TSTP Solution File: GRP420-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP420-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:38:27 EDT 2022
% Result : Unsatisfiable 19.95s 20.31s
% Output : Refutation 20.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 2
% Syntax : Number of clauses : 171 ( 171 unt; 0 nHn; 2 RR)
% Number of literals : 171 ( 170 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 21 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 684 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(3,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V)),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(4,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)),inverse(multiply(U,multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)))))))))),multiply(X,multiply(inverse(multiply(Z,inverse(multiply(inverse(U),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(15,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(Y),inverse(multiply(multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)),inverse(multiply(W,multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)))))))))),multiply(U,multiply(inverse(multiply(V,inverse(multiply(inverse(W),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(V,X1)))),
inference('PARAMODULATE',[status(thm)],[3,single_axiom,theory(equality)]) ).
cnf(19,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(U)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y) = U,
inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]) ).
cnf(20,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(U),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(24,plain,
multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = multiply(inverse(multiply(U,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(U,V)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,3,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(90,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(multiply(U,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(Y),inverse(multiply(multiply(U,V),inverse(multiply(inverse(multiply(U,V)),multiply(U,V)))))))),
inference('PARAMODULATE',[status(thm)],[single_axiom,20,theory(equality)]) ).
cnf(163,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z))),
inference('PARAMODULATE',[status(thm)],[90,90,theory(equality)]) ).
cnf(164,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[19,90,theory(equality)]) ).
cnf(165,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))) = Y,
inference('PARAMODULATE',[status(thm)],[20,90,theory(equality)]) ).
cnf(265,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)],[163,163,theory(equality)]) ).
cnf(270,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)],[5,163,theory(equality)]),5,theory(equality)]) ).
cnf(292,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)],[270,270,theory(equality)]) ).
cnf(293,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)],[270,270,theory(equality)]) ).
cnf(294,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)],[163,270,theory(equality)]) ).
cnf(309,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(Z,U))))),inverse(multiply(multiply(Z,U),inverse(multiply(inverse(multiply(V,U)),multiply(V,U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,163,theory(equality)]) ).
cnf(327,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))))))),inverse(multiply(inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V))),inverse(multiply(U,inverse(multiply(inverse(multiply(Z,inverse(multiply(U,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(Z,V)))))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,6,theory(equality)]) ).
cnf(330,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))) = inverse(inverse(multiply(inverse(multiply(U,Y)),multiply(U,Z)))),
inference('PARAMODULATE',[status(thm)],[6,165,theory(equality)]) ).
cnf(335,plain,
multiply(inverse(inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),U)))),inverse(multiply(U,inverse(multiply(inverse(U),U))))) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[164,165,theory(equality)]) ).
cnf(344,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))),multiply(inverse(multiply(U,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),W)))),inverse(multiply(W,inverse(multiply(inverse(W),W)))))) = multiply(U,V),
inference('PARAMODULATE',[status(thm)],[165,24,theory(equality)]) ).
cnf(464,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)],[292,293,theory(equality)]) ).
cnf(572,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U)))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U)))),
inference('PARAMODULATE',[status(thm)],[163,464,theory(equality)]) ).
cnf(589,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U)))),multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(W,V)),X1))) = multiply(inverse(multiply(Y1,multiply(Z1,multiply(W,U)))),multiply(Y1,multiply(Z1,X1))),
inference('PARAMODULATE',[status(thm)],[464,292,theory(equality)]) ).
cnf(628,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1))) = multiply(inverse(multiply(Y1,multiply(Z1,multiply(V,W)))),multiply(Y1,multiply(Z1,X1))),
inference('PARAMODULATE',[status(thm)],[464,24,theory(equality)]) ).
cnf(744,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1)))) = inverse(multiply(inverse(multiply(Y1,multiply(Z1,multiply(V,W)))),multiply(Y1,multiply(Z1,X1)))),
inference('PARAMODULATE',[status(thm)],[572,24,theory(equality)]) ).
cnf(844,plain,
multiply(multiply(X,Y),inverse(multiply(inverse(multiply(X,Y)),multiply(X,Y)))) = multiply(multiply(X,Y),inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[164,309,theory(equality)]),335,theory(equality)]) ).
cnf(905,plain,
multiply(X,inverse(multiply(inverse(X),X))) = multiply(X,inverse(multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,multiply(Z,U))))),
inference('PARAMODULATE',[status(thm)],[844,5,theory(equality)]) ).
cnf(907,plain,
multiply(X,inverse(multiply(inverse(X),X))) = multiply(X,inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[905,5,theory(equality)]) ).
cnf(908,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[907,907,theory(equality)]) ).
cnf(909,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[5,908,theory(equality)]) ).
cnf(910,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[165,908,theory(equality)]) ).
cnf(911,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U))))) = Y,
inference('PARAMODULATE',[status(thm)],[164,908,theory(equality)]) ).
cnf(950,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[908,909,theory(equality)]) ).
cnf(1066,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,908,theory(equality)]),911,theory(equality)]) ).
cnf(1072,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(inverse(multiply(inverse(V),V)))))))))) = U,
inference('PARAMODULATE',[status(thm)],[910,950,theory(equality)]) ).
cnf(1110,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[330,1066,theory(equality)]) ).
cnf(1111,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1066,1066,theory(equality)]) ).
cnf(1112,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[270,1066,theory(equality)]) ).
cnf(1114,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1066,theory(equality)]) ).
cnf(1116,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)],[163,1066,theory(equality)]) ).
cnf(1123,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)))),inverse(multiply(Z,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1066,theory(equality)]) ).
cnf(1147,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[1110,1110,theory(equality)]) ).
cnf(1198,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,1111,theory(equality)]),1123,theory(equality)]) ).
cnf(1253,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1198,1066,theory(equality)]) ).
cnf(1254,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[950,1198,theory(equality)]) ).
cnf(1255,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(multiply(inverse(Y),Y))),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[908,1198,theory(equality)]) ).
cnf(1256,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,X)),
inference('PARAMODULATE',[status(thm)],[270,1198,theory(equality)]) ).
cnf(1274,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y)))),
inference('PARAMODULATE',[status(thm)],[265,1198,theory(equality)]) ).
cnf(1276,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(X,multiply(inverse(U),U)))) = inverse(multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y)))),
inference('PARAMODULATE',[status(thm)],[572,1198,theory(equality)]) ).
cnf(1355,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1253,theory(equality)]) ).
cnf(1427,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[910,1254,theory(equality)]),1123,theory(equality)]) ).
cnf(1474,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1254,theory(equality)]) ).
cnf(1504,plain,
multiply(inverse(X),X) = inverse(inverse(multiply(inverse(Y),Y))),
inference('PARAMODULATE',[status(thm)],[1427,1427,theory(equality)]) ).
cnf(1507,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[908,1427,theory(equality)]) ).
cnf(1510,plain,
multiply(inverse(X),X) = multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1254,1427,theory(equality)]) ).
cnf(1512,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1253,1427,theory(equality)]) ).
cnf(1516,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference('PARAMODULATE',[status(thm)],[1253,1427,theory(equality)]) ).
cnf(1519,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),inverse(inverse(multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[1254,1427,theory(equality)]) ).
cnf(1571,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(multiply(inverse(Z),Z))))),inverse(multiply(X,inverse(multiply(inverse(U),U)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1427,theory(equality)]) ).
cnf(1635,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1427,1504,theory(equality)]) ).
cnf(1636,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1504,1427,theory(equality)]) ).
cnf(1637,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1253,1504,theory(equality)]) ).
cnf(1638,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(inverse(inverse(multiply(inverse(Y),Y))))),
inference('PARAMODULATE',[status(thm)],[1147,1504,theory(equality)]) ).
cnf(1639,plain,
multiply(inverse(X),X) = inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[1427,1504,theory(equality)]) ).
cnf(1640,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))) = inverse(inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1504,1504,theory(equality)]) ).
cnf(1928,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1507,1507,theory(equality)]) ).
cnf(2323,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)],[1112,1112,theory(equality)]) ).
cnf(2379,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),U)) = multiply(inverse(multiply(Z,inverse(multiply(inverse(V),V)))),multiply(inverse(multiply(Y,inverse(multiply(inverse(W),W)))),U)),
inference('PARAMODULATE',[status(thm)],[1112,950,theory(equality)]) ).
cnf(2848,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(multiply(inverse(W),W),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1510,theory(equality)]) ).
cnf(3351,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(W),W))),multiply(U,Z))),multiply(inverse(X1),X1))),
inference('PARAMODULATE',[status(thm)],[265,1255,theory(equality)]) ).
cnf(4300,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(inverse(multiply(inverse(U),U))),multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[1256,1427,theory(equality)]) ).
cnf(4401,plain,
multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(inverse(multiply(inverse(V),V))),inverse(multiply(X,inverse(multiply(inverse(W),W))))))),
inference('PARAMODULATE',[status(thm)],[1256,1114,theory(equality)]) ).
cnf(4498,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,multiply(V,W)))),multiply(inverse(multiply(inverse(multiply(V,X1)),U)),multiply(inverse(multiply(Y1,X1)),multiply(Y1,W))))) = multiply(inverse(multiply(Z1,Y)),multiply(Z1,X)),
inference('PARAMODULATE',[status(thm)],[1256,294,theory(equality)]) ).
cnf(4942,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(V),V))),multiply(inverse(U),Z))),multiply(inverse(W),W)),
inference('PARAMODULATE',[status(thm)],[464,1516,theory(equality)]) ).
cnf(5595,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z))))),inverse(inverse(multiply(inverse(U),U))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1635,theory(equality)]) ).
cnf(6424,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(V),V)))),
inference('PARAMODULATE',[status(thm)],[1116,1928,theory(equality)]) ).
cnf(6461,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = inverse(multiply(inverse(multiply(V,multiply(inverse(U),Z))),multiply(V,multiply(inverse(W),W)))),
inference('PARAMODULATE',[status(thm)],[1116,1256,theory(equality)]) ).
cnf(6590,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(U))))) = inverse(multiply(inverse(multiply(V,U)),multiply(V,inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[1116,950,theory(equality)]) ).
cnf(6601,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(U),V)),Y)),multiply(inverse(multiply(W,V)),multiply(W,U)))),
inference('PARAMODULATE',[status(thm)],[1116,1256,theory(equality)]) ).
cnf(6880,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = inverse(multiply(inverse(multiply(V,multiply(inverse(Y),Z))),multiply(V,inverse(inverse(multiply(inverse(W),W)))))),
inference('PARAMODULATE',[status(thm)],[265,1519,theory(equality)]) ).
cnf(7526,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(V),V)),Z)),inverse(inverse(multiply(inverse(W),W))))),
inference('PARAMODULATE',[status(thm)],[294,1637,theory(equality)]) ).
cnf(7527,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V)))))) = Y,
inference('PARAMODULATE',[status(thm)],[910,1637,theory(equality)]) ).
cnf(7546,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(W),W)),multiply(U,Z))),inverse(inverse(multiply(inverse(X1),X1))))),
inference('PARAMODULATE',[status(thm)],[265,1637,theory(equality)]) ).
cnf(8449,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = inverse(multiply(inverse(multiply(multiply(inverse(W),W),multiply(U,Z))),inverse(inverse(multiply(inverse(X1),X1))))),
inference('PARAMODULATE',[status(thm)],[265,1640,theory(equality)]) ).
cnf(9561,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z)) = multiply(inverse(multiply(inverse(U),U)),multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[2323,910,theory(equality)]) ).
cnf(9980,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[9561,911,theory(equality)]) ).
cnf(9982,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1066,theory(equality)]) ).
cnf(10003,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))))),inverse(multiply(inverse(U),U))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1510,theory(equality)]) ).
cnf(10004,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))))),multiply(inverse(U),U)) = Y,
inference('PARAMODULATE',[status(thm)],[911,1639,theory(equality)]) ).
cnf(10017,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z))))))),multiply(inverse(U),U)) = Y,
inference('PARAMODULATE',[status(thm)],[911,1427,theory(equality)]) ).
cnf(10019,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,908,theory(equality)]) ).
cnf(10031,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,inverse(U))),multiply(Z,inverse(inverse(multiply(inverse(V),V))))))))) = U,
inference('PARAMODULATE',[status(thm)],[950,911,theory(equality)]) ).
cnf(10129,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),inverse(multiply(inverse(Z),Z))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1512,theory(equality)]) ).
cnf(10131,plain,
multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(multiply(inverse(U),U),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1636,theory(equality)]) ).
cnf(10161,plain,
multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))))),inverse(multiply(inverse(multiply(inverse(U),U)),inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,1640,theory(equality)]) ).
cnf(10320,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[9980,1427,theory(equality)]) ).
cnf(10384,plain,
multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),multiply(inverse(multiply(inverse(Z),Z)),U)))),inverse(multiply(U,inverse(multiply(inverse(V),V))))) = Y,
inference('PARAMODULATE',[status(thm)],[911,9980,theory(equality)]) ).
cnf(10543,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[9982,1427,theory(equality)]) ).
cnf(10546,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(U))))) = U,
inference('PARAMODULATE',[status(thm)],[9982,950,theory(equality)]) ).
cnf(10669,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(inverse(inverse(multiply(inverse(U),U))))))))) = Y,
inference('PARAMODULATE',[status(thm)],[9982,1638,theory(equality)]) ).
cnf(10872,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[10543,1504,theory(equality)]) ).
cnf(10873,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[10320,10543,theory(equality)]) ).
cnf(10878,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = multiply(inverse(U),Z),
inference('PARAMODULATE',[status(thm)],[10543,1256,theory(equality)]) ).
cnf(10879,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[10546,10878,theory(equality)]) ).
cnf(10881,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(inverse(Z),Z))) = Y,
inference('REWRITE',[status(thm)],[10003,10879,theory(equality)]) ).
cnf(10882,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[10004,10881,theory(equality)]) ).
cnf(10884,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[10017,10882,theory(equality)]) ).
cnf(10885,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(inverse(Z)))) = Z,
inference('REWRITE',[status(thm)],[10031,10884,theory(equality)]) ).
cnf(10886,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(inverse(Z),Z)))))) = Y,
inference('REWRITE',[status(thm)],[1072,10885,theory(equality)]) ).
cnf(10888,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(U),U))) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[6880,10886,theory(equality)]) ).
cnf(10889,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(multiply(Z,multiply(U,Y))),multiply(Z,multiply(U,X)))),
inference('REWRITE',[status(thm)],[1274,10888,theory(equality)]) ).
cnf(10918,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1)))) = multiply(inverse(X1),multiply(V,W)),
inference('REWRITE',[status(thm)],[744,10889,theory(equality)]) ).
cnf(10993,plain,
inverse(multiply(inverse(multiply(X,multiply(inverse(Y),Z))),multiply(X,multiply(inverse(U),U)))) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[1276,10889,theory(equality)]) ).
cnf(10994,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(Y,Z)),multiply(Y,U)))) = multiply(inverse(U),Z),
inference('REWRITE',[status(thm)],[6461,10993,theory(equality)]) ).
cnf(10995,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[6590,10879,10994,theory(equality)]) ).
cnf(10996,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[10019,10995,theory(equality)]) ).
cnf(10997,plain,
multiply(inverse(multiply(multiply(inverse(X),X),inverse(Y))),inverse(inverse(multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[10161,10996,theory(equality)]) ).
cnf(10998,plain,
multiply(inverse(inverse(X)),inverse(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[10131,10997,theory(equality)]) ).
cnf(11002,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),inverse(multiply(inverse(Z),Z))) = Y,
inference('REWRITE',[status(thm)],[10129,10998,theory(equality)]) ).
cnf(11006,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),Y)),inverse(inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[7527,10998,theory(equality)]) ).
cnf(11007,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),multiply(inverse(V),V)))) = multiply(U,Z),
inference('REWRITE',[status(thm)],[7546,11006,theory(equality)]) ).
cnf(11008,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z),Z)),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[1355,11007,theory(equality)]) ).
cnf(11009,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),inverse(multiply(inverse(V),V))))) = multiply(U,Z),
inference('REWRITE',[status(thm)],[1474,11008,theory(equality)]) ).
cnf(11013,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[2848,11009,theory(equality)]) ).
cnf(11014,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),multiply(X,Y))),multiply(inverse(U),U))),
inference('REWRITE',[status(thm)],[3351,11009,theory(equality)]) ).
cnf(11017,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(multiply(inverse(Z),Z),multiply(X,Y))),inverse(inverse(multiply(inverse(U),U))))),
inference('REWRITE',[status(thm)],[8449,11009,theory(equality)]) ).
cnf(11019,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,X)))) = Z,
inference('REWRITE',[status(thm)],[7526,11006,theory(equality)]) ).
cnf(11020,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('REWRITE',[status(thm)],[6601,11019,theory(equality)]) ).
cnf(11021,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(Z),Z)))),
inference('REWRITE',[status(thm)],[6424,11020,theory(equality)]) ).
cnf(11046,plain,
inverse(multiply(inverse(X),inverse(inverse(multiply(inverse(Y),Y))))) = X,
inference('REWRITE',[status(thm)],[5595,11021,theory(equality)]) ).
cnf(11047,plain,
multiply(X,Y) = multiply(multiply(inverse(Z),Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[11017,11046,theory(equality)]) ).
cnf(11048,plain,
multiply(X,Y) = inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))),
inference('REWRITE',[status(thm)],[11013,11047,theory(equality)]) ).
cnf(11049,plain,
multiply(X,Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),multiply(X,Y)),
inference('REWRITE',[status(thm)],[11014,11048,theory(equality)]) ).
cnf(11055,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(inverse(U),Z)),multiply(inverse(V),V)),
inference('REWRITE',[status(thm)],[4942,11049,theory(equality)]) ).
cnf(11061,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[4300,11049,theory(equality)]) ).
cnf(11062,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(Z),U),
inference('REWRITE',[status(thm)],[11055,11061,theory(equality)]) ).
cnf(11183,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,inverse(multiply(Z,inverse(multiply(W,inverse(multiply(inverse(W),W)))))))),X1))) = multiply(inverse(multiply(V,W)),X1),
inference('REWRITE',[status(thm)],[628,11062,theory(equality)]) ).
cnf(11184,plain,
inverse(multiply(inverse(multiply(X,Y)),Z)) = multiply(inverse(Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[10918,11183,theory(equality)]) ).
cnf(11451,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))))),inverse(multiply(V,inverse(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,inverse(multiply(V,inverse(multiply(U,inverse(multiply(inverse(U),U))))))))))))))) = Y,
inference('REWRITE',[status(thm)],[327,11184,theory(equality)]) ).
cnf(11526,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))))),multiply(X,inverse(multiply(inverse(V),inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))),inverse(multiply(U,inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(multiply(inverse(U),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))))))))))))))))) = V,
inference('REWRITE',[status(thm)],[4,11184,theory(equality)]) ).
cnf(11539,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))))))) = inverse(multiply(inverse(multiply(U,inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W))))))))))),multiply(U,inverse(multiply(inverse(Z),inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W))))))))),inverse(multiply(X1,inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(inverse(X1),inverse(multiply(W,inverse(multiply(inverse(W),W)))))))))))))))))),
inference('REWRITE',[status(thm)],[15,11184,theory(equality)]) ).
cnf(11560,plain,
inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))))))),multiply(inverse(multiply(U,inverse(multiply(Z,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),W)))),inverse(multiply(W,inverse(multiply(inverse(W),W)))))) = multiply(U,V),
inference('REWRITE',[status(thm)],[344,11184,theory(equality)]) ).
cnf(11592,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,U)))),multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(W,V)),X1))) = multiply(inverse(multiply(W,U)),X1),
inference('REWRITE',[status(thm)],[589,11062,theory(equality)]) ).
cnf(11593,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[4498,11061,11592,theory(equality)]) ).
cnf(11601,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(inverse(Y))) = Y,
inference('REWRITE',[status(thm)],[10885,11593,theory(equality)]) ).
cnf(11602,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[10669,11046,11601,theory(equality)]) ).
cnf(11603,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[11601,11602,theory(equality)]) ).
cnf(11611,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),inverse(multiply(inverse(Z),Z))),inverse(multiply(X,inverse(multiply(inverse(U),U)))))) = Y,
inference('REWRITE',[status(thm)],[1571,11603,theory(equality)]) ).
cnf(11630,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(Y))),multiply(inverse(multiply(inverse(Z),Z)),U)),inverse(multiply(U,inverse(multiply(inverse(V),V))))) = Y,
inference('REWRITE',[status(thm)],[10384,11603,theory(equality)]) ).
cnf(11653,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[11602,11603,theory(equality)]) ).
cnf(11654,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[10872,11653,theory(equality)]) ).
cnf(11655,plain,
X = multiply(inverse(multiply(inverse(Y),Y)),X),
inference('REWRITE',[status(thm)],[10873,11654,theory(equality)]) ).
cnf(11658,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[11002,11603,11655,theory(equality)]) ).
cnf(11661,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[11611,11603,11184,11658,theory(equality)]) ).
cnf(11663,plain,
X = multiply(X,multiply(inverse(Y),Y)),
inference('REWRITE',[status(thm)],[1507,11658,theory(equality)]) ).
cnf(11664,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[11061,11663,theory(equality)]) ).
cnf(11671,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(Y),multiply(inverse(X),Z)),
inference('REWRITE',[status(thm)],[2379,11663,11664,11655,theory(equality)]) ).
cnf(11678,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[11630,11663,11603,11653,11664,11655,theory(equality)]) ).
cnf(11687,plain,
multiply(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))),inverse(multiply(inverse(Z),inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X))))),inverse(multiply(Y,inverse(multiply(inverse(X),inverse(multiply(inverse(Y),inverse(X)))))))))))) = Z,
inference('REWRITE',[status(thm)],[11526,11603,11661,11664,11593,theory(equality)]) ).
cnf(11692,plain,
inverse(multiply(multiply(multiply(inverse(X),inverse(multiply(Y,inverse(X)))),multiply(inverse(multiply(Z,inverse(multiply(Y,inverse(U))))),V)),inverse(V))) = multiply(Z,U),
inference('REWRITE',[status(thm)],[11560,11603,11661,11664,11593,theory(equality)]) ).
cnf(11694,plain,
multiply(multiply(X,multiply(inverse(Y),inverse(multiply(Z,inverse(Y))))),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,inverse(Y)))),inverse(multiply(Z,multiply(inverse(Y),inverse(multiply(Z,inverse(Y))))))))) = X,
inference('REWRITE',[status(thm)],[11451,11603,11661,11664,11593,theory(equality)]) ).
cnf(11701,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(X)))) = inverse(Y),
inference('REWRITE',[status(thm)],[11539,11687,11603,11661,11664,11593,theory(equality)]) ).
cnf(11702,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[11694,11603,11701,theory(equality)]) ).
cnf(11706,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(Z)))),Y) = multiply(X,Z),
inference('REWRITE',[status(thm)],[11692,11603,11678,11671,11701,theory(equality)]) ).
cnf(11710,plain,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
inference('REWRITE',[status(thm)],[4401,11653,11664,11663,11593,theory(equality)]) ).
cnf(12055,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11702,11706,theory(equality)]),11603,11710,theory(equality)]) ).
cnf(12056,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_3,12055,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP420-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.09 % Command : run-snark %s %d
% 0.09/0.28 % Computer : n013.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 14 03:35:59 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.37 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 *
% 0.13/0.37 *
% 0.13/0.38 #<PACKAGE "SNARK-USER">
% 0.13/0.38 *
% 0.13/0.38 SNARK-TPTP-OPTIONS
% 0.13/0.38 *
% 0.13/0.38 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.13/0.38 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.13/0.38 (USE-FACTORING :POS)
% 0.13/0.38 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.13/0.38 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.13/0.38 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.13/0.38 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.13/0.38 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.13/0.38 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.13/0.38 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.13/0.38 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.13/0.38 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.13/0.38 (DECLARE-TPTP-SYMBOLS2))
% 0.13/0.38 *
% 0.13/0.38 "."
% 0.13/0.38 *
% 0.13/0.38 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T03:35:59
% 0.13/0.38 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-14T03:35:59
% 19.95/20.31
% 19.95/20.31
% 19.95/20.31 #||
% 19.95/20.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.95/20.31 % SZS output start Refutation
% See solution above
% 20.04/20.40 ||#
% 20.04/20.40
% 20.04/20.40 ; Summary of computation:
% 20.04/20.40 ; 42457 formulas have been input or derived (from 97 formulas).
% 20.04/20.40 ; 12056 (28%) were retained. Of these,
% 20.04/20.40 ; 11819 (98%) were simplified or subsumed later,
% 20.04/20.40 ; 237 ( 2%) are still being kept.
% 20.04/20.40 ;
% 20.04/20.40 ; Run time in seconds excluding printing time:
% 20.04/20.40 ; 0.001 0% Read assertion file (1 call)
% 20.04/20.40 ; 0.000 0% Assert (2 calls)
% 20.04/20.40 ; 4.396 22% Process new row (41,920 calls)
% 20.04/20.40 ; 0.047 0% Resolution (192 calls)
% 20.04/20.40 ; 1.417 7% Paramodulation (96 calls)
% 20.04/20.40 ; 6.636 34% Forward simplification (39,583 calls)
% 20.04/20.40 ; 4.907 25% Backward simplification (12,056 calls)
% 20.04/20.40 ; 2.093 11% Ordering (235,655 calls)
% 20.04/20.40 ; 0.000 0% Sortal reasoning (32 calls)
% 20.04/20.40 ; 0.000 0% Purity testing (1 call)
% 20.04/20.40 ; 0.265 1% Other
% 20.04/20.40 ; 19.762 Total
% 20.04/20.40 ; 20.021 Real time
% 20.04/20.40 ;
% 20.04/20.40 ; Term-hash-array has 30,820 terms in all.
% 20.04/20.40 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 20.04/20.40 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 20.04/20.40 ; Path-index has 992 entries (23,721 at peak, 31,975 added, 30,983 deleted).
% 20.04/20.40 ; Path-index has 46,049 nodes (55,898 at peak, 69,226 added, 23,177 deleted).
% 20.04/20.40 ; Trie-index has 992 entries (23,721 at peak, 31,975 added, 30,983 deleted).
% 20.04/20.40 ; Trie-index has 4,997 nodes (234,192 at peak, 361,006 added, 356,009 deleted).
% 20.04/20.40 ; Retrieved 280,942 generalization terms in 527,647 calls.
% 20.04/20.40 ; Retrieved 64,441 instance terms in 12,372 calls.
% 20.04/20.40 ; Retrieved 267,262 unifiable terms in 1,278 calls.
% 20.04/20.40 ;
% 20.04/20.40 ; The agenda of backward simplifiable rows to process has 2 entries:
% 20.04/20.40 ; 2 with value 0
% 20.04/20.40 ; The agenda of rows to process has 19 entries:
% 20.04/20.40 ; 1 with value 26 2 with value 31 1 with value 34
% 20.04/20.40 ; 3 with value 28 3 with value 32 2 with value 35
% 20.04/20.40 ; 1 with value 29 2 with value 33 4 with value 36
% 20.04/20.40 ; The agenda of rows to give has 229 entries:
% 20.04/20.40 ; 1 with value (4 21) 7 with value (4 33) 13 with value (4 42)
% 20.04/20.40 ; 1 with value (4 25) 6 with value (4 34) 10 with value (4 43)
% 20.04/20.40 ; 6 with value (4 26) 12 with value (4 35) 8 with value (4 44)
% 20.04/20.40 ; 1 with value (4 27) 17 with value (4 36) 10 with value (4 45)
% 20.04/20.40 ; 7 with value (4 28) 15 with value (4 37) 8 with value (4 46)
% 20.04/20.40 ; 9 with value (4 29) 16 with value (4 38) 10 with value (4 47)
% 20.04/20.40 ; 4 with value (4 30) 12 with value (4 39) 6 with value (4 49)
% 20.04/20.40 ; 4 with value (4 31) 21 with value (4 40) 2 with value (4 50)
% 20.04/20.40 ; 7 with value (4 32) 14 with value (4 41) 2 with value (4 52)
% 20.04/20.40 Evaluation took:
% 20.04/20.40 20.024 seconds of real time
% 20.04/20.40 18.400223 seconds of user run time
% 20.04/20.40 1.453009 seconds of system run time
% 20.04/20.40 [Run times include 4.225 seconds GC run time.]
% 20.04/20.40 0 calls to %EVAL
% 20.04/20.40 0 page faults and
% 20.04/20.40 667,767,008 bytes consed.
% 20.04/20.40 :PROOF-FOUND
% 20.04/20.40 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T03:36:19
% 20.04/20.40 :PROOF-FOUND
% 20.04/20.40 *
%------------------------------------------------------------------------------