%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 06:54:38 AM UTC 2026
% Result : Unsatisfiable 86.92s 15.06s
% Output : CNFRefutation 86.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of clauses : 130 ( 66 unt; 0 nHn; 103 RR)
% Number of literals : 257 ( 22 equ; 129 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 237 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(y_plus_z,hypothesis,
sum(y,z,'y$uplus$uz') ).
cnf(x_plus__y_plus_z,hypothesis,
sum(x,'y$uplus$uz','x$u$uplus$uy$uplus$uz') ).
cnf(x_plus_y,hypothesis,
sum(x,y,'x$uplus$uy') ).
cnf(x_plus_y__plus_z,hypothesis,
sum('x$uplus$uy',z,'x$uplus$uy$u$uplus$uz') ).
cnf(prove_equality,negated_conjecture,
'x$u$uplus$uy$uplus$uz' != 'x$uplus$uy$u$uplus$uz' ).
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_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) ).
cnf(distributivity1,axiom,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity2,axiom,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity4,axiom,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ) ).
cnf(distributivity5,axiom,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ) ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$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,
sum(y,z,'y$uplus$uz'),
inference(clausification,[status(esa)],[y_plus_z]) ).
cnf(c1,plain,
sum(x,'y$uplus$uz','x$u$uplus$uy$uplus$uz'),
inference(clausification,[status(esa)],[x_plus__y_plus_z]) ).
cnf(c2,plain,
sum(x,y,'x$uplus$uy'),
inference(clausification,[status(esa)],[x_plus_y]) ).
cnf(c3,plain,
sum('x$uplus$uy',z,'x$uplus$uy$u$uplus$uz'),
inference(clausification,[status(esa)],[x_plus_y__plus_z]) ).
cnf(c4,plain,
'x$uplus$uy$u$uplus$uz' != 'x$u$uplus$uy$uplus$uz',
inference(clausification,[status(esa)],[prove_equality]) ).
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(c12,plain,
product(X0,'multiplicative$uidentity',X0),
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c13,plain,
( sum(X4,X5,X6)
| ~ product(X3,X2,X6)
| ~ product(X3,X1,X5)
| ~ product(X3,X0,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c14,plain,
( ~ sum(X5,X3,X1)
| ~ sum(X6,X4,X2)
| ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c16,plain,
( product(X6,X4,X2)
| ~ sum(X5,X3,X6)
| ~ product(X5,X4,X0)
| ~ product(X3,X4,X1)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity4]) ).
cnf(c17,plain,
( ~ sum(X0,X6,X4)
| ~ product(X5,X1,X6)
| ~ sum(X0,X5,X3)
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(clausification,[status(esa)],[distributivity5]) ).
cnf(c24,plain,
product(X0,inverse(X0),'additive$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,X1,add(X1,X0)),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
( ~ sum(X1,X2,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d2,plain,
add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ sum(X2,X1,X0)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[d0,c25]) ).
cnf(d4,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c26,c6]) ).
cnf(d5,plain,
( ~ product(X2,y,X0)
| product(X3,'x$uplus$uy',X1)
| ~ sum(x,X2,X3)
| ~ sum(x,X0,X1) ),
inference(resolution,[status(thm)],[c17,c2]) ).
cnf(d6,plain,
( ~ product('y$uplus$uz',y,X0)
| product('x$u$uplus$uy$uplus$uz','x$uplus$uy',X1)
| ~ sum(x,X0,X1) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( product('x$u$uplus$uy$uplus$uz','x$uplus$uy','x$uplus$uy')
| ~ product('y$uplus$uz',y,y) ),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( ~ product(X3,'additive$uidentity',X1)
| product(X4,X0,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c10]) ).
cnf(d9,plain,
( ~ product(z,'additive$uidentity',X0)
| product('y$uplus$uz',y,X1)
| ~ sum(y,X0,X1) ),
inference(resolution,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( product('y$uplus$uz',y,y)
| ~ product(z,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d9,c10]) ).
cnf(d11,plain,
product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d12,plain,
( ~ product(X1,inverse(X1),X0)
| 'additive$uidentity' = X0 ),
inference(resolution,[status(thm)],[c26,c24]) ).
cnf(d13,plain,
( ~ product(X3,X0,X4)
| ~ product(X3,X1,'additive$uidentity')
| product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(d14,plain,
( ~ product(X0,'additive$uidentity',X2)
| ~ product(X0,X1,'additive$uidentity')
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
( ~ product(X0,'additive$uidentity',X1)
| product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[d14,c24]) ).
cnf(d16,plain,
product(X0,inverse(X0),multiply('additive$uidentity',X0)),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
'additive$uidentity' = multiply('additive$uidentity',X0),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
product(X0,'additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
product('y$uplus$uz',y,y),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
product('x$u$uplus$uy$uplus$uz','x$uplus$uy','x$uplus$uy'),
inference(resolution,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
multiply('x$u$uplus$uy$uplus$uz','x$uplus$uy') = 'x$uplus$uy',
inference(resolution,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[d4,d11]) ).
cnf(d23,plain,
( ~ product('additive$uidentity',y,X0)
| product(x,'x$uplus$uy',X1)
| ~ sum(x,X0,X1) ),
inference(resolution,[status(thm)],[d5,c10]) ).
cnf(d24,plain,
( ~ product('additive$uidentity',y,'additive$uidentity')
| product(x,'x$uplus$uy',x) ),
inference(resolution,[status(thm)],[d23,c10]) ).
cnf(d25,plain,
product('additive$uidentity',X0,'additive$uidentity'),
inference(superposition,[status(thm)],[d17,c6]) ).
cnf(d26,plain,
product(x,'x$uplus$uy',x),
inference(resolution,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
sum('y$uplus$uz',x,'x$u$uplus$uy$uplus$uz'),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d28,plain,
( ~ product(X3,X5,X1)
| product(X4,add(X0,X5),X2)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c5]) ).
cnf(d29,plain,
( ~ product(x,X2,X0)
| product('x$u$uplus$uy$uplus$uz',add('y$uplus$uz',X2),X1)
| ~ sum('y$uplus$uz',X0,X1) ),
inference(resolution,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
( product('x$u$uplus$uy$uplus$uz',add('y$uplus$uz',X0),'x$u$uplus$uy$uplus$uz')
| ~ product(x,X0,x) ),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
product('x$u$uplus$uy$uplus$uz',add('y$uplus$uz','x$uplus$uy'),'x$u$uplus$uy$uplus$uz'),
inference(resolution,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( ~ product(X3,X4,X0)
| ~ product(X3,X5,X1)
| ~ product(X3,add(X4,X5),X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c13,c5]) ).
cnf(d33,plain,
( ~ product(X2,add(X4,X1),X3)
| ~ product(X2,X4,X0)
| sum(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
( ~ product(x,'additive$uidentity',X0)
| product('x$u$uplus$uy$uplus$uz','y$uplus$uz',X1)
| ~ sum('y$uplus$uz',X0,X1) ),
inference(resolution,[status(thm)],[d8,d27]) ).
cnf(d35,plain,
( product('x$u$uplus$uy$uplus$uz','y$uplus$uz','y$uplus$uz')
| ~ product(x,'additive$uidentity','additive$uidentity') ),
inference(resolution,[status(thm)],[d34,c10]) ).
cnf(d36,plain,
product('x$u$uplus$uy$uplus$uz','y$uplus$uz','y$uplus$uz'),
inference(resolution,[status(thm)],[d18,d35]) ).
cnf(d37,plain,
( ~ product('x$u$uplus$uy$uplus$uz',add('y$uplus$uz',X0),X1)
| sum('y$uplus$uz',multiply(X0,'x$u$uplus$uy$uplus$uz'),X1) ),
inference(resolution,[status(thm)],[d36,d33]) ).
cnf(d38,plain,
sum('y$uplus$uz',multiply('x$uplus$uy','x$u$uplus$uy$uplus$uz'),'x$u$uplus$uy$uplus$uz'),
inference(resolution,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
sum('y$uplus$uz',multiply('x$u$uplus$uy$uplus$uz','x$uplus$uy'),'x$u$uplus$uy$uplus$uz'),
inference(demodulation,[status(thm)],[d38,d22]) ).
cnf(d40,plain,
sum('y$uplus$uz','x$uplus$uy','x$u$uplus$uy$uplus$uz'),
inference(demodulation,[status(thm)],[d39,d21]) ).
cnf(d41,plain,
'x$u$uplus$uy$uplus$uz' = add('x$uplus$uy','y$uplus$uz'),
inference(resolution,[status(thm)],[d40,d3]) ).
cnf(d42,plain,
'x$u$uplus$uy$uplus$uz' = add('y$uplus$uz','x$uplus$uy'),
inference(demodulation,[status(thm)],[d41,d2]) ).
cnf(d43,plain,
sum(z,y,'y$uplus$uz'),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d44,plain,
( ~ product(X2,y,X0)
| product(X3,'y$uplus$uz',X1)
| ~ sum(z,X2,X3)
| ~ sum(z,X0,X1) ),
inference(resolution,[status(thm)],[c17,d43]) ).
cnf(d45,plain,
( ~ product('additive$uidentity',y,X0)
| product(z,'y$uplus$uz',X1)
| ~ sum(z,X0,X1) ),
inference(resolution,[status(thm)],[d44,c10]) ).
cnf(d46,plain,
( ~ product('additive$uidentity',y,'additive$uidentity')
| product(z,'y$uplus$uz',z) ),
inference(resolution,[status(thm)],[d45,c10]) ).
cnf(d47,plain,
product(z,'y$uplus$uz',z),
inference(resolution,[status(thm)],[d25,d46]) ).
cnf(d48,plain,
( ~ product(z,X2,X0)
| product('x$uplus$uy$u$uplus$uz',add('x$uplus$uy',X2),X1)
| ~ sum('x$uplus$uy',X0,X1) ),
inference(resolution,[status(thm)],[d28,c3]) ).
cnf(d49,plain,
( product('x$uplus$uy$u$uplus$uz',add('x$uplus$uy',X0),'x$uplus$uy$u$uplus$uz')
| ~ product(z,X0,z) ),
inference(resolution,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
product('x$uplus$uy$u$uplus$uz',add('x$uplus$uy','y$uplus$uz'),'x$uplus$uy$u$uplus$uz'),
inference(resolution,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
product('x$uplus$uy$u$uplus$uz',add('y$uplus$uz','x$uplus$uy'),'x$uplus$uy$u$uplus$uz'),
inference(demodulation,[status(thm)],[d50,d2]) ).
cnf(d52,plain,
product(add('y$uplus$uz','x$uplus$uy'),'x$uplus$uy$u$uplus$uz','x$uplus$uy$u$uplus$uz'),
inference(resolution,[status(thm)],[d51,c8]) ).
cnf(d53,plain,
product('x$u$uplus$uy$uplus$uz','x$uplus$uy$u$uplus$uz','x$uplus$uy$u$uplus$uz'),
inference(demodulation,[status(thm)],[d52,d42]) ).
cnf(d54,plain,
( ~ product('x$u$uplus$uy$uplus$uz','x$uplus$uy$u$uplus$uz',X0)
| 'x$uplus$uy$u$uplus$uz' = X0 ),
inference(resolution,[status(thm)],[d53,c26]) ).
cnf(d55,plain,
( ~ product(X0,X3,x)
| ~ product(X1,X3,'y$uplus$uz')
| product(X2,X3,'x$u$uplus$uy$uplus$uz')
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d56,plain,
( ~ product(x,X0,x)
| ~ product('y$uplus$uz',X0,'y$uplus$uz')
| product('x$u$uplus$uy$uplus$uz',X0,'x$u$uplus$uy$uplus$uz') ),
inference(resolution,[status(thm)],[d55,c1]) ).
cnf(d57,plain,
sum(z,'x$uplus$uy','x$uplus$uy$u$uplus$uz'),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d58,plain,
( ~ product(X2,'x$uplus$uy',X0)
| product(X3,'x$uplus$uy$u$uplus$uz',X1)
| ~ sum(z,X2,X3)
| ~ sum(z,X0,X1) ),
inference(resolution,[status(thm)],[c17,d57]) ).
cnf(d59,plain,
( ~ product(y,'x$uplus$uy',X0)
| product('y$uplus$uz','x$uplus$uy$u$uplus$uz',X1)
| ~ sum(z,X0,X1) ),
inference(resolution,[status(thm)],[d58,d43]) ).
cnf(d60,plain,
( product('y$uplus$uz','x$uplus$uy$u$uplus$uz','y$uplus$uz')
| ~ product(y,'x$uplus$uy',y) ),
inference(resolution,[status(thm)],[d59,d43]) ).
cnf(d61,plain,
sum(y,x,'x$uplus$uy'),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d62,plain,
( ~ product(X2,x,X0)
| product(X3,'x$uplus$uy',X1)
| ~ sum(y,X2,X3)
| ~ sum(y,X0,X1) ),
inference(resolution,[status(thm)],[d61,c17]) ).
cnf(d63,plain,
( ~ product('additive$uidentity',x,X0)
| product(y,'x$uplus$uy',X1)
| ~ sum(y,X0,X1) ),
inference(resolution,[status(thm)],[d62,c10]) ).
cnf(d64,plain,
( ~ product('additive$uidentity',x,'additive$uidentity')
| product(y,'x$uplus$uy',y) ),
inference(resolution,[status(thm)],[d63,c10]) ).
cnf(d65,plain,
product(y,'x$uplus$uy',y),
inference(resolution,[status(thm)],[d25,d64]) ).
cnf(d66,plain,
product('y$uplus$uz','x$uplus$uy$u$uplus$uz','y$uplus$uz'),
inference(resolution,[status(thm)],[d65,d60]) ).
cnf(d67,plain,
( product('x$u$uplus$uy$uplus$uz','x$uplus$uy$u$uplus$uz','x$u$uplus$uy$uplus$uz')
| ~ product(x,'x$uplus$uy$u$uplus$uz',x) ),
inference(resolution,[status(thm)],[d66,d56]) ).
cnf(d68,plain,
( ~ product('additive$uidentity',X3,X1)
| product(X0,add(X0,X3),X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,c10]) ).
cnf(d69,plain,
( ~ product('additive$uidentity',X1,'additive$uidentity')
| product(X0,add(X0,X1),X0) ),
inference(resolution,[status(thm)],[d68,c10]) ).
cnf(d70,plain,
product(X0,add(X0,X1),X0),
inference(resolution,[status(thm)],[d25,d69]) ).
cnf(d71,plain,
( ~ product('additive$uidentity','additive$uidentity',X1)
| product(X0,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d72,plain,
( ~ product('additive$uidentity','additive$uidentity','additive$uidentity')
| product(X0,X0,X0) ),
inference(resolution,[status(thm)],[d71,c10]) ).
cnf(d73,plain,
( ~ product(X0,'multiplicative$uidentity',X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c26,c12]) ).
cnf(d74,plain,
( ~ product('additive$uidentity','additive$uidentity',X0)
| product('additive$uidentity','multiplicative$uidentity',X0) ),
inference(resolution,[status(thm)],[d14,c12]) ).
cnf(d75,plain,
product('additive$uidentity','multiplicative$uidentity',multiply('additive$uidentity','additive$uidentity')),
inference(resolution,[status(thm)],[d74,d11]) ).
cnf(d76,plain,
'additive$uidentity' = multiply('additive$uidentity','additive$uidentity'),
inference(resolution,[status(thm)],[d75,d73]) ).
cnf(d77,plain,
product('additive$uidentity','additive$uidentity','additive$uidentity'),
inference(superposition,[status(thm)],[d76,d11]) ).
cnf(d78,plain,
product(X0,X0,X0),
inference(resolution,[status(thm)],[d77,d72]) ).
cnf(d79,plain,
( ~ product(X0,add(X0,X1),X2)
| sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[d78,d33]) ).
cnf(d80,plain,
sum(X0,multiply(X1,X0),X0),
inference(resolution,[status(thm)],[d79,d70]) ).
cnf(d81,plain,
X0 = add(multiply(X1,X0),X0),
inference(resolution,[status(thm)],[d80,d3]) ).
cnf(d82,plain,
X1 = add(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d81,d2]) ).
cnf(d83,plain,
( ~ product(X3,X0,X4)
| ~ product(X3,X1,X5)
| product(X3,X2,add(X4,X5))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c5]) ).
cnf(d84,plain,
( ~ product(X0,z,X1)
| ~ product(X0,'x$uplus$uy',X2)
| product(X0,'x$uplus$uy$u$uplus$uz',add(X1,X2)) ),
inference(resolution,[status(thm)],[d83,d57]) ).
cnf(d85,plain,
( product(X0,'x$uplus$uy$u$uplus$uz',add(multiply(z,X0),X1))
| ~ product(X0,'x$uplus$uy',X1) ),
inference(resolution,[status(thm)],[d84,d11]) ).
cnf(d86,plain,
product(x,'x$uplus$uy$u$uplus$uz',add(multiply(z,x),x)),
inference(resolution,[status(thm)],[d85,d26]) ).
cnf(d87,plain,
product(x,'x$uplus$uy$u$uplus$uz',add(x,multiply(z,x))),
inference(demodulation,[status(thm)],[d86,d2]) ).
cnf(d88,plain,
product(x,'x$uplus$uy$u$uplus$uz',x),
inference(demodulation,[status(thm)],[d87,d82]) ).
cnf(d89,plain,
product('x$u$uplus$uy$uplus$uz','x$uplus$uy$u$uplus$uz','x$u$uplus$uy$uplus$uz'),
inference(resolution,[status(thm)],[d88,d67]) ).
cnf(d90,plain,
'x$uplus$uy$u$uplus$uz' = 'x$u$uplus$uy$uplus$uz',
inference(resolution,[status(thm)],[d89,d54]) ).
cnf(d91,plain,
$false,
inference(resolution,[status(thm)],[c4,d90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n009.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 22:34:44 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 86.92/15.06 % SZS status Unsatisfiable for theBenchmark.p
% 86.92/15.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------