TSTP Solution File: GRP423-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP423-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n008.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 11:38:31 EDT 2022
% Result : Unsatisfiable 6.45s 6.61s
% Output : Refutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 2
% Syntax : Number of clauses : 178 ( 178 unt; 0 nHn; 2 RR)
% Number of literals : 178 ( 177 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 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 : 789 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(3,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(Z),inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(6,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).
cnf(7,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(8,plain,
multiply(inverse(X),inverse(multiply(inverse(inverse(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(X),X)))))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(24,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V))) = inverse(multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V))),
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(25,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),U))))))),multiply(X,U))) = multiply(inverse(U),Z),
inference('PARAMODULATE',[status(thm)],[single_axiom,6,theory(equality)]) ).
cnf(28,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,6,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(38,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))) = multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V))),
inference('PARAMODULATE',[status(thm)],[28,28,theory(equality)]) ).
cnf(39,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)) = multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[28,28,theory(equality)]) ).
cnf(40,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V)))) = inverse(multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V)))),
inference('PARAMODULATE',[status(thm)],[6,28,theory(equality)]) ).
cnf(47,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U))))),multiply(inverse(multiply(Z,U)),inverse(multiply(inverse(multiply(V,U)),multiply(V,U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[7,6,theory(equality)]) ).
cnf(48,plain,
multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),U)) = multiply(inverse(multiply(V,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),multiply(V,U)),
inference('PARAMODULATE',[status(thm)],[28,7,theory(equality)]) ).
cnf(51,plain,
inverse(multiply(inverse(inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),U)))),multiply(inverse(U),inverse(multiply(inverse(U),U))))) = multiply(inverse(Z),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[7,7,theory(equality)]) ).
cnf(123,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[38,39,theory(equality)]) ).
cnf(129,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(multiply(V,Z)),inverse(multiply(inverse(W),W))))))),multiply(X,W))) = multiply(inverse(W),multiply(V,U)),
inference('PARAMODULATE',[status(thm)],[single_axiom,39,theory(equality)]) ).
cnf(200,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U)),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,X1)))) = multiply(inverse(multiply(inverse(multiply(W,Y)),X1)),inverse(multiply(inverse(U),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(W,Y)),X1)),multiply(inverse(multiply(W,Y)),X1)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(W,Y)),X1)),multiply(inverse(multiply(W,Y)),X1)))),inverse(multiply(inverse(multiply(inverse(multiply(W,Y)),X1)),multiply(inverse(multiply(W,Y)),X1))))))))),
inference('PARAMODULATE',[status(thm)],[3,39,theory(equality)]) ).
cnf(356,plain,
multiply(inverse(X),multiply(inverse(multiply(Y,Z)),multiply(Y,U))) = multiply(inverse(X),multiply(inverse(multiply(V,Z)),multiply(V,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,38,theory(equality)]),129,theory(equality)]) ).
cnf(361,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(U,V)),multiply(U,W))),multiply(inverse(multiply(X1,V)),multiply(X1,W))))))))),multiply(X,multiply(Y1,multiply(X1,W))))) = multiply(inverse(multiply(Y1,multiply(X1,W))),Z),
inference('PARAMODULATE',[status(thm)],[25,24,theory(equality)]) ).
cnf(367,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U) = multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),U),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,6,theory(equality)]),361,theory(equality)]) ).
cnf(387,plain,
multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U))) = multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,U))),
inference('PARAMODULATE',[status(thm)],[356,single_axiom,theory(equality)]) ).
cnf(553,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))) = multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,47,theory(equality)]),51,theory(equality)]) ).
cnf(622,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,Y)))) = multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(multiply(U,Y)),multiply(U,Y)))),
inference('PARAMODULATE',[status(thm)],[553,553,theory(equality)]) ).
cnf(661,plain,
multiply(inverse(X),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))) = multiply(inverse(X),inverse(multiply(inverse(multiply(U,Z)),multiply(U,Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,622,theory(equality)]),25,theory(equality)]) ).
cnf(662,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))) = multiply(X,inverse(multiply(inverse(multiply(U,Z)),multiply(U,Z)))),
inference('PARAMODULATE',[status(thm)],[661,single_axiom,theory(equality)]) ).
cnf(710,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U)))),inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U)))))))))),multiply(X,inverse(multiply(inverse(multiply(V,U)),multiply(V,U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,662,theory(equality)]) ).
cnf(728,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(X),X))),multiply(inverse(inverse(multiply(Y,multiply(inverse(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X)))),U)))),V)) = multiply(inverse(multiply(W,multiply(inverse(U),inverse(multiply(inverse(U),U))))),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[48,48,theory(equality)]) ).
cnf(823,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,multiply(inverse(Y),inverse(multiply(inverse(Y),Y))))),multiply(X,Z))),U)),multiply(inverse(multiply(V,multiply(inverse(inverse(multiply(inverse(multiply(W,X1)),multiply(W,Y)))),Z))),multiply(V,Y1)))) = inverse(multiply(inverse(multiply(Z1,U)),multiply(Z1,multiply(X1,Y1)))),
inference('PARAMODULATE',[status(thm)],[40,48,theory(equality)]) ).
cnf(826,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),V))),multiply(X,W))),multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(U),inverse(multiply(inverse(U),U))))),multiply(X1,V))),Y1))) = inverse(multiply(inverse(multiply(Z1,multiply(Z,W))),multiply(Z1,Y1))),
inference('PARAMODULATE',[status(thm)],[24,48,theory(equality)]) ).
cnf(853,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,48,theory(equality)]),25,theory(equality)]) ).
cnf(867,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),W)),multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),W)))))))),multiply(inverse(multiply(X1,multiply(inverse(V),inverse(multiply(inverse(V),V))))),multiply(X1,W)))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),W)),Z),
inference('PARAMODULATE',[status(thm)],[25,48,theory(equality)]) ).
cnf(879,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(multiply(U,X)),multiply(U,V))))))) = multiply(inverse(multiply(W,multiply(inverse(V),inverse(multiply(inverse(V),V))))),multiply(W,inverse(multiply(inverse(Z),multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))))))))))),
inference('PARAMODULATE',[status(thm)],[48,3,theory(equality)]) ).
cnf(882,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),
inference('PARAMODULATE',[status(thm)],[48,853,theory(equality)]) ).
cnf(906,plain,
multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(inverse(Y)),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X)))) = Y,
inference('PARAMODULATE',[status(thm)],[853,3,theory(equality)]) ).
cnf(953,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[882,882,theory(equality)]) ).
cnf(954,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[6,953,theory(equality)]) ).
cnf(955,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(multiply(Z,U)),multiply(Z,U))),
inference('PARAMODULATE',[status(thm)],[387,953,theory(equality)]) ).
cnf(956,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[28,953,theory(equality)]) ).
cnf(957,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[28,953,theory(equality)]) ).
cnf(958,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,U))),Y),
inference('PARAMODULATE',[status(thm)],[367,953,theory(equality)]) ).
cnf(959,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Y),Y))))) = Y,
inference('PARAMODULATE',[status(thm)],[7,953,theory(equality)]) ).
cnf(961,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))) = multiply(X,inverse(multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[662,953,theory(equality)]) ).
cnf(962,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(inverse(Y)),inverse(multiply(inverse(inverse(Y)),inverse(Y))))) = Y,
inference('PARAMODULATE',[status(thm)],[853,953,theory(equality)]) ).
cnf(963,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,X))),
inference('PARAMODULATE',[status(thm)],[6,953,theory(equality)]) ).
cnf(964,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[6,953,theory(equality)]) ).
cnf(965,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(U,Z))) = multiply(inverse(V),V),
inference('PARAMODULATE',[status(thm)],[38,953,theory(equality)]) ).
cnf(967,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Z)),multiply(inverse(U),U))) = multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,Y))),
inference('PARAMODULATE',[status(thm)],[387,953,theory(equality)]) ).
cnf(968,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(U),U)))) = Y,
inference('PARAMODULATE',[status(thm)],[853,953,theory(equality)]) ).
cnf(969,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(U),U))))) = Y,
inference('PARAMODULATE',[status(thm)],[7,953,theory(equality)]) ).
cnf(971,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z))) = multiply(inverse(Z),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[single_axiom,953,theory(equality)]) ).
cnf(1003,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(inverse(U),U)),V))) = inverse(multiply(inverse(multiply(W,multiply(inverse(Y),Z))),multiply(W,V))),
inference('PARAMODULATE',[status(thm)],[24,953,theory(equality)]) ).
cnf(1018,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[954,954,theory(equality)]) ).
cnf(1019,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[953,1018,theory(equality)]) ).
cnf(1020,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1018,1018,theory(equality)]) ).
cnf(1026,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[955,955,theory(equality)]) ).
cnf(1027,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[1026,1026,theory(equality)]) ).
cnf(1057,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(multiply(V,Z)),W))),multiply(inverse(multiply(X1,multiply(V,U))),multiply(X1,W)))) = multiply(X,multiply(inverse(Y1),Y1)),
inference('PARAMODULATE',[status(thm)],[1026,24,theory(equality)]) ).
cnf(1166,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[956,953,theory(equality)]) ).
cnf(1400,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[958,958,theory(equality)]) ).
cnf(1431,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[959,953,theory(equality)]) ).
cnf(1432,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[961,961,theory(equality)]) ).
cnf(1449,plain,
multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,inverse(multiply(inverse(V),V)))),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[956,1432,theory(equality)]) ).
cnf(1668,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))))),multiply(inverse(U),inverse(multiply(inverse(V),V))))) = U,
inference('PARAMODULATE',[status(thm)],[1431,1020,theory(equality)]) ).
cnf(1669,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(multiply(inverse(U),U)),multiply(inverse(V),V))))))) = Y,
inference('PARAMODULATE',[status(thm)],[1431,1020,theory(equality)]) ).
cnf(1698,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(inverse(Y)),inverse(multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[962,953,theory(equality)]) ).
cnf(1699,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1026,1698,theory(equality)]) ).
cnf(1736,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(inverse(Z)),inverse(multiply(inverse(U),U)))))),multiply(inverse(multiply(inverse(inverse(multiply(inverse(V),V))),Y)),W))) = inverse(multiply(inverse(multiply(X1,Z)),multiply(X1,W))),
inference('PARAMODULATE',[status(thm)],[24,1698,theory(equality)]) ).
cnf(1970,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,V))),multiply(inverse(multiply(inverse(V),U)),multiply(inverse(W),W))))) = inverse(multiply(inverse(multiply(X1,Y)),multiply(X1,X))),
inference('PARAMODULATE',[status(thm)],[963,963,theory(equality)]) ).
cnf(1990,plain,
inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(multiply(Y,Z)),U))),multiply(inverse(V),V))) = inverse(multiply(inverse(multiply(inverse(multiply(W,multiply(Y,X1))),multiply(W,U))),multiply(inverse(multiply(inverse(multiply(Y1,Z)),multiply(Y1,X1))),X))),
inference('PARAMODULATE',[status(thm)],[963,39,theory(equality)]) ).
cnf(2015,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,inverse(multiply(inverse(V),V))))),
inference('PARAMODULATE',[status(thm)],[964,1432,theory(equality)]) ).
cnf(2022,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(multiply(inverse(U),U)),multiply(inverse(V),V)))),
inference('PARAMODULATE',[status(thm)],[964,1019,theory(equality)]) ).
cnf(2027,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Z)),U))) = inverse(multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),multiply(inverse(multiply(inverse(W),W)),U))),
inference('PARAMODULATE',[status(thm)],[964,964,theory(equality)]) ).
cnf(2037,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(Z,U)))) = inverse(multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(inverse(U),V)),multiply(inverse(W),W)))),
inference('PARAMODULATE',[status(thm)],[964,956,theory(equality)]) ).
cnf(2051,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),U)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(V),V)),Y)),multiply(inverse(multiply(W,Z)),multiply(W,U)))),
inference('PARAMODULATE',[status(thm)],[964,957,theory(equality)]) ).
cnf(2274,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))),multiply(inverse(U),U)) = multiply(inverse(multiply(inverse(V),V)),multiply(inverse(multiply(inverse(W),W)),X)),
inference('PARAMODULATE',[status(thm)],[1166,1027,theory(equality)]) ).
cnf(2286,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Z)),U))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(V),V))),multiply(inverse(multiply(inverse(W),W)),U))),
inference('PARAMODULATE',[status(thm)],[964,1166,theory(equality)]) ).
cnf(2288,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),U)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(V),V)),Y)),multiply(inverse(multiply(inverse(U),Z)),multiply(inverse(W),W)))),
inference('PARAMODULATE',[status(thm)],[964,1166,theory(equality)]) ).
cnf(3084,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Z)),multiply(inverse(U),U))) = multiply(X,multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,X1))),multiply(inverse(multiply(Y1,W)),multiply(Y1,X1)))),multiply(inverse(Z),Y))),
inference('PARAMODULATE',[status(thm)],[967,965,theory(equality)]) ).
cnf(3142,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Z)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(U,V)),multiply(U,W))),multiply(inverse(multiply(X1,V)),Y1))),multiply(inverse(multiply(Z1,multiply(X1,W))),multiply(Z1,Y1))))) = multiply(X,multiply(inverse(multiply(U1,Z)),multiply(U1,Y))),
inference('PARAMODULATE',[status(thm)],[967,24,theory(equality)]) ).
cnf(3246,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(Y)),Z)))),multiply(inverse(Z),inverse(multiply(inverse(U),U)))) = Y,
inference('PARAMODULATE',[status(thm)],[968,953,theory(equality)]) ).
cnf(3283,plain,
inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),U)),Y)) = inverse(multiply(inverse(multiply(V,U)),multiply(V,multiply(inverse(Z),inverse(multiply(inverse(W),W)))))),
inference('PARAMODULATE',[status(thm)],[6,968,theory(equality)]) ).
cnf(3341,plain,
multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),U)),Y)),V) = multiply(inverse(multiply(inverse(multiply(W,U)),multiply(W,multiply(inverse(Z),inverse(multiply(inverse(X1),X1)))))),V),
inference('PARAMODULATE',[status(thm)],[367,968,theory(equality)]) ).
cnf(3342,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Z,inverse(Y))),multiply(Z,U)))),V))) = multiply(inverse(multiply(W,multiply(X1,multiply(inverse(U),inverse(multiply(inverse(Y1),Y1)))))),multiply(W,multiply(X1,V))),
inference('PARAMODULATE',[status(thm)],[123,968,theory(equality)]) ).
cnf(3425,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(inverse(U),U)),V)))),multiply(inverse(V),inverse(multiply(inverse(W),W))))) = multiply(inverse(Y),Z),
inference('PARAMODULATE',[status(thm)],[969,957,theory(equality)]) ).
cnf(3426,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[969,1699,theory(equality)]),3246,theory(equality)]) ).
cnf(3481,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(inverse(multiply(inverse(multiply(V,X)),multiply(V,W)))),multiply(inverse(W),inverse(multiply(inverse(X1),X1))))))),
inference('PARAMODULATE',[status(thm)],[963,969,theory(equality)]) ).
cnf(3493,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,multiply(inverse(U),inverse(multiply(inverse(V),V))))),multiply(Z,W))) = multiply(inverse(multiply(X1,Y)),multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(Y1,X)),multiply(Y1,U)))),W))),
inference('PARAMODULATE',[status(thm)],[38,969,theory(equality)]) ).
cnf(3517,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(U,Z)))),multiply(inverse(V),W)))),multiply(inverse(W),inverse(multiply(inverse(X1),X1))))) = V,
inference('PARAMODULATE',[status(thm)],[969,965,theory(equality)]) ).
cnf(3526,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,V)))),multiply(inverse(V),inverse(multiply(inverse(W),W)))))))),multiply(U,inverse(multiply(inverse(X1),X1)))) = Y,
inference('PARAMODULATE',[status(thm)],[968,969,theory(equality)]) ).
cnf(3565,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[957,3426,theory(equality)]) ).
cnf(3567,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),Y),
inference('PARAMODULATE',[status(thm)],[1400,3426,theory(equality)]) ).
cnf(3576,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[1431,3426,theory(equality)]) ).
cnf(3577,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[2015,3576,theory(equality)]) ).
cnf(3618,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,multiply(inverse(U),inverse(multiply(inverse(U),U))))),multiply(Z,V)))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(W,X)),multiply(W,U)))),V)),Y),
inference('REWRITE',[status(thm)],[867,3577,theory(equality)]) ).
cnf(3623,plain,
inverse(multiply(inverse(X),multiply(inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))))))) = X,
inference('REWRITE',[status(thm)],[710,3577,theory(equality)]) ).
cnf(3628,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U)),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,X1)))) = multiply(inverse(multiply(inverse(multiply(W,Y)),X1)),U),
inference('REWRITE',[status(thm)],[200,3623,theory(equality)]) ).
cnf(3629,plain,
multiply(inverse(multiply(X,Y)),Z) = inverse(multiply(inverse(multiply(U,Z)),multiply(U,multiply(X,Y)))),
inference('REWRITE',[status(thm)],[823,969,3628,theory(equality)]) ).
cnf(3633,plain,
multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),U)),Y)),V) = multiply(multiply(inverse(multiply(inverse(Z),inverse(multiply(inverse(W),W)))),U),V),
inference('REWRITE',[status(thm)],[3341,3629,theory(equality)]) ).
cnf(3638,plain,
inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),U)),Y)) = multiply(inverse(multiply(inverse(Z),inverse(multiply(inverse(V),V)))),U),
inference('REWRITE',[status(thm)],[3283,3629,theory(equality)]) ).
cnf(3643,plain,
inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y)))),Z),multiply(inverse(multiply(inverse(inverse(multiply(inverse(U),U))),Z)),V))) = inverse(multiply(inverse(multiply(W,X)),multiply(W,V))),
inference('REWRITE',[status(thm)],[1736,3629,theory(equality)]) ).
cnf(3653,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[3526,969,3629,theory(equality)]) ).
cnf(3654,plain,
multiply(inverse(inverse(X)),multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Y),Y)))))) = X,
inference('REWRITE',[status(thm)],[906,3653,theory(equality)]) ).
cnf(3656,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(X),X)))))) = Y,
inference('REWRITE',[status(thm)],[8,3654,theory(equality)]) ).
cnf(3657,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))) = multiply(X,Y),
inference('REWRITE',[status(thm)],[3481,969,3629,theory(equality)]) ).
cnf(3712,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Z)),U))) = inverse(multiply(multiply(inverse(Z),Y),multiply(inverse(multiply(inverse(V),V)),U))),
inference('REWRITE',[status(thm)],[2286,3657,theory(equality)]) ).
cnf(3725,plain,
multiply(inverse(X),multiply(inverse(multiply(Y,Z)),U)) = inverse(multiply(inverse(multiply(inverse(multiply(V,multiply(Y,W))),multiply(V,U))),multiply(inverse(multiply(inverse(multiply(X1,Z)),multiply(X1,W))),X))),
inference('REWRITE',[status(thm)],[1990,3657,theory(equality)]) ).
cnf(3726,plain,
multiply(inverse(X),multiply(Y,Z)) = inverse(multiply(inverse(multiply(U,multiply(Y,Z))),multiply(U,X))),
inference('REWRITE',[status(thm)],[826,969,3725,theory(equality)]) ).
cnf(3874,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(inverse(U),U)),V))) = multiply(inverse(V),multiply(inverse(Y),Z)),
inference('REWRITE',[status(thm)],[1003,3726,theory(equality)]) ).
cnf(3879,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Z)),U))) = multiply(inverse(U),multiply(inverse(Y),Z)),
inference('REWRITE',[status(thm)],[2027,3874,theory(equality)]) ).
cnf(3889,plain,
multiply(inverse(X),multiply(inverse(Y),Z)) = inverse(multiply(multiply(inverse(Z),Y),multiply(inverse(multiply(inverse(U),U)),X))),
inference('REWRITE',[status(thm)],[3712,3879,theory(equality)]) ).
cnf(3892,plain,
inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[1668,3657,3879,theory(equality)]) ).
cnf(3898,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))))) = Y,
inference('REWRITE',[status(thm)],[1669,3879,theory(equality)]) ).
cnf(3909,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Z)) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[3425,3726,3874,theory(equality)]) ).
cnf(3911,plain,
inverse(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))) = X,
inference('REWRITE',[status(thm)],[3898,3909,theory(equality)]) ).
cnf(3922,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(multiply(inverse(U),U)),X)),
inference('REWRITE',[status(thm)],[2274,3911,theory(equality)]) ).
cnf(3923,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = multiply(inverse(Z),Y),
inference('REWRITE',[status(thm)],[2022,3911,theory(equality)]) ).
cnf(3930,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(U),U)),Z)),multiply(inverse(multiply(V,X)),multiply(V,Y)))),
inference('REWRITE',[status(thm)],[2051,3923,theory(equality)]) ).
cnf(3938,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(U),U)),Z)),multiply(inverse(multiply(inverse(Y),X)),multiply(inverse(V),V)))),
inference('REWRITE',[status(thm)],[2288,3923,theory(equality)]) ).
cnf(3953,plain,
multiply(inverse(multiply(X,Y)),Z) = inverse(multiply(inverse(multiply(inverse(multiply(X,U)),Z)),multiply(inverse(multiply(inverse(Y),U)),multiply(inverse(V),V)))),
inference('REWRITE',[status(thm)],[2037,3923,theory(equality)]) ).
cnf(3955,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[3576,3923,theory(equality)]) ).
cnf(3956,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(multiply(U,X)),multiply(U,V))))))) = multiply(inverse(multiply(W,multiply(inverse(V),inverse(multiply(inverse(V),V))))),multiply(W,inverse(multiply(inverse(Z),inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))))))))),
inference('REWRITE',[status(thm)],[879,3955,theory(equality)]) ).
cnf(3957,plain,
inverse(multiply(inverse(X),inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))))) = X,
inference('REWRITE',[status(thm)],[3623,3955,theory(equality)]) ).
cnf(3965,plain,
inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y)))),Z),multiply(inverse(Z),U))) = inverse(multiply(inverse(multiply(V,X)),multiply(V,U))),
inference('REWRITE',[status(thm)],[3643,3955,theory(equality)]) ).
cnf(3968,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[3567,3955,theory(equality)]) ).
cnf(3982,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(Z),multiply(inverse(multiply(U,X)),multiply(U,Y)))),
inference('REWRITE',[status(thm)],[3930,3968,theory(equality)]) ).
cnf(4013,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Z)),multiply(inverse(U),U))) = multiply(X,multiply(multiply(inverse(multiply(inverse(V),W)),multiply(inverse(multiply(X1,V)),multiply(X1,W))),multiply(inverse(Z),Y))),
inference('REWRITE',[status(thm)],[3084,3982,theory(equality)]) ).
cnf(4029,plain,
inverse(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(Z,X)),multiply(Z,Y))),multiply(inverse(U),V)))),multiply(inverse(V),inverse(multiply(inverse(W),W))))) = U,
inference('REWRITE',[status(thm)],[3517,3982,theory(equality)]) ).
cnf(4052,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X),X)))),Y)),multiply(Z,U)) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V,Z)),multiply(V,X)))),Y)),U),
inference('REWRITE',[status(thm)],[3618,3982,theory(equality)]) ).
cnf(4099,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(Z),multiply(inverse(multiply(inverse(Y),X)),multiply(inverse(U),U)))),
inference('REWRITE',[status(thm)],[3938,3968,theory(equality)]) ).
cnf(4100,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(multiply(inverse(U),Y)),multiply(inverse(multiply(X,U)),Z)),
inference('REWRITE',[status(thm)],[3953,4099,theory(equality)]) ).
cnf(4116,plain,
inverse(multiply(inverse(inverse(multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),multiply(inverse(Z),U)))),multiply(inverse(U),inverse(multiply(inverse(V),V))))) = Z,
inference('REWRITE',[status(thm)],[4029,4100,theory(equality)]) ).
cnf(4117,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Z)),multiply(inverse(U),U))) = multiply(X,multiply(multiply(inverse(multiply(V,W)),multiply(V,W)),multiply(inverse(Z),Y))),
inference('REWRITE',[status(thm)],[4013,4100,theory(equality)]) ).
cnf(4122,plain,
multiply(inverse(X),multiply(inverse(Y),Z)) = inverse(multiply(multiply(inverse(Z),Y),X)),
inference('REWRITE',[status(thm)],[3889,3968,theory(equality)]) ).
cnf(4178,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,V))),inverse(multiply(multiply(inverse(W),W),multiply(inverse(V),U)))))) = inverse(multiply(inverse(multiply(X1,Y)),multiply(X1,X))),
inference('REWRITE',[status(thm)],[1970,4122,theory(equality)]) ).
cnf(4182,plain,
X = multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,X)),
inference('REWRITE',[status(thm)],[1449,3892,4122,theory(equality)]) ).
cnf(4184,plain,
inverse(X) = multiply(inverse(X),inverse(multiply(inverse(X),X))),
inference('REWRITE',[status(thm)],[971,4182,theory(equality)]) ).
cnf(4234,plain,
multiply(inverse(X),multiply(inverse(inverse(multiply(Y,multiply(inverse(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X)))),U)))),V)) = multiply(inverse(multiply(W,inverse(U))),multiply(W,V)),
inference('REWRITE',[status(thm)],[728,4184,theory(equality)]) ).
cnf(4235,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))) = Y,
inference('REWRITE',[status(thm)],[3656,4184,theory(equality)]) ).
cnf(4240,plain,
multiply(inverse(multiply(inverse(inverse(X)),Y)),multiply(Z,U)) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V,Z)),multiply(V,X)))),Y)),U),
inference('REWRITE',[status(thm)],[4052,4184,theory(equality)]) ).
cnf(4255,plain,
multiply(inverse(inverse(multiply(multiply(inverse(X),X),multiply(inverse(inverse(Y)),Z)))),U) = multiply(multiply(inverse(multiply(inverse(Y),inverse(multiply(inverse(V),V)))),Z),U),
inference('REWRITE',[status(thm)],[3633,4122,4240,theory(equality)]) ).
cnf(4256,plain,
inverse(inverse(multiply(multiply(inverse(X),X),multiply(inverse(inverse(Y)),Z)))) = multiply(inverse(multiply(inverse(Y),inverse(multiply(inverse(U),U)))),Z),
inference('REWRITE',[status(thm)],[3638,4122,4240,theory(equality)]) ).
cnf(4269,plain,
multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(multiply(U,X)),multiply(U,V))))))) = multiply(inverse(multiply(W,inverse(V))),multiply(W,inverse(multiply(inverse(Z),inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))),inverse(multiply(inverse(multiply(U,X)),multiply(U,V)))))))))),
inference('REWRITE',[status(thm)],[3956,4184,theory(equality)]) ).
cnf(4352,plain,
inverse(inverse(multiply(multiply(inverse(X),X),multiply(Y,Z)))) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[3657,4122,theory(equality)]) ).
cnf(4353,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[4116,4352,theory(equality)]) ).
cnf(4360,plain,
multiply(multiply(inverse(inverse(X)),Y),Z) = multiply(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(U),U)))),Y),Z),
inference('REWRITE',[status(thm)],[4255,4352,theory(equality)]) ).
cnf(4364,plain,
inverse(multiply(multiply(inverse(inverse(inverse(X))),Y),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(U,X)),multiply(U,Z))),
inference('REWRITE',[status(thm)],[3965,4360,theory(equality)]) ).
cnf(4367,plain,
multiply(inverse(inverse(X)),Y) = multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Z),Z)))),Y),
inference('REWRITE',[status(thm)],[4256,4352,theory(equality)]) ).
cnf(4384,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),U)))) = multiply(X,multiply(inverse(multiply(V,U)),multiply(V,Z))),
inference('REWRITE',[status(thm)],[967,4122,theory(equality)]) ).
cnf(4392,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),U)))) = multiply(X,multiply(multiply(inverse(multiply(V,W)),multiply(V,W)),multiply(inverse(U),Z))),
inference('REWRITE',[status(thm)],[4117,4122,theory(equality)]) ).
cnf(4398,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[3922,3968,theory(equality)]) ).
cnf(4414,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),multiply(inverse(multiply(V,Z)),W))),multiply(inverse(multiply(X1,multiply(V,U))),multiply(X1,W)))) = X,
inference('REWRITE',[status(thm)],[1057,4398,theory(equality)]) ).
cnf(4415,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(inverse(multiply(U,Z)),multiply(U,Y))),
inference('REWRITE',[status(thm)],[3142,4414,theory(equality)]) ).
cnf(4424,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(Z),multiply(inverse(U),inverse(multiply(inverse(V),V)))))) = multiply(inverse(multiply(W,Y)),multiply(W,multiply(inverse(inverse(multiply(inverse(multiply(X1,X)),multiply(X1,U)))),Z))),
inference('REWRITE',[status(thm)],[3493,4415,theory(equality)]) ).
cnf(4480,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),U)))) = multiply(X,inverse(multiply(inverse(Z),U))),
inference('REWRITE',[status(thm)],[4384,4415,theory(equality)]) ).
cnf(4491,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(multiply(inverse(multiply(U,V)),multiply(U,V)),multiply(inverse(Z),Y))),
inference('REWRITE',[status(thm)],[4392,4480,theory(equality)]) ).
cnf(4499,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X))),
inference('REWRITE',[status(thm)],[4178,4352,4415,4122,4480,theory(equality)]) ).
cnf(4505,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(multiply(inverse(Z),inverse(Y))),U))) = multiply(inverse(multiply(V,multiply(W,multiply(inverse(Z),inverse(multiply(inverse(X1),X1)))))),multiply(V,multiply(W,U))),
inference('REWRITE',[status(thm)],[3342,4499,theory(equality)]) ).
cnf(4512,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(Z),multiply(inverse(U),inverse(multiply(inverse(V),V)))))) = multiply(inverse(multiply(W,Y)),multiply(W,multiply(inverse(multiply(inverse(U),X)),Z))),
inference('REWRITE',[status(thm)],[4424,4499,theory(equality)]) ).
cnf(4516,plain,
inverse(multiply(multiply(inverse(inverse(inverse(X))),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4364,4499,theory(equality)]) ).
cnf(4519,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),X)),Z)) = multiply(inverse(multiply(U,inverse(Y))),multiply(U,inverse(multiply(inverse(Z),inverse(multiply(inverse(X),X)))))),
inference('REWRITE',[status(thm)],[4269,4499,theory(equality)]) ).
cnf(4528,plain,
multiply(inverse(X),multiply(inverse(inverse(multiply(Y,multiply(inverse(multiply(inverse(X),Y)),Z)))),U)) = multiply(inverse(multiply(V,inverse(Z))),multiply(V,U)),
inference('REWRITE',[status(thm)],[4234,4499,theory(equality)]) ).
cnf(4559,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('REWRITE',[status(thm)],[3957,4499,theory(equality)]) ).
cnf(4560,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),X)),Z)) = multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)),
inference('REWRITE',[status(thm)],[4519,4559,theory(equality)]) ).
cnf(4561,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference('REWRITE',[status(thm)],[4367,4559,theory(equality)]) ).
cnf(4564,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4516,4561,theory(equality)]) ).
cnf(4565,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4353,4561,4564,theory(equality)]) ).
cnf(4567,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(inverse(Z),Y)),
inference('REWRITE',[status(thm)],[4491,4565,theory(equality)]) ).
cnf(4568,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4559,4565,4122,4567,theory(equality)]) ).
cnf(4574,plain,
multiply(inverse(multiply(X,Y)),inverse(multiply(inverse(Z),inverse(U)))) = multiply(inverse(multiply(V,Y)),multiply(V,multiply(inverse(multiply(inverse(U),X)),Z))),
inference('REWRITE',[status(thm)],[4512,4565,4122,4567,theory(equality)]) ).
cnf(4576,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(inverse(multiply(Z,multiply(U,inverse(Y)))),multiply(Z,multiply(U,X))),
inference('REWRITE',[status(thm)],[4505,4565,4122,3968,4574,4567,theory(equality)]) ).
cnf(4609,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[3565,4565,theory(equality)]) ).
cnf(4612,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),X)),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[4560,4568,4609,theory(equality)]) ).
cnf(4616,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference('REWRITE',[status(thm)],[4576,4568,4609,theory(equality)]) ).
cnf(4619,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[4235,4616,theory(equality)]) ).
cnf(4654,plain,
multiply(inverse(X),multiply(multiply(X,Y),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[4528,4568,4609,4612,4561,theory(equality)]) ).
cnf(5158,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4619,4654,theory(equality)]),4568,theory(equality)]) ).
cnf(5159,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_3,5158,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP423-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 13:35:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 *
% 0.21/0.47 *
% 0.21/0.48 #<PACKAGE "SNARK-USER">
% 0.21/0.48 *
% 0.21/0.48 SNARK-TPTP-OPTIONS
% 0.21/0.48 *
% 0.21/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48 (USE-FACTORING :POS)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48 *
% 0.21/0.48 "."
% 0.21/0.48 *
% 0.21/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T13:35:07
% 0.21/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-13T13:35:07
% 6.45/6.61
% 6.45/6.61
% 6.45/6.61 #||
% 6.45/6.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.45/6.61 % SZS output start Refutation
% See solution above
% 6.45/6.66 ||#
% 6.45/6.66
% 6.45/6.66 ; Summary of computation:
% 6.45/6.66 ; 19793 formulas have been input or derived (from 63 formulas).
% 6.45/6.66 ; 5159 (26%) were retained. Of these,
% 6.45/6.66 ; 4645 (90%) were simplified or subsumed later,
% 6.45/6.66 ; 514 (10%) are still being kept.
% 6.45/6.66 ;
% 6.45/6.66 ; Run time in seconds excluding printing time:
% 6.45/6.66 ; 0.001 0% Read assertion file (1 call)
% 6.45/6.66 ; 0.000 0% Assert (2 calls)
% 6.45/6.66 ; 1.127 18% Process new row (19,481 calls)
% 6.45/6.66 ; 0.019 0% Resolution (124 calls)
% 6.45/6.66 ; 0.508 8% Paramodulation (62 calls)
% 6.45/6.66 ; 2.251 37% Forward simplification (16,667 calls)
% 6.45/6.66 ; 1.159 19% Backward simplification (5,159 calls)
% 6.45/6.66 ; 0.976 16% Ordering (130,698 calls)
% 6.45/6.66 ; 0.000 0% Sortal reasoning (32 calls)
% 6.45/6.66 ; 0.000 0% Purity testing (1 call)
% 6.45/6.66 ; 0.086 1% Other
% 6.45/6.66 ; 6.127 Total
% 6.45/6.66 ; 6.183 Real time
% 6.45/6.66 ;
% 6.45/6.66 ; Term-hash-array has 20,427 terms in all.
% 6.45/6.66 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 6.45/6.66 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 6.45/6.66 ; Path-index has 2,287 entries (13,470 at peak, 22,170 added, 19,883 deleted).
% 6.45/6.66 ; Path-index has 15,665 nodes (18,879 at peak, 24,093 added, 8,428 deleted).
% 6.45/6.66 ; Trie-index has 2,287 entries (13,470 at peak, 22,170 added, 19,883 deleted).
% 6.45/6.66 ; Trie-index has 12,006 nodes (104,416 at peak, 154,750 added, 142,744 deleted).
% 6.45/6.66 ; Retrieved 172,886 generalization terms in 211,501 calls.
% 6.45/6.66 ; Retrieved 56,088 instance terms in 5,750 calls.
% 6.45/6.66 ; Retrieved 192,145 unifiable terms in 807 calls.
% 6.45/6.66 ;
% 6.45/6.66 ; The agenda of rows to process has 10 entries:
% 6.45/6.66 ; 2 with value 23 1 with value 26 2 with value 28
% 6.45/6.66 ; 1 with value 25 4 with value 27
% 6.45/6.66 ; The agenda of rows to give has 506 entries:
% 6.45/6.66 ; 1 with value (4 20) 19 with value (4 34) 27 with value (4 47)
% 6.45/6.66 ; 2 with value (4 21) 18 with value (4 35) 18 with value (4 48)
% 6.45/6.66 ; 4 with value (4 22) 23 with value (4 36) 12 with value (4 49)
% 6.45/6.66 ; 3 with value (4 23) 21 with value (4 37) 14 with value (4 50)
% 6.45/6.66 ; 3 with value (4 24) 22 with value (4 38) 15 with value (4 51)
% 6.45/6.66 ; 1 with value (4 25) 27 with value (4 39) 4 with value (4 52)
% 6.45/6.66 ; 1 with value (4 26) 29 with value (4 40) 1 with value (4 53)
% 6.45/6.66 ; 4 with value (4 27) 24 with value (4 41) 5 with value (4 54)
% 6.45/6.66 ; 8 with value (4 28) 30 with value (4 42) 1 with value (4 55)
% 6.45/6.66 ; 7 with value (4 29) 24 with value (4 43) 1 with value (4 56)
% 6.45/6.66 ; 6 with value (4 30) 30 with value (4 44) 1 with value (4 57)
% 6.45/6.66 ; 14 with value (4 31) 31 with value (4 45) 1 with value (4 58)
% 6.45/6.66 ; 13 with value (4 32) 26 with value (4 46) 1 with value (4 59)
% 6.45/6.66 ; 14 with value (4 33)
% 6.45/6.66 Evaluation took:
% 6.45/6.66 6.184 seconds of real time
% 6.45/6.66 5.758709 seconds of user run time
% 6.45/6.66 0.425008 seconds of system run time
% 6.45/6.66 [Run times include 0.823 seconds GC run time.]
% 6.45/6.66 0 calls to %EVAL
% 6.45/6.66 0 page faults and
% 6.45/6.66 379,854,240 bytes consed.
% 6.45/6.66 :PROOF-FOUND
% 6.45/6.66 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T13:35:13
% 6.45/6.66 :PROOF-FOUND
% 6.45/6.66 *
%------------------------------------------------------------------------------