%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET002+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 07:59:19 PM UTC 2025 % Result : Theorem 4.09s 4.31s % Output : Proof 4.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET002+3 : TPTP v9.2.0. Released v2.2.0. % 0.12/0.14 % Command : duper %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 14:47:23 EDT 2025 % 0.14/0.36 % CPUTime : % 4.09/4.31 SZS status Theorem for theBenchmark.p % 4.09/4.31 SZS output start Proof for theBenchmark.p % 4.09/4.31 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), subset B C → Eq (union B C) C) True % 4.09/4.31 Clause #5 (by assumption #[]): Eq (∀ (B : Iota), subset B B) True % 4.09/4.31 Clause #7 (by assumption #[]): Eq (Not (∀ (B : Iota), Eq (union B B) B)) True % 4.09/4.31 Clause #8 (by clausification #[5]): ∀ (a : Iota), Eq (subset a a) True % 4.09/4.31 Clause #9 (by clausification #[7]): Eq (∀ (B : Iota), Eq (union B B) B) False % 4.09/4.31 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (Not (Eq (union (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a))) True % 4.09/4.31 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Eq (union (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)) False % 4.09/4.31 Clause #12 (by clausification #[11]): ∀ (a : Iota), Ne (union (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a) % 4.09/4.31 Clause #13 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), subset a C → Eq (union a C) C) True % 4.09/4.31 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (union a a_1) a_1) True % 4.09/4.31 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (union a a_1) a_1) True) % 4.09/4.31 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (union a a_1) a_1) % 4.09/4.31 Clause #17 (by superposition #[16, 8]): ∀ (a : Iota), Or (Eq (union a a) a) (Eq False True) % 4.09/4.31 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (union a a) a % 4.09/4.31 Clause #20 (by backward contextual literal cutting #[18, 12]): False % 4.09/4.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------