%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM753^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 07:57:14 PM UTC 2025 % Result : Theorem 3.69s 3.87s % Output : Proof 3.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM753^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n010.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 08:23:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.69/3.87 SZS status Theorem for theBenchmark.p % 3.69/3.87 SZS output start Proof for theBenchmark.p % 3.69/3.87 Clause #0 (by assumption #[]): Eq (eq x y) True % 3.69/3.87 Clause #1 (by assumption #[]): Eq (moref z u) True % 3.69/3.87 Clause #2 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), moref Xx Xy → eq Xx Xz → eq Xy Xu → moref Xz Xu) True % 3.69/3.87 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), moref Xx Xy → moref (pf Xz Xx) (pf Xz Xy)) True % 3.69/3.87 Clause #4 (by assumption #[]): Eq (∀ (Xx : frac), eq Xx Xx) True % 3.69/3.87 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), eq Xx Xy → eq Xz Xu → eq (pf Xx Xz) (pf Xy Xu)) True % 3.69/3.87 Clause #6 (by assumption #[]): Eq (Not (moref (pf x z) (pf y u))) True % 3.69/3.87 Clause #7 (by clausification #[4]): ∀ (a : frac), Eq (eq a a) True % 3.69/3.87 Clause #8 (by clausification #[6]): Eq (moref (pf x z) (pf y u)) False % 3.69/3.87 Clause #9 (by clausification #[2]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), moref a Xy → eq a Xz → eq Xy Xu → moref Xz Xu) True % 3.69/3.87 Clause #10 (by clausification #[9]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), moref a a_1 → eq a Xz → eq a_1 Xu → moref Xz Xu) True % 3.69/3.87 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : frac), Eq (∀ (Xu : frac), moref a a_1 → eq a a_2 → eq a_1 Xu → moref a_2 Xu) True % 3.69/3.87 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : frac), Eq (moref a a_1 → eq a a_2 → eq a_1 a_3 → moref a_2 a_3) True % 3.69/3.87 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (moref a a_1) False) (Eq (eq a a_2 → eq a_1 a_3 → moref a_2 a_3) True) % 3.69/3.87 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (moref a a_1) False) (Or (Eq (eq a a_2) False) (Eq (eq a_1 a_3 → moref a_2 a_3) True)) % 3.69/3.87 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : frac), % 3.69/3.87 Or (Eq (moref a a_1) False) (Or (Eq (eq a a_2) False) (Or (Eq (eq a_1 a_3) False) (Eq (moref a_2 a_3) True))) % 3.69/3.87 Clause #17 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), moref a Xy → moref (pf Xz a) (pf Xz Xy)) True % 3.69/3.87 Clause #18 (by clausification #[17]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), moref a a_1 → moref (pf Xz a) (pf Xz a_1)) True % 3.69/3.87 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : frac), Eq (moref a a_1 → moref (pf a_2 a) (pf a_2 a_1)) True % 3.69/3.87 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : frac), Or (Eq (moref a a_1) False) (Eq (moref (pf a_2 a) (pf a_2 a_1)) True) % 3.69/3.87 Clause #21 (by superposition #[20, 1]): ∀ (a : frac), Or (Eq (moref (pf a z) (pf a u)) True) (Eq False True) % 3.69/3.87 Clause #22 (by clausification #[21]): ∀ (a : frac), Eq (moref (pf a z) (pf a u)) True % 3.69/3.87 Clause #23 (by superposition #[22, 15]): ∀ (a a_1 a_2 : frac), % 3.69/3.87 Or (Eq True False) (Or (Eq (eq (pf a z) a_1) False) (Or (Eq (eq (pf a u) a_2) False) (Eq (moref a_1 a_2) True))) % 3.69/3.87 Clause #29 (by clausification #[5]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), eq a Xy → eq Xz Xu → eq (pf a Xz) (pf Xy Xu)) True % 3.69/3.87 Clause #30 (by clausification #[29]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), eq a a_1 → eq Xz Xu → eq (pf a Xz) (pf a_1 Xu)) True % 3.69/3.87 Clause #31 (by clausification #[30]): ∀ (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 % 3.69/3.87 Clause #32 (by clausification #[31]): ∀ (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 % 3.69/3.87 Clause #33 (by clausification #[32]): ∀ (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) % 3.69/3.87 Clause #34 (by clausification #[33]): ∀ (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)) % 3.69/3.87 Clause #35 (by superposition #[34, 0]): ∀ (a a_1 : frac), Or (Eq (eq a a_1) False) (Or (Eq (eq (pf x a) (pf y a_1)) True) (Eq False True)) % 3.69/3.87 Clause #37 (by clausification #[23]): ∀ (a a_1 a_2 : frac), Or (Eq (eq (pf a z) a_1) False) (Or (Eq (eq (pf a u) a_2) False) (Eq (moref a_1 a_2) True)) % 3.69/3.87 Clause #38 (by superposition #[37, 7]): ∀ (a a_1 : frac), Or (Eq (eq (pf a u) a_1) False) (Or (Eq (moref (pf a z) a_1) True) (Eq False True)) % 3.69/3.87 Clause #39 (by clausification #[38]): ∀ (a a_1 : frac), Or (Eq (eq (pf a u) a_1) False) (Eq (moref (pf a z) a_1) True) % 3.69/3.87 Clause #53 (by clausification #[35]): ∀ (a a_1 : frac), Or (Eq (eq a a_1) False) (Eq (eq (pf x a) (pf y a_1)) True) % 3.69/3.87 Clause #57 (by superposition #[53, 7]): ∀ (a : frac), Or (Eq (eq (pf x a) (pf y a)) True) (Eq False True) % 3.69/3.87 Clause #58 (by clausification #[57]): ∀ (a : frac), Eq (eq (pf x a) (pf y a)) True % 3.69/3.87 Clause #60 (by superposition #[58, 39]): Or (Eq True False) (Eq (moref (pf x z) (pf y u)) True) % 3.69/3.87 Clause #64 (by clausification #[60]): Eq (moref (pf x z) (pf y u)) True % 3.69/3.87 Clause #65 (by superposition #[64, 8]): Eq True False % 3.69/3.87 Clause #68 (by clausification #[65]): False % 3.69/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------