TSTP Solution File: GRP121-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:36:18 EDT 2022
% Result : Unsatisfiable 16.62s 16.79s
% Output : Refutation 16.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,Z))),multiply(Z,multiply(Z,Z)))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(single_axiom2,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom2) ).
cnf(prove_order3,negated_conjecture,
multiply(a,identity) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).
cnf(5,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y)))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom2,theory(equality)]) ).
cnf(6,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,identity))),identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom2,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(7,plain,
multiply(X,multiply(multiply(X,Y),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z)))))) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(11,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,identity))),identity)) = X,
inference('PARAMODULATE',[status(thm)],[6,single_axiom2,theory(equality)]) ).
cnf(12,plain,
multiply(X,multiply(multiply(X,Y),identity)) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(Y,identity))),
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(14,plain,
multiply(identity,multiply(multiply(identity,X),identity)) = multiply(identity,multiply(identity,multiply(X,identity))),
inference('PARAMODULATE',[status(thm)],[11,11,theory(equality)]) ).
cnf(16,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X,identity)),identity))) = X,
inference('PARAMODULATE',[status(thm)],[11,14,theory(equality)]) ).
cnf(17,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X),identity)),identity)) = X,
inference('PARAMODULATE',[status(thm)],[11,14,theory(equality)]) ).
cnf(18,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,X)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),
inference('PARAMODULATE',[status(thm)],[14,14,theory(equality)]) ).
cnf(20,plain,
X = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X),identity),identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,14,theory(equality)]),11,theory(equality)]) ).
cnf(24,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X,identity),identity)))) = X,
inference('PARAMODULATE',[status(thm)],[16,14,theory(equality)]) ).
cnf(26,plain,
multiply(identity,multiply(X,identity)) = multiply(multiply(identity,X),identity),
inference('PARAMODULATE',[status(thm)],[17,17,theory(equality)]) ).
cnf(27,plain,
multiply(identity,multiply(multiply(identity,multiply(X,identity)),identity)) = multiply(multiply(identity,multiply(multiply(identity,X),identity)),identity),
inference('PARAMODULATE',[status(thm)],[17,17,theory(equality)]) ).
cnf(28,plain,
multiply(identity,multiply(multiply(identity,multiply(X,identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,single_axiom,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(30,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),identity) = X,
inference('PARAMODULATE',[status(thm)],[11,26,theory(equality)]) ).
cnf(31,plain,
multiply(identity,multiply(multiply(multiply(identity,multiply(identity,X)),identity),identity)) = X,
inference('PARAMODULATE',[status(thm)],[17,26,theory(equality)]) ).
cnf(32,plain,
multiply(multiply(identity,multiply(identity,X)),identity) = multiply(identity,multiply(identity,multiply(X,identity))),
inference('PARAMODULATE',[status(thm)],[14,26,theory(equality)]) ).
cnf(33,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,X),identity))),identity) = X,
inference('PARAMODULATE',[status(thm)],[17,26,theory(equality)]) ).
cnf(34,plain,
multiply(identity,multiply(multiply(X,identity),identity)) = multiply(multiply(multiply(identity,X),identity),identity),
inference('PARAMODULATE',[status(thm)],[26,26,theory(equality)]) ).
cnf(37,plain,
multiply(identity,multiply(multiply(multiply(identity,X),identity),identity)) = multiply(multiply(identity,multiply(identity,multiply(X,identity))),identity),
inference('PARAMODULATE',[status(thm)],[26,14,theory(equality)]) ).
cnf(65,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,X))),identity) = multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),
inference('PARAMODULATE',[status(thm)],[30,30,theory(equality)]) ).
cnf(66,plain,
multiply(identity,X) = multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(X,identity))))),identity),
inference('PARAMODULATE',[status(thm)],[26,30,theory(equality)]) ).
cnf(68,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference('PARAMODULATE',[status(thm)],[6,30,theory(equality)]) ).
cnf(69,plain,
X = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X)),identity)),identity),
inference('PARAMODULATE',[status(thm)],[26,31,theory(equality)]) ).
cnf(81,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,X))),identity),identity) = X,
inference('PARAMODULATE',[status(thm)],[33,32,theory(equality)]) ).
cnf(83,plain,
multiply(multiply(identity,multiply(identity,multiply(X,identity))),identity) = multiply(multiply(multiply(identity,multiply(identity,X)),identity),identity),
inference('PARAMODULATE',[status(thm)],[33,31,theory(equality)]) ).
cnf(84,plain,
multiply(multiply(identity,multiply(identity,multiply(X,identity))),identity) = multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))),
inference('PARAMODULATE',[status(thm)],[33,5,theory(equality)]) ).
cnf(85,plain,
multiply(multiply(multiply(identity,X),identity),identity) = multiply(multiply(identity,multiply(X,identity)),identity),
inference('PARAMODULATE',[status(thm)],[26,34,theory(equality)]) ).
cnf(86,plain,
multiply(identity,multiply(multiply(multiply(X,identity),identity),identity)) = multiply(multiply(multiply(multiply(identity,X),identity),identity),identity),
inference('PARAMODULATE',[status(thm)],[26,34,theory(equality)]) ).
cnf(101,plain,
multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))) = multiply(multiply(identity,multiply(multiply(identity,X),identity)),identity),
inference('PARAMODULATE',[status(thm)],[69,5,theory(equality)]) ).
cnf(102,plain,
multiply(multiply(multiply(identity,multiply(identity,X)),identity),identity) = multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))),
inference('PARAMODULATE',[status(thm)],[81,5,theory(equality)]) ).
cnf(143,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(multiply(X,Y),identity)),identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,12,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(146,plain,
multiply(X,multiply(multiply(X,multiply(identity,multiply(identity,Y))),identity)) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(identity,multiply(identity,multiply(Y,identity))))),
inference('PARAMODULATE',[status(thm)],[12,32,theory(equality)]) ).
cnf(176,plain,
multiply(multiply(multiply(X,X),multiply(X,X)),multiply(multiply(multiply(X,X),multiply(Y,identity)),identity)) = multiply(multiply(X,multiply(multiply(X,Y),identity)),identity),
inference('PARAMODULATE',[status(thm)],[143,143,theory(equality)]) ).
cnf(178,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(Y,identity)),identity)) = multiply(multiply(X,multiply(multiply(X,X),multiply(Y,Z))),multiply(Z,multiply(Z,Z))),
inference('PARAMODULATE',[status(thm)],[143,single_axiom,theory(equality)]) ).
cnf(436,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,X),Y))),multiply(Y,multiply(Y,Y))) = X,
inference('PARAMODULATE',[status(thm)],[17,28,theory(equality)]) ).
cnf(438,plain,
identity = multiply(multiply(identity,multiply(identity,multiply(identity,X))),multiply(X,multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,single_axiom2,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(444,plain,
identity = multiply(X,multiply(multiply(multiply(X,identity),identity),multiply(multiply(multiply(X,identity),identity),multiply(multiply(X,identity),identity)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,24,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(456,plain,
multiply(multiply(X,identity),identity) = multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,X),identity),identity),Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,86,theory(equality)]),11,theory(equality)]) ).
cnf(491,plain,
multiply(multiply(multiply(identity,multiply(identity,multiply(identity,X))),multiply(identity,multiply(identity,multiply(identity,X)))),X) = multiply(X,multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,438,theory(equality)]),81,single_axiom2,theory(equality)]) ).
cnf(492,plain,
multiply(identity,multiply(identity,X)) = multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,438,theory(equality)]),single_axiom2,69,theory(equality)]) ).
cnf(498,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z)))))) = multiply(identity,multiply(identity,multiply(multiply(identity,Y),Z))),
inference('PARAMODULATE',[status(thm)],[single_axiom,436,theory(equality)]) ).
cnf(513,plain,
multiply(multiply(X,X),multiply(multiply(X,identity),identity)) = multiply(multiply(multiply(X,identity),identity),multiply(multiply(multiply(X,identity),identity),multiply(multiply(X,identity),identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,444,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(525,plain,
identity = multiply(X,multiply(multiply(X,X),multiply(multiply(X,identity),identity))),
inference('REWRITE',[status(thm)],[444,513,theory(equality)]) ).
cnf(527,plain,
identity = multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),multiply(identity,X)),multiply(identity,multiply(multiply(X,identity),identity)))),
inference('PARAMODULATE',[status(thm)],[525,34,theory(equality)]) ).
cnf(564,plain,
multiply(multiply(X,X),multiply(multiply(X,Y),identity)) = multiply(multiply(X,multiply(multiply(X,X),Y)),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,68,theory(equality)]),30,theory(equality)]) ).
cnf(567,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference('REWRITE',[status(thm)],[68,564,theory(equality)]) ).
cnf(570,plain,
multiply(multiply(X,X),multiply(multiply(X,X),multiply(multiply(X,identity),identity))) = X,
inference('PARAMODULATE',[status(thm)],[143,564,theory(equality)]) ).
cnf(577,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(multiply(X,X),Y)))),identity) = multiply(identity,multiply(identity,multiply(multiply(X,X),multiply(multiply(X,Y),identity)))),
inference('PARAMODULATE',[status(thm)],[32,564,theory(equality)]) ).
cnf(623,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(Y,identity)),identity))) = Y,
inference('PARAMODULATE',[status(thm)],[24,567,theory(equality)]) ).
cnf(625,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,X))),identity) = multiply(Y,multiply(multiply(Y,Y),multiply(multiply(Y,X),identity))),
inference('PARAMODULATE',[status(thm)],[65,567,theory(equality)]) ).
cnf(626,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,X)),identity)) = multiply(Y,multiply(multiply(Y,Y),multiply(multiply(Y,X),identity))),
inference('PARAMODULATE',[status(thm)],[18,567,theory(equality)]) ).
cnf(627,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(identity,multiply(Y,identity))),identity))) = multiply(identity,Y),
inference('PARAMODULATE',[status(thm)],[567,16,theory(equality)]) ).
cnf(641,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(multiply(multiply(X,X),multiply(X,X)),multiply(multiply(multiply(X,X),Y),identity))),identity)) = multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))),identity),
inference('PARAMODULATE',[status(thm)],[564,567,theory(equality)]) ).
cnf(705,plain,
multiply(multiply(identity,X),multiply(identity,multiply(multiply(X,X),multiply(multiply(X,identity),identity)))) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,527,theory(equality)]),513,theory(equality)]) ).
cnf(736,plain,
multiply(multiply(multiply(identity,X),multiply(identity,X)),multiply(multiply(multiply(identity,X),identity),identity)) = multiply(identity,multiply(multiply(X,X),multiply(multiply(X,identity),identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,705,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(758,plain,
multiply(multiply(X,multiply(X,X)),identity) = multiply(X,multiply(multiply(X,X),identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[625,525,theory(equality)]),single_axiom2,491,81,736,theory(equality)]) ).
cnf(781,plain,
multiply(identity,multiply(X,multiply(multiply(X,X),identity))) = multiply(multiply(identity,multiply(X,multiply(X,X))),identity),
inference('PARAMODULATE',[status(thm)],[26,758,theory(equality)]) ).
cnf(783,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(X,multiply(multiply(X,X),identity))),identity)) = multiply(X,X),
inference('PARAMODULATE',[status(thm)],[143,758,theory(equality)]) ).
cnf(792,plain,
multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,X))),multiply(multiply(multiply(identity,multiply(identity,X)),identity),identity)) = multiply(multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),identity),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[83,758,theory(equality)]),736,577,theory(equality)]) ).
cnf(813,plain,
multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))),identity) = multiply(multiply(X,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[564,626,theory(equality)]),641,theory(equality)]) ).
cnf(824,plain,
multiply(X,multiply(multiply(identity,Y),identity)) = multiply(X,multiply(identity,multiply(Y,identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,627,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(836,plain,
multiply(X,multiply(identity,multiply(identity,multiply(Y,identity)))) = multiply(X,multiply(identity,multiply(multiply(identity,Y),identity))),
inference('PARAMODULATE',[status(thm)],[824,32,theory(equality)]) ).
cnf(837,plain,
multiply(X,multiply(multiply(identity,multiply(Y,identity)),identity)) = multiply(X,multiply(multiply(multiply(identity,Y),identity),identity)),
inference('PARAMODULATE',[status(thm)],[824,34,theory(equality)]) ).
cnf(839,plain,
multiply(X,multiply(multiply(identity,multiply(multiply(identity,Y),identity)),identity)) = multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,identity)),identity))),
inference('PARAMODULATE',[status(thm)],[824,824,theory(equality)]) ).
cnf(847,plain,
multiply(X,multiply(multiply(identity,multiply(Y,multiply(Y,Y))),identity)) = multiply(X,multiply(identity,multiply(Y,multiply(multiply(Y,Y),identity)))),
inference('PARAMODULATE',[status(thm)],[824,758,theory(equality)]) ).
cnf(913,plain,
multiply(identity,multiply(multiply(X,multiply(X,X)),identity)) = multiply(identity,multiply(X,multiply(multiply(X,X),identity))),
inference('PARAMODULATE',[status(thm)],[26,781,theory(equality)]) ).
cnf(1149,plain,
multiply(X,multiply(multiply(multiply(identity,multiply(identity,multiply(Y,Z))),multiply(Z,multiply(Z,Z))),identity)) = multiply(X,multiply(multiply(multiply(identity,multiply(identity,multiply(Y,identity))),identity),identity)),
inference('PARAMODULATE',[status(thm)],[837,28,theory(equality)]) ).
cnf(1682,plain,
multiply(multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(multiply(identity,multiply(identity,X)),identity)),multiply(multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(multiply(identity,multiply(identity,X)),identity)),multiply(multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))),identity))) = multiply(multiply(identity,multiply(identity,X)),identity),
inference('PARAMODULATE',[status(thm)],[570,102,theory(equality)]) ).
cnf(1787,plain,
multiply(multiply(X,multiply(identity,multiply(Y,identity))),identity) = multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[176,627,theory(equality)]),623,176,theory(equality)]) ).
cnf(1921,plain,
multiply(multiply(X,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),identity) = multiply(multiply(X,multiply(Z,multiply(multiply(Z,Z),multiply(multiply(Z,Y),identity)))),identity),
inference('PARAMODULATE',[status(thm)],[1787,625,theory(equality)]) ).
cnf(1933,plain,
multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))) = multiply(identity,multiply(X,multiply(multiply(identity,Y),identity))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,1787,theory(equality)]),66,theory(equality)]) ).
cnf(1937,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity)),identity)) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))),identity)),identity),
inference('PARAMODULATE',[status(thm)],[27,1787,theory(equality)]) ).
cnf(1948,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),identity)),identity)) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(multiply(identity,Y),identity))),identity)),identity),
inference('PARAMODULATE',[status(thm)],[27,1787,theory(equality)]) ).
cnf(1976,plain,
multiply(X,multiply(multiply(identity,multiply(multiply(Y,multiply(identity,multiply(Z,identity))),identity)),identity)) = multiply(X,multiply(multiply(multiply(identity,multiply(Y,multiply(multiply(identity,Z),identity))),identity),identity)),
inference('PARAMODULATE',[status(thm)],[837,1787,theory(equality)]) ).
cnf(1977,plain,
multiply(X,multiply(identity,multiply(identity,multiply(multiply(Y,multiply(identity,multiply(Z,identity))),identity)))) = multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,multiply(multiply(identity,Z),identity))),identity))),
inference('PARAMODULATE',[status(thm)],[836,1787,theory(equality)]) ).
cnf(1981,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(Y,multiply(identity,multiply(Z,identity)))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,multiply(multiply(identity,Z),identity)),identity)))),
inference('PARAMODULATE',[status(thm)],[567,1787,theory(equality)]) ).
cnf(1982,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(Y,multiply(multiply(identity,Z),identity))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,multiply(identity,multiply(Z,identity))),identity)))),
inference('PARAMODULATE',[status(thm)],[567,1787,theory(equality)]) ).
cnf(1988,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),Z))),multiply(Z,multiply(Z,Z))),
inference('PARAMODULATE',[status(thm)],[28,1787,theory(equality)]) ).
cnf(1989,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),identity))),identity) = multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),Z))),multiply(Z,multiply(Z,Z))),
inference('PARAMODULATE',[status(thm)],[84,1787,theory(equality)]) ).
cnf(2068,plain,
multiply(identity,multiply(X,multiply(identity,multiply(multiply(multiply(identity,Y),identity),identity)))) = multiply(identity,multiply(X,multiply(multiply(identity,multiply(identity,multiply(Y,identity))),identity))),
inference('PARAMODULATE',[status(thm)],[1933,85,theory(equality)]) ).
cnf(2070,plain,
multiply(identity,multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,identity)),identity)))) = multiply(identity,multiply(X,multiply(multiply(identity,multiply(multiply(identity,Y),identity)),identity))),
inference('PARAMODULATE',[status(thm)],[1933,85,theory(equality)]) ).
cnf(2078,plain,
multiply(identity,multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,identity)),identity)))) = multiply(identity,multiply(X,multiply(identity,multiply(multiply(multiply(identity,Y),identity),identity)))),
inference('PARAMODULATE',[status(thm)],[1933,37,theory(equality)]) ).
cnf(2084,plain,
multiply(identity,multiply(X,multiply(multiply(identity,multiply(identity,multiply(Y,Z))),multiply(Z,multiply(Z,Z))))) = multiply(identity,multiply(X,multiply(multiply(identity,multiply(identity,multiply(Y,identity))),identity))),
inference('PARAMODULATE',[status(thm)],[1933,28,theory(equality)]) ).
cnf(2122,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),Z))),multiply(Z,multiply(Z,Z))) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(multiply(identity,Y),identity))),identity)),identity),
inference('PARAMODULATE',[status(thm)],[101,1933,theory(equality)]) ).
cnf(2125,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),Z))),multiply(Z,multiply(Z,Z))) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))),identity)),identity),
inference('PARAMODULATE',[status(thm)],[101,1933,theory(equality)]) ).
cnf(2194,plain,
multiply(multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),Z))),multiply(Z,multiply(Z,Z))) = Y,
inference('PARAMODULATE',[status(thm)],[143,178,theory(equality)]) ).
cnf(2195,plain,
multiply(multiply(X,X),multiply(multiply(X,identity),identity)) = multiply(multiply(X,multiply(multiply(X,X),multiply(identity,Y))),multiply(Y,multiply(Y,Y))),
inference('PARAMODULATE',[status(thm)],[178,single_axiom2,theory(equality)]) ).
cnf(2262,plain,
multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,Z),identity))))),identity) = multiply(multiply(X,Y),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,single_axiom,theory(equality)]),641,564,theory(equality)]) ).
cnf(2400,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z)))))) = multiply(U,multiply(multiply(U,U),multiply(multiply(U,Y),Z))),
inference('PARAMODULATE',[status(thm)],[single_axiom,2194,theory(equality)]) ).
cnf(2589,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X,Y)))),multiply(identity,multiply(Y,multiply(Y,Y)))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,491,theory(equality)]),438,theory(equality)]) ).
cnf(2617,plain,
multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(identity,X))) = multiply(identity,multiply(X,multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2195,491,theory(equality)]),438,491,81,theory(equality)]) ).
cnf(2622,plain,
multiply(identity,multiply(identity,X)) = multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(identity,multiply(X,multiply(X,X))))),
inference('REWRITE',[status(thm)],[492,2617,theory(equality)]) ).
cnf(2660,plain,
multiply(identity,multiply(X,multiply(multiply(X,X),identity))) = multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),multiply(identity,X)),identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[781,2617,theory(equality)]),758,theory(equality)]) ).
cnf(2672,plain,
multiply(multiply(identity,multiply(identity,X)),multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,X))),identity)) = multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[781,2617,theory(equality)]),2660,theory(equality)]) ).
cnf(2673,plain,
multiply(identity,multiply(multiply(identity,multiply(X,multiply(X,X))),identity)) = multiply(multiply(identity,multiply(identity,X)),multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,X))),identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[913,2617,theory(equality)]),2660,theory(equality)]) ).
cnf(2751,plain,
multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,Y))) = multiply(identity,multiply(identity,multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,5,theory(equality)]),2622,2617,theory(equality)]) ).
cnf(2777,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(multiply(X,X),Y)))),identity) = multiply(multiply(identity,multiply(identity,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))),
inference('REWRITE',[status(thm)],[577,2751,theory(equality)]) ).
cnf(2811,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(identity,Y))) = multiply(X,multiply(multiply(X,X),multiply(identity,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,2195,theory(equality)]),2622,2617,491,81,736,theory(equality)]) ).
cnf(2841,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,multiply(Y,identity)),identity))))),multiply(multiply(multiply(identity,multiply(identity,Y)),multiply(identity,multiply(identity,Y))),multiply(multiply(multiply(identity,multiply(identity,Y)),identity),identity))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,837,theory(equality)]),736,513,theory(equality)]) ).
cnf(2888,plain,
multiply(X,Y) = multiply(multiply(identity,multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,Y))),identity)),identity),
inference('PARAMODULATE',[status(thm)],[69,2751,theory(equality)]) ).
cnf(2909,plain,
multiply(X,multiply(identity,multiply(identity,Y))) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,X),identity),identity),Y))),
inference('PARAMODULATE',[status(thm)],[2751,20,theory(equality)]) ).
cnf(2910,plain,
multiply(multiply(X,identity),identity) = multiply(multiply(X,multiply(identity,multiply(identity,Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[456,2909,theory(equality)]) ).
cnf(2914,plain,
multiply(multiply(identity,multiply(identity,X)),Y) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,multiply(Y,identity)),identity)))),
inference('PARAMODULATE',[status(thm)],[2751,16,theory(equality)]) ).
cnf(2917,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X)),Y)),multiply(multiply(multiply(identity,multiply(identity,Y)),multiply(identity,multiply(identity,Y))),multiply(multiply(multiply(identity,multiply(identity,Y)),identity),identity))) = X,
inference('REWRITE',[status(thm)],[2841,2914,theory(equality)]) ).
cnf(2930,plain,
multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,Y))),multiply(identity,multiply(identity,Z))) = multiply(identity,multiply(identity,multiply(multiply(X,Y),Z))),
inference('PARAMODULATE',[status(thm)],[2751,2751,theory(equality)]) ).
cnf(2954,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(X,Y))))),multiply(identity,multiply(identity,multiply(Y,multiply(Y,Y))))) = multiply(identity,X),
inference('PARAMODULATE',[status(thm)],[2751,5,theory(equality)]) ).
cnf(2956,plain,
multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),multiply(identity,multiply(identity,multiply(identity,multiply(identity,Y))))),identity),identity) = multiply(identity,multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[81,2751,theory(equality)]),single_axiom2,2930,theory(equality)]) ).
cnf(3004,plain,
multiply(multiply(identity,multiply(identity,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,multiply(multiply(X,Y),identity)),identity)))) = multiply(identity,multiply(identity,Y)),
inference('PARAMODULATE',[status(thm)],[2751,143,theory(equality)]) ).
cnf(3061,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),multiply(identity,multiply(identity,Z))) = multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),Z))),
inference('PARAMODULATE',[status(thm)],[2751,1933,theory(equality)]) ).
cnf(3241,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,Y)) = multiply(X,multiply(multiply(X,X),Y)),
inference('PARAMODULATE',[status(thm)],[2811,5,theory(equality)]) ).
cnf(3358,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z)))))) = multiply(multiply(U,multiply(U,U)),multiply(identity,multiply(multiply(U,Y),Z))),
inference('REWRITE',[status(thm)],[2400,3241,theory(equality)]) ).
cnf(3362,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),Z))),multiply(Z,multiply(Z,Z))) = Y,
inference('REWRITE',[status(thm)],[2194,3241,theory(equality)]) ).
cnf(3371,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(multiply(identity,Z),identity))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,multiply(identity,multiply(Z,identity))),identity)))),
inference('REWRITE',[status(thm)],[1982,3241,theory(equality)]) ).
cnf(3372,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(identity,multiply(Z,identity)))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,multiply(multiply(identity,Z),identity)),identity)))),
inference('REWRITE',[status(thm)],[1981,3241,theory(equality)]) ).
cnf(3419,plain,
multiply(multiply(X,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),identity) = multiply(multiply(X,multiply(multiply(Z,multiply(Z,Z)),multiply(identity,multiply(multiply(Z,Y),identity)))),identity),
inference('REWRITE',[status(thm)],[1921,3241,theory(equality)]) ).
cnf(3429,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference('REWRITE',[status(thm)],[567,3241,theory(equality)]) ).
cnf(3443,plain,
identity = multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,identity),identity))),
inference('REWRITE',[status(thm)],[525,3241,theory(equality)]) ).
cnf(3445,plain,
identity = multiply(multiply(X,multiply(X,X)),multiply(multiply(multiply(identity,X),identity),identity)),
inference('PARAMODULATE',[status(thm)],[3443,34,theory(equality)]) ).
cnf(3451,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),X) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2751,3443,theory(equality)]),single_axiom2,24,theory(equality)]) ).
cnf(3527,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X))),identity) = multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(identity,multiply(multiply(multiply(identity,X),identity),Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,3445,theory(equality)]),3241,single_axiom2,theory(equality)]) ).
cnf(3549,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X,multiply(X,X))))),multiply(identity,X)) = identity,
inference('PARAMODULATE',[status(thm)],[3451,2617,theory(equality)]) ).
cnf(3555,plain,
multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,Y),identity)) = multiply(X,multiply(multiply(X,X),multiply(Y,identity))),
inference('PARAMODULATE',[status(thm)],[824,3241,theory(equality)]) ).
cnf(3650,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,multiply(multiply(Y,Y),Z)))),multiply(multiply(identity,Z),multiply(multiply(identity,Z),multiply(identity,Z))))) = multiply(Y,multiply(Y,Y)),
inference('PARAMODULATE',[status(thm)],[single_axiom,3241,theory(equality)]) ).
cnf(3651,plain,
multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,multiply(Y,identity))),identity)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,3241,theory(equality)]),3555,564,single_axiom2,theory(equality)]) ).
cnf(3672,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(multiply(Y,multiply(Y,Y)),identity)),identity)) = multiply(multiply(X,multiply(multiply(X,X),multiply(Y,multiply(multiply(Y,Y),Z)))),multiply(multiply(identity,Z),multiply(multiply(identity,Z),multiply(identity,Z)))),
inference('PARAMODULATE',[status(thm)],[178,3241,theory(equality)]) ).
cnf(3724,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity))),identity) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3362,single_axiom2,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(3725,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity)),identity) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3362,26,theory(equality)]),single_axiom2,theory(equality)]) ).
cnf(3752,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(identity,Y)),multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,multiply(Z,Z)),multiply(Z,multiply(Z,Z))))) = multiply(identity,multiply(multiply(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[3362,3362,theory(equality)]) ).
cnf(3796,plain,
multiply(identity,X) = multiply(multiply(identity,multiply(multiply(Y,multiply(Y,Y)),multiply(identity,multiply(multiply(Y,X),identity)))),identity),
inference('PARAMODULATE',[status(thm)],[26,3724,theory(equality)]) ).
cnf(3802,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(identity,Y)),identity) = multiply(identity,multiply(multiply(X,Y),identity)),
inference('PARAMODULATE',[status(thm)],[3724,3724,theory(equality)]) ).
cnf(3870,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity)),multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity))),multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity)),multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity))),multiply(Y,identity))) = multiply(multiply(X,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity)),
inference('PARAMODULATE',[status(thm)],[570,3725,theory(equality)]) ).
cnf(4163,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(multiply(identity,Y),identity)) = multiply(identity,multiply(X,multiply(Y,identity))),
inference('PARAMODULATE',[status(thm)],[3651,3651,theory(equality)]) ).
cnf(4176,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(identity,multiply(Y,Z))),multiply(Z,multiply(Z,Z))) = multiply(multiply(identity,multiply(X,multiply(Y,identity))),identity),
inference('PARAMODULATE',[status(thm)],[3362,3651,theory(equality)]) ).
cnf(4217,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))),multiply(identity,multiply(multiply(X,X),multiply(multiply(X,Y),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3429,3241,theory(equality)]),564,theory(equality)]) ).
cnf(4228,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),multiply(multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),multiply(identity,multiply(identity,multiply(X,multiply(X,X))))),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3429,3451,theory(equality)]),758,single_axiom2,theory(equality)]) ).
cnf(4244,plain,
multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))) = multiply(identity,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,3549,theory(equality)]),491,81,single_axiom2,theory(equality)]) ).
cnf(4247,plain,
multiply(multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X))),identity) = multiply(multiply(multiply(identity,X),multiply(identity,multiply(multiply(multiply(identity,X),identity),Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[3527,4244,theory(equality)]) ).
cnf(4251,plain,
multiply(multiply(multiply(identity,X),multiply(identity,Y)),identity) = multiply(identity,multiply(multiply(X,Y),identity)),
inference('REWRITE',[status(thm)],[3802,4244,theory(equality)]) ).
cnf(4275,plain,
multiply(X,Y) = multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,X))),multiply(identity,multiply(identity,multiply(identity,Y)))),identity),identity),
inference('REWRITE',[status(thm)],[2888,4251,theory(equality)]) ).
cnf(4277,plain,
multiply(multiply(identity,X),multiply(identity,Y)) = multiply(identity,multiply(X,Y)),
inference('REWRITE',[status(thm)],[2956,4275,theory(equality)]) ).
cnf(4356,plain,
multiply(identity,X) = multiply(multiply(multiply(identity,multiply(Y,multiply(Y,Y))),multiply(identity,multiply(identity,multiply(multiply(Y,X),identity)))),identity),
inference('REWRITE',[status(thm)],[3796,4277,theory(equality)]) ).
cnf(4447,plain,
multiply(multiply(identity,X),multiply(multiply(identity,Y),identity)) = multiply(identity,multiply(X,multiply(Y,identity))),
inference('REWRITE',[status(thm)],[4163,4244,theory(equality)]) ).
cnf(4449,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(Y,Z))),multiply(Z,multiply(Z,Z))) = multiply(multiply(identity,multiply(X,multiply(Y,identity))),identity),
inference('REWRITE',[status(thm)],[4176,4244,theory(equality)]) ).
cnf(4450,plain,
multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,X)),multiply(multiply(identity,multiply(X,Y)),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[4217,4447,4244,theory(equality)]) ).
cnf(4471,plain,
multiply(X,multiply(multiply(X,Y),multiply(identity,Z))) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[7,4244,theory(equality)]) ).
cnf(4530,plain,
multiply(X,multiply(multiply(X,multiply(identity,multiply(identity,Y))),identity)) = multiply(X,multiply(multiply(X,identity),multiply(identity,multiply(identity,multiply(Y,identity))))),
inference('REWRITE',[status(thm)],[146,4471,theory(equality)]) ).
cnf(4531,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),multiply(multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),identity),multiply(identity,multiply(identity,multiply(multiply(X,multiply(X,X)),identity))))) = multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),
inference('REWRITE',[status(thm)],[4228,4530,theory(equality)]) ).
cnf(4537,plain,
multiply(multiply(identity,multiply(identity,X)),multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(identity,multiply(identity,multiply(X,identity))))) = multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),identity),
inference('REWRITE',[status(thm)],[2672,4530,theory(equality)]) ).
cnf(4538,plain,
multiply(identity,multiply(multiply(identity,multiply(X,multiply(X,X))),identity)) = multiply(multiply(identity,multiply(identity,X)),multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(identity,multiply(identity,multiply(X,identity))))),
inference('REWRITE',[status(thm)],[2673,4530,theory(equality)]) ).
cnf(4552,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(identity,Z))) = multiply(identity,multiply(identity,multiply(multiply(identity,Y),Z))),
inference('REWRITE',[status(thm)],[498,4244,theory(equality)]) ).
cnf(4559,plain,
multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(Y,Z),identity))))),identity) = multiply(multiply(X,Y),multiply(identity,Z)),
inference('REWRITE',[status(thm)],[2262,4244,theory(equality)]) ).
cnf(4581,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(identity,Z))) = multiply(multiply(U,multiply(U,U)),multiply(identity,multiply(multiply(U,Y),Z))),
inference('REWRITE',[status(thm)],[3358,4244,theory(equality)]) ).
cnf(4582,plain,
multiply(multiply(multiply(identity,X),multiply(identity,Y)),multiply(identity,Z)) = multiply(identity,multiply(multiply(X,Y),Z)),
inference('REWRITE',[status(thm)],[3752,4244,theory(equality)]) ).
cnf(4611,plain,
multiply(multiply(identity,X),multiply(multiply(identity,Y),multiply(identity,Z))) = multiply(identity,multiply(X,multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[4277,4277,theory(equality)]) ).
cnf(4623,plain,
multiply(multiply(identity,X),Y) = multiply(identity,multiply(X,multiply(multiply(identity,multiply(identity,multiply(Y,identity))),identity))),
inference('REWRITE',[status(thm)],[2084,2589,4611,theory(equality)]) ).
cnf(4643,plain,
multiply(identity,multiply(X,multiply(identity,multiply(multiply(multiply(identity,Y),identity),identity)))) = multiply(multiply(identity,X),Y),
inference('REWRITE',[status(thm)],[2068,4623,theory(equality)]) ).
cnf(4644,plain,
multiply(identity,multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,identity)),identity)))) = multiply(multiply(identity,X),Y),
inference('REWRITE',[status(thm)],[2078,4643,theory(equality)]) ).
cnf(4645,plain,
multiply(multiply(identity,X),Y) = multiply(identity,multiply(X,multiply(multiply(identity,multiply(multiply(identity,Y),identity)),identity))),
inference('REWRITE',[status(thm)],[2070,4644,theory(equality)]) ).
cnf(4693,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(X,X))),multiply(identity,Y)) = multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,X)),Y)),
inference('PARAMODULATE',[status(thm)],[3241,4277,theory(equality)]) ).
cnf(4694,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(X,X))),multiply(identity,multiply(multiply(identity,multiply(X,Y)),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[4450,4693,theory(equality)]) ).
cnf(5152,plain,
multiply(multiply(multiply(identity,X),multiply(identity,X)),multiply(identity,multiply(multiply(X,multiply(multiply(X,Y),identity)),identity))) = multiply(identity,Y),
inference('PARAMODULATE',[status(thm)],[4582,143,theory(equality)]) ).
cnf(5157,plain,
multiply(multiply(multiply(identity,X),multiply(identity,Y)),Z) = multiply(multiply(identity,multiply(X,Y)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4582,11,theory(equality)]),4623,theory(equality)]) ).
cnf(5209,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(X,X))),multiply(identity,multiply(multiply(identity,multiply(X,multiply(Y,identity))),identity))) = multiply(identity,Y),
inference('PARAMODULATE',[status(thm)],[4582,3651,theory(equality)]) ).
cnf(5245,plain,
multiply(multiply(identity,multiply(identity,multiply(identity,multiply(X,multiply(Y,Z))))),multiply(multiply(multiply(identity,Y),multiply(identity,Z)),multiply(multiply(identity,multiply(Y,Z)),multiply(identity,multiply(Y,Z))))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,4582,theory(equality)]),4277,theory(equality)]) ).
cnf(5389,plain,
multiply(multiply(multiply(identity,X),identity),Y) = multiply(multiply(identity,multiply(X,identity)),Y),
inference('PARAMODULATE',[status(thm)],[5157,single_axiom2,theory(equality)]) ).
cnf(5594,plain,
multiply(multiply(X,identity),identity) = multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(Y,Z))))),multiply(multiply(multiply(identity,Y),multiply(identity,Z)),multiply(multiply(identity,multiply(Y,Z)),multiply(identity,multiply(Y,Z))))),
inference('PARAMODULATE',[status(thm)],[2910,5157,theory(equality)]) ).
cnf(5895,plain,
multiply(X,multiply(multiply(X,identity),Y)) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),Y)),
inference('PARAMODULATE',[status(thm)],[4471,11,theory(equality)]) ).
cnf(5989,plain,
multiply(X,multiply(multiply(X,Y),identity)) = multiply(X,multiply(multiply(X,identity),multiply(Y,identity))),
inference('REWRITE',[status(thm)],[12,5895,theory(equality)]) ).
cnf(6025,plain,
multiply(multiply(X,Y),identity) = multiply(multiply(X,identity),multiply(Y,identity)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,5989,theory(equality)]),143,theory(equality)]) ).
cnf(6361,plain,
multiply(identity,X) = multiply(multiply(multiply(identity,multiply(Y,multiply(Y,Y))),identity),multiply(multiply(identity,multiply(identity,multiply(multiply(Y,X),identity))),identity)),
inference('REWRITE',[status(thm)],[4356,6025,theory(equality)]) ).
cnf(6484,plain,
multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(multiply(multiply(identity,multiply(X,Y)),identity),identity)) = Y,
inference('REWRITE',[status(thm)],[3725,6025,theory(equality)]) ).
cnf(6489,plain,
multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(multiply(identity,multiply(multiply(X,Y),identity)),identity)) = Y,
inference('REWRITE',[status(thm)],[3724,6025,theory(equality)]) ).
cnf(6499,plain,
multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(multiply(X,multiply(X,X)),identity)) = multiply(multiply(multiply(identity,X),multiply(identity,multiply(multiply(multiply(identity,X),identity),Y))),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[4247,6025,theory(equality)]) ).
cnf(6806,plain,
multiply(X,multiply(multiply(multiply(identity,multiply(identity,multiply(Y,Z))),identity),multiply(multiply(Z,multiply(Z,Z)),identity))) = multiply(X,multiply(multiply(multiply(identity,multiply(identity,multiply(Y,identity))),identity),identity)),
inference('REWRITE',[status(thm)],[1149,6025,theory(equality)]) ).
cnf(6927,plain,
multiply(multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(multiply(identity,multiply(identity,X)),identity)),multiply(multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(multiply(identity,multiply(identity,X)),identity)),multiply(multiply(multiply(identity,multiply(identity,multiply(X,Y))),identity),multiply(multiply(Y,multiply(Y,Y)),identity)))) = multiply(multiply(identity,multiply(identity,X)),identity),
inference('REWRITE',[status(thm)],[1682,6025,theory(equality)]) ).
cnf(7061,plain,
multiply(multiply(X,multiply(Y,Z)),identity) = multiply(multiply(X,identity),multiply(multiply(Y,identity),multiply(Z,identity))),
inference('PARAMODULATE',[status(thm)],[6025,6025,theory(equality)]) ).
cnf(7116,plain,
multiply(multiply(X,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),identity) = multiply(multiply(X,identity),Y),
inference('REWRITE',[status(thm)],[3419,6489,7061,theory(equality)]) ).
cnf(7117,plain,
multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))),identity) = multiply(multiply(X,identity),Y),
inference('REWRITE',[status(thm)],[813,7116,theory(equality)]) ).
cnf(7118,plain,
multiply(multiply(X,identity),multiply(Y,Z)) = multiply(multiply(X,Y),multiply(identity,Z)),
inference('REWRITE',[status(thm)],[4559,7117,theory(equality)]) ).
cnf(7556,plain,
multiply(multiply(multiply(X,identity),multiply(X,identity)),multiply(multiply(multiply(X,multiply(multiply(X,identity),Y)),identity),identity)) = Y,
inference('PARAMODULATE',[status(thm)],[143,6025,theory(equality)]) ).
cnf(7577,plain,
multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity) = multiply(multiply(X,identity),multiply(multiply(identity,multiply(Y,identity)),identity)),
inference('PARAMODULATE',[status(thm)],[6025,5389,theory(equality)]) ).
cnf(7640,plain,
multiply(multiply(X,multiply(Y,multiply(multiply(Y,Y),Z))),identity) = multiply(multiply(X,identity),multiply(multiply(Y,Y),multiply(multiply(Y,Z),identity))),
inference('PARAMODULATE',[status(thm)],[6025,564,theory(equality)]) ).
cnf(7643,plain,
multiply(multiply(X,X),identity) = multiply(X,X),
inference('REWRITE',[status(thm)],[783,3443,7118,7640,theory(equality)]) ).
cnf(7652,plain,
multiply(X,multiply(multiply(identity,multiply(Y,multiply(Y,Y))),identity)) = multiply(X,multiply(identity,multiply(Y,multiply(Y,Y)))),
inference('REWRITE',[status(thm)],[847,7643,theory(equality)]) ).
cnf(7696,plain,
multiply(identity,multiply(identity,multiply(X,multiply(X,X)))) = multiply(multiply(identity,multiply(identity,X)),multiply(multiply(multiply(identity,multiply(identity,X)),identity),multiply(identity,multiply(identity,multiply(X,identity))))),
inference('REWRITE',[status(thm)],[4538,7652,theory(equality)]) ).
cnf(7699,plain,
multiply(identity,multiply(identity,multiply(X,multiply(X,X)))) = multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),identity),
inference('REWRITE',[status(thm)],[4537,7696,theory(equality)]) ).
cnf(7701,plain,
multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,X))),multiply(multiply(multiply(identity,multiply(identity,X)),identity),identity)) = multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),
inference('REWRITE',[status(thm)],[792,7699,theory(equality)]) ).
cnf(7729,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X)),Y)),multiply(identity,multiply(identity,multiply(Y,multiply(Y,Y))))) = X,
inference('REWRITE',[status(thm)],[2917,7701,theory(equality)]) ).
cnf(7786,plain,
multiply(identity,multiply(identity,multiply(identity,X))) = multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))),
inference('REWRITE',[status(thm)],[4531,4244,7696,theory(equality)]) ).
cnf(7795,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(identity,multiply(Z,identity)))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,multiply(multiply(identity,Z),identity))))),
inference('REWRITE',[status(thm)],[3372,7786,theory(equality)]) ).
cnf(7800,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(multiply(identity,Z),identity))),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,multiply(identity,multiply(Z,identity)))))),
inference('REWRITE',[status(thm)],[3371,7786,theory(equality)]) ).
cnf(7805,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(X,X))),multiply(identity,multiply(multiply(identity,multiply(X,Y)),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,Y)))),
inference('REWRITE',[status(thm)],[4694,7786,theory(equality)]) ).
cnf(7806,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))) = multiply(identity,X),
inference('REWRITE',[status(thm)],[5209,7786,7805,theory(equality)]) ).
cnf(7809,plain,
multiply(multiply(identity,multiply(X,Y)),multiply(identity,multiply(identity,multiply(Y,multiply(Y,Y))))) = multiply(identity,X),
inference('REWRITE',[status(thm)],[2954,7806,theory(equality)]) ).
cnf(7810,plain,
multiply(identity,multiply(identity,multiply(identity,X))) = X,
inference('REWRITE',[status(thm)],[7729,7809,theory(equality)]) ).
cnf(7811,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(multiply(identity,Z),identity))),identity))) = multiply(Y,multiply(identity,multiply(Z,identity))),
inference('REWRITE',[status(thm)],[7800,7810,theory(equality)]) ).
cnf(7812,plain,
multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,multiply(Y,multiply(identity,multiply(Z,identity)))),identity))) = multiply(Y,multiply(multiply(identity,Z),identity)),
inference('REWRITE',[status(thm)],[7795,7810,theory(equality)]) ).
cnf(7816,plain,
multiply(multiply(X,multiply(Y,Z)),multiply(multiply(multiply(identity,Y),multiply(identity,Z)),multiply(multiply(identity,multiply(Y,Z)),multiply(identity,multiply(Y,Z))))) = X,
inference('REWRITE',[status(thm)],[5245,7810,theory(equality)]) ).
cnf(7828,plain,
multiply(multiply(X,identity),identity) = X,
inference('REWRITE',[status(thm)],[5594,7816,7810,theory(equality)]) ).
cnf(7830,plain,
multiply(multiply(multiply(X,identity),multiply(X,identity)),multiply(X,multiply(multiply(X,identity),Y))) = Y,
inference('REWRITE',[status(thm)],[7556,7828,theory(equality)]) ).
cnf(7865,plain,
multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(identity,multiply(X,Y))) = Y,
inference('REWRITE',[status(thm)],[6484,7828,theory(equality)]) ).
cnf(7867,plain,
multiply(X,multiply(multiply(identity,multiply(multiply(Y,multiply(identity,multiply(Z,identity))),identity)),identity)) = multiply(X,multiply(identity,multiply(Y,multiply(multiply(identity,Z),identity)))),
inference('REWRITE',[status(thm)],[1976,7828,theory(equality)]) ).
cnf(7869,plain,
multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(multiply(identity,Y),identity))),identity)),identity),
inference('REWRITE',[status(thm)],[1948,7867,theory(equality)]) ).
cnf(7870,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),Z))),multiply(Z,multiply(Z,Z))) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[2122,7869,theory(equality)]) ).
cnf(7872,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity)),identity)) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[1988,7870,theory(equality)]) ).
cnf(7873,plain,
multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))) = multiply(multiply(identity,multiply(multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))),identity)),identity),
inference('REWRITE',[status(thm)],[1937,7872,theory(equality)]) ).
cnf(7874,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(multiply(identity,Y),identity)),Z))),multiply(Z,multiply(Z,Z))) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[2125,7873,theory(equality)]) ).
cnf(7875,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),identity))),identity) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[1989,7874,theory(equality)]) ).
cnf(7979,plain,
multiply(X,multiply(multiply(multiply(identity,multiply(identity,multiply(Y,Z))),identity),multiply(multiply(Z,multiply(Z,Z)),identity))) = multiply(X,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference('REWRITE',[status(thm)],[6806,7828,theory(equality)]) ).
cnf(7987,plain,
multiply(identity,multiply(X,identity)) = multiply(multiply(identity,multiply(identity,X)),identity),
inference('REWRITE',[status(thm)],[6927,7830,7828,7118,7979,theory(equality)]) ).
cnf(7988,plain,
multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))) = multiply(identity,multiply(identity,multiply(X,multiply(multiply(identity,Y),identity)))),
inference('REWRITE',[status(thm)],[7875,7828,7987,theory(equality)]) ).
cnf(7995,plain,
multiply(multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))),multiply(identity,multiply(identity,Z))) = multiply(identity,multiply(identity,multiply(multiply(X,multiply(identity,multiply(Y,identity))),Z))),
inference('REWRITE',[status(thm)],[3061,7988,theory(equality)]) ).
cnf(7998,plain,
multiply(X,multiply(multiply(identity,multiply(Y,multiply(identity,multiply(Z,identity)))),identity)) = multiply(X,multiply(identity,multiply(multiply(identity,multiply(Y,multiply(multiply(identity,Z),identity))),identity))),
inference('REWRITE',[status(thm)],[1977,single_axiom2,7995,theory(equality)]) ).
cnf(8008,plain,
multiply(identity,X) = multiply(multiply(multiply(identity,multiply(Y,multiply(Y,Y))),identity),multiply(identity,multiply(Y,X))),
inference('REWRITE',[status(thm)],[6361,7828,7987,theory(equality)]) ).
cnf(8023,plain,
multiply(multiply(multiply(identity,X),multiply(identity,X)),multiply(identity,multiply(multiply(X,Y),identity))) = multiply(multiply(identity,multiply(identity,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))),
inference('REWRITE',[status(thm)],[2777,4582,564,7987,theory(equality)]) ).
cnf(8024,plain,
multiply(identity,X) = multiply(identity,multiply(identity,X)),
inference('REWRITE',[status(thm)],[3004,5152,8023,theory(equality)]) ).
cnf(8036,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),multiply(identity,Z))) = multiply(identity,multiply(multiply(identity,Y),Z)),
inference('REWRITE',[status(thm)],[4552,8024,theory(equality)]) ).
cnf(8037,plain,
multiply(identity,multiply(multiply(identity,X),Y)) = multiply(multiply(Z,multiply(Z,Z)),multiply(identity,multiply(multiply(Z,X),Y))),
inference('REWRITE',[status(thm)],[4581,8036,theory(equality)]) ).
cnf(8045,plain,
multiply(identity,multiply(multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))),identity)) = multiply(X,multiply(multiply(identity,Y),identity)),
inference('REWRITE',[status(thm)],[7812,8037,theory(equality)]) ).
cnf(8047,plain,
multiply(identity,multiply(multiply(identity,multiply(X,multiply(multiply(identity,Y),identity))),identity)) = multiply(X,multiply(identity,multiply(Y,identity))),
inference('REWRITE',[status(thm)],[7811,8037,theory(equality)]) ).
cnf(8049,plain,
multiply(X,multiply(multiply(identity,multiply(Y,multiply(identity,multiply(Z,identity)))),identity)) = multiply(X,multiply(Y,multiply(identity,multiply(Z,identity)))),
inference('REWRITE',[status(thm)],[7998,8047,theory(equality)]) ).
cnf(8050,plain,
multiply(identity,multiply(X,multiply(identity,multiply(Y,identity)))) = multiply(X,multiply(multiply(identity,Y),identity)),
inference('REWRITE',[status(thm)],[8045,8049,theory(equality)]) ).
cnf(8052,plain,
multiply(X,multiply(multiply(identity,multiply(Y,identity)),identity)) = multiply(multiply(identity,X),Y),
inference('REWRITE',[status(thm)],[4644,8024,8050,theory(equality)]) ).
cnf(8056,plain,
multiply(X,multiply(multiply(identity,multiply(multiply(identity,Y),identity)),identity)) = multiply(X,multiply(identity,Y)),
inference('REWRITE',[status(thm)],[839,single_axiom2,8052,theory(equality)]) ).
cnf(8061,plain,
multiply(multiply(identity,X),Y) = multiply(identity,multiply(X,multiply(identity,Y))),
inference('REWRITE',[status(thm)],[4645,8056,theory(equality)]) ).
cnf(8062,plain,
multiply(multiply(identity,X),multiply(Y,identity)) = multiply(X,multiply(multiply(identity,Y),identity)),
inference('REWRITE',[status(thm)],[8050,8061,theory(equality)]) ).
cnf(8089,plain,
multiply(X,multiply(multiply(identity,multiply(Y,identity)),identity)) = multiply(X,multiply(identity,Y)),
inference('REWRITE',[status(thm)],[8056,single_axiom2,8062,theory(equality)]) ).
cnf(8098,plain,
multiply(multiply(X,multiply(multiply(identity,Y),identity)),identity) = multiply(multiply(X,identity),multiply(identity,Y)),
inference('REWRITE',[status(thm)],[7577,8089,theory(equality)]) ).
cnf(8122,plain,
multiply(X,multiply(identity,Y)) = multiply(multiply(identity,X),Y),
inference('REWRITE',[status(thm)],[8052,8089,theory(equality)]) ).
cnf(8126,plain,
multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(multiply(X,multiply(X,X)),identity)) = multiply(multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),Y)),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[6499,8024,8122,theory(equality)]) ).
cnf(8153,plain,
multiply(multiply(multiply(identity,X),multiply(identity,multiply(Y,Z))),multiply(Z,multiply(Z,Z))) = multiply(multiply(X,multiply(Y,identity)),identity),
inference('REWRITE',[status(thm)],[4449,single_axiom2,8122,theory(equality)]) ).
cnf(8206,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity))),multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity))),multiply(Y,identity))) = multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),
inference('REWRITE',[status(thm)],[3870,single_axiom2,8122,theory(equality)]) ).
cnf(8259,plain,
multiply(X,multiply(multiply(Y,multiply(Y,Y)),identity)) = multiply(X,multiply(identity,multiply(Y,multiply(Y,Y)))),
inference('REWRITE',[status(thm)],[7652,single_axiom2,8122,theory(equality)]) ).
cnf(8260,plain,
multiply(identity,X) = X,
inference('REWRITE',[status(thm)],[8008,7865,single_axiom2,8122,theory(equality)]) ).
cnf(8266,plain,
multiply(X,multiply(multiply(Y,multiply(Y,Y)),identity)) = multiply(X,multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[8259,8260,theory(equality)]) ).
cnf(8269,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,multiply(multiply(Y,Y),Z)))),multiply(Z,multiply(Z,Z)))) = multiply(Y,multiply(Y,Y)),
inference('REWRITE',[status(thm)],[3650,8260,theory(equality)]) ).
cnf(8270,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(Y,multiply(Y,Y))),identity)) = multiply(multiply(X,multiply(multiply(X,X),multiply(Y,multiply(multiply(Y,Y),Z)))),multiply(Z,multiply(Z,Z))),
inference('REWRITE',[status(thm)],[3672,8266,8260,theory(equality)]) ).
cnf(8271,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(Y,multiply(Y,Y))),identity))) = multiply(Y,multiply(Y,Y)),
inference('REWRITE',[status(thm)],[8269,8270,theory(equality)]) ).
cnf(8280,plain,
multiply(multiply(X,identity),multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[7118,8260,theory(equality)]) ).
cnf(8281,plain,
multiply(multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity))),multiply(multiply(multiply(multiply(X,multiply(X,X)),identity),multiply(X,Y)),multiply(multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),multiply(Y,identity)))) = multiply(multiply(X,multiply(X,X)),multiply(multiply(X,Y),identity)),
inference('REWRITE',[status(thm)],[8206,7828,8260,7061,8280,theory(equality)]) ).
cnf(8305,plain,
multiply(multiply(X,multiply(X,X)),Y) = multiply(X,multiply(multiply(X,X),Y)),
inference('REWRITE',[status(thm)],[3241,8260,theory(equality)]) ).
cnf(8306,plain,
multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(Y,multiply(Y,Y))),identity)) = multiply(Y,multiply(Y,Y)),
inference('REWRITE',[status(thm)],[8271,8305,theory(equality)]) ).
cnf(8325,plain,
multiply(multiply(X,multiply(Y,identity)),identity) = multiply(multiply(X,identity),Y),
inference('REWRITE',[status(thm)],[8098,8260,theory(equality)]) ).
cnf(8383,plain,
multiply(X,Y) = multiply(multiply(Z,multiply(Z,Z)),multiply(multiply(Z,X),Y)),
inference('REWRITE',[status(thm)],[8037,8260,theory(equality)]) ).
cnf(8385,plain,
multiply(multiply(X,multiply(X,X)),identity) = multiply(X,multiply(X,X)),
inference('REWRITE',[status(thm)],[8306,8383,theory(equality)]) ).
cnf(8408,plain,
multiply(multiply(multiply(X,identity),multiply(X,identity)),multiply(multiply(multiply(Y,multiply(Y,Y)),multiply(Y,X)),multiply(multiply(X,identity),multiply(X,identity)))) = multiply(X,identity),
inference('REWRITE',[status(thm)],[8281,8385,8383,theory(equality)]) ).
cnf(8412,plain,
multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X))) = multiply(multiply(X,multiply(multiply(X,identity),Y)),multiply(Y,multiply(Y,Y))),
inference('REWRITE',[status(thm)],[8126,8385,8260,theory(equality)]) ).
cnf(8420,plain,
multiply(multiply(X,multiply(Y,Z)),multiply(Z,multiply(Z,Z))) = multiply(multiply(X,identity),Y),
inference('REWRITE',[status(thm)],[8153,8325,8260,theory(equality)]) ).
cnf(8422,plain,
multiply(multiply(X,identity),X) = multiply(multiply(X,identity),multiply(X,identity)),
inference('REWRITE',[status(thm)],[8412,8420,theory(equality)]) ).
cnf(8423,plain,
multiply(multiply(multiply(X,identity),X),multiply(X,multiply(multiply(X,identity),Y))) = Y,
inference('REWRITE',[status(thm)],[7830,8422,theory(equality)]) ).
cnf(8425,plain,
multiply(multiply(multiply(X,identity),X),multiply(multiply(multiply(Y,multiply(Y,Y)),multiply(Y,X)),multiply(multiply(X,identity),X))) = multiply(X,identity),
inference('REWRITE',[status(thm)],[8408,8422,theory(equality)]) ).
cnf(8464,plain,
multiply(multiply(X,multiply(X,X)),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[7865,8385,8260,theory(equality)]) ).
cnf(8466,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[8425,8423,8464,theory(equality)]) ).
cnf(8512,plain,
$false,
inference('REWRITE',[status(thm)],[prove_order3,8466,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 09:32:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T09:32:48
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n022.cluster.edu at 2022-06-14T09:32:48
% 16.62/16.79
% 16.62/16.79
% 16.62/16.79 #||
% 16.62/16.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.62/16.79 % SZS output start Refutation
% See solution above
% 16.65/16.84 ||#
% 16.65/16.84
% 16.65/16.84 ; Summary of computation:
% 16.65/16.84 ; 42695 formulas have been input or derived (from 144 formulas).
% 16.65/16.84 ; 8512 (20%) were retained. Of these,
% 16.65/16.84 ; 8471 (100%) were simplified or subsumed later,
% 16.65/16.84 ; 41 ( 0%) are still being kept.
% 16.65/16.84 ;
% 16.65/16.84 ; Run time in seconds excluding printing time:
% 16.65/16.84 ; 0.001 0% Read assertion file (1 call)
% 16.65/16.84 ; 0.000 0% Assert (3 calls)
% 16.65/16.84 ; 1.695 10% Process new row (38,984 calls)
% 16.65/16.84 ; 0.018 0% Resolution (286 calls)
% 16.65/16.84 ; 0.584 4% Paramodulation (143 calls)
% 16.65/16.84 ; 5.305 32% Forward simplification (37,771 calls)
% 16.65/16.84 ; 2.918 18% Backward simplification (8,512 calls)
% 16.65/16.84 ; 5.650 35% Ordering (677,184 calls)
% 16.65/16.84 ; 0.000 0% Sortal reasoning (32 calls)
% 16.65/16.84 ; 0.000 0% Purity testing (1 call)
% 16.65/16.84 ; 0.153 1% Other
% 16.65/16.84 ; 16.324 Total
% 16.65/16.84 ; 16.372 Real time
% 16.65/16.84 ;
% 16.65/16.84 ; Term-hash-array has 21,740 terms in all.
% 16.65/16.84 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 16.65/16.84 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 16.65/16.84 ; Path-index has 152 entries (10,637 at peak, 24,152 added, 24,000 deleted).
% 16.65/16.84 ; Path-index has 2,632 nodes (4,826 at peak, 6,278 added, 3,646 deleted).
% 16.65/16.84 ; Trie-index has 152 entries (10,637 at peak, 24,152 added, 24,000 deleted).
% 16.65/16.84 ; Trie-index has 997 nodes (130,425 at peak, 311,816 added, 310,819 deleted).
% 16.65/16.84 ; Retrieved 1,155,253 generalization terms in 577,470 calls.
% 16.65/16.84 ; Retrieved 200,766 instance terms in 13,360 calls.
% 16.65/16.84 ; Retrieved 83,017 unifiable terms in 1,600 calls.
% 16.65/16.84 ;
% 16.65/16.84 ; The agenda of backward simplifiable rows to process has 3163 entries:
% 16.65/16.84 ; 3163 with value 0
% 16.65/16.84 ; The agenda of rows to process has 211 entries:
% 16.65/16.84 ; 27 with value 41 7 with value 45 2 with value 50
% 16.65/16.84 ; 35 with value 42 3 with value 46 1 with value 51
% 16.65/16.84 ; 42 with value 43 7 with value 47 1 with value 52
% 16.65/16.84 ; 78 with value 44 8 with value 48
% 16.65/16.84 ; The agenda of input rows to give has 1 entry:
% 16.65/16.84 ; 1 with value 15
% 16.65/16.84 ; The agenda of rows to give has 39 entries:
% 16.65/16.84 ; 1 with value (4 14) 1 with value (4 29) 1 with value (4 40)
% 16.65/16.84 ; 1 with value (4 17) 4 with value (4 30) 1 with value (4 41)
% 16.65/16.84 ; 1 with value (4 19) 1 with value (4 31) 1 with value (4 42)
% 16.65/16.84 ; 2 with value (4 20) 2 with value (4 32) 2 with value (4 47)
% 16.65/16.84 ; 1 with value (4 21) 1 with value (4 33) 2 with value (4 48)
% 16.65/16.84 ; 1 with value (4 23) 1 with value (4 34) 1 with value (4 54)
% 16.65/16.84 ; 1 with value (4 24) 1 with value (4 35) 1 with value (4 55)
% 16.65/16.84 ; 2 with value (4 25) 1 with value (4 37) 1 with value (4 57)
% 16.65/16.84 ; 2 with value (4 26) 2 with value (4 39) 1 with value (4 63)
% 16.65/16.84 ; 2 with value (4 27)
% 16.65/16.84 Evaluation took:
% 16.65/16.84 16.373 seconds of real time
% 16.65/16.84 14.95936 seconds of user run time
% 16.65/16.84 1.411958 seconds of system run time
% 16.65/16.84 [Run times include 2.423 seconds GC run time.]
% 16.65/16.84 0 calls to %EVAL
% 16.65/16.84 0 page faults and
% 16.65/16.84 1,045,851,072 bytes consed.
% 16.65/16.84 :PROOF-FOUND
% 16.65/16.84 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T09:33:04
% 16.65/16.84 :PROOF-FOUND
% 16.65/16.84 *
%------------------------------------------------------------------------------