%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM762^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 4.11s 4.28s % Output : Proof 4.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM762^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.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 08:10:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.11/4.28 SZS status Theorem for theBenchmark.p % 4.11/4.28 SZS output start Proof for theBenchmark.p % 4.11/4.28 Clause #0 (by assumption #[]): Eq (moref x y) True % 4.11/4.28 Clause #1 (by assumption #[]): Eq (Not (moref z u) → eq z u) True % 4.11/4.28 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), moref Xx Xy → eq Xx Xz → eq Xy Xu → moref Xz Xu) True % 4.11/4.28 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), moref Xx Xy → moref (pf Xx Xz) (pf Xy Xz)) True % 4.11/4.28 Clause #5 (by assumption #[]): Eq (∀ (Xx : frac), eq Xx Xx) True % 4.11/4.28 Clause #6 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), eq Xx Xy → eq Xz Xu → eq (pf Xx Xz) (pf Xy Xu)) True % 4.11/4.28 Clause #7 (by assumption #[]): Eq (∀ (Xx Xy Xz Xu : frac), moref Xx Xy → moref Xz Xu → moref (pf Xx Xz) (pf Xy Xu)) True % 4.11/4.28 Clause #8 (by assumption #[]): Eq (Not (moref (pf x z) (pf y u))) True % 4.11/4.28 Clause #13 (by clausification #[1]): Or (Eq (Not (moref z u)) False) (Eq (eq z u) True) % 4.11/4.28 Clause #14 (by clausification #[13]): Or (Eq (eq z u) True) (Eq (moref z u) True) % 4.11/4.28 Clause #15 (by clausification #[5]): ∀ (a : frac), Eq (eq a a) True % 4.11/4.28 Clause #16 (by clausification #[8]): Eq (moref (pf x z) (pf y u)) False % 4.11/4.28 Clause #17 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), moref a Xy → eq a Xz → eq Xy Xu → moref Xz Xu) True % 4.11/4.28 Clause #18 (by clausification #[17]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), moref a a_1 → eq a Xz → eq a_1 Xu → moref Xz Xu) True % 4.11/4.28 Clause #19 (by clausification #[18]): ∀ (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 % 4.11/4.28 Clause #20 (by clausification #[19]): ∀ (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 % 4.11/4.28 Clause #21 (by clausification #[20]): ∀ (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) % 4.11/4.28 Clause #22 (by clausification #[21]): ∀ (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)) % 4.11/4.28 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : frac), % 4.11/4.28 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))) % 4.11/4.28 Clause #25 (by clausification #[4]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), moref a Xy → moref (pf a Xz) (pf Xy Xz)) True % 4.11/4.28 Clause #26 (by clausification #[25]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), moref a a_1 → moref (pf a Xz) (pf a_1 Xz)) True % 4.11/4.28 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : frac), Eq (moref a a_1 → moref (pf a a_2) (pf a_1 a_2)) True % 4.11/4.28 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : frac), Or (Eq (moref a a_1) False) (Eq (moref (pf a a_2) (pf a_1 a_2)) True) % 4.11/4.28 Clause #29 (by superposition #[28, 0]): ∀ (a : frac), Or (Eq (moref (pf x a) (pf y a)) True) (Eq False True) % 4.11/4.28 Clause #30 (by clausification #[29]): ∀ (a : frac), Eq (moref (pf x a) (pf y a)) True % 4.11/4.28 Clause #31 (by superposition #[30, 23]): ∀ (a a_1 a_2 : frac), % 4.11/4.28 Or (Eq True False) (Or (Eq (eq (pf x a) a_1) False) (Or (Eq (eq (pf y a) a_2) False) (Eq (moref a_1 a_2) True))) % 4.11/4.28 Clause #37 (by clausification #[6]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), eq a Xy → eq Xz Xu → eq (pf a Xz) (pf Xy Xu)) True % 4.11/4.28 Clause #38 (by clausification #[37]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), eq a a_1 → eq Xz Xu → eq (pf a Xz) (pf a_1 Xu)) True % 4.11/4.28 Clause #39 (by clausification #[38]): ∀ (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 % 4.11/4.28 Clause #40 (by clausification #[39]): ∀ (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 % 4.11/4.28 Clause #41 (by clausification #[40]): ∀ (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) % 4.11/4.28 Clause #42 (by clausification #[41]): ∀ (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)) % 4.11/4.28 Clause #44 (by superposition #[42, 15]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Or (Eq (eq (pf a_2 a) (pf a_2 a_1)) True) (Eq False True)) % 4.11/4.28 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Eq (eq (pf a_2 a) (pf a_2 a_1)) True) % 4.11/4.29 Clause #46 (by superposition #[45, 14]): ∀ (a : frac), Or (Eq (eq (pf a z) (pf a u)) True) (Or (Eq False True) (Eq (moref z u) True)) % 4.11/4.29 Clause #49 (by clausification #[46]): ∀ (a : frac), Or (Eq (eq (pf a z) (pf a u)) True) (Eq (moref z u) True) % 4.11/4.29 Clause #52 (by clausification #[7]): ∀ (a : frac), Eq (∀ (Xy Xz Xu : frac), moref a Xy → moref Xz Xu → moref (pf a Xz) (pf Xy Xu)) True % 4.11/4.29 Clause #53 (by clausification #[52]): ∀ (a a_1 : frac), Eq (∀ (Xz Xu : frac), moref a a_1 → moref Xz Xu → moref (pf a Xz) (pf a_1 Xu)) True % 4.11/4.29 Clause #54 (by clausification #[53]): ∀ (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 % 4.11/4.29 Clause #55 (by clausification #[54]): ∀ (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 % 4.11/4.29 Clause #56 (by clausification #[55]): ∀ (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) % 4.11/4.29 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : frac), % 4.11/4.29 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)) % 4.11/4.29 Clause #58 (by superposition #[57, 0]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Or (Eq (moref (pf x a) (pf y a_1)) True) (Eq False True)) % 4.11/4.29 Clause #60 (by clausification #[58]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Eq (moref (pf x a) (pf y a_1)) True) % 4.11/4.29 Clause #63 (by clausification #[31]): ∀ (a a_1 a_2 : frac), Or (Eq (eq (pf x a) a_1) False) (Or (Eq (eq (pf y a) a_2) False) (Eq (moref a_1 a_2) True)) % 4.11/4.29 Clause #65 (by superposition #[63, 15]): ∀ (a a_1 : frac), Or (Eq (eq (pf y a) a_1) False) (Or (Eq (moref (pf x a) a_1) True) (Eq False True)) % 4.11/4.29 Clause #99 (by clausification #[65]): ∀ (a a_1 : frac), Or (Eq (eq (pf y a) a_1) False) (Eq (moref (pf x a) a_1) True) % 4.11/4.29 Clause #100 (by superposition #[99, 49]): Or (Eq (moref (pf x z) (pf y u)) True) (Or (Eq False True) (Eq (moref z u) True)) % 4.11/4.29 Clause #101 (by clausification #[100]): Or (Eq (moref (pf x z) (pf y u)) True) (Eq (moref z u) True) % 4.11/4.29 Clause #102 (by superposition #[101, 16]): Or (Eq (moref z u) True) (Eq True False) % 4.11/4.29 Clause #107 (by clausification #[102]): Eq (moref z u) True % 4.11/4.29 Clause #116 (by superposition #[107, 60]): Or (Eq True False) (Eq (moref (pf x z) (pf y u)) True) % 4.11/4.29 Clause #119 (by clausification #[116]): Eq (moref (pf x z) (pf y u)) True % 4.11/4.29 Clause #120 (by superposition #[119, 16]): Eq True False % 4.11/4.29 Clause #125 (by clausification #[120]): False % 4.11/4.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------