%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : FLD041-3 : 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 : 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 3.31s 16.29s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of clauses : 101 ( 26 unt; 12 nHn; 101 RR)
% Number of literals : 252 ( 0 equ; 143 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 160 ( 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(not_sum_4,negated_conjecture,
~ sum('additive$uidentity',b,'additive$uidentity') ).
cnf(product_5,negated_conjecture,
product(a,b,'additive$uidentity') ).
cnf(associativity_addition_2,axiom,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X0)
| sum('additive$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$uidentity') ) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ) ).
cnf(distributivity_1,axiom,
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ) ).
cnf(distributivity_2,axiom,
( ~ sum(X5,X6,X2)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X3,X4,X0)
| product(X0,X1,X2) ) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined('multiplicative$uidentity') ).
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(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,
~ sum('additive$uidentity',b,'additive$uidentity'),
inference(clausification,[status(esa)],[not_sum_4]) ).
cnf(c4,plain,
product(a,b,'additive$uidentity'),
inference(clausification,[status(esa)],[product_5]) ).
cnf(c6,plain,
( ~ sum(X5,X2,X4)
| ~ sum(X5,X0,X3)
| sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_addition_2]) ).
cnf(c7,plain,
( ~ defined(X0)
| sum('additive$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(X5,X1,X4)
| ~ product(X3,X0,X5)
| product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity_multiplication_1]) ).
cnf(c11,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(c12,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X0,X0) ),
inference(clausification,[status(esa)],[existence_of_identity_multiplication]) ).
cnf(c13,plain,
( ~ defined(X0)
| product('multiplicative$uinverse'(X0),X0,'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity') ),
inference(clausification,[status(esa)],[existence_of_inverse_multiplication]) ).
cnf(c14,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_multiplication]) ).
cnf(c15,plain,
( ~ sum(X3,X5,X6)
| ~ product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_1]) ).
cnf(c16,plain,
( ~ sum(X3,X5,X6)
| product(X6,X4,X2)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X0)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity_2]) ).
cnf(c21,plain,
defined('multiplicative$uidentity'),
inference(clausification,[status(esa)],[well_definedness_of_multiplicative_identity]) ).
cnf(c23,plain,
( ~ defined(X1)
| sum(X0,X1,add(X0,X1))
| ~ defined(X0) ),
inference(clausification,[status(esa)],[totality_of_addition]) ).
cnf(c24,plain,
( ~ defined(X1)
| product(X0,X1,multiply(X0,X1))
| ~ defined(X0) ),
inference(clausification,[status(esa)],[totality_of_multiplication]) ).
cnf(d0,plain,
( ~ defined(X2)
| ~ sum('additive$uinverse'(X2),X3,X1)
| ~ sum(X2,X0,X3)
| sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c6,c8]) ).
cnf(d1,plain,
( ~ defined(X0)
| sum('additive$uidentity',X1,'additive$uidentity')
| ~ sum(X0,X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( product(X0,'multiplicative$uinverse'(X0),'multiplicative$uidentity')
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c13,c14]) ).
cnf(d3,plain,
( ~ defined(X0)
| product(X0,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c14,c12]) ).
cnf(d4,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X3,X2)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c12]) ).
cnf(d5,plain,
( ~ defined(X0)
| product('multiplicative$uidentity',X1,X0)
| ~ product(X0,'multiplicative$uidentity',X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ defined(X0)
| ~ defined('multiplicative$uidentity')
| product('multiplicative$uidentity',multiply(X0,'multiplicative$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d5,c24]) ).
cnf(d7,plain,
( product('multiplicative$uidentity',multiply(X0,'multiplicative$uidentity'),X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c21,d6]) ).
cnf(d8,plain,
( product(multiply(X0,'multiplicative$uidentity'),'multiplicative$uidentity',X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d7,c14]) ).
cnf(d9,plain,
product(b,a,'additive$uidentity'),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d10,plain,
( product(b,X2,X1)
| ~ product(a,X0,X2)
| ~ product('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c10,d9]) ).
cnf(d11,plain,
( ~ product(b,X2,X1)
| ~ product(a,X0,X2)
| product('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c11,d9]) ).
cnf(d12,plain,
( product('additive$uidentity',X0,'additive$uidentity')
| ~ product(a,X0,a) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( ~ defined(a)
| product('additive$uidentity','multiplicative$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
product('additive$uidentity','multiplicative$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
( product(b,X0,'additive$uidentity')
| ~ product(a,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( ~ defined(a)
| ~ defined('multiplicative$uidentity')
| product(b,multiply(a,'multiplicative$uidentity'),'additive$uidentity') ),
inference(resolution,[status(thm)],[d15,c24]) ).
cnf(d17,plain,
( product(b,multiply(a,'multiplicative$uidentity'),'additive$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
product(b,multiply(a,'multiplicative$uidentity'),'additive$uidentity'),
inference(resolution,[status(thm)],[c21,d17]) ).
cnf(d19,plain,
product(multiply(a,'multiplicative$uidentity'),b,'additive$uidentity'),
inference(resolution,[status(thm)],[d18,c14]) ).
cnf(d20,plain,
( ~ product(multiply(a,'multiplicative$uidentity'),X2,X1)
| ~ product(b,X0,X2)
| product('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[d19,c11]) ).
cnf(d21,plain,
( ~ defined(a)
| product('additive$uidentity',X0,a)
| ~ product(b,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
( product('additive$uidentity',X0,a)
| ~ product(b,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined(b)
| product('additive$uidentity','multiplicative$uinverse'(b),a) ),
inference(resolution,[status(thm)],[d22,d2]) ).
cnf(d24,plain,
( product('additive$uidentity','multiplicative$uinverse'(b),a)
| sum('additive$uidentity',b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d23]) ).
cnf(d25,plain,
product('additive$uidentity','multiplicative$uinverse'(b),a),
inference(resolution,[status(thm)],[c3,d24]) ).
cnf(d26,plain,
( ~ defined(b)
| product('additive$uidentity',X0,b)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d11,d3]) ).
cnf(d27,plain,
( product('additive$uidentity',X0,b)
| ~ product(a,X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c1,d26]) ).
cnf(d28,plain,
( sum('additive$uidentity',a,'additive$uidentity')
| ~ defined(a)
| product('additive$uidentity','multiplicative$uinverse'(a),b) ),
inference(resolution,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
( product('additive$uidentity','multiplicative$uinverse'(a),b)
| sum('additive$uidentity',a,'additive$uidentity') ),
inference(resolution,[status(thm)],[c0,d28]) ).
cnf(d30,plain,
product('additive$uidentity','multiplicative$uinverse'(a),b),
inference(resolution,[status(thm)],[c2,d29]) ).
cnf(d31,plain,
product('multiplicative$uinverse'(a),'additive$uidentity',b),
inference(resolution,[status(thm)],[d30,c14]) ).
cnf(d32,plain,
( product('multiplicative$uinverse'(a),X2,X1)
| ~ product('additive$uidentity',X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[d31,c10]) ).
cnf(d33,plain,
( product('multiplicative$uinverse'(a),a,X0)
| ~ product(b,'multiplicative$uinverse'(b),X0) ),
inference(resolution,[status(thm)],[d32,d25]) ).
cnf(d34,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined(b)
| product('multiplicative$uinverse'(a),a,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d33,d2]) ).
cnf(d35,plain,
( product('multiplicative$uinverse'(a),a,'multiplicative$uidentity')
| sum('additive$uidentity',b,'additive$uidentity') ),
inference(resolution,[status(thm)],[c1,d34]) ).
cnf(d36,plain,
product('multiplicative$uinverse'(a),a,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[c3,d35]) ).
cnf(d37,plain,
product(a,'multiplicative$uinverse'(a),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d36,c14]) ).
cnf(d38,plain,
( ~ product(X3,'multiplicative$uinverse'(X0),X1)
| ~ product(X4,'multiplicative$uinverse'(X0),X2)
| ~ sum(X0,X3,X4)
| sum('multiplicative$uidentity',X1,X2)
| sum('additive$uidentity',X0,'additive$uidentity')
| ~ defined(X0) ),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d39,plain,
( ~ product(X0,'multiplicative$uinverse'(a),X1)
| sum('multiplicative$uidentity',b,X1)
| sum('additive$uidentity',a,'additive$uidentity')
| ~ sum(a,'additive$uidentity',X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( ~ product(X0,'multiplicative$uinverse'(a),X1)
| sum('multiplicative$uidentity',b,X1)
| sum('additive$uidentity',a,'additive$uidentity')
| ~ sum(a,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d39]) ).
cnf(d41,plain,
( ~ product(X0,'multiplicative$uinverse'(a),X1)
| sum('multiplicative$uidentity',b,X1)
| ~ sum(a,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c2,d40]) ).
cnf(d42,plain,
( sum('multiplicative$uidentity',b,'multiplicative$uidentity')
| ~ sum(a,'additive$uidentity',a) ),
inference(resolution,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c23,c9]) ).
cnf(d44,plain,
( ~ defined(X0)
| ~ product(X3,X0,X1)
| ~ product(X4,X0,X2)
| ~ sum('multiplicative$uidentity',X3,X4)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c12]) ).
cnf(d45,plain,
( ~ product(X1,a,X0)
| ~ sum('multiplicative$uidentity',b,X1)
| sum(a,'additive$uidentity',X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[d44,d9]) ).
cnf(d46,plain,
( ~ product(X1,a,X0)
| ~ sum('multiplicative$uidentity',b,X1)
| sum(a,'additive$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d45]) ).
cnf(d47,plain,
( ~ product(X2,a,X0)
| product(X3,a,X1)
| ~ sum(b,X2,X3)
| ~ sum('additive$uidentity',X0,X1) ),
inference(resolution,[status(thm)],[c16,d9]) ).
cnf(d48,plain,
( ~ defined(a)
| product(X0,a,X1)
| ~ sum('additive$uidentity',a,X1)
| ~ sum(b,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d47,c12]) ).
cnf(d49,plain,
( product(X0,a,X1)
| ~ sum('additive$uidentity',a,X1)
| ~ sum(b,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d48]) ).
cnf(d50,plain,
( ~ defined(a)
| product(X0,a,a)
| ~ sum(b,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d49,c7]) ).
cnf(d51,plain,
( product(X0,a,a)
| ~ sum(b,'multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[c0,d50]) ).
cnf(d52,plain,
( ~ defined('multiplicative$uidentity')
| ~ defined(b)
| product(add(b,'multiplicative$uidentity'),a,a) ),
inference(resolution,[status(thm)],[d51,c23]) ).
cnf(d53,plain,
( product(add(b,'multiplicative$uidentity'),a,a)
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c1,d52]) ).
cnf(d54,plain,
product(add(b,'multiplicative$uidentity'),a,a),
inference(resolution,[status(thm)],[c21,d53]) ).
cnf(d55,plain,
( ~ sum('multiplicative$uidentity',b,add(b,'multiplicative$uidentity'))
| sum(a,'additive$uidentity',a) ),
inference(resolution,[status(thm)],[d54,d46]) ).
cnf(d56,plain,
( ~ defined(b)
| ~ defined('multiplicative$uidentity')
| sum(a,'additive$uidentity',a) ),
inference(resolution,[status(thm)],[d55,d43]) ).
cnf(d57,plain,
( sum(a,'additive$uidentity',a)
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[c1,d56]) ).
cnf(d58,plain,
sum(a,'additive$uidentity',a),
inference(resolution,[status(thm)],[c21,d57]) ).
cnf(d59,plain,
sum('multiplicative$uidentity',b,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d58,d42]) ).
cnf(d60,plain,
( sum('additive$uidentity',b,'additive$uidentity')
| ~ defined('multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d59,d1]) ).
cnf(d61,plain,
sum('additive$uidentity',b,'additive$uidentity'),
inference(resolution,[status(thm)],[c21,d60]) ).
cnf(d62,plain,
$false,
inference(resolution,[status(thm)],[c3,d61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n007.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 27 02:24:39 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/16.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/16.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------