TSTP Solution File: GRP014-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 11:35:15 EDT 2022
% Result : Unsatisfiable 2.73s 2.89s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 2
% Syntax : Number of clauses : 167 ( 167 unt; 0 nHn; 2 RR)
% Number of literals : 167 ( 166 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 20 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 658 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(group_axiom,axiom,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(inverse(X),Z))),U),inverse(multiply(Y,U))))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',group_axiom) ).
cnf(prove_associativity,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(3,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),U),inverse(multiply(Y,U))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),Z))),W),inverse(multiply(V,W)))),
inference('PARAMODULATE',[status(thm)],[group_axiom,group_axiom,theory(equality)]) ).
cnf(6,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),U),inverse(multiply(Y,U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[group_axiom,3,theory(equality)]) ).
cnf(7,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),multiply(inverse(inverse(Y)),multiply(inverse(Y),Z)))),U),inverse(multiply(X,U)))) = Z,
inference('PARAMODULATE',[status(thm)],[group_axiom,3,theory(equality)]) ).
cnf(16,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),inverse(multiply(multiply(inverse(multiply(inverse(W),multiply(inverse(inverse(U)),Y))),X1),inverse(multiply(W,X1))))))),Y1),inverse(multiply(V,Y1)))),
inference('PARAMODULATE',[status(thm)],[3,group_axiom,theory(equality)]) ).
cnf(36,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(X),Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(U),Y)),V),inverse(multiply(U,V)))),
inference('PARAMODULATE',[status(thm)],[group_axiom,6,theory(equality)]) ).
cnf(39,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z)))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(U)),Y))),W),inverse(multiply(V,W)))),
inference('PARAMODULATE',[status(thm)],[6,group_axiom,theory(equality)]) ).
cnf(52,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z)))) = inverse(multiply(multiply(inverse(multiply(inverse(U),Y)),V),inverse(multiply(U,V)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,6,theory(equality)]),group_axiom,theory(equality)]) ).
cnf(56,plain,
multiply(inverse(X),multiply(X,inverse(inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z),U)),V)),W)),inverse(multiply(Z,V))))),U))),X1),inverse(multiply(Y,X1))))))) = W,
inference('PARAMODULATE',[status(thm)],[6,3,theory(equality)]) ).
cnf(60,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(inverse(Z)),multiply(inverse(Z),Y)),
inference('PARAMODULATE',[status(thm)],[6,7,theory(equality)]) ).
cnf(61,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),multiply(inverse(Y),multiply(Y,Z)))),U),inverse(multiply(X,U)))) = Z,
inference('PARAMODULATE',[status(thm)],[7,7,theory(equality)]) ).
cnf(62,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(Z),multiply(Z,Y)),
inference('PARAMODULATE',[status(thm)],[60,60,theory(equality)]) ).
cnf(63,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),multiply(Y,Z))) = multiply(inverse(U),multiply(U,multiply(X,Z))),
inference('PARAMODULATE',[status(thm)],[62,62,theory(equality)]) ).
cnf(64,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(Y,Z))),U),inverse(multiply(inverse(X),U))))) = Z,
inference('PARAMODULATE',[status(thm)],[group_axiom,62,theory(equality)]) ).
cnf(65,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(Y,Z))),U),inverse(multiply(V,U)))))) = multiply(V,Z),
inference('PARAMODULATE',[status(thm)],[6,62,theory(equality)]) ).
cnf(77,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),multiply(Y,Z))) = multiply(inverse(inverse(X)),multiply(inverse(U),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[63,63,theory(equality)]) ).
cnf(78,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,multiply(X,Z)))) = multiply(inverse(U),multiply(U,multiply(inverse(V),multiply(V,Z)))),
inference('PARAMODULATE',[status(thm)],[62,63,theory(equality)]) ).
cnf(79,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,U)))) = multiply(inverse(V),multiply(V,multiply(X,multiply(Y,U)))),
inference('PARAMODULATE',[status(thm)],[63,63,theory(equality)]) ).
cnf(97,plain,
X = inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(Y,multiply(Z,X)))),U),inverse(multiply(inverse(Z),U)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,63,theory(equality)]),group_axiom,theory(equality)]) ).
cnf(144,plain,
multiply(inverse(X),multiply(inverse(Y),multiply(Y,Z))) = multiply(inverse(X),multiply(inverse(U),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[77,61,theory(equality)]) ).
cnf(145,plain,
multiply(X,multiply(inverse(Y),multiply(Y,Z))) = multiply(X,multiply(inverse(U),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[144,61,theory(equality)]) ).
cnf(146,plain,
multiply(X,multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,U)))) = multiply(X,multiply(inverse(V),multiply(V,multiply(Y,U)))),
inference('PARAMODULATE',[status(thm)],[145,145,theory(equality)]) ).
cnf(159,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(Y,Z))),multiply(X,U)),inverse(multiply(inverse(V),multiply(V,U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[64,62,theory(equality)]) ).
cnf(360,plain,
multiply(X,multiply(Y,inverse(multiply(multiply(inverse(multiply(inverse(X),Z)),U),inverse(multiply(inverse(Y),U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[group_axiom,36,theory(equality)]) ).
cnf(361,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(inverse(Y),U))))))) = Z,
inference('PARAMODULATE',[status(thm)],[6,36,theory(equality)]) ).
cnf(380,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),multiply(Y,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(inverse(X),U))))))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[63,36,theory(equality)]),6,theory(equality)]) ).
cnf(438,plain,
inverse(multiply(multiply(inverse(X),Y),inverse(multiply(inverse(Z),Y)))) = inverse(multiply(multiply(inverse(X),U),inverse(multiply(inverse(Z),U)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[97,36,theory(equality)]),6,theory(equality)]) ).
cnf(482,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(Z),U),inverse(multiply(inverse(inverse(inverse(X))),U)))))),V),inverse(multiply(Y,V))))) = inverse(multiply(multiply(inverse(multiply(inverse(W),inverse(multiply(multiply(inverse(multiply(inverse(X1),Z)),Y1),inverse(multiply(X1,Y1)))))),Z1),inverse(multiply(W,Z1)))),
inference('PARAMODULATE',[status(thm)],[3,36,theory(equality)]) ).
cnf(543,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(multiply(inverse(inverse(Z)),U)),V),inverse(multiply(inverse(inverse(inverse(X))),V)))))),W),inverse(multiply(Y,W))))) = inverse(multiply(multiply(inverse(U),X1),inverse(multiply(Z,X1)))),
inference('PARAMODULATE',[status(thm)],[3,360,theory(equality)]) ).
cnf(547,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),multiply(W,inverse(multiply(multiply(inverse(multiply(inverse(inverse(U)),Y)),X1),inverse(multiply(inverse(W),X1)))))))),Y1),inverse(multiply(V,Y1)))),
inference('PARAMODULATE',[status(thm)],[3,360,theory(equality)]) ).
cnf(625,plain,
inverse(multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))) = inverse(multiply(multiply(inverse(X),U),inverse(multiply(Z,U)))),
inference('PARAMODULATE',[status(thm)],[438,61,theory(equality)]) ).
cnf(626,plain,
inverse(multiply(multiply(X,Y),inverse(multiply(Z,Y)))) = inverse(multiply(multiply(X,U),inverse(multiply(Z,U)))),
inference('PARAMODULATE',[status(thm)],[625,61,theory(equality)]) ).
cnf(668,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = multiply(multiply(X,U),inverse(multiply(Z,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[361,626,theory(equality)]),361,theory(equality)]) ).
cnf(711,plain,
multiply(inverse(inverse(multiply(X,Y))),multiply(inverse(Z),multiply(Z,inverse(multiply(U,Y))))) = multiply(inverse(V),multiply(V,multiply(multiply(X,W),inverse(multiply(U,W))))),
inference('PARAMODULATE',[status(thm)],[63,668,theory(equality)]) ).
cnf(804,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = multiply(multiply(inverse(multiply(inverse(U),Y)),V),inverse(multiply(U,V))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[361,52,theory(equality)]),361,theory(equality)]) ).
cnf(855,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),Y)),Z))),multiply(inverse(U),multiply(U,inverse(multiply(X,Z))))) = multiply(inverse(V),multiply(V,multiply(multiply(inverse(multiply(inverse(W),Y)),X1),inverse(multiply(W,X1))))),
inference('PARAMODULATE',[status(thm)],[63,804,theory(equality)]) ).
cnf(908,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = inverse(multiply(multiply(inverse(multiply(inverse(U),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(V),W)),X1)),Y)),inverse(multiply(V,X1))))),W))),Y1),inverse(multiply(U,Y1)))),
inference('PARAMODULATE',[status(thm)],[3,804,theory(equality)]) ).
cnf(1056,plain,
multiply(inverse(X),multiply(inverse(Y),multiply(Y,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(X,U))))))) = Z,
inference('PARAMODULATE',[status(thm)],[380,61,theory(equality)]) ).
cnf(1062,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,multiply(X,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(V,U)))))))) = multiply(inverse(inverse(V)),Z),
inference('PARAMODULATE',[status(thm)],[78,1056,theory(equality)]) ).
cnf(1104,plain,
multiply(multiply(inverse(multiply(inverse(X),multiply(inverse(Y),multiply(Y,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(V,U)))))))),W),inverse(multiply(X,W))) = multiply(multiply(inverse(Z),X1),inverse(multiply(V,X1))),
inference('PARAMODULATE',[status(thm)],[804,1056,theory(equality)]) ).
cnf(1192,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(inverse(Y)),Z)),U),inverse(multiply(V,U)))))) = multiply(V,multiply(inverse(W),multiply(W,inverse(multiply(multiply(inverse(Z),X1),inverse(multiply(Y,X1))))))),
inference('PARAMODULATE',[status(thm)],[65,1056,theory(equality)]) ).
cnf(1505,plain,
multiply(multiply(inverse(X),multiply(X,Y)),inverse(multiply(Z,inverse(Z)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[159,6,theory(equality)]),6,theory(equality)]) ).
cnf(1609,plain,
multiply(inverse(inverse(X)),multiply(inverse(multiply(inverse(Y),multiply(Y,Z))),Z)) = X,
inference('PARAMODULATE',[status(thm)],[1056,1505,theory(equality)]) ).
cnf(1621,plain,
X = multiply(inverse(Y),multiply(Y,multiply(X,inverse(multiply(Z,inverse(Z)))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[63,1505,theory(equality)]),1609,theory(equality)]) ).
cnf(1625,plain,
multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(Z,inverse(Z)))) = multiply(inverse(U),multiply(U,inverse(multiply(multiply(inverse(Y),V),inverse(multiply(X,V)))))),
inference('PARAMODULATE',[status(thm)],[1505,1056,theory(equality)]) ).
cnf(1628,plain,
multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(Z,inverse(Z)))) = multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(U),Y)),V),inverse(multiply(U,V))))),
inference('PARAMODULATE',[status(thm)],[1505,6,theory(equality)]) ).
cnf(1656,plain,
multiply(inverse(inverse(X)),Y) = multiply(inverse(Z),multiply(Z,multiply(X,multiply(Y,inverse(multiply(U,inverse(U))))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,1505,theory(equality)]),1609,theory(equality)]) ).
cnf(1703,plain,
multiply(inverse(inverse(inverse(inverse(X)))),multiply(inverse(inverse(inverse(multiply(inverse(Y),multiply(Y,Z))))),multiply(inverse(U),multiply(U,Z)))) = multiply(inverse(V),multiply(V,X)),
inference('PARAMODULATE',[status(thm)],[79,1609,theory(equality)]) ).
cnf(1770,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = multiply(X,inverse(multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[1505,1621,theory(equality)]) ).
cnf(1774,plain,
multiply(X,inverse(Y)) = multiply(inverse(Z),multiply(Z,multiply(multiply(X,U),inverse(multiply(Y,U))))),
inference('PARAMODULATE',[status(thm)],[1621,668,theory(equality)]) ).
cnf(1785,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),Y)),Z))),multiply(inverse(U),multiply(U,inverse(multiply(X,Z))))) = multiply(inverse(multiply(inverse(V),Y)),inverse(V)),
inference('REWRITE',[status(thm)],[855,1774,theory(equality)]) ).
cnf(1787,plain,
multiply(inverse(inverse(multiply(X,Y))),multiply(inverse(Z),multiply(Z,inverse(multiply(U,Y))))) = multiply(X,inverse(U)),
inference('REWRITE',[status(thm)],[711,1774,theory(equality)]) ).
cnf(1788,plain,
multiply(inverse(multiply(inverse(X),Y)),inverse(X)) = multiply(inverse(multiply(inverse(Z),Y)),inverse(Z)),
inference('REWRITE',[status(thm)],[1785,1787,theory(equality)]) ).
cnf(1791,plain,
multiply(inverse(inverse(inverse(X))),X) = multiply(inverse(inverse(inverse(Y))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[78,1621,theory(equality)]),1656,theory(equality)]) ).
cnf(1826,plain,
X = multiply(inverse(Y),multiply(Y,multiply(X,inverse(multiply(multiply(multiply(Z,U),inverse(multiply(V,U))),inverse(multiply(multiply(Z,W),inverse(multiply(V,W))))))))),
inference('PARAMODULATE',[status(thm)],[1621,626,theory(equality)]) ).
cnf(1892,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = multiply(multiply(inverse(multiply(inverse(inverse(inverse(U))),U)),V),inverse(multiply(inverse(inverse(Y)),V))),
inference('PARAMODULATE',[status(thm)],[804,1791,theory(equality)]) ).
cnf(1904,plain,
multiply(inverse(X),multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(X,Z)))))))),multiply(inverse(inverse(inverse(U))),U))) = Y,
inference('PARAMODULATE',[status(thm)],[1056,1791,theory(equality)]) ).
cnf(1918,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,U)))) = multiply(inverse(inverse(inverse(inverse(multiply(X,multiply(Y,U)))))),multiply(inverse(inverse(inverse(V))),V)),
inference('PARAMODULATE',[status(thm)],[79,1791,theory(equality)]) ).
cnf(1943,plain,
multiply(inverse(multiply(X,Y)),X) = multiply(inverse(multiply(inverse(Z),Y)),inverse(Z)),
inference('PARAMODULATE',[status(thm)],[1788,61,theory(equality)]) ).
cnf(1944,plain,
multiply(inverse(multiply(X,Y)),X) = multiply(inverse(multiply(Z,Y)),Z),
inference('PARAMODULATE',[status(thm)],[1943,1943,theory(equality)]) ).
cnf(1945,plain,
multiply(inverse(inverse(X)),multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),Y)) = X,
inference('PARAMODULATE',[status(thm)],[1609,1944,theory(equality)]) ).
cnf(1951,plain,
multiply(inverse(multiply(inverse(inverse(inverse(X))),X)),inverse(inverse(inverse(Y)))) = multiply(inverse(multiply(Z,Y)),Z),
inference('PARAMODULATE',[status(thm)],[1944,1791,theory(equality)]) ).
cnf(1953,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(Y,Z)),Y),inverse(multiply(U,inverse(U))))))) = Z,
inference('PARAMODULATE',[status(thm)],[6,1944,theory(equality)]) ).
cnf(1955,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,multiply(Z,U))),Y),inverse(multiply(inverse(X),inverse(Z)))))) = U,
inference('PARAMODULATE',[status(thm)],[64,1944,theory(equality)]) ).
cnf(1971,plain,
multiply(multiply(X,Y),inverse(multiply(inverse(multiply(Z,U)),Z))) = multiply(multiply(X,V),inverse(multiply(inverse(multiply(Y,U)),V))),
inference('PARAMODULATE',[status(thm)],[668,1944,theory(equality)]) ).
cnf(1992,plain,
multiply(inverse(X),multiply(X,multiply(multiply(Y,Z),inverse(multiply(multiply(inverse(U),Y),inverse(multiply(inverse(multiply(V,Z)),V))))))) = U,
inference('PARAMODULATE',[status(thm)],[361,1944,theory(equality)]) ).
cnf(2025,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,Z)),Y),inverse(multiply(inverse(X),U))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(U,Z))),W),inverse(multiply(V,W)))),
inference('PARAMODULATE',[status(thm)],[36,1944,theory(equality)]) ).
cnf(2070,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,inverse(Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[360,1770,theory(equality)]) ).
cnf(2080,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1505,1770,theory(equality)]),1505,theory(equality)]) ).
cnf(2098,plain,
multiply(X,inverse(multiply(multiply(multiply(Y,Z),inverse(multiply(U,Z))),inverse(multiply(multiply(Y,V),inverse(multiply(U,V))))))) = multiply(X,inverse(multiply(W,inverse(W)))),
inference('PARAMODULATE',[status(thm)],[1770,626,theory(equality)]) ).
cnf(2122,plain,
multiply(inverse(multiply(X,inverse(Y))),X) = multiply(inverse(multiply(Z,inverse(Z))),Y),
inference('PARAMODULATE',[status(thm)],[1944,2080,theory(equality)]) ).
cnf(2126,plain,
multiply(multiply(inverse(multiply(X,inverse(X))),multiply(multiply(Y,inverse(Y)),Z)),inverse(multiply(U,inverse(U)))) = Z,
inference('PARAMODULATE',[status(thm)],[1505,2080,theory(equality)]) ).
cnf(2128,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1609,2080,theory(equality)]),1609,theory(equality)]) ).
cnf(2181,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),U))),V),inverse(multiply(W,V)))))) = multiply(W,U),
inference('PARAMODULATE',[status(thm)],[65,2080,theory(equality)]) ).
cnf(2189,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,inverse(Y))),Z),inverse(multiply(U,Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),inverse(inverse(U))))),W),inverse(multiply(V,W)))),
inference('PARAMODULATE',[status(thm)],[3,2080,theory(equality)]) ).
cnf(2196,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(inverse(Z),multiply(Z,inverse(X))),
inference('PARAMODULATE',[status(thm)],[62,2128,theory(equality)]) ).
cnf(2199,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = multiply(multiply(U,inverse(U)),inverse(multiply(Z,inverse(X)))),
inference('PARAMODULATE',[status(thm)],[668,2128,theory(equality)]) ).
cnf(2200,plain,
multiply(X,multiply(inverse(Y),multiply(Y,inverse(Z)))) = multiply(X,multiply(inverse(Z),multiply(U,inverse(U)))),
inference('PARAMODULATE',[status(thm)],[145,2128,theory(equality)]) ).
cnf(2202,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),multiply(Z,inverse(Z)))) = multiply(inverse(U),multiply(U,multiply(X,inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[63,2128,theory(equality)]) ).
cnf(2205,plain,
multiply(inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z)))),multiply(U,inverse(U))) = Y,
inference('PARAMODULATE',[status(thm)],[6,2128,theory(equality)]) ).
cnf(2209,plain,
multiply(X,multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,inverse(Y))))) = multiply(X,multiply(inverse(U),multiply(U,multiply(V,inverse(V))))),
inference('PARAMODULATE',[status(thm)],[146,2128,theory(equality)]) ).
cnf(2212,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),multiply(inverse(Y),multiply(Z,inverse(Z))))),U),inverse(multiply(X,U)))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[61,2128,theory(equality)]) ).
cnf(2224,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,inverse(Y))))) = multiply(inverse(U),multiply(U,multiply(X,multiply(V,inverse(V))))),
inference('PARAMODULATE',[status(thm)],[79,2128,theory(equality)]) ).
cnf(2227,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,multiply(X,inverse(Z))))) = multiply(inverse(U),multiply(U,multiply(inverse(Z),multiply(V,inverse(V))))),
inference('PARAMODULATE',[status(thm)],[78,2128,theory(equality)]) ).
cnf(2238,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(Z,inverse(Z)))),U),inverse(multiply(V,U)))))) = multiply(V,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[65,2128,theory(equality)]) ).
cnf(2251,plain,
multiply(X,multiply(Y,inverse(Y))) = inverse(inverse(X)),
inference('PARAMODULATE',[status(thm)],[2070,2128,theory(equality)]) ).
cnf(2254,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,multiply(X,inverse(Z))))) = multiply(inverse(U),multiply(U,inverse(inverse(inverse(Z))))),
inference('REWRITE',[status(thm)],[2227,2251,theory(equality)]) ).
cnf(2255,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,inverse(Y))))) = multiply(inverse(U),multiply(U,inverse(inverse(X)))),
inference('REWRITE',[status(thm)],[2224,2251,theory(equality)]) ).
cnf(2258,plain,
multiply(X,multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,inverse(Y))))) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[2209,2251,theory(equality)]) ).
cnf(2259,plain,
inverse(inverse(inverse(inverse(X)))) = multiply(inverse(Y),multiply(Y,inverse(inverse(X)))),
inference('REWRITE',[status(thm)],[2255,2258,theory(equality)]) ).
cnf(2262,plain,
inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Z)),U)),V)),inverse(multiply(Y,U))))),Z))),W),inverse(multiply(X,W))))))) = V,
inference('REWRITE',[status(thm)],[56,2259,theory(equality)]) ).
cnf(2263,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,multiply(X,inverse(Z))))) = inverse(inverse(inverse(inverse(inverse(Z))))),
inference('REWRITE',[status(thm)],[2254,2259,theory(equality)]) ).
cnf(2264,plain,
inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))))))) = multiply(inverse(inverse(Z)),X),
inference('REWRITE',[status(thm)],[1062,2263,theory(equality)]) ).
cnf(2267,plain,
multiply(inverse(X),multiply(multiply(inverse(inverse(X)),Y),multiply(inverse(inverse(inverse(Z))),Z))) = Y,
inference('REWRITE',[status(thm)],[1904,2264,theory(equality)]) ).
cnf(2271,plain,
inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z)))))) = Y,
inference('REWRITE',[status(thm)],[2205,2251,theory(equality)]) ).
cnf(2272,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),U)),inverse(multiply(X,Z))))),Y)) = U,
inference('REWRITE',[status(thm)],[2262,2271,theory(equality)]) ).
cnf(2279,plain,
multiply(inverse(inverse(X)),inverse(inverse(inverse(Y)))) = multiply(inverse(Z),multiply(Z,multiply(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[2202,2251,theory(equality)]) ).
cnf(2319,plain,
X = multiply(inverse(inverse(X)),inverse(inverse(inverse(multiply(multiply(multiply(Y,Z),inverse(multiply(U,Z))),inverse(multiply(multiply(Y,V),inverse(multiply(U,V))))))))),
inference('REWRITE',[status(thm)],[1826,2279,theory(equality)]) ).
cnf(2324,plain,
multiply(inverse(inverse(multiply(X,Y))),inverse(inverse(inverse(multiply(multiply(inverse(Z),X),inverse(multiply(inverse(multiply(U,Y)),U))))))) = Z,
inference('REWRITE',[status(thm)],[1992,2279,theory(equality)]) ).
cnf(2345,plain,
X = multiply(inverse(inverse(X)),inverse(inverse(inverse(multiply(Y,inverse(Y)))))),
inference('REWRITE',[status(thm)],[1621,2279,theory(equality)]) ).
cnf(2356,plain,
multiply(X,inverse(Y)) = multiply(inverse(inverse(multiply(X,Z))),inverse(inverse(inverse(multiply(Y,Z))))),
inference('REWRITE',[status(thm)],[1774,2279,theory(equality)]) ).
cnf(2367,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(Y))))),Z),inverse(multiply(X,Z)))) = inverse(Y),
inference('REWRITE',[status(thm)],[2212,2251,theory(equality)]) ).
cnf(2369,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(inverse(inverse(inverse(Y)))),Z),inverse(multiply(U,Z)))))) = multiply(U,inverse(Y)),
inference('REWRITE',[status(thm)],[2238,2251,theory(equality)]) ).
cnf(2371,plain,
multiply(X,multiply(inverse(Y),multiply(Y,inverse(Z)))) = multiply(X,inverse(inverse(inverse(Z)))),
inference('REWRITE',[status(thm)],[2200,2251,theory(equality)]) ).
cnf(2414,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(inverse(Y)),Z)),U),inverse(multiply(V,U)))))) = multiply(V,inverse(inverse(inverse(multiply(multiply(inverse(Z),W),inverse(multiply(Y,W))))))),
inference('REWRITE',[status(thm)],[1192,2371,theory(equality)]) ).
cnf(2436,plain,
multiply(multiply(inverse(multiply(inverse(X),inverse(inverse(inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z)))))))),V),inverse(multiply(X,V))) = multiply(multiply(inverse(Y),W),inverse(multiply(U,W))),
inference('REWRITE',[status(thm)],[1104,2371,theory(equality)]) ).
cnf(2482,plain,
inverse(inverse(inverse(X))) = multiply(inverse(Y),multiply(Y,inverse(X))),
inference('REWRITE',[status(thm)],[2196,2251,theory(equality)]) ).
cnf(2558,plain,
inverse(inverse(inverse(multiply(multiply(inverse(multiply(X,Y)),X),inverse(multiply(Z,inverse(Z))))))) = Y,
inference('REWRITE',[status(thm)],[1953,2482,theory(equality)]) ).
cnf(2559,plain,
inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(X)))),Y),inverse(multiply(Z,Y)))))) = multiply(Z,inverse(X)),
inference('REWRITE',[status(thm)],[2369,2482,theory(equality)]) ).
cnf(2560,plain,
inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(multiply(X,inverse(X))),multiply(multiply(Y,inverse(Y)),Z))),U),inverse(multiply(V,U)))))) = multiply(V,Z),
inference('REWRITE',[status(thm)],[2181,2482,theory(equality)]) ).
cnf(2598,plain,
inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)),Y)),Z),inverse(multiply(U,Z)))))) = multiply(U,inverse(inverse(inverse(multiply(multiply(inverse(Y),V),inverse(multiply(X,V))))))),
inference('REWRITE',[status(thm)],[2414,2482,theory(equality)]) ).
cnf(2600,plain,
multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(Z,inverse(Z)))) = inverse(inverse(inverse(multiply(multiply(inverse(Y),U),inverse(multiply(X,U)))))),
inference('REWRITE',[status(thm)],[1625,2482,theory(equality)]) ).
cnf(2612,plain,
inverse(inverse(inverse(multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))))) = inverse(multiply(multiply(inverse(multiply(inverse(U),multiply(inverse(inverse(Z)),X))),V),inverse(multiply(U,V)))),
inference('REWRITE',[status(thm)],[39,2482,theory(equality)]) ).
cnf(2676,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(inverse(Y))),Y)) = X,
inference('REWRITE',[status(thm)],[1945,2251,theory(equality)]) ).
cnf(2677,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(Y)),multiply(inverse(Z),multiply(Z,U)))) = inverse(inverse(multiply(X,multiply(Y,U)))),
inference('REWRITE',[status(thm)],[1918,2676,theory(equality)]) ).
cnf(2681,plain,
inverse(inverse(X)) = multiply(inverse(Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[1703,1609,2677,theory(equality)]) ).
cnf(2697,plain,
multiply(inverse(inverse(X)),inverse(inverse(inverse(Y)))) = inverse(inverse(multiply(X,inverse(Y)))),
inference('REWRITE',[status(thm)],[2279,2681,theory(equality)]) ).
cnf(2700,plain,
X = inverse(inverse(multiply(X,inverse(multiply(multiply(multiply(Y,Z),inverse(multiply(U,Z))),inverse(multiply(multiply(Y,V),inverse(multiply(U,V))))))))),
inference('REWRITE',[status(thm)],[2319,2697,theory(equality)]) ).
cnf(2708,plain,
inverse(inverse(multiply(multiply(X,Y),inverse(multiply(multiply(inverse(Z),X),inverse(multiply(inverse(multiply(U,Y)),U))))))) = Z,
inference('REWRITE',[status(thm)],[2324,2697,theory(equality)]) ).
cnf(2713,plain,
X = inverse(inverse(multiply(X,inverse(multiply(Y,inverse(Y)))))),
inference('REWRITE',[status(thm)],[2345,2697,theory(equality)]) ).
cnf(2714,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference('REWRITE',[status(thm)],[2558,2713,theory(equality)]) ).
cnf(2726,plain,
inverse(inverse(multiply(multiply(X,Y),inverse(multiply(multiply(inverse(Z),X),Y))))) = Z,
inference('REWRITE',[status(thm)],[2708,2714,theory(equality)]) ).
cnf(2732,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(X,U),inverse(multiply(inverse(multiply(Y,Z)),U))),
inference('REWRITE',[status(thm)],[1971,2714,theory(equality)]) ).
cnf(2739,plain,
multiply(X,inverse(Y)) = inverse(inverse(multiply(multiply(X,Z),inverse(multiply(Y,Z))))),
inference('REWRITE',[status(thm)],[2356,2697,theory(equality)]) ).
cnf(2741,plain,
multiply(X,inverse(multiply(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[2726,2739,theory(equality)]) ).
cnf(2746,plain,
multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(Z,inverse(Z)))) = inverse(multiply(inverse(Y),inverse(X))),
inference('REWRITE',[status(thm)],[2600,2739,theory(equality)]) ).
cnf(2747,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,inverse(multiply(multiply(inverse(multiply(inverse(Z),X)),U),inverse(multiply(Z,U))))),
inference('REWRITE',[status(thm)],[1628,2746,theory(equality)]) ).
cnf(2754,plain,
inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)),Y)),inverse(inverse(inverse(inverse(Z))))),inverse(Z))) = inverse(multiply(multiply(inverse(Y),U),inverse(multiply(X,U)))),
inference('REWRITE',[status(thm)],[543,2739,2747,theory(equality)]) ).
cnf(2755,plain,
inverse(multiply(multiply(inverse(X),inverse(inverse(inverse(inverse(Y))))),inverse(Y))) = inverse(multiply(multiply(inverse(multiply(inverse(Z),inverse(multiply(multiply(inverse(multiply(inverse(U),X)),V),inverse(multiply(U,V)))))),W),inverse(multiply(Z,W)))),
inference('REWRITE',[status(thm)],[482,2739,2747,theory(equality)]) ).
cnf(2766,plain,
inverse(multiply(inverse(multiply(inverse(inverse(X)),Y)),inverse(Z))) = multiply(Z,inverse(multiply(inverse(Y),inverse(X)))),
inference('REWRITE',[status(thm)],[2598,2739,theory(equality)]) ).
cnf(2775,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(X))),multiply(multiply(Y,inverse(Y)),Z))),inverse(U))) = multiply(U,Z),
inference('REWRITE',[status(thm)],[2560,2739,theory(equality)]) ).
cnf(2776,plain,
inverse(multiply(inverse(inverse(inverse(inverse(X)))),inverse(Y))) = multiply(Y,inverse(X)),
inference('REWRITE',[status(thm)],[2559,2739,theory(equality)]) ).
cnf(2798,plain,
multiply(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(Z))))),U),inverse(multiply(X,U))) = multiply(multiply(inverse(Y),V),inverse(multiply(Z,V))),
inference('REWRITE',[status(thm)],[2436,2739,theory(equality)]) ).
cnf(2813,plain,
inverse(inverse(inverse(multiply(inverse(X),inverse(Y))))) = multiply(inverse(inverse(Y)),X),
inference('REWRITE',[status(thm)],[2264,2739,theory(equality)]) ).
cnf(2814,plain,
inverse(inverse(multiply(inverse(inverse(inverse(X))),multiply(inverse(inverse(multiply(Y,Z))),multiply(inverse(multiply(inverse(multiply(inverse(Y),X)),Z)),U))))) = U,
inference('REWRITE',[status(thm)],[2272,2766,2813,theory(equality)]) ).
cnf(2815,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = inverse(multiply(multiply(inverse(multiply(inverse(U),inverse(multiply(inverse(inverse(inverse(V))),multiply(inverse(inverse(multiply(W,X1))),multiply(inverse(multiply(inverse(multiply(inverse(W),V)),X1)),Y)))))),Y1),inverse(multiply(U,Y1)))),
inference('REWRITE',[status(thm)],[908,2766,2813,theory(equality)]) ).
cnf(2823,plain,
multiply(inverse(X),multiply(multiply(inverse(inverse(X)),Y),inverse(inverse(inverse(multiply(inverse(Z),inverse(inverse(Z)))))))) = Y,
inference('REWRITE',[status(thm)],[2267,2813,theory(equality)]) ).
cnf(2839,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = multiply(multiply(inverse(inverse(inverse(inverse(multiply(inverse(U),inverse(inverse(U))))))),V),inverse(multiply(inverse(inverse(Y)),V))),
inference('REWRITE',[status(thm)],[1892,2813,theory(equality)]) ).
cnf(2845,plain,
inverse(inverse(multiply(inverse(inverse(multiply(inverse(X),inverse(inverse(X))))),inverse(Y)))) = multiply(inverse(multiply(Z,Y)),Z),
inference('REWRITE',[status(thm)],[1951,2697,2813,theory(equality)]) ).
cnf(2847,plain,
inverse(multiply(inverse(X),inverse(Y))) = inverse(multiply(multiply(inverse(multiply(inverse(Z),multiply(inverse(inverse(Y)),X))),U),inverse(multiply(Z,U)))),
inference('REWRITE',[status(thm)],[2612,2739,theory(equality)]) ).
cnf(2860,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,inverse(Y))),Z),inverse(multiply(U,Z))))) = inverse(multiply(inverse(inverse(inverse(U))),inverse(X))),
inference('REWRITE',[status(thm)],[2189,2847,theory(equality)]) ).
cnf(2876,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z))))) = inverse(multiply(inverse(multiply(V,inverse(multiply(multiply(inverse(multiply(inverse(inverse(U)),Y)),W),inverse(multiply(inverse(V),W)))))),inverse(X))),
inference('REWRITE',[status(thm)],[547,2847,theory(equality)]) ).
cnf(2895,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z))))) = inverse(multiply(inverse(inverse(multiply(inverse(Y),inverse(U)))),inverse(X))),
inference('REWRITE',[status(thm)],[16,2847,theory(equality)]) ).
cnf(2901,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(U,Z))))) = multiply(X,inverse(inverse(multiply(inverse(inverse(U)),Y)))),
inference('REWRITE',[status(thm)],[2876,2776,2741,2813,2895,theory(equality)]) ).
cnf(2919,plain,
multiply(X,inverse(inverse(inverse(inverse(inverse(inverse(Y))))))) = inverse(multiply(inverse(inverse(inverse(Y))),inverse(X))),
inference('REWRITE',[status(thm)],[2860,2251,2901,theory(equality)]) ).
cnf(2934,plain,
inverse(multiply(multiply(inverse(X),inverse(inverse(inverse(inverse(Y))))),inverse(Y))) = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[2755,2367,2681,2901,theory(equality)]) ).
cnf(2935,plain,
inverse(inverse(multiply(inverse(inverse(X)),Y))) = inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(X,Z)))),
inference('REWRITE',[status(thm)],[2754,2934,theory(equality)]) ).
cnf(2944,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(Y,Z)),Y),inverse(multiply(inverse(X),U))))) = inverse(inverse(inverse(inverse(multiply(U,Z))))),
inference('REWRITE',[status(thm)],[2025,2681,2935,theory(equality)]) ).
cnf(2945,plain,
inverse(inverse(inverse(inverse(inverse(inverse(X)))))) = X,
inference('REWRITE',[status(thm)],[1955,2681,2944,theory(equality)]) ).
cnf(2946,plain,
multiply(X,Y) = inverse(multiply(inverse(inverse(inverse(Y))),inverse(X))),
inference('REWRITE',[status(thm)],[2919,2945,theory(equality)]) ).
cnf(2950,plain,
multiply(multiply(inverse(multiply(inverse(X),Y)),Z),inverse(multiply(X,Z))) = inverse(inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[2815,2814,2681,2935,theory(equality)]) ).
cnf(2957,plain,
inverse(inverse(inverse(inverse(multiply(inverse(X),inverse(Y)))))) = multiply(multiply(inverse(X),Z),inverse(multiply(Y,Z))),
inference('REWRITE',[status(thm)],[2798,2950,theory(equality)]) ).
cnf(2973,plain,
inverse(inverse(inverse(X))) = multiply(inverse(inverse(multiply(inverse(Y),inverse(inverse(Y))))),inverse(X)),
inference('REWRITE',[status(thm)],[2839,2945,2697,2957,2950,theory(equality)]) ).
cnf(2974,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = multiply(inverse(multiply(Y,X)),Y),
inference('REWRITE',[status(thm)],[2845,2973,theory(equality)]) ).
cnf(2983,plain,
X = multiply(inverse(multiply(Y,inverse(Y))),X),
inference('REWRITE',[status(thm)],[2122,2945,2974,theory(equality)]) ).
cnf(2991,plain,
multiply(multiply(multiply(X,inverse(X)),Y),inverse(multiply(Z,inverse(Z)))) = Y,
inference('REWRITE',[status(thm)],[2126,2983,theory(equality)]) ).
cnf(2992,plain,
inverse(multiply(inverse(multiply(multiply(X,inverse(X)),Y)),inverse(Z))) = multiply(Z,Y),
inference('REWRITE',[status(thm)],[2775,2983,theory(equality)]) ).
cnf(2996,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(inverse(Z)))) = inverse(inverse(inverse(inverse(multiply(Y,Z))))),
inference('REWRITE',[status(thm)],[2944,2946,2974,theory(equality)]) ).
cnf(2997,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[2823,2713,2996,theory(equality)]) ).
cnf(3003,plain,
X = multiply(X,inverse(multiply(multiply(multiply(Y,Z),inverse(multiply(U,Z))),inverse(multiply(multiply(Y,V),inverse(multiply(U,V))))))),
inference('REWRITE',[status(thm)],[2700,2997,theory(equality)]) ).
cnf(3004,plain,
X = multiply(X,inverse(multiply(Y,inverse(Y)))),
inference('REWRITE',[status(thm)],[2098,3003,theory(equality)]) ).
cnf(3005,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference('REWRITE',[status(thm)],[2991,3004,theory(equality)]) ).
cnf(3007,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference('REWRITE',[status(thm)],[2992,3005,theory(equality)]) ).
cnf(3017,plain,
multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(Z,inverse(X))),
inference('REWRITE',[status(thm)],[2199,3005,theory(equality)]) ).
cnf(3023,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[2732,3007,3017,theory(equality)]) ).
cnf(3024,plain,
$false,
inference('REWRITE',[status(thm)],[prove_associativity,3023,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 23:42:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.49 SNARK-TPTP-OPTIONS
% 0.20/0.49 *
% 0.20/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49 (USE-FACTORING :POS)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49 *
% 0.20/0.49 "."
% 0.20/0.49 *
% 0.20/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T23:42:44
% 0.20/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-13T23:42:44
% 2.73/2.89
% 2.73/2.89
% 2.73/2.89 #||
% 2.73/2.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.73/2.89 % SZS output start Refutation
% See solution above
% 2.73/2.96 ||#
% 2.73/2.96
% 2.73/2.96 ; Summary of computation:
% 2.73/2.96 ; 10877 formulas have been input or derived (from 46 formulas).
% 2.73/2.96 ; 3024 (28%) were retained. Of these,
% 2.73/2.96 ; 3006 (99%) were simplified or subsumed later,
% 2.73/2.96 ; 18 ( 1%) are still being kept.
% 2.73/2.96 ;
% 2.73/2.96 ; Run time in seconds excluding printing time:
% 2.73/2.96 ; 0.001 0% Read assertion file (1 call)
% 2.73/2.96 ; 0.000 0% Assert (2 calls)
% 2.73/2.96 ; 0.675 28% Process new row (8,704 calls)
% 2.73/2.96 ; 0.008 0% Resolution (90 calls)
% 2.73/2.96 ; 0.272 11% Paramodulation (45 calls)
% 2.73/2.96 ; 0.771 32% Forward simplification (7,351 calls)
% 2.73/2.96 ; 0.547 23% Backward simplification (3,024 calls)
% 2.73/2.96 ; 0.075 3% Ordering (15,071 calls)
% 2.73/2.96 ; 0.000 0% Sortal reasoning (32 calls)
% 2.73/2.96 ; 0.000 0% Purity testing (1 call)
% 2.73/2.96 ; 0.055 2% Other
% 2.73/2.96 ; 2.404 Total
% 2.73/2.96 ; 2.475 Real time
% 2.73/2.96 ;
% 2.73/2.96 ; Term-hash-array has 16,794 terms in all.
% 2.73/2.96 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.73/2.96 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.73/2.96 ; Path-index has 77 entries (12,936 at peak, 17,421 added, 17,344 deleted).
% 2.73/2.96 ; Path-index has 17,018 nodes (22,251 at peak, 27,221 added, 10,203 deleted).
% 2.73/2.96 ; Trie-index has 77 entries (12,936 at peak, 17,421 added, 17,344 deleted).
% 2.73/2.96 ; Trie-index has 294 nodes (96,262 at peak, 128,457 added, 128,163 deleted).
% 2.73/2.96 ; Retrieved 14,644 generalization terms in 101,240 calls.
% 2.73/2.96 ; Retrieved 17,862 instance terms in 3,112 calls.
% 2.73/2.96 ; Retrieved 96,009 unifiable terms in 603 calls.
% 2.73/2.96 ;
% 2.73/2.96 ; The agenda of backward simplifiable rows to process has 1928 entries:
% 2.73/2.96 ; 1928 with value 0
% 2.73/2.96 ; The agenda of rows to process has 173 entries:
% 2.73/2.96 ; 1 with value 26 3 with value 42 4 with value 54
% 2.73/2.96 ; 2 with value 30 5 with value 43 5 with value 55
% 2.73/2.96 ; 4 with value 31 2 with value 44 4 with value 56
% 2.73/2.96 ; 2 with value 32 8 with value 45 3 with value 57
% 2.73/2.96 ; 2 with value 34 12 with value 46 3 with value 58
% 2.73/2.96 ; 4 with value 35 8 with value 47 2 with value 60
% 2.73/2.96 ; 7 with value 36 16 with value 48 1 with value 62
% 2.73/2.96 ; 2 with value 37 5 with value 49 3 with value 63
% 2.73/2.96 ; 7 with value 38 14 with value 50 2 with value 64
% 2.73/2.96 ; 6 with value 39 7 with value 51 1 with value 65
% 2.73/2.96 ; 6 with value 40 9 with value 52 1 with value 66
% 2.73/2.96 ; 4 with value 41 8 with value 53
% 2.73/2.96 ; The agenda of rows to give has 15 entries:
% 2.73/2.96 ; 1 with value (4 18) 4 with value (4 25) 1 with value (4 33)
% 2.73/2.96 ; 1 with value (4 20) 1 with value (4 27) 1 with value (4 38)
% 2.73/2.96 ; 3 with value (4 23) 1 with value (4 30) 1 with value (4 43)
% 2.73/2.96 ; 1 with value (4 24)
% 2.73/2.96 Evaluation took:
% 2.73/2.96 2.476 seconds of real time
% 2.73/2.96 2.313223 seconds of user run time
% 2.73/2.96 0.163118 seconds of system run time
% 2.73/2.96 [Run times include 0.471 seconds GC run time.]
% 2.73/2.96 0 calls to %EVAL
% 2.73/2.96 0 page faults and
% 2.73/2.96 192,054,928 bytes consed.
% 2.73/2.96 :PROOF-FOUND
% 2.73/2.96 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T23:42:46
% 2.73/2.96 :PROOF-FOUND
% 2.73/2.96 *
%------------------------------------------------------------------------------