%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 4.65s 1.07s
% Output : Proof 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 38 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( divides(X,Z)
| divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',remainder) ).
fof(f3_nnf,plain,
! [X,Y,Z,U] :
( divides(X,Z)
| divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z,U] :
( divides(X,Z)
| divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,X3)
| ~ product(X1,X2,X3)
| ~ prime(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p11,plain,
( divides(X0,X1)
| ~ divides(X0,X2)
| ~ product(X1,X1,X2)
| ~ prime(X0) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(f4,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
fof(f4_nnf,plain,
prime(a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
prime(a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p13,plain,
( divides(a,X0)
| ~ divides(a,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[p11,c4]) ).
cnf(f0,axiom,
product(X,X,square(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square) ).
fof(f0_nnf,plain,
! [X] : product(X,X,square(X)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(X,X,square(X)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(X0,X0,square(X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( divides(a,X0)
| ~ divides(a,square(X0)) ),
inference(resolution,[status(thm)],[p13,c0]) ).
cnf(f2,axiom,
( divides(X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( divides(X,Z)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( divides(X,Z)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f5,hypothesis,
product(a,square(c),square(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
fof(f5_nnf,plain,
product(a,square(c),square(b)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
product(a,square(c),square(b)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p9,plain,
divides(a,square(b)),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(p16,plain,
divides(a,b),
inference(resolution,[status(thm)],[p14,p9]) ).
cnf(f6,negated_conjecture,
~ divides(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divides_b) ).
fof(f6_nnf,plain,
~ divides(a,b),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ divides(a,b),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ divides(a,b),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
$false,
inference(resolution,[status(thm)],[p16,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 02:39:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.65/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.65/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------