TSTP Solution File: SET987+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET987+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 14:48:14 EDT 2023
% Result : Theorem 3.66s 3.84s
% Output : Proof 3.66s
% 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 : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:10:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.66/3.84 SZS status Theorem for theBenchmark.p
% 3.66/3.84 SZS output start Proof for theBenchmark.p
% 3.66/3.84 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (in A B) → Eq (set_difference (set_union2 B (singleton A)) (singleton A)) B)) True
% 3.66/3.84 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_difference (set_union2 A B) B) (set_difference A B)) True
% 3.66/3.84 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A (singleton B)) A) (Not (in B A))) True
% 3.66/3.84 Clause #35 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_difference (set_union2 a B) B) (set_difference a B)) True
% 3.66/3.84 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (set_union2 a a_1) a_1) (set_difference a a_1)) True
% 3.66/3.84 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (set_difference (set_union2 a a_1) a_1) (set_difference a a_1)
% 3.66/3.84 Clause #39 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a (singleton B)) a) (Not (in B a))) True
% 3.66/3.84 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a (singleton a_1)) a) (Not (in a_1 a))) True
% 3.66/3.84 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a (singleton a_1)) a) True) (Eq (Not (in a_1 a)) False)
% 3.66/3.84 Clause #43 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference a_1 (singleton a)) a_1)
% 3.66/3.84 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (set_difference a (singleton a_1)) a) (Eq (in a_1 a) True)
% 3.66/3.84 Clause #46 (by clausification #[7]): Eq (∀ (A B : Iota), Not (in A B) → Eq (set_difference (set_union2 B (singleton A)) (singleton A)) B) False
% 3.66/3.84 Clause #47 (by clausification #[46]): ∀ (a : Iota),
% 3.66/3.84 Eq
% 3.66/3.84 (Not
% 3.66/3.84 (∀ (B : Iota),
% 3.66/3.84 Not (in (skS.0 2 a) B) → Eq (set_difference (set_union2 B (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) B))
% 3.66/3.84 True
% 3.66/3.84 Clause #48 (by clausification #[47]): ∀ (a : Iota),
% 3.66/3.84 Eq
% 3.66/3.84 (∀ (B : Iota),
% 3.66/3.84 Not (in (skS.0 2 a) B) → Eq (set_difference (set_union2 B (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) B)
% 3.66/3.84 False
% 3.66/3.84 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 3.66/3.84 Eq
% 3.66/3.84 (Not
% 3.66/3.84 (Not (in (skS.0 2 a) (skS.0 3 a a_1)) →
% 3.66/3.84 Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a)))
% 3.66/3.84 (skS.0 3 a a_1)))
% 3.66/3.84 True
% 3.66/3.84 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.66/3.84 Eq
% 3.66/3.84 (Not (in (skS.0 2 a) (skS.0 3 a a_1)) →
% 3.66/3.84 Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1))
% 3.66/3.84 False
% 3.66/3.84 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 2 a) (skS.0 3 a a_1))) True
% 3.66/3.84 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota),
% 3.66/3.84 Eq (Eq (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1))
% 3.66/3.84 False
% 3.66/3.84 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False
% 3.66/3.84 Clause #54 (by superposition #[53, 44]): ∀ (a a_1 : Iota), Or (Eq (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1)) (Eq False True)
% 3.66/3.84 Clause #71 (by clausification #[52]): ∀ (a a_1 : Iota),
% 3.66/3.84 Ne (set_difference (set_union2 (skS.0 3 a a_1) (singleton (skS.0 2 a))) (singleton (skS.0 2 a))) (skS.0 3 a a_1)
% 3.66/3.84 Clause #72 (by forward demodulation #[71, 37]): ∀ (a a_1 : Iota), Ne (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1)
% 3.66/3.84 Clause #81 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (set_difference (skS.0 3 a a_1) (singleton (skS.0 2 a))) (skS.0 3 a a_1)
% 3.66/3.84 Clause #82 (by forward contextual literal cutting #[81, 72]): False
% 3.66/3.84 SZS output end Proof for theBenchmark.p
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