%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM670^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 07:57:01 PM UTC 2025 % Result : Theorem 3.73s 3.93s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM670^1 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n003.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 07:01:38 EDT 2025 % 0.12/0.34 % CPUTime : % 3.73/3.93 SZS status Theorem for theBenchmark.p % 3.73/3.93 SZS output start Proof for theBenchmark.p % 3.73/3.93 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True % 3.73/3.93 Clause #2 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (pl Xx Xy) (pl Xy Xx)) True % 3.73/3.93 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), Eq (pl (pl Xx Xy) Xz) (pl Xx (pl Xy Xz))) True % 3.73/3.93 Clause #4 (by assumption #[]): Eq (Not (Not (∀ (Xx_0 : nat), Ne (pl x z) (pl (pl y z) Xx_0)))) True % 3.73/3.93 Clause #9 (by clausification #[0]): Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False % 3.73/3.93 Clause #10 (by clausification #[9]): ∀ (a : nat), Eq (Not (Ne x (pl y (skS.0 0 a)))) True % 3.73/3.93 Clause #11 (by clausification #[10]): ∀ (a : nat), Eq (Ne x (pl y (skS.0 0 a))) False % 3.73/3.93 Clause #12 (by clausification #[11]): ∀ (a : nat), Eq x (pl y (skS.0 0 a)) % 3.73/3.93 Clause #13 (by clausification #[2]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (pl a Xy) (pl Xy a)) True % 3.73/3.93 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (Eq (pl a a_1) (pl a_1 a)) True % 3.73/3.93 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Eq (pl a a_1) (pl a_1 a) % 3.73/3.93 Clause #16 (by clausification #[4]): Eq (Not (∀ (Xx_0 : nat), Ne (pl x z) (pl (pl y z) Xx_0))) False % 3.73/3.93 Clause #17 (by clausification #[16]): Eq (∀ (Xx_0 : nat), Ne (pl x z) (pl (pl y z) Xx_0)) True % 3.73/3.93 Clause #18 (by clausification #[17]): ∀ (a : nat), Eq (Ne (pl x z) (pl (pl y z) a)) True % 3.73/3.93 Clause #19 (by clausification #[18]): ∀ (a : nat), Ne (pl x z) (pl (pl y z) a) % 3.73/3.93 Clause #20 (by forward demodulation #[19, 15]): ∀ (a : nat), Ne (pl z x) (pl (pl y z) a) % 3.73/3.93 Clause #21 (by forward demodulation #[20, 15]): ∀ (a : nat), Ne (pl z x) (pl (pl z y) a) % 3.73/3.93 Clause #23 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), Eq (pl (pl a Xy) Xz) (pl a (pl Xy Xz))) True % 3.73/3.93 Clause #24 (by clausification #[23]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), Eq (pl (pl a a_1) Xz) (pl a (pl a_1 Xz))) True % 3.73/3.93 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : nat), Eq (Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2))) True % 3.73/3.93 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : nat), Eq (pl (pl a a_1) a_2) (pl a (pl a_1 a_2)) % 3.73/3.93 Clause #27 (by backward demodulation #[26, 21]): ∀ (a : nat), Ne (pl z x) (pl z (pl y a)) % 3.73/3.93 Clause #34 (by superposition #[27, 12]): Ne (pl z x) (pl z x) % 3.73/3.93 Clause #36 (by eliminate resolved literals #[34]): False % 3.73/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------