%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET063+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 07:59:32 PM UTC 2025 % Result : Theorem 3.54s 3.74s % Output : Proof 3.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET063+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.13 % Command : duper %s % 0.14/0.34 % Computer : n012.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 : Thu Oct 2 14:25:53 EDT 2025 % 0.14/0.34 % CPUTime : % 3.54/3.74 SZS status Theorem for theBenchmark.p % 3.54/3.74 SZS output start Proof for theBenchmark.p % 3.54/3.74 Clause #0 (by assumption #[]): Eq (∀ (B : Iota), subset empty_set B) True % 3.54/3.74 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 3.54/3.74 Clause #6 (by assumption #[]): Eq (Not (∀ (B : Iota), subset B empty_set → Eq B empty_set)) True % 3.54/3.74 Clause #8 (by clausification #[0]): ∀ (a : Iota), Eq (subset empty_set a) True % 3.54/3.74 Clause #11 (by clausification #[6]): Eq (∀ (B : Iota), subset B empty_set → Eq B empty_set) False % 3.54/3.74 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (Not (subset (skS.0 0 a) empty_set → Eq (skS.0 0 a) empty_set)) True % 3.54/3.74 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (subset (skS.0 0 a) empty_set → Eq (skS.0 0 a) empty_set) False % 3.54/3.74 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (subset (skS.0 0 a) empty_set) True % 3.54/3.74 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (Eq (skS.0 0 a) empty_set) False % 3.54/3.74 Clause #41 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 3.54/3.74 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 3.54/3.74 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 3.54/3.74 Clause #45 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 3.54/3.74 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 3.54/3.74 Clause #48 (by superposition #[46, 8]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True)) % 3.54/3.74 Clause #51 (by clausification #[48]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False) % 3.54/3.74 Clause #52 (by superposition #[51, 14]): ∀ (a : Iota), Or (Eq empty_set (skS.0 0 a)) (Eq False True) % 3.54/3.74 Clause #55 (by clausification #[52]): ∀ (a : Iota), Eq empty_set (skS.0 0 a) % 3.54/3.74 Clause #57 (by clausification #[15]): ∀ (a : Iota), Ne (skS.0 0 a) empty_set % 3.54/3.74 Clause #58 (by forward demodulation #[57, 55]): Ne empty_set empty_set % 3.54/3.74 Clause #59 (by eliminate resolved literals #[58]): False % 3.54/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------