TSTP Solution File: SET867+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 14:47:53 EDT 2023
% Result : Theorem 3.75s 3.98s
% Output : Proof 3.75s
% 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 : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n027.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 15:20:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.75/3.98 SZS status Theorem for theBenchmark.p
% 3.75/3.98 SZS output start Proof for theBenchmark.p
% 3.75/3.98 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True
% 3.75/3.98 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (union A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D A)))) True
% 3.75/3.98 Clause #6 (by assumption #[]): Eq (Not (Eq (union empty_set) empty_set)) True
% 3.75/3.98 Clause #11 (by clausification #[6]): Eq (Eq (union empty_set) empty_set) False
% 3.75/3.98 Clause #12 (by clausification #[11]): Ne (union empty_set) empty_set
% 3.75/3.98 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True
% 3.75/3.98 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True)
% 3.75/3.98 Clause #28 (by clausification #[19]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set)
% 3.75/3.98 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True)
% 3.75/3.99 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False)
% 3.75/3.99 Clause #31 (by destructive equality resolution #[30]): ∀ (a : Iota), Eq (in a empty_set) False
% 3.75/3.99 Clause #36 (by clausification #[2]): ∀ (a : Iota),
% 3.75/3.99 Eq (∀ (B : Iota), Iff (Eq B (union a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D a)))) True
% 3.75/3.99 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 3.75/3.99 Eq (Iff (Eq a (union a_1)) (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1)))) True
% 3.75/3.99 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 3.75/3.99 Or (Eq (Eq a (union a_1)) True) (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) False)
% 3.75/3.99 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota),
% 3.75/3.99 Or (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) False) (Eq a (union a_1))
% 3.75/3.99 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.75/3.99 Or (Eq a (union a_1))
% 3.75/3.99 (Eq (Not (Iff (in (skS.0 3 a a_1 a_2) a) (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1)))) True)
% 3.75/3.99 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.75/3.99 Or (Eq a (union a_1))
% 3.75/3.99 (Eq (Iff (in (skS.0 3 a a_1 a_2) a) (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1))) False)
% 3.75/3.99 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota),
% 3.75/3.99 Or (Eq a (union a_1))
% 3.75/3.99 (Or (Eq (in (skS.0 3 a a_1 a_2) a) True) (Eq (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1)) True))
% 3.75/3.99 Clause #114 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.75/3.99 Or (Eq a (union a_1))
% 3.75/3.99 (Or (Eq (in (skS.0 3 a a_1 a_2) a) True)
% 3.75/3.99 (Eq (And (in (skS.0 3 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) (in (skS.0 5 a a_1 a_2 a_3) a_1)) True))
% 3.75/3.99 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.75/3.99 Or (Eq a (union a_1)) (Or (Eq (in (skS.0 3 a a_1 a_2) a) True) (Eq (in (skS.0 5 a a_1 a_2 a_3) a_1) True))
% 3.75/3.99 Clause #126 (by superposition #[115, 31]): ∀ (a a_1 : Iota), Or (Eq a (union empty_set)) (Or (Eq (in (skS.0 3 a empty_set a_1) a) True) (Eq True False))
% 3.75/3.99 Clause #135 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq a (union empty_set)) (Eq (in (skS.0 3 a empty_set a_1) a) True)
% 3.75/3.99 Clause #141 (by superposition #[135, 31]): Or (Eq empty_set (union empty_set)) (Eq True False)
% 3.75/3.99 Clause #152 (by clausification #[141]): Eq empty_set (union empty_set)
% 3.75/3.99 Clause #153 (by forward contextual literal cutting #[152, 12]): False
% 3.75/3.99 SZS output end Proof for theBenchmark.p
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