%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU153+1 : TPTP v9.2.0. Released v3.3.0. % 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 : Fri Oct 3 08:00:59 PM UTC 2025 % Result : Theorem 42.56s 42.78s % Output : Proof 42.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU153+1 : TPTP v9.2.0. Released v3.3.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 06:43:08 EDT 2025 % 0.13/0.35 % CPUTime : % 42.56/42.78 SZS status Theorem for theBenchmark.p % 42.56/42.78 SZS output start Proof for theBenchmark.p % 42.56/42.78 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 42.56/42.78 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 42.56/42.78 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 % 42.56/42.78 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_intersection2 A B) empty_set)) True % 42.56/42.78 Clause #9 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B)))) True % 42.56/42.78 Clause #30 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 42.56/42.78 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 42.56/42.78 Clause #40 (by clausification #[32]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 42.56/42.78 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 42.56/42.78 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 42.56/42.78 Clause #43 (by destructive equality resolution #[42]): ∀ (a : Iota), Eq (in a empty_set) False % 42.56/42.78 Clause #45 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_intersection2 a B) empty_set)) True % 42.56/42.78 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_intersection2 a a_1) empty_set)) True % 42.56/42.78 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) % 42.56/42.78 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 % 42.56/42.78 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 % 42.56/42.78 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) % 42.56/42.78 Clause #64 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_intersection2 a a_1) empty_set) % 42.56/42.78 Clause #67 (by clausification #[9]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B))) False % 42.56/42.78 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 % 42.56/42.78 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 % 42.56/42.78 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 42.56/42.78 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 % 42.56/42.78 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 42.56/42.78 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 % 42.56/42.78 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 % 42.56/42.78 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a) (skS.0 5 a a_1)) True % 42.56/42.78 Clause #74 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 4 a)) (skS.0 5 a a_1)) True % 42.56/42.78 Clause #76 (by clausification #[4]): ∀ (a : Iota), % 42.56/42.78 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 % 42.56/42.78 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 42.56/42.78 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 % 42.56/42.78 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 42.56/42.78 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 % 42.56/42.78 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 42.56/42.78 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) % 42.71/42.91 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)) % 42.71/42.91 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) % 42.71/42.91 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)) % 42.71/42.91 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)) % 42.71/42.91 Clause #156 (by destructive equality resolution #[155]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 42.71/42.91 Clause #157 (by destructive equality resolution #[156]): ∀ (a : Iota), Eq (in a (singleton a)) True % 42.71/42.91 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) % 42.71/42.91 Clause #267 (by clausification #[80]): ∀ (a a_1 a_2 : Iota), % 42.71/42.91 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)) % 42.71/42.91 Clause #268 (by clausification #[267]): ∀ (a a_1 a_2 a_3 : Iota), % 42.71/42.91 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) % 42.71/42.91 Clause #269 (by clausification #[268]): ∀ (a a_1 a_2 a_3 : Iota), % 42.71/42.91 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)) % 42.71/42.91 Clause #271 (by clausification #[269]): ∀ (a a_1 a_2 a_3 : Iota), % 42.71/42.91 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))) % 42.71/42.91 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)) % 42.71/42.91 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)) % 42.71/42.91 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) % 42.71/42.91 Clause #282 (by superposition #[281, 73]): ∀ (a a_1 : Iota), % 42.71/42.91 Or (Eq (in (skS.0 4 a) (set_intersection2 (singleton (skS.0 4 a)) (skS.0 5 a a_1))) True) (Eq False True) % 42.71/42.91 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 % 42.71/42.91 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 % 42.71/42.91 Clause #15476 (by forward demodulation #[15475, 11010]): ∀ (a : Iota), Eq (in (skS.0 4 a) empty_set) True % 42.71/42.91 Clause #15477 (by superposition #[15476, 43]): Eq True False % 42.71/42.91 Clause #15532 (by clausification #[15477]): False % 42.71/42.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------