%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM761^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:57:16 PM UTC 2025 % Result : Theorem 3.55s 3.79s % Output : Proof 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM761^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.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 08:58:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.55/3.79 SZS status Theorem for theBenchmark.p % 3.55/3.79 SZS output start Proof for theBenchmark.p % 3.55/3.79 Clause #0 (by assumption #[]): Eq (Not (moref x y) → eq x y) True % 3.55/3.79 Clause #1 (by assumption #[]): Eq (moref z u) True % 3.55/3.79 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), eq Xx Xy → moref Xz Xu → moref (pf Xx Xz) (pf Xy Xu)) True % 3.55/3.79 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), moref Xx Xy → moref Xz Xu → moref (pf Xx Xz) (pf Xy Xu)) True % 3.55/3.79 Clause #5 (by assumption #[]): Eq (Not (moref (pf x z) (pf y u))) True % 3.55/3.79 Clause #10 (by clausification #[0]): Or (Eq (Not (moref x y)) False) (Eq (eq x y) True) % 3.55/3.79 Clause #11 (by clausification #[10]): Or (Eq (eq x y) True) (Eq (moref x y) True) % 3.55/3.79 Clause #12 (by clausification #[5]): Eq (moref (pf x z) (pf y u)) False % 3.55/3.79 Clause #13 (by clausification #[4]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), moref a Xy → moref Xz Xu → moref (pf a Xz) (pf Xy Xu)) True % 3.55/3.79 Clause #14 (by clausification #[13]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), moref a a_1 → moref Xz Xu → moref (pf a Xz) (pf a_1 Xu)) True % 3.55/3.79 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : frac), Eq (∀ (Xu : frac), moref a a_1 → moref a_2 Xu → moref (pf a a_2) (pf a_1 Xu)) True % 3.55/3.79 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : frac), Eq (moref a a_1 → moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True % 3.55/3.79 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (moref a a_1) False) (Eq (moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True) % 3.55/3.79 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : frac), % 3.55/3.79 Or (Eq (moref a a_1) False) (Or (Eq (moref a_2 a_3) False) (Eq (moref (pf a a_2) (pf a_1 a_3)) True)) % 3.55/3.79 Clause #20 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), eq a Xy → moref Xz Xu → moref (pf a Xz) (pf Xy Xu)) True % 3.55/3.79 Clause #21 (by clausification #[20]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), eq a a_1 → moref Xz Xu → moref (pf a Xz) (pf a_1 Xu)) True % 3.55/3.79 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : frac), Eq (∀ (Xu : frac), eq a a_1 → moref a_2 Xu → moref (pf a a_2) (pf a_1 Xu)) True % 3.55/3.79 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : frac), Eq (eq a a_1 → moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True % 3.55/3.79 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : frac), Or (Eq (eq a a_1) False) (Eq (moref a_2 a_3 → moref (pf a a_2) (pf a_1 a_3)) True) % 3.55/3.79 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : frac), % 3.55/3.79 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)) % 3.55/3.79 Clause #26 (by superposition #[25, 11]): ∀ (a a_1 : frac), % 3.55/3.79 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))) % 3.55/3.79 Clause #38 (by clausification #[26]): ∀ (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)) % 3.55/3.79 Clause #39 (by superposition #[38, 1]): Or (Eq (moref (pf x z) (pf y u)) True) (Or (Eq (moref x y) True) (Eq False True)) % 3.55/3.79 Clause #53 (by clausification #[39]): Or (Eq (moref (pf x z) (pf y u)) True) (Eq (moref x y) True) % 3.55/3.79 Clause #54 (by superposition #[53, 12]): Or (Eq (moref x y) True) (Eq True False) % 3.55/3.79 Clause #59 (by clausification #[54]): Eq (moref x y) True % 3.55/3.79 Clause #63 (by superposition #[59, 18]): ∀ (a a_1 : frac), Or (Eq True False) (Or (Eq (moref a a_1) False) (Eq (moref (pf x a) (pf y a_1)) True)) % 3.55/3.79 Clause #78 (by clausification #[63]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Eq (moref (pf x a) (pf y a_1)) True) % 3.55/3.79 Clause #79 (by superposition #[78, 1]): Or (Eq (moref (pf x z) (pf y u)) True) (Eq False True) % 3.55/3.79 Clause #92 (by clausification #[79]): Eq (moref (pf x z) (pf y u)) True % 3.55/3.79 Clause #93 (by superposition #[92, 12]): Eq True False % 3.55/3.79 Clause #99 (by clausification #[93]): False % 3.55/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------