%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD026-3 : 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 : n001.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 07:10:48 AM UTC 2026
% Result : Unsatisfiable 34.02s 5.33s
% Output : CNFRefutation 34.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 22
% Syntax : Number of clauses : 119 ( 30 unt; 22 nHn; 119 RR)
% Number of literals : 313 ( 0 equ; 177 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; 4 con; 0-1 aty)
% Number of variables : 184 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(b_is_defined,hypothesis,
defined(b) ).
cnf(not_sum_3,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(product_4,negated_conjecture,
product('multiplicative$uidentity',a,b) ).
cnf(not_product_5,negated_conjecture,
~ product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uinverse'(b)) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
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$uidentity') ) ).
cnf(commutativity_addition,axiom,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X0)
| product('multiplicative$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(well_definedness_of_additive_identity,axiom,
defined('additive$uidentity') ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$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,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
defined(b),
inference(clausification,[status(esa)],[b_is_defined]) ).
cnf(c2,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_3]) ).
cnf(c3,plain,
product('multiplicative$uidentity',a,b),
inference(clausification,[status(esa)],[product_4]) ).
cnf(c4,plain,
~ product('multiplicative$uidentity','multiplicative$uinverse'(a),'multiplicative$uinverse'(b)),
inference(clausification,[status(esa)],[not_product_5]) ).
cnf(c5,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c6,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(c7,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c8,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c9,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c10,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c11,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c12,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c13,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(c14,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c15,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(c18,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c21,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c22,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| defined('multiplicative$uinverse'(X0)) ),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c25,plain,
( ~ 'less$uor$uequal'(X1,X0)
| ~ 'less$uor$uequal'(X0,X1)
| sum('additive$uidentity',X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c27,plain,
( ~ defined(X1)
| ~ defined(X0)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c28,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$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d1,plain,
( ~ sum(X3,X0,X1)
| sum(X3,'additive$uidentity',X2)
| ~ sum(X1,'additive$uinverse'(X0),X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ defined(X0)
| sum(X1,'additive$uidentity','additive$uidentity')
| ~ sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
product(a,'multiplicative$uidentity',b),
inference(resolution,[status(thm)],[c14,c3]) ).
cnf(d4,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c14,c12]) ).
cnf(d5,plain,
( ~ product('multiplicative$uidentity',X2,X1)
| ~ product(a,X0,X2)
| product(b,X0,X1) ),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(d6,plain,
( product(b,X0,b)
| ~ product(a,X0,a) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( ~ defined(a)
| product(b,'multiplicative$uidentity',b) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
product(b,'multiplicative$uidentity',b),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( ~ product(X3,'multiplicative$uidentity',X1)
| ~ product(X4,'multiplicative$uidentity',X2)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d10,plain,
( ~ product(X1,'multiplicative$uidentity',X2)
| sum(X0,b,X2)
| ~ sum(X0,b,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ sum(X0,b,a)
| sum(X0,b,b)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( ~ sum(X3,'additive$uidentity',X1)
| sum(X3,X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d13,plain,
( ~ defined(X0)
| ~ sum(X1,'additive$uidentity','additive$uidentity')
| sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( ~ product('multiplicative$uinverse'(X0),X3,X2)
| ~ product(X0,X1,X3)
| product('multiplicative$uidentity',X1,X2)
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d15,plain,
( ~ defined('multiplicative$uinverse'(X0))
| product('multiplicative$uidentity',X1,'multiplicative$uinverse'(X0))
| ~ product(X0,X1,'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
( ~ product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| sum('additive$uidentity',b,'additive$uidentity')
| ~ defined('multiplicative$uinverse'(b))
| ~ defined(b) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( ~ product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| sum('additive$uidentity',b,'additive$uidentity')
| ~ defined('multiplicative$uinverse'(b)) ),
inference(resolution,[status(thm)],[c1,d16]) ).
cnf(d18,plain,
( ~ 'less$uor$uequal'('additive$uidentity',a)
| ~ 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d19,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c27]) ).
cnf(d20,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c9,c7]) ).
cnf(d21,plain,
( sum(X0,'additive$uidentity','additive$uidentity')
| defined('multiplicative$uinverse'(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c22,c9]) ).
cnf(d22,plain,
( defined('multiplicative$uinverse'(X2))
| ~ defined(X2)
| ~ 'less$uor$uequal'(X2,X0)
| 'less$uor$uequal'('additive$uidentity',X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c28,d21]) ).
cnf(d23,plain,
( ~ defined(X1)
| 'less$uor$uequal'('additive$uidentity',X1)
| ~ 'less$uor$uequal'(X0,X1)
| defined('multiplicative$uinverse'(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity',X0)
| defined('multiplicative$uinverse'(X0))
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( ~ sum('additive$uinverse'(X0),X3,X2)
| ~ sum(X0,X1,X3)
| sum('additive$uidentity',X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d26,plain,
( ~ defined(X0)
| sum('additive$uidentity',X1,'additive$uidentity')
| ~ sum(X0,X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d25,c8]) ).
cnf(d27,plain,
( ~ defined(X0)
| sum('additive$uidentity','additive$uidentity','additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
sum('additive$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'('additive$uidentity',X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d28,c28]) ).
cnf(d30,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c12]) ).
cnf(d31,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
( product('multiplicative$uidentity',b,a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d31,d3]) ).
cnf(d33,plain,
product('multiplicative$uidentity',b,a),
inference(resolution,[status(thm)],[c0,d32]) ).
cnf(d34,plain,
product(b,'multiplicative$uidentity',a),
inference(resolution,[status(thm)],[d33,c14]) ).
cnf(d35,plain,
product('multiplicative$uidentity',b,b),
inference(resolution,[status(thm)],[d8,c14]) ).
cnf(d36,plain,
( product('multiplicative$uidentity',X2,X1)
| ~ product(b,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[d35,c10]) ).
cnf(d37,plain,
( product('multiplicative$uidentity',X0,a)
| ~ product(b,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
product('multiplicative$uidentity',a,a),
inference(resolution,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
product(a,'multiplicative$uidentity',a),
inference(resolution,[status(thm)],[d38,c14]) ).
cnf(d40,plain,
( ~ product(X2,'multiplicative$uidentity',X0)
| ~ product(X3,'multiplicative$uidentity',X1)
| ~ sum(a,X2,X3)
| sum(b,X0,X1) ),
inference(resolution,[status(thm)],[c15,d3]) ).
cnf(d41,plain,
( ~ defined(X0)
| ~ product(X1,'multiplicative$uidentity',X2)
| sum(b,X0,X2)
| ~ sum(a,X0,X1) ),
inference(resolution,[status(thm)],[d40,d4]) ).
cnf(d42,plain,
( sum(b,X0,a)
| ~ sum(a,X0,a)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
( ~ defined(a)
| sum(b,'additive$uidentity',a)
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d42,d20]) ).
cnf(d44,plain,
( sum(b,'additive$uidentity',a)
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d43]) ).
cnf(d45,plain,
sum(b,'additive$uidentity',a),
inference(resolution,[status(thm)],[c18,d44]) ).
cnf(d46,plain,
( ~ 'less$uor$uequal'('additive$uidentity',b)
| 'less$uor$uequal'('additive$uidentity',a) ),
inference(resolution,[status(thm)],[d45,d29]) ).
cnf(d47,plain,
( defined('multiplicative$uinverse'(b))
| ~ defined(b)
| 'less$uor$uequal'('additive$uidentity',a) ),
inference(resolution,[status(thm)],[d46,d24]) ).
cnf(d48,plain,
( 'less$uor$uequal'('additive$uidentity',a)
| defined('multiplicative$uinverse'(b)) ),
inference(resolution,[status(thm)],[c1,d47]) ).
cnf(d49,plain,
( ~ 'less$uor$uequal'(a,'additive$uidentity')
| defined('multiplicative$uinverse'(b)) ),
inference(resolution,[status(thm)],[d48,d18]) ).
cnf(d50,plain,
( ~ defined(X2)
| ~ 'less$uor$uequal'(X2,X0)
| 'less$uor$uequal'(X2,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c28,d20]) ).
cnf(d51,plain,
( defined('multiplicative$uinverse'(X1))
| ~ defined(X1)
| ~ 'less$uor$uequal'(X0,X1)
| 'less$uor$uequal'(X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d50,d21]) ).
cnf(d52,plain,
( ~ defined(X0)
| 'less$uor$uequal'(X0,'additive$uidentity')
| defined('multiplicative$uinverse'(X0))
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d51,d19]) ).
cnf(d53,plain,
( ~ 'less$uor$uequal'(b,X0)
| 'less$uor$uequal'(a,X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d45,c28]) ).
cnf(d54,plain,
( ~ 'less$uor$uequal'(b,'additive$uidentity')
| 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d53,d28]) ).
cnf(d55,plain,
( defined('multiplicative$uinverse'(b))
| ~ defined(b)
| 'less$uor$uequal'(a,'additive$uidentity') ),
inference(resolution,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
( 'less$uor$uequal'(a,'additive$uidentity')
| defined('multiplicative$uinverse'(b)) ),
inference(resolution,[status(thm)],[c1,d55]) ).
cnf(d57,plain,
( defined('multiplicative$uinverse'(b))
| defined('multiplicative$uinverse'(b)) ),
inference(resolution,[status(thm)],[d56,d49]) ).
cnf(d58,plain,
( ~ product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| sum('additive$uidentity',b,'additive$uidentity') ),
inference(resolution,[status(thm)],[d57,d17]) ).
cnf(d59,plain,
( sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0)
| product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c14,c13]) ).
cnf(d60,plain,
( ~ defined(X1)
| product(b,X0,X1)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d61,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d60,d59]) ).
cnf(d62,plain,
( product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| sum('additive$uidentity',a,'additive$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d61]) ).
cnf(d63,plain,
( product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c2,d62]) ).
cnf(d64,plain,
product(b,'multiplicative$uinverse'(a),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c21,d63]) ).
cnf(d65,plain,
sum('additive$uidentity',b,'additive$uidentity'),
inference(resolution,[status(thm)],[d64,d58]) ).
cnf(d66,plain,
sum(b,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d65,c9]) ).
cnf(d67,plain,
( sum(b,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d66,d13]) ).
cnf(d68,plain,
( sum(X0,b,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d67,c9]) ).
cnf(d69,plain,
( sum(a,b,b)
| ~ defined(a)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d68,d11]) ).
cnf(d70,plain,
sum(a,b,b),
inference(resolution,[status(thm)],[c0,d69]) ).
cnf(d71,plain,
( sum(a,'additive$uidentity','additive$uidentity')
| ~ defined(b) ),
inference(resolution,[status(thm)],[d70,d2]) ).
cnf(d72,plain,
sum(a,'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c1,d71]) ).
cnf(d73,plain,
sum('additive$uidentity',a,'additive$uidentity'),
inference(resolution,[status(thm)],[d72,c9]) ).
cnf(d74,plain,
$false,
inference(resolution,[status(thm)],[c2,d73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD026-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n001.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 02:30:00 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.02/5.33 % SZS status Unsatisfiable for theBenchmark.p
% 34.02/5.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------