%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD067-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:10:59 AM UTC 2026
% Result : Unsatisfiable 13.36s 3.75s
% Output : CNFRefutation 13.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 9 unt; 0 nHn; 21 RR)
% Number of literals : 41 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(less_or_equal_3,negated_conjecture,
'less$uor$uequal'(a,b) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ 'less$uor$uequal'('additive$uidentity',add(b,'additive$uinverse'(a))) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ 'less$uor$uequal'(X0,X2)
| ~ defined(X1)
| 'less$uor$uequal'(add(X0,X1),add(X2,X1)) ) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X2,X0)
| ~ 'less$uor$uequal'(X2,X1)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
'less$uor$uequal'(a,b),
inference(clausification,[status(esa)],[less_or_equal_3]) ).
cnf(c3,plain,
~ 'less$uor$uequal'('additive$uidentity',add(b,'additive$uinverse'(a))),
inference(clausification,[status(esa)],[not_less_or_equal_4]) ).
cnf(c6,plain,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c15,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c22,plain,
( ~ 'less$uor$uequal'(X0,X2)
| ~ defined(X1)
| 'less$uor$uequal'(add(X0,X1),add(X2,X1)) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(c29,plain,
( ~ equalish(X2,X0)
| ~ 'less$uor$uequal'(X2,X1)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[compatibility_of_equality_and_order_relation]) ).
cnf(d0,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'(add(X1,'additive$uinverse'(X1)),X0)
| 'less$uor$uequal'('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c29,c6]) ).
cnf(d1,plain,
( ~ 'less$uor$uequal'(X0,X1)
| ~ defined('additive$uinverse'(X0))
| 'less$uor$uequal'('additive$uidentity',add(X1,'additive$uinverse'(X0)))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c22]) ).
cnf(d2,plain,
( ~ 'less$uor$uequal'(a,b)
| ~ defined('additive$uinverse'(a))
| ~ defined(a) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'(a,b)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
~ defined(a),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c0,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD067-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 02:33:46 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.36/3.75 % SZS status Unsatisfiable for theBenchmark.p
% 13.36/3.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------