%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU123+1 : TPTP v9.2.0. Released v3.3.0. % 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 08:00:54 PM UTC 2025 % Result : Theorem 4.27s 4.56s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU123+1 : TPTP v9.2.0. Released v3.3.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:15:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.27/4.56 SZS status Theorem for theBenchmark.p % 4.27/4.56 SZS output start Proof for theBenchmark.p % 4.27/4.56 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq A B) (And (subset A B) (subset B A))) True % 4.27/4.56 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), subset empty_set A) True % 4.27/4.56 Clause #8 (by assumption #[]): Eq (Not (∀ (A : Iota), subset A empty_set → Eq A empty_set)) True % 4.27/4.56 Clause #12 (by clausification #[7]): ∀ (a : Iota), Eq (subset empty_set a) True % 4.27/4.56 Clause #29 (by clausification #[8]): Eq (∀ (A : Iota), subset A empty_set → Eq A empty_set) False % 4.27/4.56 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (Not (subset (skS.0 2 a) empty_set → Eq (skS.0 2 a) empty_set)) True % 4.27/4.56 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (subset (skS.0 2 a) empty_set → Eq (skS.0 2 a) empty_set) False % 4.27/4.56 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (subset (skS.0 2 a) empty_set) True % 4.27/4.56 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (Eq (skS.0 2 a) empty_set) False % 4.27/4.56 Clause #35 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq a B) (And (subset a B) (subset B a))) True % 4.27/4.56 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 4.27/4.56 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 4.27/4.56 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 4.27/4.56 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 4.27/4.56 Clause #42 (by superposition #[40, 12]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True)) % 4.27/4.56 Clause #45 (by clausification #[42]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False) % 4.27/4.56 Clause #46 (by superposition #[45, 32]): ∀ (a : Iota), Or (Eq empty_set (skS.0 2 a)) (Eq False True) % 4.27/4.56 Clause #47 (by clausification #[46]): ∀ (a : Iota), Eq empty_set (skS.0 2 a) % 4.27/4.56 Clause #49 (by clausification #[33]): ∀ (a : Iota), Ne (skS.0 2 a) empty_set % 4.27/4.56 Clause #50 (by forward demodulation #[49, 47]): Ne empty_set empty_set % 4.27/4.56 Clause #51 (by eliminate resolved literals #[50]): False % 4.27/4.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------