%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM757^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:57:15 PM UTC 2025 % Result : Theorem 5.54s 5.76s % Output : Proof 5.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : NUM757^1 : TPTP v9.2.0. Released v3.7.0. % 0.00/0.11 % Command : duper %s % 0.10/0.30 % Computer : n007.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Fri Oct 3 08:52:38 EDT 2025 % 0.10/0.30 % CPUTime : % 5.54/5.76 SZS status Theorem for theBenchmark.p % 5.54/5.76 SZS output start Proof for theBenchmark.p % 5.54/5.76 Clause #0 (by assumption #[]): Eq (lessf (pf x z) (pf y z)) True % 5.54/5.76 Clause #2 (by assumption #[]): Eq % 5.54/5.76 (∀ (Xx Xy : frac), % 5.54/5.76 Not % 5.54/5.76 ((eq Xx Xy → Not (moref Xx Xy)) → % 5.54/5.76 Not (Not ((moref Xx Xy → Not (lessf Xx Xy)) → Not (lessf Xx Xy → Not (eq Xx Xy)))))) % 5.54/5.76 True % 5.54/5.76 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), moref Xx Xy → moref (pf Xx Xz) (pf Xy Xz)) True % 5.54/5.76 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), eq Xx Xy → eq (pf Xx Xz) (pf Xy Xz)) True % 5.54/5.76 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy : frac), Not (eq Xx Xy) → Not (moref Xx Xy) → lessf Xx Xy) True % 5.54/5.76 Clause #6 (by assumption #[]): Eq (Not (lessf x y)) True % 5.54/5.76 Clause #11 (by clausification #[6]): Eq (lessf x y) False % 5.54/5.76 Clause #12 (by clausification #[5]): ∀ (a : frac), Eq (∀ (Xy : frac), Not (eq a Xy) → Not (moref a Xy) → lessf a Xy) True % 5.54/5.76 Clause #13 (by clausification #[12]): ∀ (a a_1 : frac), Eq (Not (eq a a_1) → Not (moref a a_1) → lessf a a_1) True % 5.54/5.76 Clause #14 (by clausification #[13]): ∀ (a a_1 : frac), Or (Eq (Not (eq a a_1)) False) (Eq (Not (moref a a_1) → lessf a a_1) True) % 5.54/5.76 Clause #15 (by clausification #[14]): ∀ (a a_1 : frac), Or (Eq (Not (moref a a_1) → lessf a a_1) True) (Eq (eq a a_1) True) % 5.54/5.76 Clause #16 (by clausification #[15]): ∀ (a a_1 : frac), Or (Eq (eq a a_1) True) (Or (Eq (Not (moref a a_1)) False) (Eq (lessf a a_1) True)) % 5.54/5.76 Clause #17 (by clausification #[16]): ∀ (a a_1 : frac), Or (Eq (eq a a_1) True) (Or (Eq (lessf a a_1) True) (Eq (moref a a_1) True)) % 5.54/5.76 Clause #18 (by superposition #[17, 11]): Or (Eq (eq x y) True) (Or (Eq (moref x y) True) (Eq True False)) % 5.54/5.76 Clause #19 (by clausification #[18]): Or (Eq (eq x y) True) (Eq (moref x y) True) % 5.54/5.76 Clause #20 (by clausification #[2]): ∀ (a : frac), % 5.54/5.76 Eq % 5.54/5.76 (∀ (Xy : frac), % 5.54/5.76 Not % 5.54/5.76 ((eq a Xy → Not (moref a Xy)) → Not (Not ((moref a Xy → Not (lessf a Xy)) → Not (lessf a Xy → Not (eq a Xy)))))) % 5.54/5.76 True % 5.54/5.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : frac), % 5.54/5.76 Eq % 5.54/5.76 (Not % 5.54/5.76 ((eq a a_1 → Not (moref a a_1)) → % 5.54/5.76 Not (Not ((moref a a_1 → Not (lessf a a_1)) → Not (lessf a a_1 → Not (eq a a_1)))))) % 5.54/5.76 True % 5.54/5.76 Clause #22 (by clausification #[21]): ∀ (a a_1 : frac), % 5.54/5.76 Eq % 5.54/5.76 ((eq a a_1 → Not (moref a a_1)) → % 5.54/5.76 Not (Not ((moref a a_1 → Not (lessf a a_1)) → Not (lessf a a_1 → Not (eq a a_1))))) % 5.54/5.76 False % 5.54/5.76 Clause #24 (by clausification #[22]): ∀ (a a_1 : frac), Eq (Not (Not ((moref a a_1 → Not (lessf a a_1)) → Not (lessf a a_1 → Not (eq a a_1))))) False % 5.54/5.76 Clause #27 (by clausification #[24]): ∀ (a a_1 : frac), Eq (Not ((moref a a_1 → Not (lessf a a_1)) → Not (lessf a a_1 → Not (eq a a_1)))) True % 5.54/5.76 Clause #28 (by clausification #[27]): ∀ (a a_1 : frac), Eq ((moref a a_1 → Not (lessf a a_1)) → Not (lessf a a_1 → Not (eq a a_1))) False % 5.54/5.76 Clause #29 (by clausification #[28]): ∀ (a a_1 : frac), Eq (moref a a_1 → Not (lessf a a_1)) True % 5.54/5.76 Clause #30 (by clausification #[28]): ∀ (a a_1 : frac), Eq (Not (lessf a a_1 → Not (eq a a_1))) False % 5.54/5.76 Clause #31 (by clausification #[29]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Eq (Not (lessf a a_1)) True) % 5.54/5.76 Clause #32 (by clausification #[31]): ∀ (a a_1 : frac), Or (Eq (moref a a_1) False) (Eq (lessf a a_1) False) % 5.54/5.76 Clause #34 (by clausification #[30]): ∀ (a a_1 : frac), Eq (lessf a a_1 → Not (eq a a_1)) True % 5.54/5.76 Clause #35 (by clausification #[34]): ∀ (a a_1 : frac), Or (Eq (lessf a a_1) False) (Eq (Not (eq a a_1)) True) % 5.54/5.76 Clause #36 (by clausification #[35]): ∀ (a a_1 : frac), Or (Eq (lessf a a_1) False) (Eq (eq a a_1) False) % 5.54/5.76 Clause #37 (by superposition #[36, 0]): Or (Eq (eq (pf x z) (pf y z)) False) (Eq False True) % 5.54/5.76 Clause #39 (by clausification #[37]): Eq (eq (pf x z) (pf y z)) False % 5.54/5.76 Clause #41 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), moref a Xy → moref (pf a Xz) (pf Xy Xz)) True % 5.54/5.76 Clause #42 (by clausification #[41]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), moref a a_1 → moref (pf a Xz) (pf a_1 Xz)) True % 5.54/5.76 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : frac), Eq (moref a a_1 → moref (pf a a_2) (pf a_1 a_2)) True % 5.54/5.78 Clause #44 (by clausification #[43]): ∀ (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) % 5.54/5.78 Clause #45 (by superposition #[44, 19]): ∀ (a : frac), Or (Eq (moref (pf x a) (pf y a)) True) (Or (Eq (eq x y) True) (Eq False True)) % 5.54/5.78 Clause #46 (by clausification #[4]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), eq a Xy → eq (pf a Xz) (pf Xy Xz)) True % 5.54/5.78 Clause #47 (by clausification #[46]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), eq a a_1 → eq (pf a Xz) (pf a_1 Xz)) True % 5.54/5.78 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : frac), Eq (eq a a_1 → eq (pf a a_2) (pf a_1 a_2)) True % 5.54/5.78 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Eq (eq (pf a a_2) (pf a_1 a_2)) True) % 5.54/5.78 Clause #51 (by clausification #[45]): ∀ (a : frac), Or (Eq (moref (pf x a) (pf y a)) True) (Eq (eq x y) True) % 5.54/5.78 Clause #52 (by superposition #[51, 32]): ∀ (a : frac), Or (Eq (eq x y) True) (Or (Eq True False) (Eq (lessf (pf x a) (pf y a)) False)) % 5.54/5.78 Clause #54 (by clausification #[52]): ∀ (a : frac), Or (Eq (eq x y) True) (Eq (lessf (pf x a) (pf y a)) False) % 5.54/5.78 Clause #55 (by superposition #[54, 0]): Or (Eq (eq x y) True) (Eq False True) % 5.54/5.78 Clause #57 (by clausification #[55]): Eq (eq x y) True % 5.54/5.78 Clause #62 (by superposition #[57, 49]): ∀ (a : frac), Or (Eq True False) (Eq (eq (pf x a) (pf y a)) True) % 5.54/5.78 Clause #66 (by clausification #[62]): ∀ (a : frac), Eq (eq (pf x a) (pf y a)) True % 5.54/5.78 Clause #67 (by superposition #[66, 39]): Eq True False % 5.54/5.78 Clause #70 (by clausification #[67]): False % 5.54/5.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------