%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM765^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 07:57:17 PM UTC 2025 % Result : Theorem 3.92s 4.16s % Output : Proof 3.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM765^1 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n013.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 07:50:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.92/4.16 SZS status Theorem for theBenchmark.p % 3.92/4.16 SZS output start Proof for theBenchmark.p % 3.92/4.16 Clause #0 (by assumption #[]): Eq (Not (moref x y) → eq x y) True % 3.92/4.16 Clause #1 (by assumption #[]): Eq (Not (moref z u) → eq z u) True % 3.92/4.16 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), eq Xx Xy → eq Xz Xu → eq (pf Xx Xz) (pf Xy Xu)) True % 3.92/4.16 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), moref Xx Xy → (Not (moref Xz Xu) → eq Xz Xu) → moref (pf Xx Xz) (pf Xy Xu)) True % 3.92/4.16 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), (Not (moref Xx Xy) → eq Xx Xy) → moref Xz Xu → moref (pf Xx Xz) (pf Xy Xu)) True % 3.92/4.16 Clause #6 (by assumption #[]): Eq (Not (Not (moref (pf x z) (pf y u)) → eq (pf x z) (pf y u))) True % 3.92/4.16 Clause #11 (by clausification #[1]): Or (Eq (Not (moref z u)) False) (Eq (eq z u) True) % 3.92/4.16 Clause #12 (by clausification #[11]): Or (Eq (eq z u) True) (Eq (moref z u) True) % 3.92/4.16 Clause #13 (by clausification #[0]): Or (Eq (Not (moref x y)) False) (Eq (eq x y) True) % 3.92/4.16 Clause #14 (by clausification #[13]): Or (Eq (eq x y) True) (Eq (moref x y) True) % 3.92/4.16 Clause #15 (by clausification #[6]): Eq (Not (moref (pf x z) (pf y u)) → eq (pf x z) (pf y u)) False % 3.92/4.16 Clause #16 (by clausification #[15]): Eq (Not (moref (pf x z) (pf y u))) True % 3.92/4.16 Clause #17 (by clausification #[15]): Eq (eq (pf x z) (pf y u)) False % 3.92/4.16 Clause #18 (by clausification #[16]): Eq (moref (pf x z) (pf y u)) False % 3.92/4.16 Clause #19 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), eq a Xy → eq Xz Xu → eq (pf a Xz) (pf Xy Xu)) True % 3.92/4.16 Clause #20 (by clausification #[19]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), eq a a_1 → eq Xz Xu → eq (pf a Xz) (pf a_1 Xu)) True % 3.92/4.16 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : frac), Eq (∀ (Xu : frac), eq a a_1 → eq a_2 Xu → eq (pf a a_2) (pf a_1 Xu)) True % 3.92/4.16 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : frac), Eq (eq a a_1 → eq a_2 a_3 → eq (pf a a_2) (pf a_1 a_3)) True % 3.92/4.16 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (eq a a_1) False) (Eq (eq a_2 a_3 → eq (pf a a_2) (pf a_1 a_3)) True) % 3.92/4.16 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (eq a a_1) False) (Or (Eq (eq a_2 a_3) False) (Eq (eq (pf a a_2) (pf a_1 a_3)) True)) % 3.92/4.16 Clause #26 (by superposition #[24, 14]): ∀ (a a_1 : frac), % 3.92/4.16 Or (Eq (eq a a_1) False) (Or (Eq (eq (pf x a) (pf y a_1)) True) (Or (Eq False True) (Eq (moref x y) True))) % 3.92/4.16 Clause #27 (by clausification #[5]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), (Not (moref a Xy) → eq a Xy) → moref Xz Xu → moref (pf a Xz) (pf Xy Xu)) True % 3.92/4.16 Clause #28 (by clausification #[27]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), (Not (moref a a_1) → eq a a_1) → moref Xz Xu → moref (pf a Xz) (pf a_1 Xu)) True % 3.92/4.16 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : frac), % 3.92/4.16 Eq (∀ (Xu : frac), (Not (moref a a_1) → eq a a_1) → moref a_2 Xu → moref (pf a a_2) (pf a_1 Xu)) True % 3.92/4.16 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : frac), Eq ((Not (moref a a_1) → eq a a_1) → moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True % 3.92/4.16 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : frac), % 3.92/4.16 Or (Eq (Not (moref a a_1) → eq a a_1) False) (Eq (moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True) % 3.92/4.16 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (moref a a_1 → moref (pf a_2 a) (pf a_3 a_1)) True) (Eq (Not (moref a_2 a_3)) True) % 3.92/4.16 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (moref a a_1 → moref (pf a_2 a) (pf a_3 a_1)) True) (Eq (eq a_2 a_3) False) % 3.92/4.16 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : frac), % 3.92/4.16 Or (Eq (Not (moref a a_1)) True) (Or (Eq (moref a_2 a_3) False) (Eq (moref (pf a a_2) (pf a_1 a_3)) True)) % 3.92/4.16 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : frac), % 3.92/4.16 Or (Eq (moref a a_1) False) (Or (Eq (moref (pf a_2 a) (pf a_3 a_1)) True) (Eq (moref a_2 a_3) False)) % 3.92/4.16 Clause #36 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : frac), % 3.92/4.16 Or (Eq (eq a a_1) False) (Or (Eq (moref a_2 a_3) False) (Eq (moref (pf a a_2) (pf a_1 a_3)) True)) % 3.92/4.16 Clause #38 (by superposition #[36, 14]): ∀ (a a_1 : frac), % 3.96/4.18 Or (Eq (moref a a_1) False) (Or (Eq (moref (pf x a) (pf y a_1)) True) (Or (Eq False True) (Eq (moref x y) True))) % 3.96/4.18 Clause #39 (by clausification #[4]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), moref a Xy → (Not (moref Xz Xu) → eq Xz Xu) → moref (pf a Xz) (pf Xy Xu)) True % 3.96/4.18 Clause #40 (by clausification #[39]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), moref a a_1 → (Not (moref Xz Xu) → eq Xz Xu) → moref (pf a Xz) (pf a_1 Xu)) True % 3.96/4.18 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : frac), % 3.96/4.18 Eq (∀ (Xu : frac), moref a a_1 → (Not (moref a_2 Xu) → eq a_2 Xu) → moref (pf a a_2) (pf a_1 Xu)) True % 3.96/4.18 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : frac), Eq (moref a a_1 → (Not (moref a_2 a_3) → eq a_2 a_3) → moref (pf a a_2) (pf a_1 a_3)) True % 3.96/4.18 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : frac), % 3.96/4.18 Or (Eq (moref a a_1) False) (Eq ((Not (moref a_2 a_3) → eq a_2 a_3) → moref (pf a a_2) (pf a_1 a_3)) True) % 3.96/4.18 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : frac), % 3.96/4.18 Or (Eq (moref a a_1) False) % 3.96/4.18 (Or (Eq (Not (moref a_2 a_3) → eq a_2 a_3) False) (Eq (moref (pf a a_2) (pf a_1 a_3)) True)) % 3.96/4.18 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : frac), % 3.96/4.18 Or (Eq (moref a a_1) False) (Or (Eq (moref (pf a a_2) (pf a_1 a_3)) True) (Eq (eq a_2 a_3) False)) % 3.96/4.18 Clause #51 (by clausification #[26]): ∀ (a a_1 : frac), Or (Eq (eq a a_1) False) (Or (Eq (eq (pf x a) (pf y a_1)) True) (Eq (moref x y) True)) % 3.96/4.18 Clause #52 (by superposition #[51, 12]): Or (Eq (eq (pf x z) (pf y u)) True) (Or (Eq (moref x y) True) (Or (Eq False True) (Eq (moref z u) True))) % 3.96/4.18 Clause #60 (by clausification #[52]): Or (Eq (eq (pf x z) (pf y u)) True) (Or (Eq (moref x y) True) (Eq (moref z u) True)) % 3.96/4.18 Clause #61 (by superposition #[60, 17]): Or (Eq (moref x y) True) (Or (Eq (moref z u) True) (Eq True False)) % 3.96/4.18 Clause #66 (by clausification #[61]): Or (Eq (moref x y) True) (Eq (moref z u) True) % 3.96/4.18 Clause #69 (by superposition #[66, 46]): ∀ (a a_1 : frac), % 3.96/4.18 Or (Eq (moref z u) True) (Or (Eq True False) (Or (Eq (moref (pf x a) (pf y a_1)) True) (Eq (eq a a_1) False))) % 3.96/4.18 Clause #70 (by clausification #[69]): ∀ (a a_1 : frac), Or (Eq (moref z u) True) (Or (Eq (moref (pf x a) (pf y a_1)) True) (Eq (eq a a_1) False)) % 3.96/4.18 Clause #71 (by superposition #[70, 12]): Or (Eq (moref z u) True) (Or (Eq (moref (pf x z) (pf y u)) True) (Or (Eq False True) (Eq (moref z u) True))) % 3.96/4.18 Clause #83 (by clausification #[71]): Or (Eq (moref z u) True) (Or (Eq (moref (pf x z) (pf y u)) True) (Eq (moref z u) True)) % 3.96/4.18 Clause #84 (by eliminate duplicate literals #[83]): Or (Eq (moref z u) True) (Eq (moref (pf x z) (pf y u)) True) % 3.96/4.18 Clause #85 (by superposition #[84, 18]): Or (Eq (moref z u) True) (Eq True False) % 3.96/4.18 Clause #90 (by clausification #[85]): Eq (moref z u) True % 3.96/4.18 Clause #98 (by superposition #[90, 35]): ∀ (a a_1 : frac), Or (Eq True False) (Or (Eq (moref (pf a z) (pf a_1 u)) True) (Eq (moref a a_1) False)) % 3.96/4.18 Clause #101 (by clausification #[38]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Or (Eq (moref (pf x a) (pf y a_1)) True) (Eq (moref x y) True)) % 3.96/4.18 Clause #102 (by superposition #[101, 90]): Or (Eq (moref (pf x z) (pf y u)) True) (Or (Eq (moref x y) True) (Eq False True)) % 3.96/4.18 Clause #103 (by clausification #[98]): ∀ (a a_1 : frac), Or (Eq (moref (pf a z) (pf a_1 u)) True) (Eq (moref a a_1) False) % 3.96/4.18 Clause #142 (by clausification #[102]): Or (Eq (moref (pf x z) (pf y u)) True) (Eq (moref x y) True) % 3.96/4.18 Clause #143 (by superposition #[142, 18]): Or (Eq (moref x y) True) (Eq True False) % 3.96/4.18 Clause #150 (by clausification #[143]): Eq (moref x y) True % 3.96/4.18 Clause #159 (by superposition #[150, 103]): Or (Eq (moref (pf x z) (pf y u)) True) (Eq True False) % 3.96/4.18 Clause #169 (by clausification #[159]): Eq (moref (pf x z) (pf y u)) True % 3.96/4.18 Clause #170 (by superposition #[169, 18]): Eq True False % 3.96/4.18 Clause #176 (by clausification #[170]): False % 3.96/4.18 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------