%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:18:31 PM UTC 2026
% Result : Unsatisfiable 4.75s 1.10s
% Output : Proof 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 94 ( 37 ~; 57 |; 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 : 43 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( divides(factor_of(X),X)
| ~ less(X,a)
| ~ less(n1,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factor2) ).
fof(f6_nnf,plain,
! [X] :
( divides(factor_of(X),X)
| ~ less(X,a)
| ~ less(n1,X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( divides(factor_of(X),X)
| ~ less(X,a)
| ~ less(n1,X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( divides(factor_of(X0),X0)
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f3,axiom,
( less(n1,divisor(X))
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor1) ).
fof(f3_nnf,plain,
! [X] :
( less(n1,divisor(X))
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( less(n1,divisor(X))
| prime(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less(n1,divisor(X0))
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p13,plain,
( prime(X0)
| divides(factor_of(divisor(X0)),divisor(X0))
| ~ less(divisor(X0),a) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(f4,axiom,
( less(divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor2) ).
fof(f4_nnf,plain,
! [X] :
( less(divisor(X),X)
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( less(divisor(X),X)
| prime(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( less(divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p17,plain,
( prime(a)
| prime(a)
| divides(factor_of(divisor(a)),divisor(a)) ),
inference(resolution,[status(thm)],[p13,c4]) ).
cnf(p21,plain,
( prime(a)
| divides(factor_of(divisor(a)),divisor(a)) ),
inference(factoring,[status(thm)],[p17]) ).
cnf(f1,axiom,
( divides(X,Z)
| ~ divides(Y,Z)
| ~ divides(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_divide) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( divides(X,Z)
| ~ divides(Y,Z)
| ~ divides(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( divides(X,Z)
| ~ divides(Y,Z)
| ~ divides(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p23,plain,
( divides(factor_of(divisor(a)),X0)
| ~ divides(divisor(a),X0)
| prime(a) ),
inference(resolution,[status(thm)],[p21,c1]) ).
cnf(f2,axiom,
( divides(divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime) ).
fof(f2_nnf,plain,
! [X] :
( divides(divisor(X),X)
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( divides(divisor(X),X)
| prime(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( divides(divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p24,plain,
( prime(a)
| divides(factor_of(divisor(a)),a)
| prime(a) ),
inference(resolution,[status(thm)],[p23,c2]) ).
cnf(p25,plain,
( divides(factor_of(divisor(a)),a)
| prime(a) ),
inference(factoring,[status(thm)],[p24]) ).
cnf(f5,axiom,
( prime(factor_of(X))
| ~ less(X,a)
| ~ less(n1,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',factor1) ).
fof(f5_nnf,plain,
! [X] :
( prime(factor_of(X))
| ~ less(X,a)
| ~ less(n1,X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( prime(factor_of(X))
| ~ less(X,a)
| ~ less(n1,X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( prime(factor_of(X0))
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p11,plain,
( prime(X0)
| prime(factor_of(divisor(X0)))
| ~ less(divisor(X0),a) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(p15,plain,
( prime(a)
| prime(a)
| prime(factor_of(divisor(a))) ),
inference(resolution,[status(thm)],[p11,c4]) ).
cnf(p16,plain,
( prime(a)
| prime(factor_of(divisor(a))) ),
inference(factoring,[status(thm)],[p15]) ).
cnf(f8,negated_conjecture,
( ~ divides(X,a)
| ~ prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_has_prime_divisor) ).
fof(f8_nnf,plain,
! [X] :
( ~ divides(X,a)
| ~ prime(X) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] :
( ~ divides(X,a)
| ~ prime(X) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ divides(X0,a)
| ~ prime(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p18,plain,
( ~ divides(factor_of(divisor(a)),a)
| prime(a) ),
inference(resolution,[status(thm)],[p16,c8]) ).
cnf(p27,plain,
( prime(a)
| prime(a) ),
inference(resolution,[status(thm)],[p25,p18]) ).
cnf(p30,plain,
prime(a),
inference(factoring,[status(thm)],[p27]) ).
cnf(p31,plain,
~ divides(a,a),
inference(resolution,[status(thm)],[p30,c8]) ).
cnf(f0,axiom,
divides(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divide_self) ).
fof(f0_nnf,plain,
! [X] : divides(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : divides(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divides(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p32,plain,
$false,
inference(resolution,[status(thm)],[p31,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.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 : Thu Sep 24 02:43:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.75/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------