%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD040-3 : 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 07:10:52 AM UTC 2026
% Result : Unsatisfiable 51.87s 6.87s
% Output : CNFRefutation 51.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of clauses : 102 ( 27 unt; 10 nHn; 102 RR)
% Number of literals : 268 ( 0 equ; 162 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 185 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_is_defined,hypothesis,
defined(a) ).
cnf(not_sum_2,negated_conjecture,
~ sum('additive$uidentity',a,'additive$uidentity') ).
cnf(sum_3,negated_conjecture,
sum('additive$uidentity','additive$uidentity','multiplicative$uinverse'(a)) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$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_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_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ 'less$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(different_identities,axiom,
~ sum('additive$uidentity','additive$uidentity','multiplicative$uidentity') ).
cnf(c0,plain,
defined(a),
inference(clausification,[status(esa)],[a_is_defined]) ).
cnf(c1,plain,
~ sum('additive$uidentity',a,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_2]) ).
cnf(c2,plain,
sum('additive$uidentity','additive$uidentity','multiplicative$uinverse'(a)),
inference(clausification,[status(esa)],[sum_3]) ).
cnf(c3,plain,
( ~ sum(X5,X1,X4)
| ~ sum(X3,X0,X5)
| sum(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_1]) ).
cnf(c4,plain,
( ~ sum(X5,X2,X4)
| ~ sum(X5,X0,X3)
| sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c5,plain,
( ~ defined(X0)
| sum('additive$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_addition]) ).
cnf(c6,plain,
( ~ defined(X0)
| sum('additive$uinverse'(X0),X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_addition]) ).
cnf(c7,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_addition]) ).
cnf(c9,plain,
( ~ product(X5,X2,X4)
| ~ product(X5,X0,X3)
| product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_2]) ).
cnf(c10,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c11,plain,
( ~ defined(X0)
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c12,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
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_1]) ).
cnf(c14,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(c16,plain,
defined('additive$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_additive_identity]) ).
cnf(c19,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c23,plain,
( ~ 'less$uor$uequal'(X1,X0)
| sum('additive$uidentity',X0,X1)
| ~ 'less$uor$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[antisymmetry_of_order_relation]) ).
cnf(c25,plain,
( ~ defined(X1)
| 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'(X0,X1)
| ~ defined(X0) ),
inference(clausification,[status(esa)],[totality_of_order_relation]) ).
cnf(c26,plain,
( ~ sum(X4,X1,X3)
| ~ 'less$uor$uequal'(X0,X4)
| 'less$uor$uequal'(X2,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[compatibility_of_order_relation_and_addition]) ).
cnf(c28,plain,
~ sum('additive$uidentity','additive$uidentity','multiplicative$uidentity'),
inference(clausification,[status(esa)],[different_identities]) ).
cnf(d0,plain,
( ~ 'less$uor$uequal'('additive$uidentity',X0)
| 'less$uor$uequal'('multiplicative$uinverse'(a),X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c26,c2]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum(X0,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d2,plain,
( ~ defined(X2)
| ~ sum('additive$uinverse'(X2),X3,X1)
| ~ sum(X2,X0,X3)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c4,c6]) ).
cnf(d3,plain,
( ~ defined(X0)
| sum('additive$uidentity',X1,'additive$uidentity')
| ~ sum(X0,X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( ~ defined(X0)
| sum('additive$uidentity','additive$uidentity','additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
sum('additive$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( 'less$uor$uequal'('multiplicative$uinverse'(a),'additive$uidentity')
| ~ 'less$uor$uequal'('additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( 'less$uor$uequal'(X0,X0)
| ~ defined(X0)
| ~ defined(X0) ),
inference(factoring,[status(thm)],[c25]) ).
cnf(d8,plain,
( ~ defined(X0)
| sum(X0,'additive$uinverse'(X0),'additive$uidentity') ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d9,plain,
( ~ defined(X1)
| ~ 'less$uor$uequal'(X1,X0)
| 'less$uor$uequal'('additive$uidentity',X2)
| ~ sum(X0,'additive$uinverse'(X1),X2) ),
inference(resolution,[status(thm)],[c26,d8]) ).
cnf(d10,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ 'less$uor$uequal'(X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity','additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
'less$uor$uequal'('additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
'less$uor$uequal'('multiplicative$uinverse'(a),'additive$uidentity'),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( ~ sum(X2,'additive$uidentity',X0)
| sum(X2,'multiplicative$uinverse'(a),X1)
| ~ sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d15,plain,
( sum(X0,'multiplicative$uinverse'(a),'additive$uidentity')
| ~ sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d5,d14]) ).
cnf(d16,plain,
( sum('multiplicative$uinverse'(a),X0,'additive$uidentity')
| ~ sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
( ~ 'less$uor$uequal'('multiplicative$uinverse'(a),X1)
| 'less$uor$uequal'('additive$uidentity',X2)
| ~ sum(X1,X0,X2)
| ~ sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d16,c26]) ).
cnf(d18,plain,
( 'less$uor$uequal'('additive$uidentity',X1)
| ~ sum(X0,'additive$uidentity','additive$uidentity')
| ~ sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( ~ defined(X0)
| 'less$uor$uequal'('additive$uidentity',X0)
| ~ sum(X0,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c11,c12]) ).
cnf(d21,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(d22,plain,
( ~ defined(X0)
| ~ product(X0,X3,X2)
| ~ product('multiplicative$uidentity',X1,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,d21]) ).
cnf(d23,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)],[c14,d21]) ).
cnf(d24,plain,
( ~ defined(X1)
| product(X2,'multiplicative$uidentity',X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( product('additive$uidentity','multiplicative$uidentity',X0)
| ~ sum('additive$uidentity','additive$uidentity',X0)
| ~ defined('additive$uidentity')
| ~ defined('additive$uidentity') ),
inference(resolution,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
( product('additive$uidentity','multiplicative$uidentity',X0)
| ~ sum('additive$uidentity','additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c16,d25]) ).
cnf(d27,plain,
product('additive$uidentity','multiplicative$uidentity','multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
product('multiplicative$uidentity','additive$uidentity','multiplicative$uinverse'(a)),
inference(resolution,[status(thm)],[d27,c12]) ).
cnf(d29,plain,
( product(X0,'additive$uidentity',X1)
| ~ product(X0,'multiplicative$uinverse'(a),X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product(a,'additive$uidentity','multiplicative$uidentity')
| ~ defined(a) ),
inference(resolution,[status(thm)],[d29,d20]) ).
cnf(d31,plain,
( product(a,'additive$uidentity','multiplicative$uidentity')
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d30]) ).
cnf(d32,plain,
product(a,'additive$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[c1,d31]) ).
cnf(d33,plain,
product('additive$uidentity',a,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d32,c12]) ).
cnf(d34,plain,
( sum('additive$uidentity',X2,'additive$uidentity')
| ~ defined(X2)
| ~ product(X3,X2,X0)
| ~ product(X4,X2,X1)
| ~ sum('multiplicative$uinverse'(X2),X3,X4)
| sum('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d35,plain,
( ~ sum(X3,X0,X1)
| sum(X3,'additive$uidentity',X2)
| ~ sum(X1,'additive$uinverse'(X0),X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d36,plain,
( ~ defined(X0)
| sum(X1,'additive$uidentity','additive$uidentity')
| ~ sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d35,d8]) ).
cnf(d37,plain,
( ~ sum(X3,'additive$uidentity',X1)
| sum(X3,X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d38,plain,
( ~ defined(X0)
| ~ sum(X1,'additive$uidentity','additive$uidentity')
| sum(X1,X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d37,c5]) ).
cnf(d39,plain,
( ~ sum('additive$uidentity',X2,X1)
| ~ sum('additive$uidentity',X0,X2)
| sum('multiplicative$uinverse'(a),X0,X1) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d40,plain,
( sum('multiplicative$uinverse'(a),'additive$uidentity',X0)
| ~ sum('additive$uidentity','additive$uidentity',X0) ),
inference(resolution,[status(thm)],[d39,d5]) ).
cnf(d41,plain,
( sum('multiplicative$uinverse'(a),X0,X0)
| ~ defined(X0)
| ~ sum('additive$uidentity','additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
( sum('multiplicative$uinverse'(a),X0,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d5,d41]) ).
cnf(d43,plain,
( sum('multiplicative$uinverse'(a),'additive$uidentity','additive$uidentity')
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d42,d36]) ).
cnf(d44,plain,
sum('multiplicative$uinverse'(a),'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d43,c0]) ).
cnf(d45,plain,
( ~ product('additive$uidentity',a,X0)
| ~ product('additive$uidentity',a,X1)
| sum('multiplicative$uidentity',X0,X1)
| sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a) ),
inference(resolution,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
( ~ product('additive$uidentity',a,X0)
| ~ product('additive$uidentity',a,X1)
| sum('multiplicative$uidentity',X0,X1)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d45]) ).
cnf(d47,plain,
( ~ product('additive$uidentity',a,X0)
| ~ product('additive$uidentity',a,X1)
| sum('multiplicative$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c1,d46]) ).
cnf(d48,plain,
( ~ product('additive$uidentity',a,X0)
| sum('multiplicative$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d33,d47]) ).
cnf(d49,plain,
sum('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d48,d33]) ).
cnf(d50,plain,
( sum('additive$uidentity','multiplicative$uidentity','additive$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d49,d3]) ).
cnf(d51,plain,
sum('additive$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c19,d50]) ).
cnf(d52,plain,
sum('multiplicative$uidentity','additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d51,c7]) ).
cnf(d53,plain,
( 'less$uor$uequal'('additive$uidentity','multiplicative$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d52,d19]) ).
cnf(d54,plain,
'less$uor$uequal'('additive$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[c19,d53]) ).
cnf(d55,plain,
( ~ 'less$uor$uequal'('multiplicative$uidentity','additive$uidentity')
| ~ 'less$uor$uequal'('additive$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c23,c28]) ).
cnf(d56,plain,
( ~ 'less$uor$uequal'('multiplicative$uinverse'(a),X1)
| 'less$uor$uequal'(X0,X2)
| ~ sum(X1,X0,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d42,c26]) ).
cnf(d57,plain,
( 'less$uor$uequal'(X0,X1)
| ~ sum('additive$uidentity',X0,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d56,d13]) ).
cnf(d58,plain,
( 'less$uor$uequal'('multiplicative$uidentity','additive$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d51,d57]) ).
cnf(d59,plain,
'less$uor$uequal'('multiplicative$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c19,d58]) ).
cnf(d60,plain,
~ 'less$uor$uequal'('additive$uidentity','multiplicative$uidentity'),
inference(resolution,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[d60,d54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 02:24:55 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.87/6.87 % SZS status Unsatisfiable for theBenchmark.p
% 51.87/6.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------