TSTP Solution File: GRP422-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP422-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:38:31 EDT 2022
% Result : Unsatisfiable 4.77s 4.94s
% Output : Refutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 2
% Syntax : Number of clauses : 150 ( 150 unt; 0 nHn; 6 RR)
% Number of literals : 150 ( 149 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 652 ( 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_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(3,plain,
inverse(multiply(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(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(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(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(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(953,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[882,882,theory(equality)]) ).
cnf(954,plain,
multiply(multiply(inverse(X),X),a2) != a2,
inference('PARAMODULATE',[status(thm)],[prove_these_axioms_2,953,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(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(964,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(965,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(966,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(968,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(969,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(970,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(972,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(1004,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(1025,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference('PARAMODULATE',[status(thm)],[955,955,theory(equality)]) ).
cnf(1026,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[953,1025,theory(equality)]) ).
cnf(1028,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[1025,1025,theory(equality)]) ).
cnf(1034,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[956,956,theory(equality)]) ).
cnf(1035,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(U),U))),
inference('PARAMODULATE',[status(thm)],[1034,1034,theory(equality)]) ).
cnf(1065,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)],[1034,24,theory(equality)]) ).
cnf(1188,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(1422,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference('PARAMODULATE',[status(thm)],[959,959,theory(equality)]) ).
cnf(1453,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(1454,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference('PARAMODULATE',[status(thm)],[962,962,theory(equality)]) ).
cnf(1455,plain,
multiply(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))),a2) != a2,
inference('PARAMODULATE',[status(thm)],[954,1454,theory(equality)]) ).
cnf(1474,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)],[957,1454,theory(equality)]) ).
cnf(1563,plain,
multiply(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z))))),inverse(multiply(inverse(U),U))),a2) != a2,
inference('PARAMODULATE',[status(thm)],[1455,1028,theory(equality)]) ).
cnf(1722,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)],[1453,1028,theory(equality)]) ).
cnf(1723,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)],[1453,1028,theory(equality)]) ).
cnf(1752,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(inverse(Y)),inverse(multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[963,953,theory(equality)]) ).
cnf(1753,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(multiply(inverse(Y),Y))),multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[1034,1752,theory(equality)]) ).
cnf(1790,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)],[24,1752,theory(equality)]) ).
cnf(2064,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)],[964,964,theory(equality)]) ).
cnf(2086,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)],[964,39,theory(equality)]) ).
cnf(2113,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)],[965,1454,theory(equality)]) ).
cnf(2120,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)],[965,1026,theory(equality)]) ).
cnf(2125,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)],[965,965,theory(equality)]) ).
cnf(2136,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)],[965,957,theory(equality)]) ).
cnf(2152,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)],[965,958,theory(equality)]) ).
cnf(2189,plain,
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))) = inverse(multiply(inverse(multiply(X1,V)),multiply(X1,W))),
inference('PARAMODULATE',[status(thm)],[965,6,theory(equality)]) ).
cnf(2384,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)],[1188,1035,theory(equality)]) ).
cnf(2396,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)],[965,1188,theory(equality)]) ).
cnf(2398,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)],[965,1188,theory(equality)]) ).
cnf(3276,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)],[968,24,theory(equality)]) ).
cnf(3380,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)],[969,953,theory(equality)]) ).
cnf(3417,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)],[6,969,theory(equality)]) ).
cnf(3475,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)],[367,969,theory(equality)]) ).
cnf(3562,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)],[970,958,theory(equality)]) ).
cnf(3563,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[970,1753,theory(equality)]),3380,theory(equality)]) ).
cnf(3622,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)],[964,970,theory(equality)]) ).
cnf(3658,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)],[970,966,theory(equality)]) ).
cnf(3711,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(inverse(multiply(inverse(Z),Z))),Y),
inference('PARAMODULATE',[status(thm)],[1422,3563,theory(equality)]) ).
cnf(3720,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('PARAMODULATE',[status(thm)],[1453,3563,theory(equality)]) ).
cnf(3721,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(multiply(inverse(Z),Z))))),
inference('REWRITE',[status(thm)],[2113,3720,theory(equality)]) ).
cnf(3762,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)],[867,3721,theory(equality)]) ).
cnf(3767,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)],[710,3721,theory(equality)]) ).
cnf(3772,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)],[200,3767,theory(equality)]) ).
cnf(3773,plain,
multiply(inverse(multiply(X,Y)),Z) = inverse(multiply(inverse(multiply(U,Z)),multiply(U,multiply(X,Y)))),
inference('REWRITE',[status(thm)],[823,970,3772,theory(equality)]) ).
cnf(3777,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)],[3475,3773,theory(equality)]) ).
cnf(3782,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)],[3417,3773,theory(equality)]) ).
cnf(3787,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)],[1790,3773,theory(equality)]) ).
cnf(3801,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(Z),Z))) = multiply(X,Y),
inference('REWRITE',[status(thm)],[3622,970,3773,theory(equality)]) ).
cnf(3860,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)],[2396,3801,theory(equality)]) ).
cnf(3873,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)],[2086,3801,theory(equality)]) ).
cnf(3874,plain,
multiply(inverse(X),multiply(Y,Z)) = inverse(multiply(inverse(multiply(U,multiply(Y,Z))),multiply(U,X))),
inference('REWRITE',[status(thm)],[826,970,3873,theory(equality)]) ).
cnf(4023,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)],[1004,3874,theory(equality)]) ).
cnf(4028,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)],[2125,4023,theory(equality)]) ).
cnf(4038,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)],[3860,4028,theory(equality)]) ).
cnf(4041,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),a2) != a2,
inference('REWRITE',[status(thm)],[1563,3801,4028,theory(equality)]) ).
cnf(4043,plain,
inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = Y,
inference('REWRITE',[status(thm)],[1722,3801,4028,theory(equality)]) ).
cnf(4049,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)],[1723,4028,theory(equality)]) ).
cnf(4060,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Z)) = multiply(inverse(Y),Z),
inference('REWRITE',[status(thm)],[3562,3874,4023,theory(equality)]) ).
cnf(4062,plain,
inverse(multiply(inverse(X),multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))) = X,
inference('REWRITE',[status(thm)],[4049,4060,theory(equality)]) ).
cnf(4073,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(multiply(inverse(U),U)),X)),
inference('REWRITE',[status(thm)],[2384,4062,theory(equality)]) ).
cnf(4074,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = multiply(inverse(Z),Y),
inference('REWRITE',[status(thm)],[2120,4062,theory(equality)]) ).
cnf(4081,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)],[2152,4074,theory(equality)]) ).
cnf(4089,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)],[2398,4074,theory(equality)]) ).
cnf(4104,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)],[2136,4074,theory(equality)]) ).
cnf(4106,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = Y,
inference('REWRITE',[status(thm)],[3720,4074,theory(equality)]) ).
cnf(4108,plain,
inverse(multiply(inverse(X),inverse(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z)))))) = X,
inference('REWRITE',[status(thm)],[3767,4106,theory(equality)]) ).
cnf(4116,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)],[3787,4106,theory(equality)]) ).
cnf(4119,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[3711,4106,theory(equality)]) ).
cnf(4133,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = inverse(multiply(inverse(Z),multiply(inverse(multiply(U,X)),multiply(U,Y)))),
inference('REWRITE',[status(thm)],[4081,4119,theory(equality)]) ).
cnf(4173,plain,
inverse(multiply(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(multiply(Z,X)),multiply(Z,Y))),multiply(inverse(U),V))) = inverse(multiply(inverse(multiply(W,U)),multiply(W,V))),
inference('REWRITE',[status(thm)],[2189,4133,theory(equality)]) ).
cnf(4181,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)],[3658,4133,theory(equality)]) ).
cnf(4204,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)],[3762,4133,theory(equality)]) ).
cnf(4252,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)],[4089,4119,theory(equality)]) ).
cnf(4253,plain,
multiply(inverse(multiply(X,Y)),Z) = multiply(inverse(multiply(inverse(U),Y)),multiply(inverse(multiply(X,U)),Z)),
inference('REWRITE',[status(thm)],[4104,4252,theory(equality)]) ).
cnf(4262,plain,
inverse(multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),multiply(inverse(Z),U))) = inverse(multiply(inverse(multiply(V,Z)),multiply(V,U))),
inference('REWRITE',[status(thm)],[4173,4253,theory(equality)]) ).
cnf(4269,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)],[4181,4253,theory(equality)]) ).
cnf(4275,plain,
multiply(inverse(X),multiply(inverse(Y),Z)) = inverse(multiply(multiply(inverse(Z),Y),X)),
inference('REWRITE',[status(thm)],[4038,4119,theory(equality)]) ).
cnf(4333,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)],[2064,4275,theory(equality)]) ).
cnf(4338,plain,
X = multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,X)),
inference('REWRITE',[status(thm)],[1474,4043,4275,theory(equality)]) ).
cnf(4340,plain,
inverse(X) = multiply(inverse(X),inverse(multiply(inverse(X),X))),
inference('REWRITE',[status(thm)],[972,4338,theory(equality)]) ).
cnf(4396,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)],[4204,4340,theory(equality)]) ).
cnf(4411,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)],[3777,4275,4396,theory(equality)]) ).
cnf(4412,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)],[3782,4275,4396,theory(equality)]) ).
cnf(4508,plain,
inverse(inverse(multiply(multiply(inverse(X),X),multiply(Y,Z)))) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[3801,4275,theory(equality)]) ).
cnf(4509,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('REWRITE',[status(thm)],[4269,4508,theory(equality)]) ).
cnf(4516,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)],[4411,4508,theory(equality)]) ).
cnf(4520,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)],[4116,4516,theory(equality)]) ).
cnf(4523,plain,
multiply(inverse(inverse(X)),Y) = multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(Z),Z)))),Y),
inference('REWRITE',[status(thm)],[4412,4508,theory(equality)]) ).
cnf(4540,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)],[968,4275,theory(equality)]) ).
cnf(4554,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[4073,4119,theory(equality)]) ).
cnf(4570,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)],[1065,4554,theory(equality)]) ).
cnf(4571,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(X,multiply(inverse(multiply(U,Z)),multiply(U,Y))),
inference('REWRITE',[status(thm)],[3276,4570,theory(equality)]) ).
cnf(4637,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Y),multiply(inverse(Z),U)))) = multiply(X,inverse(multiply(inverse(Z),U))),
inference('REWRITE',[status(thm)],[4540,4571,theory(equality)]) ).
cnf(4657,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,X))),
inference('REWRITE',[status(thm)],[4333,4508,4571,4275,4637,theory(equality)]) ).
cnf(4674,plain,
inverse(multiply(multiply(inverse(inverse(inverse(X))),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4520,4657,theory(equality)]) ).
cnf(4715,plain,
inverse(multiply(multiply(inverse(multiply(X,Y)),multiply(X,Y)),multiply(inverse(Z),U))) = multiply(inverse(U),Z),
inference('REWRITE',[status(thm)],[4262,4657,theory(equality)]) ).
cnf(4717,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference('REWRITE',[status(thm)],[4108,4657,theory(equality)]) ).
cnf(4719,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference('REWRITE',[status(thm)],[4523,4717,theory(equality)]) ).
cnf(4722,plain,
inverse(multiply(multiply(inverse(X),Y),multiply(inverse(Y),Z))) = multiply(inverse(Z),X),
inference('REWRITE',[status(thm)],[4674,4719,theory(equality)]) ).
cnf(4723,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4509,4719,4722,theory(equality)]) ).
cnf(4754,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference('REWRITE',[status(thm)],[4715,4723,theory(equality)]) ).
cnf(4767,plain,
$false,
inference('REWRITE',[status(thm)],[4041,4754,4723,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP422-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 21:24:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T21:24:10
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-13T21:24:10
% 4.77/4.94
% 4.77/4.94
% 4.77/4.94 #||
% 4.77/4.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.77/4.94 % SZS output start Refutation
% See solution above
% 4.82/5.00 ||#
% 4.82/5.00
% 4.82/5.00 ; Summary of computation:
% 4.82/5.00 ; 20398 formulas have been input or derived (from 61 formulas).
% 4.82/5.00 ; 4767 (23%) were retained. Of these,
% 4.82/5.00 ; 4669 (98%) were simplified or subsumed later,
% 4.82/5.00 ; 98 ( 2%) are still being kept.
% 4.82/5.00 ;
% 4.82/5.00 ; Run time in seconds excluding printing time:
% 4.82/5.00 ; 0.000 0% Read assertion file (1 call)
% 4.82/5.00 ; 0.000 0% Assert (2 calls)
% 4.82/5.00 ; 0.885 20% Process new row (16,846 calls)
% 4.82/5.00 ; 0.011 0% Resolution (120 calls)
% 4.82/5.00 ; 0.465 10% Paramodulation (60 calls)
% 4.82/5.00 ; 1.533 34% Forward simplification (14,344 calls)
% 4.82/5.00 ; 1.127 25% Backward simplification (4,767 calls)
% 4.82/5.00 ; 0.368 8% Ordering (37,609 calls)
% 4.82/5.00 ; 0.001 0% Sortal reasoning (32 calls)
% 4.82/5.00 ; 0.000 0% Purity testing (1 call)
% 4.82/5.00 ; 0.087 2% Other
% 4.82/5.00 ; 4.477 Total
% 4.82/5.00 ; 4.538 Real time
% 4.82/5.00 ;
% 4.82/5.00 ; Term-hash-array has 18,906 terms in all.
% 4.82/5.00 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 4.82/5.00 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 4.82/5.00 ; Path-index has 680 entries (13,747 at peak, 20,169 added, 19,489 deleted).
% 4.82/5.00 ; Path-index has 15,640 nodes (19,956 at peak, 24,207 added, 8,567 deleted).
% 4.82/5.00 ; Trie-index has 680 entries (13,747 at peak, 20,169 added, 19,489 deleted).
% 4.82/5.00 ; Trie-index has 2,759 nodes (107,877 at peak, 146,347 added, 143,588 deleted).
% 4.82/5.00 ; Retrieved 68,679 generalization terms in 142,515 calls.
% 4.82/5.00 ; Retrieved 49,159 instance terms in 4,960 calls.
% 4.82/5.00 ; Retrieved 192,083 unifiable terms in 812 calls.
% 4.82/5.00 ;
% 4.82/5.00 ; The agenda of backward simplifiable rows to process has 2891 entries:
% 4.82/5.00 ; 2891 with value 0
% 4.82/5.00 ; The agenda of rows to process has 344 entries:
% 4.82/5.00 ; 23 with value 36 37 with value 43 4 with value 50
% 4.82/5.00 ; 25 with value 37 18 with value 44 7 with value 51
% 4.82/5.00 ; 28 with value 38 24 with value 45 7 with value 52
% 4.82/5.00 ; 20 with value 39 28 with value 46 4 with value 53
% 4.82/5.00 ; 21 with value 40 10 with value 47 4 with value 54
% 4.82/5.00 ; 17 with value 41 8 with value 48 2 with value 55
% 4.82/5.00 ; 38 with value 42 19 with value 49
% 4.82/5.00 ; The agenda of rows to give has 94 entries:
% 4.82/5.00 ; 1 with value (4 16) 5 with value (4 35) 4 with value (4 45)
% 4.82/5.00 ; 1 with value (4 18) 7 with value (4 36) 3 with value (4 46)
% 4.82/5.00 ; 1 with value (4 21) 3 with value (4 37) 5 with value (4 47)
% 4.82/5.00 ; 2 with value (4 23) 1 with value (4 38) 4 with value (4 48)
% 4.82/5.00 ; 2 with value (4 24) 1 with value (4 39) 3 with value (4 49)
% 4.82/5.00 ; 4 with value (4 28) 3 with value (4 40) 3 with value (4 50)
% 4.82/5.00 ; 1 with value (4 29) 5 with value (4 41) 1 with value (4 51)
% 4.82/5.00 ; 5 with value (4 30) 7 with value (4 42) 3 with value (4 52)
% 4.82/5.00 ; 1 with value (4 31) 3 with value (4 43) 1 with value (4 53)
% 4.82/5.00 ; 3 with value (4 32) 3 with value (4 44) 2 with value (4 55)
% 4.82/5.00 ; 6 with value (4 33)
% 4.82/5.00 Evaluation took:
% 4.82/5.00 4.539 seconds of real time
% 4.82/5.00 4.2611 seconds of user run time
% 4.82/5.00 0.278181 seconds of system run time
% 4.82/5.00 [Run times include 0.671 seconds GC run time.]
% 4.82/5.00 0 calls to %EVAL
% 4.82/5.00 0 page faults and
% 4.82/5.00 303,268,600 bytes consed.
% 4.82/5.00 :PROOF-FOUND
% 4.82/5.00 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T21:24:15
% 4.82/5.00 :PROOF-FOUND
% 4.82/5.00 *
%------------------------------------------------------------------------------