%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM713^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 07:57:10 PM UTC 2025 % Result : Theorem 3.47s 3.67s % Output : Proof 3.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM713^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 07:32:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.47/3.67 SZS status Theorem for theBenchmark.p % 3.47/3.67 SZS output start Proof for theBenchmark.p % 3.47/3.67 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx_0 : nat), Ne x (pl y Xx_0))) True % 3.47/3.67 Clause #2 (by assumption #[]): Eq (∀ (Xx Xy : nat), Eq (ts Xx Xy) (ts Xy Xx)) True % 3.47/3.67 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), Eq (ts Xx (pl Xy Xz)) (pl (ts Xx Xy) (ts Xx Xz))) True % 3.47/3.67 Clause #4 (by assumption #[]): Eq (Not (Not (∀ (Xx_0 : nat), Ne (ts x z) (pl (ts y z) Xx_0)))) True % 3.47/3.67 Clause #9 (by clausification #[0]): Eq (∀ (Xx_0 : nat), Ne x (pl y Xx_0)) False % 3.47/3.67 Clause #10 (by clausification #[9]): ∀ (a : nat), Eq (Not (Ne x (pl y (skS.0 0 a)))) True % 3.47/3.67 Clause #11 (by clausification #[10]): ∀ (a : nat), Eq (Ne x (pl y (skS.0 0 a))) False % 3.47/3.67 Clause #12 (by clausification #[11]): ∀ (a : nat), Eq x (pl y (skS.0 0 a)) % 3.47/3.67 Clause #13 (by clausification #[2]): ∀ (a : nat), Eq (∀ (Xy : nat), Eq (ts a Xy) (ts Xy a)) True % 3.47/3.67 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (Eq (ts a a_1) (ts a_1 a)) True % 3.47/3.67 Clause #15 (by clausification #[14]): ∀ (a a_1 : nat), Eq (ts a a_1) (ts a_1 a) % 3.47/3.67 Clause #16 (by clausification #[4]): Eq (Not (∀ (Xx_0 : nat), Ne (ts x z) (pl (ts y z) Xx_0))) False % 3.47/3.67 Clause #17 (by clausification #[16]): Eq (∀ (Xx_0 : nat), Ne (ts x z) (pl (ts y z) Xx_0)) True % 3.47/3.67 Clause #18 (by clausification #[17]): ∀ (a : nat), Eq (Ne (ts x z) (pl (ts y z) a)) True % 3.47/3.67 Clause #19 (by clausification #[18]): ∀ (a : nat), Ne (ts x z) (pl (ts y z) a) % 3.47/3.67 Clause #20 (by forward demodulation #[19, 15]): ∀ (a : nat), Ne (ts z x) (pl (ts y z) a) % 3.47/3.67 Clause #21 (by forward demodulation #[20, 15]): ∀ (a : nat), Ne (ts z x) (pl (ts z y) a) % 3.47/3.67 Clause #22 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), Eq (ts a (pl Xy Xz)) (pl (ts a Xy) (ts a Xz))) True % 3.47/3.67 Clause #23 (by clausification #[22]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), Eq (ts a (pl a_1 Xz)) (pl (ts a a_1) (ts a Xz))) True % 3.47/3.67 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : nat), Eq (Eq (ts a (pl a_1 a_2)) (pl (ts a a_1) (ts a a_2))) True % 3.47/3.67 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : nat), Eq (ts a (pl a_1 a_2)) (pl (ts a a_1) (ts a a_2)) % 3.47/3.67 Clause #26 (by superposition #[25, 21]): ∀ (a : nat), Ne (ts z x) (ts z (pl y a)) % 3.47/3.67 Clause #29 (by superposition #[26, 12]): Ne (ts z x) (ts z x) % 3.47/3.67 Clause #30 (by eliminate resolved literals #[29]): False % 3.47/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------