%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM458+2 : TPTP v9.2.0. Released v4.0.0. % 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 07:56:31 PM UTC 2025 % Result : Theorem 119.08s 119.27s % Output : Proof 119.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM458+2 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n031.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 : Fri Oct 3 07:07:38 EDT 2025 % 0.14/0.35 % CPUTime : % 119.08/119.27 SZS status Theorem for theBenchmark.p % 119.08/119.27 SZS output start Proof for theBenchmark.p % 119.08/119.27 Clause #1 (by assumption #[]): Eq (aNaturalNumber0 sz00) True % 119.08/119.27 Clause #5 (by assumption #[]): Eq (∀ (W0 W1 : Iota), And (aNaturalNumber0 W0) (aNaturalNumber0 W1) → Eq (sdtpldt0 W0 W1) (sdtpldt0 W1 W0)) True % 119.08/119.27 Clause #7 (by assumption #[]): Eq (∀ (W0 : Iota), aNaturalNumber0 W0 → And (Eq (sdtpldt0 W0 sz00) W0) (Eq W0 (sdtpldt0 sz00 W0))) True % 119.08/119.27 Clause #19 (by assumption #[]): Eq (aNaturalNumber0 xm) True % 119.08/119.27 Clause #20 (by assumption #[]): Eq (Not (Or (Exists fun W0 => And (aNaturalNumber0 W0) (Eq (sdtpldt0 xm W0) xm)) (sdtlseqdt0 xm xm))) True % 119.08/119.27 Clause #56 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (W1 : Iota), And (aNaturalNumber0 a) (aNaturalNumber0 W1) → Eq (sdtpldt0 a W1) (sdtpldt0 W1 a)) True % 119.08/119.27 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (And (aNaturalNumber0 a) (aNaturalNumber0 a_1) → Eq (sdtpldt0 a a_1) (sdtpldt0 a_1 a)) True % 119.08/119.27 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 119.08/119.27 Or (Eq (And (aNaturalNumber0 a) (aNaturalNumber0 a_1)) False) (Eq (Eq (sdtpldt0 a a_1) (sdtpldt0 a_1 a)) True) % 119.08/119.27 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 119.08/119.27 Or (Eq (Eq (sdtpldt0 a a_1) (sdtpldt0 a_1 a)) True) % 119.08/119.27 (Or (Eq (aNaturalNumber0 a) False) (Eq (aNaturalNumber0 a_1) False)) % 119.08/119.27 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), % 119.08/119.27 Or (Eq (aNaturalNumber0 a) False) (Or (Eq (aNaturalNumber0 a_1) False) (Eq (sdtpldt0 a a_1) (sdtpldt0 a_1 a))) % 119.08/119.27 Clause #61 (by superposition #[60, 19]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Or (Eq (sdtpldt0 xm a) (sdtpldt0 a xm)) (Eq False True)) % 119.08/119.27 Clause #168 (by clausification #[7]): ∀ (a : Iota), Eq (aNaturalNumber0 a → And (Eq (sdtpldt0 a sz00) a) (Eq a (sdtpldt0 sz00 a))) True % 119.08/119.27 Clause #169 (by clausification #[168]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Eq (And (Eq (sdtpldt0 a sz00) a) (Eq a (sdtpldt0 sz00 a))) True) % 119.08/119.27 Clause #170 (by clausification #[169]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Eq (Eq a (sdtpldt0 sz00 a)) True) % 119.08/119.27 Clause #172 (by clausification #[170]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Eq a (sdtpldt0 sz00 a)) % 119.08/119.27 Clause #173 (by superposition #[172, 19]): Or (Eq xm (sdtpldt0 sz00 xm)) (Eq False True) % 119.08/119.27 Clause #189 (by clausification #[173]): Eq xm (sdtpldt0 sz00 xm) % 119.08/119.27 Clause #806 (by clausification #[20]): Eq (Or (Exists fun W0 => And (aNaturalNumber0 W0) (Eq (sdtpldt0 xm W0) xm)) (sdtlseqdt0 xm xm)) False % 119.08/119.27 Clause #808 (by clausification #[806]): Eq (Exists fun W0 => And (aNaturalNumber0 W0) (Eq (sdtpldt0 xm W0) xm)) False % 119.08/119.27 Clause #1580 (by clausification #[61]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Eq (sdtpldt0 xm a) (sdtpldt0 a xm)) % 119.08/119.27 Clause #1582 (by superposition #[1580, 1]): Or (Eq (sdtpldt0 xm sz00) (sdtpldt0 sz00 xm)) (Eq False True) % 119.08/119.27 Clause #1634 (by clausification #[1582]): Eq (sdtpldt0 xm sz00) (sdtpldt0 sz00 xm) % 119.08/119.27 Clause #1635 (by forward demodulation #[1634, 189]): Eq (sdtpldt0 xm sz00) xm % 119.08/119.27 Clause #36945 (by clausification #[808]): ∀ (a : Iota), Eq (And (aNaturalNumber0 a) (Eq (sdtpldt0 xm a) xm)) False % 119.08/119.27 Clause #36946 (by clausification #[36945]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Eq (Eq (sdtpldt0 xm a) xm) False) % 119.08/119.27 Clause #36947 (by clausification #[36946]): ∀ (a : Iota), Or (Eq (aNaturalNumber0 a) False) (Ne (sdtpldt0 xm a) xm) % 119.08/119.27 Clause #36949 (by superposition #[36947, 1]): Or (Ne (sdtpldt0 xm sz00) xm) (Eq False True) % 119.08/119.27 Clause #37301 (by clausification #[36949]): Ne (sdtpldt0 xm sz00) xm % 119.08/119.27 Clause #37302 (by forward demodulation #[37301, 1635]): Ne xm xm % 119.08/119.27 Clause #37303 (by eliminate resolved literals #[37302]): False % 119.08/119.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------