TSTP Solution File: SEU620^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU620^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 16:43:02 EDT 2023
% Result : Theorem 3.78s 3.97s
% Output : Proof 3.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU620^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 21:46:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.78/3.97 SZS status Theorem for theBenchmark.p
% 3.78/3.97 SZS output start Proof for theBenchmark.p
% 3.78/3.97 Clause #1 (by assumption #[]): Eq
% 3.78/3.97 (Eq kpairiskpair
% 3.78/3.97 (∀ (Xx Xy : Iota),
% 3.78/3.97 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.78/3.97 True
% 3.78/3.97 Clause #2 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 3.78/3.97 True
% 3.78/3.97 Clause #3 (by assumption #[]): Eq (Not (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True
% 3.78/3.97 Clause #4 (by clausification #[3]): Eq (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False
% 3.78/3.97 Clause #5 (by clausification #[4]): Eq kpairiskpair True
% 3.78/3.97 Clause #6 (by clausification #[4]): Eq (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False
% 3.78/3.97 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy))) True
% 3.78/3.97 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy)) False
% 3.78/3.97 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1)))) True
% 3.78/3.97 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1))) False
% 3.78/3.97 Clause #11 (by clausification #[1]): Eq kpairiskpair
% 3.78/3.97 (∀ (Xx Xy : Iota),
% 3.78/3.97 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97 Clause #12 (by forward demodulation #[11, 5]): Eq True
% 3.78/3.97 (∀ (Xx Xy : Iota),
% 3.78/3.97 iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97 Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 3.78/3.97 Eq
% 3.78/3.97 (∀ (Xy : Iota),
% 3.78/3.97 iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97 True
% 3.78/3.97 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 3.78/3.97 Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True
% 3.78/3.97 Clause #15 (by clausification #[2]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)
% 3.78/3.97 Clause #16 (by argument congruence #[15]): ∀ (a : Iota),
% 3.78/3.97 Eq (kpair a)
% 3.78/3.97 ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a)
% 3.78/3.97 Clause #18 (by betaEtaReduce #[16]): ∀ (a : Iota),
% 3.78/3.97 Eq (kpair a) fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)
% 3.78/3.97 Clause #19 (by argument congruence #[18]): ∀ (a a_1 : Iota),
% 3.78/3.97 Eq (kpair a a_1)
% 3.78/3.97 ((fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) a_1)
% 3.78/3.97 Clause #24 (by betaEtaReduce #[19]): ∀ (a a_1 : Iota),
% 3.78/3.97 Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 3.78/3.97 Clause #25 (by backward demodulation #[24, 14]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True
% 3.78/3.97 Clause #28 (by superposition #[25, 10]): Eq True False
% 3.78/3.97 Clause #31 (by clausification #[28]): False
% 3.78/3.97 SZS output end Proof for theBenchmark.p
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