TSTP Solution File: SEU654^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU654^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 16:43:14 EDT 2023
% Result : Theorem 6.58s 6.86s
% Output : Proof 6.58s
% 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 : SEU654^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8042.1875MB
% 0.13/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Aug 23 21:35:38 EDT 2023
% 0.13/0.38 % CPUTime :
% 6.58/6.86 SZS status Theorem for theBenchmark.p
% 6.58/6.86 SZS output start Proof for theBenchmark.p
% 6.58/6.86 Clause #0 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 6.58/6.86 True
% 6.58/6.86 Clause #1 (by assumption #[]): Eq
% 6.58/6.86 (Eq setukpairinjR2
% 6.58/6.86 (∀ (Xx Xy Xz Xu : Iota),
% 6.58/6.86 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 6.58/6.86 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.86 Eq Xy Xu))
% 6.58/6.86 True
% 6.58/6.86 Clause #2 (by assumption #[]): Eq (Not (setukpairinjR2 → ∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)) True
% 6.58/6.86 Clause #3 (by clausification #[2]): Eq (setukpairinjR2 → ∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu) False
% 6.58/6.86 Clause #4 (by clausification #[3]): Eq setukpairinjR2 True
% 6.58/6.86 Clause #5 (by clausification #[3]): Eq (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu) False
% 6.58/6.86 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (∀ (Xy Xz Xu : Iota), Eq (kpair (skS.0 0 a) Xy) (kpair Xz Xu) → Eq Xy Xu)) True
% 6.58/6.86 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Xy Xz Xu : Iota), Eq (kpair (skS.0 0 a) Xy) (kpair Xz Xu) → Eq Xy Xu) False
% 6.58/6.86 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 6.58/6.86 Eq (Not (∀ (Xz Xu : Iota), Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair Xz Xu) → Eq (skS.0 1 a a_1) Xu)) True
% 6.58/6.86 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota),
% 6.58/6.86 Eq (∀ (Xz Xu : Iota), Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair Xz Xu) → Eq (skS.0 1 a a_1) Xu) False
% 6.58/6.86 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 6.58/6.86 Eq
% 6.58/6.86 (Not (∀ (Xu : Iota), Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) Xu) → Eq (skS.0 1 a a_1) Xu))
% 6.58/6.86 True
% 6.58/6.86 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 6.58/6.86 Eq (∀ (Xu : Iota), Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) Xu) → Eq (skS.0 1 a a_1) Xu)
% 6.58/6.86 False
% 6.58/6.86 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.86 Eq
% 6.58/6.86 (Not
% 6.58/6.86 (Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 6.58/6.86 Eq (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)))
% 6.58/6.86 True
% 6.58/6.86 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.86 Eq
% 6.58/6.86 (Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) →
% 6.58/6.86 Eq (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3))
% 6.58/6.86 False
% 6.58/6.86 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.86 Eq (Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) True
% 6.58/6.86 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) False
% 6.58/6.86 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), Eq (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))
% 6.58/6.86 Clause #17 (by clausification #[1]): Eq setukpairinjR2
% 6.58/6.86 (∀ (Xx Xy Xz Xu : Iota),
% 6.58/6.86 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 6.58/6.86 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.86 Eq Xy Xu)
% 6.58/6.86 Clause #18 (by forward demodulation #[17, 4]): Eq True
% 6.58/6.86 (∀ (Xx Xy Xz Xu : Iota),
% 6.58/6.86 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 6.58/6.86 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.86 Eq Xy Xu)
% 6.58/6.86 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 6.58/6.86 Eq
% 6.58/6.86 (∀ (Xy Xz Xu : Iota),
% 6.58/6.86 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))
% 6.58/6.86 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.86 Eq Xy Xu)
% 6.58/6.86 True
% 6.58/6.86 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 6.58/6.86 Eq
% 6.58/6.86 (∀ (Xz Xu : Iota),
% 6.58/6.86 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.86 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.89 Eq a_1 Xu)
% 6.58/6.89 True
% 6.58/6.89 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 6.58/6.89 Eq
% 6.58/6.89 (∀ (Xu : Iota),
% 6.58/6.89 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.89 (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin Xu emptyset)) emptyset)) →
% 6.58/6.89 Eq a_1 Xu)
% 6.58/6.89 True
% 6.58/6.89 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.89 Eq
% 6.58/6.89 (Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.89 (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin a_3 emptyset)) emptyset)) →
% 6.58/6.89 Eq a_1 a_3)
% 6.58/6.89 True
% 6.58/6.89 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.89 Or
% 6.58/6.89 (Eq
% 6.58/6.89 (Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.89 (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin a_3 emptyset)) emptyset)))
% 6.58/6.89 False)
% 6.58/6.89 (Eq (Eq a_1 a_3) True)
% 6.58/6.89 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.89 Or (Eq (Eq a a_1) True)
% 6.58/6.89 (Ne (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin a emptyset)) emptyset))
% 6.58/6.89 (setadjoin (setadjoin a_3 emptyset) (setadjoin (setadjoin a_3 (setadjoin a_1 emptyset)) emptyset)))
% 6.58/6.89 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.89 Or
% 6.58/6.89 (Ne (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.89 (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin a_3 emptyset)) emptyset)))
% 6.58/6.89 (Eq a_1 a_3)
% 6.58/6.89 Clause #27 (by clausification #[0]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)
% 6.58/6.89 Clause #28 (by argument congruence #[27]): ∀ (a : Iota),
% 6.58/6.89 Eq (kpair a)
% 6.58/6.89 ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a)
% 6.58/6.89 Clause #30 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), Ne (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)
% 6.58/6.89 Clause #31 (by betaEtaReduce #[28]): ∀ (a : Iota),
% 6.58/6.89 Eq (kpair a) fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)
% 6.58/6.89 Clause #32 (by argument congruence #[31]): ∀ (a a_1 : Iota),
% 6.58/6.89 Eq (kpair a a_1)
% 6.58/6.89 ((fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) a_1)
% 6.58/6.89 Clause #35 (by betaEtaReduce #[32]): ∀ (a a_1 : Iota),
% 6.58/6.89 Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 6.58/6.89 Clause #36 (by backward demodulation #[35, 25]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.58/6.89 Or
% 6.58/6.89 (Ne (kpair a a_1)
% 6.58/6.89 (setadjoin (setadjoin a_2 emptyset) (setadjoin (setadjoin a_2 (setadjoin a_3 emptyset)) emptyset)))
% 6.58/6.89 (Eq a_1 a_3)
% 6.58/6.89 Clause #38 (by forward demodulation #[36, 35]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3)
% 6.58/6.89 Clause #39 (by superposition #[38, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 6.58/6.89 Or (Ne (kpair (skS.0 0 a) (skS.0 1 a a_1)) (kpair a_2 a_3)) (Eq (skS.0 3 a a_1 a_4 a_5) a_3)
% 6.58/6.89 Clause #60 (by equality resolution #[39]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)
% 6.58/6.89 Clause #89 (by forward contextual literal cutting #[60, 30]): False
% 6.58/6.89 SZS output end Proof for theBenchmark.p
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