%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD061-1 : 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 : n018.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 52.90s 17.46s
% Output : CNFRefutation 52.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 12 unt; 0 nHn; 27 RR)
% Number of literals : 64 ( 0 equ; 43 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(less_or_equal_5,negated_conjecture,
'less$uor$uequal'(a,b) ).
cnf(less_or_equal_6,negated_conjecture,
'less$uor$uequal'(c,d) ).
cnf(not_less_or_equal_7,negated_conjecture,
~ 'less$uor$uequal'(add(a,c),add(d,b)) ).
cnf(commutativity_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ) ).
cnf(transitivity_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X2,X1)
| ~ 'less$uor$uequal'(X0,X2)
| '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(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,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c4,plain,
'less$uor$uequal'(a,b),
inference(clausification,[status(esa)],[less_or_equal_5]) ).
cnf(c5,plain,
'less$uor$uequal'(c,d),
inference(clausification,[status(esa)],[less_or_equal_6]) ).
cnf(c6,plain,
~ 'less$uor$uequal'(add(a,c),add(d,b)),
inference(clausification,[status(esa)],[not_less_or_equal_7]) ).
cnf(c10,plain,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c23,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,
( ~ '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(c32,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'(add(X1,X0),X3)
| ~ 'less$uor$uequal'(add(X2,X0),X3)
| ~ 'less$uor$uequal'(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c25,c23]) ).
cnf(d1,plain,
( ~ defined(X1)
| ~ defined(X0)
| ~ 'less$uor$uequal'(add(X1,X0),X2)
| 'less$uor$uequal'(add(X0,X1),X2) ),
inference(resolution,[status(thm)],[c32,c10]) ).
cnf(d2,plain,
( ~ 'less$uor$uequal'(X0,X2)
| ~ defined(X1)
| 'less$uor$uequal'(add(X1,X0),add(X2,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( 'less$uor$uequal'(add(X3,X1),add(X2,X0))
| ~ 'less$uor$uequal'(X3,X0)
| ~ defined(X1)
| ~ 'less$uor$uequal'(X1,X2)
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ 'less$uor$uequal'(c,d)
| ~ 'less$uor$uequal'(a,b)
| ~ defined(b)
| ~ defined(c) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( ~ 'less$uor$uequal'(c,d)
| ~ 'less$uor$uequal'(a,b)
| ~ defined(c) ),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
( ~ 'less$uor$uequal'(c,d)
| ~ 'less$uor$uequal'(a,b) ),
inference(resolution,[status(thm)],[c2,d5]) ).
cnf(d7,plain,
~ 'less$uor$uequal'(c,d),
inference(resolution,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c5,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD061-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 02:35:07 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.90/17.46 % SZS status Unsatisfiable for theBenchmark.p
% 52.90/17.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------