TSTP Solution File: NUM016^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 : Thu Aug 31 10:54:21 EDT 2023
% Result : Theorem 3.64s 3.82s
% Output : Proof 3.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.16/0.36 % Computer : n010.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Aug 25 08:34:20 EDT 2023
% 0.16/0.36 % CPUTime :
% 3.64/3.82 SZS status Theorem for theBenchmark.p
% 3.64/3.82 SZS output start Proof for theBenchmark.p
% 3.64/3.82 Clause #0 (by assumption #[]): Eq
% 3.64/3.82 (Not
% 3.64/3.82 (Not
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), divides X X))
% 3.64/3.82 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X)))
% 3.64/3.82 (prime a))
% 3.64/3.82 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X)))))
% 3.64/3.82 True
% 3.64/3.82 Clause #1 (by clausification #[0]): Eq
% 3.64/3.82 (Not
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), divides X X))
% 3.64/3.82 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X)))
% 3.64/3.82 (prime a))
% 3.64/3.82 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X))))
% 3.64/3.82 False
% 3.64/3.82 Clause #2 (by clausification #[1]): Eq
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), divides X X))
% 3.64/3.82 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X)))
% 3.64/3.82 (prime a))
% 3.64/3.82 (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X)))
% 3.64/3.82 True
% 3.64/3.82 Clause #3 (by clausification #[2]): Eq (∀ (X : Iota), Or (Or (Not (prime X)) (Not (less a X))) (less (factorial_plus_one a) X)) True
% 3.64/3.82 Clause #4 (by clausification #[2]): Eq
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And
% 3.64/3.82 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), divides X X))
% 3.64/3.82 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.82 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.82 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.82 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X)))
% 3.64/3.85 (prime a))
% 3.64/3.85 True
% 3.64/3.85 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
% 3.64/3.85 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)
% 3.64/3.85 Clause #7 (by clausification #[6]): ∀ (a_1 : Iota),
% 3.64/3.85 Or (Eq (less (factorial_plus_one a) a_1) True) (Or (Eq (Not (prime a_1)) True) (Eq (Not (less a a_1)) True))
% 3.64/3.85 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))
% 3.64/3.85 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))
% 3.64/3.85 Clause #11 (by clausification #[4]): Eq
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), divides X X))
% 3.64/3.85 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (less (prime_divisor X) X)))
% 3.64/3.85 True
% 3.64/3.85 Clause #15 (by clausification #[11]): Eq
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), divides X X))
% 3.64/3.85 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))))
% 3.64/3.85 True
% 3.64/3.85 Clause #18 (by clausification #[15]): Eq (∀ (X : Iota), Or (prime X) (prime (prime_divisor X))) True
% 3.64/3.85 Clause #19 (by clausification #[15]): Eq
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), divides X X))
% 3.64/3.85 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.85 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.85 (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)))
% 3.64/3.85 True
% 3.64/3.85 Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (Or (prime a) (prime (prime_divisor a))) True
% 3.64/3.85 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (prime a) True) (Eq (prime (prime_divisor a)) True)
% 3.64/3.85 Clause #22 (by superposition #[21, 9]): ∀ (a_1 : Iota),
% 3.64/3.85 Or (Eq (prime a_1) True)
% 3.64/3.85 (Or (Eq (less (factorial_plus_one a) (prime_divisor a_1)) True)
% 3.64/3.85 (Or (Eq True False) (Eq (less a (prime_divisor a_1)) False)))
% 3.64/3.85 Clause #23 (by clausification #[19]): Eq (∀ (X : Iota), Or (prime X) (divides (prime_divisor X) X)) True
% 3.64/3.85 Clause #24 (by clausification #[19]): Eq
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And
% 3.64/3.85 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.85 (∀ (X : Iota), divides X X))
% 3.64/3.85 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.87 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.87 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.87 (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)))
% 3.64/3.87 True
% 3.64/3.87 Clause #25 (by clausification #[23]): ∀ (a : Iota), Eq (Or (prime a) (divides (prime_divisor a) a)) True
% 3.64/3.87 Clause #26 (by clausification #[25]): ∀ (a : Iota), Or (Eq (prime a) True) (Eq (divides (prime_divisor a) a) True)
% 3.64/3.87 Clause #27 (by clausification #[22]): ∀ (a_1 : Iota),
% 3.64/3.87 Or (Eq (prime a_1) True)
% 3.64/3.87 (Or (Eq (less (factorial_plus_one a) (prime_divisor a_1)) True) (Eq (less a (prime_divisor a_1)) False))
% 3.64/3.87 Clause #28 (by clausification #[24]): Eq (∀ (X Y : Iota), Or (Not (divides X (factorial_plus_one Y))) (less Y X)) True
% 3.64/3.87 Clause #29 (by clausification #[24]): Eq
% 3.64/3.87 (And
% 3.64/3.87 (And
% 3.64/3.87 (And
% 3.64/3.87 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.87 (∀ (X : Iota), divides X X))
% 3.64/3.87 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.87 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.87 (∀ (X : Iota), less X (factorial_plus_one X)))
% 3.64/3.87 True
% 3.64/3.87 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (divides a (factorial_plus_one Y))) (less Y a)) True
% 3.64/3.87 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Or (Not (divides a (factorial_plus_one a_1))) (less a_1 a)) True
% 3.64/3.87 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)
% 3.64/3.87 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)
% 3.64/3.87 Clause #34 (by superposition #[33, 26]): ∀ (a : Iota),
% 3.64/3.87 Or (Eq (less a (prime_divisor (factorial_plus_one a))) True)
% 3.64/3.87 (Or (Eq (prime (factorial_plus_one a)) True) (Eq False True))
% 3.64/3.87 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)
% 3.64/3.87 Clause #36 (by superposition #[35, 27]): Or (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.87 (Or (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.87 (Or (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True) (Eq True False)))
% 3.64/3.87 Clause #37 (by clausification #[36]): Or (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.87 (Or (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.87 (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True))
% 3.64/3.87 Clause #38 (by eliminate duplicate literals #[37]): Or (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.87 (Eq (less (factorial_plus_one a) (prime_divisor (factorial_plus_one a))) True)
% 3.64/3.87 Clause #39 (by clausification #[29]): Eq (∀ (X : Iota), less X (factorial_plus_one X)) True
% 3.64/3.87 Clause #40 (by clausification #[29]): Eq
% 3.64/3.87 (And
% 3.64/3.87 (And
% 3.64/3.87 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.87 (∀ (X : Iota), divides X X))
% 3.64/3.87 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.87 (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))))
% 3.64/3.87 True
% 3.64/3.87 Clause #41 (by clausification #[39]): ∀ (a : Iota), Eq (less a (factorial_plus_one a)) True
% 3.64/3.87 Clause #42 (by clausification #[40]): Eq (∀ (X Y : Iota), Or (Not (divides X Y)) (Not (less Y X))) True
% 3.64/3.87 Clause #43 (by clausification #[40]): Eq
% 3.64/3.87 (And
% 3.64/3.87 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.87 (∀ (X : Iota), divides X X))
% 3.64/3.87 (∀ (X Y Z : Iota), Or (Or (Not (divides X Y)) (Not (divides Y Z))) (divides X Z)))
% 3.64/3.87 True
% 3.64/3.87 Clause #44 (by clausification #[42]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Not (divides a Y)) (Not (less Y a))) True
% 3.64/3.87 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Or (Not (divides a a_1)) (Not (less a_1 a))) True
% 3.64/3.87 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (Not (divides a a_1)) True) (Eq (Not (less a_1 a)) True)
% 3.64/3.87 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (Not (less a a_1)) True) (Eq (divides a_1 a) False)
% 3.64/3.88 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (divides a a_1) False) (Eq (less a_1 a) False)
% 3.64/3.88 Clause #49 (by superposition #[48, 26]): ∀ (a : Iota), Or (Eq (less a (prime_divisor a)) False) (Or (Eq (prime a) True) (Eq False True))
% 3.64/3.88 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (less a (prime_divisor a)) False) (Eq (prime a) True)
% 3.64/3.88 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))
% 3.64/3.88 Clause #52 (by clausification #[51]): Or (Eq (prime (factorial_plus_one a)) True) (Eq (prime (factorial_plus_one a)) True)
% 3.64/3.88 Clause #53 (by eliminate duplicate literals #[52]): Eq (prime (factorial_plus_one a)) True
% 3.64/3.88 Clause #55 (by superposition #[53, 9]): Or (Eq (less (factorial_plus_one a) (factorial_plus_one a)) True)
% 3.64/3.88 (Or (Eq True False) (Eq (less a (factorial_plus_one a)) False))
% 3.64/3.88 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)
% 3.64/3.88 Clause #57 (by forward demodulation #[56, 41]): Or (Eq (less (factorial_plus_one a) (factorial_plus_one a)) True) (Eq True False)
% 3.64/3.88 Clause #58 (by clausification #[57]): Eq (less (factorial_plus_one a) (factorial_plus_one a)) True
% 3.64/3.88 Clause #60 (by clausification #[43]): Eq
% 3.64/3.88 (And (And (∀ (X : Iota), Not (less X X)) (∀ (X Y : Iota), Or (Not (less X Y)) (Not (less Y X))))
% 3.64/3.88 (∀ (X : Iota), divides X X))
% 3.64/3.88 True
% 3.64/3.88 Clause #69 (by clausification #[60]): Eq (∀ (X : Iota), divides X X) True
% 3.64/3.88 Clause #71 (by clausification #[69]): ∀ (a : Iota), Eq (divides a a) True
% 3.64/3.88 Clause #73 (by superposition #[71, 48]): ∀ (a : Iota), Or (Eq True False) (Eq (less a a) False)
% 3.64/3.88 Clause #75 (by clausification #[73]): ∀ (a : Iota), Eq (less a a) False
% 3.64/3.88 Clause #77 (by superposition #[75, 58]): Eq False True
% 3.64/3.88 Clause #78 (by clausification #[77]): False
% 3.64/3.88 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------