%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:11:01 AM UTC 2026
% Result : Unsatisfiable 5.62s 3.16s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 12 unt; 0 nHn; 20 RR)
% Number of literals : 40 ( 0 equ; 26 neg)
% Maximal clause size : 5 ( 2 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; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(less_or_equal_3,negated_conjecture,
'less$uor$uequal'('additive$uidentity',a) ).
cnf(less_or_equal_4,negated_conjecture,
'less$uor$uequal'('additive$uidentity',b) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ 'less$uor$uequal'('additive$uidentity',multiply(a,b)) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( ~ product(X1,X2,X0)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| 'less$uor$uequal'('additive$uidentity',X0) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_3]) ).
cnf(c3,plain,
'less$uor$uequal'('additive$uidentity',b),
inference(clausification,[status(esa)],[less_or_equal_4]) ).
cnf(c4,plain,
~ 'less$uor$uequal'('additive$uidentity',multiply(a,b)),
inference(clausification,[status(esa)],[not_less_or_equal_5]) ).
cnf(c24,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(c29,plain,
( ~ product(X1,X2,X0)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| 'less$uor$uequal'('additive$uidentity',X0) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_multiplication]) ).
cnf(d0,plain,
( ~ defined(X0)
| ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| 'less$uor$uequal'('additive$uidentity',multiply(X0,X1)) ),
inference(resolution,[status(thm)],[c29,c24]) ).
cnf(d1,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'('additive$uidentity',b)
| ~ defined(a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ 'less$uor$uequal'('additive$uidentity',b)
| ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'('additive$uidentity',b)
| ~ 'less$uor$uequal'('additive$uidentity',a) ),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
~ 'less$uor$uequal'('additive$uidentity',b),
inference(resolution,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c3,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 02:34:59 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.62/3.16 % SZS status Unsatisfiable for theBenchmark.p
% 5.62/3.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------