352 (by backward demodulation #[350, 201]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False)))
% 8.56/8.87 Clause #356 (by backward demodulation #[350, 255]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True)))
% 8.56/8.87 Clause #365 (by clausification #[356]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True))
% 8.56/8.87 Clause #369 (by falseElim #[365]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True False) True)
% 8.56/8.87 Clause #374 (by equality factoring #[369]): Or (Ne True True) (Eq (skS.0 1 True False) True)
% 8.56/8.87 Clause #375 (by clausification #[374]): Or (Eq (skS.0 1 True False) True) (Or (Eq True False) (Eq True False))
% 8.56/8.87 Clause #377 (by clausification #[375]): Or (Eq (skS.0 1 True False) True) (Eq True False)
% 8.56/8.87 Clause #378 (by clausification #[377]): Eq (skS.0 1 True False) True
% 8.56/8.87 Clause #380 (by clausification #[352]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False))
% 8.56/8.87 Clause #384 (by falseElim #[380]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True False) False)
% 8.56/8.87 Clause #385 (by superposition #[384, 378]): ∀ (a : Prop), Or (Eq a True) (Eq False True)
% 8.56/8.87 Clause #389 (by clausification #[385]): ∀ (a : Prop), Eq a True
% 8.56/8.87 Clause #391 (by falseElim #[389]): False
% 8.56/8.87 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------