TSTP Solution File: SET926+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET926+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 14:48:05 EDT 2023
% Result : Theorem 3.91s 4.07s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET926+1 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15 % Command : duper %s
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 12:02:25 EDT 2023
% 0.15/0.37 % CPUTime :
% 3.91/4.07 SZS status Theorem for theBenchmark.p
% 3.91/4.07 SZS output start Proof for theBenchmark.p
% 3.91/4.07 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) (singleton A)) (Not (in A B))) True
% 3.91/4.07 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True
% 3.91/4.07 Clause #6 (by assumption #[]): Eq
% 3.91/4.07 (Not
% 3.91/4.07 (∀ (A B : Iota),
% 3.91/4.07 Or (Eq (set_difference (singleton A) B) empty_set) (Eq (set_difference (singleton A) B) (singleton A))))
% 3.91/4.07 True
% 3.91/4.07 Clause #15 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True
% 3.91/4.07 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True
% 3.91/4.07 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) True) (Eq (in a a_1) False)
% 3.91/4.07 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_difference (singleton a) a_1) empty_set)
% 3.91/4.07 Clause #20 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) (singleton a)) (Not (in a B))) True
% 3.91/4.07 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) (singleton a)) (Not (in a a_1))) True
% 3.91/4.07 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) (singleton a)) True) (Eq (Not (in a a_1)) False)
% 3.91/4.07 Clause #24 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (Not (in a a_1)) False) (Eq (set_difference (singleton a) a_1) (singleton a))
% 3.91/4.07 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (set_difference (singleton a) a_1) (singleton a)) (Eq (in a a_1) True)
% 3.91/4.07 Clause #32 (by clausification #[6]): Eq
% 3.91/4.07 (∀ (A B : Iota),
% 3.91/4.07 Or (Eq (set_difference (singleton A) B) empty_set) (Eq (set_difference (singleton A) B) (singleton A)))
% 3.91/4.07 False
% 3.91/4.07 Clause #33 (by clausification #[32]): ∀ (a : Iota),
% 3.91/4.07 Eq
% 3.91/4.07 (Not
% 3.91/4.07 (∀ (B : Iota),
% 3.91/4.07 Or (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set)
% 3.91/4.07 (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a)))))
% 3.91/4.07 True
% 3.91/4.07 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 3.91/4.07 Eq
% 3.91/4.07 (∀ (B : Iota),
% 3.91/4.07 Or (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set)
% 3.91/4.07 (Eq (set_difference (singleton (skS.0 2 a)) B) (singleton (skS.0 2 a))))
% 3.91/4.07 False
% 3.91/4.07 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 3.91/4.07 Eq
% 3.91/4.07 (Not
% 3.91/4.07 (Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set)
% 3.91/4.07 (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a)))))
% 3.91/4.07 True
% 3.91/4.07 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 3.91/4.07 Eq
% 3.91/4.07 (Or (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set)
% 3.91/4.07 (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))))
% 3.91/4.07 False
% 3.91/4.07 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))) False
% 3.91/4.07 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) False
% 3.91/4.07 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) (singleton (skS.0 2 a))
% 3.91/4.07 Clause #40 (by superposition #[39, 25]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a)))
% 3.91/4.07 Clause #41 (by clausification #[38]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set
% 3.91/4.07 Clause #43 (by eliminate resolved literals #[40]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True
% 3.91/4.07 Clause #45 (by superposition #[43, 19]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set)
% 3.91/4.07 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set
% 3.91/4.07 Clause #48 (by forward contextual literal cutting #[47, 41]): False
% 3.91/4.07 SZS output end Proof for theBenchmark.p
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