%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP119-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:36:14 EDT 2022

% Result   : Unsatisfiable 16.48s 16.67s
% Output   : Refutation 16.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   61
%            Number of leaves      :    3
% Syntax   : Number of clauses     :  290 ( 290 unt;   0 nHn;   3 RR)
%            Number of literals    :  290 ( 289 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  544 (   0 sgn)

% 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(single_axiom2,axiom,
    multiply(identity,identity) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom2) ).

cnf(prove_order4,negated_conjecture,
    multiply(a,multiply(a,multiply(a,a))) != identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order4) ).

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(45,plain,
    multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))) = multiply(identity,multiply(identity,multiply(multiply(X,identity),identity))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,single_axiom,theory(equality)]),single_axiom2,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(75,plain,
    multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),identity) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(X,identity))))),
    inference('PARAMODULATE',[status(thm)],[32,32,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(144,plain,
    multiply(X,multiply(multiply(X,multiply(identity,Y)),identity)) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(identity,multiply(Y,identity)))),
    inference('PARAMODULATE',[status(thm)],[12,26,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(177,plain,
    multiply(multiply(multiply(identity,X),multiply(identity,X)),multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity)) = identity,
    inference('PARAMODULATE',[status(thm)],[143,26,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(446,plain,
    identity = multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X)),identity)),multiply(multiply(X,identity),multiply(multiply(X,identity),multiply(X,identity)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,18,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(582,plain,
    multiply(X,multiply(multiply(X,X),multiply(multiply(X,multiply(multiply(Y,Y),multiply(multiply(Y,Z),identity))),identity))) = multiply(Y,multiply(multiply(Y,Y),Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,564,theory(equality)]),564,single_axiom2,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(634,plain,
    multiply(X,multiply(multiply(X,X),multiply(multiply(X,X),multiply(multiply(X,Y),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X,X),Y),identity)))),
    inference('PARAMODULATE',[status(thm)],[567,564,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(782,plain,
    multiply(multiply(X,X),multiply(multiply(X,identity),identity)) = multiply(multiply(multiply(X,multiply(X,X)),identity),identity),
    inference('PARAMODULATE',[status(thm)],[564,758,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(790,plain,
    multiply(X,multiply(X,multiply(multiply(X,X),identity))) = multiply(X,multiply(multiply(X,multiply(X,X)),identity)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,758,theory(equality)]),12,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(834,plain,
    multiply(X,multiply(multiply(identity,multiply(identity,Y)),identity)) = multiply(X,multiply(identity,multiply(identity,multiply(Y,identity)))),
    inference('PARAMODULATE',[status(thm)],[824,824,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(936,plain,
    multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),multiply(identity,X)),identity)) = multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[627,782,theory(equality)]),582,736,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(2190,plain,
    multiply(identity,multiply(multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity),multiply(multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity),multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,X),multiply(identity,X)),identity),identity))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,177,theory(equality)]),single_axiom2,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(2371,plain,
    multiply(multiply(X,X),multiply(multiply(X,Y),identity)) = multiply(multiply(X,multiply(multiply(X,X),identity)),multiply(multiply(multiply(Y,identity),multiply(multiply(Y,identity),multiply(Y,identity))),multiply(multiply(multiply(Y,identity),multiply(multiply(Y,identity),multiply(Y,identity))),multiply(multiply(Y,identity),multiply(multiply(Y,identity),multiply(Y,identity)))))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,446,theory(equality)]),69,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(2599,plain,
    multiply(multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),identity),multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),identity)),multiply(identity,multiply(X,identity))) = multiply(multiply(identity,multiply(X,identity)),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity)))),
    inference('PARAMODULATE',[status(thm)],[491,75,theory(equality)]) ).

cnf(2601,plain,
    multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(X,identity))))),multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(X,identity)))))),multiply(multiply(identity,X),identity)) = multiply(multiply(identity,multiply(X,identity)),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity)))),
    inference('PARAMODULATE',[status(thm)],[824,491,theory(equality)]) ).

cnf(2602,plain,
    multiply(multiply(identity,multiply(X,identity)),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity)))) = multiply(multiply(multiply(identity,X),identity),multiply(multiply(multiply(identity,X),identity),multiply(multiply(identity,X),identity))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[491,824,theory(equality)]),2601,theory(equality)]) ).

cnf(2613,plain,
    multiply(multiply(multiply(identity,multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),identity)))),multiply(identity,multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),identity))))),multiply(identity,multiply(Y,identity))) = multiply(multiply(identity,multiply(Y,identity)),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))),
    inference('PARAMODULATE',[status(thm)],[491,567,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(2618,plain,
    multiply(multiply(identity,multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity)),multiply(multiply(identity,multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity)),multiply(identity,multiply(multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),identity)),identity)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(identity,X),multiply(identity,X)),identity),identity))),
    inference('REWRITE',[status(thm)],[2190,2617,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(2677,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),multiply(identity,X)),identity))) = multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,multiply(X,X))),identity)),
    inference('PARAMODULATE',[status(thm)],[790,2617,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(2792,plain,
    multiply(multiply(identity,multiply(identity,multiply(identity,X))),multiply(identity,multiply(identity,Y))) = multiply(Z,multiply(multiply(Z,Z),multiply(multiply(Z,X),Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,2194,theory(equality)]),2622,2617,theory(equality)]) ).

cnf(2796,plain,
    multiply(multiply(identity,multiply(identity,multiply(identity,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X,X),Y),identity)))),
    inference('REWRITE',[status(thm)],[634,2792,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(2878,plain,
    multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),X) = multiply(multiply(identity,X),multiply(identity,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2589,177,theory(equality)]),20,2796,2618,2617,single_axiom2,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(3063,plain,
    multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,X)),identity))),multiply(identity,multiply(identity,Y))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,identity))),Y))),
    inference('PARAMODULATE',[status(thm)],[2751,834,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(3433,plain,
    multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity)))),multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity))))),multiply(identity,multiply(Y,identity))) = multiply(multiply(identity,multiply(Y,identity)),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[2613,3241,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(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(3454,plain,
    identity = multiply(multiply(multiply(identity,multiply(identity,X)),multiply(identity,multiply(identity,multiply(X,X)))),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3443,2751,theory(equality)]),31,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(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(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(3835,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(multiply(identity,multiply(X,Y)),identity),
    inference('PARAMODULATE',[status(thm)],[3724,3725,theory(equality)]) ).

cnf(3980,plain,
    multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(identity,X)))),identity),multiply(X,identity)) = multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity))),
    inference('PARAMODULATE',[status(thm)],[2878,75,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(4205,plain,
    multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity)))),multiply(Y,identity)) = multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity))),
    inference('PARAMODULATE',[status(thm)],[2878,3429,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(4230,plain,
    identity = multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,Y),identity)))),multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))))),multiply(identity,multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3454,3429,theory(equality)]),3063,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(4245,plain,
    multiply(multiply(X,X),multiply(multiply(X,Y),identity)) = multiply(multiply(X,multiply(multiply(X,X),identity)),multiply(identity,multiply(Y,identity))),
    inference('REWRITE',[status(thm)],[2371,4244,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(4348,plain,
    multiply(multiply(multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))),multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity))))),multiply(identity,multiply(Y,identity))) = multiply(multiply(identity,multiply(Y,identity)),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[3433,4277,theory(equality)]) ).

cnf(4353,plain,
    multiply(multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))),multiply(Y,identity)) = multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity))),
    inference('REWRITE',[status(thm)],[4205,4277,theory(equality)]) ).

cnf(4354,plain,
    identity = multiply(multiply(multiply(multiply(identity,multiply(X,multiply(X,X))),multiply(identity,multiply(identity,multiply(multiply(X,Y),identity)))),multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(identity,Y)),identity))),multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))))),multiply(identity,multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[4230,4277,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(4444,plain,
    multiply(multiply(multiply(identity,X),multiply(identity,Y)),identity) = multiply(multiply(identity,multiply(X,Y)),identity),
    inference('REWRITE',[status(thm)],[3835,4244,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(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(4540,plain,
    multiply(X,multiply(multiply(X,multiply(identity,Y)),identity)) = multiply(X,multiply(multiply(X,identity),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[144,4471,theory(equality)]) ).

cnf(4545,plain,
    multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity)))) = multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),
    inference('REWRITE',[status(thm)],[936,4540,theory(equality)]) ).

cnf(4548,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity))))) = multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,multiply(X,X))),identity)),
    inference('REWRITE',[status(thm)],[2677,4540,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(4610,plain,
    multiply(multiply(multiply(identity,X),identity),multiply(identity,Y)) = multiply(identity,multiply(multiply(X,identity),Y)),
    inference('PARAMODULATE',[status(thm)],[4277,26,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(4868,plain,
    multiply(multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity)))),multiply(identity,multiply(multiply(identity,multiply(multiply(X,Y),identity)),identity))) = multiply(identity,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[143,4251,theory(equality)]),4540,4245,theory(equality)]) ).

cnf(5129,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,X)),identity))) = multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity))))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[790,4444,theory(equality)]),4540,758,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(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(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(6951,plain,
    multiply(multiply(identity,X),multiply(identity,multiply(multiply(X,Y),identity))) = multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4277,5989,theory(equality)]),4611,theory(equality)]) ).

cnf(7059,plain,
    multiply(multiply(multiply(identity,X),Y),identity) = multiply(multiply(identity,multiply(X,identity)),multiply(Y,identity)),
    inference('PARAMODULATE',[status(thm)],[6025,26,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(7295,plain,
    multiply(multiply(identity,multiply(X,identity)),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity)))) = multiply(multiply(multiply(identity,X),multiply(multiply(identity,X),identity)),multiply(identity,multiply(multiply(identity,X),identity))),
    inference('REWRITE',[status(thm)],[2602,7118,theory(equality)]) ).

cnf(7449,plain,
    identity = multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(multiply(identity,multiply(identity,multiply(multiply(X,Y),identity))),identity)),multiply(multiply(identity,Y),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity))))),
    inference('REWRITE',[status(thm)],[4354,2878,33,7059,7118,theory(equality)]) ).

cnf(7450,plain,
    multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(multiply(identity,multiply(identity,multiply(multiply(X,Y),identity))),identity)),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))) = multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(multiply(identity,Y),identity))),
    inference('REWRITE',[status(thm)],[4348,7295,4353,7059,7118,theory(equality)]) ).

cnf(7476,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(X,identity)))) = multiply(multiply(multiply(identity,X),multiply(multiply(identity,X),identity)),multiply(identity,multiply(multiply(identity,X),identity))),
    inference('REWRITE',[status(thm)],[2599,7295,3980,81,7118,theory(equality)]) ).

cnf(7477,plain,
    identity = multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(multiply(identity,multiply(identity,multiply(multiply(X,Y),identity))),identity)),multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(multiply(identity,Y),identity)))),
    inference('REWRITE',[status(thm)],[7449,7476,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(7579,plain,
    multiply(X,multiply(multiply(identity,multiply(Y,Z)),identity)) = multiply(X,multiply(multiply(multiply(identity,Y),identity),multiply(identity,multiply(Z,identity)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[824,6025,theory(equality)]),4610,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(7656,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity))))) = multiply(multiply(identity,X),multiply(identity,multiply(X,multiply(X,X)))),
    inference('REWRITE',[status(thm)],[4548,7652,theory(equality)]) ).

cnf(7657,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,X)),identity))) = multiply(multiply(identity,X),multiply(identity,multiply(X,multiply(X,X)))),
    inference('REWRITE',[status(thm)],[5129,7656,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(8020,plain,
    multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(identity,multiply(X,Y))),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))) = multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(multiply(identity,Y),identity))),
    inference('REWRITE',[status(thm)],[7450,7828,7987,theory(equality)]) ).

cnf(8021,plain,
    identity = multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(identity,multiply(X,Y))),multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(multiply(identity,Y),identity)))),
    inference('REWRITE',[status(thm)],[7477,7828,7987,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(8055,plain,
    multiply(multiply(multiply(identity,X),multiply(multiply(multiply(identity,X),identity),multiply(identity,multiply(X,identity)))),multiply(identity,multiply(X,Y))) = multiply(identity,Y),
    inference('REWRITE',[status(thm)],[4868,single_axiom2,8052,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(8063,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(X,X))) = multiply(multiply(identity,X),multiply(identity,multiply(X,multiply(X,X)))),
    inference('REWRITE',[status(thm)],[7657,7643,8024,8062,theory(equality)]) ).

cnf(8087,plain,
    multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(identity,multiply(X,Y))),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))) = multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(Y,identity))),
    inference('REWRITE',[status(thm)],[8020,single_axiom2,8062,theory(equality)]) ).

cnf(8088,plain,
    identity = multiply(multiply(multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),multiply(identity,multiply(X,Y))),multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[8021,single_axiom2,8062,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(8122,plain,
    multiply(X,multiply(identity,Y)) = multiply(multiply(identity,X),Y),
    inference('REWRITE',[status(thm)],[8052,8089,theory(equality)]) ).

cnf(8124,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(X,X))) = multiply(multiply(identity,X),multiply(X,multiply(X,X))),
    inference('REWRITE',[status(thm)],[8063,8024,8122,theory(equality)]) ).

cnf(8138,plain,
    multiply(multiply(identity,X),multiply(multiply(X,Y),identity)) = multiply(multiply(identity,X),multiply(multiply(identity,multiply(X,identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[6951,8024,8122,theory(equality)]) ).

cnf(8185,plain,
    multiply(X,multiply(multiply(Y,Z),identity)) = multiply(X,multiply(multiply(multiply(identity,Y),identity),multiply(identity,multiply(Z,identity)))),
    inference('REWRITE',[status(thm)],[7579,single_axiom2,8122,theory(equality)]) ).

cnf(8187,plain,
    multiply(multiply(identity,X),multiply(X,X)) = multiply(identity,multiply(multiply(X,multiply(X,X)),identity)),
    inference('REWRITE',[status(thm)],[4545,7643,8185,theory(equality)]) ).

cnf(8189,plain,
    multiply(multiply(multiply(multiply(identity,X),multiply(X,X)),multiply(identity,multiply(X,Y))),multiply(multiply(identity,multiply(Y,identity)),multiply(identity,multiply(Y,identity)))) = multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(Y,identity))),
    inference('REWRITE',[status(thm)],[8087,8187,theory(equality)]) ).

cnf(8190,plain,
    identity = multiply(multiply(multiply(multiply(identity,X),multiply(X,X)),multiply(identity,multiply(X,Y))),multiply(multiply(multiply(identity,Y),multiply(multiply(identity,Y),identity)),multiply(identity,multiply(Y,identity)))),
    inference('REWRITE',[status(thm)],[8088,8187,theory(equality)]) ).

cnf(8191,plain,
    multiply(multiply(multiply(identity,X),multiply(X,X)),multiply(identity,multiply(X,Y))) = multiply(identity,Y),
    inference('REWRITE',[status(thm)],[8055,7643,8185,theory(equality)]) ).

cnf(8192,plain,
    multiply(multiply(identity,X),multiply(X,X)) = multiply(multiply(multiply(identity,X),multiply(multiply(identity,X),identity)),multiply(identity,multiply(X,identity))),
    inference('REWRITE',[status(thm)],[8189,7643,8138,8191,theory(equality)]) ).

cnf(8196,plain,
    identity = multiply(multiply(identity,X),multiply(X,multiply(X,X))),
    inference('REWRITE',[status(thm)],[8190,8124,8192,8191,theory(equality)]) ).

cnf(8197,plain,
    multiply(multiply(identity,X),multiply(multiply(identity,X),multiply(X,X))) = identity,
    inference('REWRITE',[status(thm)],[8124,8196,theory(equality)]) ).

cnf(8260,plain,
    multiply(identity,X) = X,
    inference('REWRITE',[status(thm)],[8008,7865,single_axiom2,8122,theory(equality)]) ).

cnf(8428,plain,
    multiply(X,multiply(X,multiply(X,X))) = identity,
    inference('REWRITE',[status(thm)],[8197,8260,theory(equality)]) ).

cnf(8429,plain,
    $false,
    inference('REWRITE',[status(thm)],[prove_order4,8428,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP119-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14  % Command  : run-snark %s %d
% 0.15/0.36  % Computer : n022.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Tue Jun 14 00:35:18 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.49  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50  * 
% 0.22/0.50  * 
% 0.22/0.50  #<PACKAGE "SNARK-USER">
% 0.22/0.50  * 
% 0.22/0.50  SNARK-TPTP-OPTIONS
% 0.22/0.50  * 
% 0.22/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51   (USE-FACTORING :POS)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51  * 
% 0.22/0.51  "."
% 0.22/0.51  * 
% 0.22/0.51  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T00:35:18
% 0.22/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n022.cluster.edu at 2022-06-14T00:35:18
% 16.48/16.67  
% 16.48/16.67  
% 16.48/16.67  #||
% 16.48/16.67  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.48/16.67  % SZS output start Refutation
% See solution above
% 16.57/16.74  ||#
% 16.57/16.74  
% 16.57/16.74  ; Summary of computation:
% 16.57/16.74  ;     42557 formulas have been input or derived (from 144 formulas).
% 16.57/16.74  ;      8429 (20%) were retained.  Of these,
% 16.57/16.74  ;         8329 (99%) were simplified or subsumed later,
% 16.57/16.74  ;          100 ( 1%) are still being kept.
% 16.57/16.74  ; 
% 16.57/16.74  ; Run time in seconds excluding printing time:
% 16.57/16.74  ;     0.001   0%   Read assertion file          (1 call)
% 16.57/16.74  ;     0.000   0%   Assert                       (3 calls)
% 16.57/16.74  ;     1.700  11%   Process new row              (38,773 calls)
% 16.57/16.74  ;     0.029   0%   Resolution                   (286 calls)
% 16.57/16.74  ;     0.631   4%   Paramodulation               (143 calls)
% 16.57/16.74  ;     5.483  34%   Forward simplification       (37,560 calls)
% 16.57/16.74  ;     3.041  19%   Backward simplification      (8,429 calls)
% 16.57/16.74  ;     5.129  32%   Ordering                     (675,350 calls)
% 16.57/16.74  ;     0.000   0%   Sortal reasoning             (32 calls)
% 16.57/16.74  ;     0.000   0%   Purity testing               (1 call)
% 16.57/16.74  ;     0.149   1%   Other
% 16.57/16.74  ;    16.163        Total
% 16.57/16.74  ;    16.233        Real time
% 16.57/16.74  ; 
% 16.57/16.74  ; Term-hash-array has 21,535 terms in all.
% 16.57/16.74  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 16.57/16.74  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 16.57/16.74  ; Path-index has 374 entries (10,639 at peak, 23,884 added, 23,510 deleted).
% 16.57/16.74  ; Path-index has 2,745 nodes (4,833 at peak, 6,149 added, 3,404 deleted).
% 16.57/16.74  ; Trie-index has 374 entries (10,639 at peak, 23,884 added, 23,510 deleted).
% 16.57/16.74  ; Trie-index has 2,801 nodes (130,435 at peak, 309,820 added, 307,019 deleted).
% 16.57/16.74  ; Retrieved 1,150,198 generalization terms in 574,943 calls.
% 16.57/16.74  ; Retrieved 199,528 instance terms in 13,243 calls.
% 16.57/16.74  ; Retrieved 83,017 unifiable terms in 1,602 calls.
% 16.57/16.74  ; 
% 16.57/16.74  ; The agenda of backward simplifiable rows to process has 3236 entries:
% 16.57/16.74  ;  3236 with value 0
% 16.57/16.74  ; The agenda of rows to process has 211 entries:
% 16.57/16.74  ;    27 with value 41              7 with value 45               2 with value 50
% 16.57/16.74  ;    35 with value 42              3 with value 46               1 with value 51
% 16.57/16.74  ;    42 with value 43              7 with value 47               1 with value 52
% 16.57/16.74  ;    78 with value 44              8 with value 48
% 16.57/16.74  ; The agenda of input rows to give has 1 entry:
% 16.57/16.74  ;     1 with value 15
% 16.57/16.74  ; The agenda of rows to give has 98 entries:
% 16.57/16.74  ;     1 with value (4 14)          3 with value (4 33)           2 with value (4 48)
% 16.57/16.74  ;     1 with value (4 19)          5 with value (4 34)           1 with value (4 50)
% 16.57/16.74  ;     1 with value (4 20)          1 with value (4 35)           1 with value (4 51)
% 16.57/16.74  ;     2 with value (4 21)          2 with value (4 36)           1 with value (4 52)
% 16.57/16.74  ;     2 with value (4 22)          3 with value (4 37)           1 with value (4 53)
% 16.57/16.74  ;     5 with value (4 24)          4 with value (4 38)           1 with value (4 57)
% 16.57/16.74  ;     3 with value (4 25)          4 with value (4 39)           1 with value (4 58)
% 16.57/16.74  ;     3 with value (4 26)          6 with value (4 40)           1 with value (4 59)
% 16.57/16.74  ;     1 with value (4 27)          3 with value (4 41)           1 with value (4 60)
% 16.57/16.74  ;     7 with value (4 28)          3 with value (4 42)           2 with value (4 62)
% 16.57/16.74  ;     3 with value (4 29)          3 with value (4 43)           2 with value (4 63)
% 16.57/16.74  ;     2 with value (4 30)          1 with value (4 45)           2 with value (4 64)
% 16.57/16.74  ;     2 with value (4 31)          2 with value (4 46)           1 with value (4 71)
% 16.57/16.74  ;     5 with value (4 32)          3 with value (4 47)
% 16.57/16.74  Evaluation took:
% 16.57/16.74    16.234 seconds of real time
% 16.57/16.74    14.768945 seconds of user run time
% 16.57/16.74    1.464618 seconds of system run time
% 16.57/16.74    [Run times include 2.387 seconds GC run time.]
% 16.57/16.74    0 calls to %EVAL
% 16.57/16.74    0 page faults and
% 16.57/16.74    1,048,000,872 bytes consed.
% 16.57/16.74  :PROOF-FOUND
% 16.57/16.74  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T00:35:34
% 16.57/16.74  :PROOF-FOUND
% 16.57/16.74  * 
%------------------------------------------------------------------------------