%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM664^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 3.58s 3.75s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM664^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n018.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 07:22:23 EDT 2025 % 0.14/0.34 % CPUTime : % 3.58/3.75 SZS status Theorem for theBenchmark.p % 3.58/3.75 SZS output start Proof for theBenchmark.p % 3.58/3.75 Clause #0 (by assumption #[]): Eq (less x y) True % 3.58/3.75 Clause #1 (by assumption #[]): Eq (Not (less y z) → Eq y z) True % 3.58/3.75 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), less Xx Xy → less Xy Xz → less Xx Xz) True % 3.58/3.75 Clause #4 (by assumption #[]): Eq (Not (less x z)) True % 3.58/3.75 Clause #9 (by clausification #[4]): Eq (less x z) False % 3.58/3.75 Clause #10 (by clausification #[1]): Or (Eq (Not (less y z)) False) (Eq (Eq y z) True) % 3.58/3.75 Clause #11 (by clausification #[10]): Or (Eq (Eq y z) True) (Eq (less y z) True) % 3.58/3.75 Clause #12 (by clausification #[11]): Or (Eq (less y z) True) (Eq y z) % 3.58/3.75 Clause #13 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), less a Xy → less Xy Xz → less a Xz) True % 3.58/3.75 Clause #14 (by clausification #[13]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), less a a_1 → less a_1 Xz → less a Xz) True % 3.58/3.75 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : nat), Eq (less a a_1 → less a_1 a_2 → less a a_2) True % 3.58/3.75 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : nat), Or (Eq (less a a_1) False) (Eq (less a_1 a_2 → less a a_2) True) % 3.58/3.75 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : nat), Or (Eq (less a a_1) False) (Or (Eq (less a_1 a_2) False) (Eq (less a a_2) True)) % 3.58/3.75 Clause #18 (by superposition #[17, 0]): ∀ (a : nat), Or (Eq (less y a) False) (Or (Eq (less x a) True) (Eq False True)) % 3.58/3.75 Clause #20 (by clausification #[18]): ∀ (a : nat), Or (Eq (less y a) False) (Eq (less x a) True) % 3.58/3.75 Clause #21 (by superposition #[20, 12]): Or (Eq (less x z) True) (Or (Eq False True) (Eq y z)) % 3.58/3.75 Clause #22 (by clausification #[21]): Or (Eq (less x z) True) (Eq y z) % 3.58/3.75 Clause #23 (by superposition #[22, 9]): Or (Eq y z) (Eq True False) % 3.58/3.75 Clause #25 (by clausification #[23]): Eq y z % 3.58/3.75 Clause #26 (by backward demodulation #[25, 0]): Eq (less x z) True % 3.58/3.75 Clause #30 (by superposition #[26, 9]): Eq True False % 3.58/3.75 Clause #32 (by clausification #[30]): False % 3.58/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------