TSTP Solution File: SET954+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 14:48:09 EDT 2023
% Result : Theorem 80.87s 81.10s
% Output : Proof 80.99s
% 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 : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 08:31:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 80.87/81.10 SZS status Theorem for theBenchmark.p
% 80.87/81.10 SZS output start Proof for theBenchmark.p
% 80.87/81.10 Clause #4 (by assumption #[]): Eq (∀ (A B C D : Iota), Iff (in (ordered_pair A B) (cartesian_product2 C D)) (And (in A C) (in B D))) True
% 80.87/81.10 Clause #7 (by assumption #[]): Eq
% 80.87/81.10 (Not
% 80.87/81.10 (∀ (A B C D : Iota),
% 80.87/81.10 in (ordered_pair A B) (cartesian_product2 C D) → in (ordered_pair B A) (cartesian_product2 D C)))
% 80.87/81.10 True
% 80.87/81.10 Clause #38 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C D : Iota), Iff (in (ordered_pair a B) (cartesian_product2 C D)) (And (in a C) (in B D))) True
% 80.87/81.10 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 80.87/81.10 Eq (∀ (C D : Iota), Iff (in (ordered_pair a a_1) (cartesian_product2 C D)) (And (in a C) (in a_1 D))) True
% 80.87/81.10 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 80.87/81.10 Eq (∀ (D : Iota), Iff (in (ordered_pair a a_1) (cartesian_product2 a_2 D)) (And (in a a_2) (in a_1 D))) True
% 80.87/81.10 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Eq (Iff (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) (And (in a a_2) (in a_1 a_3))) True
% 80.87/81.10 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) True) (Eq (And (in a a_2) (in a_1 a_3)) False)
% 80.87/81.10 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (And (in a a_2) (in a_1 a_3)) True)
% 80.87/81.10 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_3) False))
% 80.87/81.10 Clause #55 (by clausification #[7]): Eq (∀ (A B C D : Iota), in (ordered_pair A B) (cartesian_product2 C D) → in (ordered_pair B A) (cartesian_product2 D C))
% 80.87/81.10 False
% 80.87/81.10 Clause #56 (by clausification #[55]): ∀ (a : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (Not
% 80.87/81.10 (∀ (B C D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) B) (cartesian_product2 C D) →
% 80.87/81.10 in (ordered_pair B (skS.0 2 a)) (cartesian_product2 D C)))
% 80.87/81.10 True
% 80.87/81.10 Clause #57 (by clausification #[56]): ∀ (a : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (∀ (B C D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) B) (cartesian_product2 C D) →
% 80.87/81.10 in (ordered_pair B (skS.0 2 a)) (cartesian_product2 D C))
% 80.87/81.10 False
% 80.87/81.10 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (Not
% 80.87/81.10 (∀ (C D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)))
% 80.87/81.10 True
% 80.87/81.10 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (∀ (C D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C))
% 80.87/81.10 False
% 80.87/81.10 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (Not
% 80.87/81.10 (∀ (D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))))
% 80.87/81.10 True
% 80.87/81.10 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (∀ (D : Iota),
% 80.87/81.10 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2)))
% 80.87/81.10 False
% 80.87/81.10 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (Not
% 80.87/81.10 (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))))
% 80.87/81.10 True
% 80.87/81.10 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.87/81.10 Eq
% 80.87/81.10 (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) →
% 80.87/81.10 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2)))
% 80.87/81.10 False
% 80.87/81.10 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.99/81.20 Eq (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)))
% 80.99/81.20 True
% 80.99/81.20 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 80.99/81.20 Eq (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2)))
% 80.99/81.20 False
% 80.99/81.20 Clause #99 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (in a_1 a_3) True)
% 80.99/81.20 Clause #100 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (in a a_2) True)
% 80.99/81.20 Clause #101 (by superposition #[99, 64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True) (Eq False True)
% 80.99/81.20 Clause #102 (by superposition #[100, 64]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq False True)
% 80.99/81.20 Clause #445 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True
% 80.99/81.20 Clause #573 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True
% 80.99/81.20 Clause #575 (by superposition #[573, 44]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 80.99/81.20 Or (Eq (in (ordered_pair (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) a_5)) True)
% 80.99/81.20 (Or (Eq True False) (Eq (in a_2 a_5) False))
% 80.99/81.20 Clause #2689 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 80.99/81.20 Or (Eq (in (ordered_pair (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) a_5)) True)
% 80.99/81.20 (Eq (in a_2 a_5) False)
% 80.99/81.20 Clause #2691 (by superposition #[2689, 445]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 80.99/81.20 Or
% 80.99/81.20 (Eq
% 80.99/81.20 (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a_2))
% 80.99/81.20 (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) (skS.0 4 a_2 a_5 a_6)))
% 80.99/81.20 True)
% 80.99/81.20 (Eq False True)
% 80.99/81.20 Clause #8951 (by clausification #[2691]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 80.99/81.20 Eq
% 80.99/81.20 (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a_2)) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) (skS.0 4 a_2 a_5 a_6)))
% 80.99/81.20 True
% 80.99/81.20 Clause #8952 (by superposition #[8951, 65]): Eq True False
% 80.99/81.20 Clause #8958 (by clausification #[8952]): False
% 80.99/81.20 SZS output end Proof for theBenchmark.p
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