%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET605+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:00:14 PM UTC 2025 % Result : Theorem 3.99s 4.16s % Output : Proof 3.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET605+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n021.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 : Thu Oct 2 13:48:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.99/4.16 SZS status Theorem for theBenchmark.p % 3.99/4.16 SZS output start Proof for theBenchmark.p % 3.99/4.16 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), subset B (union B C)) True % 3.99/4.16 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq (difference B C) empty_set) (subset B C)) True % 3.99/4.16 Clause #11 (by assumption #[]): Eq (Not (∀ (B C : Iota), Eq (difference B (union B C)) empty_set)) True % 3.99/4.16 Clause #15 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), subset a (union a C)) True % 3.99/4.16 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True % 3.99/4.16 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq (difference a C) empty_set) (subset a C)) True % 3.99/4.16 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (Eq (difference a a_1) empty_set) (subset a a_1)) True % 3.99/4.16 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (Eq (difference a a_1) empty_set) True) (Eq (subset a a_1) False) % 3.99/4.16 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (difference a a_1) empty_set) % 3.99/4.16 Clause #30 (by superposition #[29, 16]): ∀ (a a_1 : Iota), Or (Eq (difference a (union a a_1)) empty_set) (Eq False True) % 3.99/4.16 Clause #33 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (difference a (union a a_1)) empty_set % 3.99/4.16 Clause #64 (by clausification #[11]): Eq (∀ (B C : Iota), Eq (difference B (union B C)) empty_set) False % 3.99/4.16 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), Eq (difference (skS.0 1 a) (union (skS.0 1 a) C)) empty_set)) True % 3.99/4.16 Clause #66 (by clausification #[65]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (difference (skS.0 1 a) (union (skS.0 1 a) C)) empty_set) False % 3.99/4.16 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (Not (Eq (difference (skS.0 1 a) (union (skS.0 1 a) (skS.0 2 a a_1))) empty_set)) True % 3.99/4.16 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (Eq (difference (skS.0 1 a) (union (skS.0 1 a) (skS.0 2 a a_1))) empty_set) False % 3.99/4.16 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Ne (difference (skS.0 1 a) (union (skS.0 1 a) (skS.0 2 a a_1))) empty_set % 3.99/4.16 Clause #70 (by forward demodulation #[69, 33]): Ne empty_set empty_set % 3.99/4.16 Clause #71 (by eliminate resolved literals #[70]): False % 3.99/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------