TSTP Solution File: GRP055-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP055-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:35:44 EDT 2022
% Result : Unsatisfiable 6.14s 6.30s
% Output : Refutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 2
% Syntax : Number of clauses : 181 ( 178 unt; 0 nHn; 5 RR)
% Number of literals : 185 ( 184 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 790 ( 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(3,plain,
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,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,953,theory(equality)]) ).
cnf(955,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[6,953,theory(equality)]) ).
cnf(956,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(957,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(958,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(959,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(960,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(962,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(963,plain,
( multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[954,953,theory(equality)]) ).
cnf(964,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(965,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(966,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(967,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(969,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(970,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(971,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(973,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(1005,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(1020,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[955,955,theory(equality)]) ).
cnf(1021,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[953,1020,theory(equality)]) ).
cnf(1022,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1020,1020,theory(equality)]) ).
cnf(1028,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[956,956,theory(equality)]) ).
cnf(1029,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[1028,1028,theory(equality)]) ).
cnf(1059,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)],[1028,24,theory(equality)]) ).
cnf(1168,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)],[957,953,theory(equality)]) ).
cnf(1402,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[959,959,theory(equality)]) ).
cnf(1433,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[960,953,theory(equality)]) ).
cnf(1434,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[962,962,theory(equality)]) ).
cnf(1451,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)],[957,1434,theory(equality)]) ).
cnf(1680,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)],[1433,1022,theory(equality)]) ).
cnf(1681,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)],[1433,1022,theory(equality)]) ).
cnf(1711,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(inverse(Y)),inverse(multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[964,953,theory(equality)]) ).
cnf(1712,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1028,1711,theory(equality)]) ).
cnf(1749,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)],[24,1711,theory(equality)]) ).
cnf(1984,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)],[965,965,theory(equality)]) ).
cnf(2006,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)],[965,39,theory(equality)]) ).
cnf(2031,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)],[966,1434,theory(equality)]) ).
cnf(2038,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)],[966,1021,theory(equality)]) ).
cnf(2043,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)],[966,966,theory(equality)]) ).
cnf(2053,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)],[966,957,theory(equality)]) ).
cnf(2067,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)],[966,958,theory(equality)]) ).
cnf(2292,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)],[1168,1029,theory(equality)]) ).
cnf(2304,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)],[966,1168,theory(equality)]) ).
cnf(2306,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)],[966,1168,theory(equality)]) ).
cnf(3106,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)],[969,967,theory(equality)]) ).
cnf(3164,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)],[969,24,theory(equality)]) ).
cnf(3268,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)],[970,953,theory(equality)]) ).
cnf(3305,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)],[6,970,theory(equality)]) ).
cnf(3363,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)],[367,970,theory(equality)]) ).
cnf(3364,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)],[123,970,theory(equality)]) ).
cnf(3447,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)],[971,958,theory(equality)]) ).
cnf(3448,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[971,1712,theory(equality)]),3268,theory(equality)]) ).
cnf(3503,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)],[965,971,theory(equality)]) ).
cnf(3516,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)],[38,971,theory(equality)]) ).
cnf(3540,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)],[971,967,theory(equality)]) ).
cnf(3549,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)],[970,971,theory(equality)]) ).
cnf(3588,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[958,3448,theory(equality)]) ).
cnf(3590,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),Y),
inference('PARAMODULATE',[status(thm)],[1402,3448,theory(equality)]) ).
cnf(3599,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[1433,3448,theory(equality)]) ).
cnf(3600,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[2031,3599,theory(equality)]) ).
cnf(3641,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)],[867,3600,theory(equality)]) ).
cnf(3646,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)],[710,3600,theory(equality)]) ).
cnf(3651,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)],[200,3646,theory(equality)]) ).
cnf(3652,plain,
multiply(inverse(multiply(X,Y)),Z) = inverse(multiply(inverse(multiply(U,Z)),multiply(U,multiply(X,Y)))),
inference('REWRITE',[status(thm)],[823,971,3651,theory(equality)]) ).
cnf(3656,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)],[3363,3652,theory(equality)]) ).
cnf(3661,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)],[3305,3652,theory(equality)]) ).
cnf(3666,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)],[1749,3652,theory(equality)]) ).
cnf(3676,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[3549,971,3652,theory(equality)]) ).
cnf(3677,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)],[906,3676,theory(equality)]) ).
cnf(3679,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(inverse(X),X)))))) = Y,
inference('REWRITE',[status(thm)],[8,3677,theory(equality)]) ).
cnf(3680,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))) = multiply(X,Y),
inference('REWRITE',[status(thm)],[3503,971,3652,theory(equality)]) ).
cnf(3735,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)],[2304,3680,theory(equality)]) ).
cnf(3748,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)],[2006,3680,theory(equality)]) ).
cnf(3749,plain,
multiply(inverse(X),multiply(Y,Z)) = inverse(multiply(inverse(multiply(U,multiply(Y,Z))),multiply(U,X))),
inference('REWRITE',[status(thm)],[826,971,3748,theory(equality)]) ).
cnf(3897,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)],[1005,3749,theory(equality)]) ).
cnf(3902,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)],[2043,3897,theory(equality)]) ).
cnf(3912,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)],[3735,3902,theory(equality)]) ).
cnf(3915,plain,
inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[1680,3680,3902,theory(equality)]) ).
cnf(3921,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)],[1681,3902,theory(equality)]) ).
cnf(3932,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Z)) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[3447,3749,3897,theory(equality)]) ).
cnf(3934,plain,
inverse(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))) = X,
inference('REWRITE',[status(thm)],[3921,3932,theory(equality)]) ).
cnf(3945,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(multiply(inverse(U),U)),X)),
inference('REWRITE',[status(thm)],[2292,3934,theory(equality)]) ).
cnf(3946,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = multiply(inverse(Z),Y),
inference('REWRITE',[status(thm)],[2038,3934,theory(equality)]) ).
cnf(3953,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)],[2067,3946,theory(equality)]) ).
cnf(3961,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)],[2306,3946,theory(equality)]) ).
cnf(3976,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)],[2053,3946,theory(equality)]) ).
cnf(3978,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[3599,3946,theory(equality)]) ).
cnf(3979,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)],[879,3978,theory(equality)]) ).
cnf(3980,plain,
inverse(multiply(inverse(X),inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))))) = X,
inference('REWRITE',[status(thm)],[3646,3978,theory(equality)]) ).
cnf(3988,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)],[3666,3978,theory(equality)]) ).
cnf(3991,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[3590,3978,theory(equality)]) ).
cnf(4005,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(Z),multiply(inverse(multiply(U,X)),multiply(U,Y)))),
inference('REWRITE',[status(thm)],[3953,3991,theory(equality)]) ).
cnf(4036,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)],[3106,4005,theory(equality)]) ).
cnf(4052,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)],[3540,4005,theory(equality)]) ).
cnf(4075,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)],[3641,4005,theory(equality)]) ).
cnf(4123,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)],[3961,3991,theory(equality)]) ).
cnf(4124,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(multiply(inverse(U),Y)),multiply(inverse(multiply(X,U)),Z)),
inference('REWRITE',[status(thm)],[3976,4123,theory(equality)]) ).
cnf(4140,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)],[4052,4124,theory(equality)]) ).
cnf(4141,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)],[4036,4124,theory(equality)]) ).
cnf(4146,plain,
multiply(inverse(X),multiply(inverse(Y),Z)) = inverse(multiply(multiply(inverse(Z),Y),X)),
inference('REWRITE',[status(thm)],[3912,3991,theory(equality)]) ).
cnf(4202,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)],[1984,4146,theory(equality)]) ).
cnf(4207,plain,
X = multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,X)),
inference('REWRITE',[status(thm)],[1451,3915,4146,theory(equality)]) ).
cnf(4209,plain,
inverse(X) = multiply(inverse(X),inverse(multiply(inverse(X),X))),
inference('REWRITE',[status(thm)],[973,4207,theory(equality)]) ).
cnf(4259,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)],[728,4209,theory(equality)]) ).
cnf(4260,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))) = Y,
inference('REWRITE',[status(thm)],[3679,4209,theory(equality)]) ).
cnf(4265,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)],[4075,4209,theory(equality)]) ).
cnf(4280,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)],[3656,4146,4265,theory(equality)]) ).
cnf(4281,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)],[3661,4146,4265,theory(equality)]) ).
cnf(4294,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)],[3979,4209,theory(equality)]) ).
cnf(4377,plain,
inverse(inverse(multiply(multiply(inverse(X),X),multiply(Y,Z)))) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[3680,4146,theory(equality)]) ).
cnf(4378,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[4140,4377,theory(equality)]) ).
cnf(4385,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)],[4280,4377,theory(equality)]) ).
cnf(4389,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)],[3988,4385,theory(equality)]) ).
cnf(4392,plain,
multiply(inverse(inverse(X)),Y) = multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Z),Z)))),Y),
inference('REWRITE',[status(thm)],[4281,4377,theory(equality)]) ).
cnf(4409,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)],[969,4146,theory(equality)]) ).
cnf(4417,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)],[4141,4146,theory(equality)]) ).
cnf(4423,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[3945,3991,theory(equality)]) ).
cnf(4439,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)],[1059,4423,theory(equality)]) ).
cnf(4440,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(inverse(multiply(U,Z)),multiply(U,Y))),
inference('REWRITE',[status(thm)],[3164,4439,theory(equality)]) ).
cnf(4449,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)],[3516,4440,theory(equality)]) ).
cnf(4506,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),U)))) = multiply(X,inverse(multiply(inverse(Z),U))),
inference('REWRITE',[status(thm)],[4409,4440,theory(equality)]) ).
cnf(4517,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)],[4417,4506,theory(equality)]) ).
cnf(4526,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X))),
inference('REWRITE',[status(thm)],[4202,4377,4440,4146,4506,theory(equality)]) ).
cnf(4532,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)],[3364,4526,theory(equality)]) ).
cnf(4539,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)],[4449,4526,theory(equality)]) ).
cnf(4543,plain,
inverse(multiply(multiply(inverse(inverse(inverse(X))),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4389,4526,theory(equality)]) ).
cnf(4546,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)],[4294,4526,theory(equality)]) ).
cnf(4555,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)],[4259,4526,theory(equality)]) ).
cnf(4586,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('REWRITE',[status(thm)],[3980,4526,theory(equality)]) ).
cnf(4587,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),X)),Z)) = multiply(inverse(multiply(U,inverse(Y))),multiply(U,Z)),
inference('REWRITE',[status(thm)],[4546,4586,theory(equality)]) ).
cnf(4588,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference('REWRITE',[status(thm)],[4392,4586,theory(equality)]) ).
cnf(4591,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4543,4588,theory(equality)]) ).
cnf(4592,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4378,4588,4591,theory(equality)]) ).
cnf(4594,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(inverse(Z),Y)),
inference('REWRITE',[status(thm)],[4517,4592,theory(equality)]) ).
cnf(4595,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4586,4592,4146,4594,theory(equality)]) ).
cnf(4601,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)],[4539,4592,4146,4594,theory(equality)]) ).
cnf(4603,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(inverse(multiply(Z,multiply(U,inverse(Y)))),multiply(Z,multiply(U,X))),
inference('REWRITE',[status(thm)],[4532,4592,4146,3991,4601,4594,theory(equality)]) ).
cnf(4636,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[3588,4592,theory(equality)]) ).
cnf(4639,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),X)),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[4587,4595,4636,theory(equality)]) ).
cnf(4643,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference('REWRITE',[status(thm)],[4603,4595,4636,theory(equality)]) ).
cnf(4646,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[4260,4643,theory(equality)]) ).
cnf(4678,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[963,4592,theory(equality)]) ).
cnf(4682,plain,
multiply(inverse(X),multiply(multiply(X,Y),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[4555,4595,4636,4639,4588,theory(equality)]) ).
cnf(5186,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4646,4682,theory(equality)]),4595,theory(equality)]) ).
cnf(5187,plain,
$false,
inference('REWRITE',[status(thm)],[4678,5186,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 08:20:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:20:08
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n009.cluster.edu at 2022-06-14T08:20:08
% 6.14/6.30
% 6.14/6.30
% 6.14/6.30 #||
% 6.14/6.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.14/6.30 % SZS output start Refutation
% See solution above
% 6.14/6.38 ||#
% 6.14/6.38
% 6.14/6.38 ; Summary of computation:
% 6.14/6.38 ; 19890 formulas have been input or derived (from 65 formulas).
% 6.14/6.38 ; 5187 (26%) were retained. Of these,
% 6.14/6.38 ; 4673 (90%) were simplified or subsumed later,
% 6.14/6.38 ; 514 (10%) are still being kept.
% 6.14/6.38 ;
% 6.14/6.38 ; Run time in seconds excluding printing time:
% 6.14/6.38 ; 0.001 0% Read assertion file (1 call)
% 6.14/6.38 ; 0.000 0% Assert (2 calls)
% 6.14/6.38 ; 1.024 18% Process new row (19,577 calls)
% 6.14/6.38 ; 0.013 0% Resolution (128 calls)
% 6.14/6.38 ; 0.444 8% Paramodulation (64 calls)
% 6.14/6.38 ; 0.001 0% Condensing (70 calls)
% 6.14/6.38 ; 0.001 0% Forward subsumption (70 calls)
% 6.14/6.38 ; 0.001 0% Backward subsumption (28 calls)
% 6.14/6.38 ; 0.000 0% Clause clause subsumption (192 calls)
% 6.14/6.38 ; 1.986 34% Forward simplification (16,757 calls)
% 6.14/6.38 ; 1.188 20% Backward simplification (5,187 calls)
% 6.14/6.38 ; 1.074 18% Ordering (131,052 calls)
% 6.14/6.38 ; 0.000 0% Sortal reasoning (32 calls)
% 6.14/6.38 ; 0.000 0% Purity testing (1 call)
% 6.14/6.38 ; 0.079 1% Other
% 6.14/6.38 ; 5.812 Total
% 6.14/6.38 ; 5.894 Real time
% 6.14/6.38 ;
% 6.14/6.38 ; Term-hash-array has 20,491 terms in all.
% 6.14/6.38 ; Feature-vector-row-index has 0 entries (22 at peak, 28 added, 28 deleted).
% 6.14/6.38 ; Feature-vector-row-index has 1 node (93 at peak, 165 added, 164 deleted).
% 6.14/6.38 ; Retrieved 239 possibly forward subsuming rows in 70 calls.
% 6.14/6.38 ; Retrieved 28 possibly backward subsumed rows in 28 calls.
% 6.14/6.38 ; Path-index has 2,288 entries (13,515 at peak, 22,270 added, 19,982 deleted).
% 6.14/6.38 ; Path-index has 15,728 nodes (19,113 at peak, 24,326 added, 8,598 deleted).
% 6.14/6.38 ; Trie-index has 2,288 entries (13,515 at peak, 22,270 added, 19,982 deleted).
% 6.14/6.38 ; Trie-index has 12,007 nodes (104,921 at peak, 155,425 added, 143,418 deleted).
% 6.14/6.38 ; Retrieved 173,276 generalization terms in 212,992 calls.
% 6.14/6.38 ; Retrieved 56,125 instance terms in 5,750 calls.
% 6.14/6.38 ; Retrieved 192,973 unifiable terms in 847 calls.
% 6.14/6.38 ;
% 6.14/6.38 ; The agenda of rows to process has 10 entries:
% 6.14/6.38 ; 2 with value 23 1 with value 26 2 with value 28
% 6.14/6.38 ; 1 with value 25 4 with value 27
% 6.14/6.38 ; The agenda of rows to give has 506 entries:
% 6.14/6.38 ; 1 with value (4 20) 19 with value (4 34) 27 with value (4 47)
% 6.14/6.38 ; 2 with value (4 21) 18 with value (4 35) 18 with value (4 48)
% 6.14/6.38 ; 4 with value (4 22) 23 with value (4 36) 12 with value (4 49)
% 6.14/6.38 ; 3 with value (4 23) 21 with value (4 37) 14 with value (4 50)
% 6.14/6.38 ; 3 with value (4 24) 22 with value (4 38) 15 with value (4 51)
% 6.14/6.38 ; 1 with value (4 25) 27 with value (4 39) 4 with value (4 52)
% 6.14/6.38 ; 1 with value (4 26) 29 with value (4 40) 1 with value (4 53)
% 6.14/6.38 ; 4 with value (4 27) 24 with value (4 41) 5 with value (4 54)
% 6.14/6.38 ; 8 with value (4 28) 30 with value (4 42) 1 with value (4 55)
% 6.14/6.38 ; 7 with value (4 29) 24 with value (4 43) 1 with value (4 56)
% 6.14/6.38 ; 6 with value (4 30) 30 with value (4 44) 1 with value (4 57)
% 6.14/6.38 ; 14 with value (4 31) 31 with value (4 45) 1 with value (4 58)
% 6.14/6.38 ; 13 with value (4 32) 26 with value (4 46) 1 with value (4 59)
% 6.14/6.38 ; 14 with value (4 33)
% 6.14/6.38 Evaluation took:
% 6.14/6.38 5.895 seconds of real time
% 6.14/6.38 5.502592 seconds of user run time
% 6.14/6.38 0.392077 seconds of system run time
% 6.14/6.38 [Run times include 0.804 seconds GC run time.]
% 6.14/6.38 0 calls to %EVAL
% 6.14/6.38 0 page faults and
% 6.14/6.38 382,557,472 bytes consed.
% 6.14/6.38 :PROOF-FOUND
% 6.14/6.38 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:20:14
% 6.14/6.38 :PROOF-FOUND
% 6.14/6.38 *
%------------------------------------------------------------------------------