TSTP Solution File: GRP416-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP416-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.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 11:38:26 EDT 2022
% Result : Unsatisfiable 3.72s 3.92s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 2
% Syntax : Number of clauses : 158 ( 158 unt; 0 nHn; 5 RR)
% Number of literals : 158 ( 157 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 19 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 587 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(Z)))),inverse(multiply(inverse(X),X)))))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(3,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X)))))) = multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(Z)))),inverse(multiply(inverse(U),U))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(6,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(inverse(Z))))),inverse(multiply(inverse(X),X))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(7,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X))))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(24,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[single_axiom,6,theory(equality)]) ).
cnf(31,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X))))))) = inverse(multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y)))),
inference('PARAMODULATE',[status(thm)],[7,6,theory(equality)]) ).
cnf(42,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(Z))))))),inverse(multiply(inverse(Y),Y))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,24,theory(equality)]) ).
cnf(43,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[7,24,theory(equality)]) ).
cnf(44,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(inverse(Y),Y)))))))) = Z,
inference('PARAMODULATE',[status(thm)],[6,24,theory(equality)]) ).
cnf(46,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X)))))) = inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(Y,U)),Z)),inverse(multiply(inverse(U),U)))))),
inference('PARAMODULATE',[status(thm)],[24,24,theory(equality)]) ).
cnf(47,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y))) = multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(Z)))),inverse(multiply(inverse(U),U))))),
inference('PARAMODULATE',[status(thm)],[3,24,theory(equality)]) ).
cnf(50,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(inverse(V))))),inverse(multiply(inverse(U),U))))))),inverse(multiply(inverse(X),X))))) = multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(U,W)),V)),inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[6,24,theory(equality)]) ).
cnf(90,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y))) = inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,Z))),inverse(multiply(inverse(U),U)))))),
inference('PARAMODULATE',[status(thm)],[42,7,theory(equality)]) ).
cnf(102,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(inverse(multiply(Z,inverse(U))))))))),multiply(X,inverse(inverse(U))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(inverse(multiply(Z,inverse(U)))))))),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(inverse(multiply(Z,inverse(U)))))))))) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[42,42,theory(equality)]) ).
cnf(112,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Z)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))) = multiply(inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(multiply(V,X)),multiply(V,inverse(inverse(multiply(X,inverse(Y))))))))),multiply(U,inverse(inverse(Z))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(V,X)),multiply(V,inverse(inverse(multiply(X,inverse(Y)))))))),inverse(multiply(inverse(multiply(V,X)),multiply(V,inverse(inverse(multiply(X,inverse(Y)))))))))),
inference('PARAMODULATE',[status(thm)],[24,42,theory(equality)]) ).
cnf(113,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))) = multiply(inverse(X),X),
inference('REWRITE',[status(thm)],[102,112,theory(equality)]) ).
cnf(116,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(inverse(Y),Y)))) = inverse(multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),inverse(multiply(inverse(Y),Y)))),
inference('PARAMODULATE',[status(thm)],[43,7,theory(equality)]) ).
cnf(151,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),U)),Z)),inverse(multiply(inverse(U),U))))))),
inference('PARAMODULATE',[status(thm)],[44,44,theory(equality)]) ).
cnf(212,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(inverse(Y),Y)))) = inverse(multiply(inverse(multiply(inverse(multiply(U,Y)),multiply(U,inverse(inverse(multiply(V,inverse(multiply(inverse(multiply(inverse(multiply(X,V)),Z)),inverse(multiply(inverse(V),V)))))))))),inverse(multiply(inverse(Y),Y)))),
inference('PARAMODULATE',[status(thm)],[116,44,theory(equality)]) ).
cnf(359,plain,
multiply(inverse(X),inverse(inverse(multiply(X,inverse(multiply(multiply(inverse(X),X),inverse(multiply(inverse(X),X)))))))) = inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),
inference('PARAMODULATE',[status(thm)],[44,113,theory(equality)]) ).
cnf(377,plain,
multiply(inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),inverse(Z))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))) = Z,
inference('PARAMODULATE',[status(thm)],[42,113,theory(equality)]) ).
cnf(379,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),Z)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))) = Z,
inference('PARAMODULATE',[status(thm)],[43,113,theory(equality)]) ).
cnf(384,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),X)),U)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(multiply(inverse(Z),Z)),inverse(inverse(U))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))))),
inference('PARAMODULATE',[status(thm)],[24,113,theory(equality)]) ).
cnf(389,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))),inverse(multiply(inverse(multiply(inverse(multiply(Z,multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(Z,inverse(U)))),inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,113,theory(equality)]) ).
cnf(522,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),X)),U)),inverse(multiply(inverse(X),X))))))) = inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(multiply(inverse(Z),Z)),inverse(inverse(U))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))))))),
inference('PARAMODULATE',[status(thm)],[31,113,theory(equality)]) ).
cnf(589,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(inverse(multiply(U,V)))))),inverse(multiply(inverse(U),U))))))))),inverse(multiply(inverse(Y),Y))) = multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,W)),multiply(X1,V))),inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[47,43,theory(equality)]) ).
cnf(600,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(V)))),inverse(multiply(inverse(U),U))))))))),inverse(multiply(inverse(Y),Y))) = multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(U,W)),multiply(inverse(multiply(inverse(multiply(X1,Y1)),multiply(X1,inverse(inverse(multiply(Y1,V)))))),inverse(multiply(inverse(Y1),Y1))))),inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[47,47,theory(equality)]) ).
cnf(601,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(V)))),inverse(multiply(inverse(U),U)))))),inverse(multiply(inverse(X),X)))))) = multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(U,W)),multiply(inverse(multiply(inverse(multiply(X1,Y1)),multiply(X1,inverse(inverse(multiply(Y1,V)))))),inverse(multiply(inverse(Y1),Y1))))),inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[3,47,theory(equality)]) ).
cnf(778,plain,
multiply(inverse(multiply(inverse(multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(U)))),inverse(multiply(inverse(Y),Y))))))),multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(U)))),inverse(multiply(inverse(Y),Y))))),V)))))),inverse(multiply(U,multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(U)))),inverse(multiply(inverse(Y),Y)))))))) = inverse(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,W)),multiply(X1,V))),inverse(multiply(inverse(W),W)))))),
inference('PARAMODULATE',[status(thm)],[90,single_axiom,theory(equality)]) ).
cnf(848,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y))))))))) = Z,
inference('PARAMODULATE',[status(thm)],[44,151,theory(equality)]) ).
cnf(962,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),inverse(multiply(inverse(Z),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))))))) = inverse(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X),X),U)),Z)),inverse(multiply(inverse(U),U))))))),
inference('PARAMODULATE',[status(thm)],[151,113,theory(equality)]) ).
cnf(987,plain,
multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y))))),inverse(multiply(inverse(V),inverse(multiply(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,W)),multiply(X1,inverse(U)))),inverse(multiply(inverse(W),W))))),multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y))))))))))))) = inverse(inverse(multiply(Y1,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y))))))),Y1)),V)),inverse(multiply(inverse(Y1),Y1))))))),
inference('PARAMODULATE',[status(thm)],[151,3,theory(equality)]) ).
cnf(1007,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(multiply(inverse(V),V)),inverse(multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(U),U))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(multiply(inverse(V),V)),inverse(multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(U),U))))))))),Z)),inverse(multiply(multiply(inverse(U),U),multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(multiply(inverse(V),V)),inverse(multiply(inverse(inverse(multiply(inverse(U),U))),inverse(multiply(inverse(U),U)))))))))))))),
inference('PARAMODULATE',[status(thm)],[151,113,theory(equality)]) ).
cnf(1018,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[848,7,theory(equality)]) ).
cnf(1019,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(multiply(inverse(Y),Y)))) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[848,113,theory(equality)]) ).
cnf(1036,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,Z)))),multiply(X,inverse(inverse(U))))),inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(multiply(Y,Z))))) = multiply(V,inverse(multiply(inverse(multiply(inverse(multiply(W,V)),multiply(W,inverse(multiply(Y,inverse(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(inverse(Z),Z)))))))))))),inverse(multiply(inverse(V),V))))),
inference('PARAMODULATE',[status(thm)],[47,848,theory(equality)]) ).
cnf(1077,plain,
multiply(inverse(multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y))))))),multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y))))),inverse(multiply(inverse(V),inverse(multiply(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(X1,W)),multiply(X1,inverse(U)))),inverse(multiply(inverse(W),W))))),multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,U))),inverse(multiply(inverse(Y),Y)))))))))))))) = V,
inference('PARAMODULATE',[status(thm)],[848,3,theory(equality)]) ).
cnf(1091,plain,
multiply(X,multiply(Y,Z)) = multiply(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,inverse(X)))),inverse(multiply(inverse(Y),Y)))))),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[1018,single_axiom,theory(equality)]) ).
cnf(1100,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(inverse(multiply(multiply(U,Z),V)))))),inverse(multiply(inverse(multiply(U,Z)),multiply(U,Z))))) = V,
inference('PARAMODULATE',[status(thm)],[43,1018,theory(equality)]) ).
cnf(1101,plain,
inverse(multiply(multiply(X,Y),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,Y))),multiply(inverse(multiply(X,U)),inverse(V)))),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y))))))) = V,
inference('PARAMODULATE',[status(thm)],[single_axiom,1018,theory(equality)]) ).
cnf(1102,plain,
inverse(inverse(multiply(multiply(X,Y),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,Y))),multiply(inverse(multiply(X,U)),V))),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))))))) = V,
inference('PARAMODULATE',[status(thm)],[7,1018,theory(equality)]) ).
cnf(1138,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(multiply(X,U),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,U))),Z)),inverse(multiply(inverse(multiply(X,U)),multiply(X,U)))))))),
inference('PARAMODULATE',[status(thm)],[151,1018,theory(equality)]) ).
cnf(1142,plain,
multiply(X,inverse(inverse(multiply(multiply(Y,Z),inverse(multiply(inverse(U),inverse(multiply(inverse(multiply(V,Z)),multiply(V,Z))))))))) = inverse(inverse(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),W)),U)),inverse(multiply(inverse(W),W))))))),
inference('PARAMODULATE',[status(thm)],[151,1018,theory(equality)]) ).
cnf(1144,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(multiply(Y,Z),X)),U)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,Z))),multiply(inverse(multiply(Y,W)),inverse(inverse(U))))),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[24,1018,theory(equality)]) ).
cnf(1149,plain,
inverse(multiply(multiply(X,Y),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,Y))),V)),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y))))))) = inverse(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,U)),W)),V)),inverse(multiply(inverse(W),W)))))),
inference('PARAMODULATE',[status(thm)],[46,1018,theory(equality)]) ).
cnf(1173,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1019,1019,theory(equality)]) ).
cnf(1174,plain,
multiply(multiply(inverse(X),X),a2) != a2,
inference('PARAMODULATE',[status(thm)],[prove_these_axioms_2,1173,theory(equality)]) ).
cnf(1175,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[1018,1173,theory(equality)]) ).
cnf(1176,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(U),U)),
inference('PARAMODULATE',[status(thm)],[1018,1173,theory(equality)]) ).
cnf(1177,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),X))))))) = X,
inference('PARAMODULATE',[status(thm)],[7,1173,theory(equality)]) ).
cnf(1178,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(X)),inverse(X))))))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,1173,theory(equality)]) ).
cnf(1181,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(U),U)))) = Z,
inference('PARAMODULATE',[status(thm)],[43,1173,theory(equality)]) ).
cnf(1196,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(U),U)))))) = multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[24,1173,theory(equality)]) ).
cnf(1211,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1173,1175,theory(equality)]) ).
cnf(1212,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(inverse(Y),Z)),
inference('PARAMODULATE',[status(thm)],[1175,1175,theory(equality)]) ).
cnf(1213,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(U),U)),
inference('PARAMODULATE',[status(thm)],[1175,1173,theory(equality)]) ).
cnf(1241,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(U),U)),
inference('PARAMODULATE',[status(thm)],[1176,1176,theory(equality)]) ).
cnf(1271,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))))) = X,
inference('PARAMODULATE',[status(thm)],[1177,1173,theory(equality)]) ).
cnf(1318,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(X,Y)),multiply(inverse(U),U)),
inference('PARAMODULATE',[status(thm)],[1241,1271,theory(equality)]) ).
cnf(1319,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[1212,1271,theory(equality)]) ).
cnf(1324,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),inverse(multiply(inverse(U),U))))))) = X,
inference('PARAMODULATE',[status(thm)],[1271,1211,theory(equality)]) ).
cnf(1333,plain,
multiply(inverse(multiply(X,inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))))))),multiply(inverse(U),V)) = multiply(inverse(multiply(W,U)),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[1175,1271,theory(equality)]) ).
cnf(1342,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(U),U)))))))),inverse(multiply(inverse(V),V))))))) = X,
inference('PARAMODULATE',[status(thm)],[1271,1271,theory(equality)]) ).
cnf(1358,plain,
multiply(inverse(multiply(X,inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))))))),multiply(U,V)) = multiply(inverse(multiply(inverse(W),W)),multiply(U,V)),
inference('PARAMODULATE',[status(thm)],[1319,1271,theory(equality)]) ).
cnf(1359,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1318,1178,theory(equality)]) ).
cnf(1360,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z)))))) = X,
inference('PARAMODULATE',[status(thm)],[1178,1173,theory(equality)]) ).
cnf(1366,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),X)),U)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(inverse(multiply(inverse(Z),Z)),inverse(inverse(U))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))),
inference('REWRITE',[status(thm)],[384,1360,theory(equality)]) ).
cnf(1367,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))),X)),U)),inverse(multiply(inverse(X),X))))))) = multiply(multiply(inverse(Z),Z),multiply(inverse(multiply(inverse(Z),Z)),inverse(inverse(U)))),
inference('REWRITE',[status(thm)],[522,1360,theory(equality)]) ).
cnf(1368,plain,
multiply(inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),inverse(Z))))))),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))) = Z,
inference('REWRITE',[status(thm)],[377,1360,theory(equality)]) ).
cnf(1369,plain,
multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),Z))))) = Z,
inference('REWRITE',[status(thm)],[379,1360,theory(equality)]) ).
cnf(1370,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))))) = X,
inference('REWRITE',[status(thm)],[1368,1369,theory(equality)]) ).
cnf(1375,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),Z)))) = inverse(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X),X),U)),Z)),inverse(multiply(inverse(U),U))))))),
inference('REWRITE',[status(thm)],[962,1360,theory(equality)]) ).
cnf(1393,plain,
multiply(X,multiply(Y,inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(Z),Z)),inverse(multiply(inverse(U),U)))))))) = multiply(X,multiply(inverse(V),V)),
inference('PARAMODULATE',[status(thm)],[1359,1271,theory(equality)]) ).
cnf(1407,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1360,1360,theory(equality)]),1360,theory(equality)]) ).
cnf(1408,plain,
inverse(inverse(multiply(X,inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))))))) = X,
inference('REWRITE',[status(thm)],[1324,1407,theory(equality)]) ).
cnf(1412,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),
inference('REWRITE',[status(thm)],[359,1408,theory(equality)]) ).
cnf(1426,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),X)),Z)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(Z))))),multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1366,1412,theory(equality)]) ).
cnf(1427,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),X)),Z)),inverse(multiply(inverse(X),X))))))) = multiply(multiply(inverse(Y),Y),multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(Z)))),
inference('REWRITE',[status(thm)],[1367,1412,theory(equality)]) ).
cnf(1428,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[1370,1412,theory(equality)]) ).
cnf(1437,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(multiply(inverse(multiply(inverse(U),U)),multiply(inverse(U),U)),inverse(multiply(inverse(multiply(multiply(X,Y),Z)),inverse(multiply(multiply(inverse(U),U),multiply(inverse(multiply(inverse(U),U)),multiply(inverse(U),U))))))))),
inference('REWRITE',[status(thm)],[1007,1407,1412,theory(equality)]) ).
cnf(1461,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X)),inverse(multiply(inverse(multiply(inverse(multiply(Y,multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X)))),multiply(Y,inverse(Z)))),inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X)))))))) = Z,
inference('REWRITE',[status(thm)],[389,1412,theory(equality)]) ).
cnf(1472,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(inverse(multiply(multiply(inverse(X),X),Y)))) = multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),inverse(inverse(Y)))),
inference('REWRITE',[status(thm)],[1375,1427,1412,theory(equality)]) ).
cnf(1473,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),X)),Z)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(multiply(multiply(inverse(Y),Y),Z))))),multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1426,1472,theory(equality)]) ).
cnf(1546,plain,
multiply(inverse(inverse(X)),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))) = X,
inference('PARAMODULATE',[status(thm)],[1428,1176,theory(equality)]) ).
cnf(1558,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[1407,1211,theory(equality)]) ).
cnf(1561,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(Z),Y),
inference('PARAMODULATE',[status(thm)],[1407,1176,theory(equality)]) ).
cnf(1586,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(inverse(Y),Y)))) = inverse(multiply(multiply(inverse(inverse(inverse(multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(X,U)),Z)),inverse(multiply(inverse(U),U)))))))),Y),inverse(multiply(inverse(Y),Y)))),
inference('REWRITE',[status(thm)],[212,1561,theory(equality)]) ).
cnf(1645,plain,
inverse(multiply(multiply(inverse(inverse(inverse(multiply(X,Y)))),X),inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[1181,1561,theory(equality)]) ).
cnf(1657,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(U),U)))))) = multiply(multiply(inverse(inverse(inverse(Z))),Y),inverse(multiply(inverse(Y),Y))),
inference('REWRITE',[status(thm)],[1196,1561,theory(equality)]) ).
cnf(1667,plain,
multiply(inverse(X),multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(multiply(multiply(inverse(Y),Y),X))))),multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1473,1561,1428,1657,theory(equality)]) ).
cnf(1718,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(inverse(Y),Y)))) = inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(Z))),X),inverse(multiply(inverse(X),X))))),Y),inverse(multiply(inverse(Y),Y)))),
inference('REWRITE',[status(thm)],[1586,1657,theory(equality)]) ).
cnf(1782,plain,
multiply(multiply(inverse(inverse(inverse(X))),inverse(multiply(Y,Z))),inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(multiply(Y,Z))))) = multiply(U,inverse(multiply(multiply(inverse(inverse(multiply(Y,inverse(inverse(multiply(Z,inverse(multiply(inverse(X),inverse(multiply(inverse(Z),Z)))))))))),U),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[1036,1561,theory(equality)]) ).
cnf(1789,plain,
multiply(X,inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(Y))),Z),inverse(multiply(inverse(Z),Z))))),X),inverse(multiply(inverse(X),X))))) = multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),Y)),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[50,1561,theory(equality)]) ).
cnf(1797,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X)),inverse(multiply(Y,inverse(multiply(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X)))))))) = Y,
inference('REWRITE',[status(thm)],[1461,1546,1561,theory(equality)]) ).
cnf(1802,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(multiply(X,Y),Z))),
inference('REWRITE',[status(thm)],[1437,1797,theory(equality)]) ).
cnf(1807,plain,
multiply(X,multiply(Y,Z)) = multiply(inverse(multiply(U,inverse(multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(inverse(Y),Y)))))),multiply(U,Z)),
inference('REWRITE',[status(thm)],[1091,1561,theory(equality)]) ).
cnf(1854,plain,
multiply(multiply(inverse(inverse(inverse(multiply(X,multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z))))))),X),inverse(multiply(inverse(X),X))) = multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(multiply(inverse(inverse(inverse(multiply(V,Y)))),V),inverse(multiply(inverse(V),V))))),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[600,1561,theory(equality)]) ).
cnf(1876,plain,
inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z)))),X),inverse(multiply(inverse(X),X)))))) = multiply(U,inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(multiply(inverse(inverse(inverse(multiply(V,Y)))),V),inverse(multiply(inverse(V),V))))),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[601,1561,theory(equality)]) ).
cnf(1892,plain,
multiply(multiply(inverse(inverse(inverse(X))),multiply(Y,Z)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(multiply(inverse(Z),U),multiply(inverse(multiply(Y,U)),inverse(inverse(X))))),multiply(inverse(Z),Z)),
inference('REWRITE',[status(thm)],[1144,1657,1561,theory(equality)]) ).
cnf(1896,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(multiply(X,U),multiply(multiply(inverse(U),Y),Z)))),
inference('REWRITE',[status(thm)],[1138,1407,1561,theory(equality)]) ).
cnf(1898,plain,
multiply(X,inverse(inverse(multiply(multiply(Y,Z),U)))) = inverse(multiply(multiply(inverse(inverse(inverse(U))),inverse(multiply(X,multiply(Y,Z)))),inverse(multiply(inverse(inverse(multiply(X,multiply(Y,Z)))),inverse(multiply(X,multiply(Y,Z))))))),
inference('REWRITE',[status(thm)],[1142,1657,1407,1561,theory(equality)]) ).
cnf(1957,plain,
inverse(multiply(multiply(X,Y),multiply(multiply(inverse(Y),Z),multiply(inverse(multiply(X,Z)),inverse(U))))) = U,
inference('REWRITE',[status(thm)],[1101,1407,1561,theory(equality)]) ).
cnf(1958,plain,
inverse(inverse(multiply(multiply(X,Y),multiply(multiply(inverse(Y),Z),multiply(inverse(multiply(X,Z)),U))))) = U,
inference('REWRITE',[status(thm)],[1102,1407,1561,theory(equality)]) ).
cnf(1960,plain,
inverse(multiply(multiply(X,Y),multiply(multiply(inverse(Y),Z),U))) = multiply(multiply(inverse(inverse(inverse(U))),inverse(multiply(X,Z))),inverse(multiply(inverse(inverse(multiply(X,Z))),inverse(multiply(X,Z))))),
inference('REWRITE',[status(thm)],[1149,1657,1407,1561,theory(equality)]) ).
cnf(2000,plain,
multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(multiply(inverse(Z),Y),inverse(multiply(inverse(Y),Y))))),inverse(multiply(inverse(U),inverse(multiply(multiply(V,inverse(multiply(multiply(inverse(inverse(Z)),V),inverse(multiply(inverse(V),V))))),multiply(Y,inverse(multiply(multiply(inverse(Z),Y),inverse(multiply(inverse(Y),Y))))))))))))) = multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(multiply(inverse(Z),Y),inverse(multiply(inverse(Y),Y))))),U)))),
inference('REWRITE',[status(thm)],[987,1898,1657,1561,theory(equality)]) ).
cnf(2003,plain,
multiply(inverse(multiply(X,multiply(Y,inverse(multiply(multiply(inverse(Z),Y),inverse(multiply(inverse(Y),Y))))))),multiply(X,inverse(inverse(multiply(multiply(Y,inverse(multiply(multiply(inverse(Z),Y),inverse(multiply(inverse(Y),Y))))),U))))) = U,
inference('REWRITE',[status(thm)],[1077,2000,1561,theory(equality)]) ).
cnf(2061,plain,
inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(X,Y),Z)))),multiply(X,Y)),multiply(inverse(Y),Y))) = Z,
inference('REWRITE',[status(thm)],[1100,1892,1561,theory(equality)]) ).
cnf(2085,plain,
multiply(multiply(inverse(inverse(inverse(multiply(X,multiply(multiply(inverse(inverse(inverse(multiply(Y,Z)))),Y),inverse(multiply(inverse(Y),Y))))))),X),inverse(multiply(inverse(X),X))) = multiply(U,inverse(multiply(multiply(inverse(Z),U),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[589,1561,theory(equality)]) ).
cnf(2088,plain,
multiply(inverse(X),inverse(multiply(Y,multiply(Z,inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z)))))))) = inverse(multiply(U,inverse(multiply(multiply(inverse(X),U),inverse(multiply(inverse(U),U)))))),
inference('REWRITE',[status(thm)],[778,2003,1561,theory(equality)]) ).
cnf(2207,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z)) = multiply(inverse(multiply(inverse(Z),multiply(inverse(Y),multiply(inverse(U),U)))),multiply(inverse(V),V)),
inference('PARAMODULATE',[status(thm)],[1213,1407,theory(equality)]) ).
cnf(2212,plain,
multiply(inverse(multiply(inverse(X),X)),a2) != a2,
inference('PARAMODULATE',[status(thm)],[1174,1558,theory(equality)]) ).
cnf(2253,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('PARAMODULATE',[status(thm)],[1407,1558,theory(equality)]) ).
cnf(2323,plain,
multiply(multiply(inverse(inverse(inverse(multiply(X,multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z))))))),X),inverse(multiply(inverse(X),X))) = multiply(U,multiply(inverse(multiply(Z,U)),multiply(multiply(inverse(inverse(inverse(multiply(V,Y)))),V),inverse(multiply(inverse(V),V))))),
inference('REWRITE',[status(thm)],[1854,2253,theory(equality)]) ).
cnf(2324,plain,
inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z)))),X),inverse(multiply(inverse(X),X)))))) = multiply(U,multiply(inverse(multiply(Z,U)),multiply(multiply(inverse(inverse(inverse(multiply(V,Y)))),V),inverse(multiply(inverse(V),V))))),
inference('REWRITE',[status(thm)],[1876,2253,theory(equality)]) ).
cnf(2339,plain,
multiply(X,inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(Y))),Z),inverse(multiply(inverse(Z),Z))))),X),inverse(multiply(inverse(X),X))))) = multiply(U,multiply(inverse(multiply(Z,U)),Y)),
inference('REWRITE',[status(thm)],[1789,2253,theory(equality)]) ).
cnf(2350,plain,
multiply(inverse(multiply(X,Y)),Z) = inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(Z))),X),inverse(multiply(inverse(X),X))))),Y),inverse(multiply(inverse(Y),Y)))),
inference('REWRITE',[status(thm)],[1718,2253,theory(equality)]) ).
cnf(2351,plain,
multiply(X,multiply(inverse(multiply(Y,X)),Z)) = multiply(U,multiply(inverse(multiply(Y,U)),Z)),
inference('REWRITE',[status(thm)],[2339,2350,theory(equality)]) ).
cnf(2395,plain,
inverse(inverse(multiply(X,multiply(Y,inverse(multiply(Y,multiply(inverse(Z),Z))))))) = X,
inference('REWRITE',[status(thm)],[1342,2253,theory(equality)]) ).
cnf(2396,plain,
multiply(X,multiply(Y,inverse(multiply(Y,multiply(inverse(Z),Z))))) = multiply(X,multiply(inverse(U),U)),
inference('REWRITE',[status(thm)],[1393,2253,theory(equality)]) ).
cnf(2405,plain,
multiply(inverse(multiply(X,inverse(multiply(X,multiply(inverse(Y),Y))))),multiply(inverse(Z),U)) = multiply(inverse(multiply(V,Z)),multiply(V,U)),
inference('REWRITE',[status(thm)],[1333,2253,theory(equality)]) ).
cnf(2407,plain,
multiply(inverse(multiply(X,inverse(multiply(X,multiply(inverse(Y),Y))))),multiply(Z,U)) = multiply(inverse(multiply(inverse(V),V)),multiply(Z,U)),
inference('REWRITE',[status(thm)],[1358,2253,theory(equality)]) ).
cnf(2427,plain,
multiply(multiply(inverse(inverse(inverse(X))),inverse(multiply(Y,Z))),inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(multiply(Y,Z))))) = multiply(U,inverse(multiply(multiply(inverse(inverse(multiply(Y,inverse(inverse(multiply(Z,X)))))),U),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[1782,2253,theory(equality)]) ).
cnf(2460,plain,
multiply(X,inverse(inverse(multiply(Y,Z)))) = inverse(inverse(multiply(multiply(X,Y),Z))),
inference('REWRITE',[status(thm)],[1802,2253,theory(equality)]) ).
cnf(2467,plain,
multiply(X,inverse(inverse(multiply(Y,Z)))) = inverse(inverse(multiply(multiply(X,U),multiply(multiply(inverse(U),Y),Z)))),
inference('REWRITE',[status(thm)],[1896,2253,theory(equality)]) ).
cnf(2473,plain,
inverse(inverse(multiply(multiply(X,Y),multiply(inverse(multiply(X,Y)),Z)))) = Z,
inference('REWRITE',[status(thm)],[1958,2460,2467,theory(equality)]) ).
cnf(2488,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1359,1558,theory(equality)]) ).
cnf(2546,plain,
multiply(X,multiply(inverse(multiply(Y,X)),Z)) = multiply(inverse(multiply(inverse(Z),multiply(Y,inverse(multiply(inverse(U),U))))),multiply(inverse(V),V)),
inference('PARAMODULATE',[status(thm)],[1213,2351,theory(equality)]) ).
cnf(2564,plain,
multiply(inverse(multiply(X,inverse(inverse(multiply(Y,Z))))),multiply(inverse(U),U)) = inverse(multiply(multiply(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[1428,2460,theory(equality)]) ).
cnf(2565,plain,
multiply(inverse(X),multiply(inverse(Y),Y)) = inverse(multiply(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Y),Y)),X)),
inference('REWRITE',[status(thm)],[1667,2564,theory(equality)]) ).
cnf(2588,plain,
multiply(X,inverse(inverse(multiply(multiply(inverse(multiply(Y,X)),Z),U)))) = multiply(V,multiply(inverse(multiply(Y,V)),inverse(inverse(multiply(Z,U))))),
inference('PARAMODULATE',[status(thm)],[2351,2460,theory(equality)]) ).
cnf(2594,plain,
multiply(X,inverse(inverse(multiply(multiply(inverse(multiply(Y,X)),Z),U)))) = inverse(inverse(multiply(multiply(V,multiply(inverse(multiply(Y,V)),Z)),U))),
inference('PARAMODULATE',[status(thm)],[2460,2351,theory(equality)]) ).
cnf(2605,plain,
multiply(inverse(inverse(inverse(multiply(multiply(X,Y),Z)))),multiply(X,U)) = inverse(multiply(multiply(inverse(U),Y),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1176,2460,theory(equality)]),2564,theory(equality)]) ).
cnf(2622,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[2061,1407,2605,theory(equality)]) ).
cnf(2632,plain,
multiply(inverse(X),multiply(inverse(Y),Y)) = inverse(X),
inference('REWRITE',[status(thm)],[2565,2622,theory(equality)]) ).
cnf(2645,plain,
multiply(X,multiply(inverse(multiply(Y,X)),Z)) = inverse(multiply(inverse(Z),multiply(Y,inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[2546,2632,theory(equality)]) ).
cnf(2652,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z)) = inverse(multiply(inverse(Z),inverse(Y))),
inference('REWRITE',[status(thm)],[2207,2632,theory(equality)]) ).
cnf(2668,plain,
multiply(inverse(multiply(X,inverse(multiply(X,multiply(inverse(Y),Y))))),multiply(Z,U)) = inverse(multiply(inverse(U),inverse(Z))),
inference('REWRITE',[status(thm)],[2407,2652,theory(equality)]) ).
cnf(2669,plain,
inverse(multiply(inverse(X),inverse(inverse(Y)))) = multiply(inverse(multiply(Z,Y)),multiply(Z,X)),
inference('REWRITE',[status(thm)],[2405,2668,theory(equality)]) ).
cnf(2689,plain,
multiply(X,multiply(Y,Z)) = inverse(multiply(inverse(Z),inverse(inverse(inverse(multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(inverse(Y),Y)))))))),
inference('REWRITE',[status(thm)],[1807,2669,theory(equality)]) ).
cnf(2691,plain,
multiply(inverse(X),inverse(inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z))))),inverse(inverse(inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z)))))))))) = inverse(multiply(U,inverse(multiply(multiply(inverse(X),U),inverse(multiply(inverse(U),U)))))),
inference('REWRITE',[status(thm)],[2088,2689,theory(equality)]) ).
cnf(2772,plain,
inverse(inverse(multiply(inverse(X),inverse(inverse(Y))))) = multiply(inverse(X),Y),
inference('REWRITE',[status(thm)],[1561,2669,theory(equality)]) ).
cnf(2773,plain,
inverse(X) = inverse(multiply(Y,inverse(multiply(multiply(inverse(X),Y),inverse(multiply(inverse(Y),Y)))))),
inference('REWRITE',[status(thm)],[2691,2632,2772,theory(equality)]) ).
cnf(2775,plain,
inverse(multiply(multiply(inverse(inverse(X)),Y),inverse(multiply(inverse(Y),Y)))) = multiply(Z,multiply(inverse(multiply(Y,Z)),multiply(multiply(inverse(inverse(inverse(multiply(U,X)))),U),inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[2324,2773,theory(equality)]) ).
cnf(2777,plain,
multiply(multiply(inverse(inverse(inverse(multiply(X,multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z))))))),X),inverse(multiply(inverse(X),X))) = inverse(multiply(multiply(inverse(inverse(Y)),Z),inverse(multiply(inverse(Z),Z)))),
inference('REWRITE',[status(thm)],[2323,2775,theory(equality)]) ).
cnf(2778,plain,
X = multiply(Y,inverse(multiply(multiply(inverse(X),Y),inverse(multiply(inverse(Y),Y))))),
inference('REWRITE',[status(thm)],[2085,1645,2777,theory(equality)]) ).
cnf(2779,plain,
multiply(multiply(inverse(inverse(inverse(X))),inverse(multiply(Y,Z))),inverse(multiply(inverse(inverse(multiply(Y,Z))),inverse(multiply(Y,Z))))) = inverse(multiply(Y,inverse(inverse(multiply(Z,X))))),
inference('REWRITE',[status(thm)],[2427,2778,theory(equality)]) ).
cnf(2795,plain,
inverse(multiply(multiply(X,Y),multiply(multiply(inverse(Y),Z),U))) = inverse(multiply(X,inverse(inverse(multiply(Z,U))))),
inference('REWRITE',[status(thm)],[1960,2779,theory(equality)]) ).
cnf(2796,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[1957,2473,2460,2795,theory(equality)]) ).
cnf(2802,plain,
multiply(X,multiply(Y,inverse(multiply(Y,multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[2395,2796,theory(equality)]) ).
cnf(2803,plain,
X = multiply(X,multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[2396,2802,theory(equality)]) ).
cnf(2812,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[2488,2803,theory(equality)]) ).
cnf(2814,plain,
multiply(X,multiply(inverse(multiply(Y,X)),Z)) = inverse(multiply(inverse(Z),Y)),
inference('REWRITE',[status(thm)],[2645,2812,theory(equality)]) ).
cnf(2832,plain,
multiply(X,multiply(multiply(inverse(multiply(Y,X)),Z),U)) = multiply(inverse(multiply(inverse(Z),Y)),U),
inference('REWRITE',[status(thm)],[2594,2814,2796,theory(equality)]) ).
cnf(2840,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(multiply(X,Z)),Y)),
inference('REWRITE',[status(thm)],[2588,2814,2832,2796,theory(equality)]) ).
cnf(2843,plain,
inverse(multiply(inverse(multiply(X,a2)),X)) != a2,
inference('REWRITE',[status(thm)],[2212,2840,theory(equality)]) ).
cnf(2881,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference('REWRITE',[status(thm)],[1645,2812,2796,theory(equality)]) ).
cnf(2883,plain,
$false,
inference('REWRITE',[status(thm)],[2843,2881,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP416-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 13:21:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47 *
% 0.18/0.47 "."
% 0.18/0.47 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:21:21
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-14T13:21:21
% 3.72/3.92
% 3.72/3.92
% 3.72/3.92 #||
% 3.72/3.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.72/3.92 % SZS output start Refutation
% See solution above
% 3.72/3.95 ||#
% 3.72/3.95
% 3.72/3.95 ; Summary of computation:
% 3.72/3.95 ; 9087 formulas have been input or derived (from 49 formulas).
% 3.72/3.95 ; 2883 (32%) were retained. Of these,
% 3.72/3.95 ; 2816 (98%) were simplified or subsumed later,
% 3.72/3.95 ; 67 ( 2%) are still being kept.
% 3.72/3.95 ;
% 3.72/3.95 ; Run time in seconds excluding printing time:
% 3.72/3.95 ; 0.001 0% Read assertion file (1 call)
% 3.72/3.95 ; 0.000 0% Assert (2 calls)
% 3.72/3.95 ; 0.930 27% Process new row (8,506 calls)
% 3.72/3.95 ; 0.005 0% Resolution (96 calls)
% 3.72/3.95 ; 0.228 7% Paramodulation (48 calls)
% 3.72/3.95 ; 1.237 36% Forward simplification (7,829 calls)
% 3.72/3.95 ; 0.733 21% Backward simplification (2,883 calls)
% 3.72/3.95 ; 0.270 8% Ordering (23,481 calls)
% 3.72/3.95 ; 0.002 0% Sortal reasoning (32 calls)
% 3.72/3.95 ; 0.000 0% Purity testing (1 call)
% 3.72/3.95 ; 0.049 1% Other
% 3.72/3.95 ; 3.455 Total
% 3.72/3.95 ; 3.487 Real time
% 3.72/3.95 ;
% 3.72/3.95 ; Term-hash-array has 14,146 terms in all.
% 3.72/3.95 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 3.72/3.95 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 3.72/3.95 ; Path-index has 260 entries (7,089 at peak, 15,560 added, 15,300 deleted).
% 3.72/3.95 ; Path-index has 30,480 nodes (32,604 at peak, 48,458 added, 17,978 deleted).
% 3.72/3.95 ; Trie-index has 260 entries (7,089 at peak, 15,560 added, 15,300 deleted).
% 3.72/3.95 ; Trie-index has 1,115 nodes (125,449 at peak, 227,883 added, 226,768 deleted).
% 3.72/3.95 ; Retrieved 26,941 generalization terms in 197,175 calls.
% 3.72/3.95 ; Retrieved 16,202 instance terms in 3,286 calls.
% 3.72/3.95 ; Retrieved 58,796 unifiable terms in 777 calls.
% 3.72/3.95 ;
% 3.72/3.95 ; The agenda of backward simplifiable rows to process has 477 entries:
% 3.72/3.95 ; 477 with value 0
% 3.72/3.95 ; The agenda of rows to process has 50 entries:
% 3.72/3.95 ; 10 with value 44 3 with value 47 5 with value 50
% 3.72/3.95 ; 10 with value 45 7 with value 48 5 with value 51
% 3.72/3.95 ; 2 with value 46 6 with value 49 2 with value 52
% 3.72/3.95 ; The agenda of rows to give has 64 entries:
% 3.72/3.95 ; 1 with value (4 16) 5 with value (4 26) 1 with value (4 34)
% 3.72/3.95 ; 1 with value (4 18) 5 with value (4 27) 4 with value (4 35)
% 3.72/3.95 ; 1 with value (4 20) 1 with value (4 28) 1 with value (4 36)
% 3.72/3.95 ; 1 with value (4 22) 4 with value (4 29) 2 with value (4 37)
% 3.72/3.95 ; 7 with value (4 23) 7 with value (4 30) 1 with value (4 38)
% 3.72/3.95 ; 1 with value (4 24) 6 with value (4 31) 1 with value (4 42)
% 3.72/3.95 ; 7 with value (4 25) 6 with value (4 32) 1 with value (4 51)
% 3.72/3.95 Evaluation took:
% 3.72/3.95 3.488 seconds of real time
% 3.72/3.95 3.27262 seconds of user run time
% 3.72/3.95 0.214796 seconds of system run time
% 3.72/3.95 [Run times include 0.625 seconds GC run time.]
% 3.72/3.95 0 calls to %EVAL
% 3.72/3.95 0 page faults and
% 3.72/3.95 271,221,792 bytes consed.
% 3.72/3.95 :PROOF-FOUND
% 3.72/3.95 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:21:25
% 3.72/3.95 :PROOF-FOUND
% 3.72/3.95 *
%------------------------------------------------------------------------------