%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET867+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:00:37 PM UTC 2025 % Result : Theorem 3.86s 4.06s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET867+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n018.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 14:44:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.86/4.06 SZS status Theorem for theBenchmark.p % 3.86/4.06 SZS output start Proof for theBenchmark.p % 3.86/4.06 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 3.86/4.06 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (union A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D A)))) True % 3.86/4.06 Clause #6 (by assumption #[]): Eq (Not (Eq (union empty_set) empty_set)) True % 3.86/4.06 Clause #11 (by clausification #[6]): Eq (Eq (union empty_set) empty_set) False % 3.86/4.06 Clause #12 (by clausification #[11]): Ne (union empty_set) empty_set % 3.86/4.06 Clause #17 (by clausification #[1]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 3.86/4.06 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 3.86/4.06 Clause #28 (by clausification #[19]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 3.86/4.06 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 3.86/4.06 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 3.86/4.06 Clause #31 (by destructive equality resolution #[30]): ∀ (a : Iota), Eq (in a empty_set) False % 3.86/4.06 Clause #36 (by clausification #[2]): ∀ (a : Iota), % 3.86/4.06 Eq (∀ (B : Iota), Iff (Eq B (union a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D a)))) True % 3.86/4.06 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.86/4.06 Eq (Iff (Eq a (union a_1)) (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1)))) True % 3.86/4.06 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.86/4.06 Or (Eq (Eq a (union a_1)) True) (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) False) % 3.86/4.06 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), % 3.86/4.06 Or (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) False) (Eq a (union a_1)) % 3.86/4.06 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.86/4.06 Or (Eq a (union a_1)) % 3.86/4.06 (Eq (Not (Iff (in (skS.0 3 a a_1 a_2) a) (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1)))) True) % 3.86/4.06 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.86/4.06 Or (Eq a (union a_1)) % 3.86/4.06 (Eq (Iff (in (skS.0 3 a a_1 a_2) a) (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1))) False) % 3.86/4.06 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 3.86/4.06 Or (Eq a (union a_1)) % 3.86/4.06 (Or (Eq (in (skS.0 3 a a_1 a_2) a) True) (Eq (Exists fun D => And (in (skS.0 3 a a_1 a_2) D) (in D a_1)) True)) % 3.86/4.06 Clause #114 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.06 Or (Eq a (union a_1)) % 3.86/4.06 (Or (Eq (in (skS.0 3 a a_1 a_2) a) True) % 3.86/4.06 (Eq (And (in (skS.0 3 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) (in (skS.0 5 a a_1 a_2 a_3) a_1)) True)) % 3.86/4.06 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 a_3 : Iota), % 3.86/4.06 Or (Eq a (union a_1)) (Or (Eq (in (skS.0 3 a a_1 a_2) a) True) (Eq (in (skS.0 5 a a_1 a_2 a_3) a_1) True)) % 3.86/4.06 Clause #126 (by superposition #[115, 31]): ∀ (a a_1 : Iota), Or (Eq a (union empty_set)) (Or (Eq (in (skS.0 3 a empty_set a_1) a) True) (Eq True False)) % 3.86/4.06 Clause #135 (by clausification #[126]): ∀ (a a_1 : Iota), Or (Eq a (union empty_set)) (Eq (in (skS.0 3 a empty_set a_1) a) True) % 3.86/4.06 Clause #141 (by superposition #[135, 31]): Or (Eq empty_set (union empty_set)) (Eq True False) % 3.86/4.06 Clause #152 (by clausification #[141]): Eq empty_set (union empty_set) % 3.86/4.06 Clause #153 (by forward contextual literal cutting #[152, 12]): False % 3.86/4.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------