%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM014-1 : 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 : n003.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 11.21s 2.05s
% Output : CNFRefutation 11.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 3 nHn; 15 RR)
% Number of literals : 31 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 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 : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(square,axiom,
product(X0,X0,square(X0)) ).
cnf(divides,axiom,
( divides(X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(remainder,axiom,
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,X3)
| ~ product(X1,X2,X3)
| ~ prime(X0) ) ).
cnf(a_is_prime,hypothesis,
prime(a) ).
cnf(a_equals_b_squared_by_c_squared,hypothesis,
product(a,square(c),square(b)) ).
cnf(prove_a_divides_b,negated_conjecture,
~ divides(a,b) ).
cnf(c0,plain,
product(X0,X0,square(X0)),
inference(clausification,[status(esa)],[square]) ).
cnf(c2,plain,
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[divides]) ).
cnf(c3,plain,
( ~ divides(X0,X3)
| divides(X0,X2)
| ~ prime(X0)
| ~ product(X1,X2,X3)
| divides(X0,X1) ),
inference(clausification,[status(esa)],[remainder]) ).
cnf(c4,plain,
prime(a),
inference(clausification,[status(esa)],[a_is_prime]) ).
cnf(c5,plain,
product(a,square(c),square(b)),
inference(clausification,[status(esa)],[a_equals_b_squared_by_c_squared]) ).
cnf(c6,plain,
~ divides(a,b),
inference(clausification,[status(esa)],[prove_a_divides_b]) ).
cnf(d0,plain,
( ~ prime(X0)
| divides(X0,X1)
| divides(X0,X1)
| ~ divides(X0,square(X1)) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
divides(a,square(b)),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d2,plain,
( ~ prime(a)
| divides(a,b) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
divides(a,b),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.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 01:54:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.21/2.05 % SZS status Unsatisfiable for theBenchmark.p
% 11.21/2.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------