%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD010-5 : 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 : n004.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 07:10:44 AM UTC 2026
% Result : Unsatisfiable 41.80s 11.16s
% Output : CNFRefutation 41.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 21
% Syntax : Number of clauses : 134 ( 28 unt; 9 nHn; 134 RR)
% Number of literals : 352 ( 0 equ; 215 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 194 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_sum_1,negated_conjecture,
~ sum('additive$uidentity','multiplicative$uidentity','additive$uidentity') ).
cnf(not_sum_2,negated_conjecture,
~ sum('additive$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity') ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$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(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(distributivity_1,axiom,
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ) ).
cnf(distributivity_2,axiom,
( ~ sum(X5,X6,X2)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ) ).
cnf(totality_of_addition,axiom,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',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(c0,plain,
~ sum('additive$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_1]) ).
cnf(c1,plain,
~ sum('additive$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[not_sum_2]) ).
cnf(c4,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c6,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c7,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c8,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c9,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c10,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,'additive$uidentity')
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c11,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c12,plain,
( ~ sum(X3,X5,X6)
| ~ product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_1]) ).
cnf(c13,plain,
( ~ sum(X3,X5,X6)
| product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_2]) ).
cnf(c15,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c16,plain,
( ~ defined(X0)
| defined('additive$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_additive_inverse]) ).
cnf(c18,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c19,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c20,plain,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_addition]) ).
cnf(c21,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(c22,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(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,
( ~ 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)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c11,c9]) ).
cnf(d1,plain,
( ~ defined(X0)
| ~ product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c8,c9]) ).
cnf(d2,plain,
( product(X0,X1,multiply(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c21,c11]) ).
cnf(d3,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c9]) ).
cnf(d4,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ defined(X0)
| ~ defined('multiplicative$uidentity')
| product('multiplicative$uidentity',multiply('multiplicative$uidentity',X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( product('multiplicative$uidentity',multiply('multiplicative$uidentity',X0),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c18,d5]) ).
cnf(d7,plain,
( product(multiply('multiplicative$uidentity',X0),'multiplicative$uidentity',X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X1,X4,X3)
| ~ product(X0,X2,X4)
| ~ product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c7,d2]) ).
cnf(d9,plain,
( ~ defined(X0)
| ~ product('multiplicative$uidentity','multiplicative$uidentity',X1)
| product(X0,X1,X0)
| ~ defined('multiplicative$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ product('multiplicative$uidentity','multiplicative$uidentity',X1)
| product(X0,X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c18,d9]) ).
cnf(d11,plain,
( ~ defined('multiplicative$uidentity')
| sum('additive$uidentity','multiplicative$uidentity','additive$uidentity')
| product('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d12,plain,
( product('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( product('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[c18,d12]) ).
cnf(d14,plain,
( defined('multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c19,c0]) ).
cnf(d15,plain,
defined('multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[c18,d14]) ).
cnf(d16,plain,
product('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( product(X0,'multiplicative$uinverse'('multiplicative$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
( product(X0,X1,'multiplicative$uidentity')
| ~ product(X0,X1,'multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined(X0)
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ~ product(X0,X1,'multiplicative$uinverse'('multiplicative$uidentity'))
| product(X0,X1,'multiplicative$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c18,d18]) ).
cnf(d20,plain,
( ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity','multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d15,d20]) ).
cnf(d22,plain,
product('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d21,c11]) ).
cnf(d23,plain,
( product('multiplicative$uidentity',X2,X1)
| ~ product('multiplicative$uidentity',X0,X2)
| ~ product('multiplicative$uinverse'('multiplicative$uidentity'),X0,X1) ),
inference(resolution,[status(thm)],[d16,c7]) ).
cnf(d24,plain,
( ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d25,plain,
product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d15,d24]) ).
cnf(d26,plain,
( ~ product('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'),X0)
| product('multiplicative$uidentity',X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
product('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
( ~ defined(X0)
| ~ product(X3,'multiplicative$uidentity',X1)
| ~ product(X4,'multiplicative$uidentity',X2)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,d0]) ).
cnf(d29,plain,
( ~ product(X1,'multiplicative$uidentity',X2)
| ~ defined(X0)
| sum(X0,'multiplicative$uidentity',X2)
| ~ sum(X0,'multiplicative$uidentity',X1) ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( ~ defined(X0)
| ~ sum(X0,'multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| sum(X0,'multiplicative$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
( ~ defined('multiplicative$uidentity')
| ~ defined('multiplicative$uidentity')
| product(X0,multiply('multiplicative$uidentity','multiplicative$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d10,d2]) ).
cnf(d32,plain,
( product(X0,multiply('multiplicative$uidentity','multiplicative$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c18,d31]) ).
cnf(d33,plain,
( ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| ~ product('multiplicative$uidentity',multiply('multiplicative$uidentity','multiplicative$uidentity'),X0)
| product('multiplicative$uidentity',X0,'multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d23,d32]) ).
cnf(d34,plain,
( ~ product('multiplicative$uidentity',multiply('multiplicative$uidentity','multiplicative$uidentity'),X0)
| product('multiplicative$uidentity',X0,'multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d15,d33]) ).
cnf(d35,plain,
( ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| product('multiplicative$uinverse'('multiplicative$uidentity'),multiply('multiplicative$uidentity','multiplicative$uidentity'),'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d19,d32]) ).
cnf(d36,plain,
product('multiplicative$uinverse'('multiplicative$uidentity'),multiply('multiplicative$uidentity','multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d15,d35]) ).
cnf(d37,plain,
( ~ product('multiplicative$uinverse'('multiplicative$uidentity'),X2,X1)
| ~ product('multiplicative$uinverse'('multiplicative$uidentity'),X0,X2)
| product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d25,c8]) ).
cnf(d38,plain,
( ~ product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity',X0)
| product('multiplicative$uidentity',multiply('multiplicative$uidentity','multiplicative$uidentity'),X0) ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( product('multiplicative$uidentity',X0,'multiplicative$uinverse'('multiplicative$uidentity'))
| ~ product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
( product('multiplicative$uidentity',X2,X1)
| ~ product('multiplicative$uidentity',X0,X2)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d27,c7]) ).
cnf(d41,plain,
( ~ defined(X0)
| ~ product(X3,'multiplicative$uidentity',X1)
| product(X4,'multiplicative$uidentity',X2)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,d0]) ).
cnf(d42,plain,
( product(X1,'multiplicative$uidentity',X2)
| ~ defined(X0)
| ~ sum(X0,'multiplicative$uidentity',X2)
| ~ sum(X0,'multiplicative$uidentity',X1) ),
inference(resolution,[status(thm)],[d41,d27]) ).
cnf(d43,plain,
( ~ defined('multiplicative$uidentity')
| product('multiplicative$uidentity','multiplicative$uidentity',X0)
| ~ defined('additive$uidentity')
| ~ sum('additive$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d42,c4]) ).
cnf(d44,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',X0)
| ~ defined('multiplicative$uidentity')
| ~ sum('additive$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c15,d43]) ).
cnf(d45,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',X0)
| ~ sum('additive$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c18,d44]) ).
cnf(d46,plain,
( ~ defined('multiplicative$uidentity')
| ~ defined('additive$uidentity')
| product('multiplicative$uidentity','multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d45,c20]) ).
cnf(d47,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c15,d46]) ).
cnf(d48,plain,
product('multiplicative$uidentity','multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity')),
inference(resolution,[status(thm)],[c18,d47]) ).
cnf(d49,plain,
( ~ product('multiplicative$uidentity','multiplicative$uidentity',X0)
| product('multiplicative$uidentity',X0,add('additive$uidentity','multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d48,d40]) ).
cnf(d50,plain,
( product('multiplicative$uinverse'('multiplicative$uidentity'),X2,X1)
| ~ product('multiplicative$uinverse'('multiplicative$uidentity'),X0,X2)
| ~ product('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d25,c7]) ).
cnf(d51,plain,
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(d52,plain,
( ~ defined('multiplicative$uidentity')
| ~ defined('additive$uidentity')
| product('multiplicative$uidentity','multiplicative$uidentity',add('multiplicative$uidentity','additive$uidentity')) ),
inference(resolution,[status(thm)],[d45,d51]) ).
cnf(d53,plain,
( product('multiplicative$uidentity','multiplicative$uidentity',add('multiplicative$uidentity','additive$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c15,d52]) ).
cnf(d54,plain,
product('multiplicative$uidentity','multiplicative$uidentity',add('multiplicative$uidentity','additive$uidentity')),
inference(resolution,[status(thm)],[c18,d53]) ).
cnf(d55,plain,
( product(X0,add('multiplicative$uidentity','additive$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d54,d10]) ).
cnf(d56,plain,
( product('multiplicative$uinverse'('multiplicative$uidentity'),add('multiplicative$uidentity','additive$uidentity'),'multiplicative$uidentity')
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d55,d19]) ).
cnf(d57,plain,
product('multiplicative$uinverse'('multiplicative$uidentity'),add('multiplicative$uidentity','additive$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d15,d56]) ).
cnf(d58,plain,
( product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity',X0)
| ~ product('multiplicative$uidentity',add('multiplicative$uidentity','additive$uidentity'),X0) ),
inference(resolution,[status(thm)],[d57,d50]) ).
cnf(d59,plain,
( ~ product('multiplicative$uidentity','multiplicative$uidentity',add('multiplicative$uidentity','additive$uidentity'))
| product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d58,d49]) ).
cnf(d60,plain,
product('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity')),
inference(resolution,[status(thm)],[d54,d59]) ).
cnf(d61,plain,
product('multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity'),'multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[d60,d39]) ).
cnf(d62,plain,
product(add('additive$uidentity','multiplicative$uidentity'),'multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[d61,c11]) ).
cnf(d63,plain,
( ~ defined(X0)
| ~ sum(X0,'multiplicative$uidentity',add('additive$uidentity','multiplicative$uidentity'))
| sum(X0,'multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d62,d29]) ).
cnf(d64,plain,
( ~ defined('multiplicative$uidentity')
| ~ defined('additive$uidentity')
| ~ defined('additive$uidentity')
| sum('additive$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[d63,c20]) ).
cnf(d65,plain,
( ~ defined('multiplicative$uidentity')
| sum('additive$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')) ),
inference(resolution,[status(thm)],[c15,d64]) ).
cnf(d66,plain,
sum('additive$uidentity','multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[c18,d65]) ).
cnf(d67,plain,
( ~ defined('additive$uidentity')
| sum('additive$uidentity','multiplicative$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d66,d30]) ).
cnf(d68,plain,
sum('additive$uidentity','multiplicative$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[c15,d67]) ).
cnf(d69,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'('multiplicative$uinverse'('multiplicative$uidentity'),X1)
| ~ sum(X0,'multiplicative$uidentity',X1) ),
inference(resolution,[status(thm)],[d66,c25]) ).
cnf(d70,plain,
( 'less$uor$uequal'('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity')
| ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d69,d68]) ).
cnf(d71,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d72,plain,
( ~ defined(X2)
| ~ 'less$uor$uequal'(X2,X0)
| 'less$uor$uequal'(X2,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c25,d71]) ).
cnf(d73,plain,
( ~ defined('additive$uidentity')
| ~ 'less$uor$uequal'(X0,'additive$uinverse'('additive$uidentity'))
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d72,c5]) ).
cnf(d74,plain,
( ~ 'less$uor$uequal'(X0,'additive$uinverse'('additive$uidentity'))
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c15,d73]) ).
cnf(d75,plain,
( 'less$uor$uequal'('additive$uinverse'('additive$uidentity'),X0)
| ~ defined(X0)
| ~ defined('additive$uinverse'('additive$uidentity'))
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d74,c24]) ).
cnf(d76,plain,
( 'less$uor$uequal'('additive$uinverse'('additive$uidentity'),'additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity'))
| 'less$uor$uequal'('additive$uinverse'('additive$uidentity'),'additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity'))
| ~ defined('additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[d75,d74]) ).
cnf(d77,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uinverse'(X1),X0)
| 'less$uor$uequal'('additive$uidentity',X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d78,plain,
( ~ defined('additive$uinverse'('additive$uidentity'))
| 'less$uor$uequal'('additive$uidentity',X0)
| ~ defined('additive$uidentity')
| ~ sum('additive$uidentity','additive$uidentity',X0) ),
inference(resolution,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
( 'less$uor$uequal'('additive$uidentity',X0)
| ~ defined('additive$uinverse'('additive$uidentity'))
| ~ sum('additive$uidentity','additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c15,d78]) ).
cnf(d80,plain,
( ~ defined('additive$uidentity')
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[d79,c4]) ).
cnf(d81,plain,
( 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ defined('additive$uinverse'('additive$uidentity')) ),
inference(resolution,[status(thm)],[c15,d80]) ).
cnf(d82,plain,
( ~ defined('additive$uidentity')
| 'less$uor$uequal'('additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d81,c16]) ).
cnf(d83,plain,
'less$uor$uequal'('additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c15,d82]) ).
cnf(d84,plain,
'less$uor$uequal'('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d83,d70]) ).
cnf(d85,plain,
( ~ 'less$uor$uequal'('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ 'less$uor$uequal'('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c22,c1]) ).
cnf(d86,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'(X1,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c25,c4]) ).
cnf(d87,plain,
( ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| 'less$uor$uequal'('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d66,d86]) ).
cnf(d88,plain,
( 'less$uor$uequal'('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity'))
| ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[c18,d87]) ).
cnf(d89,plain,
'less$uor$uequal'('multiplicative$uidentity','multiplicative$uinverse'('multiplicative$uidentity')),
inference(resolution,[status(thm)],[d83,d88]) ).
cnf(d90,plain,
~ 'less$uor$uequal'('multiplicative$uinverse'('multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d89,d85]) ).
cnf(d91,plain,
$false,
inference(resolution,[status(thm)],[d90,d84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 27 02:20:51 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.80/11.16 % SZS status Unsatisfiable for theBenchmark.p
% 41.80/11.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------