%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM015-1 : 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 : n015.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 68 ( 36 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_a_has_prime_divisor,axiom,
! [VAR_0] :
( ~ divides(VAR_0,a)
| ~ prime(VAR_0) ),
file('theBenchmark.p',prove_a_has_prime_divisor) ).
cnf(c_1,plain,
( ~ divides(A,a)
| ~ prime(A) ),
inference(clausify,[status(thm)],[prove_a_has_prime_divisor]) ).
fof(factor1,axiom,
! [VAR_0] :
( prime(factor_of(VAR_0))
| ~ less(VAR_0,a)
| ~ less(n1,VAR_0) ),
file('theBenchmark.p',factor1) ).
cnf(c_2,plain,
( prime(factor_of(A))
| ~ less(A,a)
| ~ less(n1,A) ),
inference(clausify,[status(thm)],[factor1]) ).
fof(divisor2,axiom,
! [VAR_0] :
( less(divisor(VAR_0),VAR_0)
| prime(VAR_0) ),
file('theBenchmark.p',divisor2) ).
cnf(c_3,plain,
( less(divisor(A),A)
| prime(A) ),
inference(clausify,[status(thm)],[divisor2]) ).
fof(divisor1,axiom,
! [VAR_0] :
( less(n1,divisor(VAR_0))
| prime(VAR_0) ),
file('theBenchmark.p',divisor1) ).
cnf(c_4,plain,
( less(n1,divisor(A))
| prime(A) ),
inference(clausify,[status(thm)],[divisor1]) ).
fof(prime,axiom,
! [VAR_0] :
( divides(divisor(VAR_0),VAR_0)
| prime(VAR_0) ),
file('theBenchmark.p',prime) ).
cnf(c_5,plain,
( divides(divisor(A),A)
| prime(A) ),
inference(clausify,[status(thm)],[prime]) ).
cnf(c_6,plain,
( divides(divisor(A),A)
| ~ divides(A,a) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_7,plain,
( less(n1,divisor(A))
| ~ divides(A,a) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_8,plain,
( less(divisor(A),A)
| ~ divides(A,a) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_9,plain,
( ~ less(A,a)
| ~ less(n1,A)
| ~ divides(factor_of(A),a) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(factor2,axiom,
! [VAR_0] :
( divides(factor_of(VAR_0),VAR_0)
| ~ less(VAR_0,a)
| ~ less(n1,VAR_0) ),
file('theBenchmark.p',factor2) ).
cnf(c_11,plain,
( divides(factor_of(A),A)
| ~ less(A,a)
| ~ less(n1,A) ),
inference(clausify,[status(thm)],[factor2]) ).
fof(transitive_divide,axiom,
! [VAR_0,VAR_1,VAR_2] :
( divides(VAR_0,VAR_2)
| ~ divides(VAR_1,VAR_2)
| ~ divides(VAR_0,VAR_1) ),
file('theBenchmark.p',transitive_divide) ).
cnf(c_12,plain,
( divides(A,C)
| ~ divides(B,C)
| ~ divides(A,B) ),
inference(clausify,[status(thm)],[transitive_divide]) ).
fof(divide_self,axiom,
! [VAR_0] : divides(VAR_0,VAR_0),
file('theBenchmark.p',divide_self) ).
cnf(c_13,plain,
divides(A,A),
inference(clausify,[status(thm)],[divide_self]) ).
cnf(c_31,plain,
( ~ divides(a,a)
| ~ less(n1,divisor(a))
| ~ divides(factor_of(divisor(a)),a) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_15,plain,
( ~ less(n1,divisor(a))
| ~ divides(factor_of(divisor(a)),a) ),
inference(resolve,[status(thm)],[c_13,c_31]) ).
cnf(c_20,plain,
less(divisor(a),a),
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_21,plain,
less(n1,divisor(a)),
inference(resolve,[status(thm)],[c_7,c_13]) ).
cnf(c_22,plain,
divides(divisor(a),a),
inference(resolve,[status(thm)],[c_6,c_13]) ).
cnf(c_23,plain,
~ divides(factor_of(divisor(a)),a),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_27,plain,
( ~ divides(A,a)
| ~ divides(factor_of(divisor(a)),A) ),
inference(resolve,[status(thm)],[c_23,c_12]) ).
cnf(c_32,plain,
( ~ less(divisor(a),a)
| ~ less(n1,divisor(a))
| ~ divides(divisor(a),a) ),
inference(resolve,[status(thm)],[c_27,c_11]) ).
cnf(c_33,plain,
( ~ less(divisor(a),a)
| ~ less(n1,divisor(a)) ),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_34,plain,
~ less(divisor(a),a),
inference(resolve,[status(thm)],[c_21,c_33]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 01:56:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2852254 was started by sandbox2 on n015,
% 0.11/0.37 % Sat Sep 26 01:56:27 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 19.
% 0.11/0.38 % Level of proof is 5.
% 0.11/0.38 % Maximum clause weight is 10.000.
% 0.11/0.38 % Given clauses 13.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------