TSTP Solution File: GRP437-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 11:38:45 EDT 2022
% Result : Unsatisfiable 2.65s 2.85s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 2
% Syntax : Number of clauses : 206 ( 206 unt; 0 nHn; 2 RR)
% Number of literals : 206 ( 205 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 38 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 853 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(U,Y))),X))))) = U,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(3,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,U))),inverse(V))),multiply(V,multiply(Z,X))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(4,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),multiply(inverse(U),inverse(multiply(V,W))))))),inverse(multiply(W,multiply(U,Z)))) = V,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(6,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(U))),multiply(U,multiply(V,X))))) = multiply(W,multiply(multiply(inverse(W),inverse(multiply(Z,V))),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(16,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,U))),Z))),inverse(Y))) = U,
inference('PARAMODULATE',[status(thm)],[3,6,theory(equality)]) ).
cnf(17,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U))) = multiply(V,multiply(multiply(inverse(V),inverse(multiply(Y,Z))),inverse(U))),
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(18,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(X,multiply(U,inverse(V))),multiply(V,multiply(Y,Z)))))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,6,theory(equality)]) ).
cnf(19,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(multiply(multiply(Z,multiply(U,inverse(V))),multiply(V,multiply(W,Y))))),multiply(Z,multiply(U,X))))) = W,
inference('PARAMODULATE',[status(thm)],[3,6,theory(equality)]) ).
cnf(64,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(U,V))),inverse(W))))),X1))),inverse(Y))) = inverse(multiply(multiply(W,multiply(U,inverse(Y1))),multiply(Y1,multiply(V,X1)))),
inference('PARAMODULATE',[status(thm)],[16,6,theory(equality)]) ).
cnf(66,plain,
multiply(X,multiply(multiply(inverse(X),inverse(Y)),inverse(Z))) = multiply(U,multiply(multiply(inverse(U),inverse(Y)),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[17,single_axiom,theory(equality)]) ).
cnf(74,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,multiply(multiply(inverse(Z),inverse(U)),inverse(V))))),W))),inverse(Y))) = multiply(multiply(inverse(W),inverse(U)),inverse(V)),
inference('PARAMODULATE',[status(thm)],[16,66,theory(equality)]) ).
cnf(75,plain,
multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U)) = inverse(multiply(multiply(U,multiply(Y,inverse(V))),multiply(V,multiply(Z,X)))),
inference('REWRITE',[status(thm)],[64,74,theory(equality)]) ).
cnf(82,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,multiply(U,V)))) = inverse(multiply(multiply(X,multiply(Y,inverse(W))),multiply(W,multiply(U,V)))),
inference('PARAMODULATE',[status(thm)],[75,75,theory(equality)]) ).
cnf(137,plain,
multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,multiply(X,multiply(U,inverse(Y)))))),Z))) = U,
inference('PARAMODULATE',[status(thm)],[18,single_axiom,theory(equality)]) ).
cnf(143,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),inverse(U)))),inverse(Y))) = inverse(multiply(V,multiply(W,inverse(multiply(multiply(U,multiply(Z,inverse(X1))),multiply(X1,multiply(V,W))))))),
inference('PARAMODULATE',[status(thm)],[16,18,theory(equality)]) ).
cnf(146,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(U,multiply(V,inverse(W))),multiply(W,multiply(Y,Z))))))),multiply(X1,multiply(multiply(inverse(X1),inverse(V)),X))))) = inverse(U),
inference('PARAMODULATE',[status(thm)],[single_axiom,18,theory(equality)]) ).
cnf(173,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(U,X))))) = multiply(inverse(V),inverse(multiply(Y,multiply(Z,multiply(U,inverse(V)))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,137,theory(equality)]) ).
cnf(174,plain,
multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,U))),Z))) = multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(V,U))),V))),
inference('PARAMODULATE',[status(thm)],[137,16,theory(equality)]) ).
cnf(201,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(X,multiply(U,Y))))),Z))) = U,
inference('PARAMODULATE',[status(thm)],[137,173,theory(equality)]) ).
cnf(202,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(U,X))))) = multiply(V,inverse(multiply(Y,multiply(Z,multiply(U,V))))),
inference('PARAMODULATE',[status(thm)],[173,173,theory(equality)]) ).
cnf(257,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,U))) = inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U))),
inference('PARAMODULATE',[status(thm)],[82,18,theory(equality)]) ).
cnf(258,plain,
inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(Y)),inverse(Z))),multiply(Z,U))) = inverse(multiply(multiply(V,multiply(multiply(inverse(V),inverse(Y)),inverse(W))),multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[257,66,theory(equality)]) ).
cnf(314,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(inverse(Z),X))),multiply(inverse(multiply(inverse(U),inverse(multiply(multiply(inverse(Z),inverse(multiply(V,W))),V)))),inverse(multiply(X1,U))))))),inverse(W)) = X1,
inference('PARAMODULATE',[status(thm)],[4,16,theory(equality)]) ).
cnf(327,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(Z)),inverse(U))),multiply(U,multiply(inverse(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(X1,V))),multiply(inverse(Y1),inverse(multiply(Z,Z1))))))),X))))) = inverse(multiply(Z1,multiply(Y1,X1))),
inference('PARAMODULATE',[status(thm)],[3,4,theory(equality)]) ).
cnf(328,plain,
multiply(inverse(X),inverse(multiply(inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(U,Y))),multiply(inverse(V),inverse(multiply(W,X1))))))),multiply(inverse(multiply(X1,multiply(V,U))),inverse(multiply(multiply(X,multiply(Y1,inverse(Z1))),multiply(Z1,W))))))) = Y1,
inference('PARAMODULATE',[status(thm)],[18,4,theory(equality)]) ).
cnf(347,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(U,multiply(V,W)))) = multiply(X1,inverse(multiply(U,multiply(V,multiply(inverse(multiply(Y1,multiply(Z1,multiply(multiply(inverse(Z1),inverse(multiply(Z,Y1))),multiply(inverse(Y),inverse(multiply(W,X))))))),X1))))),
inference('PARAMODULATE',[status(thm)],[202,4,theory(equality)]) ).
cnf(348,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),inverse(multiply(multiply(U,multiply(multiply(inverse(U),inverse(V)),inverse(W))),multiply(W,V)))) = inverse(multiply(X,multiply(Y,Z))),
inference('REWRITE',[status(thm)],[327,347,theory(equality)]) ).
cnf(468,plain,
inverse(multiply(multiply(inverse(X),inverse(multiply(Y,Z))),Y)) = inverse(multiply(multiply(inverse(X),inverse(multiply(U,Z))),U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,174,theory(equality)]),16,theory(equality)]) ).
cnf(497,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),inverse(U))))) = inverse(multiply(multiply(inverse(V),inverse(multiply(W,multiply(U,multiply(Z,inverse(V)))))),W)),
inference('PARAMODULATE',[status(thm)],[468,3,theory(equality)]) ).
cnf(501,plain,
inverse(multiply(X,multiply(Y,inverse(multiply(multiply(Z,multiply(U,inverse(V))),multiply(V,multiply(X,Y))))))) = inverse(multiply(multiply(inverse(W),inverse(multiply(X1,multiply(Z,multiply(U,inverse(W)))))),X1)),
inference('PARAMODULATE',[status(thm)],[468,19,theory(equality)]) ).
cnf(508,plain,
inverse(multiply(multiply(inverse(X),inverse(Y)),Z)) = inverse(multiply(multiply(inverse(X),inverse(multiply(U,inverse(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(Y,V))),Z))))))),U)),
inference('PARAMODULATE',[status(thm)],[468,single_axiom,theory(equality)]) ).
cnf(510,plain,
inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U))),multiply(U,multiply(Y,inverse(V))))) = inverse(multiply(multiply(inverse(W),inverse(multiply(X1,multiply(V,multiply(Z,inverse(W)))))),X1)),
inference('PARAMODULATE',[status(thm)],[468,6,theory(equality)]) ).
cnf(538,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(Z)),inverse(U))),multiply(U,Z)))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[348,16,theory(equality)]) ).
cnf(539,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(U,Y))),U))))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[538,16,theory(equality)]) ).
cnf(541,plain,
multiply(inverse(X),multiply(multiply(inverse(Y),inverse(multiply(multiply(inverse(Z),inverse(multiply(U,Y))),U))),inverse(Z))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[538,75,theory(equality)]) ).
cnf(545,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(inverse(Y),inverse(Z))),multiply(Z,multiply(multiply(U,multiply(multiply(inverse(U),inverse(V)),inverse(W))),X))))) = multiply(W,V),
inference('PARAMODULATE',[status(thm)],[3,538,theory(equality)]) ).
cnf(548,plain,
multiply(X,multiply(inverse(X),inverse(Y))) = multiply(Z,multiply(inverse(Z),inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[66,538,theory(equality)]),538,theory(equality)]) ).
cnf(557,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),inverse(U))))),inverse(multiply(multiply(V,W),multiply(U,Z)))) = multiply(X1,multiply(multiply(inverse(X1),inverse(W)),inverse(V))),
inference('PARAMODULATE',[status(thm)],[4,538,theory(equality)]) ).
cnf(585,plain,
multiply(inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(Y)),inverse(Z))),multiply(Z,Y))),inverse(multiply(multiply(U,inverse(multiply(multiply(V,multiply(inverse(W),inverse(X1))),multiply(X1,multiply(Y1,U))))),multiply(V,inverse(W))))) = Y1,
inference('PARAMODULATE',[status(thm)],[19,538,theory(equality)]) ).
cnf(621,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[548,538,theory(equality)]),538,theory(equality)]) ).
cnf(643,plain,
multiply(X,Y) = multiply(Z,multiply(inverse(Z),inverse(multiply(multiply(U,multiply(multiply(inverse(U),inverse(multiply(V,Y))),inverse(W))),multiply(W,multiply(V,inverse(X))))))),
inference('PARAMODULATE',[status(thm)],[548,3,theory(equality)]) ).
cnf(662,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(Z,multiply(inverse(Z),inverse(inverse(X)))),
inference('PARAMODULATE',[status(thm)],[548,621,theory(equality)]) ).
cnf(663,plain,
multiply(X,multiply(multiply(Y,inverse(Y)),inverse(Z))) = multiply(U,multiply(multiply(inverse(U),inverse(inverse(X))),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[66,621,theory(equality)]) ).
cnf(675,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(U,inverse(U)))) = inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[257,621,theory(equality)]) ).
cnf(676,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,inverse(Z)))),U))),inverse(Y))) = inverse(U),
inference('PARAMODULATE',[status(thm)],[16,621,theory(equality)]) ).
cnf(679,plain,
multiply(multiply(inverse(X),inverse(multiply(Y,inverse(Y)))),inverse(Z)) = inverse(multiply(multiply(Z,multiply(U,inverse(V))),multiply(V,multiply(inverse(U),X)))),
inference('PARAMODULATE',[status(thm)],[75,621,theory(equality)]) ).
cnf(697,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,multiply(Z,inverse(Z))),
inference('PARAMODULATE',[status(thm)],[662,662,theory(equality)]) ).
cnf(703,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(Y)) = inverse(multiply(multiply(U,multiply(V,inverse(V))),multiply(inverse(U),multiply(Z,X)))),
inference('PARAMODULATE',[status(thm)],[75,662,theory(equality)]) ).
cnf(718,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(inverse(Y),multiply(U,X))))) = multiply(V,multiply(multiply(inverse(V),inverse(multiply(inverse(W),U))),inverse(W))),
inference('PARAMODULATE',[status(thm)],[6,662,theory(equality)]) ).
cnf(813,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(Y))) = multiply(U,multiply(multiply(inverse(U),inverse(multiply(V,Z))),V)),
inference('PARAMODULATE',[status(thm)],[16,539,theory(equality)]) ).
cnf(816,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(inverse(Y),inverse(Z))),multiply(Z,multiply(U,X))))) = multiply(V,multiply(multiply(inverse(V),inverse(multiply(W,U))),W)),
inference('PARAMODULATE',[status(thm)],[3,539,theory(equality)]) ).
cnf(823,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(Y)),multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(U,multiply(V,inverse(V))))),U))))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[539,697,theory(equality)]) ).
cnf(827,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(multiply(inverse(Z),inverse(multiply(U,V))),U),X))),multiply(inverse(Z),inverse(multiply(W,V))))))) = W,
inference('PARAMODULATE',[status(thm)],[4,539,theory(equality)]) ).
cnf(843,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(U)) = inverse(multiply(multiply(U,inverse(Y)),multiply(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(X1,V))),X1))),multiply(Z,X)))),
inference('PARAMODULATE',[status(thm)],[75,539,theory(equality)]) ).
cnf(846,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),Z)))),inverse(multiply(multiply(U,multiply(multiply(inverse(U),inverse(multiply(inverse(V),W))),inverse(X1))),multiply(X1,inverse(V))))) = W,
inference('PARAMODULATE',[status(thm)],[3,539,theory(equality)]) ).
cnf(854,plain,
inverse(multiply(multiply(inverse(X),inverse(Y)),Y)) = inverse(multiply(multiply(inverse(X),inverse(inverse(Z))),inverse(Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[468,539,theory(equality)]),508,theory(equality)]) ).
cnf(879,plain,
inverse(multiply(multiply(inverse(X),inverse(Y)),Y)) = inverse(multiply(multiply(inverse(X),inverse(Z)),Z)),
inference('PARAMODULATE',[status(thm)],[854,854,theory(equality)]) ).
cnf(880,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(Y))) = inverse(multiply(multiply(inverse(Y),inverse(Z)),Z)),
inference('PARAMODULATE',[status(thm)],[879,621,theory(equality)]) ).
cnf(914,plain,
multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(multiply(inverse(Z),inverse(U)),U))),multiply(inverse(Z),inverse(V))))) = multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(W,V))),W))),
inference('PARAMODULATE',[status(thm)],[174,879,theory(equality)]) ).
cnf(960,plain,
inverse(multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),Z))),multiply(U,inverse(U)))) = inverse(multiply(multiply(inverse(X),inverse(multiply(V,inverse(Y)))),V)),
inference('PARAMODULATE',[status(thm)],[468,880,theory(equality)]) ).
cnf(964,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(multiply(U,inverse(U)),inverse(V)))),X))))) = multiply(inverse(V),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[single_axiom,880,theory(equality)]) ).
cnf(978,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,inverse(Z)),inverse(U)))),multiply(inverse(U),inverse(V))))),inverse(Y))) = V,
inference('PARAMODULATE',[status(thm)],[16,880,theory(equality)]) ).
cnf(1135,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(inverse(multiply(Y,multiply(Z,inverse(multiply(U,inverse(U)))))))),inverse(V)))) = inverse(multiply(multiply(Y,multiply(Z,inverse(W))),multiply(W,inverse(V)))),
inference('PARAMODULATE',[status(thm)],[257,663,theory(equality)]) ).
cnf(1162,plain,
multiply(multiply(inverse(X),inverse(inverse(X))),inverse(Y)) = multiply(multiply(Z,inverse(Z)),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,663,theory(equality)]),74,theory(equality)]) ).
cnf(1206,plain,
multiply(multiply(X,inverse(X)),inverse(Y)) = multiply(multiply(Z,inverse(Z)),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[1162,1162,theory(equality)]) ).
cnf(1207,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference('PARAMODULATE',[status(thm)],[621,1206,theory(equality)]) ).
cnf(1263,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,1207,theory(equality)]),676,theory(equality)]) ).
cnf(1268,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,1207,theory(equality)]),964,theory(equality)]) ).
cnf(1271,plain,
inverse(multiply(multiply(inverse(X),inverse(multiply(Y,inverse(Z)))),Y)) = inverse(multiply(multiply(inverse(X),inverse(multiply(multiply(U,inverse(U)),inverse(multiply(V,inverse(V)))))),Z)),
inference('PARAMODULATE',[status(thm)],[468,1207,theory(equality)]) ).
cnf(1314,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(multiply(Z,inverse(Z)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[662,1263,theory(equality)]),1268,theory(equality)]) ).
cnf(1346,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(Z,multiply(inverse(Z),inverse(inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[548,1268,theory(equality)]) ).
cnf(1353,plain,
multiply(multiply(inverse(X),inverse(Y)),Y) = multiply(multiply(inverse(X),inverse(Z)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1268,879,theory(equality)]),1268,theory(equality)]) ).
cnf(1354,plain,
multiply(multiply(X,inverse(X)),inverse(Y)) = multiply(multiply(inverse(Y),inverse(Z)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1268,880,theory(equality)]),1268,theory(equality)]) ).
cnf(1368,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(inverse(multiply(Z,inverse(Z)))))),U)) = inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,inverse(inverse(U))))),
inference('PARAMODULATE',[status(thm)],[257,1268,theory(equality)]) ).
cnf(1370,plain,
multiply(multiply(inverse(inverse(inverse(X))),inverse(multiply(Y,inverse(multiply(Z,inverse(Z)))))),inverse(U)) = inverse(multiply(multiply(U,multiply(Y,inverse(V))),multiply(V,X))),
inference('PARAMODULATE',[status(thm)],[75,1268,theory(equality)]) ).
cnf(1388,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Z,inverse(Z)),Y),
inference('PARAMODULATE',[status(thm)],[1314,1314,theory(equality)]) ).
cnf(1390,plain,
inverse(multiply(inverse(X),multiply(Y,inverse(Y)))) = inverse(multiply(multiply(inverse(X),inverse(Z)),Z)),
inference('PARAMODULATE',[status(thm)],[879,1314,theory(equality)]) ).
cnf(1405,plain,
multiply(X,multiply(inverse(Y),multiply(Z,inverse(Z)))) = multiply(U,multiply(multiply(inverse(U),inverse(inverse(X))),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[66,1314,theory(equality)]) ).
cnf(1443,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(multiply(U,Y),multiply(V,inverse(V)))))),Z))) = U,
inference('PARAMODULATE',[status(thm)],[201,1314,theory(equality)]) ).
cnf(1492,plain,
multiply(inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U))),multiply(U,multiply(Y,multiply(V,inverse(V)))))),multiply(W,inverse(W))) = Z,
inference('PARAMODULATE',[status(thm)],[3,1314,theory(equality)]) ).
cnf(1498,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(multiply(multiply(multiply(Z,multiply(U,inverse(V))),multiply(V,multiply(W,X1))),multiply(multiply(inverse(X1),inverse(multiply(U,W))),inverse(Z))),X),
inference('PARAMODULATE',[status(thm)],[1314,75,theory(equality)]) ).
cnf(1550,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,U)),inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U)))),W) = multiply(multiply(X1,inverse(X1)),W),
inference('PARAMODULATE',[status(thm)],[1388,257,theory(equality)]) ).
cnf(1551,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,multiply(U,V))),multiply(multiply(inverse(V),inverse(multiply(Y,U))),inverse(X))),W) = multiply(multiply(X1,inverse(X1)),W),
inference('PARAMODULATE',[status(thm)],[1388,75,theory(equality)]) ).
cnf(1555,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(multiply(inverse(X),inverse(Z)),Z),
inference('PARAMODULATE',[status(thm)],[1314,1353,theory(equality)]) ).
cnf(1560,plain,
multiply(X,multiply(multiply(inverse(Y),inverse(Z)),Z)) = multiply(U,multiply(multiply(inverse(U),inverse(inverse(X))),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[663,1353,theory(equality)]) ).
cnf(1579,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(U),inverse(V)),V))))) = multiply(W,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(U),inverse(X)),W))))),
inference('PARAMODULATE',[status(thm)],[202,1353,theory(equality)]) ).
cnf(1584,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(multiply(inverse(Z),inverse(U))))),multiply(multiply(inverse(Z),inverse(V)),V))) = inverse(multiply(multiply(X,multiply(Y,inverse(W))),multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[257,1353,theory(equality)]) ).
cnf(1601,plain,
multiply(X,multiply(Y,multiply(Z,U))) = multiply(multiply(inverse(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(U,V))),multiply(inverse(Z),inverse(multiply(X,Y))))))),inverse(X1)),X1),
inference('PARAMODULATE',[status(thm)],[1353,4,theory(equality)]) ).
cnf(1815,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,inverse(Z)),U))),V))),inverse(Y))) = multiply(inverse(V),inverse(inverse(U))),
inference('PARAMODULATE',[status(thm)],[16,1346,theory(equality)]) ).
cnf(1817,plain,
multiply(inverse(multiply(inverse(X),inverse(Y))),inverse(inverse(inverse(X)))) = Y,
inference('REWRITE',[status(thm)],[978,1815,theory(equality)]) ).
cnf(1841,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,U)),inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U)))),W) = multiply(X1,multiply(inverse(X1),inverse(inverse(W)))),
inference('PARAMODULATE',[status(thm)],[1346,257,theory(equality)]) ).
cnf(1854,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(X,multiply(U,inverse(multiply(V,inverse(V))))),multiply(W,multiply(inverse(W),inverse(inverse(multiply(Y,Z))))))))))) = U,
inference('PARAMODULATE',[status(thm)],[18,1346,theory(equality)]) ).
cnf(1892,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(Y),inverse(Z)))) = multiply(Z,inverse(inverse(Y))),
inference('PARAMODULATE',[status(thm)],[1354,1817,theory(equality)]) ).
cnf(1895,plain,
multiply(inverse(X),inverse(inverse(inverse(Y)))) = multiply(multiply(Z,inverse(multiply(U,multiply(Y,multiply(X,Z))))),U),
inference('PARAMODULATE',[status(thm)],[1817,201,theory(equality)]) ).
cnf(1897,plain,
inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U))),multiply(U,multiply(Y,inverse(V))))) = inverse(multiply(inverse(Z),inverse(inverse(inverse(V))))),
inference('REWRITE',[status(thm)],[510,1895,theory(equality)]) ).
cnf(1898,plain,
multiply(X,Y) = multiply(Z,multiply(inverse(Z),inverse(multiply(inverse(Y),inverse(inverse(inverse(X))))))),
inference('REWRITE',[status(thm)],[643,1897,theory(equality)]) ).
cnf(1901,plain,
inverse(multiply(X,multiply(Y,inverse(multiply(multiply(Z,multiply(U,inverse(V))),multiply(V,multiply(X,Y))))))) = inverse(multiply(inverse(U),inverse(inverse(inverse(Z))))),
inference('REWRITE',[status(thm)],[501,1895,theory(equality)]) ).
cnf(1924,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(Y),inverse(inverse(inverse(Z))))),multiply(U,multiply(multiply(inverse(U),inverse(Y)),X))))) = inverse(Z),
inference('REWRITE',[status(thm)],[146,1901,theory(equality)]) ).
cnf(1928,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),inverse(U)))),inverse(Y))) = inverse(multiply(inverse(Z),inverse(inverse(inverse(U))))),
inference('REWRITE',[status(thm)],[143,1901,theory(equality)]) ).
cnf(1933,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),inverse(inverse(inverse(X)))))) = Y,
inference('REWRITE',[status(thm)],[18,1901,theory(equality)]) ).
cnf(1934,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),inverse(U))))) = inverse(multiply(inverse(Z),inverse(inverse(inverse(U))))),
inference('REWRITE',[status(thm)],[497,1895,theory(equality)]) ).
cnf(1935,plain,
multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(Y))))),inverse(multiply(multiply(Z,U),multiply(Y,X)))) = multiply(V,multiply(multiply(inverse(V),inverse(U)),inverse(Z))),
inference('REWRITE',[status(thm)],[557,1934,theory(equality)]) ).
cnf(1944,plain,
multiply(inverse(X),inverse(inverse(inverse(Y)))) = multiply(Z,multiply(U,multiply(multiply(inverse(U),inverse(multiply(X,Z))),inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[1817,single_axiom,theory(equality)]) ).
cnf(1947,plain,
multiply(multiply(inverse(X),inverse(Y)),multiply(Y,inverse(Z))) = multiply(U,multiply(multiply(inverse(U),inverse(inverse(inverse(X)))),inverse(Z))),
inference('PARAMODULATE',[status(thm)],[66,1817,theory(equality)]) ).
cnf(1970,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(inverse(multiply(inverse(Z),inverse(U))),inverse(V))),multiply(V,multiply(inverse(inverse(inverse(Z))),X))))) = multiply(W,multiply(multiply(inverse(W),inverse(U)),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[6,1817,theory(equality)]) ).
cnf(1975,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(Y)))) = inverse(X),
inference('PARAMODULATE',[status(thm)],[1933,621,theory(equality)]) ).
cnf(1979,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(multiply(Y,multiply(Z,inverse(U))),multiply(U,multiply(inverse(Z),X)))),
inference('REWRITE',[status(thm)],[679,1975,theory(equality)]) ).
cnf(1983,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(Y))) = inverse(Z),
inference('REWRITE',[status(thm)],[676,1975,theory(equality)]) ).
cnf(1985,plain,
inverse(X) = multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),Z)),
inference('REWRITE',[status(thm)],[813,1983,theory(equality)]) ).
cnf(1988,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))))) = inverse(X),
inference('REWRITE',[status(thm)],[823,1985,theory(equality)]) ).
cnf(2001,plain,
inverse(multiply(multiply(inverse(X),inverse(multiply(Y,inverse(Z)))),Y)) = inverse(multiply(inverse(X),Z)),
inference('REWRITE',[status(thm)],[1271,1988,theory(equality)]) ).
cnf(2012,plain,
inverse(multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),Z))),multiply(U,inverse(U)))) = inverse(multiply(inverse(X),Y)),
inference('REWRITE',[status(thm)],[960,2001,theory(equality)]) ).
cnf(2015,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(U)) = inverse(multiply(multiply(U,inverse(Y)),multiply(multiply(V,inverse(V)),multiply(Z,X)))),
inference('REWRITE',[status(thm)],[843,1985,theory(equality)]) ).
cnf(2023,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(inverse(Z),U))),inverse(V))),multiply(V,inverse(Z))))) = U,
inference('REWRITE',[status(thm)],[846,1985,theory(equality)]) ).
cnf(2028,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(inverse(Y),inverse(Z))),multiply(Z,multiply(U,X))))) = inverse(U),
inference('REWRITE',[status(thm)],[816,1985,theory(equality)]) ).
cnf(2032,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(Y)),inverse(Z)))) = multiply(Z,Y),
inference('REWRITE',[status(thm)],[545,2028,theory(equality)]) ).
cnf(2049,plain,
multiply(X,inverse(multiply(Y,multiply(Z,inverse(multiply(U,inverse(U))))))) = inverse(multiply(multiply(Y,multiply(Z,inverse(V))),multiply(V,inverse(X)))),
inference('REWRITE',[status(thm)],[1135,2032,theory(equality)]) ).
cnf(2096,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(inverse(Y),multiply(U,X))))) = inverse(U),
inference('REWRITE',[status(thm)],[718,1983,theory(equality)]) ).
cnf(2104,plain,
multiply(X,inverse(multiply(inverse(inverse(inverse(Y))),multiply(Y,multiply(Z,X))))) = inverse(Z),
inference('PARAMODULATE',[status(thm)],[single_axiom,1933,theory(equality)]) ).
cnf(2105,plain,
multiply(X,multiply(inverse(X),inverse(Y))) = inverse(inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,1933,theory(equality)]),1975,theory(equality)]) ).
cnf(2106,plain,
multiply(X,Y) = inverse(inverse(inverse(multiply(inverse(Y),inverse(inverse(inverse(X))))))),
inference('REWRITE',[status(thm)],[1898,2105,theory(equality)]) ).
cnf(2126,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(X,multiply(U,inverse(multiply(V,inverse(V))))),inverse(inverse(inverse(inverse(multiply(Y,Z))))))))))) = U,
inference('REWRITE',[status(thm)],[1854,2105,theory(equality)]) ).
cnf(2131,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,U)),inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U)))),W) = inverse(inverse(inverse(inverse(W)))),
inference('REWRITE',[status(thm)],[1841,2105,theory(equality)]) ).
cnf(2132,plain,
inverse(inverse(inverse(inverse(X)))) = multiply(multiply(Y,inverse(Y)),X),
inference('REWRITE',[status(thm)],[1550,2131,theory(equality)]) ).
cnf(2137,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),Z))),inverse(U)) = inverse(multiply(multiply(U,inverse(Y)),inverse(inverse(inverse(inverse(multiply(Z,X))))))),
inference('REWRITE',[status(thm)],[2015,2132,theory(equality)]) ).
cnf(2138,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,Y)))))))))) = inverse(multiply(multiply(Z,multiply(U,inverse(U))),multiply(inverse(Z),multiply(X,Y)))),
inference('REWRITE',[status(thm)],[703,2132,2137,theory(equality)]) ).
cnf(2139,plain,
multiply(X,inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(Y,X))))))))))) = inverse(Y),
inference('REWRITE',[status(thm)],[2096,2138,theory(equality)]) ).
cnf(2140,plain,
inverse(inverse(inverse(inverse(inverse(multiply(inverse(X),inverse(Y))))))) = multiply(Y,inverse(inverse(X))),
inference('REWRITE',[status(thm)],[1892,2132,theory(equality)]) ).
cnf(2145,plain,
inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,Y))))))))),inverse(Y))))))) = inverse(X),
inference('REWRITE',[status(thm)],[2139,2140,theory(equality)]) ).
cnf(2151,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,multiply(U,V))),multiply(multiply(inverse(V),inverse(multiply(Y,U))),inverse(X))),W) = inverse(inverse(inverse(inverse(W)))),
inference('REWRITE',[status(thm)],[1551,2132,theory(equality)]) ).
cnf(2152,plain,
multiply(X,multiply(Y,inverse(Y))) = inverse(inverse(inverse(inverse(X)))),
inference('REWRITE',[status(thm)],[1498,2151,theory(equality)]) ).
cnf(2153,plain,
inverse(inverse(inverse(inverse(inverse(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),Z)))))))) = inverse(multiply(inverse(X),Y)),
inference('REWRITE',[status(thm)],[2012,2152,theory(equality)]) ).
cnf(2160,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(multiply(Y,inverse(multiply(Z,inverse(inverse(inverse(inverse(multiply(U,Y)))))))),Z))) = U,
inference('REWRITE',[status(thm)],[1443,2152,theory(equality)]) ).
cnf(2166,plain,
multiply(X,inverse(inverse(inverse(inverse(inverse(Y)))))) = multiply(Z,multiply(multiply(inverse(Z),inverse(inverse(X))),inverse(Y))),
inference('REWRITE',[status(thm)],[1405,2152,theory(equality)]) ).
cnf(2180,plain,
multiply(multiply(inverse(X),inverse(Y)),multiply(Y,inverse(Z))) = multiply(inverse(X),inverse(inverse(inverse(inverse(inverse(Z)))))),
inference('REWRITE',[status(thm)],[1947,2166,theory(equality)]) ).
cnf(2186,plain,
multiply(X,multiply(multiply(inverse(Y),inverse(Z)),Z)) = multiply(X,inverse(inverse(inverse(inverse(inverse(Y)))))),
inference('REWRITE',[status(thm)],[1560,2166,theory(equality)]) ).
cnf(2197,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(multiply(inverse(Z),inverse(U))))),inverse(inverse(inverse(inverse(inverse(Z))))))) = inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U))),
inference('REWRITE',[status(thm)],[1584,2186,theory(equality)]) ).
cnf(2203,plain,
multiply(X,inverse(multiply(Y,multiply(Z,inverse(inverse(inverse(inverse(inverse(U))))))))) = multiply(V,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(U),inverse(X)),V))))),
inference('REWRITE',[status(thm)],[1579,2186,theory(equality)]) ).
cnf(2239,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(Y))))),inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(Z)))),inverse(Z)))))))))) = inverse(Y),
inference('REWRITE',[status(thm)],[1924,2140,2203,theory(equality)]) ).
cnf(2273,plain,
inverse(inverse(inverse(inverse(inverse(inverse(X)))))) = inverse(multiply(multiply(inverse(X),inverse(Y)),Y)),
inference('REWRITE',[status(thm)],[1390,2152,theory(equality)]) ).
cnf(2296,plain,
multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(inverse(inverse(inverse(inverse(inverse(Z))))))),multiply(inverse(Z),inverse(U))))) = multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(V,U))),V))),
inference('REWRITE',[status(thm)],[914,2273,theory(equality)]) ).
cnf(2311,plain,
inverse(inverse(multiply(inverse(inverse(inverse(X))),Y))) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[2153,2106,2273,theory(equality)]) ).
cnf(2327,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(Y))))),inverse(inverse(inverse(inverse(multiply(inverse(inverse(Z)),inverse(Z))))))))) = inverse(Y),
inference('REWRITE',[status(thm)],[2239,2311,theory(equality)]) ).
cnf(2353,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(multiply(X,Y),inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(Y))))))))))))))))))))))))))))))))))))) = inverse(X),
inference('REWRITE',[status(thm)],[2145,2140,2311,theory(equality)]) ).
cnf(2367,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = multiply(multiply(inverse(X),inverse(Y)),Y),
inference('REWRITE',[status(thm)],[1555,2152,theory(equality)]) ).
cnf(2368,plain,
multiply(X,multiply(Y,multiply(Z,U))) = inverse(inverse(inverse(inverse(inverse(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(U,V))),multiply(inverse(Z),inverse(multiply(X,Y))))))))))),
inference('REWRITE',[status(thm)],[1601,2367,theory(equality)]) ).
cnf(2464,plain,
inverse(inverse(inverse(inverse(inverse(multiply(multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(U))),multiply(U,inverse(inverse(inverse(inverse(Y))))))))))) = Z,
inference('REWRITE',[status(thm)],[1492,2152,theory(equality)]) ).
cnf(2498,plain,
inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(Y,inverse(Z)))))))) = inverse(multiply(multiply(X,multiply(Y,inverse(U))),multiply(U,inverse(Z)))),
inference('REWRITE',[status(thm)],[675,2152,theory(equality)]) ).
cnf(2501,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(X))),multiply(X,Y)))))))))) = Y,
inference('REWRITE',[status(thm)],[2464,2032,2498,theory(equality)]) ).
cnf(2502,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[2023,1268,2353,2311,2140,2132,2137,2498,theory(equality)]) ).
cnf(2516,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(Y))))),multiply(inverse(inverse(Z)),inverse(Z))))) = inverse(Y),
inference('REWRITE',[status(thm)],[2327,2502,theory(equality)]) ).
cnf(2535,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(U,Y)))),Z))) = U,
inference('REWRITE',[status(thm)],[2160,2502,theory(equality)]) ).
cnf(2539,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(X,multiply(U,inverse(multiply(V,inverse(V))))),multiply(Y,Z))))))) = U,
inference('REWRITE',[status(thm)],[2126,2502,theory(equality)]) ).
cnf(2543,plain,
multiply(X,multiply(Y,multiply(Z,U))) = inverse(multiply(V,multiply(W,multiply(multiply(inverse(W),inverse(multiply(U,V))),multiply(inverse(Z),inverse(multiply(X,Y))))))),
inference('REWRITE',[status(thm)],[2368,2502,theory(equality)]) ).
cnf(2561,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference('REWRITE',[status(thm)],[827,1985,2543,theory(equality)]) ).
cnf(2587,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,multiply(Z,multiply(U,V))),multiply(inverse(multiply(Z,multiply(U,V))),inverse(multiply(multiply(X,multiply(W,inverse(X1))),multiply(X1,Y))))))) = W,
inference('REWRITE',[status(thm)],[328,2543,theory(equality)]) ).
cnf(2590,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[314,16,2543,theory(equality)]) ).
cnf(2594,plain,
inverse(multiply(X,multiply(Y,inverse(Z)))) = inverse(multiply(multiply(X,multiply(Y,inverse(U))),multiply(U,inverse(Z)))),
inference('REWRITE',[status(thm)],[2498,2502,theory(equality)]) ).
cnf(2600,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,inverse(inverse(X))),
inference('REWRITE',[status(thm)],[2140,2502,theory(equality)]) ).
cnf(2609,plain,
multiply(inverse(inverse(inverse(X))),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[2501,2502,theory(equality)]) ).
cnf(2610,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference('REWRITE',[status(thm)],[2104,2609,theory(equality)]) ).
cnf(2613,plain,
multiply(multiply(inverse(X),inverse(Y)),multiply(Y,inverse(Z))) = multiply(inverse(X),inverse(Z)),
inference('REWRITE',[status(thm)],[2180,2502,theory(equality)]) ).
cnf(2615,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(multiply(inverse(Z),inverse(U))))),inverse(Z))) = inverse(multiply(multiply(X,multiply(Y,inverse(V))),multiply(V,U))),
inference('REWRITE',[status(thm)],[2197,2502,theory(equality)]) ).
cnf(2622,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),inverse(Z)))) = multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(U,Z))),U))),
inference('REWRITE',[status(thm)],[2296,2613,2502,theory(equality)]) ).
cnf(2633,plain,
multiply(inverse(X),multiply(inverse(inverse(Y)),inverse(Y))) = inverse(X),
inference('REWRITE',[status(thm)],[541,2610,2622,theory(equality)]) ).
cnf(2645,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference('REWRITE',[status(thm)],[2516,2105,2502,2311,2600,2633,theory(equality)]) ).
cnf(2660,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),inverse(U)))),inverse(Y))) = inverse(multiply(inverse(Z),inverse(U))),
inference('REWRITE',[status(thm)],[1928,2645,theory(equality)]) ).
cnf(2664,plain,
multiply(inverse(X),inverse(Y)) = multiply(multiply(Z,inverse(multiply(U,multiply(Y,multiply(X,Z))))),U),
inference('REWRITE',[status(thm)],[1895,2645,theory(equality)]) ).
cnf(2672,plain,
multiply(inverse(multiply(inverse(X),inverse(Y))),inverse(multiply(multiply(Z,U),multiply(Y,X)))) = multiply(V,multiply(multiply(inverse(V),inverse(U)),inverse(Z))),
inference('REWRITE',[status(thm)],[1935,2645,theory(equality)]) ).
cnf(2674,plain,
multiply(inverse(X),inverse(Y)) = multiply(Z,multiply(U,multiply(multiply(inverse(U),inverse(multiply(X,Z))),inverse(Y)))),
inference('REWRITE',[status(thm)],[1944,2645,theory(equality)]) ).
cnf(2686,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(inverse(multiply(inverse(Z),inverse(U))),inverse(V))),multiply(V,multiply(inverse(Z),X))))) = multiply(W,multiply(multiply(inverse(W),inverse(U)),inverse(Y))),
inference('REWRITE',[status(thm)],[1970,2645,theory(equality)]) ).
cnf(2690,plain,
multiply(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(Z,inverse(Z)))))),inverse(U)) = inverse(multiply(multiply(U,multiply(Y,inverse(V))),multiply(V,X))),
inference('REWRITE',[status(thm)],[1370,2645,theory(equality)]) ).
cnf(2692,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[1933,2610,2645,theory(equality)]) ).
cnf(2707,plain,
inverse(multiply(multiply(X,Y),Z)) = inverse(multiply(multiply(X,multiply(Y,inverse(U))),multiply(U,Z))),
inference('REWRITE',[status(thm)],[1368,2561,2692,theory(equality)]) ).
cnf(2716,plain,
multiply(multiply(inverse(X),inverse(multiply(Y,inverse(multiply(Z,inverse(Z)))))),inverse(U)) = inverse(multiply(multiply(U,Y),X)),
inference('REWRITE',[status(thm)],[2690,2707,theory(equality)]) ).
cnf(2717,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(multiply(inverse(Z),inverse(U)))),multiply(inverse(Z),X)))) = multiply(V,multiply(multiply(inverse(V),inverse(U)),inverse(Y))),
inference('REWRITE',[status(thm)],[2686,2707,theory(equality)]) ).
cnf(2729,plain,
inverse(multiply(X,multiply(Y,inverse(Z)))) = inverse(multiply(multiply(X,Y),inverse(Z))),
inference('REWRITE',[status(thm)],[2594,2707,theory(equality)]) ).
cnf(2731,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z)))))) = Y,
inference('REWRITE',[status(thm)],[2539,2692,2610,2729,theory(equality)]) ).
cnf(2732,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,multiply(Z,multiply(U,V))),multiply(inverse(multiply(Z,multiply(U,V))),inverse(multiply(multiply(X,W),Y)))))) = W,
inference('REWRITE',[status(thm)],[2587,2707,theory(equality)]) ).
cnf(2745,plain,
multiply(X,inverse(multiply(Y,multiply(Z,inverse(multiply(U,inverse(U))))))) = inverse(multiply(multiply(Y,Z),inverse(X))),
inference('REWRITE',[status(thm)],[2049,2707,theory(equality)]) ).
cnf(2752,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(multiply(Y,Z),multiply(inverse(Z),X))),
inference('REWRITE',[status(thm)],[1979,2707,theory(equality)]) ).
cnf(2753,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[2732,2590,2692,2752,theory(equality)]) ).
cnf(2754,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference('REWRITE',[status(thm)],[2731,2753,theory(equality)]) ).
cnf(2755,plain,
multiply(multiply(inverse(X),inverse(Y)),inverse(Z)) = inverse(multiply(multiply(Z,Y),X)),
inference('REWRITE',[status(thm)],[2716,2754,theory(equality)]) ).
cnf(2756,plain,
multiply(X,Y) = inverse(multiply(inverse(Y),inverse(X))),
inference('REWRITE',[status(thm)],[2660,2032,2610,2755,theory(equality)]) ).
cnf(2770,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,U)),multiply(inverse(U),X)))) = multiply(V,multiply(multiply(inverse(V),inverse(Z)),inverse(Y))),
inference('REWRITE',[status(thm)],[2717,2756,theory(equality)]) ).
cnf(2773,plain,
inverse(multiply(X,Y)) = multiply(Z,multiply(multiply(inverse(Z),inverse(Y)),inverse(X))),
inference('REWRITE',[status(thm)],[2672,2610,2756,theory(equality)]) ).
cnf(2778,plain,
multiply(inverse(X),inverse(Y)) = multiply(Z,inverse(multiply(Y,multiply(X,Z)))),
inference('REWRITE',[status(thm)],[2674,2773,theory(equality)]) ).
cnf(2785,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(multiply(inverse(Y),inverse(Z)),Z))) = Y,
inference('REWRITE',[status(thm)],[2535,2778,theory(equality)]) ).
cnf(2793,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('REWRITE',[status(thm)],[2770,2692,2778,2773,theory(equality)]) ).
cnf(2818,plain,
inverse(multiply(inverse(multiply(multiply(X,inverse(Y)),Z)),X)) = inverse(multiply(inverse(Z),Y)),
inference('REWRITE',[status(thm)],[2001,2793,theory(equality)]) ).
cnf(2821,plain,
inverse(multiply(X,Y)) = multiply(Z,inverse(multiply(X,multiply(Y,Z)))),
inference('REWRITE',[status(thm)],[2773,2793,theory(equality)]) ).
cnf(2850,plain,
inverse(multiply(X,Y)) = multiply(multiply(Z,inverse(multiply(U,multiply(X,multiply(Y,Z))))),U),
inference('REWRITE',[status(thm)],[2664,2793,theory(equality)]) ).
cnf(2889,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference('REWRITE',[status(thm)],[2785,2561,2793,theory(equality)]) ).
cnf(2968,plain,
multiply(X,inverse(multiply(Y,Z))) = inverse(multiply(multiply(Y,Z),inverse(X))),
inference('REWRITE',[status(thm)],[2745,2754,theory(equality)]) ).
cnf(2983,plain,
inverse(multiply(X,Y)) = multiply(inverse(multiply(multiply(Z,multiply(X,multiply(Y,U))),inverse(U))),Z),
inference('REWRITE',[status(thm)],[2850,2968,theory(equality)]) ).
cnf(2999,plain,
inverse(multiply(X,Y)) = inverse(multiply(multiply(X,multiply(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[2821,2968,theory(equality)]) ).
cnf(3019,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y))),Z) = Z,
inference('REWRITE',[status(thm)],[585,2889,2999,2968,2793,2707,theory(equality)]) ).
cnf(3065,plain,
inverse(multiply(inverse(X),Y)) = inverse(multiply(inverse(multiply(Z,X)),multiply(Z,Y))),
inference('REWRITE',[status(thm)],[258,2999,2590,2968,2793,2707,theory(equality)]) ).
cnf(3066,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[3019,3065,theory(equality)]) ).
cnf(3069,plain,
inverse(multiply(multiply(X,multiply(Y,multiply(Z,U))),inverse(U))) = inverse(multiply(multiply(X,Y),Z)),
inference('REWRITE',[status(thm)],[2615,2692,2793,2707,theory(equality)]) ).
cnf(3088,plain,
inverse(multiply(X,Y)) = multiply(inverse(multiply(multiply(Z,X),Y)),Z),
inference('REWRITE',[status(thm)],[2983,3069,theory(equality)]) ).
cnf(3089,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[2818,2692,3088,theory(equality)]) ).
cnf(3091,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[3066,3089,theory(equality)]) ).
cnf(3092,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_2,3091,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n018.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 : Mon Jun 13 21:00:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T21:00:43
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-13T21:00:43
% 2.65/2.85
% 2.65/2.85
% 2.65/2.85 #||
% 2.65/2.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.65/2.85 % SZS output start Refutation
% See solution above
% 2.65/2.91 ||#
% 2.65/2.91
% 2.65/2.91 ; Summary of computation:
% 2.65/2.91 ; 8359 formulas have been input or derived (from 45 formulas).
% 2.65/2.91 ; 3092 (37%) were retained. Of these,
% 2.65/2.91 ; 2924 (95%) were simplified or subsumed later,
% 2.65/2.91 ; 168 ( 5%) are still being kept.
% 2.65/2.91 ;
% 2.65/2.91 ; Run time in seconds excluding printing time:
% 2.65/2.91 ; 0.001 0% Read assertion file (1 call)
% 2.65/2.91 ; 0.000 0% Assert (2 calls)
% 2.65/2.91 ; 0.699 29% Process new row (7,006 calls)
% 2.65/2.91 ; 0.007 0% Resolution (88 calls)
% 2.65/2.91 ; 0.185 8% Paramodulation (44 calls)
% 2.65/2.91 ; 0.703 30% Forward simplification (6,291 calls)
% 2.65/2.91 ; 0.579 24% Backward simplification (3,092 calls)
% 2.65/2.91 ; 0.165 7% Ordering (20,172 calls)
% 2.65/2.91 ; 0.000 0% Sortal reasoning (32 calls)
% 2.65/2.91 ; 0.000 0% Purity testing (1 call)
% 2.65/2.91 ; 0.042 2% Other
% 2.65/2.91 ; 2.381 Total
% 2.65/2.91 ; 2.442 Real time
% 2.65/2.91 ;
% 2.65/2.91 ; Term-hash-array has 19,509 terms in all.
% 2.65/2.91 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.65/2.91 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.65/2.91 ; Path-index has 1,042 entries (11,870 at peak, 20,811 added, 19,769 deleted).
% 2.65/2.91 ; Path-index has 34,064 nodes (39,658 at peak, 48,641 added, 14,577 deleted).
% 2.65/2.91 ; Trie-index has 1,042 entries (11,870 at peak, 20,811 added, 19,769 deleted).
% 2.65/2.91 ; Trie-index has 5,775 nodes (69,675 at peak, 145,632 added, 139,857 deleted).
% 2.65/2.91 ; Retrieved 19,968 generalization terms in 87,672 calls.
% 2.65/2.91 ; Retrieved 19,875 instance terms in 3,358 calls.
% 2.65/2.91 ; Retrieved 85,505 unifiable terms in 547 calls.
% 2.65/2.91 ;
% 2.65/2.91 ; The agenda of backward simplifiable rows to process has 1237 entries:
% 2.65/2.91 ; 1237 with value 0
% 2.65/2.91 ; The agenda of rows to process has 77 entries:
% 2.65/2.91 ; 4 with value 31 4 with value 40 5 with value 46
% 2.65/2.91 ; 1 with value 32 7 with value 41 4 with value 47
% 2.65/2.91 ; 6 with value 35 4 with value 42 2 with value 48
% 2.65/2.91 ; 4 with value 36 3 with value 43 3 with value 49
% 2.65/2.91 ; 4 with value 37 6 with value 44 2 with value 51
% 2.65/2.91 ; 3 with value 38 13 with value 45 1 with value 53
% 2.65/2.91 ; 1 with value 39
% 2.65/2.91 ; The agenda of rows to give has 165 entries:
% 2.65/2.91 ; 1 with value (4 11) 8 with value (4 29) 10 with value (4 41)
% 2.65/2.91 ; 1 with value (4 13) 2 with value (4 30) 6 with value (4 42)
% 2.65/2.91 ; 2 with value (4 15) 4 with value (4 31) 11 with value (4 43)
% 2.65/2.91 ; 1 with value (4 17) 5 with value (4 32) 3 with value (4 44)
% 2.65/2.91 ; 1 with value (4 18) 7 with value (4 33) 5 with value (4 45)
% 2.65/2.91 ; 1 with value (4 20) 10 with value (4 34) 5 with value (4 46)
% 2.65/2.91 ; 2 with value (4 22) 8 with value (4 35) 5 with value (4 47)
% 2.65/2.91 ; 1 with value (4 23) 8 with value (4 36) 3 with value (4 48)
% 2.65/2.91 ; 3 with value (4 24) 5 with value (4 37) 2 with value (4 50)
% 2.65/2.91 ; 4 with value (4 25) 11 with value (4 38) 1 with value (4 51)
% 2.65/2.91 ; 5 with value (4 26) 8 with value (4 39) 1 with value (4 55)
% 2.65/2.91 ; 5 with value (4 27) 4 with value (4 40) 1 with value (4 57)
% 2.65/2.91 ; 5 with value (4 28)
% 2.65/2.91 Evaluation took:
% 2.65/2.91 2.443 seconds of real time
% 2.65/2.91 2.290394 seconds of user run time
% 2.65/2.91 0.152181 seconds of system run time
% 2.65/2.91 [Run times include 0.471 seconds GC run time.]
% 2.65/2.91 0 calls to %EVAL
% 2.65/2.91 0 page faults and
% 2.65/2.91 203,728,840 bytes consed.
% 2.65/2.91 :PROOF-FOUND
% 2.65/2.91 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T21:00:45
% 2.65/2.91 :PROOF-FOUND
% 2.65/2.91 *
%------------------------------------------------------------------------------