%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU123+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:00:54 PM UTC 2025 % Result : Theorem 3.65s 3.89s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU123+2 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.14 % Command : duper %s % 0.14/0.36 % Computer : n016.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 : Fri Oct 3 03:59:08 EDT 2025 % 0.14/0.36 % CPUTime : % 3.65/3.89 SZS status Theorem for theBenchmark.p % 3.65/3.89 SZS output start Proof for theBenchmark.p % 3.65/3.89 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq A B) (And (subset A B) (subset B A))) True % 3.65/3.89 Clause #15 (by assumption #[]): Eq (∀ (A : Iota), subset empty_set A) True % 3.65/3.89 Clause #17 (by assumption #[]): Eq (Not (∀ (A : Iota), subset A empty_set → Eq A empty_set)) True % 3.65/3.89 Clause #22 (by clausification #[15]): ∀ (a : Iota), Eq (subset empty_set a) True % 3.65/3.89 Clause #52 (by clausification #[17]): Eq (∀ (A : Iota), subset A empty_set → Eq A empty_set) False % 3.65/3.89 Clause #53 (by clausification #[52]): ∀ (a : Iota), Eq (Not (subset (skS.0 2 a) empty_set → Eq (skS.0 2 a) empty_set)) True % 3.65/3.89 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (subset (skS.0 2 a) empty_set → Eq (skS.0 2 a) empty_set) False % 3.65/3.89 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (subset (skS.0 2 a) empty_set) True % 3.65/3.89 Clause #56 (by clausification #[54]): ∀ (a : Iota), Eq (Eq (skS.0 2 a) empty_set) False % 3.65/3.89 Clause #64 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq a B) (And (subset a B) (subset B a))) True % 3.65/3.89 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 3.65/3.89 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 3.65/3.89 Clause #68 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 3.65/3.89 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 3.65/3.89 Clause #71 (by superposition #[69, 22]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True)) % 3.65/3.89 Clause #74 (by clausification #[71]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False) % 3.65/3.89 Clause #75 (by superposition #[74, 55]): ∀ (a : Iota), Or (Eq empty_set (skS.0 2 a)) (Eq False True) % 3.65/3.89 Clause #76 (by clausification #[75]): ∀ (a : Iota), Eq empty_set (skS.0 2 a) % 3.65/3.89 Clause #78 (by clausification #[56]): ∀ (a : Iota), Ne (skS.0 2 a) empty_set % 3.65/3.89 Clause #79 (by forward demodulation #[78, 76]): Ne empty_set empty_set % 3.65/3.89 Clause #80 (by eliminate resolved literals #[79]): False % 3.65/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------