%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD068-4 : 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 : n007.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 11.43s 2.12s
% Output : CNFRefutation 11.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 13 unt; 0 nHn; 31 RR)
% Number of literals : 62 ( 0 equ; 33 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(sum_4,negated_conjecture,
sum(b,'additive$uinverse'(a),u) ).
cnf(less_or_equal_5,negated_conjecture,
'less$uor$uequal'('additive$uidentity',u) ).
cnf(not_less_or_equal_6,negated_conjecture,
~ 'less$uor$uequal'(a,b) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
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$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ 'less$uor$uequal'(X2,X3)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c3,plain,
sum(b,'additive$uinverse'(a),u),
inference(clausification,[status(esa)],[sum_4]) ).
cnf(c4,plain,
'less$uor$uequal'('additive$uidentity',u),
inference(clausification,[status(esa)],[less_or_equal_5]) ).
cnf(c5,plain,
~ 'less$uor$uequal'(a,b),
inference(clausification,[status(esa)],[not_less_or_equal_6]) ).
cnf(c7,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c8,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c9,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c10,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
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,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(d1,plain,
( ~ sum(b,X2,X1)
| ~ sum('additive$uinverse'(a),X0,X2)
| sum(u,X0,X1) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d2,plain,
( ~ defined(a)
| sum(u,a,X0)
| ~ sum(b,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( sum(u,a,X0)
| ~ sum(b,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( ~ defined(b)
| sum(u,a,b) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
sum(u,a,b),
inference(resolution,[status(thm)],[c1,d4]) ).
cnf(d6,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X1,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c29,c8]) ).
cnf(d7,plain,
( ~ 'less$uor$uequal'('additive$uidentity',u)
| 'less$uor$uequal'(a,b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ 'less$uor$uequal'('additive$uidentity',u)
| 'less$uor$uequal'(a,b) ),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
'less$uor$uequal'(a,b),
inference(resolution,[status(thm)],[c4,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c5,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD068-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 02:32:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.43/2.12 % SZS status Unsatisfiable for theBenchmark.p
% 11.43/2.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------