TSTP Solution File: SET881+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 3.45s 3.72s
% Output : Proof 3.45s
% 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 : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:38:57 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.45/3.72 SZS status Theorem for theBenchmark.p
% 3.45/3.72 SZS output start Proof for theBenchmark.p
% 3.45/3.72 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True
% 3.45/3.72 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True
% 3.45/3.72 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True
% 3.45/3.72 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_difference (singleton A) (unordered_pair A B)) empty_set)) True
% 3.45/3.72 Clause #16 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True
% 3.45/3.72 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True
% 3.45/3.72 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a)
% 3.45/3.72 Clause #19 (by clausification #[2]): ∀ (a : Iota),
% 3.45/3.72 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True
% 3.45/3.72 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 3.45/3.72 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True
% 3.45/3.72 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.72 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True
% 3.45/3.72 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.72 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True)
% 3.45/3.72 Clause #32 (by clausification #[7]): Eq (∀ (A B : Iota), Eq (set_difference (singleton A) (unordered_pair A B)) empty_set) False
% 3.45/3.72 Clause #33 (by clausification #[32]): ∀ (a : Iota),
% 3.45/3.72 Eq (Not (∀ (B : Iota), Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) B)) empty_set)) True
% 3.45/3.72 Clause #34 (by clausification #[33]): ∀ (a : Iota),
% 3.45/3.72 Eq (∀ (B : Iota), Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) B)) empty_set) False
% 3.45/3.72 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 3.45/3.72 Eq (Not (Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set)) True
% 3.45/3.72 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 3.45/3.72 Eq (Eq (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set) False
% 3.45/3.72 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Ne (set_difference (singleton (skS.0 3 a)) (unordered_pair (skS.0 3 a) (skS.0 4 a a_1))) empty_set
% 3.45/3.72 Clause #38 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True
% 3.45/3.72 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True
% 3.45/3.72 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) True) (Eq (in a a_1) False)
% 3.45/3.72 Clause #42 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_difference (singleton a) a_1) empty_set)
% 3.45/3.72 Clause #44 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 3.45/3.72 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2))
% 3.45/3.72 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True)
% 3.45/3.72 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.45/3.72 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False))
% 3.45/3.72 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False))
% 3.45/3.72 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2))
% 3.45/3.72 Clause #51 (by destructive equality resolution #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2)
% 3.45/3.72 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True
% 3.45/3.73 Clause #54 (by superposition #[52, 42]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_difference (singleton a) (unordered_pair a_1 a)) empty_set)
% 3.45/3.73 Clause #78 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (set_difference (singleton a) (unordered_pair a_1 a)) empty_set
% 3.45/3.73 Clause #80 (by superposition #[78, 18]): ∀ (a a_1 : Iota), Eq (set_difference (singleton a) (unordered_pair a a_1)) empty_set
% 3.45/3.73 Clause #83 (by backward contextual literal cutting #[80, 37]): False
% 3.45/3.73 SZS output end Proof for theBenchmark.p
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