%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM662^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 07:56:59 PM UTC 2025 % Result : Theorem 3.51s 3.71s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM662^1 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 07:58:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.51/3.71 SZS status Theorem for theBenchmark.p % 3.51/3.71 SZS output start Proof for theBenchmark.p % 3.51/3.71 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx_0 : nat), Ne y (pl x Xx_0))) True % 3.51/3.71 Clause #1 (by assumption #[]): Eq (Not (∀ (Xx : nat), Ne z (pl y Xx))) True % 3.51/3.71 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), Eq (pl (pl Xx Xy) Xz) (pl Xx (pl Xy Xz))) True % 3.51/3.71 Clause #4 (by assumption #[]): Eq (Not (Not (∀ (Xx_0 : nat), Ne z (pl x Xx_0)))) True % 3.51/3.71 Clause #9 (by clausification #[1]): Eq (∀ (Xx : nat), Ne z (pl y Xx)) False % 3.51/3.71 Clause #10 (by clausification #[9]): ∀ (a : nat), Eq (Not (Ne z (pl y (skS.0 0 a)))) True % 3.51/3.71 Clause #11 (by clausification #[10]): ∀ (a : nat), Eq (Ne z (pl y (skS.0 0 a))) False % 3.51/3.71 Clause #12 (by clausification #[11]): ∀ (a : nat), Eq z (pl y (skS.0 0 a)) % 3.51/3.71 Clause #13 (by clausification #[0]): Eq (∀ (Xx_0 : nat), Ne y (pl x Xx_0)) False % 3.51/3.71 Clause #14 (by clausification #[13]): ∀ (a : nat), Eq (Not (Ne y (pl x (skS.0 1 a)))) True % 3.51/3.71 Clause #15 (by clausification #[14]): ∀ (a : nat), Eq (Ne y (pl x (skS.0 1 a))) False % 3.51/3.71 Clause #16 (by clausification #[15]): ∀ (a : nat), Eq y (pl x (skS.0 1 a)) % 3.51/3.71 Clause #17 (by clausification #[4]): Eq (Not (∀ (Xx_0 : nat), Ne z (pl x Xx_0))) False % 3.51/3.71 Clause #18 (by clausification #[17]): Eq (∀ (Xx_0 : nat), Ne z (pl x Xx_0)) True % 3.51/3.71 Clause #19 (by clausification #[18]): ∀ (a : nat), Eq (Ne z (pl x a)) True % 3.51/3.71 Clause #20 (by clausification #[19]): ∀ (a : nat), Ne z (pl x a) % 3.51/3.71 Clause #22 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), Eq (pl (pl a Xy) Xz) (pl a (pl Xy Xz))) True % 3.51/3.71 Clause #23 (by clausification #[22]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), Eq (pl (pl a a_1) Xz) (pl a (pl a_1 Xz))) True % 3.51/3.71 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : nat), Eq (Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2))) True % 3.51/3.71 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : nat), Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2)) % 3.51/3.71 Clause #28 (by superposition #[25, 16]): ∀ (a a_1 : nat), Eq (pl y a) (pl x (pl (skS.0 1 a_1) a)) % 3.51/3.71 Clause #29 (by superposition #[28, 20]): ∀ (a : nat), Ne z (pl y a) % 3.51/3.71 Clause #31 (by backward contextual literal cutting #[29, 12]): False % 3.51/3.71 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------