%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD059-3 : 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 : n005.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 07:10:57 AM UTC 2026
% Result : Unsatisfiable 18.91s 4.25s
% Output : CNFRefutation 18.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 11 unt; 4 nHn; 42 RR)
% Number of literals : 111 ( 0 equ; 74 neg)
% Maximal clause size : 6 ( 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; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(less_or_equal_2,negated_conjecture,
'less$uor$uequal'('additive$uidentity',a) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ 'less$uor$uequal'('additive$uidentity',add(a,a)) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(totality_of_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ) ).
cnf(transitivity_of_order_relation,axiom,
( ~ 'less$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$uequal'(X0,X1) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_2]) ).
cnf(c2,plain,
~ 'less$uor$uequal'('additive$uidentity',add(a,a)),
inference(clausification,[status(esa)],[not_less_or_equal_3]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c6,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c17,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c21,plain,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_addition]) ).
cnf(c23,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c24,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(c25,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c26,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(d0,plain,
( ~ defined(X0)
| ~ sum(X2,X0,X1)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c26,c5]) ).
cnf(d1,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'('additive$uidentity','additive$uinverse'(X0))
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| ~ 'less$uor$uequal'(a,X0) ),
inference(resolution,[status(thm)],[c24,c1]) ).
cnf(d3,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X0,a)
| ~ defined(X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[c25,d2]) ).
cnf(d4,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X0,a)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( ~ defined(X1)
| ~ sum(X2,X1,X0)
| ~ 'less$uor$uequal'('additive$uinverse'(X1),X2)
| 'less$uor$uequal'('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c26,c6]) ).
cnf(d6,plain,
( ~ defined(X0)
| ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uinverse'(X0),X1)
| 'less$uor$uequal'('additive$uidentity',add(X1,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d5,c21]) ).
cnf(d7,plain,
( ~ 'less$uor$uequal'('additive$uinverse'(a),a)
| ~ defined(a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
~ 'less$uor$uequal'('additive$uinverse'(a),a),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( 'less$uor$uequal'('additive$uidentity','additive$uinverse'(a))
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
( 'less$uor$uequal'(a,'additive$uidentity')
| ~ defined(a)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( 'less$uor$uequal'(a,'additive$uidentity')
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d10]) ).
cnf(d12,plain,
( ~ 'less$uor$uequal'(X0,X3)
| ~ 'less$uor$uequal'(X3,X0)
| ~ sum(X2,X3,X1)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c26,c23]) ).
cnf(d13,plain,
( ~ defined(X0)
| ~ defined(X2)
| ~ 'less$uor$uequal'('additive$uidentity',X2)
| 'less$uor$uequal'(X1,add(X2,X0))
| ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d12,c21]) ).
cnf(d14,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'(a,'additive$uidentity')
| ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ defined(a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d14]) ).
cnf(d16,plain,
~ 'less$uor$uequal'(a,'additive$uidentity'),
inference(resolution,[status(thm)],[c1,d15]) ).
cnf(d17,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
~ defined(a),
inference(resolution,[status(thm)],[d17,c17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c0,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 02:32:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.91/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 18.91/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------