TSTP Solution File: GRP058-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP058-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n019.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 11:35:46 EDT 2022
% Result : Unsatisfiable 1.65s 1.81s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 2
% Syntax : Number of clauses : 185 ( 183 unt; 0 nHn; 4 RR)
% Number of literals : 188 ( 187 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 652 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,inverse(multiply(Y,multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(U,Y))),X)))) = U,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(3,plain,
multiply(X,inverse(multiply(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,U))),multiply(V,inverse(V))),multiply(Z,X)))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(6,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(U,X)))) = multiply(multiply(multiply(V,inverse(V)),inverse(multiply(Y,U))),multiply(W,inverse(W))),
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(14,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,U))),Z))),multiply(V,inverse(V))) = U,
inference('PARAMODULATE',[status(thm)],[3,6,theory(equality)]) ).
cnf(15,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(multiply(multiply(Z,multiply(U,inverse(U))),multiply(V,Y)))),multiply(Z,X)))) = V,
inference('PARAMODULATE',[status(thm)],[3,6,theory(equality)]) ).
cnf(20,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(U,V))))))),inverse(multiply(W,inverse(multiply(multiply(U,multiply(X1,inverse(X1))),multiply(V,W)))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,6,theory(equality)]) ).
cnf(39,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(inverse(Y))),multiply(Z,inverse(Z))) = Y,
inference('PARAMODULATE',[status(thm)],[14,14,theory(equality)]) ).
cnf(40,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,Z))) = multiply(multiply(U,inverse(U)),inverse(multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[single_axiom,14,theory(equality)]) ).
cnf(45,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(U,Y))),multiply(V,inverse(V)))))),multiply(W,inverse(W))) = multiply(U,multiply(X1,inverse(X1))),
inference('PARAMODULATE',[status(thm)],[14,3,theory(equality)]) ).
cnf(63,plain,
multiply(multiply(X,inverse(X)),inverse(Y)) = multiply(multiply(Z,inverse(Z)),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[40,single_axiom,theory(equality)]) ).
cnf(65,plain,
multiply(multiply(X,inverse(X)),inverse(Y)) = multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(U,inverse(U)))),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[63,63,theory(equality)]) ).
cnf(66,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(inverse(Y))),multiply(multiply(Z,inverse(Z)),inverse(multiply(U,inverse(U))))) = Y,
inference('PARAMODULATE',[status(thm)],[39,63,theory(equality)]) ).
cnf(67,plain,
multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))),inverse(inverse(Z))),multiply(U,inverse(U))) = Z,
inference('PARAMODULATE',[status(thm)],[39,63,theory(equality)]) ).
cnf(69,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(multiply(multiply(Z,inverse(Z)),inverse(multiply(U,Y))),multiply(V,inverse(V)))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,63,theory(equality)]) ).
cnf(70,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,multiply(Z,inverse(Z))),
inference('REWRITE',[status(thm)],[45,69,theory(equality)]) ).
cnf(72,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,63,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(87,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[63,72,theory(equality)]) ).
cnf(88,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(multiply(Z,inverse(Z)),X)))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,72,theory(equality)]) ).
cnf(89,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),multiply(U,X)))) = inverse(U),
inference('PARAMODULATE',[status(thm)],[3,72,theory(equality)]) ).
cnf(90,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,Z)))),inverse(multiply(Z,multiply(U,inverse(U))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,72,theory(equality)]) ).
cnf(91,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(multiply(Y,inverse(Y)),Z))),multiply(U,inverse(U))) = inverse(Z),
inference('PARAMODULATE',[status(thm)],[14,72,theory(equality)]) ).
cnf(95,plain,
multiply(X,inverse(multiply(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),multiply(U,inverse(U))),multiply(V,X)))) = inverse(V),
inference('PARAMODULATE',[status(thm)],[3,72,theory(equality)]) ).
cnf(99,plain,
multiply(X,multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z))))) = multiply(X,multiply(U,inverse(U))),
inference('PARAMODULATE',[status(thm)],[70,63,theory(equality)]) ).
cnf(102,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(inverse(Y),multiply(Z,inverse(Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,87,theory(equality)]) ).
cnf(110,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,87,theory(equality)]),95,theory(equality)]) ).
cnf(111,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(Z,X)))) = inverse(Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,87,theory(equality)]),91,theory(equality)]) ).
cnf(161,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))))),multiply(U,X)))) = inverse(U),
inference('PARAMODULATE',[status(thm)],[111,110,theory(equality)]) ).
cnf(263,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),U))) = inverse(multiply(multiply(V,inverse(V)),inverse(inverse(U)))),
inference('PARAMODULATE',[status(thm)],[89,39,theory(equality)]) ).
cnf(268,plain,
inverse(X) = multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),inverse(multiply(multiply(multiply(U,inverse(U)),multiply(V,inverse(V))),multiply(X,multiply(W,inverse(W)))))),
inference('PARAMODULATE',[status(thm)],[65,89,theory(equality)]) ).
cnf(274,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))),inverse(multiply(multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))),V))) = inverse(multiply(multiply(W,inverse(W)),inverse(inverse(V)))),
inference('PARAMODULATE',[status(thm)],[89,66,theory(equality)]) ).
cnf(294,plain,
multiply(inverse(multiply(X,multiply(Y,inverse(Y)))),inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),U))) = inverse(inverse(multiply(multiply(V,inverse(V)),inverse(multiply(U,X))))),
inference('PARAMODULATE',[status(thm)],[111,90,theory(equality)]) ).
cnf(300,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(Y))),inverse(multiply(inverse(multiply(Z,multiply(U,inverse(U)))),multiply(V,inverse(V))))) = inverse(multiply(multiply(W,inverse(W)),inverse(multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[90,90,theory(equality)]) ).
cnf(321,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = inverse(multiply(multiply(multiply(U,inverse(U)),inverse(multiply(V,inverse(V)))),inverse(inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[111,67,theory(equality)]) ).
cnf(323,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),U))) = inverse(multiply(multiply(multiply(V,inverse(V)),inverse(multiply(W,inverse(W)))),inverse(inverse(U)))),
inference('PARAMODULATE',[status(thm)],[89,67,theory(equality)]) ).
cnf(335,plain,
multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y))) = inverse(inverse(multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[91,87,theory(equality)]) ).
cnf(336,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(Y),inverse(inverse(multiply(Z,inverse(Z))))))) = Y,
inference('PARAMODULATE',[status(thm)],[88,91,theory(equality)]) ).
cnf(344,plain,
X = inverse(inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(X,multiply(Z,inverse(Z)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[91,111,theory(equality)]),39,theory(equality)]) ).
cnf(404,plain,
multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y))) = multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))),
inference('PARAMODULATE',[status(thm)],[335,335,theory(equality)]) ).
cnf(438,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U)))))),multiply(V,X)))) = inverse(V),
inference('PARAMODULATE',[status(thm)],[111,335,theory(equality)]) ).
cnf(535,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,multiply(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,multiply(V,inverse(V))))),U)),
inference('PARAMODULATE',[status(thm)],[70,344,theory(equality)]) ).
cnf(551,plain,
multiply(multiply(multiply(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,multiply(Z,inverse(Z))))),Y),inverse(inverse(U))),multiply(V,inverse(V))) = U,
inference('PARAMODULATE',[status(thm)],[39,344,theory(equality)]) ).
cnf(590,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,Z)))),inverse(multiply(Z,multiply(inverse(multiply(inverse(inverse(multiply(U,inverse(U)))),multiply(V,multiply(W,inverse(W))))),V)))) = Y,
inference('PARAMODULATE',[status(thm)],[90,344,theory(equality)]) ).
cnf(642,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = multiply(multiply(U,inverse(U)),inverse(multiply(Y,multiply(Z,multiply(V,inverse(V)))))),
inference('PARAMODULATE',[status(thm)],[15,single_axiom,theory(equality)]) ).
cnf(651,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(U,Y)))),Z))) = U,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,39,theory(equality)]),39,theory(equality)]) ).
cnf(689,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(multiply(U,multiply(V,inverse(V))),W))),multiply(U,X)))) = inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(W,Y)))),
inference('PARAMODULATE',[status(thm)],[15,90,theory(equality)]) ).
cnf(716,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = multiply(U,inverse(multiply(Y,multiply(Z,U)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,651,theory(equality)]) ).
cnf(717,plain,
multiply(multiply(X,inverse(X)),inverse(inverse(multiply(Y,multiply(Z,inverse(Z)))))) = Y,
inference('PARAMODULATE',[status(thm)],[651,14,theory(equality)]) ).
cnf(718,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(Z))))) = multiply(U,inverse(multiply(Y,multiply(X,U)))),
inference('PARAMODULATE',[status(thm)],[90,651,theory(equality)]) ).
cnf(719,plain,
multiply(inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,X)))),Y)),inverse(multiply(inverse(U),Z))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,651,theory(equality)]) ).
cnf(762,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(U,Y)))),Z)),inverse(multiply(multiply(V,multiply(W,inverse(W))),U))),multiply(V,X)))) = multiply(X1,inverse(X1)),
inference('PARAMODULATE',[status(thm)],[15,651,theory(equality)]) ).
cnf(772,plain,
multiply(inverse(X),inverse(Y)) = multiply(Z,inverse(multiply(multiply(multiply(U,inverse(U)),inverse(inverse(Y))),multiply(X,Z)))),
inference('PARAMODULATE',[status(thm)],[716,39,theory(equality)]) ).
cnf(783,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))))) = multiply(U,inverse(multiply(multiply(V,inverse(V)),multiply(X,U)))),
inference('PARAMODULATE',[status(thm)],[716,404,theory(equality)]) ).
cnf(784,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(Y)) = multiply(inverse(multiply(Z,inverse(Z))),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[716,66,theory(equality)]),772,theory(equality)]) ).
cnf(823,plain,
multiply(X,inverse(multiply(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(multiply(U,multiply(V,Z)))))),multiply(W,inverse(W))),multiply(X1,X)))) = inverse(multiply(U,multiply(V,X1))),
inference('PARAMODULATE',[status(thm)],[3,716,theory(equality)]) ).
cnf(831,plain,
multiply(inverse(inverse(multiply(X,multiply(Y,inverse(Y))))),inverse(multiply(inverse(Z),X))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,717,theory(equality)]) ).
cnf(857,plain,
multiply(inverse(multiply(X,inverse(X))),Y) = multiply(inverse(multiply(Z,inverse(Z))),Y),
inference('PARAMODULATE',[status(thm)],[784,344,theory(equality)]) ).
cnf(858,plain,
multiply(inverse(inverse(multiply(inverse(inverse(X)),multiply(Y,inverse(Y))))),inverse(multiply(Z,inverse(Z)))) = X,
inference('PARAMODULATE',[status(thm)],[831,72,theory(equality)]) ).
cnf(902,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y))))),Z) = multiply(inverse(multiply(U,inverse(U))),Z),
inference('PARAMODULATE',[status(thm)],[857,110,theory(equality)]) ).
cnf(903,plain,
multiply(inverse(multiply(X,inverse(X))),Y) = multiply(inverse(multiply(inverse(multiply(Z,inverse(Z))),inverse(inverse(multiply(U,inverse(U)))))),Y),
inference('PARAMODULATE',[status(thm)],[857,857,theory(equality)]) ).
cnf(906,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),multiply(Z,inverse(multiply(U,inverse(U))))))) = inverse(Z),
inference('PARAMODULATE',[status(thm)],[111,857,theory(equality)]) ).
cnf(922,plain,
multiply(X,inverse(multiply(multiply(Y,inverse(multiply(multiply(inverse(multiply(Z,inverse(Z))),multiply(U,inverse(U))),multiply(V,Y)))),multiply(inverse(multiply(W,inverse(W))),X)))) = V,
inference('PARAMODULATE',[status(thm)],[15,857,theory(equality)]) ).
cnf(936,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(inverse(Y)))),inverse(multiply(Z,multiply(U,inverse(U))))) = multiply(multiply(V,inverse(V)),inverse(multiply(Z,Y))),
inference('PARAMODULATE',[status(thm)],[718,39,theory(equality)]) ).
cnf(991,plain,
multiply(X,inverse(multiply(Y,multiply(Z,inverse(Z))))) = multiply(U,inverse(multiply(Y,multiply(inverse(multiply(inverse(inverse(multiply(V,inverse(V)))),multiply(X,multiply(W,inverse(W))))),U)))),
inference('PARAMODULATE',[status(thm)],[718,344,theory(equality)]) ).
cnf(992,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,multiply(V,inverse(V))))),U)))) = multiply(W,inverse(multiply(Y,multiply(X,W)))),
inference('PARAMODULATE',[status(thm)],[718,344,theory(equality)]) ).
cnf(999,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(multiply(U,multiply(V,inverse(V))),multiply(W,inverse(multiply(Y,multiply(X1,W))))))),multiply(U,X)))) = inverse(X1),
inference('PARAMODULATE',[status(thm)],[15,718,theory(equality)]) ).
cnf(1002,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(multiply(X,multiply(Z,inverse(Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,718,theory(equality)]),823,theory(equality)]) ).
cnf(1146,plain,
multiply(inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,X)))),Y)),inverse(multiply(U,Z))) = inverse(multiply(inverse(inverse(multiply(V,inverse(V)))),multiply(U,multiply(W,inverse(W))))),
inference('PARAMODULATE',[status(thm)],[719,344,theory(equality)]) ).
cnf(1181,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(X))),multiply(Y,inverse(Y))))),inverse(Z)) = inverse(multiply(inverse(inverse(Z)),multiply(U,inverse(U)))),
inference('PARAMODULATE',[status(thm)],[831,858,theory(equality)]) ).
cnf(1183,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = inverse(inverse(inverse(multiply(inverse(inverse(Z)),multiply(U,inverse(U)))))),
inference('PARAMODULATE',[status(thm)],[111,858,theory(equality)]) ).
cnf(1282,plain,
inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z))))) = inverse(multiply(X,multiply(Y,multiply(U,inverse(U))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,642,theory(equality)]),823,theory(equality)]) ).
cnf(1286,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(Y,multiply(Z,multiply(U,inverse(U)))))),multiply(V,X)))) = inverse(multiply(Y,multiply(Z,V))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,642,theory(equality)]),91,theory(equality)]) ).
cnf(1287,plain,
inverse(multiply(inverse(multiply(X,inverse(X))),multiply(multiply(Y,inverse(Y)),Z))) = inverse(Z),
inference('REWRITE',[status(thm)],[438,1286,theory(equality)]) ).
cnf(1307,plain,
multiply(multiply(multiply(multiply(X,multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(X,multiply(Y,multiply(U,inverse(U)))))),inverse(inverse(V))),multiply(W,inverse(W))) = V,
inference('PARAMODULATE',[status(thm)],[39,1282,theory(equality)]) ).
cnf(1326,plain,
multiply(multiply(multiply(X,multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(X,multiply(Y,multiply(U,inverse(U)))))),inverse(multiply(inverse(V),inverse(inverse(multiply(W,inverse(W))))))) = V,
inference('PARAMODULATE',[status(thm)],[336,1282,theory(equality)]) ).
cnf(1419,plain,
multiply(inverse(X),inverse(inverse(multiply(Y,inverse(Y))))) = multiply(Z,inverse(multiply(inverse(multiply(U,inverse(U))),multiply(X,Z)))),
inference('PARAMODULATE',[status(thm)],[718,1287,theory(equality)]) ).
cnf(1426,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,1287,theory(equality)]),39,theory(equality)]) ).
cnf(1428,plain,
inverse(inverse(multiply(X,multiply(Y,inverse(Y))))) = multiply(inverse(multiply(Z,inverse(Z))),X),
inference('PARAMODULATE',[status(thm)],[1426,717,theory(equality)]) ).
cnf(1431,plain,
inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,X)))),Y)) = multiply(inverse(multiply(U,inverse(U))),Z),
inference('PARAMODULATE',[status(thm)],[1426,651,theory(equality)]) ).
cnf(1436,plain,
inverse(multiply(X,inverse(multiply(Y,inverse(Y))))) = inverse(multiply(X,multiply(inverse(multiply(Z,inverse(Z))),multiply(U,inverse(U))))),
inference('PARAMODULATE',[status(thm)],[1282,1426,theory(equality)]) ).
cnf(1464,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,multiply(V,inverse(V))))),U),X)),
inference('PARAMODULATE',[status(thm)],[1426,344,theory(equality)]) ).
cnf(1607,plain,
multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(Y))),inverse(multiply(Z,inverse(Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[858,1428,theory(equality)]) ).
cnf(1621,plain,
inverse(inverse(inverse(X))) = inverse(multiply(multiply(Y,inverse(Y)),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1428,91,theory(equality)]),1426,theory(equality)]) ).
cnf(1644,plain,
multiply(inverse(X),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = multiply(Z,inverse(inverse(inverse(multiply(X,Z))))),
inference('REWRITE',[status(thm)],[783,1621,theory(equality)]) ).
cnf(1656,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(multiply(U,multiply(V,inverse(V))),W))),multiply(U,X)))) = inverse(inverse(inverse(inverse(multiply(W,Y))))),
inference('REWRITE',[status(thm)],[689,1621,theory(equality)]) ).
cnf(1657,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,X)))),Y))))) = inverse(Z),
inference('REWRITE',[status(thm)],[999,1656,theory(equality)]) ).
cnf(1678,plain,
multiply(inverse(inverse(inverse(inverse(inverse(X))))),inverse(multiply(Y,multiply(Z,inverse(Z))))) = multiply(multiply(U,inverse(U)),inverse(multiply(Y,X))),
inference('REWRITE',[status(thm)],[936,1621,theory(equality)]) ).
cnf(1684,plain,
multiply(inverse(multiply(X,multiply(Y,inverse(Y)))),inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),U))) = inverse(inverse(inverse(inverse(inverse(multiply(U,X)))))),
inference('REWRITE',[status(thm)],[294,1621,theory(equality)]) ).
cnf(1692,plain,
multiply(inverse(inverse(inverse(inverse(X)))),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(U,inverse(U))))) = inverse(inverse(inverse(inverse(multiply(X,Y))))),
inference('REWRITE',[status(thm)],[300,1621,theory(equality)]) ).
cnf(1710,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))),inverse(multiply(multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))),V))) = inverse(inverse(inverse(inverse(inverse(V))))),
inference('REWRITE',[status(thm)],[274,1621,theory(equality)]) ).
cnf(1711,plain,
inverse(X) = inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(Y,inverse(Y)))))))),
inference('REWRITE',[status(thm)],[268,1710,theory(equality)]) ).
cnf(1714,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),U))) = inverse(inverse(inverse(inverse(inverse(U))))),
inference('REWRITE',[status(thm)],[263,1621,theory(equality)]) ).
cnf(1717,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = inverse(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),inverse(inverse(X)))),
inference('REWRITE',[status(thm)],[323,1714,theory(equality)]) ).
cnf(1718,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = inverse(inverse(inverse(inverse(inverse(Z))))),
inference('REWRITE',[status(thm)],[321,1717,theory(equality)]) ).
cnf(1735,plain,
multiply(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))),Y) = multiply(inverse(multiply(Z,inverse(Z))),Y),
inference('REWRITE',[status(thm)],[902,1621,theory(equality)]) ).
cnf(1737,plain,
multiply(X,inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(Y,inverse(Y))))))),multiply(Z,X)))) = inverse(Z),
inference('REWRITE',[status(thm)],[161,1621,theory(equality)]) ).
cnf(1815,plain,
multiply(inverse(inverse(inverse(inverse(multiply(X,Y))))),inverse(multiply(Y,multiply(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,multiply(V,inverse(V))))),U)))) = X,
inference('REWRITE',[status(thm)],[590,1621,theory(equality)]) ).
cnf(1826,plain,
multiply(inverse(inverse(inverse(inverse(multiply(X,multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,U)))))))),inverse(multiply(V,inverse(multiply(multiply(Z,multiply(W,inverse(W))),multiply(U,V)))))) = X,
inference('REWRITE',[status(thm)],[20,1621,theory(equality)]) ).
cnf(1845,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),multiply(inverse(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,inverse(U))))),X)),
inference('PARAMODULATE',[status(thm)],[1426,1428,theory(equality)]) ).
cnf(1869,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(multiply(X,inverse(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,inverse(U))))))),
inference('PARAMODULATE',[status(thm)],[1002,1428,theory(equality)]) ).
cnf(1892,plain,
multiply(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y)))))),inverse(multiply(inverse(Z),multiply(U,inverse(U))))) = Z,
inference('PARAMODULATE',[status(thm)],[102,1428,theory(equality)]) ).
cnf(1894,plain,
inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(multiply(Z,inverse(Z)))))),multiply(U,inverse(U))))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[111,1428,theory(equality)]) ).
cnf(1910,plain,
inverse(multiply(X,inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))))) = inverse(multiply(X,multiply(inverse(multiply(Z,inverse(Z))),multiply(U,inverse(U))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1282,1428,theory(equality)]),1621,theory(equality)]) ).
cnf(1913,plain,
inverse(inverse(multiply(inverse(multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z)))))),multiply(U,inverse(U))))) = multiply(V,inverse(multiply(X,multiply(Y,V)))),
inference('PARAMODULATE',[status(thm)],[716,1428,theory(equality)]) ).
cnf(1955,plain,
multiply(X,multiply(multiply(Y,inverse(Y)),inverse(inverse(inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),multiply(U,inverse(U)))))))) = multiply(X,multiply(V,inverse(V))),
inference('PARAMODULATE',[status(thm)],[99,1428,theory(equality)]) ).
cnf(1973,plain,
multiply(X,inverse(inverse(inverse(multiply(multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(multiply(U,inverse(U)))))),X),multiply(V,inverse(V))))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,1428,theory(equality)]) ).
cnf(1981,plain,
inverse(inverse(multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(Z))),multiply(U,X)))))) = inverse(multiply(Y,U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1428,6,theory(equality)]),1426,theory(equality)]) ).
cnf(1990,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(multiply(Z,inverse(Z))),X)))) = multiply(multiply(U,inverse(U)),inverse(multiply(Y,inverse(inverse(inverse(inverse(multiply(V,inverse(V))))))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[642,1428,theory(equality)]),1621,theory(equality)]) ).
cnf(1992,plain,
multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(inverse(multiply(U,inverse(U))),Y)))),inverse(inverse(V))),multiply(W,inverse(W))) = V,
inference('PARAMODULATE',[status(thm)],[67,1428,theory(equality)]) ).
cnf(2032,plain,
inverse(inverse(X)) = multiply(multiply(Y,inverse(Y)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[88,1621,theory(equality)]),88,theory(equality)]) ).
cnf(2036,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(multiply(Z,inverse(Z))),X)))) = inverse(inverse(inverse(multiply(Y,inverse(inverse(inverse(inverse(multiply(U,inverse(U)))))))))),
inference('REWRITE',[status(thm)],[1990,2032,theory(equality)]) ).
cnf(2040,plain,
multiply(X,inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(multiply(Y,inverse(multiply(Z,inverse(Z))))))),X),multiply(U,inverse(U))))))) = Y,
inference('REWRITE',[status(thm)],[1973,2032,theory(equality)]) ).
cnf(2041,plain,
multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X,multiply(Y,inverse(Y)))),multiply(inverse(multiply(Z,inverse(Z))),X))))),inverse(inverse(U))),multiply(V,inverse(V))) = U,
inference('REWRITE',[status(thm)],[1992,2032,theory(equality)]) ).
cnf(2043,plain,
multiply(X,inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = multiply(X,multiply(Z,inverse(Z))),
inference('REWRITE',[status(thm)],[1955,1711,2032,theory(equality)]) ).
cnf(2087,plain,
inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),Y)))) = inverse(inverse(inverse(inverse(inverse(Y))))),
inference('REWRITE',[status(thm)],[1718,2032,theory(equality)]) ).
cnf(2089,plain,
multiply(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))),inverse(multiply(inverse(Y),multiply(Z,inverse(Z))))) = Y,
inference('REWRITE',[status(thm)],[1892,2087,theory(equality)]) ).
cnf(2105,plain,
multiply(inverse(inverse(inverse(inverse(inverse(X))))),inverse(multiply(Y,multiply(Z,inverse(Z))))) = inverse(inverse(inverse(multiply(Y,X)))),
inference('REWRITE',[status(thm)],[1678,2032,theory(equality)]) ).
cnf(2106,plain,
inverse(inverse(inverse(multiply(inverse(X),multiply(Y,inverse(Y)))))) = X,
inference('REWRITE',[status(thm)],[2089,2105,theory(equality)]) ).
cnf(2108,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = inverse(Z),
inference('REWRITE',[status(thm)],[1183,2106,theory(equality)]) ).
cnf(2109,plain,
inverse(multiply(X,inverse(multiply(Y,inverse(Y))))) = inverse(X),
inference('REWRITE',[status(thm)],[906,2108,theory(equality)]) ).
cnf(2110,plain,
multiply(X,inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(Y))),X),multiply(Z,inverse(Z))))))) = Y,
inference('REWRITE',[status(thm)],[2040,2109,theory(equality)]) ).
cnf(2113,plain,
inverse(X) = inverse(multiply(X,multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z))))),
inference('REWRITE',[status(thm)],[1436,2109,theory(equality)]) ).
cnf(2114,plain,
inverse(multiply(X,inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))))) = inverse(X),
inference('REWRITE',[status(thm)],[1910,2113,theory(equality)]) ).
cnf(2115,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(multiply(Z,inverse(Z))),X)))) = inverse(inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[2036,2114,theory(equality)]) ).
cnf(2118,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(X))),Y))) = Y,
inference('REWRITE',[status(thm)],[922,1981,2115,theory(equality)]) ).
cnf(2121,plain,
inverse(inverse(inverse(X))) = inverse(multiply(inverse(inverse(X)),multiply(Y,inverse(Y)))),
inference('REWRITE',[status(thm)],[1181,2032,2118,theory(equality)]) ).
cnf(2134,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),multiply(inverse(inverse(inverse(inverse(multiply(Z,inverse(Z)))))),X)),
inference('REWRITE',[status(thm)],[1845,2121,theory(equality)]) ).
cnf(2136,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(X),
inference('REWRITE',[status(thm)],[1869,2114,2121,theory(equality)]) ).
cnf(2137,plain,
multiply(X,inverse(inverse(inverse(multiply(inverse(inverse(inverse(Y))),X))))) = Y,
inference('REWRITE',[status(thm)],[2110,2136,theory(equality)]) ).
cnf(2141,plain,
inverse(inverse(inverse(multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z)))))))) = multiply(U,inverse(multiply(X,multiply(Y,U)))),
inference('REWRITE',[status(thm)],[1913,2136,theory(equality)]) ).
cnf(2145,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = inverse(X),
inference('REWRITE',[status(thm)],[1894,2109,2087,2136,theory(equality)]) ).
cnf(2147,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,X)))) = inverse(Z),
inference('REWRITE',[status(thm)],[1737,2145,theory(equality)]) ).
cnf(2148,plain,
multiply(inverse(X),inverse(inverse(multiply(Y,inverse(Y))))) = inverse(X),
inference('REWRITE',[status(thm)],[1419,2147,theory(equality)]) ).
cnf(2151,plain,
multiply(multiply(multiply(X,multiply(Y,multiply(Z,inverse(Z)))),inverse(multiply(X,multiply(Y,multiply(U,inverse(U)))))),inverse(inverse(V))) = V,
inference('REWRITE',[status(thm)],[1326,2148,theory(equality)]) ).
cnf(2152,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference('REWRITE',[status(thm)],[1307,2151,theory(equality)]) ).
cnf(2160,plain,
multiply(inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,X)))),Y)),inverse(multiply(U,Z))) = inverse(multiply(inverse(inverse(multiply(V,inverse(V)))),U)),
inference('REWRITE',[status(thm)],[1146,2152,theory(equality)]) ).
cnf(2167,plain,
multiply(X,inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = X,
inference('REWRITE',[status(thm)],[2043,2152,theory(equality)]) ).
cnf(2168,plain,
inverse(X) = multiply(Y,inverse(inverse(inverse(multiply(X,Y))))),
inference('REWRITE',[status(thm)],[1644,2167,theory(equality)]) ).
cnf(2169,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference('REWRITE',[status(thm)],[2137,2168,theory(equality)]) ).
cnf(2171,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),inverse(inverse(X))),
inference('REWRITE',[status(thm)],[2134,2032,2169,theory(equality)]) ).
cnf(2172,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference('REWRITE',[status(thm)],[1607,2171,theory(equality)]) ).
cnf(2173,plain,
inverse(inverse(inverse(multiply(X,Y)))) = multiply(Z,inverse(multiply(X,multiply(Y,Z)))),
inference('REWRITE',[status(thm)],[2141,2172,theory(equality)]) ).
cnf(2193,plain,
inverse(multiply(inverse(inverse(inverse(multiply(X,Y)))),X)) = multiply(inverse(multiply(Z,inverse(Z))),Y),
inference('REWRITE',[status(thm)],[1431,2173,theory(equality)]) ).
cnf(2194,plain,
multiply(inverse(multiply(inverse(inverse(inverse(multiply(X,Y)))),X)),inverse(multiply(Z,Y))) = inverse(multiply(inverse(inverse(multiply(U,inverse(U)))),Z)),
inference('REWRITE',[status(thm)],[2160,2173,theory(equality)]) ).
cnf(2199,plain,
inverse(inverse(X)) = multiply(inverse(multiply(Y,inverse(Y))),X),
inference('REWRITE',[status(thm)],[1735,2032,2169,theory(equality)]) ).
cnf(2200,plain,
inverse(multiply(inverse(inverse(inverse(multiply(X,Y)))),X)) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[2193,2199,theory(equality)]) ).
cnf(2205,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),Y)),
inference('REWRITE',[status(thm)],[2194,2200,theory(equality)]) ).
cnf(2208,plain,
multiply(inverse(inverse(inverse(multiply(X,Y)))),X) = inverse(Y),
inference('REWRITE',[status(thm)],[1657,2173,2169,theory(equality)]) ).
cnf(2212,plain,
inverse(inverse(inverse(multiply(multiply(inverse(inverse(X)),inverse(multiply(Y,X))),Y)))) = multiply(Z,inverse(Z)),
inference('REWRITE',[status(thm)],[762,2208,2173,2152,theory(equality)]) ).
cnf(2214,plain,
X = multiply(X,multiply(inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z)),Z)),
inference('REWRITE',[status(thm)],[535,2152,theory(equality)]) ).
cnf(2216,plain,
multiply(inverse(X),inverse(Y)) = inverse(inverse(inverse(multiply(Y,X)))),
inference('REWRITE',[status(thm)],[992,2173,2214,2152,theory(equality)]) ).
cnf(2219,plain,
inverse(inverse(inverse(multiply(multiply(X,Y),inverse(Y))))) = inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),X)),
inference('REWRITE',[status(thm)],[2205,2216,theory(equality)]) ).
cnf(2220,plain,
inverse(inverse(inverse(multiply(inverse(inverse(inverse(multiply(multiply(X,Y),inverse(Y))))),X)))) = multiply(Z,inverse(Z)),
inference('REWRITE',[status(thm)],[2212,2216,theory(equality)]) ).
cnf(2225,plain,
X = inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z)),Z),X))),
inference('REWRITE',[status(thm)],[1464,2199,2152,theory(equality)]) ).
cnf(2228,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[1815,2214,2169,2152,theory(equality)]) ).
cnf(2229,plain,
inverse(inverse(inverse(X))) = inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),X)),
inference('REWRITE',[status(thm)],[2219,2228,theory(equality)]) ).
cnf(2233,plain,
X = inverse(inverse(multiply(multiply(inverse(inverse(inverse(Y))),Y),X))),
inference('REWRITE',[status(thm)],[2225,2229,theory(equality)]) ).
cnf(2235,plain,
inverse(inverse(inverse(multiply(inverse(inverse(inverse(X))),X)))) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[2220,2228,theory(equality)]) ).
cnf(2241,plain,
inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,Y))),Z)))) = inverse(multiply(X,multiply(Y,Z))),
inference('REWRITE',[status(thm)],[1286,2173,2152,theory(equality)]) ).
cnf(2246,plain,
multiply(multiply(inverse(inverse(inverse(X))),X),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[551,2229,2152,theory(equality)]) ).
cnf(2253,plain,
inverse(inverse(X)) = multiply(inverse(inverse(multiply(Y,inverse(Y)))),X),
inference('REWRITE',[status(thm)],[903,2199,2148,theory(equality)]) ).
cnf(2267,plain,
inverse(inverse(inverse(multiply(inverse(inverse(X)),Y)))) = inverse(multiply(X,Y)),
inference('REWRITE',[status(thm)],[1684,2169,2216,2253,2136,theory(equality)]) ).
cnf(2268,plain,
inverse(multiply(multiply(X,Y),Z)) = inverse(multiply(X,multiply(Y,Z))),
inference('REWRITE',[status(thm)],[2241,2267,theory(equality)]) ).
cnf(2269,plain,
inverse(multiply(inverse(X),X)) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[2235,2267,theory(equality)]) ).
cnf(2275,plain,
inverse(inverse(multiply(multiply(inverse(X),X),Y))) = Y,
inference('REWRITE',[status(thm)],[2041,2152,2169,2216,2199,2136,theory(equality)]) ).
cnf(2277,plain,
multiply(X,inverse(Y)) = inverse(inverse(inverse(multiply(Y,inverse(inverse(inverse(X))))))),
inference('REWRITE',[status(thm)],[991,2173,2253,2152,2136,theory(equality)]) ).
cnf(2278,plain,
inverse(inverse(inverse(multiply(X,Y)))) = inverse(inverse(inverse(multiply(multiply(X,multiply(Y,Z)),inverse(inverse(inverse(Z))))))),
inference('REWRITE',[status(thm)],[2173,2277,theory(equality)]) ).
cnf(2283,plain,
multiply(X,inverse(inverse(Y))) = multiply(X,Y),
inference('REWRITE',[status(thm)],[1692,2152,2169,2136,theory(equality)]) ).
cnf(2288,plain,
inverse(inverse(inverse(multiply(X,Y)))) = inverse(inverse(inverse(multiply(multiply(X,multiply(Y,Z)),inverse(Z))))),
inference('REWRITE',[status(thm)],[2278,2283,theory(equality)]) ).
cnf(2289,plain,
multiply(X,inverse(Y)) = inverse(inverse(inverse(multiply(Y,inverse(X))))),
inference('REWRITE',[status(thm)],[2277,2283,theory(equality)]) ).
cnf(2290,plain,
multiply(multiply(inverse(inverse(inverse(X))),X),Y) = Y,
inference('REWRITE',[status(thm)],[2246,2283,theory(equality)]) ).
cnf(2291,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[2233,2290,theory(equality)]) ).
cnf(2294,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[2275,2291,theory(equality)]) ).
cnf(2295,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,2294,theory(equality)]) ).
cnf(2299,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference('REWRITE',[status(thm)],[2289,2291,theory(equality)]) ).
cnf(2306,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference('REWRITE',[status(thm)],[2208,2291,theory(equality)]) ).
cnf(2308,plain,
inverse(multiply(X,Y)) = inverse(multiply(multiply(X,multiply(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[2288,2291,theory(equality)]) ).
cnf(2324,plain,
multiply(multiply(X,inverse(multiply(Y,Z))),multiply(Y,Z)) = X,
inference('REWRITE',[status(thm)],[1826,2308,2299,2152,2291,2032,theory(equality)]) ).
cnf(2325,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[2269,2269,theory(equality)]) ).
cnf(2327,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('PARAMODULATE',[status(thm)],[2324,2324,theory(equality)]) ).
cnf(2340,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2291,2268,theory(equality)]),2291,theory(equality)]) ).
cnf(2341,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference('REWRITE',[status(thm)],[2295,2340,theory(equality)]) ).
cnf(2349,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[2327,2306,theory(equality)]) ).
cnf(2350,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[2325,2349,theory(equality)]) ).
cnf(2351,plain,
$false,
inference('REWRITE',[status(thm)],[2341,2350,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP058-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.15 % Command : run-snark %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 04:20:24 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.48 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.49 *
% 0.22/0.49 *
% 0.22/0.50 #<PACKAGE "SNARK-USER">
% 0.22/0.50 *
% 0.22/0.50 SNARK-TPTP-OPTIONS
% 0.22/0.50 *
% 0.22/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.50 (USE-FACTORING :POS)
% 0.22/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.50 *
% 0.22/0.50 "."
% 0.22/0.50 *
% 0.22/0.50 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T04:20:25
% 0.22/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-14T04:20:25
% 1.65/1.81
% 1.65/1.81
% 1.65/1.81 #||
% 1.65/1.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.81 % SZS output start Refutation
% See solution above
% 1.66/1.85 ||#
% 1.66/1.85
% 1.66/1.85 ; Summary of computation:
% 1.66/1.85 ; 9300 formulas have been input or derived (from 64 formulas).
% 1.66/1.85 ; 2351 (25%) were retained. Of these,
% 1.66/1.85 ; 2302 (98%) were simplified or subsumed later,
% 1.66/1.85 ; 49 ( 2%) are still being kept.
% 1.66/1.85 ;
% 1.66/1.85 ; Run time in seconds excluding printing time:
% 1.66/1.85 ; 0.001 0% Read assertion file (1 call)
% 1.66/1.85 ; 0.000 0% Assert (2 calls)
% 1.66/1.85 ; 0.372 28% Process new row (9,165 calls)
% 1.66/1.85 ; 0.007 1% Resolution (126 calls)
% 1.66/1.85 ; 0.153 12% Paramodulation (63 calls)
% 1.66/1.85 ; 0.000 0% Condensing (2 calls)
% 1.66/1.85 ; 0.000 0% Forward subsumption (2 calls)
% 1.66/1.85 ; 0.000 0% Backward subsumption (2 calls)
% 1.66/1.85 ; 0.367 28% Forward simplification (8,509 calls)
% 1.66/1.85 ; 0.300 23% Backward simplification (2,351 calls)
% 1.66/1.85 ; 0.050 4% Ordering (21,768 calls)
% 1.66/1.85 ; 0.001 0% Sortal reasoning (32 calls)
% 1.66/1.85 ; 0.000 0% Purity testing (1 call)
% 1.66/1.85 ; 0.057 4% Other
% 1.66/1.85 ; 1.308 Total
% 1.66/1.85 ; 1.352 Real time
% 1.66/1.85 ;
% 1.66/1.85 ; Term-hash-array has 9,339 terms in all.
% 1.66/1.85 ; Feature-vector-row-index has 0 entries (1 at peak, 2 added, 2 deleted).
% 1.66/1.85 ; Feature-vector-row-index has 1 node (30 at peak, 53 added, 52 deleted).
% 1.66/1.85 ; Retrieved 0 possibly forward subsuming rows in 2 calls.
% 1.66/1.85 ; Retrieved 0 possibly backward subsumed rows in 2 calls.
% 1.66/1.85 ; Path-index has 169 entries (6,430 at peak, 9,660 added, 9,491 deleted).
% 1.66/1.85 ; Path-index has 13,516 nodes (16,396 at peak, 20,880 added, 7,364 deleted).
% 1.66/1.85 ; Trie-index has 169 entries (6,430 at peak, 9,660 added, 9,491 deleted).
% 1.66/1.85 ; Trie-index has 756 nodes (48,370 at peak, 70,835 added, 70,079 deleted).
% 1.66/1.85 ; Retrieved 26,958 generalization terms in 107,953 calls.
% 1.66/1.85 ; Retrieved 6,776 instance terms in 2,368 calls.
% 1.66/1.85 ; Retrieved 34,652 unifiable terms in 720 calls.
% 1.66/1.85 ;
% 1.66/1.85 ; The agenda of backward simplifiable rows to process has 3 entries:
% 1.66/1.85 ; 3 with value 0
% 1.66/1.85 ; The agenda of rows to process has 16 entries:
% 1.66/1.85 ; 5 with value 24 3 with value 28 1 with value 31
% 1.66/1.85 ; 3 with value 25 1 with value 30 1 with value 32
% 1.66/1.85 ; 2 with value 26
% 1.66/1.85 ; The agenda of rows to give has 40 entries:
% 1.66/1.85 ; 1 with value (4 19) 4 with value (4 26) 3 with value (4 30)
% 1.66/1.85 ; 2 with value (4 22) 2 with value (4 27) 5 with value (4 31)
% 1.66/1.85 ; 2 with value (4 23) 5 with value (4 28) 3 with value (4 32)
% 1.66/1.85 ; 7 with value (4 24) 4 with value (4 29) 1 with value (4 34)
% 1.66/1.85 ; 1 with value (4 25)
% 1.66/1.85 Evaluation took:
% 1.66/1.85 1.352 seconds of real time
% 1.66/1.85 1.239622 seconds of user run time
% 1.66/1.85 0.112986 seconds of system run time
% 1.66/1.85 [Run times include 0.194 seconds GC run time.]
% 1.66/1.85 0 calls to %EVAL
% 1.66/1.85 0 page faults and
% 1.66/1.85 128,111,552 bytes consed.
% 1.66/1.85 :PROOF-FOUND
% 1.66/1.85 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T04:20:26
% 1.66/1.85 :PROOF-FOUND
% 1.66/1.85 *
%------------------------------------------------------------------------------