%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM743^1 : 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 07:57:13 PM UTC 2025 % Result : Theorem 3.57s 3.76s % Output : Proof 3.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM743^1 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 07:20:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.57/3.76 SZS status Theorem for theBenchmark.p % 3.57/3.76 SZS output start Proof for theBenchmark.p % 3.57/3.76 Clause #0 (by assumption #[]): Eq (lessf x y) True % 3.57/3.76 Clause #1 (by assumption #[]): Eq (Not (lessf y z) → eq y z) True % 3.57/3.76 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), lessf Xx Xy → eq Xx Xz → eq Xy Xu → lessf Xz Xu) True % 3.57/3.76 Clause #4 (by assumption #[]): Eq (∀ (Xx : frac), eq Xx Xx) True % 3.57/3.76 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), lessf Xx Xy → lessf Xy Xz → lessf Xx Xz) True % 3.57/3.76 Clause #6 (by assumption #[]): Eq (Not (lessf x z)) True % 3.57/3.76 Clause #11 (by clausification #[1]): Or (Eq (Not (lessf y z)) False) (Eq (eq y z) True) % 3.57/3.76 Clause #12 (by clausification #[11]): Or (Eq (eq y z) True) (Eq (lessf y z) True) % 3.57/3.76 Clause #13 (by clausification #[4]): ∀ (a : frac), Eq (eq a a) True % 3.57/3.76 Clause #14 (by clausification #[6]): Eq (lessf x z) False % 3.57/3.76 Clause #15 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), lessf a Xy → eq a Xz → eq Xy Xu → lessf Xz Xu) True % 3.57/3.76 Clause #16 (by clausification #[15]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), lessf a a_1 → eq a Xz → eq a_1 Xu → lessf Xz Xu) True % 3.57/3.76 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : frac), Eq (∀ (Xu : frac), lessf a a_1 → eq a a_2 → eq a_1 Xu → lessf a_2 Xu) True % 3.57/3.76 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : frac), Eq (lessf a a_1 → eq a a_2 → eq a_1 a_3 → lessf a_2 a_3) True % 3.57/3.76 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (lessf a a_1) False) (Eq (eq a a_2 → eq a_1 a_3 → lessf a_2 a_3) True) % 3.57/3.76 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (lessf a a_1) False) (Or (Eq (eq a a_2) False) (Eq (eq a_1 a_3 → lessf a_2 a_3) True)) % 3.57/3.76 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : frac), % 3.57/3.76 Or (Eq (lessf a a_1) False) (Or (Eq (eq a a_2) False) (Or (Eq (eq a_1 a_3) False) (Eq (lessf a_2 a_3) True))) % 3.57/3.76 Clause #22 (by superposition #[21, 0]): ∀ (a a_1 : frac), Or (Eq (eq x a) False) (Or (Eq (eq y a_1) False) (Or (Eq (lessf a a_1) True) (Eq False True))) % 3.57/3.76 Clause #23 (by clausification #[5]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), lessf a Xy → lessf Xy Xz → lessf a Xz) True % 3.57/3.76 Clause #24 (by clausification #[23]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), lessf a a_1 → lessf a_1 Xz → lessf a Xz) True % 3.57/3.76 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : frac), Eq (lessf a a_1 → lessf a_1 a_2 → lessf a a_2) True % 3.57/3.76 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Eq (lessf a_1 a_2 → lessf a a_2) True) % 3.57/3.76 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Or (Eq (lessf a_1 a_2) False) (Eq (lessf a a_2) True)) % 3.57/3.76 Clause #28 (by superposition #[27, 0]): ∀ (a : frac), Or (Eq (lessf y a) False) (Or (Eq (lessf x a) True) (Eq False True)) % 3.57/3.76 Clause #29 (by clausification #[28]): ∀ (a : frac), Or (Eq (lessf y a) False) (Eq (lessf x a) True) % 3.57/3.76 Clause #30 (by clausification #[22]): ∀ (a a_1 : frac), Or (Eq (eq x a) False) (Or (Eq (eq y a_1) False) (Eq (lessf a a_1) True)) % 3.57/3.76 Clause #31 (by superposition #[30, 13]): ∀ (a : frac), Or (Eq (eq y a) False) (Or (Eq (lessf x a) True) (Eq False True)) % 3.57/3.76 Clause #32 (by clausification #[31]): ∀ (a : frac), Or (Eq (eq y a) False) (Eq (lessf x a) True) % 3.57/3.76 Clause #33 (by superposition #[32, 12]): Or (Eq (lessf x z) True) (Or (Eq False True) (Eq (lessf y z) True)) % 3.57/3.76 Clause #35 (by clausification #[33]): Or (Eq (lessf x z) True) (Eq (lessf y z) True) % 3.57/3.76 Clause #36 (by superposition #[35, 14]): Or (Eq (lessf y z) True) (Eq True False) % 3.57/3.76 Clause #39 (by clausification #[36]): Eq (lessf y z) True % 3.57/3.76 Clause #42 (by superposition #[39, 29]): Or (Eq True False) (Eq (lessf x z) True) % 3.57/3.76 Clause #45 (by clausification #[42]): Eq (lessf x z) True % 3.57/3.76 Clause #46 (by superposition #[45, 14]): Eq True False % 3.57/3.76 Clause #49 (by clausification #[46]): False % 3.57/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------