%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD070-2 : 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 : n006.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 22.98s 4.27s
% Output : CNFRefutation 22.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 26 unt; 2 nHn; 68 RR)
% Number of literals : 143 ( 0 equ; 75 neg)
% Maximal clause size : 4 ( 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 : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(c_is_defined,hypothesis,
defined(c) ).
cnf(add_equals_c_4,negated_conjecture,
equalish(add(a,b),c) ).
cnf(less_or_equal_5,negated_conjecture,
'less$uor$uequal'('additive$uidentity',a) ).
cnf(less_or_equal_6,negated_conjecture,
'less$uor$uequal'('additive$uidentity',b) ).
cnf(not_less_or_equal_7,negated_conjecture,
~ 'less$uor$uequal'('additive$uidentity',c) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ) ).
cnf(commutativity_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| equalish(X0,X1) ) ).
cnf(transitivity_of_order_relation,axiom,
( ~ 'less$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$uequal'(X0,X1) ) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ 'less$uor$uequal'(X0,X2)
| ~ defined(X1)
| 'less$uor$uequal'(add(X0,X1),add(X2,X1)) ) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X1,X0)
| equalish(X0,X1) ) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X2,X0)
| ~ 'less$uor$uequal'(X2,X1)
| 'less$uor$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
defined(c),
inference(clausification,[status(esa)],[c_is_defined]) ).
cnf(c3,plain,
equalish(add(a,b),c),
inference(clausification,[status(esa)],[add_equals_c_4]) ).
cnf(c4,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_5]) ).
cnf(c5,plain,
'less$uor$uequal'('additive$uidentity',b),
inference(clausification,[status(esa)],[less_or_equal_6]) ).
cnf(c6,plain,
~ 'less$uor$uequal'('additive$uidentity',c),
inference(clausification,[status(esa)],[not_less_or_equal_7]) ).
cnf(c8,plain,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c10,plain,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c17,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c22,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
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(c24,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_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(c28,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c29,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c30,plain,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(clausification,[status(esa)],[compatibility_of_equality_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'('additive$uidentity',X0)
| ~ 'less$uor$uequal'(a,X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d1,plain,
( ~ defined(X1)
| ~ equalish(X0,add('additive$uidentity',X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c29,c8]) ).
cnf(d2,plain,
( ~ equalish(X1,'additive$uidentity')
| ~ defined(X0)
| equalish(add(X1,X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,c30]) ).
cnf(d3,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c24]) ).
cnf(d4,plain,
( ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c32,d3]) ).
cnf(d5,plain,
equalish(c,add(a,b)),
inference(resolution,[status(thm)],[c28,c3]) ).
cnf(d6,plain,
( ~ defined(X2)
| ~ defined(X1)
| ~ equalish(X0,add(X2,X1))
| equalish(X0,add(X1,X2)) ),
inference(resolution,[status(thm)],[c29,c10]) ).
cnf(d7,plain,
( equalish(c,add(b,a))
| ~ defined(b)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( equalish(c,add(b,a))
| ~ defined(b) ),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
equalish(c,add(b,a)),
inference(resolution,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
( 'less$uor$uequal'(add(b,a),c)
| ~ defined(c) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
'less$uor$uequal'(add(b,a),c),
inference(resolution,[status(thm)],[c2,d10]) ).
cnf(d12,plain,
( 'less$uor$uequal'(X0,c)
| ~ equalish(add(b,a),X0) ),
inference(resolution,[status(thm)],[d11,c32]) ).
cnf(d13,plain,
( ~ equalish(b,'additive$uidentity')
| ~ defined(a)
| 'less$uor$uequal'(a,c) ),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
( 'less$uor$uequal'(a,c)
| ~ equalish(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
( ~ 'less$uor$uequal'(b,'additive$uidentity')
| equalish(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c22,c5]) ).
cnf(d16,plain,
( 'less$uor$uequal'(c,'additive$uidentity')
| ~ defined(c)
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[c24,c6]) ).
cnf(d17,plain,
( 'less$uor$uequal'(c,'additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[c2,d16]) ).
cnf(d18,plain,
'less$uor$uequal'(c,'additive$uidentity'),
inference(resolution,[status(thm)],[c17,d17]) ).
cnf(d19,plain,
( 'less$uor$uequal'(X0,'additive$uidentity')
| ~ equalish(c,X0) ),
inference(resolution,[status(thm)],[c32,d18]) ).
cnf(d20,plain,
'less$uor$uequal'(add(a,b),'additive$uidentity'),
inference(resolution,[status(thm)],[d19,d5]) ).
cnf(d21,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(d22,plain,
( 'less$uor$uequal'(add(X0,b),'additive$uidentity')
| ~ 'less$uor$uequal'(X0,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( 'less$uor$uequal'(add(X0,b),'additive$uidentity')
| ~ 'less$uor$uequal'(X0,a) ),
inference(resolution,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
( 'less$uor$uequal'(X1,'additive$uidentity')
| ~ equalish(add(X0,b),X1)
| ~ 'less$uor$uequal'(X0,a) ),
inference(resolution,[status(thm)],[d23,c32]) ).
cnf(d25,plain,
( ~ defined(b)
| ~ 'less$uor$uequal'('additive$uidentity',a)
| 'less$uor$uequal'(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[d24,c8]) ).
cnf(d26,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| 'less$uor$uequal'(b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d25]) ).
cnf(d27,plain,
'less$uor$uequal'(b,'additive$uidentity'),
inference(resolution,[status(thm)],[c4,d26]) ).
cnf(d28,plain,
equalish(b,'additive$uidentity'),
inference(resolution,[status(thm)],[d27,d15]) ).
cnf(d29,plain,
'less$uor$uequal'(a,c),
inference(resolution,[status(thm)],[d28,d14]) ).
cnf(d30,plain,
'less$uor$uequal'('additive$uidentity',c),
inference(resolution,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[c6,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 02:34:26 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.98/4.27 % SZS status Unsatisfiable for theBenchmark.p
% 22.98/4.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------