%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM016^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:56:01 PM UTC 2025 % Result : Theorem 4.11s 4.31s % Output : Proof 4.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : NUM016^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : duper %s % 0.15/0.35 % Computer : n014.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 08:37:38 EDT 2025 % 0.15/0.35 % CPUTime : % 4.11/4.31 SZS status Theorem for theBenchmark.p % 4.11/4.31 SZS output start Proof for theBenchmark.p % 4.11/4.31 Clause #0 (by assumption #[]): Eq % 4.11/4.31 (Not % 4.11/4.31 (Not % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), divides X X)) % 4.11/4.31 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X))) % 4.11/4.31 (prime a)) % 4.11/4.31 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X))))) % 4.11/4.31 True % 4.11/4.31 Clause #1 (by clausification #[0]): Eq % 4.11/4.31 (Not % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), divides X X)) % 4.11/4.31 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X))) % 4.11/4.31 (prime a)) % 4.11/4.31 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X)))) % 4.11/4.31 False % 4.11/4.31 Clause #2 (by clausification #[1]): Eq % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), divides X X)) % 4.11/4.31 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X))) % 4.11/4.31 (prime a)) % 4.11/4.31 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X))) % 4.11/4.31 True % 4.11/4.31 Clause #3 (by clausification #[2]): Eq (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X)) True % 4.11/4.31 Clause #4 (by clausification #[2]): Eq % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And % 4.11/4.31 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), divides X X)) % 4.11/4.31 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.11/4.31 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.11/4.31 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.11/4.31 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X))) % 4.17/4.33 (prime a)) % 4.17/4.33 True % 4.17/4.33 Clause #5 (by clausification #[3]): ∀ (a_1 : Iota), Eq (Or (Or (Not (prime a_1)) (Not (less a a_1))) (less (factorial_plus_one a) a_1)) True % 4.17/4.33 Clause #6 (by clausification #[5]): ∀ (a_1 : Iota), Or (Eq (Or (Not (prime a_1)) (Not (less a a_1))) True) (Eq (less (factorial_plus_one a) a_1) True) % 4.17/4.33 Clause #7 (by clausification #[6]): ∀ (a_1 : Iota), % 4.17/4.33 Or (Eq (less (factorial_plus_one a) a_1) True) (Or (Eq (Not (prime a_1)) True) (Eq (Not (less a a_1)) True)) % 4.17/4.33 Clause #8 (by clausification #[7]): ∀ (a_1 : Iota), Or (Eq (less (factorial_plus_one a) a_1) True) (Or (Eq (Not (less a a_1)) True) (Eq (prime a_1) False)) % 4.17/4.33 Clause #9 (by clausification #[8]): ∀ (a_1 : Iota), Or (Eq (less (factorial_plus_one a) a_1) True) (Or (Eq (prime a_1) False) (Eq (less a a_1) False)) % 4.17/4.33 Clause #11 (by clausification #[4]): Eq % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), divides X X)) % 4.17/4.33 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X))) % 4.17/4.33 True % 4.17/4.33 Clause #15 (by clausification #[11]): Eq % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), divides X X)) % 4.17/4.33 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X)))) % 4.17/4.33 True % 4.17/4.33 Clause #18 (by clausification #[15]): Eq (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))) True % 4.17/4.33 Clause #19 (by clausification #[15]): Eq % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), divides X X)) % 4.17/4.33 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.17/4.33 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.17/4.33 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X))) % 4.17/4.33 True % 4.17/4.33 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (Or (prime a) (prime (prime_divisor a))) True % 4.17/4.33 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (prime a) True) (Eq (prime (prime_divisor a)) True) % 4.17/4.33 Clause #22 (by superposition #[21, 9]): ∀ (a_1 : Iota), % 4.17/4.33 Or (Eq (prime a_1) True) % 4.17/4.33 (Or (Eq (less (factorial_plus_one a) (prime_divisor a_1)) True) % 4.17/4.33 (Or (Eq True False) (Eq (less a (prime_divisor a_1)) False))) % 4.17/4.33 Clause #23 (by clausification #[19]): Eq (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)) True % 4.17/4.33 Clause #24 (by clausification #[19]): Eq % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And % 4.17/4.33 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.33 (∀ (X : Iota), divides X X)) % 4.17/4.33 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.36 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.36 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.17/4.36 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X))) % 4.17/4.36 True % 4.17/4.36 Clause #25 (by clausification #[23]): ∀ (a : Iota), Eq (Or (prime a) (divides (prime_divisor a) a)) True % 4.17/4.36 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (prime a) True) (Eq (divides (prime_divisor a) a) True) % 4.17/4.36 Clause #27 (by clausification #[22]): ∀ (a_1 : Iota), % 4.17/4.36 Or (Eq (prime a_1) True) % 4.17/4.36 (Or (Eq (less (factorial_plus_one a) (prime_divisor a_1)) True) (Eq (less a (prime_divisor a_1)) False)) % 4.17/4.36 Clause #28 (by clausification #[24]): Eq (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)) True % 4.17/4.36 Clause #29 (by clausification #[24]): Eq % 4.17/4.36 (And % 4.17/4.36 (And % 4.17/4.36 (And % 4.17/4.36 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.36 (∀ (X : Iota), divides X X)) % 4.17/4.36 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.36 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.36 (∀ (X : Iota), less X (factorial_plus_one X))) % 4.17/4.36 True % 4.17/4.36 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (divides a (factorial_plus_one Y))) (less Y a)) True % 4.17/4.36 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Or (Not (divides a (factorial_plus_one a_1))) (less a_1 a)) True % 4.17/4.36 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (Not (divides a (factorial_plus_one a_1))) True) (Eq (less a_1 a) True) % 4.17/4.36 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (less a a_1) True) (Eq (divides a_1 (factorial_plus_one a)) False) % 4.17/4.36 Clause #34 (by superposition #[33, 26]): ∀ (a : Iota), % 4.17/4.36 Or (Eq (less a (prime_divisor (factorial_plus_one a))) True) % 4.17/4.36 (Or (Eq (prime (factorial_plus_one a)) True) (Eq False True)) % 4.17/4.36 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (less a (prime_divisor (factorial_plus_one a))) True) (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 Clause #36 (by superposition #[35, 27]): Or (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 (Or (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 (Or (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True) (Eq True False))) % 4.17/4.36 Clause #37 (by clausification #[36]): Or (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 (Or (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True)) % 4.17/4.36 Clause #38 (by eliminate duplicate literals #[37]): Or (Eq (prime (factorial_plus_one a)) True) % 4.17/4.36 (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True) % 4.17/4.36 Clause #39 (by clausification #[29]): Eq (∀ (X : Iota), less X (factorial_plus_one X)) True % 4.17/4.36 Clause #40 (by clausification #[29]): Eq % 4.17/4.36 (And % 4.17/4.36 (And % 4.17/4.36 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.36 (∀ (X : Iota), divides X X)) % 4.17/4.36 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.36 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X)))) % 4.17/4.36 True % 4.17/4.36 Clause #41 (by clausification #[39]): ∀ (a : Iota), Eq (less a (factorial_plus_one a)) True % 4.17/4.36 Clause #42 (by clausification #[40]): Eq (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))) True % 4.17/4.36 Clause #43 (by clausification #[40]): Eq % 4.17/4.36 (And % 4.17/4.36 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.36 (∀ (X : Iota), divides X X)) % 4.17/4.36 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z))) % 4.17/4.36 True % 4.17/4.36 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (divides a Y)) (Not (less Y a))) True % 4.17/4.36 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Or (Not (divides a a_1)) (Not (less a_1 a))) True % 4.17/4.36 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (Not (divides a a_1)) True) (Eq (Not (less a_1 a)) True) % 4.17/4.36 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Not (less a a_1)) True) (Eq (divides a_1 a) False) % 4.17/4.37 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (divides a a_1) False) (Eq (less a_1 a) False) % 4.17/4.37 Clause #49 (by superposition #[48, 26]): ∀ (a : Iota), Or (Eq (less a (prime_divisor a)) False) (Or (Eq (prime a) True) (Eq False True)) % 4.17/4.37 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (less a (prime_divisor a)) False) (Eq (prime a) True) % 4.17/4.37 Clause #51 (by superposition #[50, 38]): Or (Eq (prime (factorial_plus_one a)) True) (Or (Eq (prime (factorial_plus_one a)) True) (Eq False True)) % 4.17/4.37 Clause #52 (by clausification #[51]): Or (Eq (prime (factorial_plus_one a)) True) (Eq (prime (factorial_plus_one a)) True) % 4.17/4.37 Clause #53 (by eliminate duplicate literals #[52]): Eq (prime (factorial_plus_one a)) True % 4.17/4.37 Clause #55 (by superposition #[53, 9]): Or (Eq (less (factorial_plus_one a) (factorial_plus_one a)) True) % 4.17/4.37 (Or (Eq True False) (Eq (less a (factorial_plus_one a)) False)) % 4.17/4.37 Clause #56 (by clausification #[55]): Or (Eq (less (factorial_plus_one a) (factorial_plus_one a)) True) (Eq (less a (factorial_plus_one a)) False) % 4.17/4.37 Clause #57 (by forward demodulation #[56, 41]): Or (Eq (less (factorial_plus_one a) (factorial_plus_one a)) True) (Eq True False) % 4.17/4.37 Clause #58 (by clausification #[57]): Eq (less (factorial_plus_one a) (factorial_plus_one a)) True % 4.17/4.37 Clause #60 (by clausification #[43]): Eq % 4.17/4.37 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X)))) % 4.17/4.37 (∀ (X : Iota), divides X X)) % 4.17/4.37 True % 4.17/4.37 Clause #69 (by clausification #[60]): Eq (∀ (X : Iota), divides X X) True % 4.17/4.37 Clause #71 (by clausification #[69]): ∀ (a : Iota), Eq (divides a a) True % 4.17/4.37 Clause #73 (by superposition #[71, 48]): ∀ (a : Iota), Or (Eq True False) (Eq (less a a) False) % 4.17/4.37 Clause #75 (by clausification #[73]): ∀ (a : Iota), Eq (less a a) False % 4.17/4.37 Clause #77 (by superposition #[75, 58]): Eq False True % 4.17/4.37 Clause #78 (by clausification #[77]): False % 4.17/4.37 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------