TSTP Solution File: SEU267+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n007.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 16:41:08 EDT 2023
% Result : Theorem 4.05s 4.25s
% Output : Proof 4.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU267+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.36 % Computer : n007.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 15:44:39 EDT 2023
% 0.17/0.36 % CPUTime :
% 4.05/4.25 SZS status Theorem for theBenchmark.p
% 4.05/4.25 SZS output start Proof for theBenchmark.p
% 4.05/4.25 Clause #12 (by assumption #[]): Eq (Not (∀ (A B : Iota), And (Eq (pair_first (ordered_pair A B)) A) (Eq (pair_second (ordered_pair A B)) B))) True
% 4.05/4.25 Clause #13 (by assumption #[]): Eq
% 4.05/4.25 (∀ (A : Iota),
% 4.05/4.25 (Exists fun B => Exists fun C => Eq A (ordered_pair B C)) →
% 4.05/4.25 ∀ (B : Iota), Iff (Eq B (pair_first A)) (∀ (C D : Iota), Eq A (ordered_pair C D) → Eq B C))
% 4.05/4.25 True
% 4.05/4.25 Clause #14 (by assumption #[]): Eq
% 4.05/4.25 (∀ (A : Iota),
% 4.05/4.25 (Exists fun B => Exists fun C => Eq A (ordered_pair B C)) →
% 4.05/4.25 ∀ (B : Iota), Iff (Eq B (pair_second A)) (∀ (C D : Iota), Eq A (ordered_pair C D) → Eq B D))
% 4.05/4.25 True
% 4.05/4.25 Clause #59 (by clausification #[12]): Eq (∀ (A B : Iota), And (Eq (pair_first (ordered_pair A B)) A) (Eq (pair_second (ordered_pair A B)) B)) False
% 4.05/4.25 Clause #60 (by clausification #[59]): ∀ (a : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 (Not
% 4.05/4.25 (∀ (B : Iota),
% 4.05/4.25 And (Eq (pair_first (ordered_pair (skS.0 3 a) B)) (skS.0 3 a))
% 4.05/4.25 (Eq (pair_second (ordered_pair (skS.0 3 a) B)) B)))
% 4.05/4.25 True
% 4.05/4.25 Clause #61 (by clausification #[60]): ∀ (a : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 (∀ (B : Iota),
% 4.05/4.25 And (Eq (pair_first (ordered_pair (skS.0 3 a) B)) (skS.0 3 a)) (Eq (pair_second (ordered_pair (skS.0 3 a) B)) B))
% 4.05/4.25 False
% 4.05/4.25 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 (Not
% 4.05/4.25 (And (Eq (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a))
% 4.05/4.25 (Eq (pair_second (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 4 a a_1))))
% 4.05/4.25 True
% 4.05/4.25 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 (And (Eq (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a))
% 4.05/4.25 (Eq (pair_second (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 4 a a_1)))
% 4.05/4.25 False
% 4.05/4.25 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 4.05/4.25 Or (Eq (Eq (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a)) False)
% 4.05/4.25 (Eq (Eq (pair_second (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 4 a a_1)) False)
% 4.05/4.25 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota),
% 4.05/4.25 Or (Eq (Eq (pair_second (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 4 a a_1)) False)
% 4.05/4.25 (Ne (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a))
% 4.05/4.25 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota),
% 4.05/4.25 Or (Ne (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a))
% 4.05/4.25 (Ne (pair_second (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 4 a a_1))
% 4.05/4.25 Clause #69 (by clausification #[14]): ∀ (a : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 ((Exists fun B => Exists fun C => Eq a (ordered_pair B C)) →
% 4.05/4.25 ∀ (B : Iota), Iff (Eq B (pair_second a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B D))
% 4.05/4.25 True
% 4.05/4.25 Clause #70 (by clausification #[69]): ∀ (a : Iota),
% 4.05/4.25 Or (Eq (Exists fun B => Exists fun C => Eq a (ordered_pair B C)) False)
% 4.05/4.25 (Eq (∀ (B : Iota), Iff (Eq B (pair_second a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B D)) True)
% 4.05/4.25 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 4.05/4.25 Or (Eq (∀ (B : Iota), Iff (Eq B (pair_second a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B D)) True)
% 4.05/4.25 (Eq (Exists fun C => Eq a (ordered_pair a_1 C)) False)
% 4.05/4.25 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota),
% 4.05/4.25 Or (Eq (Exists fun C => Eq a (ordered_pair a_1 C)) False)
% 4.05/4.25 (Eq (Iff (Eq a_2 (pair_second a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_2 D)) True)
% 4.05/4.25 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.25 Or (Eq (Iff (Eq a (pair_second a_1)) (∀ (C D : Iota), Eq a_1 (ordered_pair C D) → Eq a D)) True)
% 4.05/4.25 (Eq (Eq a_1 (ordered_pair a_2 a_3)) False)
% 4.05/4.25 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.25 Or (Eq (Eq a (ordered_pair a_1 a_2)) False)
% 4.05/4.25 (Or (Eq (Eq a_3 (pair_second a)) False) (Eq (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_3 D) True))
% 4.05/4.25 Clause #104 (by clausification #[13]): ∀ (a : Iota),
% 4.05/4.25 Eq
% 4.05/4.25 ((Exists fun B => Exists fun C => Eq a (ordered_pair B C)) →
% 4.05/4.25 ∀ (B : Iota), Iff (Eq B (pair_first a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B C))
% 4.05/4.25 True
% 4.05/4.25 Clause #105 (by clausification #[104]): ∀ (a : Iota),
% 4.05/4.28 Or (Eq (Exists fun B => Exists fun C => Eq a (ordered_pair B C)) False)
% 4.05/4.28 (Eq (∀ (B : Iota), Iff (Eq B (pair_first a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B C)) True)
% 4.05/4.28 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota),
% 4.05/4.28 Or (Eq (∀ (B : Iota), Iff (Eq B (pair_first a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq B C)) True)
% 4.05/4.28 (Eq (Exists fun C => Eq a (ordered_pair a_1 C)) False)
% 4.05/4.28 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 4.05/4.28 Or (Eq (Exists fun C => Eq a (ordered_pair a_1 C)) False)
% 4.05/4.28 (Eq (Iff (Eq a_2 (pair_first a)) (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_2 C)) True)
% 4.05/4.28 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (Iff (Eq a (pair_first a_1)) (∀ (C D : Iota), Eq a_1 (ordered_pair C D) → Eq a C)) True)
% 4.05/4.28 (Eq (Eq a_1 (ordered_pair a_2 a_3)) False)
% 4.05/4.28 Clause #110 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (Eq a (ordered_pair a_1 a_2)) False)
% 4.05/4.28 (Or (Eq (Eq a_3 (pair_first a)) False) (Eq (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_3 C) True))
% 4.05/4.28 Clause #150 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (Eq a (pair_second a_1)) False)
% 4.05/4.28 (Or (Eq (∀ (C D : Iota), Eq a_1 (ordered_pair C D) → Eq a D) True) (Ne a_1 (ordered_pair a_2 a_3)))
% 4.05/4.28 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_1 D) True)
% 4.05/4.28 (Or (Ne a (ordered_pair a_2 a_3)) (Ne a_1 (pair_second a)))
% 4.05/4.28 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.05/4.28 (Or (Ne a_3 (pair_second a)) (Eq (∀ (D : Iota), Eq a (ordered_pair a_4 D) → Eq a_3 D) True))
% 4.05/4.28 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2)) (Or (Ne a_3 (pair_second a)) (Eq (Eq a (ordered_pair a_4 a_5) → Eq a_3 a_5) True))
% 4.05/4.28 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.05/4.28 (Or (Ne a_3 (pair_second a)) (Or (Eq (Eq a (ordered_pair a_4 a_5)) False) (Eq (Eq a_3 a_5) True)))
% 4.05/4.28 Clause #155 (by clausification #[154]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.05/4.28 (Or (Ne a_3 (pair_second a)) (Or (Eq (Eq a_3 a_4) True) (Ne a (ordered_pair a_5 a_4))))
% 4.05/4.28 Clause #156 (by clausification #[155]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2)) (Or (Ne a_3 (pair_second a)) (Or (Ne a (ordered_pair a_4 a_5)) (Eq a_3 a_5)))
% 4.05/4.28 Clause #157 (by destructive equality resolution #[156]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.05/4.28 Or (Ne a (pair_second (ordered_pair a_1 a_2))) (Or (Ne (ordered_pair a_1 a_2) (ordered_pair a_3 a_4)) (Eq a a_4))
% 4.05/4.28 Clause #158 (by destructive equality resolution #[157]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Ne (ordered_pair a a_1) (ordered_pair a_2 a_3)) (Eq (pair_second (ordered_pair a a_1)) a_3)
% 4.05/4.28 Clause #159 (by equality resolution #[158]): ∀ (a a_1 : Iota), Eq (pair_second (ordered_pair a a_1)) a_1
% 4.05/4.28 Clause #171 (by backward contextual literal cutting #[159, 66]): ∀ (a a_1 : Iota), Ne (pair_first (ordered_pair (skS.0 3 a) (skS.0 4 a a_1))) (skS.0 3 a)
% 4.05/4.28 Clause #193 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (Eq a (pair_first a_1)) False)
% 4.05/4.28 (Or (Eq (∀ (C D : Iota), Eq a_1 (ordered_pair C D) → Eq a C) True) (Ne a_1 (ordered_pair a_2 a_3)))
% 4.05/4.28 Clause #194 (by clausification #[193]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.05/4.28 Or (Eq (∀ (C D : Iota), Eq a (ordered_pair C D) → Eq a_1 C) True)
% 4.05/4.28 (Or (Ne a (ordered_pair a_2 a_3)) (Ne a_1 (pair_first a)))
% 4.05/4.28 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.05/4.28 (Or (Ne a_3 (pair_first a)) (Eq (∀ (D : Iota), Eq a (ordered_pair a_4 D) → Eq a_3 a_4) True))
% 4.05/4.28 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.05/4.28 Or (Ne a (ordered_pair a_1 a_2)) (Or (Ne a_3 (pair_first a)) (Eq (Eq a (ordered_pair a_4 a_5) → Eq a_3 a_4) True))
% 4.05/4.28 Clause #197 (by clausification #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.12/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.12/4.28 (Or (Ne a_3 (pair_first a)) (Or (Eq (Eq a (ordered_pair a_4 a_5)) False) (Eq (Eq a_3 a_4) True)))
% 4.12/4.28 Clause #198 (by clausification #[197]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.12/4.28 Or (Ne a (ordered_pair a_1 a_2))
% 4.12/4.28 (Or (Ne a_3 (pair_first a)) (Or (Eq (Eq a_3 a_4) True) (Ne a (ordered_pair a_4 a_5))))
% 4.12/4.28 Clause #199 (by clausification #[198]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.12/4.28 Or (Ne a (ordered_pair a_1 a_2)) (Or (Ne a_3 (pair_first a)) (Or (Ne a (ordered_pair a_4 a_5)) (Eq a_3 a_4)))
% 4.12/4.28 Clause #200 (by destructive equality resolution #[199]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.12/4.28 Or (Ne a (pair_first (ordered_pair a_1 a_2))) (Or (Ne (ordered_pair a_1 a_2) (ordered_pair a_3 a_4)) (Eq a a_3))
% 4.12/4.28 Clause #201 (by destructive equality resolution #[200]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (ordered_pair a a_1) (ordered_pair a_2 a_3)) (Eq (pair_first (ordered_pair a a_1)) a_2)
% 4.12/4.28 Clause #202 (by equality resolution #[201]): ∀ (a a_1 : Iota), Eq (pair_first (ordered_pair a a_1)) a
% 4.12/4.28 Clause #214 (by forward demodulation #[171, 202]): ∀ (a : Iota), Ne (skS.0 3 a) (skS.0 3 a)
% 4.12/4.28 Clause #215 (by eliminate resolved literals #[214]): False
% 4.12/4.28 SZS output end Proof for theBenchmark.p
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