TSTP Solution File: SEU667^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU667^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 : Thu Aug 31 16:43:18 EDT 2023
% Result : Theorem 3.90s 4.07s
% Output : Proof 3.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU667^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.36 % Computer : n014.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Wed Aug 23 14:53:04 EDT 2023
% 0.17/0.36 % CPUTime :
% 3.90/4.07 SZS status Theorem for theBenchmark.p
% 3.90/4.07 SZS output start Proof for theBenchmark.p
% 3.90/4.07 Clause #0 (by assumption #[]): Eq (Eq breln fun A B C => subset C (cartprod A B)) True
% 3.90/4.07 Clause #2 (by assumption #[]): Eq
% 3.90/4.07 (Eq dpsetconstrSub
% 3.90/4.07 (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B fun Xx Xy => Xphi Xx Xy) (cartprod A B)))
% 3.90/4.07 True
% 3.90/4.07 Clause #3 (by assumption #[]): Eq
% 3.90/4.07 (Not
% 3.90/4.07 (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B fun Xx Xy => Xphi Xx Xy)))
% 3.90/4.07 True
% 3.90/4.07 Clause #4 (by clausification #[0]): Eq breln fun A B C => subset C (cartprod A B)
% 3.90/4.07 Clause #5 (by argument congruence #[4]): ∀ (a : Iota), Eq (breln a) ((fun A B C => subset C (cartprod A B)) a)
% 3.90/4.07 Clause #8 (by betaEtaReduce #[5]): ∀ (a : Iota), Eq (breln a) fun B C => subset C (cartprod a B)
% 3.90/4.07 Clause #9 (by argument congruence #[8]): ∀ (a a_1 : Iota), Eq (breln a a_1) ((fun B C => subset C (cartprod a B)) a_1)
% 3.90/4.07 Clause #16 (by betaEtaReduce #[9]): ∀ (a a_1 : Iota), Eq (breln a a_1) fun C => subset C (cartprod a a_1)
% 3.90/4.07 Clause #17 (by argument congruence #[16]): ∀ (a a_1 a_2 : Iota), Eq (breln a a_1 a_2) ((fun C => subset C (cartprod a a_1)) a_2)
% 3.90/4.07 Clause #29 (by betaEtaReduce #[17]): ∀ (a a_1 a_2 : Iota), Eq (breln a a_1 a_2) (subset a_2 (cartprod a a_1))
% 3.90/4.07 Clause #43 (by betaEtaReduce #[2]): Eq (Eq dpsetconstrSub (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B))) True
% 3.90/4.07 Clause #44 (by clausification #[43]): Eq dpsetconstrSub (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B))
% 3.90/4.07 Clause #59 (by betaEtaReduce #[3]): Eq (Not (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi))) True
% 3.90/4.07 Clause #60 (by clausification #[59]): Eq (dpsetconstrSub → ∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi)) False
% 3.90/4.07 Clause #61 (by clausification #[60]): Eq dpsetconstrSub True
% 3.90/4.07 Clause #62 (by clausification #[60]): Eq (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), breln A B (dpsetconstr A B Xphi)) False
% 3.90/4.07 Clause #63 (by backward demodulation #[61, 44]): Eq True (∀ (A B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr A B Xphi) (cartprod A B))
% 3.90/4.07 Clause #88 (by clausification #[62]): ∀ (a : Iota),
% 3.90/4.07 Eq (Not (∀ (B : Iota) (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) B (dpsetconstr (skS.0 0 a) B Xphi))) True
% 3.90/4.07 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (∀ (B : Iota) (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) B (dpsetconstr (skS.0 0 a) B Xphi)) False
% 3.90/4.07 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota),
% 3.90/4.07 Eq
% 3.90/4.07 (Not
% 3.90/4.07 (∀ (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) Xphi)))
% 3.90/4.07 True
% 3.90/4.07 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota),
% 3.90/4.07 Eq (∀ (Xphi : Iota → Iota → Prop), breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) Xphi))
% 3.90/4.07 False
% 3.90/4.07 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop),
% 3.90/4.07 Eq (Not (breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) True
% 3.90/4.07 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop),
% 3.90/4.07 Eq (breln (skS.0 0 a) (skS.0 1 a a_1) (dpsetconstr (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) False
% 3.90/4.07 Clause #95 (by clausification #[63]): ∀ (a : Iota), Eq (∀ (B : Iota) (Xphi : Iota → Iota → Prop), subset (dpsetconstr a B Xphi) (cartprod a B)) True
% 3.90/4.07 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (∀ (Xphi : Iota → Iota → Prop), subset (dpsetconstr a a_1 Xphi) (cartprod a a_1)) True
% 3.90/4.07 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), Eq (subset (dpsetconstr a a_1 a_2) (cartprod a a_1)) True
% 3.90/4.07 Clause #98 (by superposition #[97, 29]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota → Prop), Eq (breln a a_1 (dpsetconstr a a_1 a_2)) True
% 3.90/4.07 Clause #106 (by superposition #[98, 93]): Eq True False
% 3.90/4.07 Clause #110 (by clausification #[106]): False
% 3.90/4.07 SZS output end Proof for theBenchmark.p
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