TSTP Solution File: SET874+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 14:47:54 EDT 2023
% Result : Theorem 3.77s 3.97s
% Output : Proof 3.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.16 % Command : duper %s
% 0.15/0.37 % Computer : n021.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 15:50:57 EDT 2023
% 0.15/0.37 % CPUTime :
% 3.77/3.97 SZS status Theorem for theBenchmark.p
% 3.77/3.97 SZS output start Proof for theBenchmark.p
% 3.77/3.97 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 3.77/3.97 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True
% 3.77/3.97 Clause #7 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Eq (set_union2 (singleton A) B) B) True
% 3.77/3.97 Clause #10 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_union2 (singleton A) (unordered_pair A B)) (unordered_pair A B))) True
% 3.77/3.97 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 3.77/3.97 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 3.77/3.97 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 3.77/3.97 Clause #36 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Eq (set_union2 (singleton a) B) B) True
% 3.77/3.97 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (in a a_1 → Eq (set_union2 (singleton a) a_1) a_1) True
% 3.77/3.97 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Eq (set_union2 (singleton a) a_1) a_1) True)
% 3.77/3.97 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_union2 (singleton a) a_1) a_1)
% 3.77/3.97 Clause #43 (by clausification #[10]): Eq (∀ (A B : Iota), Eq (set_union2 (singleton A) (unordered_pair A B)) (unordered_pair A B)) False
% 3.77/3.97 Clause #44 (by clausification #[43]): ∀ (a : Iota),
% 3.77/3.97 Eq
% 3.77/3.97 (Not
% 3.77/3.97 (∀ (B : Iota),
% 3.77/3.97 Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (unordered_pair (skS.0 2 a) B)))
% 3.77/3.97 True
% 3.77/3.97 Clause #45 (by clausification #[44]): ∀ (a : Iota),
% 3.77/3.97 Eq
% 3.77/3.97 (∀ (B : Iota),
% 3.77/3.97 Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) B)) (unordered_pair (skS.0 2 a) B))
% 3.77/3.97 False
% 3.77/3.97 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota),
% 3.77/3.97 Eq
% 3.77/3.97 (Not
% 3.77/3.97 (Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.77/3.97 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))))
% 3.77/3.97 True
% 3.77/3.97 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota),
% 3.77/3.97 Eq
% 3.77/3.97 (Eq (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.77/3.97 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.77/3.97 False
% 3.77/3.97 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota),
% 3.77/3.97 Ne (set_union2 (singleton (skS.0 2 a)) (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)))
% 3.77/3.97 (unordered_pair (skS.0 2 a) (skS.0 3 a a_1))
% 3.77/3.97 Clause #49 (by clausification #[3]): ∀ (a : Iota),
% 3.77/3.97 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True
% 3.77/3.97 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.77/3.97 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True
% 3.77/3.97 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.97 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True
% 3.77/3.97 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.97 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True)
% 3.77/3.97 Clause #62 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.77/3.97 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2))
% 3.77/3.97 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True)
% 3.77/3.97 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.77/3.97 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False))
% 3.77/3.97 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False))
% 3.77/3.97 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2))
% 3.77/3.97 Clause #69 (by destructive equality resolution #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 3.77/3.97 Clause #70 (by destructive equality resolution #[69]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 3.77/3.97 Clause #72 (by superposition #[70, 39]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_union2 (singleton a) (unordered_pair a_1 a)) (unordered_pair a_1 a))
% 3.77/3.97 Clause #96 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton a) (unordered_pair a_1 a)) (unordered_pair a_1 a)
% 3.77/3.97 Clause #99 (by superposition #[96, 30]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton a) (unordered_pair a a_1)) (unordered_pair a a_1)
% 3.77/3.97 Clause #102 (by backward contextual literal cutting #[99, 48]): False
% 3.77/3.97 SZS output end Proof for theBenchmark.p
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