%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM667^1 : 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 07:57:00 PM UTC 2025 % Result : Theorem 3.49s 3.70s % Output : Proof 3.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM667^1 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 07:01:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.49/3.70 SZS status Theorem for theBenchmark.p % 3.49/3.70 SZS output start Proof for theBenchmark.p % 3.49/3.70 Clause #0 (by assumption #[]): Eq (Not (less x y) → Eq x y) True % 3.49/3.70 Clause #1 (by assumption #[]): Eq (Not (less y z) → Eq y z) True % 3.49/3.70 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : nat), (Not (less Xx Xy) → Eq Xx Xy) → less Xy Xz → less Xx Xz) True % 3.49/3.70 Clause #5 (by assumption #[]): Eq (Not (Not (less x z) → Eq x z)) True % 3.49/3.70 Clause #10 (by clausification #[1]): Or (Eq (Not (less y z)) False) (Eq (Eq y z) True) % 3.49/3.70 Clause #11 (by clausification #[10]): Or (Eq (Eq y z) True) (Eq (less y z) True) % 3.49/3.70 Clause #12 (by clausification #[11]): Or (Eq (less y z) True) (Eq y z) % 3.49/3.70 Clause #13 (by clausification #[0]): Or (Eq (Not (less x y)) False) (Eq (Eq x y) True) % 3.49/3.70 Clause #14 (by clausification #[13]): Or (Eq (Eq x y) True) (Eq (less x y) True) % 3.49/3.70 Clause #15 (by clausification #[14]): Or (Eq (less x y) True) (Eq x y) % 3.49/3.70 Clause #16 (by clausification #[5]): Eq (Not (less x z) → Eq x z) False % 3.49/3.70 Clause #17 (by clausification #[16]): Eq (Not (less x z)) True % 3.49/3.70 Clause #18 (by clausification #[16]): Eq (Eq x z) False % 3.49/3.70 Clause #19 (by clausification #[17]): Eq (less x z) False % 3.49/3.70 Clause #20 (by clausification #[18]): Ne x z % 3.49/3.70 Clause #21 (by clausification #[3]): ∀ (a : nat), Eq (∀ (Xy Xz : nat), (Not (less a Xy) → Eq a Xy) → less Xy Xz → less a Xz) True % 3.49/3.70 Clause #22 (by clausification #[21]): ∀ (a a_1 : nat), Eq (∀ (Xz : nat), (Not (less a a_1) → Eq a a_1) → less a_1 Xz → less a Xz) True % 3.49/3.70 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : nat), Eq ((Not (less a a_1) → Eq a a_1) → less a_1 a_2 → less a a_2) True % 3.49/3.70 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : nat), Or (Eq (Not (less a a_1) → Eq a a_1) False) (Eq (less a_1 a_2 → less a a_2) True) % 3.49/3.70 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : nat), Or (Eq (less a a_1 → less a_2 a_1) True) (Eq (Not (less a_2 a)) True) % 3.49/3.70 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : nat), Or (Eq (Not (less a a_1)) True) (Or (Eq (less a_1 a_2) False) (Eq (less a a_2) True)) % 3.49/3.70 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : nat), Or (Eq (less a a_1) False) (Or (Eq (less a_2 a_1) True) (Eq (less a_2 a) False)) % 3.49/3.70 Clause #29 (by superposition #[28, 12]): ∀ (a : nat), Or (Eq (less a z) True) (Or (Eq (less a y) False) (Or (Eq False True) (Eq y z))) % 3.49/3.70 Clause #44 (by clausification #[29]): ∀ (a : nat), Or (Eq (less a z) True) (Or (Eq (less a y) False) (Eq y z)) % 3.49/3.70 Clause #45 (by superposition #[44, 15]): Or (Eq (less x z) True) (Or (Eq y z) (Or (Eq False True) (Eq x y))) % 3.49/3.70 Clause #46 (by clausification #[45]): Or (Eq (less x z) True) (Or (Eq y z) (Eq x y)) % 3.49/3.70 Clause #47 (by superposition #[46, 19]): Or (Eq y z) (Or (Eq x y) (Eq True False)) % 3.49/3.70 Clause #50 (by clausification #[47]): Or (Eq y z) (Eq x y) % 3.49/3.70 Clause #51 (by superposition #[50, 19]): Or (Eq y z) (Eq (less y z) False) % 3.49/3.70 Clause #54 (by superposition #[51, 12]): Or (Eq y z) (Or (Eq False True) (Eq y z)) % 3.49/3.70 Clause #55 (by clausification #[54]): Or (Eq y z) (Eq y z) % 3.49/3.70 Clause #56 (by eliminate duplicate literals #[55]): Eq y z % 3.49/3.70 Clause #58 (by backward demodulation #[56, 15]): Or (Eq (less x z) True) (Eq x y) % 3.49/3.70 Clause #65 (by forward demodulation #[58, 56]): Or (Eq (less x z) True) (Eq x z) % 3.49/3.70 Clause #66 (by forward contextual literal cutting #[65, 20]): Eq (less x z) True % 3.49/3.70 Clause #67 (by superposition #[66, 19]): Eq True False % 3.49/3.70 Clause #70 (by clausification #[67]): False % 3.49/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------