%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD067-2 : 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 : n002.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 19.08s 5.69s
% Output : CNFRefutation 19.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 14 unt; 2 nHn; 38 RR)
% Number of literals : 85 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(u_is_defined,hypothesis,
defined(u) ).
cnf(less_or_equal_4,negated_conjecture,
'less$uor$uequal'(a,b) ).
cnf(add_equals_u_5,negated_conjecture,
equalish(add(b,'additive$uinverse'(a)),u) ).
cnf(not_less_or_equal_6,negated_conjecture,
~ 'less$uor$uequal'('additive$uidentity',u) ).
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$uinverse'(X0)) ) ).
cnf(transitivity_of_order_relation,axiom,
( ~ 'less$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$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c2,plain,
defined(u),
inference(clausification,[status(esa)],[u_is_defined]) ).
cnf(c3,plain,
'less$uor$uequal'(a,b),
inference(clausification,[status(esa)],[less_or_equal_4]) ).
cnf(c4,plain,
equalish(add(b,'additive$uinverse'(a)),u),
inference(clausification,[status(esa)],[add_equals_u_5]) ).
cnf(c5,plain,
~ 'less$uor$uequal'('additive$uidentity',u),
inference(clausification,[status(esa)],[not_less_or_equal_6]) ).
cnf(c8,plain,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(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(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(X1)
| ~ 'less$uor$uequal'(add(X1,'additive$uinverse'(X1)),X0)
| 'less$uor$uequal'('additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c31,c8]) ).
cnf(d2,plain,
equalish(u,add(b,'additive$uinverse'(a))),
inference(resolution,[status(thm)],[c27,c4]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'(u,X0)
| 'less$uor$uequal'(add(b,'additive$uinverse'(a)),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'(u,X1)
| 'less$uor$uequal'(add(X0,'additive$uinverse'(a)),X1)
| ~ 'less$uor$uequal'(X0,b)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| ~ defined(a)
| ~ 'less$uor$uequal'(u,X0)
| ~ 'less$uor$uequal'(a,b)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| ~ 'less$uor$uequal'(u,X0)
| ~ 'less$uor$uequal'(a,b)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| ~ 'less$uor$uequal'(u,X0)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c3,d7]) ).
cnf(d9,plain,
( ~ defined(u)
| 'less$uor$uequal'('additive$uidentity',u)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( 'less$uor$uequal'('additive$uidentity',u)
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[c5,d10]) ).
cnf(d12,plain,
~ defined(a),
inference(resolution,[status(thm)],[d11,c17]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c0,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD067-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.41 % Computer : n002.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sun Sep 27 02:36:35 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.08/5.69 % SZS status Unsatisfiable for theBenchmark.p
% 19.08/5.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------