%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO015-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 06:54:41 AM UTC 2026
% Result : Unsatisfiable 140.63s 22.04s
% Output : CNFRefutation 140.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 23
% Syntax : Number of clauses : 191 ( 115 unt; 0 nHn; 125 RR)
% Number of literals : 338 ( 57 equ; 150 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 384 ( 30 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_times_y,negated_conjecture,
product(x,y,'x$utimes$uy') ).
cnf(x_inverse_plus_y_inverse,negated_conjecture,
sum(inverse(x),inverse(y),'x$uinverse$uplus$uy$uinverse') ).
cnf(prove_equation,negated_conjecture,
inverse('x$utimes$uy') != 'x$uinverse$uplus$uy$uinverse' ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(commutativity_of_addition,axiom,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ) ).
cnf(commutativity_of_multiplication,axiom,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ) ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) ).
cnf(multiplicative_identity1,axiom,
product('multiplicative$uidentity',X0,X0) ).
cnf(multiplicative_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity3,axiom,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity4,axiom,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity5,axiom,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(distributivity6,axiom,
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(additive_inverse1,axiom,
sum(inverse(X0),X0,'multiplicative$uidentity') ).
cnf(additive_inverse2,axiom,
sum(X0,inverse(X0),'multiplicative$uidentity') ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X0),X0,'additive$uidentity') ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') ).
cnf(addition_is_well_defined,axiom,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplication_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(x,y,'x$utimes$uy'),
inference(clausification,[status(esa)],[x_times_y]) ).
cnf(c1,plain,
sum(inverse(x),inverse(y),'x$uinverse$uplus$uy$uinverse'),
inference(clausification,[status(esa)],[x_inverse_plus_y_inverse]) ).
cnf(c2,plain,
inverse('x$utimes$uy') != 'x$uinverse$uplus$uy$uinverse',
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(c3,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c5,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c6,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c7,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c8,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c9,plain,
product('multiplicative$uidentity',X0,X0),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c10,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c11,plain,
( sum(X4,X5,X6)
| ~ product(X3,X2,X6)
| ~ product(X3,X1,X5)
| ~ product(X3,X0,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c12,plain,
( ~ sum(X5,X3,X1)
| ~ sum(X6,X4,X2)
| ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c13,plain,
( ~ sum(X6,X3,X0)
| ~ product(X6,X1,X5)
| sum(X5,X4,X2)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c14,plain,
( product(X6,X4,X2)
| ~ sum(X5,X3,X6)
| ~ product(X5,X4,X0)
| ~ product(X3,X4,X1)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c15,plain,
( ~ sum(X0,X6,X4)
| ~ product(X5,X1,X6)
| ~ sum(X0,X5,X3)
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
cnf(c16,plain,
( ~ sum(X0,X3,X5)
| sum(X0,X4,X6)
| ~ product(X2,X5,X6)
| ~ product(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity6]) ).
cnf(c19,plain,
sum(inverse(X0),X0,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c20,plain,
sum(X0,inverse(X0),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse2]) ).
cnf(c21,plain,
product(inverse(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(c22,plain,
product(X0,inverse(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c23,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c24,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X1,'additive$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c23,c8]) ).
cnf(d1,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d3,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ sum('additive$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c23,c7]) ).
cnf(d5,plain,
product(y,x,'x$utimes$uy'),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d6,plain,
( ~ sum(X3,X1,'multiplicative$uidentity')
| sum(X4,X2,X0)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(d7,plain,
( ~ sum('multiplicative$uidentity',X1,'multiplicative$uidentity')
| sum(X0,X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
( ~ sum('multiplicative$uidentity',x,'multiplicative$uidentity')
| sum(y,'x$utimes$uy',y) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d10,plain,
( ~ product('multiplicative$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c24,c9]) ).
cnf(d11,plain,
( ~ sum(X3,X4,X0)
| ~ sum(X3,X4,X2)
| ~ sum(X3,'multiplicative$uidentity',X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c10]) ).
cnf(d12,plain,
( ~ sum(X2,'multiplicative$uidentity',X1)
| ~ sum(X2,inverse(X2),X0)
| product(X0,X1,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d11,c20]) ).
cnf(d13,plain,
( ~ sum(X1,'multiplicative$uidentity',X0)
| product('multiplicative$uidentity',X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d12,c20]) ).
cnf(d14,plain,
product('multiplicative$uidentity',add(X0,'multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
add(X0,'multiplicative$uidentity') = 'multiplicative$uidentity',
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
sum('multiplicative$uidentity',X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
sum(y,'x$utimes$uy',y),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ sum(X3,X1,X0)
| sum(X4,X2,'additive$uidentity')
| ~ product(inverse(X0),X3,X4)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[c21,c11]) ).
cnf(d19,plain,
( ~ sum(X0,X1,X0)
| sum('additive$uidentity',X2,'additive$uidentity')
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[d18,c21]) ).
cnf(d20,plain,
( sum('additive$uidentity',multiply(X1,inverse(X0)),'additive$uidentity')
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
sum('additive$uidentity',multiply('x$utimes$uy',inverse(y)),'additive$uidentity'),
inference(resolution,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
'additive$uidentity' = multiply('x$utimes$uy',inverse(y)),
inference(resolution,[status(thm)],[d21,d4]) ).
cnf(d23,plain,
( ~ sum(X3,X5,X0)
| ~ sum(X4,multiply(X5,X1),X2)
| ~ product(X3,X1,X4)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d24,plain,
( ~ sum(X3,X4,X0)
| ~ sum(multiply(X1,X3),multiply(X4,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d23,d1]) ).
cnf(d25,plain,
( ~ sum(multiply(X0,inverse(x)),multiply(inverse(y),X0),X1)
| product('x$uinverse$uplus$uy$uinverse',X0,X1) ),
inference(resolution,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
( ~ sum('multiplicative$uidentity',y,'multiplicative$uidentity')
| sum(x,'x$utimes$uy',x) ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d27,plain,
sum(x,'x$utimes$uy',x),
inference(resolution,[status(thm)],[d16,d26]) ).
cnf(d28,plain,
sum('additive$uidentity',multiply('x$utimes$uy',inverse(x)),'additive$uidentity'),
inference(resolution,[status(thm)],[d20,d27]) ).
cnf(d29,plain,
'additive$uidentity' = multiply('x$utimes$uy',inverse(x)),
inference(resolution,[status(thm)],[d28,d4]) ).
cnf(d30,plain,
( product('x$uinverse$uplus$uy$uinverse','x$utimes$uy',X0)
| ~ sum('additive$uidentity',multiply(inverse(y),'x$utimes$uy'),X0) ),
inference(superposition,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( ~ sum('additive$uidentity',multiply('x$utimes$uy',inverse(y)),X0)
| product('x$uinverse$uplus$uy$uinverse','x$utimes$uy',X0) ),
inference(demodulation,[status(thm)],[d30,d3]) ).
cnf(d32,plain,
( ~ sum('additive$uidentity','additive$uidentity',X0)
| product('x$uinverse$uplus$uy$uinverse','x$utimes$uy',X0) ),
inference(demodulation,[status(thm)],[d31,d22]) ).
cnf(d33,plain,
product('x$uinverse$uplus$uy$uinverse','x$utimes$uy','additive$uidentity'),
inference(resolution,[status(thm)],[d32,c7]) ).
cnf(d34,plain,
multiply('x$uinverse$uplus$uy$uinverse','x$utimes$uy') = 'additive$uidentity',
inference(resolution,[status(thm)],[d33,d2]) ).
cnf(d35,plain,
multiply('x$utimes$uy','x$uinverse$uplus$uy$uinverse') = 'additive$uidentity',
inference(demodulation,[status(thm)],[d34,d3]) ).
cnf(d36,plain,
( ~ product(X0,'multiplicative$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c24,c10]) ).
cnf(d37,plain,
X0 = multiply('multiplicative$uidentity',X0),
inference(resolution,[status(thm)],[d36,d1]) ).
cnf(d38,plain,
( ~ sum(X3,X4,X0)
| ~ sum(X3,X5,X1)
| sum(X3,multiply(X4,X5),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c4]) ).
cnf(d39,plain,
( sum(X0,multiply(X3,X1),multiply(X2,X4))
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d38,d1]) ).
cnf(d40,plain,
( sum(X0,multiply(X3,X1),multiply(X2,add(X3,X0)))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d39,d9]) ).
cnf(d41,plain,
sum(inverse(X0),multiply(X1,X0),multiply('multiplicative$uidentity',add(X1,inverse(X0)))),
inference(resolution,[status(thm)],[d40,c19]) ).
cnf(d42,plain,
sum(inverse(X1),multiply(X0,X1),add(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
( sum(X0,multiply(X3,X1),multiply(X2,add(X0,X3)))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d39,c3]) ).
cnf(d44,plain,
sum(X0,multiply(X1,inverse(X0)),multiply('multiplicative$uidentity',add(X0,X1))),
inference(resolution,[status(thm)],[d43,c20]) ).
cnf(d45,plain,
sum(X0,multiply(X1,inverse(X0)),add(X0,X1)),
inference(demodulation,[status(thm)],[d44,d37]) ).
cnf(d46,plain,
( ~ sum(X3,X1,'multiplicative$uidentity')
| sum(multiply(X3,X0),X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d47,plain,
( sum(multiply(X0,X1),X1,X1)
| ~ sum(X0,'multiplicative$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d46,c10]) ).
cnf(d48,plain,
sum(X0,'multiplicative$uidentity','multiplicative$uidentity'),
inference(superposition,[status(thm)],[d15,c3]) ).
cnf(d49,plain,
sum(multiply(X0,X1),X1,X1),
inference(resolution,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(resolution,[status(thm)],[d49,d0]) ).
cnf(d51,plain,
( ~ sum(X3,X5,X1)
| ~ sum(X4,multiply(X0,X5),X2)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d52,plain,
( ~ sum(X3,X4,X1)
| ~ sum(multiply(X3,X0),multiply(X0,X4),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d51,d1]) ).
cnf(d53,plain,
( ~ sum(multiply(X1,X0),multiply(X0,'additive$uidentity'),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d52,c8]) ).
cnf(d54,plain,
( ~ sum(multiply(X1,X0),'additive$uidentity',X2)
| product(X0,X1,X2) ),
inference(demodulation,[status(thm)],[d53,d50]) ).
cnf(d55,plain,
multiply(X0,inverse(X0)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d2,c22]) ).
cnf(d56,plain,
( ~ sum(X3,X1,X5)
| sum(X4,X2,multiply(X0,X5))
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d57,plain,
( ~ sum(X3,X1,X4)
| sum(multiply(X0,X3),X2,multiply(X0,X4))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d56,c4]) ).
cnf(d58,plain,
( sum(multiply(inverse(X1),X0),'additive$uidentity',multiply(inverse(X1),X2))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d57,c21]) ).
cnf(d59,plain,
sum(multiply(inverse(X0),multiply(X1,X0)),'additive$uidentity',multiply(inverse(X0),X0)),
inference(resolution,[status(thm)],[d49,d58]) ).
cnf(d60,plain,
sum(multiply(inverse(X0),multiply(X1,X0)),'additive$uidentity',multiply(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d59,d3]) ).
cnf(d61,plain,
sum(multiply(inverse(X0),multiply(X1,X0)),'additive$uidentity','additive$uidentity'),
inference(demodulation,[status(thm)],[d60,d55]) ).
cnf(d62,plain,
product(multiply(X0,X1),inverse(X1),'additive$uidentity'),
inference(resolution,[status(thm)],[d61,d54]) ).
cnf(d63,plain,
( ~ sum(X3,X5,X0)
| ~ sum(X3,multiply(X5,X4),X2)
| ~ sum(X3,X4,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c4]) ).
cnf(d64,plain,
( ~ sum(X0,multiply(X1,X4),X3)
| ~ sum(X0,X4,X2)
| product(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d63,c3]) ).
cnf(d65,plain,
( ~ sum(X0,multiply(X1,'additive$uidentity'),X2)
| product(add(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[d64,c8]) ).
cnf(d66,plain,
( ~ sum(X1,'additive$uidentity',X2)
| product(add(X1,X0),X1,X2) ),
inference(demodulation,[status(thm)],[d65,d50]) ).
cnf(d67,plain,
product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[d66,c8]) ).
cnf(d68,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c23,c3]) ).
cnf(d69,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d68,d9]) ).
cnf(d70,plain,
product(add(X1,X0),X0,X0),
inference(superposition,[status(thm)],[d69,d67]) ).
cnf(d71,plain,
multiply(add(X0,X1),X1) = X1,
inference(resolution,[status(thm)],[d70,d2]) ).
cnf(d72,plain,
multiply(X1,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d71,d3]) ).
cnf(d73,plain,
product(X0,inverse(add(X1,X0)),'additive$uidentity'),
inference(superposition,[status(thm)],[d72,d62]) ).
cnf(d74,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[d9,c23]) ).
cnf(d75,plain,
( ~ product(add(X0,X2),X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[d67,c24]) ).
cnf(d76,plain,
X0 = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[d75,d1]) ).
cnf(d77,plain,
X0 = multiply(X0,add(X1,X0)),
inference(superposition,[status(thm)],[d69,d76]) ).
cnf(d78,plain,
X0 = multiply(X0,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d36,c4]) ).
cnf(d79,plain,
( sum(X0,multiply(inverse(X0),X1),multiply(X2,'multiplicative$uidentity'))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d39,c20]) ).
cnf(d80,plain,
( sum(X1,multiply(inverse(X1),X2),X0)
| ~ sum(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d79,d78]) ).
cnf(d81,plain,
sum(X0,multiply(inverse(X0),X1),add(X0,X1)),
inference(resolution,[status(thm)],[d80,c3]) ).
cnf(d82,plain,
( ~ sum(X3,X4,X1)
| ~ sum(multiply(X0,X3),multiply(X0,X4),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d51,c4]) ).
cnf(d83,plain,
( ~ sum(multiply(X0,X1),multiply(X0,'additive$uidentity'),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d82,c8]) ).
cnf(d84,plain,
( ~ sum(multiply(X0,X1),'additive$uidentity',X2)
| product(X0,X1,X2) ),
inference(demodulation,[status(thm)],[d83,d50]) ).
cnf(d85,plain,
( ~ sum(X3,X1,'multiplicative$uidentity')
| sum(multiply(X0,X3),X2,X0)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d86,plain,
( sum(multiply(X1,X0),X1,X1)
| ~ sum(X0,'multiplicative$uidentity','multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d85,c10]) ).
cnf(d87,plain,
sum(multiply(X0,X1),X0,X0),
inference(resolution,[status(thm)],[d48,d86]) ).
cnf(d88,plain,
sum(multiply(inverse(X0),multiply(X0,X1)),'additive$uidentity',multiply(inverse(X0),X0)),
inference(resolution,[status(thm)],[d87,d58]) ).
cnf(d89,plain,
sum(multiply(inverse(X0),multiply(X0,X1)),'additive$uidentity',multiply(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d88,d3]) ).
cnf(d90,plain,
sum(multiply(inverse(X0),multiply(X0,X1)),'additive$uidentity','additive$uidentity'),
inference(demodulation,[status(thm)],[d89,d55]) ).
cnf(d91,plain,
product(inverse(X0),multiply(X0,X1),'additive$uidentity'),
inference(resolution,[status(thm)],[d90,d84]) ).
cnf(d92,plain,
'additive$uidentity' = multiply('additive$uidentity',X0),
inference(resolution,[status(thm)],[d87,d0]) ).
cnf(d93,plain,
sum(inverse(y),inverse(x),'x$uinverse$uplus$uy$uinverse'),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d94,plain,
( ~ sum(X0,multiply('additive$uidentity',X3),X2)
| ~ sum(X0,X3,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d63,c8]) ).
cnf(d95,plain,
( ~ sum(inverse(y),multiply('additive$uidentity',inverse(x)),X0)
| product(inverse(y),'x$uinverse$uplus$uy$uinverse',X0) ),
inference(resolution,[status(thm)],[d94,d93]) ).
cnf(d96,plain,
( ~ sum(inverse(y),'additive$uidentity',X0)
| product(inverse(y),'x$uinverse$uplus$uy$uinverse',X0) ),
inference(demodulation,[status(thm)],[d95,d92]) ).
cnf(d97,plain,
product(inverse(y),'x$uinverse$uplus$uy$uinverse',inverse(y)),
inference(resolution,[status(thm)],[d96,c8]) ).
cnf(d98,plain,
multiply(inverse(y),'x$uinverse$uplus$uy$uinverse') = inverse(y),
inference(resolution,[status(thm)],[d97,d2]) ).
cnf(d99,plain,
multiply('x$uinverse$uplus$uy$uinverse',inverse(y)) = inverse(y),
inference(demodulation,[status(thm)],[d98,d3]) ).
cnf(d100,plain,
product(inverse('x$uinverse$uplus$uy$uinverse'),inverse(y),'additive$uidentity'),
inference(superposition,[status(thm)],[d99,d91]) ).
cnf(d101,plain,
multiply(inverse('x$uinverse$uplus$uy$uinverse'),inverse(y)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d100,d2]) ).
cnf(d102,plain,
multiply(inverse(y),inverse('x$uinverse$uplus$uy$uinverse')) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d101,d3]) ).
cnf(d103,plain,
sum(y,'additive$uidentity',add(y,inverse('x$uinverse$uplus$uy$uinverse'))),
inference(superposition,[status(thm)],[d102,d81]) ).
cnf(d104,plain,
add(y,inverse('x$uinverse$uplus$uy$uinverse')) = y,
inference(resolution,[status(thm)],[d103,d0]) ).
cnf(d105,plain,
inverse('x$uinverse$uplus$uy$uinverse') = multiply(inverse('x$uinverse$uplus$uy$uinverse'),y),
inference(superposition,[status(thm)],[d104,d77]) ).
cnf(d106,plain,
inverse('x$uinverse$uplus$uy$uinverse') = multiply(y,inverse('x$uinverse$uplus$uy$uinverse')),
inference(demodulation,[status(thm)],[d105,d3]) ).
cnf(d107,plain,
( ~ sum(X2,X0,x)
| sum(X3,X1,'x$utimes$uy')
| ~ product(X2,y,X3)
| ~ product(X0,y,X1) ),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d108,plain,
( ~ sum(X2,X0,x)
| sum(multiply(X2,y),X1,'x$utimes$uy')
| ~ product(X0,y,X1) ),
inference(resolution,[status(thm)],[d107,c4]) ).
cnf(d109,plain,
( sum(multiply(X0,y),'x$utimes$uy','x$utimes$uy')
| ~ sum(X0,x,x) ),
inference(resolution,[status(thm)],[d108,c0]) ).
cnf(d110,plain,
( ~ sum(inverse(x),inverse(y),X0)
| X0 = 'x$uinverse$uplus$uy$uinverse' ),
inference(resolution,[status(thm)],[c23,c1]) ).
cnf(d111,plain,
add(inverse(x),inverse(y)) = 'x$uinverse$uplus$uy$uinverse',
inference(resolution,[status(thm)],[d110,c3]) ).
cnf(d112,plain,
product('x$uinverse$uplus$uy$uinverse',inverse(x),inverse(x)),
inference(superposition,[status(thm)],[d111,d67]) ).
cnf(d113,plain,
multiply('x$uinverse$uplus$uy$uinverse',inverse(x)) = inverse(x),
inference(resolution,[status(thm)],[d112,d2]) ).
cnf(d114,plain,
product(inverse('x$uinverse$uplus$uy$uinverse'),inverse(x),'additive$uidentity'),
inference(superposition,[status(thm)],[d113,d91]) ).
cnf(d115,plain,
multiply(inverse('x$uinverse$uplus$uy$uinverse'),inverse(x)) = 'additive$uidentity',
inference(resolution,[status(thm)],[d114,d2]) ).
cnf(d116,plain,
multiply(inverse(x),inverse('x$uinverse$uplus$uy$uinverse')) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d115,d3]) ).
cnf(d117,plain,
sum(x,'additive$uidentity',add(x,inverse('x$uinverse$uplus$uy$uinverse'))),
inference(superposition,[status(thm)],[d116,d81]) ).
cnf(d118,plain,
add(x,inverse('x$uinverse$uplus$uy$uinverse')) = x,
inference(resolution,[status(thm)],[d117,d0]) ).
cnf(d119,plain,
sum(inverse('x$uinverse$uplus$uy$uinverse'),x,x),
inference(superposition,[status(thm)],[d118,d9]) ).
cnf(d120,plain,
sum(multiply(inverse('x$uinverse$uplus$uy$uinverse'),y),'x$utimes$uy','x$utimes$uy'),
inference(resolution,[status(thm)],[d119,d109]) ).
cnf(d121,plain,
sum(multiply(y,inverse('x$uinverse$uplus$uy$uinverse')),'x$utimes$uy','x$utimes$uy'),
inference(demodulation,[status(thm)],[d120,d3]) ).
cnf(d122,plain,
sum(inverse('x$uinverse$uplus$uy$uinverse'),'x$utimes$uy','x$utimes$uy'),
inference(demodulation,[status(thm)],[d121,d106]) ).
cnf(d123,plain,
'x$utimes$uy' = add('x$utimes$uy',inverse('x$uinverse$uplus$uy$uinverse')),
inference(resolution,[status(thm)],[d122,d74]) ).
cnf(d124,plain,
product(inverse('x$uinverse$uplus$uy$uinverse'),inverse('x$utimes$uy'),'additive$uidentity'),
inference(superposition,[status(thm)],[d123,d73]) ).
cnf(d125,plain,
multiply(inverse('x$uinverse$uplus$uy$uinverse'),inverse('x$utimes$uy')) = 'additive$uidentity',
inference(resolution,[status(thm)],[d124,d2]) ).
cnf(d126,plain,
multiply(inverse('x$utimes$uy'),inverse('x$uinverse$uplus$uy$uinverse')) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d125,d3]) ).
cnf(d127,plain,
sum('x$uinverse$uplus$uy$uinverse','additive$uidentity',add('x$uinverse$uplus$uy$uinverse',inverse('x$utimes$uy'))),
inference(superposition,[status(thm)],[d126,d45]) ).
cnf(d128,plain,
add('x$uinverse$uplus$uy$uinverse',inverse('x$utimes$uy')) = 'x$uinverse$uplus$uy$uinverse',
inference(resolution,[status(thm)],[d127,d0]) ).
cnf(d129,plain,
sum(inverse('x$utimes$uy'),multiply('x$uinverse$uplus$uy$uinverse','x$utimes$uy'),'x$uinverse$uplus$uy$uinverse'),
inference(superposition,[status(thm)],[d128,d42]) ).
cnf(d130,plain,
sum(inverse('x$utimes$uy'),multiply('x$utimes$uy','x$uinverse$uplus$uy$uinverse'),'x$uinverse$uplus$uy$uinverse'),
inference(demodulation,[status(thm)],[d129,d3]) ).
cnf(d131,plain,
sum(inverse('x$utimes$uy'),'additive$uidentity','x$uinverse$uplus$uy$uinverse'),
inference(demodulation,[status(thm)],[d130,d35]) ).
cnf(d132,plain,
'x$uinverse$uplus$uy$uinverse' = inverse('x$utimes$uy'),
inference(resolution,[status(thm)],[d131,d0]) ).
cnf(d133,plain,
'x$uinverse$uplus$uy$uinverse' != 'x$uinverse$uplus$uy$uinverse',
inference(demodulation,[status(thm)],[c2,d132]) ).
cnf(d134,plain,
( sum(multiply(X0,X1),'additive$uidentity',X1)
| ~ sum(X0,inverse(X1),'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d46,c22]) ).
cnf(d135,plain,
sum(multiply(X0,X0),'additive$uidentity',X0),
inference(resolution,[status(thm)],[d134,c20]) ).
cnf(d136,plain,
X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[d135,d0]) ).
cnf(d137,plain,
multiply(add(X0,X1),X0) = X0,
inference(resolution,[status(thm)],[d67,d2]) ).
cnf(d138,plain,
multiply(X0,add(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d137,d3]) ).
cnf(d139,plain,
X0 = add(multiply(X0,X1),X0),
inference(resolution,[status(thm)],[d87,d68]) ).
cnf(d140,plain,
X0 = add(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d139,d69]) ).
cnf(d141,plain,
'x$uinverse$uplus$uy$uinverse' = add('x$uinverse$uplus$uy$uinverse',inverse(x)),
inference(superposition,[status(thm)],[d113,d140]) ).
cnf(d142,plain,
multiply('x$uinverse$uplus$uy$uinverse','x$uinverse$uplus$uy$uinverse') = 'x$uinverse$uplus$uy$uinverse',
inference(superposition,[status(thm)],[d141,d138]) ).
cnf(d143,plain,
'x$uinverse$uplus$uy$uinverse' = 'x$uinverse$uplus$uy$uinverse',
inference(demodulation,[status(thm)],[d142,d136]) ).
cnf(d144,plain,
$false,
inference(resolution,[status(thm)],[d143,d133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO015-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:35:46 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 140.63/22.04 % SZS status Unsatisfiable for theBenchmark.p
% 140.63/22.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------