%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD058-3 : 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 : 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 07:10:56 AM UTC 2026
% Result : Unsatisfiable 11.56s 3.25s
% Output : CNFRefutation 11.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 15 unt; 2 nHn; 34 RR)
% Number of literals : 70 ( 0 equ; 38 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 39 ( 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$uequal'(a,b) ).
cnf(not_sum_5,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(sum_6,negated_conjecture,
sum('additive$uidentity',b,'additive$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
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$uequal'(X0,X1) ) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_3]) ).
cnf(c3,plain,
'less$uor$uequal'(a,b),
inference(clausification,[status(esa)],[less_or_equal_4]) ).
cnf(c4,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_5]) ).
cnf(c5,plain,
sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[sum_6]) ).
cnf(c8,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c26,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c27,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(c28,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c29,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,
( 'less$uor$uequal'(a,X0)
| ~ 'less$uor$uequal'(b,X0) ),
inference(resolution,[status(thm)],[c27,c3]) ).
cnf(d1,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c28]) ).
cnf(d2,plain,
sum(b,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c10,c5]) ).
cnf(d3,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d4,plain,
( ~ defined(X0)
| ~ sum(X2,'additive$uidentity',X1)
| ~ 'less$uor$uequal'(X0,X2)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c29,d3]) ).
cnf(d5,plain,
( 'less$uor$uequal'(X0,'additive$uidentity')
| ~ 'less$uor$uequal'(X0,b)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ defined(b)
| 'less$uor$uequal'(b,'additive$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
'less$uor$uequal'(b,'additive$uidentity'),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
'less$uor$uequal'(a,'additive$uidentity'),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c26,c4]) ).
cnf(d10,plain,
~ 'less$uor$uequal'(a,'additive$uidentity'),
inference(resolution,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD058-3 : 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 : n002.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 02:35:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.56/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 11.56/3.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------