%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM746^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 07:57:13 PM UTC 2025 % Result : Theorem 4.07s 4.23s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM746^1 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.14/0.35 % Computer : n018.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 07:35:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.07/4.23 SZS status Theorem for theBenchmark.p % 4.07/4.23 SZS output start Proof for theBenchmark.p % 4.07/4.23 Clause #0 (by assumption #[]): Eq (Not (lessf x y) → eq x y) True % 4.07/4.23 Clause #1 (by assumption #[]): Eq (Not (lessf y z) → eq y z) True % 4.07/4.23 Clause #3 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), eq Xx Xy → eq Xy Xz → eq Xx Xz) True % 4.07/4.23 Clause #4 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), lessf Xx Xy → (Not (lessf Xy Xz) → eq Xy Xz) → lessf Xx Xz) True % 4.07/4.23 Clause #5 (by assumption #[]): Eq (∀ (Xx Xy Xz : frac), (Not (lessf Xx Xy) → eq Xx Xy) → lessf Xy Xz → lessf Xx Xz) True % 4.07/4.23 Clause #6 (by assumption #[]): Eq (Not (Not (lessf x z) → eq x z)) True % 4.07/4.23 Clause #11 (by clausification #[1]): Or (Eq (Not (lessf y z)) False) (Eq (eq y z) True) % 4.07/4.23 Clause #12 (by clausification #[11]): Or (Eq (eq y z) True) (Eq (lessf y z) True) % 4.07/4.23 Clause #13 (by clausification #[0]): Or (Eq (Not (lessf x y)) False) (Eq (eq x y) True) % 4.07/4.23 Clause #14 (by clausification #[13]): Or (Eq (eq x y) True) (Eq (lessf x y) True) % 4.07/4.23 Clause #15 (by clausification #[6]): Eq (Not (lessf x z) → eq x z) False % 4.07/4.23 Clause #16 (by clausification #[15]): Eq (Not (lessf x z)) True % 4.07/4.23 Clause #17 (by clausification #[15]): Eq (eq x z) False % 4.07/4.23 Clause #18 (by clausification #[16]): Eq (lessf x z) False % 4.07/4.23 Clause #19 (by clausification #[3]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), eq a Xy → eq Xy Xz → eq a Xz) True % 4.07/4.23 Clause #20 (by clausification #[19]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), eq a a_1 → eq a_1 Xz → eq a Xz) True % 4.07/4.23 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : frac), Eq (eq a a_1 → eq a_1 a_2 → eq a a_2) True % 4.07/4.23 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Eq (eq a_1 a_2 → eq a a_2) True) % 4.07/4.23 Clause #23 (by clausification #[22]): ∀ (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)) % 4.07/4.23 Clause #25 (by superposition #[23, 14]): ∀ (a : frac), Or (Eq (eq y a) False) (Or (Eq (eq x a) True) (Or (Eq False True) (Eq (lessf x y) True))) % 4.07/4.23 Clause #26 (by clausification #[5]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), (Not (lessf a Xy) → eq a Xy) → lessf Xy Xz → lessf a Xz) True % 4.07/4.23 Clause #27 (by clausification #[26]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), (Not (lessf a a_1) → eq a a_1) → lessf a_1 Xz → lessf a Xz) True % 4.07/4.23 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : frac), Eq ((Not (lessf a a_1) → eq a a_1) → lessf a_1 a_2 → lessf a a_2) True % 4.07/4.23 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : frac), Or (Eq (Not (lessf a a_1) → eq a a_1) False) (Eq (lessf a_1 a_2 → lessf a a_2) True) % 4.07/4.23 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1 → lessf a_2 a_1) True) (Eq (eq a_2 a) False) % 4.07/4.23 Clause #34 (by clausification #[31]): ∀ (a a_1 a_2 : frac), Or (Eq (eq a a_1) False) (Or (Eq (lessf a_1 a_2) False) (Eq (lessf a a_2) True)) % 4.07/4.23 Clause #36 (by superposition #[34, 14]): ∀ (a : frac), Or (Eq (lessf y a) False) (Or (Eq (lessf x a) True) (Or (Eq False True) (Eq (lessf x y) True))) % 4.07/4.23 Clause #37 (by clausification #[4]): ∀ (a : frac), Eq (∀ (Xy Xz : frac), lessf a Xy → (Not (lessf Xy Xz) → eq Xy Xz) → lessf a Xz) True % 4.07/4.23 Clause #38 (by clausification #[37]): ∀ (a a_1 : frac), Eq (∀ (Xz : frac), lessf a a_1 → (Not (lessf a_1 Xz) → eq a_1 Xz) → lessf a Xz) True % 4.07/4.23 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : frac), Eq (lessf a a_1 → (Not (lessf a_1 a_2) → eq a_1 a_2) → lessf a a_2) True % 4.07/4.23 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Eq ((Not (lessf a_1 a_2) → eq a_1 a_2) → lessf a a_2) True) % 4.07/4.23 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : frac), % 4.07/4.23 Or (Eq (lessf a a_1) False) (Or (Eq (Not (lessf a_1 a_2) → eq a_1 a_2) False) (Eq (lessf a a_2) True)) % 4.07/4.23 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Or (Eq (lessf a a_2) True) (Eq (Not (lessf a_1 a_2)) True)) % 4.07/4.23 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Or (Eq (lessf a a_2) True) (Eq (eq a_1 a_2) False)) % 4.07/4.23 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : frac), Or (Eq (lessf a a_1) False) (Or (Eq (lessf a a_2) True) (Eq (lessf a_1 a_2) False)) % 4.07/4.26 Clause #46 (by clausification #[25]): ∀ (a : frac), Or (Eq (eq y a) False) (Or (Eq (eq x a) True) (Eq (lessf x y) True)) % 4.07/4.26 Clause #47 (by superposition #[46, 12]): Or (Eq (eq x z) True) (Or (Eq (lessf x y) True) (Or (Eq False True) (Eq (lessf y z) True))) % 4.07/4.26 Clause #48 (by clausification #[47]): Or (Eq (eq x z) True) (Or (Eq (lessf x y) True) (Eq (lessf y z) True)) % 4.07/4.26 Clause #49 (by superposition #[48, 17]): Or (Eq (lessf x y) True) (Or (Eq (lessf y z) True) (Eq True False)) % 4.07/4.26 Clause #52 (by clausification #[49]): Or (Eq (lessf x y) True) (Eq (lessf y z) True) % 4.07/4.26 Clause #55 (by superposition #[52, 43]): ∀ (a : frac), Or (Eq (lessf y z) True) (Or (Eq True False) (Or (Eq (lessf x a) True) (Eq (eq y a) False))) % 4.07/4.26 Clause #56 (by clausification #[55]): ∀ (a : frac), Or (Eq (lessf y z) True) (Or (Eq (lessf x a) True) (Eq (eq y a) False)) % 4.07/4.26 Clause #57 (by superposition #[56, 12]): Or (Eq (lessf y z) True) (Or (Eq (lessf x z) True) (Or (Eq False True) (Eq (lessf y z) True))) % 4.07/4.26 Clause #58 (by clausification #[57]): Or (Eq (lessf y z) True) (Or (Eq (lessf x z) True) (Eq (lessf y z) True)) % 4.07/4.26 Clause #59 (by eliminate duplicate literals #[58]): Or (Eq (lessf y z) True) (Eq (lessf x z) True) % 4.07/4.26 Clause #60 (by superposition #[59, 18]): Or (Eq (lessf y z) True) (Eq True False) % 4.07/4.26 Clause #64 (by clausification #[60]): Eq (lessf y z) True % 4.07/4.26 Clause #75 (by clausification #[36]): ∀ (a : frac), Or (Eq (lessf y a) False) (Or (Eq (lessf x a) True) (Eq (lessf x y) True)) % 4.07/4.26 Clause #76 (by superposition #[75, 64]): Or (Eq (lessf x z) True) (Or (Eq (lessf x y) True) (Eq False True)) % 4.07/4.26 Clause #77 (by clausification #[76]): Or (Eq (lessf x z) True) (Eq (lessf x y) True) % 4.07/4.26 Clause #78 (by forward demodulation #[77, 18]): Or (Eq False True) (Eq (lessf x y) True) % 4.07/4.26 Clause #79 (by clausification #[78]): Eq (lessf x y) True % 4.07/4.26 Clause #83 (by superposition #[79, 44]): ∀ (a : frac), Or (Eq True False) (Or (Eq (lessf x a) True) (Eq (lessf y a) False)) % 4.07/4.26 Clause #86 (by clausification #[83]): ∀ (a : frac), Or (Eq (lessf x a) True) (Eq (lessf y a) False) % 4.07/4.26 Clause #87 (by superposition #[86, 64]): Or (Eq (lessf x z) True) (Eq False True) % 4.07/4.26 Clause #90 (by clausification #[87]): Eq (lessf x z) True % 4.07/4.26 Clause #91 (by superposition #[90, 18]): Eq True False % 4.07/4.26 Clause #95 (by clausification #[91]): False % 4.07/4.26 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------