%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD069-1 : 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 : n010.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 07:11:00 AM UTC 2026
% Result : Unsatisfiable 20.48s 5.22s
% Output : CNFRefutation 20.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 16 unt; 2 nHn; 41 RR)
% Number of literals : 88 ( 0 equ; 48 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(b_not_equal_to_additive_identity_5,negated_conjecture,
~ equalish(b,'additive$uidentity') ).
cnf(add_equals_additive_identity_6,negated_conjecture,
equalish(add(a,b),'additive$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| equalish(X0,X1) ) ).
cnf(transitivity_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X2,X1)
| ~ 'less$uor$uequal'(X0,X2)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ) ).
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(symmetry_of_equality,axiom,
( ~ equalish(X1,X0)
| equalish(X0,X1) ) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X2,X0)
| ~ 'less$uor$uequal'(X2,X1)
| 'less$uor$uequal'(X0,X1) ) ).
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,
~ equalish(b,'additive$uidentity'),
inference(clausification,[status(esa)],[b_not_equal_to_additive_identity_5]) ).
cnf(c5,plain,
equalish(add(a,b),'additive$uidentity'),
inference(clausification,[status(esa)],[add_equals_additive_identity_6]) ).
cnf(c7,plain,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c16,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c21,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c22,plain,
( ~ 'less$uor$uequal'(X2,X1)
| ~ 'less$uor$uequal'(X0,X2)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_order_relation]) ).
cnf(c23,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c24,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(c27,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c31,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,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c23]) ).
cnf(d1,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'(add('additive$uidentity',X0),X1)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c31,c7]) ).
cnf(d2,plain,
equalish('additive$uidentity',add(a,b)),
inference(resolution,[status(thm)],[c27,c5]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(add(a,b),X0) ),
inference(resolution,[status(thm)],[c31,d2]) ).
cnf(d4,plain,
( 'less$uor$uequal'(add(X1,X0),X3)
| ~ 'less$uor$uequal'(add(X2,X0),X3)
| ~ 'less$uor$uequal'(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c24,c22]) ).
cnf(d5,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X1)
| 'less$uor$uequal'(add(X0,b),X1)
| ~ 'less$uor$uequal'(X0,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'less$uor$uequal'(add(X0,b),X1)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| ~ 'less$uor$uequal'(X0,a) ),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( 'less$uor$uequal'(b,X0)
| ~ defined(b)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| ~ 'less$uor$uequal'('additive$uidentity',a) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(b,X0) ),
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(b,X0) ),
inference(resolution,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( ~ defined('additive$uidentity')
| 'less$uor$uequal'(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
'less$uor$uequal'(b,'additive$uidentity'),
inference(resolution,[status(thm)],[c16,d10]) ).
cnf(d12,plain,
( equalish(b,'additive$uidentity')
| ~ 'less$uor$uequal'(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c21,c3]) ).
cnf(d13,plain,
~ 'less$uor$uequal'(b,'additive$uidentity'),
inference(resolution,[status(thm)],[c4,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.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 02:35:01 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.48/5.22 % SZS status Unsatisfiable for theBenchmark.p
% 20.48/5.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------