%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:16:02 AM UTC 2026
% Result : Unsatisfiable 0.04s 0.37s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(division_by_prime_divisor,axiom,
! [VAR_0] :
( divides(prime_divisor(VAR_0),VAR_0)
| prime(VAR_0) ),
file('theBenchmark.p',division_by_prime_divisor) ).
cnf(c_1,plain,
( divides(prime_divisor(A),A)
| prime(A) ),
inference(clausify,[status(thm)],[division_by_prime_divisor]) ).
fof(divisor_is_smaller,axiom,
! [VAR_0,VAR_1] :
( less(VAR_1,VAR_0)
| ~ divides(VAR_0,factorial_plus_one(VAR_1)) ),
file('theBenchmark.p',divisor_is_smaller) ).
cnf(c_2,plain,
( less(B,A)
| ~ divides(A,factorial_plus_one(B)) ),
inference(clausify,[status(thm)],[divisor_is_smaller]) ).
cnf(c_3,plain,
( less(A,prime_divisor(factorial_plus_one(A)))
| prime(factorial_plus_one(A)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_there_is_another_prime,axiom,
! [VAR_0] :
( less(factorial_plus_one(a),VAR_0)
| ~ less(a,VAR_0)
| ~ prime(VAR_0) ),
file('theBenchmark.p',prove_there_is_another_prime) ).
cnf(c_4,plain,
( less(factorial_plus_one(a),A)
| ~ less(a,A)
| ~ prime(A) ),
inference(clausify,[status(thm)],[prove_there_is_another_prime]) ).
fof(smaller_prime_divisors,axiom,
! [VAR_0] :
( less(prime_divisor(VAR_0),VAR_0)
| prime(VAR_0) ),
file('theBenchmark.p',smaller_prime_divisors) ).
cnf(c_5,plain,
( less(prime_divisor(A),A)
| prime(A) ),
inference(clausify,[status(thm)],[smaller_prime_divisors]) ).
fof(prime_divsiors,axiom,
! [VAR_0] :
( prime(prime_divisor(VAR_0))
| prime(VAR_0) ),
file('theBenchmark.p',prime_divsiors) ).
cnf(c_6,plain,
( prime(prime_divisor(A))
| prime(A) ),
inference(clausify,[status(thm)],[prime_divsiors]) ).
fof(a_prime_is_less_than_the_next_one,axiom,
! [VAR_0] : less(VAR_0,factorial_plus_one(VAR_0)),
file('theBenchmark.p',a_prime_is_less_than_the_next_one) ).
cnf(c_7,plain,
less(A,factorial_plus_one(A)),
inference(clausify,[status(thm)],[a_prime_is_less_than_the_next_one]) ).
fof(numbers_are_different,axiom,
! [VAR_0,VAR_1] :
( ~ less(VAR_1,VAR_0)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',numbers_are_different) ).
cnf(c_8,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[numbers_are_different]) ).
fof(nothing_is_less_than_itself,axiom,
! [VAR_0] : ~ less(VAR_0,VAR_0),
file('theBenchmark.p',nothing_is_less_than_itself) ).
cnf(c_9,plain,
~ less(A,A),
inference(clausify,[status(thm)],[nothing_is_less_than_itself]) ).
cnf(c_18,plain,
( prime(A)
| less(factorial_plus_one(a),prime_divisor(A))
| ~ less(a,prime_divisor(A)) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_19,plain,
( prime(factorial_plus_one(a))
| prime(factorial_plus_one(a))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolve,[status(thm)],[c_18,c_3]) ).
cnf(c_11,plain,
( prime(factorial_plus_one(a))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_20,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_12,plain,
~ prime(factorial_plus_one(a)),
inference(resolve,[status(thm)],[c_9,c_20]) ).
cnf(c_13,plain,
less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_15,plain,
( prime(A)
| ~ less(A,prime_divisor(A)) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_21,plain,
~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolve,[status(thm)],[c_15,c_12]) ).
cnf(c_17,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 01:53:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.04/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.36 % Process 144301 was started by sandbox2 on n019,
% 0.04/0.36 % Sat Sep 26 01:53:33 2026
% 0.04/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.36
% 0.04/0.36 % From the command line: assign(max_seconds, 300).
% 0.04/0.37
% 0.04/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.04/0.37
% 0.04/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.37 % Length of proof is 14.
% 0.04/0.37 % Level of proof is 4.
% 0.04/0.37 % Maximum clause weight is 24.000.
% 0.04/0.37 % Given clauses 10.
% 0.04/0.37
% 0.04/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------