TSTP Solution File: SET908+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 14:48:00 EDT 2023
% Result : Theorem 3.76s 4.02s
% Output : Proof 3.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET908+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n031.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 13:59:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.76/4.02 SZS status Theorem for theBenchmark.p
% 3.76/4.02 SZS output start Proof for theBenchmark.p
% 3.76/4.02 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True
% 3.76/4.02 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 3.76/4.02 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True
% 3.76/4.02 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True
% 3.76/4.02 Clause #11 (by assumption #[]): Eq (Not (∀ (A B : Iota), Ne (set_union2 (singleton A) B) empty_set)) True
% 3.76/4.02 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True
% 3.76/4.02 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True
% 3.76/4.02 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a)
% 3.76/4.02 Clause #37 (by clausification #[11]): Eq (∀ (A B : Iota), Ne (set_union2 (singleton A) B) empty_set) False
% 3.76/4.02 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Ne (set_union2 (singleton (skS.0 2 a)) B) empty_set)) True
% 3.76/4.02 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (B : Iota), Ne (set_union2 (singleton (skS.0 2 a)) B) empty_set) False
% 3.76/4.02 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Not (Ne (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set)) True
% 3.76/4.02 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Ne (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) False
% 3.76/4.02 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (set_union2 (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set
% 3.76/4.02 Clause #45 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 3.76/4.02 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 3.76/4.02 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 3.76/4.02 Clause #55 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True
% 3.76/4.02 Clause #57 (by clausification #[55]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True)
% 3.76/4.02 Clause #65 (by clausification #[57]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set)
% 3.76/4.02 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True)
% 3.76/4.02 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False)
% 3.76/4.02 Clause #68 (by destructive equality resolution #[67]): ∀ (a : Iota), Eq (in a empty_set) False
% 3.76/4.02 Clause #76 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True
% 3.76/4.02 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota),
% 3.76/4.02 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True
% 3.76/4.02 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True
% 3.76/4.02 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota),
% 3.76/4.02 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True)
% 3.76/4.02 Clause #92 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 3.76/4.02 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 3.76/4.02 Clause #94 (by clausification #[93]): ∀ (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))
% 3.76/4.02 Clause #96 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1))
% 3.76/4.02 Clause #97 (by destructive equality resolution #[96]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1)
% 3.76/4.03 Clause #98 (by destructive equality resolution #[97]): ∀ (a : Iota), Eq (in a (singleton a)) True
% 3.76/4.03 Clause #210 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2))
% 3.76/4.03 Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True)
% 3.76/4.03 Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.76/4.03 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False))
% 3.76/4.03 Clause #214 (by clausification #[212]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_2) False))
% 3.76/4.03 Clause #216 (by destructive equality resolution #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False)
% 3.76/4.03 Clause #217 (by superposition #[216, 98]): ∀ (a a_1 : Iota), Or (Eq (in a (set_union2 a_1 (singleton a))) True) (Eq False True)
% 3.76/4.03 Clause #223 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (in a (set_union2 a_1 (singleton a))) True
% 3.76/4.03 Clause #227 (by superposition #[223, 27]): ∀ (a a_1 : Iota), Eq (in a (set_union2 (singleton a) a_1)) True
% 3.76/4.03 Clause #236 (by superposition #[227, 42]): ∀ (a : Iota), Eq (in (skS.0 2 a) empty_set) True
% 3.76/4.03 Clause #242 (by superposition #[236, 68]): Eq True False
% 3.76/4.03 Clause #251 (by clausification #[242]): False
% 3.76/4.03 SZS output end Proof for theBenchmark.p
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