%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD006-1 : 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 : n016.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 07:10:42 AM UTC 2026
% Result : Unsatisfiable 11.93s 3.67s
% Output : CNFRefutation 11.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 7 unt; 0 nHn; 22 RR)
% Number of literals : 41 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_inverse_not_equal_to_additive_identity_1,negated_conjecture,
~ equalish('additive$uinverse'('additive$uidentity'),'additive$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X1,X0)
| equalish(X0,X1) ) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ) ).
cnf(c0,plain,
~ equalish('additive$uinverse'('additive$uidentity'),'additive$uidentity'),
inference(clausification,[status(esa)],[additive_inverse_not_equal_to_additive_identity_1]) ).
cnf(c2,plain,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c3,plain,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c11,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c12,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c22,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c23,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(d0,plain,
( ~ defined(X0)
| equalish('additive$uidentity',add(X0,'additive$uinverse'(X0))) ),
inference(resolution,[status(thm)],[c22,c3]) ).
cnf(d1,plain,
( ~ defined(X1)
| ~ equalish(X0,add('additive$uidentity',X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(d2,plain,
( ~ defined('additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity'))
| equalish('additive$uidentity','additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ defined('additive$uinverse'('additive$uidentity'))
| equalish('additive$uidentity','additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[c11,d2]) ).
cnf(d4,plain,
( equalish('additive$uinverse'('additive$uidentity'),'additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[d3,c22]) ).
cnf(d5,plain,
~ defined('additive$uinverse'('additive$uidentity')),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
~ defined('additive$uidentity'),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c11,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n016.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 02:25:31 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.93/3.67 % SZS status Unsatisfiable for theBenchmark.p
% 11.93/3.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------