%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 93.71s 23.57s
% Output : CNFRefutation 93.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 24
% Syntax : Number of clauses : 144 ( 78 unt; 0 nHn; 104 RR)
% Number of literals : 278 ( 33 equ; 136 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 : 308 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X0)) = X0 ).
cnf(x_plus_y,hypothesis,
sum(x,y,'x$uplus$uy') ).
cnf(x_inverse_times_y_inverse,hypothesis,
product(inverse(x),inverse(y),'x$uinverse$utimes$uy$uinverse') ).
cnf(prove_equation,negated_conjecture,
inverse('x$uplus$uy') != 'x$uinverse$utimes$uy$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(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(distributivity8,axiom,
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,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,
inverse(inverse(X0)) = X0,
inference(clausification,[status(esa)],[inverse_is_self_cancelling]) ).
cnf(c2,plain,
sum(x,y,'x$uplus$uy'),
inference(clausification,[status(esa)],[x_plus_y]) ).
cnf(c3,plain,
product(inverse(x),inverse(y),'x$uinverse$utimes$uy$uinverse'),
inference(clausification,[status(esa)],[x_inverse_times_y_inverse]) ).
cnf(c4,plain,
inverse('x$uplus$uy') != 'x$uinverse$utimes$uy$uinverse',
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(c5,plain,
sum(X0,X1,add(X0,X1)),
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c6,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c7,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c8,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c9,plain,
sum('additive$uidentity',X0,X0),
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c10,plain,
sum(X0,'additive$uidentity',X0),
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c11,plain,
product('multiplicative$uidentity',X0,X0),
inference(clausification,[status(esa)],[multiplicative_identity1]) ).
cnf(c12,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c13,plain,
( ~ product(X3,X0,X6)
| sum(X6,X5,X4)
| ~ product(X3,X1,X5)
| ~ product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c14,plain,
( ~ product(X0,X3,X5)
| product(X0,X4,X6)
| ~ sum(X5,X2,X6)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c15,plain,
( sum(X2,X5,X6)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity3]) ).
cnf(c17,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)],[distributivity5]) ).
cnf(c18,plain,
( ~ product(X6,X3,X1)
| ~ sum(X0,X6,X5)
| ~ product(X5,X4,X2)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity6]) ).
cnf(c20,plain,
( ~ product(X6,X4,X2)
| ~ sum(X5,X1,X6)
| ~ product(X5,X3,X0)
| ~ sum(X3,X1,X4)
| sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity8]) ).
cnf(c21,plain,
sum(inverse(X0),X0,'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse1]) ).
cnf(c22,plain,
sum(X0,inverse(X0),'multiplicative$uidentity'),
inference(clausification,[status(esa)],[additive_inverse2]) ).
cnf(c23,plain,
product(inverse(X0),X0,'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse1]) ).
cnf(c24,plain,
product(X0,inverse(X0),'additive$uidentity'),
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c25,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c26,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(d0,plain,
( ~ sum(X0,'additive$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c25,c10]) ).
cnf(d1,plain,
( ~ sum('additive$uidentity',X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c25,c9]) ).
cnf(d2,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d3,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c26,c6]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ sum(X3,X0,'multiplicative$uidentity')
| sum(X4,X2,X1)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d6,plain,
( ~ sum('multiplicative$uidentity',X0,'multiplicative$uidentity')
| sum(X1,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d8,plain,
( ~ product('multiplicative$uidentity',X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c26,c11]) ).
cnf(d9,plain,
( ~ sum(X3,X4,X0)
| ~ sum(X3,'multiplicative$uidentity',X1)
| ~ sum(X3,X4,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(d10,plain,
( ~ sum(X2,'multiplicative$uidentity',X1)
| ~ sum(X2,inverse(X2),X0)
| product(X0,X1,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d9,c22]) ).
cnf(d11,plain,
( ~ sum(X1,'multiplicative$uidentity',X0)
| product('multiplicative$uidentity',X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d10,c22]) ).
cnf(d12,plain,
product('multiplicative$uidentity',add(X0,'multiplicative$uidentity'),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
'multiplicative$uidentity' = add(X0,'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
sum('multiplicative$uidentity',X0,'multiplicative$uidentity'),
inference(superposition,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( sum(X1,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
sum(inverse(y),'x$uinverse$utimes$uy$uinverse',inverse(y)),
inference(resolution,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
sum('x$uinverse$utimes$uy$uinverse',inverse(y),inverse(y)),
inference(resolution,[status(thm)],[d16,c7]) ).
cnf(d18,plain,
( ~ sum(X3,X0,inverse(X1))
| sum(X4,X2,'additive$uidentity')
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c23,c15]) ).
cnf(d19,plain,
( ~ sum(X3,X0,inverse(X1))
| sum(multiply(X1,X3),X2,'additive$uidentity')
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( sum(multiply(X1,X0),'additive$uidentity','additive$uidentity')
| ~ sum(X0,inverse(X1),inverse(X1)) ),
inference(resolution,[status(thm)],[d19,c23]) ).
cnf(d21,plain,
sum(multiply(y,'x$uinverse$utimes$uy$uinverse'),'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
multiply(y,'x$uinverse$utimes$uy$uinverse') = 'additive$uidentity',
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( ~ sum(X1,X3,X5)
| sum(X2,X4,multiply(X0,X5))
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c6]) ).
cnf(d24,plain,
( ~ sum(X1,X3,X4)
| sum(X2,multiply(X3,X0),multiply(X0,X4))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
( ~ sum(X0,X2,X3)
| sum(multiply(X0,X1),multiply(X2,X1),multiply(X1,X3)) ),
inference(resolution,[status(thm)],[d24,d2]) ).
cnf(d26,plain,
sum(multiply(x,X0),multiply(y,X0),multiply(X0,'x$uplus$uy')),
inference(resolution,[status(thm)],[d25,c2]) ).
cnf(d27,plain,
( ~ product(X2,X1,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[d2,c26]) ).
cnf(d28,plain,
sum(X0,multiply(X0,X1),X0),
inference(resolution,[status(thm)],[d15,d2]) ).
cnf(d29,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(resolution,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
'additive$uidentity' = multiply(X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( ~ sum(X3,X5,X1)
| ~ sum(X4,multiply(X0,X5),X2)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c6]) ).
cnf(d32,plain,
( ~ sum(X3,X4,X1)
| ~ sum(multiply(X3,X0),multiply(X0,X4),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d31,d2]) ).
cnf(d33,plain,
( ~ sum(multiply(X1,X0),multiply(X0,'additive$uidentity'),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d32,c10]) ).
cnf(d34,plain,
( ~ sum(multiply(X1,X0),'additive$uidentity',X2)
| product(X0,X1,X2) ),
inference(demodulation,[status(thm)],[d33,d30]) ).
cnf(d35,plain,
product(inverse(y),inverse(x),'x$uinverse$utimes$uy$uinverse'),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d36,plain,
sum(inverse(x),'x$uinverse$utimes$uy$uinverse',inverse(x)),
inference(resolution,[status(thm)],[d15,d35]) ).
cnf(d37,plain,
sum('x$uinverse$utimes$uy$uinverse',inverse(x),inverse(x)),
inference(resolution,[status(thm)],[d36,c7]) ).
cnf(d38,plain,
sum(multiply(x,'x$uinverse$utimes$uy$uinverse'),'additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d20,d37]) ).
cnf(d39,plain,
product('x$uinverse$utimes$uy$uinverse',x,'additive$uidentity'),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
'additive$uidentity' = multiply(x,'x$uinverse$utimes$uy$uinverse'),
inference(resolution,[status(thm)],[d39,d27]) ).
cnf(d41,plain,
sum('additive$uidentity',multiply(y,'x$uinverse$utimes$uy$uinverse'),multiply('x$uinverse$utimes$uy$uinverse','x$uplus$uy')),
inference(superposition,[status(thm)],[d40,d26]) ).
cnf(d42,plain,
sum('additive$uidentity','additive$uidentity',multiply('x$uinverse$utimes$uy$uinverse','x$uplus$uy')),
inference(demodulation,[status(thm)],[d41,d22]) ).
cnf(d43,plain,
sum('additive$uidentity','additive$uidentity',multiply('x$uplus$uy','x$uinverse$utimes$uy$uinverse')),
inference(demodulation,[status(thm)],[d42,d4]) ).
cnf(d44,plain,
'additive$uidentity' = multiply('x$uplus$uy','x$uinverse$utimes$uy$uinverse'),
inference(resolution,[status(thm)],[d43,d1]) ).
cnf(d45,plain,
( ~ product(X1,'multiplicative$uidentity',X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c26,c12]) ).
cnf(d46,plain,
multiply(X0,'multiplicative$uidentity') = X0,
inference(resolution,[status(thm)],[d45,c6]) ).
cnf(d47,plain,
( ~ sum(X3,X1,X5)
| ~ sum(X3,X0,X4)
| sum(X3,X2,multiply(X4,X5))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d48,plain,
( ~ sum(X0,X2,X3)
| ~ sum(X0,X1,X4)
| sum(X0,multiply(X1,X2),multiply(X3,X4)) ),
inference(resolution,[status(thm)],[d47,d2]) ).
cnf(d49,plain,
( sum(X0,multiply(X1,X3),multiply(add(X3,X0),X2))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d48,d7]) ).
cnf(d50,plain,
sum(inverse(X0),multiply(X0,X1),multiply(add(X1,inverse(X0)),'multiplicative$uidentity')),
inference(resolution,[status(thm)],[d49,c21]) ).
cnf(d51,plain,
sum(inverse(X1),multiply(X1,X0),add(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d53,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d52,d7]) ).
cnf(d54,plain,
( ~ sum(X3,X1,'multiplicative$uidentity')
| ~ sum(X3,X0,X4)
| sum(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c18,c12]) ).
cnf(d55,plain,
( ~ sum(X0,X2,X1)
| ~ sum(X0,inverse(X2),'multiplicative$uidentity')
| sum(X0,'additive$uidentity',X1) ),
inference(resolution,[status(thm)],[d54,c24]) ).
cnf(d56,plain,
( sum(X0,'additive$uidentity',add(X1,X0))
| ~ sum(X0,inverse(X1),'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d55,d7]) ).
cnf(d57,plain,
( sum(X1,'additive$uidentity',add(inverse(X0),X1))
| ~ sum(X1,X0,'multiplicative$uidentity') ),
inference(superposition,[status(thm)],[c0,d56]) ).
cnf(d58,plain,
( ~ sum(X3,X4,X0)
| ~ sum(X3,X5,X1)
| ~ sum(X3,multiply(X4,X5),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c6]) ).
cnf(d59,plain,
( ~ sum(X1,multiply(X4,X2),X3)
| ~ sum(X1,X4,X0)
| product(X0,add(X1,X2),X3) ),
inference(resolution,[status(thm)],[d58,c5]) ).
cnf(d60,plain,
( ~ sum(inverse(X0),multiply(X0,X1),X2)
| product('multiplicative$uidentity',add(inverse(X0),X1),X2) ),
inference(resolution,[status(thm)],[d59,c21]) ).
cnf(d61,plain,
( ~ sum(X0,multiply('additive$uidentity',X1),X2)
| product(X0,add(X0,X1),X2) ),
inference(resolution,[status(thm)],[d59,c10]) ).
cnf(d62,plain,
( ~ sum(X1,'additive$uidentity',X2)
| product(X1,add(X1,X0),X2) ),
inference(demodulation,[status(thm)],[d61,d29]) ).
cnf(d63,plain,
product(X0,add(X0,X1),X0),
inference(resolution,[status(thm)],[d62,c10]) ).
cnf(d64,plain,
( ~ sum(x,y,X0)
| 'x$uplus$uy' = X0 ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d65,plain,
'x$uplus$uy' = add(x,y),
inference(resolution,[status(thm)],[d64,c5]) ).
cnf(d66,plain,
product(x,'x$uplus$uy',x),
inference(superposition,[status(thm)],[d65,d63]) ).
cnf(d67,plain,
x = multiply('x$uplus$uy',x),
inference(resolution,[status(thm)],[d66,d27]) ).
cnf(d68,plain,
x = multiply(x,'x$uplus$uy'),
inference(demodulation,[status(thm)],[d67,d4]) ).
cnf(d69,plain,
( product('multiplicative$uidentity',add(inverse(x),'x$uplus$uy'),X0)
| ~ sum(inverse(x),x,X0) ),
inference(superposition,[status(thm)],[d68,d60]) ).
cnf(d70,plain,
( ~ sum(inverse(x),x,X0)
| product('multiplicative$uidentity',add('x$uplus$uy',inverse(x)),X0) ),
inference(demodulation,[status(thm)],[d69,d53]) ).
cnf(d71,plain,
product('multiplicative$uidentity',add('x$uplus$uy',inverse(x)),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d70,c21]) ).
cnf(d72,plain,
'multiplicative$uidentity' = add('x$uplus$uy',inverse(x)),
inference(resolution,[status(thm)],[d71,d8]) ).
cnf(d73,plain,
( ~ sum(X0,X3,X4)
| ~ sum(X1,X3,'multiplicative$uidentity')
| sum(X2,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c20,c12]) ).
cnf(d74,plain,
( ~ sum(inverse(x),X0,X1)
| ~ sum(inverse(y),X0,'multiplicative$uidentity')
| sum('x$uinverse$utimes$uy$uinverse',X0,X1) ),
inference(resolution,[status(thm)],[d73,c3]) ).
cnf(d75,plain,
( sum('x$uinverse$utimes$uy$uinverse',X0,add(X0,inverse(x)))
| ~ sum(inverse(y),X0,'multiplicative$uidentity') ),
inference(resolution,[status(thm)],[d74,d7]) ).
cnf(d76,plain,
sum(y,x,'x$uplus$uy'),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d77,plain,
( ~ sum(X1,multiply(X3,'additive$uidentity'),X2)
| ~ sum(X1,X3,X0)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d58,c10]) ).
cnf(d78,plain,
( ~ sum(y,multiply(x,'additive$uidentity'),X0)
| product('x$uplus$uy',y,X0) ),
inference(resolution,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
( ~ sum(y,'additive$uidentity',X0)
| product('x$uplus$uy',y,X0) ),
inference(demodulation,[status(thm)],[d78,d30]) ).
cnf(d80,plain,
product('x$uplus$uy',y,y),
inference(resolution,[status(thm)],[d79,c10]) ).
cnf(d81,plain,
y = multiply(y,'x$uplus$uy'),
inference(resolution,[status(thm)],[d80,d27]) ).
cnf(d82,plain,
( product('multiplicative$uidentity',add(inverse(y),'x$uplus$uy'),X0)
| ~ sum(inverse(y),y,X0) ),
inference(superposition,[status(thm)],[d81,d60]) ).
cnf(d83,plain,
( ~ sum(inverse(y),y,X0)
| product('multiplicative$uidentity',add('x$uplus$uy',inverse(y)),X0) ),
inference(demodulation,[status(thm)],[d82,d53]) ).
cnf(d84,plain,
product('multiplicative$uidentity',add('x$uplus$uy',inverse(y)),'multiplicative$uidentity'),
inference(resolution,[status(thm)],[d83,c21]) ).
cnf(d85,plain,
'multiplicative$uidentity' = add('x$uplus$uy',inverse(y)),
inference(resolution,[status(thm)],[d84,d8]) ).
cnf(d86,plain,
sum(inverse(y),'x$uplus$uy','multiplicative$uidentity'),
inference(superposition,[status(thm)],[d85,d7]) ).
cnf(d87,plain,
sum('x$uinverse$utimes$uy$uinverse','x$uplus$uy',add('x$uplus$uy',inverse(x))),
inference(resolution,[status(thm)],[d86,d75]) ).
cnf(d88,plain,
sum('x$uinverse$utimes$uy$uinverse','x$uplus$uy','multiplicative$uidentity'),
inference(demodulation,[status(thm)],[d87,d72]) ).
cnf(d89,plain,
sum('x$uinverse$utimes$uy$uinverse','additive$uidentity',add(inverse('x$uplus$uy'),'x$uinverse$utimes$uy$uinverse')),
inference(resolution,[status(thm)],[d88,d57]) ).
cnf(d90,plain,
sum('x$uinverse$utimes$uy$uinverse','additive$uidentity',add('x$uinverse$utimes$uy$uinverse',inverse('x$uplus$uy'))),
inference(demodulation,[status(thm)],[d89,d53]) ).
cnf(d91,plain,
'x$uinverse$utimes$uy$uinverse' = add('x$uinverse$utimes$uy$uinverse',inverse('x$uplus$uy')),
inference(resolution,[status(thm)],[d90,d0]) ).
cnf(d92,plain,
sum(inverse('x$uplus$uy'),multiply('x$uplus$uy','x$uinverse$utimes$uy$uinverse'),'x$uinverse$utimes$uy$uinverse'),
inference(superposition,[status(thm)],[d91,d51]) ).
cnf(d93,plain,
sum(inverse('x$uplus$uy'),'additive$uidentity','x$uinverse$utimes$uy$uinverse'),
inference(demodulation,[status(thm)],[d92,d44]) ).
cnf(d94,plain,
inverse('x$uplus$uy') = 'x$uinverse$utimes$uy$uinverse',
inference(resolution,[status(thm)],[d93,d0]) ).
cnf(d95,plain,
$false,
inference(resolution,[status(thm)],[c4,d94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 22:36:49 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 93.71/23.57 % SZS status Unsatisfiable for theBenchmark.p
% 93.71/23.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------