TSTP Solution File: SET879+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 8.18s 8.43s
% Output : Proof 8.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.14 % Command : duper %s
% 0.11/0.34 % Computer : n005.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sat Aug 26 13:11:53 EDT 2023
% 0.11/0.34 % CPUTime :
% 8.18/8.43 SZS status Theorem for theBenchmark.p
% 8.18/8.43 SZS output start Proof for theBenchmark.p
% 8.18/8.43 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 8.18/8.43 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) True
% 8.18/8.43 Clause #5 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) (singleton B)) (singleton A)) (Ne A B))) True
% 8.18/8.43 Clause #14 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) (singleton a)) (Not (in a B))) True
% 8.18/8.43 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) (singleton a)) (Not (in a a_1))) True
% 8.18/8.43 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) True) (Eq (Not (in a a_1)) False)
% 8.18/8.43 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) False) (Eq (Not (in a a_1)) True)
% 8.18/8.43 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference (singleton a) a_1) (singleton a))
% 8.18/8.43 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) True)
% 8.18/8.43 Clause #20 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) True) (Ne (set_difference (singleton a) a_1) (singleton a))
% 8.18/8.43 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Ne (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) False)
% 8.18/8.43 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
% 8.18/8.43 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
% 8.18/8.43 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)
% 8.18/8.43 Clause #33 (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))
% 8.18/8.43 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 8.18/8.43 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False))
% 8.18/8.43 Clause #36 (by clausification #[34]): ∀ (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))
% 8.18/8.43 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1))
% 8.18/8.43 Clause #38 (by destructive equality resolution #[37]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1)
% 8.18/8.43 Clause #39 (by destructive equality resolution #[38]): ∀ (a : Iota), Eq (in a (singleton a)) True
% 8.18/8.43 Clause #42 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1))
% 8.18/8.43 Clause #43 (by destructive equality resolution #[42]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1)
% 8.18/8.43 Clause #46 (by clausification #[5]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) (singleton B)) (singleton A)) (Ne A B)) False
% 8.18/8.43 Clause #47 (by clausification #[46]): ∀ (a : Iota),
% 8.18/8.43 Eq
% 8.18/8.43 (Not
% 8.18/8.43 (∀ (B : Iota),
% 8.18/8.43 Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton B)) (singleton (skS.0 3 a))) (Ne (skS.0 3 a) B)))
% 8.18/8.43 True
% 8.18/8.43 Clause #48 (by clausification #[47]): ∀ (a : Iota),
% 8.18/8.43 Eq
% 8.18/8.43 (∀ (B : Iota),
% 8.18/8.43 Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton B)) (singleton (skS.0 3 a))) (Ne (skS.0 3 a) B))
% 8.18/8.43 False
% 8.18/8.43 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 8.18/8.43 Eq
% 8.18/8.43 (Not
% 8.18/8.43 (Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.43 (Ne (skS.0 3 a) (skS.0 4 a a_1))))
% 8.18/8.43 True
% 8.18/8.43 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 8.18/8.43 Eq
% 8.18/8.43 (Iff (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.46 (Ne (skS.0 3 a) (skS.0 4 a a_1)))
% 8.18/8.46 False
% 8.18/8.46 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) False)
% 8.18/8.46 (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) False)
% 8.18/8.46 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))) True)
% 8.18/8.46 (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) True)
% 8.18/8.46 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) False)
% 8.18/8.46 (Ne (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.46 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Ne (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.46 (Eq (skS.0 3 a) (skS.0 4 a a_1))
% 8.18/8.46 Clause #55 (by superposition #[54, 19]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (in (skS.0 3 a) (singleton (skS.0 4 a a_1))) True)
% 8.18/8.46 (Or (Ne (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (Eq (skS.0 3 a) (skS.0 4 a a_1)))
% 8.18/8.46 Clause #82 (by clausification #[52]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (Ne (skS.0 3 a) (skS.0 4 a a_1)) True)
% 8.18/8.46 (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.46 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota),
% 8.18/8.46 Or (Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a)))
% 8.18/8.46 (Ne (skS.0 3 a) (skS.0 4 a a_1))
% 8.18/8.46 Clause #127 (by eliminate resolved literals #[55]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 3 a) (singleton (skS.0 4 a a_1))) True) (Eq (skS.0 3 a) (skS.0 4 a a_1))
% 8.18/8.46 Clause #128 (by superposition #[127, 43]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (skS.0 4 a a_1)) (Or (Eq True False) (Eq (skS.0 3 a) (skS.0 4 a a_1)))
% 8.18/8.46 Clause #561 (by clausification #[128]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a) (skS.0 4 a a_1)) (Eq (skS.0 3 a) (skS.0 4 a a_1))
% 8.18/8.46 Clause #562 (by eliminate duplicate literals #[561]): ∀ (a a_1 : Iota), Eq (skS.0 3 a) (skS.0 4 a a_1)
% 8.18/8.46 Clause #568 (by backward contextual literal cutting #[562, 83]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (singleton (skS.0 3 a))
% 8.18/8.46 Clause #569 (by forward demodulation #[568, 562]): ∀ (a : Iota), Eq (set_difference (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (singleton (skS.0 3 a))
% 8.18/8.46 Clause #570 (by superposition #[569, 21]): ∀ (a : Iota),
% 8.18/8.46 Or (Ne (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) (Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False)
% 8.18/8.46 Clause #582 (by eliminate resolved literals #[570]): ∀ (a : Iota), Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False
% 8.18/8.46 Clause #583 (by superposition #[582, 39]): Eq False True
% 8.18/8.46 Clause #640 (by clausification #[583]): False
% 8.18/8.46 SZS output end Proof for theBenchmark.p
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