TSTP Solution File: SEU650^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU650^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 16:43:12 EDT 2023
% Result : Theorem 5.49s 5.69s
% Output : Proof 5.49s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU650^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.11 % Command : duper %s
% 0.10/0.31 % Computer : n027.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
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Aug 24 01:40:17 EDT 2023
% 0.10/0.32 % CPUTime :
% 5.49/5.69 SZS status Theorem for theBenchmark.p
% 5.49/5.69 SZS output start Proof for theBenchmark.p
% 5.49/5.69 Clause #0 (by assumption #[]): Eq (Eq setukpairinjR11 (∀ (Xx Xy : Iota), Eq Xx Xy → Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xx emptyset)))
% 5.49/5.69 True
% 5.49/5.69 Clause #1 (by assumption #[]): Eq
% 5.49/5.69 (Not
% 5.49/5.69 (setukpairinjR11 →
% 5.49/5.69 ∀ (Xx Xy : Iota),
% 5.49/5.69 Eq Xx Xy →
% 5.49/5.69 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin Xx emptyset) emptyset)))
% 5.49/5.69 True
% 5.49/5.69 Clause #2 (by clausification #[0]): Eq setukpairinjR11 (∀ (Xx Xy : Iota), Eq Xx Xy → Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xx emptyset))
% 5.49/5.69 Clause #4 (by clausify Prop equality #[2]): Or (Eq setukpairinjR11 False)
% 5.49/5.69 (Eq (∀ (Xx Xy : Iota), Eq Xx Xy → Eq (setadjoin Xx (setadjoin Xy emptyset)) (setadjoin Xx emptyset)) True)
% 5.49/5.69 Clause #6 (by clausification #[4]): ∀ (a : Iota),
% 5.49/5.69 Or (Eq setukpairinjR11 False)
% 5.49/5.69 (Eq (∀ (Xy : Iota), Eq a Xy → Eq (setadjoin a (setadjoin Xy emptyset)) (setadjoin a emptyset)) True)
% 5.49/5.69 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq setukpairinjR11 False) (Eq (Eq a a_1 → Eq (setadjoin a (setadjoin a_1 emptyset)) (setadjoin a emptyset)) True)
% 5.49/5.69 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq setukpairinjR11 False)
% 5.49/5.69 (Or (Eq (Eq a a_1) False) (Eq (Eq (setadjoin a (setadjoin a_1 emptyset)) (setadjoin a emptyset)) True))
% 5.49/5.69 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq setukpairinjR11 False)
% 5.49/5.69 (Or (Eq (Eq (setadjoin a (setadjoin a_1 emptyset)) (setadjoin a emptyset)) True) (Ne a a_1))
% 5.49/5.69 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota),
% 5.49/5.69 Or (Eq setukpairinjR11 False) (Or (Ne a a_1) (Eq (setadjoin a (setadjoin a_1 emptyset)) (setadjoin a emptyset)))
% 5.49/5.69 Clause #11 (by destructive equality resolution #[10]): ∀ (a : Iota), Or (Eq setukpairinjR11 False) (Eq (setadjoin a (setadjoin a emptyset)) (setadjoin a emptyset))
% 5.49/5.69 Clause #19 (by clausification #[1]): Eq
% 5.49/5.69 (setukpairinjR11 →
% 5.49/5.69 ∀ (Xx Xy : Iota),
% 5.49/5.69 Eq Xx Xy →
% 5.49/5.69 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin Xx emptyset) emptyset))
% 5.49/5.69 False
% 5.49/5.69 Clause #20 (by clausification #[19]): Eq setukpairinjR11 True
% 5.49/5.69 Clause #21 (by clausification #[19]): Eq
% 5.49/5.69 (∀ (Xx Xy : Iota),
% 5.49/5.69 Eq Xx Xy →
% 5.49/5.69 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin Xx emptyset) emptyset))
% 5.49/5.69 False
% 5.49/5.69 Clause #23 (by backward demodulation #[20, 11]): ∀ (a : Iota), Or (Eq True False) (Eq (setadjoin a (setadjoin a emptyset)) (setadjoin a emptyset))
% 5.49/5.69 Clause #27 (by clausification #[23]): ∀ (a : Iota), Eq (setadjoin a (setadjoin a emptyset)) (setadjoin a emptyset)
% 5.49/5.69 Clause #33 (by clausification #[21]): ∀ (a : Iota),
% 5.49/5.69 Eq
% 5.49/5.69 (Not
% 5.49/5.69 (∀ (Xy : Iota),
% 5.49/5.69 Eq (skS.0 2 a) Xy →
% 5.49/5.69 Eq
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) (setadjoin Xy emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)))
% 5.49/5.69 True
% 5.49/5.69 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 5.49/5.69 Eq
% 5.49/5.69 (∀ (Xy : Iota),
% 5.49/5.69 Eq (skS.0 2 a) Xy →
% 5.49/5.69 Eq
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) (setadjoin Xy emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset))
% 5.49/5.69 False
% 5.49/5.69 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 5.49/5.69 Eq
% 5.49/5.69 (Not
% 5.49/5.69 (Eq (skS.0 2 a) (skS.0 3 a a_1) →
% 5.49/5.69 Eq
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)) emptyset))
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)))
% 5.49/5.69 True
% 5.49/5.69 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 5.49/5.69 Eq
% 5.49/5.69 (Eq (skS.0 2 a) (skS.0 3 a a_1) →
% 5.49/5.69 Eq
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.69 (setadjoin (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)) emptyset))
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset))
% 5.49/5.70 False
% 5.49/5.70 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) True
% 5.49/5.70 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota),
% 5.49/5.70 Eq
% 5.49/5.70 (Eq
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)) emptyset))
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset))
% 5.49/5.70 False
% 5.49/5.70 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1)
% 5.49/5.70 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota),
% 5.49/5.70 Ne
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)) emptyset))
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)
% 5.49/5.70 Clause #41 (by forward demodulation #[40, 39]): ∀ (a : Iota),
% 5.49/5.70 Ne
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset)
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) (setadjoin (skS.0 2 a) emptyset)) emptyset))
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)
% 5.49/5.70 Clause #42 (by forward demodulation #[41, 27]): ∀ (a : Iota),
% 5.49/5.70 Ne (setadjoin (setadjoin (skS.0 2 a) emptyset) (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset))
% 5.49/5.70 (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)
% 5.49/5.70 Clause #43 (by forward demodulation #[42, 27]): ∀ (a : Iota),
% 5.49/5.70 Ne (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset) (setadjoin (setadjoin (skS.0 2 a) emptyset) emptyset)
% 5.49/5.70 Clause #44 (by eliminate resolved literals #[43]): False
% 5.49/5.70 SZS output end Proof for theBenchmark.p
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