%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD064-1 : 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 : n003.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 07:10:58 AM UTC 2026
% Result : Unsatisfiable 71.94s 22.42s
% Output : CNFRefutation 71.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of clauses : 78 ( 14 unt; 2 nHn; 78 RR)
% Number of literals : 200 ( 0 equ; 127 neg)
% Maximal clause size : 4 ( 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; 3 con; 0-2 aty)
% Number of variables : 107 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(less_or_equal_2,negated_conjecture,
'less$uor$uequal'('additive$uidentity',a) ).
cnf(not_less_or_equal_3,negated_conjecture,
~ 'less$uor$uequal'('additive$uinverse'(a),'additive$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| equalish(multiply('multiplicative$uidentity',X0),X0) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$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$uequal'(X0,X1) ) ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
'less$uor$uequal'('additive$uidentity',a),
inference(clausification,[status(esa)],[less_or_equal_2]) ).
cnf(c2,plain,
~ 'less$uor$uequal'('additive$uinverse'(a),'additive$uidentity'),
inference(clausification,[status(esa)],[not_less_or_equal_3]) ).
cnf(c4,plain,
( ~ defined(X0)
| equalish(add('additive$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c5,plain,
( ~ defined(X0)
| equalish(add(X0,'additive$uinverse'(X0)),'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c6,plain,
( ~ defined(X1)
| equalish(add(X0,X1),add(X1,X0))
| ~ defined(X0) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c8,plain,
( ~ defined(X0)
| equalish(multiply('multiplicative$uidentity',X0),X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c13,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c14,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c18,plain,
( ~ 'less$uor$uequal'(X1,X0)
| equalish(X0,X1)
| ~ 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c19,plain,
( ~ 'less$uor$uequal'(X1,X2)
| 'less$uor$uequal'(X0,X2)
| ~ 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_order_relation]) ).
cnf(c20,plain,
( ~ defined(X1)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1)
| ~ defined(X0) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c21,plain,
( ~ 'less$uor$uequal'(X1,X2)
| 'less$uor$uequal'(add(X1,X0),add(X2,X0))
| ~ defined(X0) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(c24,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_equality]) ).
cnf(c25,plain,
( ~ equalish(X1,X2)
| equalish(X0,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_equality]) ).
cnf(c26,plain,
( ~ equalish(X1,X2)
| equalish(add(X1,X0),add(X2,X0))
| ~ defined(X0) ),
inference(clausification,[status(esa)],[compatibility_of_equality_and_addition]) ).
cnf(c28,plain,
( ~ equalish(X0,X2)
| '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$uidentity','additive$uinverse'(a))
| ~ defined('additive$uidentity')
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c20,c2]) ).
cnf(d1,plain,
( 'less$uor$uequal'('additive$uidentity','additive$uinverse'(a))
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c13,d0]) ).
cnf(d2,plain,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(resolution,[status(thm)],[c24,c6]) ).
cnf(d3,plain,
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(resolution,[status(thm)],[c24,d2]) ).
cnf(d4,plain,
( ~ defined(X1)
| ~ equalish(X0,add(X1,'additive$uinverse'(X1)))
| equalish(X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d5,plain,
( ~ defined('additive$uinverse'(X0))
| ~ defined(X0)
| equalish(add('additive$uinverse'(X0),X0),'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( equalish(add('additive$uinverse'(X0),X0),'additive$uidentity')
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c14,d5]) ).
cnf(d7,plain,
( equalish(X0,multiply('multiplicative$uidentity',X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c8,c24]) ).
cnf(d8,plain,
( ~ defined(X1)
| ~ equalish(X0,X1)
| equalish(X0,multiply('multiplicative$uidentity',X1)) ),
inference(resolution,[status(thm)],[c25,d7]) ).
cnf(d9,plain,
( equalish(multiply('multiplicative$uidentity',X0),X1)
| ~ equalish(X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,c24]) ).
cnf(d10,plain,
( ~ 'less$uor$uequal'(multiply('multiplicative$uidentity',X0),X2)
| 'less$uor$uequal'(X1,X2)
| ~ equalish(X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d9,c28]) ).
cnf(d11,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c20]) ).
cnf(d12,plain,
( ~ defined(X0)
| equalish('additive$uidentity',add(X0,'additive$uinverse'(X0))) ),
inference(resolution,[status(thm)],[c24,c5]) ).
cnf(d13,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| 'less$uor$uequal'(add(X0,'additive$uinverse'(X0)),X1) ),
inference(resolution,[status(thm)],[c28,d12]) ).
cnf(d14,plain,
( ~ 'less$uor$uequal'(X1,X2)
| 'less$uor$uequal'(multiply('multiplicative$uidentity',X0),X2)
| ~ equalish(X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,c28]) ).
cnf(d15,plain,
( ~ defined(X0)
| 'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),X1)
| ~ 'less$uor$uequal'(add(X0,'additive$uinverse'(X0)),X1)
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( 'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),X1)
| ~ 'less$uor$uequal'(add(X0,'additive$uinverse'(X0)),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c13,d15]) ).
cnf(d17,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X1)
| ~ defined(X0)
| 'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
( ~ defined('additive$uidentity')
| 'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( 'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),'additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(factoring,[status(thm)],[d18]) ).
cnf(d20,plain,
'less$uor$uequal'(multiply('multiplicative$uidentity','additive$uidentity'),'additive$uidentity'),
inference(resolution,[status(thm)],[c13,d19]) ).
cnf(d21,plain,
( ~ equalish(X0,'additive$uidentity')
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( ~ equalish(X0,'additive$uidentity')
| 'less$uor$uequal'(X0,'additive$uidentity') ),
inference(resolution,[status(thm)],[c13,d21]) ).
cnf(d23,plain,
( ~ defined(X0)
| 'less$uor$uequal'(add('additive$uinverse'(X0),X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[d22,d6]) ).
cnf(d24,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'(add('additive$uidentity',X0),X1)
| 'less$uor$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c28,c4]) ).
cnf(d25,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X1)
| ~ defined(X0)
| 'less$uor$uequal'(X0,add(X1,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d24,c21]) ).
cnf(d26,plain,
( 'less$uor$uequal'(X0,X2)
| ~ 'less$uor$uequal'(add(X1,X0),X2)
| ~ 'less$uor$uequal'('additive$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d25,c19]) ).
cnf(d27,plain,
( ~ defined(X0)
| ~ 'less$uor$uequal'('additive$uidentity','additive$uinverse'(X0))
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
( ~ defined('additive$uinverse'(a))
| 'less$uor$uequal'(a,'additive$uidentity')
| ~ defined(a) ),
inference(resolution,[status(thm)],[d27,d1]) ).
cnf(d29,plain,
( 'less$uor$uequal'(a,'additive$uidentity')
| ~ defined('additive$uinverse'(a)) ),
inference(resolution,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
( ~ 'less$uor$uequal'(X0,X1)
| ~ 'less$uor$uequal'(X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c24,c18]) ).
cnf(d31,plain,
( equalish('additive$uidentity',a)
| ~ 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
( ~ defined(X0)
| equalish(X0,add('additive$uidentity',X0)) ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d33,plain,
( ~ equalish(X3,add(X1,X0))
| equalish(X3,add(X2,X0))
| ~ equalish(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c26,c25]) ).
cnf(d34,plain,
( ~ defined(X0)
| ~ equalish('additive$uidentity',X1)
| equalish(X0,add(X1,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
( equalish('additive$uinverse'(X0),'additive$uidentity')
| ~ defined(X0)
| ~ equalish('additive$uidentity',X0)
| ~ defined('additive$uinverse'(X0)) ),
inference(resolution,[status(thm)],[d34,d4]) ).
cnf(d36,plain,
( equalish('additive$uinverse'(X0),'additive$uidentity')
| ~ equalish('additive$uidentity',X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c14,d35]) ).
cnf(d37,plain,
( 'less$uor$uequal'('additive$uinverse'(X0),'additive$uidentity')
| ~ equalish('additive$uidentity',X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d36,d22]) ).
cnf(d38,plain,
( ~ equalish('additive$uidentity',a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
~ equalish('additive$uidentity',a),
inference(resolution,[status(thm)],[c0,d38]) ).
cnf(d40,plain,
~ 'less$uor$uequal'(a,'additive$uidentity'),
inference(resolution,[status(thm)],[d39,d31]) ).
cnf(d41,plain,
~ defined('additive$uinverse'(a)),
inference(resolution,[status(thm)],[d40,d29]) ).
cnf(d42,plain,
~ defined(a),
inference(resolution,[status(thm)],[d41,c14]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[c0,d42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD064-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 02:35:10 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.94/22.42 % SZS status Unsatisfiable for theBenchmark.p
% 71.94/22.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------