TSTP Solution File: BOO026-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n017.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 : Thu Jul 14 23:48:59 EDT 2022
% Result : Unsatisfiable 2.25s 2.41s
% Output : Refutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 9
% Syntax : Number of clauses : 228 ( 228 unt; 0 nHn; 56 RR)
% Number of literals : 228 ( 227 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 244 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_add_property,axiom,
multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(additive_inverse,axiom,
add(X,inverse(X)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
cnf(add_multiply_property,axiom,
add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
cnf(4,plain,
add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),add(multiply(Y,X),multiply(X,X))),
inference('REWRITE',[status(thm)],[add_multiply_property,multiply_add_property,theory(equality)]) ).
cnf(multiplicative_inverse,axiom,
multiply(X,inverse(X)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
cnf(pixley1,axiom,
add(multiply(X,inverse(X)),add(multiply(X,Y),multiply(inverse(X),Y))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
cnf(7,plain,
add(n0,add(multiply(X,Y),multiply(inverse(X),Y))) = Y,
inference('REWRITE',[status(thm)],[pixley1,multiplicative_inverse,theory(equality)]) ).
cnf(pixley2,axiom,
add(multiply(X,inverse(Y)),add(multiply(X,Y),multiply(inverse(Y),Y))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
cnf(pixley1_dual,axiom,
multiply(add(X,inverse(X)),multiply(add(X,Y),add(inverse(X),Y))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1_dual) ).
cnf(11,plain,
add(multiply(add(n0,multiply(X,inverse(Y))),n1),multiply(add(multiply(Y,X),multiply(X,X)),n1)) = X,
inference('REWRITE',[status(thm)],[pixley1_dual,multiplicative_inverse,multiply_add_property,additive_inverse,theory(equality)]) ).
cnf(pixley3_dual,axiom,
multiply(add(X,inverse(Y)),multiply(add(X,X),add(inverse(Y),X))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3_dual) ).
cnf(15,plain,
add(add(multiply(X,X),multiply(inverse(Y),X)),add(multiply(X,multiply(X,inverse(Y))),multiply(inverse(Y),multiply(X,inverse(Y))))) = X,
inference('REWRITE',[status(thm)],[pixley3_dual,4,multiply_add_property,theory(equality)]) ).
cnf(prove_multiply_add,negated_conjecture,
multiply(add(a,b),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add) ).
cnf(17,plain,
multiply(X,n1) = add(multiply(Y,X),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,additive_inverse,theory(equality)]) ).
cnf(18,plain,
add(n0,multiply(X,n1)) = X,
inference('REWRITE',[status(thm)],[7,17,theory(equality)]) ).
cnf(19,plain,
multiply(X,Y) = add(multiply(n0,X),multiply(multiply(Y,n1),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,18,theory(equality)]) ).
cnf(20,plain,
add(multiply(X,inverse(inverse(X))),add(n0,multiply(inverse(inverse(X)),inverse(X)))) = X,
inference('PARAMODULATE',[status(thm)],[pixley2,multiplicative_inverse,theory(equality)]) ).
cnf(26,plain,
add(X,n0) = add(add(n0,multiply(X,inverse(Y))),add(multiply(Y,X),multiply(X,X))),
inference('PARAMODULATE',[status(thm)],[4,multiplicative_inverse,theory(equality)]) ).
cnf(28,plain,
add(inverse(X),multiply(X,Y)) = add(multiply(Y,n1),add(n0,multiply(inverse(X),inverse(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,multiplicative_inverse,theory(equality)]),17,theory(equality)]) ).
cnf(32,plain,
add(multiply(add(n0,n0),n1),multiply(add(multiply(X,X),multiply(X,X)),n1)) = X,
inference('PARAMODULATE',[status(thm)],[11,multiplicative_inverse,theory(equality)]) ).
cnf(37,plain,
add(multiply(X,n1),multiply(n0,n1)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse,theory(equality)]),17,theory(equality)]) ).
cnf(49,plain,
X = add(X,add(multiply(X,n0),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,37,theory(equality)]),18,theory(equality)]) ).
cnf(50,plain,
multiply(X,Y) = add(multiply(multiply(Y,n1),X),multiply(multiply(n0,n1),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,37,theory(equality)]) ).
cnf(52,plain,
multiply(inverse(X),n1) = add(n0,multiply(inverse(X),inverse(X))),
inference('PARAMODULATE',[status(thm)],[17,multiplicative_inverse,theory(equality)]) ).
cnf(53,plain,
add(inverse(X),multiply(X,Y)) = add(multiply(Y,n1),multiply(inverse(X),n1)),
inference('REWRITE',[status(thm)],[28,52,theory(equality)]) ).
cnf(55,plain,
multiply(inverse(inverse(X)),n1) = add(multiply(X,inverse(inverse(X))),n0),
inference('PARAMODULATE',[status(thm)],[17,multiplicative_inverse,theory(equality)]) ).
cnf(58,plain,
multiply(X,Y) = add(multiply(Y,X),multiply(add(multiply(Y,n0),multiply(n0,n0)),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,49,theory(equality)]) ).
cnf(59,plain,
multiply(inverse(n0),X) = add(n0,multiply(multiply(X,n1),inverse(n0))),
inference('PARAMODULATE',[status(thm)],[19,multiplicative_inverse,theory(equality)]) ).
cnf(60,plain,
multiply(inverse(multiply(X,n1)),X) = add(multiply(n0,inverse(multiply(X,n1))),n0),
inference('PARAMODULATE',[status(thm)],[19,multiplicative_inverse,theory(equality)]) ).
cnf(61,plain,
multiply(X,multiply(Y,Z)) = add(multiply(multiply(n0,Y),X),multiply(multiply(multiply(Z,n1),Y),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,19,theory(equality)]) ).
cnf(62,plain,
multiply(add(X,Y),Z) = add(add(multiply(X,n0),multiply(Y,n0)),add(multiply(X,multiply(Z,n1)),multiply(Y,multiply(Z,n1)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,multiply_add_property,theory(equality)]),multiply_add_property,theory(equality)]) ).
cnf(66,plain,
add(add(add(multiply(n0,n0),multiply(multiply(X,inverse(Y)),n0)),add(multiply(n0,multiply(n1,n1)),multiply(multiply(X,inverse(Y)),multiply(n1,n1)))),multiply(add(multiply(Y,X),multiply(X,X)),n1)) = X,
inference('REWRITE',[status(thm)],[11,62,theory(equality)]) ).
cnf(67,plain,
add(multiply(X,n1),multiply(n0,Y)) = add(multiply(Y,X),multiply(multiply(X,n1),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,19,theory(equality)]),19,theory(equality)]) ).
cnf(72,plain,
multiply(X,multiply(inverse(n0),Y)) = add(multiply(n0,X),multiply(multiply(multiply(Y,n1),inverse(n0)),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,59,theory(equality)]) ).
cnf(74,plain,
multiply(n1,n1) = add(inverse(X),multiply(X,X)),
inference('PARAMODULATE',[status(thm)],[17,53,theory(equality)]) ).
cnf(75,plain,
add(multiply(X,inverse(n1)),add(inverse(n1),multiply(n1,X))) = X,
inference('PARAMODULATE',[status(thm)],[pixley2,53,theory(equality)]) ).
cnf(77,plain,
add(inverse(X),n0) = add(multiply(inverse(X),n1),multiply(inverse(X),n1)),
inference('PARAMODULATE',[status(thm)],[53,multiplicative_inverse,theory(equality)]) ).
cnf(82,plain,
add(n0,add(inverse(X),multiply(X,X))) = n1,
inference('PARAMODULATE',[status(thm)],[18,74,theory(equality)]) ).
cnf(83,plain,
add(inverse(X),multiply(X,X)) = add(inverse(Y),multiply(Y,Y)),
inference('PARAMODULATE',[status(thm)],[74,74,theory(equality)]) ).
cnf(87,plain,
multiply(inverse(n0),n1) = add(n0,multiply(add(inverse(X),multiply(X,X)),inverse(n0))),
inference('PARAMODULATE',[status(thm)],[59,74,theory(equality)]) ).
cnf(88,plain,
multiply(X,n1) = add(multiply(n0,X),multiply(add(inverse(Y),multiply(Y,Y)),X)),
inference('PARAMODULATE',[status(thm)],[19,74,theory(equality)]) ).
cnf(91,plain,
multiply(n1,n1) = add(inverse(add(X,Y)),add(Y,multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[74,multiply_add_property,theory(equality)]),4,multiply_add_property,theory(equality)]) ).
cnf(101,plain,
add(n0,add(inverse(add(X,Y)),add(Y,multiply(X,X)))) = n1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[82,multiply_add_property,theory(equality)]),4,multiply_add_property,theory(equality)]) ).
cnf(107,plain,
add(inverse(add(X,Y)),add(Y,multiply(X,X))) = add(inverse(Z),multiply(Z,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[83,multiply_add_property,theory(equality)]),4,multiply_add_property,theory(equality)]) ).
cnf(132,plain,
multiply(inverse(multiply(X,n1)),X) = add(n0,multiply(multiply(n0,n1),inverse(multiply(X,n1)))),
inference('PARAMODULATE',[status(thm)],[50,multiplicative_inverse,theory(equality)]) ).
cnf(137,plain,
add(multiply(n0,n1),multiply(multiply(X,n1),Y)) = add(multiply(Y,X),multiply(multiply(n0,n1),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,50,theory(equality)]),50,theory(equality)]) ).
cnf(139,plain,
multiply(n1,n1) = add(inverse(add(n1,n0)),n1),
inference('PARAMODULATE',[status(thm)],[91,18,theory(equality)]) ).
cnf(143,plain,
add(add(add(multiply(n0,n0),multiply(multiply(X,inverse(Y)),n0)),add(add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0)),add(multiply(inverse(add(n1,n0)),multiply(X,inverse(Y))),multiply(n1,multiply(X,inverse(Y)))))),multiply(add(multiply(Y,X),multiply(X,X)),n1)) = X,
inference('REWRITE',[status(thm)],[66,multiply_add_property,139,theory(equality)]) ).
cnf(144,plain,
add(inverse(add(n1,n0)),n1) = add(inverse(X),multiply(X,X)),
inference('REWRITE',[status(thm)],[74,139,theory(equality)]) ).
cnf(146,plain,
add(inverse(add(X,Y)),add(Y,multiply(X,X))) = add(inverse(add(n1,n0)),n1),
inference('REWRITE',[status(thm)],[107,144,theory(equality)]) ).
cnf(147,plain,
add(n0,add(inverse(add(n1,n0)),n1)) = n1,
inference('REWRITE',[status(thm)],[101,146,theory(equality)]) ).
cnf(149,plain,
multiply(X,n1) = add(multiply(n0,X),multiply(add(inverse(add(n1,n0)),n1),X)),
inference('REWRITE',[status(thm)],[88,144,theory(equality)]) ).
cnf(158,plain,
multiply(inverse(n0),n1) = add(n0,multiply(add(inverse(add(n1,n0)),n1),inverse(n0))),
inference('REWRITE',[status(thm)],[87,144,theory(equality)]) ).
cnf(168,plain,
add(add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0)),add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0)))),multiply(add(multiply(X,X),multiply(X,X)),n1)) = X,
inference('PARAMODULATE',[status(thm)],[143,multiplicative_inverse,theory(equality)]) ).
cnf(172,plain,
add(n0,add(multiply(n0,inverse(add(inverse(add(n1,n0)),n1))),n0)) = inverse(add(inverse(add(n1,n0)),n1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,60,theory(equality)]),139,theory(equality)]) ).
cnf(180,plain,
add(inverse(add(inverse(add(n1,n0)),n1)),multiply(add(inverse(add(n1,n0)),n1),X)) = add(multiply(X,n1),add(multiply(n0,inverse(add(inverse(add(n1,n0)),n1))),n0)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[53,60,theory(equality)]),139,theory(equality)]) ).
cnf(182,plain,
add(inverse(add(inverse(add(n1,n0)),n1)),n0) = add(add(multiply(n0,inverse(add(inverse(add(n1,n0)),n1))),n0),add(multiply(n0,inverse(add(inverse(add(n1,n0)),n1))),n0)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[77,60,theory(equality)]),139,theory(equality)]) ).
cnf(184,plain,
multiply(inverse(add(inverse(add(n1,n0)),n1)),n1) = add(multiply(n0,inverse(add(inverse(add(n1,n0)),n1))),n0),
inference('PARAMODULATE',[status(thm)],[60,139,theory(equality)]) ).
cnf(203,plain,
multiply(X,Y) = add(multiply(multiply(Y,inverse(inverse(Y))),X),multiply(add(n0,multiply(inverse(inverse(Y)),inverse(Y))),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,20,theory(equality)]) ).
cnf(205,plain,
multiply(X,Y) = add(multiply(multiply(add(n0,n0),n1),X),multiply(multiply(add(multiply(Y,Y),multiply(Y,Y)),n1),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,32,theory(equality)]) ).
cnf(208,plain,
add(add(multiply(X,X),multiply(X,X)),multiply(add(n0,n0),n1)) = add(X,add(add(add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X))),add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X)))),add(multiply(X,X),multiply(multiply(X,X),multiply(X,X))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,32,theory(equality)]),4,multiply_add_property,theory(equality)]) ).
cnf(209,plain,
multiply(X,X) = add(multiply(X,n1),multiply(n0,n0)),
inference('PARAMODULATE',[status(thm)],[19,67,theory(equality)]) ).
cnf(210,plain,
add(add(multiply(X,X),multiply(X,X)),multiply(add(n0,n0),n1)) = add(X,add(add(add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X))),add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X)))),add(multiply(X,X),add(multiply(multiply(X,X),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[208,209,theory(equality)]) ).
cnf(222,plain,
multiply(inverse(X),n1) = add(n0,add(multiply(inverse(X),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[52,209,theory(equality)]) ).
cnf(243,plain,
add(add(inverse(add(n1,n0)),n1),multiply(n0,n0)) = add(inverse(add(n1,n0)),n1),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[139,209,theory(equality)]),139,theory(equality)]) ).
cnf(246,plain,
multiply(X,multiply(Y,Y)) = add(multiply(multiply(Y,n1),X),multiply(multiply(n0,n0),X)),
inference('PARAMODULATE',[status(thm)],[multiply_add_property,209,theory(equality)]) ).
cnf(249,plain,
add(multiply(add(X,Y),n1),multiply(n0,n0)) = add(Y,multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[multiply_add_property,209,theory(equality)]),4,multiply_add_property,theory(equality)]) ).
cnf(251,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,multiply(X,n1)),add(multiply(multiply(X,n1),n1),multiply(n0,n0))),
inference('PARAMODULATE',[status(thm)],[19,209,theory(equality)]) ).
cnf(255,plain,
multiply(multiply(n0,n1),X) = add(multiply(multiply(X,n1),multiply(n0,n1)),add(multiply(multiply(n0,n1),n1),multiply(n0,n0))),
inference('PARAMODULATE',[status(thm)],[50,209,theory(equality)]) ).
cnf(257,plain,
add(X,multiply(X,Y)) = add(add(multiply(X,Y),multiply(X,Y)),add(add(multiply(X,n1),multiply(n0,n0)),add(multiply(X,n1),multiply(n0,n0)))),
inference('PARAMODULATE',[status(thm)],[4,209,theory(equality)]) ).
cnf(277,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(multiply(X,n0),multiply(n0,n0)),multiply(X,X)),
inference('PARAMODULATE',[status(thm)],[249,49,theory(equality)]) ).
cnf(285,plain,
add(multiply(multiply(X,Y),n1),multiply(n0,n0)) = add(multiply(multiply(Y,n1),X),add(multiply(multiply(n0,X),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,19,theory(equality)]),209,theory(equality)]) ).
cnf(299,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(inverse(n1),multiply(n1,X)),add(multiply(multiply(X,inverse(n1)),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,75,theory(equality)]),209,theory(equality)]) ).
cnf(313,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(multiply(add(multiply(X,X),multiply(X,X)),n1),add(add(add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0)),add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0))),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,32,theory(equality)]),249,multiply_add_property,139,285,209,theory(equality)]) ).
cnf(318,plain,
add(X,n0) = add(add(n0,n0),add(multiply(X,X),multiply(X,X))),
inference('PARAMODULATE',[status(thm)],[26,multiplicative_inverse,theory(equality)]) ).
cnf(333,plain,
add(n0,multiply(X,X)) = add(add(multiply(X,X),multiply(X,X)),add(n0,multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,318,theory(equality)]),4,multiply_add_property,249,theory(equality)]) ).
cnf(377,plain,
multiply(add(X,Y),Z) = add(add(multiply(X,Z),multiply(Y,Z)),add(add(multiply(multiply(Z,n0),X),multiply(multiply(n0,n0),X)),add(multiply(multiply(Z,n0),Y),multiply(multiply(n0,n0),Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[58,multiply_add_property,theory(equality)]),multiply_add_property,theory(equality)]) ).
cnf(383,plain,
multiply(X,n0) = add(multiply(n0,X),multiply(add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0))),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[58,209,theory(equality)]),277,theory(equality)]) ).
cnf(394,plain,
multiply(inverse(multiply(n0,n1)),n0) = add(n0,n0),
inference('PARAMODULATE',[status(thm)],[132,multiplicative_inverse,theory(equality)]) ).
cnf(395,plain,
add(n0,add(n0,multiply(multiply(n0,n1),inverse(add(inverse(add(n1,n0)),n1))))) = inverse(add(inverse(add(n1,n0)),n1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,132,theory(equality)]),139,theory(equality)]) ).
cnf(398,plain,
multiply(n0,n1) = add(multiply(multiply(n0,n1),n0),add(n0,n0)),
inference('PARAMODULATE',[status(thm)],[17,394,theory(equality)]) ).
cnf(417,plain,
add(multiply(multiply(n0,n1),n1),multiply(n0,n0)) = add(add(n0,n0),add(multiply(multiply(multiply(n0,n1),n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,398,theory(equality)]),209,theory(equality)]) ).
cnf(452,plain,
multiply(n0,n1) = add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),multiply(add(inverse(add(n1,n0)),n1),n0)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[149,209,theory(equality)]),277,theory(equality)]) ).
cnf(454,plain,
multiply(add(X,Y),n1) = add(add(multiply(X,n0),multiply(Y,n0)),add(add(multiply(inverse(add(n1,n0)),X),multiply(n1,X)),add(multiply(inverse(add(n1,n0)),Y),multiply(n1,Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[149,multiply_add_property,theory(equality)]),multiply_add_property,theory(equality)]) ).
cnf(458,plain,
multiply(X,Y) = add(multiply(multiply(add(n0,n0),n1),X),multiply(add(add(multiply(multiply(Y,Y),n0),multiply(multiply(Y,Y),n0)),add(add(multiply(inverse(add(n1,n0)),multiply(Y,Y)),multiply(n1,multiply(Y,Y))),add(multiply(inverse(add(n1,n0)),multiply(Y,Y)),multiply(n1,multiply(Y,Y))))),X)),
inference('REWRITE',[status(thm)],[205,454,theory(equality)]) ).
cnf(470,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X))),add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X))))),add(add(add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0)),add(multiply(inverse(add(n1,n0)),n0),multiply(n1,n0))),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[313,454,theory(equality)]) ).
cnf(471,plain,
add(multiply(add(n0,n0),n1),add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X))),add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X)))))) = X,
inference('REWRITE',[status(thm)],[168,454,theory(equality)]) ).
cnf(473,plain,
add(multiply(multiply(X,n1),n1),multiply(n0,n0)) = add(multiply(add(inverse(add(n1,n0)),n1),X),add(multiply(multiply(n0,X),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,149,theory(equality)]),209,theory(equality)]) ).
cnf(480,plain,
multiply(multiply(n0,n1),X) = add(multiply(multiply(X,n1),multiply(n0,n1)),add(multiply(add(inverse(add(n1,n0)),n1),n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0)))),
inference('REWRITE',[status(thm)],[255,473,theory(equality)]) ).
cnf(484,plain,
add(multiply(add(inverse(add(n1,n0)),n1),n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))) = add(add(n0,n0),add(multiply(multiply(multiply(n0,n1),n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[417,473,theory(equality)]) ).
cnf(486,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,multiply(X,n1)),add(multiply(add(inverse(add(n1,n0)),n1),X),add(multiply(multiply(n0,X),n1),multiply(n0,n0)))),
inference('REWRITE',[status(thm)],[251,473,theory(equality)]) ).
cnf(525,plain,
multiply(multiply(n0,n0),multiply(X,X)) = add(multiply(multiply(X,n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))),
inference('PARAMODULATE',[status(thm)],[246,209,theory(equality)]) ).
cnf(540,plain,
add(multiply(n0,n0),multiply(multiply(X,n1),Y)) = add(add(multiply(multiply(X,n1),Y),multiply(multiply(n0,n0),Y)),multiply(multiply(n0,n0),multiply(X,X))),
inference('PARAMODULATE',[status(thm)],[4,246,theory(equality)]) ).
cnf(574,plain,
add(multiply(multiply(X,n1),n1),multiply(n0,multiply(n0,n1))) = multiply(multiply(X,n1),multiply(n1,X)),
inference('PARAMODULATE',[status(thm)],[67,61,theory(equality)]) ).
cnf(599,plain,
multiply(n1,X) = add(multiply(n1,X),multiply(multiply(n0,n1),X)),
inference('PARAMODULATE',[status(thm)],[19,137,theory(equality)]) ).
cnf(601,plain,
multiply(X,Y) = add(multiply(n0,n1),multiply(multiply(X,n1),multiply(Y,n1))),
inference('PARAMODULATE',[status(thm)],[50,137,theory(equality)]) ).
cnf(611,plain,
add(multiply(n0,n1),n0) = add(add(n0,multiply(multiply(n0,n1),inverse(X))),add(multiply(X,multiply(n0,n1)),add(multiply(add(inverse(add(n1,n0)),n1),n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,137,theory(equality)]),473,209,137,theory(equality)]) ).
cnf(626,plain,
n0 = multiply(n1,n0),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[67,599,theory(equality)]),37,theory(equality)]) ).
cnf(649,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X))),add(multiply(inverse(add(n1,n0)),multiply(X,X)),multiply(n1,multiply(X,X))))),add(add(add(multiply(inverse(add(n1,n0)),n0),n0),add(multiply(inverse(add(n1,n0)),n0),n0)),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[470,626,theory(equality)]) ).
cnf(668,plain,
n0 = add(n0,multiply(multiply(n0,n1),inverse(n1))),
inference('PARAMODULATE',[status(thm)],[599,multiplicative_inverse,theory(equality)]) ).
cnf(685,plain,
n0 = add(n0,multiply(multiply(n0,n1),n0)),
inference('PARAMODULATE',[status(thm)],[599,626,theory(equality)]) ).
cnf(686,plain,
n1 = add(n1,add(n0,multiply(n0,n0))),
inference('PARAMODULATE',[status(thm)],[49,626,theory(equality)]) ).
cnf(687,plain,
multiply(n0,n1) = add(n0,multiply(inverse(n1),n0)),
inference('PARAMODULATE',[status(thm)],[17,626,theory(equality)]) ).
cnf(688,plain,
add(multiply(n0,inverse(n1)),add(inverse(n1),n0)) = n0,
inference('PARAMODULATE',[status(thm)],[75,626,theory(equality)]) ).
cnf(691,plain,
multiply(X,n1) = add(multiply(n1,X),multiply(add(n0,multiply(n0,n0)),X)),
inference('PARAMODULATE',[status(thm)],[58,626,theory(equality)]) ).
cnf(695,plain,
add(n0,multiply(n1,X)) = add(add(multiply(n1,X),multiply(n0,X)),add(n0,multiply(n0,n0))),
inference('PARAMODULATE',[status(thm)],[4,626,theory(equality)]) ).
cnf(704,plain,
add(inverse(add(n1,n0)),n1) = add(add(n0,multiply(n0,n0)),add(inverse(add(n1,n0)),n1)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,686,theory(equality)]),243,139,theory(equality)]) ).
cnf(705,plain,
add(multiply(add(inverse(add(n1,n0)),n1),n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))) = add(multiply(inverse(n1),n0),multiply(n0,n0)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,687,theory(equality)]),473,theory(equality)]) ).
cnf(706,plain,
multiply(multiply(n0,n1),X) = add(multiply(multiply(X,n1),multiply(n0,n1)),add(multiply(inverse(n1),n0),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[480,705,theory(equality)]) ).
cnf(710,plain,
add(multiply(inverse(n1),n0),multiply(n0,n0)) = add(add(n0,n0),add(multiply(multiply(multiply(n0,n1),n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[484,705,theory(equality)]) ).
cnf(711,plain,
add(multiply(n0,n1),n0) = add(add(n0,multiply(multiply(n0,n1),inverse(X))),add(multiply(X,multiply(n0,n1)),add(multiply(inverse(n1),n0),multiply(n0,n0)))),
inference('REWRITE',[status(thm)],[611,705,theory(equality)]) ).
cnf(724,plain,
add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)) = add(add(inverse(n1),n0),add(multiply(multiply(n0,inverse(n1)),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,688,theory(equality)]),209,277,theory(equality)]) ).
cnf(732,plain,
add(multiply(multiply(X,Y),n1),multiply(n0,n0)) = add(multiply(multiply(X,n1),multiply(Y,n1)),add(multiply(inverse(n1),n0),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[249,601,theory(equality)]),705,473,209,theory(equality)]) ).
cnf(733,plain,
multiply(multiply(n0,n1),X) = add(multiply(multiply(X,n0),n1),multiply(n0,n0)),
inference('REWRITE',[status(thm)],[706,732,theory(equality)]) ).
cnf(739,plain,
n0 = add(n0,add(multiply(multiply(n0,n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[685,733,theory(equality)]) ).
cnf(743,plain,
add(multiply(inverse(n1),n0),multiply(n0,n0)) = add(add(n0,n0),add(multiply(inverse(n1),n0),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[710,705,473,209,733,theory(equality)]) ).
cnf(757,plain,
add(n0,multiply(n0,n0)) = n0,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[multiplicative_inverse,733,theory(equality)]),249,394,theory(equality)]) ).
cnf(758,plain,
add(n0,multiply(X,X)) = add(add(multiply(X,X),multiply(X,X)),n0),
inference('REWRITE',[status(thm)],[333,757,theory(equality)]) ).
cnf(759,plain,
n1 = add(n1,n0),
inference('REWRITE',[status(thm)],[686,757,theory(equality)]) ).
cnf(764,plain,
add(n0,add(inverse(n1),n1)) = n1,
inference('REWRITE',[status(thm)],[147,759,theory(equality)]) ).
cnf(766,plain,
multiply(X,n1) = add(multiply(n0,X),multiply(add(inverse(n1),n1),X)),
inference('REWRITE',[status(thm)],[149,759,theory(equality)]) ).
cnf(774,plain,
multiply(inverse(n0),n1) = add(n0,multiply(add(inverse(n1),n1),inverse(n0))),
inference('REWRITE',[status(thm)],[158,759,theory(equality)]) ).
cnf(778,plain,
add(n0,add(multiply(n0,inverse(add(inverse(n1),n1))),n0)) = inverse(add(inverse(n1),n1)),
inference('REWRITE',[status(thm)],[172,759,theory(equality)]) ).
cnf(782,plain,
add(inverse(add(inverse(n1),n1)),multiply(add(inverse(n1),n1),X)) = add(multiply(X,n1),add(multiply(n0,inverse(add(inverse(n1),n1))),n0)),
inference('REWRITE',[status(thm)],[180,759,theory(equality)]) ).
cnf(784,plain,
add(inverse(add(inverse(n1),n1)),n0) = add(add(multiply(n0,inverse(add(inverse(n1),n1))),n0),add(multiply(n0,inverse(add(inverse(n1),n1))),n0)),
inference('REWRITE',[status(thm)],[182,759,theory(equality)]) ).
cnf(786,plain,
multiply(inverse(add(inverse(n1),n1)),n1) = add(multiply(n0,inverse(add(inverse(n1),n1))),n0),
inference('REWRITE',[status(thm)],[184,759,theory(equality)]) ).
cnf(811,plain,
add(n0,add(n0,multiply(multiply(n0,n1),inverse(add(inverse(n1),n1))))) = inverse(add(inverse(n1),n1)),
inference('REWRITE',[status(thm)],[395,759,theory(equality)]) ).
cnf(837,plain,
multiply(n0,n1) = add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),multiply(add(inverse(n1),n1),n0)),
inference('REWRITE',[status(thm)],[452,759,theory(equality)]) ).
cnf(839,plain,
multiply(add(X,Y),n1) = add(add(multiply(X,n0),multiply(Y,n0)),add(add(multiply(inverse(n1),X),multiply(n1,X)),add(multiply(inverse(n1),Y),multiply(n1,Y)))),
inference('REWRITE',[status(thm)],[454,759,theory(equality)]) ).
cnf(847,plain,
add(add(add(multiply(X,n0),multiply(Y,n0)),add(add(multiply(inverse(n1),X),multiply(n1,X)),add(multiply(inverse(n1),Y),multiply(n1,Y)))),multiply(n0,n0)) = add(Y,multiply(X,X)),
inference('REWRITE',[status(thm)],[249,839,theory(equality)]) ).
cnf(850,plain,
add(add(multiply(X,X),multiply(X,X)),add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(inverse(n1),n0),n0),add(multiply(inverse(n1),n0),n0)))) = add(X,add(add(add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X))),add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X)))),add(multiply(X,X),add(multiply(multiply(X,X),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[210,626,839,theory(equality)]) ).
cnf(852,plain,
multiply(X,Y) = add(multiply(add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(inverse(n1),n0),n0),add(multiply(inverse(n1),n0),n0))),X),multiply(add(add(multiply(multiply(Y,Y),n0),multiply(multiply(Y,Y),n0)),add(add(multiply(inverse(n1),multiply(Y,Y)),multiply(n1,multiply(Y,Y))),add(multiply(inverse(n1),multiply(Y,Y)),multiply(n1,multiply(Y,Y))))),X)),
inference('REWRITE',[status(thm)],[458,626,839,759,theory(equality)]) ).
cnf(854,plain,
add(add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(inverse(n1),n0),n0),add(multiply(inverse(n1),n0),n0))),add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(add(multiply(inverse(n1),multiply(X,X)),multiply(n1,multiply(X,X))),add(multiply(inverse(n1),multiply(X,X)),multiply(n1,multiply(X,X)))))) = X,
inference('REWRITE',[status(thm)],[471,626,839,759,theory(equality)]) ).
cnf(864,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,multiply(X,n1)),add(multiply(add(inverse(n1),n1),X),add(multiply(multiply(n0,X),n1),multiply(n0,n0)))),
inference('REWRITE',[status(thm)],[486,759,theory(equality)]) ).
cnf(918,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(add(multiply(inverse(n1),multiply(X,X)),multiply(n1,multiply(X,X))),add(multiply(inverse(n1),multiply(X,X)),multiply(n1,multiply(X,X))))),add(add(add(multiply(inverse(n1),n0),n0),add(multiply(inverse(n1),n0),n0)),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[649,759,theory(equality)]) ).
cnf(937,plain,
add(multiply(add(inverse(n1),n1),n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))) = add(multiply(inverse(n1),n0),multiply(n0,n0)),
inference('REWRITE',[status(thm)],[705,759,theory(equality)]) ).
cnf(957,plain,
multiply(X,n1) = add(multiply(n1,X),multiply(n0,X)),
inference('REWRITE',[status(thm)],[691,757,theory(equality)]) ).
cnf(959,plain,
add(n0,multiply(n1,X)) = add(multiply(X,n1),n0),
inference('REWRITE',[status(thm)],[695,957,757,theory(equality)]) ).
cnf(960,plain,
add(inverse(n1),n1) = n1,
inference('REWRITE',[status(thm)],[704,764,759,757,theory(equality)]) ).
cnf(967,plain,
multiply(X,n1) = add(multiply(n0,X),multiply(n1,X)),
inference('REWRITE',[status(thm)],[766,960,theory(equality)]) ).
cnf(974,plain,
multiply(inverse(n0),n1) = add(n0,multiply(n1,inverse(n0))),
inference('REWRITE',[status(thm)],[774,960,theory(equality)]) ).
cnf(977,plain,
add(n0,add(multiply(n0,inverse(n1)),n0)) = inverse(n1),
inference('REWRITE',[status(thm)],[778,960,theory(equality)]) ).
cnf(981,plain,
add(inverse(n1),multiply(n1,X)) = add(multiply(X,n1),add(multiply(n0,inverse(n1)),n0)),
inference('REWRITE',[status(thm)],[782,960,theory(equality)]) ).
cnf(983,plain,
add(inverse(n1),n0) = add(add(multiply(n0,inverse(n1)),n0),add(multiply(n0,inverse(n1)),n0)),
inference('REWRITE',[status(thm)],[784,960,theory(equality)]) ).
cnf(985,plain,
multiply(inverse(n1),n1) = add(multiply(n0,inverse(n1)),n0),
inference('REWRITE',[status(thm)],[786,960,theory(equality)]) ).
cnf(1011,plain,
add(n0,n0) = inverse(n1),
inference('REWRITE',[status(thm)],[811,668,960,theory(equality)]) ).
cnf(1033,plain,
add(multiply(inverse(n1),n0),multiply(n0,n0)) = inverse(n1),
inference('REWRITE',[status(thm)],[743,49,1011,theory(equality)]) ).
cnf(1035,plain,
add(multiply(n0,n1),n0) = add(add(n0,multiply(multiply(n0,n1),inverse(X))),add(multiply(X,multiply(n0,n1)),inverse(n1))),
inference('REWRITE',[status(thm)],[711,1033,theory(equality)]) ).
cnf(1067,plain,
multiply(n0,n1) = add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),n0),
inference('REWRITE',[status(thm)],[837,626,960,theory(equality)]) ).
cnf(1068,plain,
add(multiply(X,n1),add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),n0)) = X,
inference('REWRITE',[status(thm)],[37,1067,theory(equality)]) ).
cnf(1092,plain,
add(multiply(multiply(X,n1),n1),add(add(add(add(add(multiply(multiply(n0,n0),n0),multiply(multiply(n0,n0),n0)),add(add(add(multiply(multiply(n0,n0),n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))),add(add(multiply(multiply(n0,n0),n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),multiply(multiply(n0,n0),n0)),add(add(add(add(multiply(multiply(n0,n0),n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))),add(add(multiply(multiply(n0,n0),n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0)))),add(add(multiply(multiply(n0,n0),n1),multiply(n0,n0)),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),multiply(n0,n0))) = multiply(multiply(X,n1),multiply(n1,X)),
inference('REWRITE',[status(thm)],[574,209,377,multiply_add_property,1067,theory(equality)]) ).
cnf(1161,plain,
add(add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),n0),n0) = add(add(n0,multiply(add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),n0),inverse(X))),add(add(multiply(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),X),multiply(n0,X)),inverse(n1))),
inference('REWRITE',[status(thm)],[1035,multiply_add_property,1067,theory(equality)]) ).
cnf(1179,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,multiply(X,n1)),add(multiply(n1,X),add(multiply(multiply(n0,X),n1),multiply(n0,n0)))),
inference('REWRITE',[status(thm)],[864,960,theory(equality)]) ).
cnf(1224,plain,
n0 = inverse(n1),
inference('REWRITE',[status(thm)],[937,1033,739,626,960,theory(equality)]) ).
cnf(1225,plain,
add(multiply(X,n0),add(n0,multiply(n1,X))) = X,
inference('REWRITE',[status(thm)],[75,1224,theory(equality)]) ).
cnf(1228,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(n0,multiply(n1,X)),add(multiply(multiply(X,n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[299,1224,theory(equality)]) ).
cnf(1232,plain,
add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)) = add(add(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))),
inference('REWRITE',[status(thm)],[724,1224,theory(equality)]) ).
cnf(1249,plain,
add(add(add(multiply(X,n0),multiply(Y,n0)),add(multiply(X,n1),multiply(Y,n1))),multiply(n0,n0)) = add(Y,multiply(X,X)),
inference('REWRITE',[status(thm)],[847,967,1224,theory(equality)]) ).
cnf(1252,plain,
add(add(multiply(X,X),multiply(X,X)),add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(n0,n0),n0),add(multiply(n0,n0),n0)))) = add(X,add(add(add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X))),add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X)))),add(multiply(X,X),add(multiply(multiply(X,X),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[850,1224,theory(equality)]) ).
cnf(1254,plain,
multiply(X,Y) = add(multiply(add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(n0,n0),n0),add(multiply(n0,n0),n0))),X),multiply(add(add(multiply(multiply(Y,Y),n0),multiply(multiply(Y,Y),n0)),add(multiply(multiply(Y,Y),n1),multiply(multiply(Y,Y),n1))),X)),
inference('REWRITE',[status(thm)],[852,967,1224,theory(equality)]) ).
cnf(1255,plain,
add(add(add(multiply(n0,n0),multiply(n0,n0)),add(add(multiply(n0,n0),n0),add(multiply(n0,n0),n0))),add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(multiply(multiply(X,X),n1),multiply(multiply(X,X),n1)))) = X,
inference('REWRITE',[status(thm)],[854,967,1224,theory(equality)]) ).
cnf(1268,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(multiply(multiply(X,X),n1),multiply(multiply(X,X),n1))),add(add(add(multiply(n0,n0),n0),add(multiply(n0,n0),n0)),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[918,967,1224,theory(equality)]) ).
cnf(1278,plain,
add(n0,add(multiply(n0,n0),n0)) = n0,
inference('REWRITE',[status(thm)],[977,1224,theory(equality)]) ).
cnf(1280,plain,
add(n0,multiply(n1,X)) = add(multiply(X,n1),add(multiply(n0,n0),n0)),
inference('REWRITE',[status(thm)],[981,1224,theory(equality)]) ).
cnf(1282,plain,
add(n0,n0) = add(add(multiply(n0,n0),n0),add(multiply(n0,n0),n0)),
inference('REWRITE',[status(thm)],[983,1224,theory(equality)]) ).
cnf(1283,plain,
add(add(multiply(X,X),multiply(X,X)),add(add(multiply(n0,n0),multiply(n0,n0)),add(n0,n0))) = add(X,add(add(add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X))),add(multiply(n0,multiply(X,X)),multiply(n0,multiply(X,X)))),add(multiply(X,X),add(multiply(multiply(X,X),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[1252,1282,theory(equality)]) ).
cnf(1285,plain,
multiply(X,Y) = add(multiply(add(add(multiply(n0,n0),multiply(n0,n0)),add(n0,n0)),X),multiply(add(add(multiply(multiply(Y,Y),n0),multiply(multiply(Y,Y),n0)),add(multiply(multiply(Y,Y),n1),multiply(multiply(Y,Y),n1))),X)),
inference('REWRITE',[status(thm)],[1254,1282,theory(equality)]) ).
cnf(1286,plain,
add(add(add(multiply(n0,n0),multiply(n0,n0)),add(n0,n0)),add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(multiply(multiply(X,X),n1),multiply(multiply(X,X),n1)))) = X,
inference('REWRITE',[status(thm)],[1255,1282,theory(equality)]) ).
cnf(1289,plain,
add(multiply(X,n1),multiply(n0,n0)) = add(add(add(multiply(multiply(X,X),n0),multiply(multiply(X,X),n0)),add(multiply(multiply(X,X),n1),multiply(multiply(X,X),n1))),add(add(n0,n0),add(multiply(n0,n0),add(multiply(multiply(n0,n0),n1),multiply(n0,n0))))),
inference('REWRITE',[status(thm)],[1268,1282,theory(equality)]) ).
cnf(1290,plain,
add(add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)),n0) = add(multiply(n0,n0),n0),
inference('REWRITE',[status(thm)],[985,1067,1224,theory(equality)]) ).
cnf(1292,plain,
add(n0,multiply(n1,X)) = X,
inference('REWRITE',[status(thm)],[1068,1280,1290,theory(equality)]) ).
cnf(1296,plain,
multiply(inverse(n0),n1) = inverse(n0),
inference('REWRITE',[status(thm)],[974,1292,theory(equality)]) ).
cnf(1300,plain,
X = add(multiply(X,n1),n0),
inference('REWRITE',[status(thm)],[959,1292,theory(equality)]) ).
cnf(1302,plain,
add(multiply(X,n0),X) = X,
inference('REWRITE',[status(thm)],[1225,1292,theory(equality)]) ).
cnf(1320,plain,
add(n0,n0) = n0,
inference('REWRITE',[status(thm)],[1278,1302,theory(equality)]) ).
cnf(1321,plain,
add(add(multiply(n0,n0),multiply(n0,n0)),multiply(n0,n0)) = n0,
inference('REWRITE',[status(thm)],[1232,739,1320,theory(equality)]) ).
cnf(1325,plain,
multiply(X,n0) = add(multiply(n0,X),multiply(n0,X)),
inference('REWRITE',[status(thm)],[383,1320,1321,theory(equality)]) ).
cnf(1326,plain,
multiply(n0,n0) = n0,
inference('REWRITE',[status(thm)],[1321,1325,theory(equality)]) ).
cnf(1328,plain,
X = add(X,add(multiply(X,n0),n0)),
inference('REWRITE',[status(thm)],[49,1326,theory(equality)]) ).
cnf(1329,plain,
multiply(X,X) = X,
inference('REWRITE',[status(thm)],[209,1300,1326,theory(equality)]) ).
cnf(1339,plain,
add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),add(multiply(Y,X),X)),
inference('REWRITE',[status(thm)],[4,1329,theory(equality)]) ).
cnf(1360,plain,
add(n0,X) = add(add(X,X),n0),
inference('REWRITE',[status(thm)],[758,1329,theory(equality)]) ).
cnf(1375,plain,
multiply(inverse(X),n1) = add(n0,inverse(X)),
inference('REWRITE',[status(thm)],[222,1300,1326,theory(equality)]) ).
cnf(1378,plain,
n1 = inverse(n0),
inference('REWRITE',[status(thm)],[1296,additive_inverse,1375,theory(equality)]) ).
cnf(1379,plain,
multiply(X,multiply(n1,Y)) = multiply(X,multiply(Y,n1)),
inference('REWRITE',[status(thm)],[72,19,1378,theory(equality)]) ).
cnf(1384,plain,
add(n0,inverse(inverse(X))) = add(multiply(X,inverse(inverse(X))),n0),
inference('REWRITE',[status(thm)],[55,1375,theory(equality)]) ).
cnf(1415,plain,
multiply(X,Y) = add(multiply(multiply(Y,n1),X),multiply(n0,X)),
inference('REWRITE',[status(thm)],[246,1329,1326,theory(equality)]) ).
cnf(1419,plain,
add(X,multiply(X,Y)) = add(add(multiply(X,Y),multiply(X,Y)),add(X,X)),
inference('REWRITE',[status(thm)],[257,1300,1326,theory(equality)]) ).
cnf(1456,plain,
multiply(n0,X) = add(multiply(multiply(X,n1),n0),n0),
inference('REWRITE',[status(thm)],[525,1300,1329,1326,theory(equality)]) ).
cnf(1459,plain,
add(n0,multiply(multiply(X,n1),Y)) = add(multiply(Y,X),multiply(n0,X)),
inference('REWRITE',[status(thm)],[540,1329,1415,1326,theory(equality)]) ).
cnf(1479,plain,
multiply(X,n1) = multiply(multiply(X,n1),multiply(n1,X)),
inference('REWRITE',[status(thm)],[1092,1300,1320,1329,1326,theory(equality)]) ).
cnf(1486,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,multiply(X,n1)),multiply(X,n1)),
inference('REWRITE',[status(thm)],[1179,957,1300,1326,theory(equality)]) ).
cnf(1500,plain,
add(add(add(multiply(X,n0),multiply(Y,n0)),add(multiply(X,n1),multiply(Y,n1))),n0) = add(Y,X),
inference('REWRITE',[status(thm)],[1249,1329,1326,theory(equality)]) ).
cnf(1522,plain,
add(n0,X) = add(X,add(X,multiply(X,n0))),
inference('REWRITE',[status(thm)],[1283,1419,1300,1325,1360,1329,1320,theory(equality)]) ).
cnf(1524,plain,
multiply(X,Y) = add(multiply(n0,X),multiply(add(add(multiply(Y,n0),multiply(Y,n0)),add(multiply(Y,n1),multiply(Y,n1))),X)),
inference('REWRITE',[status(thm)],[1285,1329,1320,theory(equality)]) ).
cnf(1525,plain,
add(n0,add(add(multiply(X,n0),multiply(X,n0)),add(multiply(X,n1),multiply(X,n1)))) = X,
inference('REWRITE',[status(thm)],[1286,1329,1320,theory(equality)]) ).
cnf(1527,plain,
X = add(X,X),
inference('REWRITE',[status(thm)],[1289,1500,1300,1329,1320,theory(equality)]) ).
cnf(1541,plain,
add(n0,add(multiply(X,n0),multiply(X,n1))) = X,
inference('REWRITE',[status(thm)],[1525,1527,theory(equality)]) ).
cnf(1542,plain,
multiply(X,Y) = add(multiply(n0,X),multiply(add(multiply(Y,n0),multiply(Y,n1)),X)),
inference('REWRITE',[status(thm)],[1524,1527,theory(equality)]) ).
cnf(1573,plain,
X = add(X,multiply(X,n0)),
inference('REWRITE',[status(thm)],[1228,1300,1329,1292,theory(equality)]) ).
cnf(1574,plain,
add(n0,X) = X,
inference('REWRITE',[status(thm)],[1522,1527,1573,theory(equality)]) ).
cnf(1577,plain,
add(multiply(X,n0),multiply(X,n1)) = X,
inference('REWRITE',[status(thm)],[1541,1574,theory(equality)]) ).
cnf(1578,plain,
multiply(X,Y) = add(multiply(n0,X),multiply(Y,X)),
inference('REWRITE',[status(thm)],[1542,1577,theory(equality)]) ).
cnf(1583,plain,
multiply(X,Y) = multiply(X,multiply(Y,n1)),
inference('REWRITE',[status(thm)],[19,1578,theory(equality)]) ).
cnf(1597,plain,
multiply(multiply(X,n1),X) = add(multiply(n0,X),multiply(X,n1)),
inference('REWRITE',[status(thm)],[1486,1583,theory(equality)]) ).
cnf(1613,plain,
multiply(add(X,Y),Z) = add(add(multiply(X,n0),multiply(Y,n0)),add(multiply(X,Z),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[62,1583,theory(equality)]) ).
cnf(1638,plain,
add(b,multiply(a,n0)) != b,
inference('REWRITE',[status(thm)],[prove_multiply_add,1339,1329,1613,theory(equality)]) ).
cnf(1644,plain,
multiply(X,multiply(n1,Y)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[1379,1583,theory(equality)]) ).
cnf(1647,plain,
multiply(X,n1) = add(multiply(n0,X),multiply(X,n1)),
inference('REWRITE',[status(thm)],[1479,1597,1644,theory(equality)]) ).
cnf(1650,plain,
multiply(multiply(X,n1),X) = multiply(X,n1),
inference('REWRITE',[status(thm)],[1597,1647,theory(equality)]) ).
cnf(1678,plain,
multiply(multiply(X,n1),Y) = add(multiply(Y,X),multiply(n0,X)),
inference('REWRITE',[status(thm)],[1459,1574,theory(equality)]) ).
cnf(1679,plain,
add(X,multiply(n0,X)) = multiply(X,n1),
inference('REWRITE',[status(thm)],[1650,1329,1678,theory(equality)]) ).
cnf(1685,plain,
multiply(X,Y) = add(multiply(Y,X),multiply(multiply(n0,Y),X)),
inference('REWRITE',[status(thm)],[1583,multiply_add_property,1679,theory(equality)]) ).
cnf(1690,plain,
multiply(inverse(add(X,multiply(n0,X))),X) = add(multiply(n0,inverse(add(X,multiply(n0,X)))),n0),
inference('REWRITE',[status(thm)],[60,1679,theory(equality)]) ).
cnf(1701,plain,
X = add(add(X,multiply(n0,X)),n0),
inference('REWRITE',[status(thm)],[1300,1679,theory(equality)]) ).
cnf(1754,plain,
multiply(n0,X) = add(multiply(X,n0),n0),
inference('REWRITE',[status(thm)],[1456,1578,1678,theory(equality)]) ).
cnf(1763,plain,
X = add(X,multiply(n0,X)),
inference('REWRITE',[status(thm)],[1328,1754,theory(equality)]) ).
cnf(1777,plain,
multiply(inverse(X),X) = add(multiply(n0,inverse(X)),n0),
inference('REWRITE',[status(thm)],[1690,1763,theory(equality)]) ).
cnf(1786,plain,
X = add(X,n0),
inference('REWRITE',[status(thm)],[1701,1763,theory(equality)]) ).
cnf(1793,plain,
multiply(inverse(X),X) = multiply(n0,inverse(X)),
inference('REWRITE',[status(thm)],[1777,1786,theory(equality)]) ).
cnf(1870,plain,
inverse(inverse(X)) = multiply(X,inverse(inverse(X))),
inference('REWRITE',[status(thm)],[1384,1786,1574,theory(equality)]) ).
cnf(1898,plain,
multiply(X,Y) = multiply(X,inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[203,1685,1793,1870,1574,theory(equality)]) ).
cnf(1900,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[1870,1329,1898,theory(equality)]) ).
cnf(1919,plain,
n0 = add(multiply(n0,inverse(X)),multiply(X,n0)),
inference('REWRITE',[status(thm)],[1161,1786,1578,1574,1329,1224,theory(equality)]) ).
cnf(1936,plain,
multiply(inverse(X),X) = n0,
inference('PARAMODULATE',[status(thm)],[multiplicative_inverse,1900,theory(equality)]) ).
cnf(1938,plain,
n0 = multiply(n0,inverse(X)),
inference('REWRITE',[status(thm)],[1793,1936,theory(equality)]) ).
cnf(1943,plain,
n0 = multiply(X,n0),
inference('REWRITE',[status(thm)],[1919,1574,1938,theory(equality)]) ).
cnf(1946,plain,
$false,
inference('REWRITE',[status(thm)],[1638,1786,1943,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 19:35:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.46 *
% 0.20/0.46 #<PACKAGE "SNARK-USER">
% 0.20/0.46 *
% 0.20/0.46 SNARK-TPTP-OPTIONS
% 0.20/0.46 *
% 0.20/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46 (USE-FACTORING :POS)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T19:35:27
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-01T19:35:27
% 0.20/0.48
% 0.20/0.48 ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |n1|).
% 2.25/2.41 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |n0|).
% 2.25/2.41
% 2.25/2.41 #||
% 2.25/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.25/2.41 % SZS output start Refutation
% See solution above
% 2.25/2.47 ||#
% 2.25/2.47
% 2.25/2.47 ; Summary of computation:
% 2.25/2.47 ; 3087 formulas have been input or derived (from 87 formulas).
% 2.25/2.47 ; 1946 (63%) were retained. Of these,
% 2.25/2.47 ; 1852 (95%) were simplified or subsumed later,
% 2.25/2.47 ; 94 ( 5%) are still being kept.
% 2.25/2.47 ;
% 2.25/2.47 ; Run time in seconds excluding printing time:
% 2.25/2.47 ; 0.003 0% Read assertion file (1 call)
% 2.25/2.47 ; 0.000 0% Assert (11 calls)
% 2.25/2.47 ; 0.729 38% Process new row (2,990 calls)
% 2.25/2.47 ; 0.004 0% Resolution (172 calls)
% 2.25/2.47 ; 0.029 1% Paramodulation (86 calls)
% 2.25/2.47 ; 0.439 23% Forward simplification (2,779 calls)
% 2.25/2.47 ; 0.483 25% Backward simplification (1,941 calls)
% 2.25/2.47 ; 0.218 11% Ordering (26,621 calls)
% 2.25/2.47 ; 0.000 0% Sortal reasoning (32 calls)
% 2.25/2.47 ; 0.000 0% Purity testing (1 call)
% 2.25/2.47 ; 0.035 2% Other
% 2.25/2.47 ; 1.940 Total
% 2.25/2.47 ; 2.006 Real time
% 2.25/2.47 ;
% 2.25/2.47 ; Term-hash-array has 8,363 terms in all.
% 2.25/2.47 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.25/2.47 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.25/2.47 ; Path-index has 330 entries (3,085 at peak, 11,908 added, 11,578 deleted).
% 2.25/2.47 ; Path-index has 55,433 nodes (74,297 at peak, 124,363 added, 68,930 deleted).
% 2.25/2.47 ; Trie-index has 330 entries (3,085 at peak, 11,908 added, 11,578 deleted).
% 2.25/2.47 ; Trie-index has 1,927 nodes (95,214 at peak, 335,441 added, 333,514 deleted).
% 2.25/2.47 ; Retrieved 72,009 generalization terms in 55,704 calls.
% 2.25/2.47 ; Retrieved 12,725 instance terms in 2,355 calls.
% 2.25/2.47 ; Retrieved 4,158 unifiable terms in 861 calls.
% 2.25/2.47 ;
% 2.25/2.47 ; The agenda of backward simplifiable rows to process has 69 entries:
% 2.25/2.47 ; 69 with value 0
% 2.25/2.47 ; The agenda of rows to process has 5 entries:
% 2.25/2.47 ; 1 with value 12 1 with value 23 1 with value 42
% 2.25/2.47 ; 1 with value 18 1 with value 27
% 2.25/2.47 ; The agenda of rows to give has 82 entries:
% 2.25/2.47 ; 6 with value (4 11) 3 with value (4 21) 3 with value (4 31)
% 2.25/2.47 ; 5 with value (4 12) 2 with value (4 22) 1 with value (4 32)
% 2.25/2.47 ; 3 with value (4 13) 7 with value (4 23) 3 with value (4 33)
% 2.25/2.47 ; 5 with value (4 15) 7 with value (4 24) 1 with value (4 34)
% 2.25/2.47 ; 3 with value (4 16) 6 with value (4 25) 1 with value (4 37)
% 2.25/2.47 ; 5 with value (4 17) 3 with value (4 26) 1 with value (4 38)
% 2.25/2.47 ; 2 with value (4 18) 2 with value (4 28) 1 with value (4 54)
% 2.25/2.47 ; 6 with value (4 19) 2 with value (4 30) 1 with value (4 82)
% 2.25/2.47 ; 3 with value (4 20)
% 2.25/2.47 Evaluation took:
% 2.25/2.47 2.006 seconds of real time
% 2.25/2.47 1.878266 seconds of user run time
% 2.25/2.47 0.128223 seconds of system run time
% 2.25/2.47 [Run times include 0.375 seconds GC run time.]
% 2.25/2.47 0 calls to %EVAL
% 2.25/2.47 0 page faults and
% 2.25/2.47 185,198,432 bytes consed.
% 2.25/2.47 :PROOF-FOUND
% 2.25/2.47 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T19:35:29
% 2.25/2.47 :PROOF-FOUND
% 2.25/2.47 *
%------------------------------------------------------------------------------