%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM759^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 3.91s 4.07s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUM759^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n020.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 07:21:53 EDT 2025 % 0.15/0.36 % CPUTime : % 3.91/4.07 SZS status Theorem for theBenchmark.p % 3.91/4.07 SZS output start Proof for theBenchmark.p % 3.91/4.07 Clause #0 (by assumption #[]): Eq (eq (pf z x) (pf z y)) True % 3.91/4.07 Clause #1 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), eq (pf Xx Xz) (pf Xy Xz) → eq Xx Xy) True % 3.91/4.07 Clause #2 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), eq Xx Xy → eq Xy Xz → eq Xx Xz) True % 3.91/4.07 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy : frac), eq (pf Xx Xy) (pf Xy Xx)) True % 3.91/4.07 Clause #4 (by assumption #[]): Eq (Not (eq x y)) True % 3.91/4.07 Clause #5 (by clausification #[4]): Eq (eq x y) False % 3.91/4.07 Clause #6 (by clausification #[1]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), eq (pf a Xz) (pf Xy Xz) → eq a Xy) True % 3.91/4.07 Clause #7 (by clausification #[6]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), eq (pf a Xz) (pf a_1 Xz) → eq a a_1) True % 3.91/4.07 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : frac), Eq (eq (pf a a_1) (pf a_2 a_1) → eq a a_2) True % 3.91/4.07 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : frac), Or (Eq (eq (pf a a_1) (pf a_2 a_1)) False) (Eq (eq a a_2) True) % 3.91/4.07 Clause #10 (by clausification #[2]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), eq a Xy → eq Xy Xz → eq a Xz) True % 3.91/4.07 Clause #11 (by clausification #[10]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), eq a a_1 → eq a_1 Xz → eq a Xz) True % 3.91/4.07 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : frac), Eq (eq a a_1 → eq a_1 a_2 → eq a a_2) True % 3.91/4.07 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Eq (eq a_1 a_2 → eq a a_2) True) % 3.91/4.07 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Or (Eq (eq a_1 a_2) False) (Eq (eq a a_2) True)) % 3.91/4.07 Clause #15 (by superposition #[14, 0]): ∀ (a : frac), Or (Eq (eq (pf z y) a) False) (Or (Eq (eq (pf z x) a) True) (Eq False True)) % 3.91/4.07 Clause #16 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy : frac), eq (pf a Xy) (pf Xy a)) True % 3.91/4.07 Clause #17 (by clausification #[16]): ∀ (a a_1 : frac), Eq (eq (pf a a_1) (pf a_1 a)) True % 3.91/4.07 Clause #19 (by superposition #[17, 14]): ∀ (a a_1 a_2 : frac), Or (Eq True False) (Or (Eq (eq (pf a a_1) a_2) False) (Eq (eq (pf a_1 a) a_2) True)) % 3.91/4.07 Clause #20 (by clausification #[15]): ∀ (a : frac), Or (Eq (eq (pf z y) a) False) (Eq (eq (pf z x) a) True) % 3.91/4.07 Clause #21 (by superposition #[20, 17]): Or (Eq (eq (pf z x) (pf y z)) True) (Eq False True) % 3.91/4.07 Clause #26 (by clausification #[21]): Eq (eq (pf z x) (pf y z)) True % 3.91/4.07 Clause #30 (by clausification #[19]): ∀ (a a_1 a_2 : frac), Or (Eq (eq (pf a a_1) a_2) False) (Eq (eq (pf a_1 a) a_2) True) % 3.91/4.07 Clause #33 (by superposition #[30, 26]): Or (Eq (eq (pf x z) (pf y z)) True) (Eq False True) % 3.91/4.07 Clause #35 (by clausification #[33]): Eq (eq (pf x z) (pf y z)) True % 3.91/4.07 Clause #36 (by superposition #[35, 9]): Or (Eq True False) (Eq (eq x y) True) % 3.91/4.07 Clause #39 (by clausification #[36]): Eq (eq x y) True % 3.91/4.07 Clause #40 (by superposition #[39, 5]): Eq True False % 3.91/4.07 Clause #42 (by clausification #[40]): False % 3.91/4.07 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------