TSTP Solution File: SET873+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 3.80s 3.98s
% Output : Proof 3.80s
% 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 : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 09:26:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.80/3.98 SZS status Theorem for theBenchmark.p
% 3.80/3.98 SZS output start Proof for theBenchmark.p
% 3.80/3.98 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 3.80/3.98 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.80/3.98 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), subset (set_union2 (singleton A) B) B → in A B) True
% 3.80/3.98 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True
% 3.80/3.98 Clause #10 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_union2 (singleton A) (singleton B)) (singleton A) → Eq A B)) True
% 3.80/3.98 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Iota → subset a a) True
% 3.80/3.98 Clause #12 (by clausification #[11]): ∀ (a : Iota), Iota → Eq (subset a a) True
% 3.80/3.98 Clause #15 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (set_union2 (singleton a) B) B → in a B) True
% 3.80/3.98 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (subset (set_union2 (singleton a) a_1) a_1 → in a a_1) True
% 3.80/3.98 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (subset (set_union2 (singleton a) a_1) a_1) False) (Eq (in a a_1) True)
% 3.80/3.98 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 3.80/3.98 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 3.80/3.98 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 3.80/3.98 Clause #27 (by superposition #[26, 17]): ∀ (a a_1 : Iota), Or (Eq (subset (set_union2 a (singleton a_1)) a) False) (Eq (in a_1 a) True)
% 3.80/3.98 Clause #34 (by clausification #[10]): Eq (∀ (A B : Iota), Eq (set_union2 (singleton A) (singleton B)) (singleton A) → Eq A B) False
% 3.80/3.98 Clause #35 (by clausification #[34]): ∀ (a : Iota),
% 3.80/3.98 Eq
% 3.80/3.98 (Not
% 3.80/3.98 (∀ (B : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B))
% 3.80/3.98 True
% 3.80/3.98 Clause #36 (by clausification #[35]): ∀ (a : Iota),
% 3.80/3.98 Eq (∀ (B : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B)
% 3.80/3.98 False
% 3.80/3.98 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 3.80/3.98 Eq
% 3.80/3.98 (Not
% 3.80/3.98 (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) →
% 3.80/3.98 Eq (skS.0 2 a) (skS.0 3 a a_1)))
% 3.80/3.98 True
% 3.80/3.98 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 3.80/3.98 Eq
% 3.80/3.98 (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) →
% 3.80/3.98 Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.80/3.98 False
% 3.80/3.98 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a))) True
% 3.80/3.98 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False
% 3.80/3.98 Clause #41 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a))
% 3.80/3.98 Clause #50 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.80/3.98 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.80/3.98 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 3.80/3.98 Clause #69 (by superposition #[27, 41]): ∀ (a a_1 : Iota),
% 3.80/3.98 Or (Eq (subset (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) False)
% 3.80/3.98 (Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True)
% 3.80/3.98 Clause #70 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 3.80/3.98 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 3.80/3.98 Clause #73 (by clausification #[71]): ∀ (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))
% 3.80/3.98 Clause #76 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 3.80/3.99 Clause #77 (by destructive equality resolution #[76]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 3.80/3.99 Clause #80 (by clausification #[40]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1)
% 3.80/3.99 Clause #104 (by forward demodulation #[69, 12]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True)
% 3.80/3.99 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True
% 3.80/3.99 Clause #106 (by superposition #[105, 77]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 3 a a_1) (skS.0 2 a))
% 3.80/3.99 Clause #111 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) (skS.0 2 a)
% 3.80/3.99 Clause #112 (by forward contextual literal cutting #[111, 80]): False
% 3.80/3.99 SZS output end Proof for theBenchmark.p
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