TSTP Solution File: SET885+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET885+1 : TPTP v8.1.2. Released v3.2.0.
% 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 14:47:56 EDT 2023
% Result : Theorem 5.04s 5.38s
% Output : Proof 5.04s
% 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 : SET885+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n016.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 13:43:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.04/5.38 SZS status Theorem for theBenchmark.p
% 5.04/5.38 SZS output start Proof for theBenchmark.p
% 5.04/5.38 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 5.04/5.38 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 5.04/5.38 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
% 5.04/5.38 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True
% 5.04/5.38 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq A C)) True
% 5.04/5.38 Clause #19 (by clausification #[8]): Eq (∀ (A B C : Iota), subset (unordered_pair A B) (singleton C) → Eq A C) False
% 5.04/5.38 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (skS.0 2 a) C)) True
% 5.04/5.38 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (unordered_pair (skS.0 2 a) B) (singleton C) → Eq (skS.0 2 a) C) False
% 5.04/5.38 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota),
% 5.04/5.38 Eq (Not (∀ (C : Iota), subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → Eq (skS.0 2 a) C)) True
% 5.04/5.38 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota),
% 5.04/5.38 Eq (∀ (C : Iota), subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton C) → Eq (skS.0 2 a) C) False
% 5.04/5.38 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 5.04/5.38 Eq
% 5.04/5.38 (Not
% 5.04/5.38 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) →
% 5.04/5.38 Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)))
% 5.04/5.38 True
% 5.04/5.38 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 5.04/5.38 Eq
% 5.04/5.38 (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2)) →
% 5.04/5.38 Eq (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 5.04/5.38 False
% 5.04/5.38 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (singleton (skS.0 4 a a_1 a_2))) True
% 5.04/5.38 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)) False
% 5.04/5.38 Clause #28 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 5.04/5.38 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 5.04/5.38 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 5.04/5.38 Clause #31 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True
% 5.04/5.38 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True
% 5.04/5.38 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True)
% 5.04/5.38 Clause #40 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True)
% 5.04/5.38 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 5.04/5.38 Clause #42 (by superposition #[41, 26]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.04/5.38 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False)
% 5.04/5.38 (Or (Eq (in a (singleton (skS.0 4 a_1 a_2 a_3))) True) (Eq False True))
% 5.04/5.38 Clause #48 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 5.04/5.38 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 5.04/5.38 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 5.04/5.38 Clause #58 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 5.04/5.38 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 5.04/5.40 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True))
% 5.04/5.40 Clause #67 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 5.04/5.40 Clause #68 (by destructive equality resolution #[67]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 5.04/5.40 Clause #72 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 2 a) (skS.0 4 a a_1 a_2)
% 5.04/5.40 Clause #73 (by clausification #[3]): ∀ (a : Iota),
% 5.04/5.40 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
% 5.04/5.40 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota),
% 5.04/5.40 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
% 5.04/5.40 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 5.04/5.40 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
% 5.04/5.40 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 5.04/5.40 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)
% 5.04/5.40 Clause #97 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.04/5.40 Or (Eq (in a (unordered_pair (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False)
% 5.04/5.40 (Eq (in a (singleton (skS.0 4 a_1 a_2 a_3))) True)
% 5.04/5.40 Clause #104 (by clausification #[77]): ∀ (a a_1 a_2 : Iota),
% 5.04/5.40 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))
% 5.04/5.40 Clause #105 (by clausification #[104]): ∀ (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)
% 5.04/5.40 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.04/5.40 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))
% 5.04/5.40 Clause #108 (by clausification #[106]): ∀ (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))
% 5.04/5.40 Clause #110 (by clausification #[108]): ∀ (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))
% 5.04/5.40 Clause #111 (by destructive equality resolution #[110]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 5.04/5.40 Clause #112 (by destructive equality resolution #[111]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 5.04/5.40 Clause #116 (by superposition #[112, 30]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True
% 5.04/5.40 Clause #117 (by superposition #[116, 97]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 a) (singleton (skS.0 4 a a_1 a_2))) True)
% 5.04/5.40 Clause #407 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 4 a a_1 a_2))) True
% 5.04/5.40 Clause #408 (by superposition #[407, 68]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 4 a a_1 a_2))
% 5.04/5.40 Clause #456 (by clausification #[408]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a) (skS.0 4 a a_1 a_2)
% 5.04/5.40 Clause #457 (by forward contextual literal cutting #[456, 72]): False
% 5.04/5.40 SZS output end Proof for theBenchmark.p
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