%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:10:38 AM UTC 2026
% Result : Unsatisfiable 9.41s 2.88s
% Output : CNFRefutation 9.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 7 unt; 9 nHn; 20 RR)
% Number of literals : 65 ( 0 equ; 33 neg)
% Maximal clause size : 4 ( 2 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)
% Comments :
%------------------------------------------------------------------------------
cnf(divide_self,axiom,
divides(X0,X0) ).
cnf(transitive_divide,axiom,
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ) ).
cnf(prime,axiom,
( divides(divisor(X0),X0)
| prime(X0) ) ).
cnf(divisor1,axiom,
( less(n1,divisor(X0))
| prime(X0) ) ).
cnf(divisor2,axiom,
( less(divisor(X0),X0)
| prime(X0) ) ).
cnf(factor1,axiom,
( prime('factor$uof'(X0))
| ~ less(X0,a)
| ~ less(n1,X0) ) ).
cnf(factor2,axiom,
( divides('factor$uof'(X0),X0)
| ~ less(X0,a)
| ~ less(n1,X0) ) ).
cnf(prove_a_has_prime_divisor,negated_conjecture,
( ~ divides(X0,a)
| ~ prime(X0) ) ).
cnf(c0,plain,
divides(X0,X0),
inference(clausification,[status(esa)],[divide_self]) ).
cnf(c1,plain,
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[transitive_divide]) ).
cnf(c2,plain,
( divides(divisor(X0),X0)
| prime(X0) ),
inference(clausification,[status(esa)],[prime]) ).
cnf(c3,plain,
( less(n1,divisor(X0))
| prime(X0) ),
inference(clausification,[status(esa)],[divisor1]) ).
cnf(c4,plain,
( less(divisor(X0),X0)
| prime(X0) ),
inference(clausification,[status(esa)],[divisor2]) ).
cnf(c5,plain,
( prime('factor$uof'(X0))
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(clausification,[status(esa)],[factor1]) ).
cnf(c6,plain,
( divides('factor$uof'(X0),X0)
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(clausification,[status(esa)],[factor2]) ).
cnf(c8,plain,
( ~ divides(X0,a)
| ~ prime(X0) ),
inference(clausification,[status(esa)],[prove_a_has_prime_divisor]) ).
cnf(d0,plain,
( divides('factor$uof'(X0),X1)
| ~ divides(X0,X1)
| ~ less(n1,X0)
| ~ less(X0,a) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( ~ prime('factor$uof'(X0))
| ~ less(n1,X0)
| ~ less(X0,a)
| ~ divides(X0,a) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( prime(X0)
| ~ less(divisor(X0),a)
| ~ prime('factor$uof'(divisor(X0)))
| ~ divides(divisor(X0),a) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( prime(a)
| ~ prime('factor$uof'(divisor(a)))
| prime(a)
| ~ divides(divisor(a),a) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
~ prime(a),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d5,plain,
( ~ prime('factor$uof'(divisor(a)))
| ~ divides(divisor(a),a) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( prime(X0)
| ~ less(divisor(X0),a)
| prime('factor$uof'(divisor(X0))) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d7,plain,
( prime(a)
| prime('factor$uof'(divisor(a)))
| prime(a) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
prime('factor$uof'(divisor(a))),
inference(resolution,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
~ divides(divisor(a),a),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
prime(a),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d4,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n017.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sat Sep 26 01:48:47 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.41/2.88 % SZS status Unsatisfiable for theBenchmark.p
% 9.41/2.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------