TSTP Solution File: SEU153+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SEU153+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 16:40:28 EDT 2023
% Result : Theorem 45.07s 45.23s
% Output : Proof 45.16s
% 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 : SEU153+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n015.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 : Wed Aug 23 12:59:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 45.07/45.23 SZS status Theorem for theBenchmark.p
% 45.07/45.23 SZS output start Proof for theBenchmark.p
% 45.07/45.23 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True
% 45.07/45.23 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True
% 45.07/45.23 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_intersection2 A B)) (∀ (D : Iota), Iff (in D C) (And (in D A) (in D B)))) True
% 45.07/45.23 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_intersection2 A B) empty_set)) True
% 45.07/45.23 Clause #9 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B)))) True
% 45.07/45.23 Clause #30 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True
% 45.07/45.23 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True)
% 45.07/45.23 Clause #40 (by clausification #[32]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set)
% 45.07/45.23 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True)
% 45.07/45.23 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False)
% 45.07/45.23 Clause #43 (by destructive equality resolution #[42]): ∀ (a : Iota), Eq (in a empty_set) False
% 45.07/45.23 Clause #45 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_intersection2 a B) empty_set)) True
% 45.07/45.23 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_intersection2 a a_1) empty_set)) True
% 45.07/45.23 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Eq (set_intersection2 a a_1) empty_set) True)
% 45.07/45.23 Clause #52 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True
% 45.07/45.23 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True
% 45.07/45.23 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True)
% 45.07/45.23 Clause #64 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_intersection2 a a_1) empty_set)
% 45.07/45.23 Clause #67 (by clausification #[9]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B))) False
% 45.07/45.23 Clause #68 (by clausification #[67]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Not (And (disjoint (singleton (skS.0 4 a)) B) (in (skS.0 4 a) B)))) True
% 45.07/45.23 Clause #69 (by clausification #[68]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (disjoint (singleton (skS.0 4 a)) B) (in (skS.0 4 a) B))) False
% 45.07/45.23 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota),
% 45.07/45.23 Eq (Not (Not (And (disjoint (singleton (skS.0 4 a)) (skS.0 5 a a_1)) (in (skS.0 4 a) (skS.0 5 a a_1))))) True
% 45.07/45.23 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota),
% 45.07/45.23 Eq (Not (And (disjoint (singleton (skS.0 4 a)) (skS.0 5 a a_1)) (in (skS.0 4 a) (skS.0 5 a a_1)))) False
% 45.07/45.23 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (And (disjoint (singleton (skS.0 4 a)) (skS.0 5 a a_1)) (in (skS.0 4 a) (skS.0 5 a a_1))) True
% 45.07/45.23 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a) (skS.0 5 a a_1)) True
% 45.07/45.23 Clause #74 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 4 a)) (skS.0 5 a a_1)) True
% 45.07/45.23 Clause #76 (by clausification #[4]): ∀ (a : Iota),
% 45.07/45.23 Eq (∀ (B C : Iota), Iff (Eq C (set_intersection2 a B)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D B)))) True
% 45.07/45.23 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota),
% 45.07/45.23 Eq (∀ (C : Iota), Iff (Eq C (set_intersection2 a a_1)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D a_1)))) True
% 45.07/45.23 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota),
% 45.07/45.23 Eq (Iff (Eq a (set_intersection2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2)))) True
% 45.07/45.23 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota),
% 45.07/45.23 Or (Eq (Eq a (set_intersection2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True)
% 45.16/45.36 Clause #151 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1))
% 45.16/45.36 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True)
% 45.16/45.36 Clause #153 (by clausification #[152]): ∀ (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))
% 45.16/45.36 Clause #155 (by clausification #[153]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1))
% 45.16/45.36 Clause #156 (by destructive equality resolution #[155]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1)
% 45.16/45.36 Clause #157 (by destructive equality resolution #[156]): ∀ (a : Iota), Eq (in a (singleton a)) True
% 45.16/45.36 Clause #226 (by superposition #[74, 64]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_intersection2 (singleton (skS.0 4 a)) (skS.0 5 a a_1)) empty_set)
% 45.16/45.36 Clause #267 (by clausification #[80]): ∀ (a a_1 a_2 : Iota),
% 45.16/45.36 Or (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) (Ne a (set_intersection2 a_1 a_2))
% 45.16/45.36 Clause #268 (by clausification #[267]): ∀ (a a_1 a_2 a_3 : Iota),
% 45.16/45.36 Or (Ne a (set_intersection2 a_1 a_2)) (Eq (Iff (in a_3 a) (And (in a_3 a_1) (in a_3 a_2))) True)
% 45.16/45.36 Clause #269 (by clausification #[268]): ∀ (a a_1 a_2 a_3 : Iota),
% 45.16/45.36 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (And (in a_3 a_1) (in a_3 a_2)) False))
% 45.16/45.36 Clause #271 (by clausification #[269]): ∀ (a a_1 a_2 a_3 : Iota),
% 45.16/45.36 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Or (Eq (in a_3 a_1) False) (Eq (in a_3 a_2) False)))
% 45.16/45.36 Clause #272 (by destructive equality resolution #[271]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 a_1 a_2)) True) (Or (Eq (in a a_1) False) (Eq (in a a_2) False))
% 45.16/45.36 Clause #274 (by superposition #[272, 157]): ∀ (a a_1 : Iota), Or (Eq (in a (set_intersection2 (singleton a) a_1)) True) (Or (Eq (in a a_1) False) (Eq False True))
% 45.16/45.36 Clause #281 (by clausification #[274]): ∀ (a a_1 : Iota), Or (Eq (in a (set_intersection2 (singleton a) a_1)) True) (Eq (in a a_1) False)
% 45.16/45.36 Clause #282 (by superposition #[281, 73]): ∀ (a a_1 : Iota),
% 45.16/45.36 Or (Eq (in (skS.0 4 a) (set_intersection2 (singleton (skS.0 4 a)) (skS.0 5 a a_1))) True) (Eq False True)
% 45.16/45.36 Clause #11010 (by clausification #[226]): ∀ (a a_1 : Iota), Eq (set_intersection2 (singleton (skS.0 4 a)) (skS.0 5 a a_1)) empty_set
% 45.16/45.36 Clause #15475 (by clausification #[282]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a) (set_intersection2 (singleton (skS.0 4 a)) (skS.0 5 a a_1))) True
% 45.16/45.36 Clause #15476 (by forward demodulation #[15475, 11010]): ∀ (a : Iota), Eq (in (skS.0 4 a) empty_set) True
% 45.16/45.36 Clause #15477 (by superposition #[15476, 43]): Eq True False
% 45.16/45.36 Clause #15532 (by clausification #[15477]): False
% 45.16/45.36 SZS output end Proof for theBenchmark.p
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