TSTP Solution File: SET880+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET880+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 14:47:55 EDT 2023
% Result : Theorem 3.77s 3.98s
% 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
% 0.00/0.13 % Problem : SET880+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 10:33:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.77/3.98 SZS status Theorem for theBenchmark.p
% 3.77/3.98 SZS output start Proof for theBenchmark.p
% 3.77/3.98 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.77/3.98 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True
% 3.77/3.98 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_difference (singleton A) (singleton B)) empty_set → Eq A B)) True
% 3.77/3.98 Clause #15 (by clausification #[6]): Eq (∀ (A B : Iota), Eq (set_difference (singleton A) (singleton B)) empty_set → Eq A B) False
% 3.77/3.98 Clause #16 (by clausification #[15]): ∀ (a : Iota),
% 3.77/3.98 Eq (Not (∀ (B : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton B)) empty_set → Eq (skS.0 2 a) B)) True
% 3.77/3.98 Clause #17 (by clausification #[16]): ∀ (a : Iota),
% 3.77/3.98 Eq (∀ (B : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton B)) empty_set → Eq (skS.0 2 a) B) False
% 3.77/3.98 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 3.77/3.98 Eq
% 3.77/3.98 (Not
% 3.77/3.98 (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set →
% 3.77/3.98 Eq (skS.0 2 a) (skS.0 3 a a_1)))
% 3.77/3.98 True
% 3.77/3.98 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota),
% 3.77/3.98 Eq
% 3.77/3.98 (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set → Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.77/3.98 False
% 3.77/3.98 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set) True
% 3.77/3.98 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False
% 3.77/3.98 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) empty_set
% 3.77/3.98 Clause #23 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.77/3.98 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.77/3.98 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 3.77/3.98 Clause #33 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True
% 3.77/3.98 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True
% 3.77/3.98 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) False) (Eq (in a a_1) True)
% 3.77/3.98 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Ne (set_difference (singleton a) a_1) empty_set)
% 3.77/3.98 Clause #39 (by superposition #[38, 22]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne empty_set empty_set)
% 3.77/3.98 Clause #40 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 3.77/3.98 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 3.77/3.98 Clause #43 (by clausification #[41]): ∀ (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))
% 3.77/3.98 Clause #52 (by clausification #[21]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1)
% 3.77/3.98 Clause #53 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 3.77/3.98 Clause #54 (by destructive equality resolution #[53]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 3.77/3.98 Clause #57 (by eliminate resolved literals #[39]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True
% 3.77/3.98 Clause #58 (by superposition #[57, 54]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1))
% 3.77/3.98 Clause #61 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1)
% 3.77/3.98 Clause #62 (by forward contextual literal cutting #[61, 52]): False
% 3.77/3.98 SZS output end Proof for theBenchmark.p
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