%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU575^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:01:57 PM UTC 2025 % Result : Theorem 3.53s 3.71s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU575^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n031.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 04:00:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.53/3.71 SZS status Theorem for theBenchmark.p % 3.53/3.71 SZS output start Proof for theBenchmark.p % 3.53/3.71 Clause #0 (by assumption #[]): Eq (Eq emptysetsubset (∀ (A : Iota), subset emptyset A)) True % 3.53/3.71 Clause #1 (by assumption #[]): Eq (Eq setextsub (∀ (A B : Iota), subset A B → subset B A → Eq A B)) True % 3.53/3.71 Clause #2 (by assumption #[]): Eq (Not (emptysetsubset → setextsub → ∀ (A : Iota), subset A emptyset → Eq A emptyset)) True % 3.53/3.71 Clause #3 (by clausification #[0]): Eq emptysetsubset (∀ (A : Iota), subset emptyset A) % 3.53/3.71 Clause #10 (by clausification #[2]): Eq (emptysetsubset → setextsub → ∀ (A : Iota), subset A emptyset → Eq A emptyset) False % 3.53/3.71 Clause #11 (by clausification #[10]): Eq emptysetsubset True % 3.53/3.71 Clause #12 (by clausification #[10]): Eq (setextsub → ∀ (A : Iota), subset A emptyset → Eq A emptyset) False % 3.53/3.71 Clause #13 (by backward demodulation #[11, 3]): Eq True (∀ (A : Iota), subset emptyset A) % 3.53/3.71 Clause #16 (by clausification #[1]): Eq setextsub (∀ (A B : Iota), subset A B → subset B A → Eq A B) % 3.53/3.71 Clause #20 (by clausification #[13]): ∀ (a : Iota), Eq (subset emptyset a) True % 3.53/3.71 Clause #21 (by clausification #[12]): Eq setextsub True % 3.53/3.71 Clause #22 (by clausification #[12]): Eq (∀ (A : Iota), subset A emptyset → Eq A emptyset) False % 3.53/3.71 Clause #23 (by backward demodulation #[21, 16]): Eq True (∀ (A B : Iota), subset A B → subset B A → Eq A B) % 3.53/3.71 Clause #24 (by clausification #[22]): ∀ (a : Iota), Eq (Not (subset (skS.0 1 a) emptyset → Eq (skS.0 1 a) emptyset)) True % 3.53/3.71 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (subset (skS.0 1 a) emptyset → Eq (skS.0 1 a) emptyset) False % 3.53/3.71 Clause #26 (by clausification #[25]): ∀ (a : Iota), Eq (subset (skS.0 1 a) emptyset) True % 3.53/3.71 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (Eq (skS.0 1 a) emptyset) False % 3.53/3.71 Clause #28 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → subset B a → Eq a B) True % 3.53/3.71 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (subset a a_1 → subset a_1 a → Eq a a_1) True % 3.53/3.71 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (subset a_1 a → Eq a a_1) True) % 3.53/3.71 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (subset a_1 a) False) (Eq (Eq a a_1) True)) % 3.53/3.71 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (subset a_1 a) False) (Eq a a_1)) % 3.53/3.71 Clause #34 (by superposition #[32, 20]): ∀ (a : Iota), Or (Eq (subset a emptyset) False) (Or (Eq emptyset a) (Eq False True)) % 3.53/3.71 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (subset a emptyset) False) (Eq emptyset a) % 3.53/3.71 Clause #36 (by superposition #[35, 26]): ∀ (a : Iota), Or (Eq emptyset (skS.0 1 a)) (Eq False True) % 3.53/3.71 Clause #39 (by clausification #[36]): ∀ (a : Iota), Eq emptyset (skS.0 1 a) % 3.53/3.71 Clause #41 (by clausification #[27]): ∀ (a : Iota), Ne (skS.0 1 a) emptyset % 3.53/3.71 Clause #42 (by forward demodulation #[41, 39]): Ne emptyset emptyset % 3.53/3.71 Clause #43 (by eliminate resolved literals #[42]): False % 3.53/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------