TSTP Solution File: GRP504-1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP504-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:39:11 EDT 2022
% Result : Unsatisfiable 2.68s 2.85s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 3
% Syntax : Number of clauses : 174 ( 174 unt; 0 nHn; 3 RR)
% Number of literals : 174 ( 173 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 681 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X,inverse(double_divide(Y,Z))),double_divide(inverse(Y),inverse(double_divide(U,double_divide(X,U))))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
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(4,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[prove_these_axioms_3,multiply,theory(equality)]) ).
cnf(5,plain,
double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(Z,inverse(double_divide(U,Y)))),inverse(double_divide(V,double_divide(X,V))))) = double_divide(inverse(U),inverse(double_divide(W,double_divide(Z,W)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(7,plain,
double_divide(inverse(X),inverse(double_divide(Y,double_divide(Z,Y)))) = double_divide(inverse(X),inverse(double_divide(U,double_divide(Z,U)))),
inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]) ).
cnf(9,plain,
double_divide(double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(Z,inverse(double_divide(U,Y)))),inverse(double_divide(V,double_divide(X,V))))),double_divide(inverse(W),inverse(double_divide(X1,double_divide(inverse(U),X1))))) = double_divide(Z,W),
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(19,plain,
double_divide(X,double_divide(Y,inverse(double_divide(Z,double_divide(U,double_divide(X,U)))))) = double_divide(inverse(Z),inverse(double_divide(V,double_divide(Y,V)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]),9,theory(equality)]) ).
cnf(27,plain,
inverse(double_divide(X,double_divide(Y,X))) = inverse(double_divide(Z,double_divide(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,7,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(37,plain,
double_divide(double_divide(X,inverse(double_divide(Y,double_divide(Z,Y)))),double_divide(inverse(U),inverse(double_divide(V,double_divide(X,V))))) = double_divide(Z,U),
inference('PARAMODULATE',[status(thm)],[single_axiom,27,theory(equality)]) ).
cnf(45,plain,
double_divide(inverse(double_divide(double_divide(X,inverse(double_divide(Y,Z))),X)),inverse(double_divide(U,double_divide(inverse(Y),U)))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,19,theory(equality)]) ).
cnf(46,plain,
double_divide(double_divide(X,inverse(double_divide(Y,Z))),double_divide(U,double_divide(X,inverse(double_divide(Y,double_divide(V,double_divide(U,V))))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,19,theory(equality)]) ).
cnf(76,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(double_divide(double_divide(Y,inverse(double_divide(X,Z))),Y),U))),Z) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,45,theory(equality)]) ).
cnf(106,plain,
double_divide(double_divide(inverse(double_divide(double_divide(X,inverse(double_divide(Y,inverse(Y)))),X)),inverse(double_divide(Z,U))),Z) = U,
inference('PARAMODULATE',[status(thm)],[76,76,theory(equality)]) ).
cnf(112,plain,
inverse(double_divide(X,double_divide(double_divide(inverse(Y),inverse(double_divide(double_divide(double_divide(Z,inverse(double_divide(Y,U))),Z),V))),X))) = inverse(double_divide(U,V)),
inference('PARAMODULATE',[status(thm)],[27,76,theory(equality)]) ).
cnf(127,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),X)))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,76,theory(equality)]),112,theory(equality)]) ).
cnf(134,plain,
double_divide(X,Y) = double_divide(inverse(Z),inverse(double_divide(inverse(double_divide(Z,double_divide(U,double_divide(X,U)))),Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,76,theory(equality)]),112,theory(equality)]) ).
cnf(169,plain,
double_divide(X,double_divide(Y,X)) = double_divide(Z,double_divide(Y,Z)),
inference('PARAMODULATE',[status(thm)],[127,134,theory(equality)]) ).
cnf(170,plain,
double_divide(X,Y) = double_divide(inverse(double_divide(X,Z)),inverse(double_divide(inverse(double_divide(U,double_divide(Z,U))),Y))),
inference('PARAMODULATE',[status(thm)],[134,27,theory(equality)]) ).
cnf(183,plain,
double_divide(X,inverse(double_divide(Y,double_divide(Z,Y)))) = double_divide(X,inverse(double_divide(U,double_divide(Z,U)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[134,7,theory(equality)]),134,theory(equality)]) ).
cnf(185,plain,
double_divide(X,Y) = double_divide(inverse(Z),inverse(double_divide(inverse(double_divide(Z,double_divide(double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,V)),X))),V))),Y))),
inference('PARAMODULATE',[status(thm)],[134,127,theory(equality)]) ).
cnf(206,plain,
double_divide(X,double_divide(Y,X)) = double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U))),
inference('PARAMODULATE',[status(thm)],[169,169,theory(equality)]) ).
cnf(224,plain,
double_divide(X,double_divide(double_divide(Y,Z),X)) = double_divide(double_divide(U,double_divide(Y,U)),double_divide(V,double_divide(Z,V))),
inference('PARAMODULATE',[status(thm)],[169,206,theory(equality)]) ).
cnf(259,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(inverse(Z),Y))),X)) = double_divide(U,double_divide(V,double_divide(inverse(double_divide(double_divide(W,inverse(double_divide(Z,U))),W)),V))),
inference('PARAMODULATE',[status(thm)],[206,45,theory(equality)]) ).
cnf(276,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(Z,Y))),X)) = double_divide(double_divide(double_divide(U,inverse(V)),double_divide(inverse(double_divide(Z,inverse(double_divide(W,V)))),inverse(double_divide(X1,double_divide(U,X1))))),double_divide(Y1,double_divide(inverse(W),Y1))),
inference('PARAMODULATE',[status(thm)],[206,5,theory(equality)]) ).
cnf(360,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,double_divide(double_divide(Z,U),Y))),V))) = double_divide(inverse(double_divide(X,Z)),inverse(double_divide(U,V))),
inference('PARAMODULATE',[status(thm)],[170,170,theory(equality)]) ).
cnf(364,plain,
double_divide(inverse(double_divide(X,Y)),inverse(double_divide(double_divide(X,Y),Z))) = double_divide(inverse(U),inverse(double_divide(U,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[134,170,theory(equality)]),360,theory(equality)]) ).
cnf(376,plain,
double_divide(double_divide(X,Y),Z) = double_divide(inverse(double_divide(U,double_divide(Y,U))),inverse(double_divide(inverse(double_divide(V,double_divide(double_divide(W,double_divide(X,W)),V))),Z))),
inference('PARAMODULATE',[status(thm)],[170,206,theory(equality)]) ).
cnf(527,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(double_divide(U,double_divide(Y,U)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[170,224,theory(equality)]),376,theory(equality)]) ).
cnf(617,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = double_divide(inverse(Z),inverse(double_divide(Z,Y))),
inference('PARAMODULATE',[status(thm)],[364,364,theory(equality)]) ).
cnf(628,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(double_divide(double_divide(inverse(Y),inverse(double_divide(Y,Z))),inverse(X)),U))),Z) = U,
inference('PARAMODULATE',[status(thm)],[76,617,theory(equality)]) ).
cnf(642,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(Z),inverse(double_divide(Z,double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,Y)),X)))))),
inference('PARAMODULATE',[status(thm)],[617,127,theory(equality)]) ).
cnf(644,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(inverse(U),inverse(double_divide(U,Z)))))) = double_divide(X,inverse(double_divide(V,double_divide(inverse(Y),V)))),
inference('PARAMODULATE',[status(thm)],[183,617,theory(equality)]) ).
cnf(690,plain,
double_divide(X,double_divide(Y,double_divide(Z,Y))) = double_divide(X,double_divide(U,double_divide(Z,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,27,theory(equality)]),37,theory(equality)]) ).
cnf(786,plain,
double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,double_divide(U,double_divide(Z,U))))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,134,theory(equality)]),134,theory(equality)]) ).
cnf(859,plain,
double_divide(double_divide(double_divide(X,Y),Z),double_divide(X,double_divide(U,double_divide(Y,U)))) = Z,
inference('PARAMODULATE',[status(thm)],[786,169,theory(equality)]) ).
cnf(860,plain,
double_divide(double_divide(double_divide(double_divide(X,Y),X),Z),double_divide(U,double_divide(Y,U))) = Z,
inference('PARAMODULATE',[status(thm)],[786,206,theory(equality)]) ).
cnf(862,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(U,double_divide(V,double_divide(Z,V))))) = double_divide(Y,U),
inference('PARAMODULATE',[status(thm)],[786,169,theory(equality)]) ).
cnf(870,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(U,double_divide(double_divide(Y,inverse(double_divide(X,Z))),double_divide(V,double_divide(U,V)))),
inference('PARAMODULATE',[status(thm)],[76,786,theory(equality)]) ).
cnf(895,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(Z)),X)) = double_divide(inverse(Y),inverse(double_divide(U,double_divide(Z,U)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[786,single_axiom,theory(equality)]),870,theory(equality)]) ).
cnf(912,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(Y,double_divide(Z,Y)))),double_divide(U,double_divide(V,double_divide(W,double_divide(U,W))))) = double_divide(Z,inverse(double_divide(X,double_divide(X1,double_divide(V,X1))))),
inference('PARAMODULATE',[status(thm)],[786,19,theory(equality)]) ).
cnf(944,plain,
double_divide(X,double_divide(double_divide(Y,Z),X)) = double_divide(Y,double_divide(double_divide(U,Z),U)),
inference('PARAMODULATE',[status(thm)],[224,859,theory(equality)]) ).
cnf(945,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(X,Y),X),Z),U),double_divide(Y,Z)) = U,
inference('PARAMODULATE',[status(thm)],[786,859,theory(equality)]) ).
cnf(946,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(double_divide(X,Y),X),Z),Y),U),Z) = U,
inference('PARAMODULATE',[status(thm)],[859,859,theory(equality)]) ).
cnf(949,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(Y,double_divide(U,double_divide(inverse(double_divide(X,Z)),U))),
inference('PARAMODULATE',[status(thm)],[76,859,theory(equality)]) ).
cnf(951,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(inverse(Z),Y))),X)) = double_divide(double_divide(inverse(double_divide(U,inverse(double_divide(Z,V)))),inverse(V)),U),
inference('REWRITE',[status(thm)],[259,949,theory(equality)]) ).
cnf(955,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,double_divide(U,double_divide(V,U)))) = double_divide(Y,double_divide(Z,V)),
inference('PARAMODULATE',[status(thm)],[859,169,theory(equality)]) ).
cnf(1193,plain,
double_divide(double_divide(X,Y),X) = double_divide(double_divide(Z,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[786,944,theory(equality)]),862,theory(equality)]) ).
cnf(1323,plain,
double_divide(double_divide(double_divide(X,Y),X),double_divide(Z,double_divide(U,Z))) = double_divide(Y,U),
inference('PARAMODULATE',[status(thm)],[860,1193,theory(equality)]) ).
cnf(1324,plain,
double_divide(double_divide(X,double_divide(Y,Z)),X) = double_divide(double_divide(U,double_divide(Y,U)),Z),
inference('PARAMODULATE',[status(thm)],[527,1193,theory(equality)]) ).
cnf(1325,plain,
double_divide(double_divide(X,Y),X) = double_divide(double_divide(double_divide(Z,U),Z),double_divide(Y,U)),
inference('PARAMODULATE',[status(thm)],[1193,1193,theory(equality)]) ).
cnf(1326,plain,
double_divide(double_divide(double_divide(X,Y),X),double_divide(Z,double_divide(U,double_divide(Y,U)))) = Z,
inference('PARAMODULATE',[status(thm)],[859,1193,theory(equality)]) ).
cnf(1343,plain,
double_divide(double_divide(double_divide(double_divide(double_divide(X,double_divide(Y,X)),Z),Y),U),double_divide(double_divide(V,Z),V)) = U,
inference('PARAMODULATE',[status(thm)],[859,1193,theory(equality)]) ).
cnf(1382,plain,
double_divide(double_divide(X,Y),Z) = double_divide(double_divide(double_divide(double_divide(U,X),U),Y),double_divide(double_divide(V,Z),V)),
inference('PARAMODULATE',[status(thm)],[944,945,theory(equality)]) ).
cnf(1446,plain,
double_divide(double_divide(X,Y),double_divide(Z,inverse(double_divide(U,double_divide(X,U))))) = double_divide(inverse(Y),inverse(double_divide(V,double_divide(double_divide(double_divide(W,Z),W),V)))),
inference('PARAMODULATE',[status(thm)],[945,37,theory(equality)]) ).
cnf(1572,plain,
double_divide(double_divide(double_divide(X,Y),X),Z) = double_divide(double_divide(double_divide(U,Y),U),Z),
inference('PARAMODULATE',[status(thm)],[946,1193,theory(equality)]) ).
cnf(1736,plain,
double_divide(X,double_divide(double_divide(double_divide(Y,Z),Y),inverse(double_divide(U,double_divide(V,double_divide(X,V)))))) = double_divide(inverse(U),inverse(double_divide(double_divide(W,double_divide(X1,W)),double_divide(Z,X1)))),
inference('PARAMODULATE',[status(thm)],[19,1323,theory(equality)]) ).
cnf(1767,plain,
double_divide(double_divide(X,double_divide(Y,double_divide(Z,double_divide(U,double_divide(V,double_divide(Z,V)))))),X) = double_divide(Y,U),
inference('PARAMODULATE',[status(thm)],[786,1324,theory(equality)]) ).
cnf(1828,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(double_divide(inverse(double_divide(U,double_divide(V,U))),double_divide(Y,Z)),inverse(double_divide(W,double_divide(V,W)))),
inference('PARAMODULATE',[status(thm)],[183,1324,theory(equality)]) ).
cnf(1845,plain,
double_divide(X,double_divide(Y,inverse(double_divide(Z,X)))) = double_divide(double_divide(U,double_divide(V,U)),double_divide(Y,inverse(double_divide(Z,double_divide(W,double_divide(V,W)))))),
inference('PARAMODULATE',[status(thm)],[1324,46,theory(equality)]) ).
cnf(1895,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(double_divide(Z,double_divide(U,Z))))),X) = double_divide(double_divide(V,double_divide(W,V)),double_divide(U,inverse(double_divide(Y,double_divide(X1,double_divide(W,X1)))))),
inference('PARAMODULATE',[status(thm)],[1324,19,theory(equality)]) ).
cnf(2089,plain,
double_divide(X,double_divide(double_divide(double_divide(Y,Z),Y),inverse(double_divide(U,double_divide(V,double_divide(X,V)))))) = double_divide(inverse(U),inverse(double_divide(double_divide(W,Z),double_divide(double_divide(X1,W),X1)))),
inference('PARAMODULATE',[status(thm)],[19,1325,theory(equality)]) ).
cnf(2221,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(Y,double_divide(Z,Y)))),double_divide(U,double_divide(V,double_divide(W,double_divide(U,W))))) = double_divide(double_divide(inverse(X),inverse(Z)),V),
inference('PARAMODULATE',[status(thm)],[786,895,theory(equality)]) ).
cnf(2223,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(Y,inverse(double_divide(X,double_divide(U,double_divide(Z,U))))),
inference('REWRITE',[status(thm)],[912,2221,theory(equality)]) ).
cnf(2228,plain,
double_divide(double_divide(inverse(X),inverse(Y)),inverse(X)) = inverse(double_divide(Z,double_divide(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[786,895,theory(equality)]),862,theory(equality)]) ).
cnf(2282,plain,
double_divide(X,double_divide(inverse(double_divide(inverse(inverse(Y)),inverse(Y))),inverse(double_divide(inverse(Z),X)))) = inverse(double_divide(U,double_divide(Z,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[127,895,theory(equality)]),360,theory(equality)]) ).
cnf(2315,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(double_divide(Z,double_divide(U,Z))))),X) = double_divide(double_divide(V,double_divide(W,V)),double_divide(double_divide(inverse(Y),inverse(U)),W)),
inference('PARAMODULATE',[status(thm)],[1324,895,theory(equality)]) ).
cnf(2348,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(double_divide(double_divide(Z,U),Z))),X)) = double_divide(inverse(Y),inverse(double_divide(V,double_divide(double_divide(double_divide(W,U),W),V)))),
inference('PARAMODULATE',[status(thm)],[895,1572,theory(equality)]) ).
cnf(2353,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(double_divide(double_divide(Z,U),Z))),X)) = double_divide(inverse(Y),inverse(double_divide(double_divide(V,double_divide(W,V)),double_divide(U,W)))),
inference('PARAMODULATE',[status(thm)],[895,1323,theory(equality)]) ).
cnf(2414,plain,
inverse(double_divide(X,double_divide(Y,X))) = double_divide(double_divide(Z,inverse(Y)),Z),
inference('PARAMODULATE',[status(thm)],[1193,2228,theory(equality)]) ).
cnf(2419,plain,
double_divide(inverse(double_divide(X,double_divide(Y,X))),double_divide(Z,double_divide(U,Z))) = double_divide(inverse(Y),U),
inference('PARAMODULATE',[status(thm)],[1323,2414,theory(equality)]) ).
cnf(2424,plain,
double_divide(double_divide(inverse(double_divide(X,double_divide(Y,X))),Z),double_divide(U,double_divide(inverse(Y),U))) = Z,
inference('PARAMODULATE',[status(thm)],[860,2414,theory(equality)]) ).
cnf(2476,plain,
double_divide(double_divide(X,double_divide(double_divide(Y,inverse(Z)),Y)),double_divide(inverse(U),inverse(double_divide(V,double_divide(X,V))))) = double_divide(Z,U),
inference('PARAMODULATE',[status(thm)],[37,2414,theory(equality)]) ).
cnf(2492,plain,
double_divide(X,double_divide(inverse(double_divide(Y,inverse(Z))),inverse(double_divide(inverse(inverse(double_divide(U,double_divide(Z,U)))),X)))) = Y,
inference('PARAMODULATE',[status(thm)],[127,2414,theory(equality)]) ).
cnf(2548,plain,
double_divide(double_divide(X,inverse(double_divide(Y,inverse(double_divide(Z,double_divide(U,Z)))))),double_divide(inverse(V),inverse(double_divide(W,double_divide(X,W))))) = double_divide(double_divide(Y,inverse(U)),V),
inference('PARAMODULATE',[status(thm)],[37,2414,theory(equality)]) ).
cnf(2793,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X) = double_divide(Z,inverse(double_divide(U,double_divide(Y,U)))),
inference('PARAMODULATE',[status(thm)],[183,2223,theory(equality)]) ).
cnf(2796,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(double_divide(inverse(inverse(double_divide(Z,U))),inverse(inverse(Z))),Y)) = U,
inference('PARAMODULATE',[status(thm)],[127,2223,theory(equality)]) ).
cnf(2803,plain,
double_divide(double_divide(inverse(double_divide(double_divide(X,Y),X)),inverse(Z)),U) = double_divide(Z,inverse(double_divide(Y,U))),
inference('PARAMODULATE',[status(thm)],[2223,1323,theory(equality)]) ).
cnf(2804,plain,
double_divide(double_divide(X,Y),inverse(double_divide(inverse(double_divide(Z,inverse(Z))),X))) = Y,
inference('REWRITE',[status(thm)],[106,2803,theory(equality)]) ).
cnf(2819,plain,
double_divide(inverse(double_divide(double_divide(double_divide(inverse(X),inverse(Y)),Z),Y)),inverse(double_divide(U,double_divide(inverse(X),U)))) = double_divide(V,double_divide(Z,V)),
inference('PARAMODULATE',[status(thm)],[45,2223,theory(equality)]) ).
cnf(2896,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(Y,inverse(double_divide(X,double_divide(double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,V)),Z))),V)))),
inference('PARAMODULATE',[status(thm)],[2223,127,theory(equality)]) ).
cnf(3067,plain,
double_divide(double_divide(X,Y),inverse(double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),X))) = Y,
inference('PARAMODULATE',[status(thm)],[2804,2804,theory(equality)]) ).
cnf(3080,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Y))),Z))) = double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,X)),Z))),
inference('PARAMODULATE',[status(thm)],[2804,127,theory(equality)]) ).
cnf(3094,plain,
double_divide(X,Y) = double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),inverse(double_divide(U,double_divide(double_divide(double_divide(V,double_divide(X,V)),Y),U)))),
inference('PARAMODULATE',[status(thm)],[19,2804,theory(equality)]) ).
cnf(3109,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(X,Y))),inverse(double_divide(inverse(double_divide(Z,inverse(Z))),inverse(U)))) = inverse(double_divide(U,Y)),
inference('PARAMODULATE',[status(thm)],[2804,617,theory(equality)]) ).
cnf(3129,plain,
double_divide(inverse(X),inverse(double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Y))),Z))))) = double_divide(inverse(double_divide(Z,U)),inverse(U)),
inference('PARAMODULATE',[status(thm)],[617,2804,theory(equality)]) ).
cnf(3228,plain,
double_divide(X,Y) = double_divide(inverse(inverse(inverse(double_divide(Z,inverse(Z))))),inverse(double_divide(U,double_divide(double_divide(double_divide(V,double_divide(X,V)),Y),U)))),
inference('PARAMODULATE',[status(thm)],[19,3067,theory(equality)]) ).
cnf(3248,plain,
double_divide(double_divide(inverse(double_divide(X,double_divide(Y,X))),Z),inverse(double_divide(inverse(inverse(double_divide(U,inverse(U)))),inverse(double_divide(V,double_divide(Y,V)))))) = Z,
inference('PARAMODULATE',[status(thm)],[3067,183,theory(equality)]) ).
cnf(3323,plain,
double_divide(X,double_divide(Y,inverse(double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),X)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1326,3067,theory(equality)]),955,theory(equality)]) ).
cnf(3328,plain,
double_divide(double_divide(X,inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),Z)),U))),double_divide(inverse(V),inverse(double_divide(W,double_divide(X,W))))) = double_divide(double_divide(Z,U),V),
inference('PARAMODULATE',[status(thm)],[37,3067,theory(equality)]) ).
cnf(3343,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),inverse(inverse(Z))),X) = double_divide(inverse(U),inverse(double_divide(U,double_divide(Y,Z)))),
inference('PARAMODULATE',[status(thm)],[617,2793,theory(equality)]) ).
cnf(3365,plain,
double_divide(inverse(double_divide(double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X),Z)),inverse(double_divide(U,double_divide(inverse(V),U)))) = double_divide(Y,V),
inference('PARAMODULATE',[status(thm)],[45,2793,theory(equality)]) ).
cnf(3397,plain,
double_divide(double_divide(inverse(double_divide(X,inverse(Y))),inverse(Z)),X) = double_divide(Z,inverse(double_divide(inverse(double_divide(Y,U)),double_divide(inverse(V),inverse(double_divide(V,U)))))),
inference('PARAMODULATE',[status(thm)],[2793,617,theory(equality)]) ).
cnf(3433,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X) = double_divide(Z,inverse(double_divide(double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,V)),Y))),V))),
inference('PARAMODULATE',[status(thm)],[2793,127,theory(equality)]) ).
cnf(3438,plain,
double_divide(X,double_divide(inverse(double_divide(inverse(double_divide(Y,Z)),inverse(U))),inverse(double_divide(inverse(double_divide(U,inverse(double_divide(V,double_divide(Z,V))))),X)))) = Y,
inference('PARAMODULATE',[status(thm)],[127,2793,theory(equality)]) ).
cnf(3519,plain,
double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(Z,Y)),inverse(X))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,2793,theory(equality)]),2548,theory(equality)]) ).
cnf(3635,plain,
double_divide(X,double_divide(Y,double_divide(Z,double_divide(inverse(U),Z)))) = double_divide(inverse(double_divide(X,U)),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[859,3519,theory(equality)]) ).
cnf(3652,plain,
double_divide(X,double_divide(inverse(double_divide(Y,inverse(Z))),inverse(double_divide(inverse(U),X)))) = double_divide(inverse(double_divide(U,Z)),inverse(Y)),
inference('PARAMODULATE',[status(thm)],[127,3519,theory(equality)]) ).
cnf(3654,plain,
double_divide(inverse(double_divide(double_divide(X,inverse(double_divide(Y,double_divide(Z,Y)))),X)),inverse(inverse(double_divide(U,Z)))) = U,
inference('REWRITE',[status(thm)],[3438,3652,theory(equality)]) ).
cnf(3656,plain,
double_divide(inverse(double_divide(inverse(double_divide(X,double_divide(Y,X))),Y)),inverse(Z)) = Z,
inference('REWRITE',[status(thm)],[2492,3652,theory(equality)]) ).
cnf(3657,plain,
double_divide(inverse(double_divide(X,Y)),inverse(inverse(inverse(Y)))) = inverse(double_divide(Z,double_divide(X,Z))),
inference('REWRITE',[status(thm)],[2282,3652,theory(equality)]) ).
cnf(3729,plain,
double_divide(double_divide(X,inverse(Y)),double_divide(inverse(double_divide(Z,inverse(U))),inverse(double_divide(V,double_divide(X,V))))) = double_divide(inverse(double_divide(Y,U)),inverse(Z)),
inference('PARAMODULATE',[status(thm)],[single_axiom,3519,theory(equality)]) ).
cnf(3804,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(Z,Y))),X)) = inverse(Z),
inference('REWRITE',[status(thm)],[276,2424,3729,theory(equality)]) ).
cnf(3832,plain,
inverse(inverse(X)) = double_divide(double_divide(inverse(double_divide(Y,inverse(double_divide(X,Z)))),inverse(Z)),Y),
inference('REWRITE',[status(thm)],[951,3804,theory(equality)]) ).
cnf(3986,plain,
double_divide(double_divide(X,inverse(double_divide(double_divide(inverse(double_divide(Y,Z)),inverse(U)),Y))),double_divide(inverse(V),inverse(double_divide(W,double_divide(X,W))))) = double_divide(double_divide(U,inverse(Z)),V),
inference('PARAMODULATE',[status(thm)],[37,3519,theory(equality)]) ).
cnf(4014,plain,
double_divide(inverse(X),double_divide(Y,double_divide(Z,double_divide(U,double_divide(Y,U))))) = double_divide(inverse(double_divide(V,double_divide(X,V))),Z),
inference('PARAMODULATE',[status(thm)],[786,3804,theory(equality)]) ).
cnf(4020,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(inverse(Z),Y)) = inverse(Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3804,690,theory(equality)]),2419,theory(equality)]) ).
cnf(4051,plain,
double_divide(double_divide(X,inverse(inverse(Y))),double_divide(inverse(Z),inverse(double_divide(U,double_divide(X,U))))) = double_divide(inverse(double_divide(V,double_divide(Y,V))),Z),
inference('PARAMODULATE',[status(thm)],[37,3804,theory(equality)]) ).
cnf(4064,plain,
double_divide(X,double_divide(inverse(double_divide(double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),U))),Z)),X)) = inverse(U),
inference('PARAMODULATE',[status(thm)],[3804,127,theory(equality)]) ).
cnf(4068,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(Z,Y))),inverse(double_divide(U,double_divide(V,double_divide(X,V)))))) = double_divide(inverse(U),inverse(inverse(Z))),
inference('PARAMODULATE',[status(thm)],[19,3804,theory(equality)]) ).
cnf(4090,plain,
double_divide(X,double_divide(inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),Z)),U)),X)) = inverse(double_divide(Z,U)),
inference('PARAMODULATE',[status(thm)],[3804,3067,theory(equality)]) ).
cnf(4145,plain,
double_divide(double_divide(X,Y),X) = double_divide(inverse(double_divide(inverse(Z),Z)),inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1325,4020,theory(equality)]),3635,theory(equality)]) ).
cnf(4155,plain,
double_divide(X,double_divide(inverse(double_divide(Y,double_divide(Z,Y))),inverse(double_divide(inverse(inverse(U)),X)))) = double_divide(inverse(U),Z),
inference('PARAMODULATE',[status(thm)],[127,4020,theory(equality)]) ).
cnf(4176,plain,
double_divide(double_divide(inverse(double_divide(X,double_divide(double_divide(Y,inverse(Z)),X))),inverse(U)),Y) = double_divide(U,inverse(inverse(Z))),
inference('PARAMODULATE',[status(thm)],[2223,4020,theory(equality)]) ).
cnf(4181,plain,
double_divide(double_divide(double_divide(X,double_divide(Y,X)),Z),Y) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[860,4020,theory(equality)]),1382,theory(equality)]) ).
cnf(4184,plain,
double_divide(double_divide(X,Y),double_divide(double_divide(Z,X),Z)) = Y,
inference('REWRITE',[status(thm)],[1343,4181,theory(equality)]) ).
cnf(4185,plain,
double_divide(X,double_divide(double_divide(double_divide(Y,Z),Y),inverse(double_divide(U,double_divide(V,double_divide(X,V)))))) = double_divide(inverse(U),inverse(Z)),
inference('REWRITE',[status(thm)],[2089,4184,theory(equality)]) ).
cnf(4187,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(X),inverse(double_divide(double_divide(Z,double_divide(U,Z)),double_divide(Y,U)))),
inference('REWRITE',[status(thm)],[1736,4185,theory(equality)]) ).
cnf(4188,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(double_divide(double_divide(Z,U),Z))),X)) = double_divide(inverse(Y),inverse(U)),
inference('REWRITE',[status(thm)],[2353,4187,theory(equality)]) ).
cnf(4189,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(X),inverse(double_divide(Z,double_divide(double_divide(double_divide(U,Y),U),Z)))),
inference('REWRITE',[status(thm)],[2348,4188,theory(equality)]) ).
cnf(4195,plain,
double_divide(double_divide(X,Y),double_divide(Z,inverse(double_divide(U,double_divide(X,U))))) = double_divide(inverse(Y),inverse(Z)),
inference('REWRITE',[status(thm)],[1446,4189,theory(equality)]) ).
cnf(4197,plain,
double_divide(inverse(inverse(inverse(X))),inverse(inverse(Y))) = double_divide(inverse(double_divide(Z,double_divide(X,Z))),Y),
inference('REWRITE',[status(thm)],[4051,4195,theory(equality)]) ).
cnf(4199,plain,
double_divide(inverse(double_divide(inverse(inverse(inverse(X))),inverse(inverse(X)))),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[3656,4197,theory(equality)]) ).
cnf(4200,plain,
double_divide(inverse(inverse(double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X))),inverse(inverse(U))) = double_divide(double_divide(Z,inverse(Y)),U),
inference('REWRITE',[status(thm)],[3986,4195,theory(equality)]) ).
cnf(4211,plain,
double_divide(inverse(inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(X,inverse(X)))),Y)),Z))),inverse(inverse(U))) = double_divide(double_divide(Y,Z),U),
inference('REWRITE',[status(thm)],[3328,4195,theory(equality)]) ).
cnf(4225,plain,
double_divide(inverse(double_divide(double_divide(X,inverse(Y)),X)),inverse(inverse(Z))) = double_divide(Y,Z),
inference('REWRITE',[status(thm)],[2476,4195,theory(equality)]) ).
cnf(4226,plain,
double_divide(double_divide(X,double_divide(Y,X)),double_divide(Z,Y)) = Z,
inference('REWRITE',[status(thm)],[3654,4225,theory(equality)]) ).
cnf(4227,plain,
double_divide(inverse(inverse(double_divide(X,Y))),inverse(inverse(X))) = Y,
inference('REWRITE',[status(thm)],[2796,4226,theory(equality)]) ).
cnf(4232,plain,
double_divide(double_divide(X,double_divide(inverse(Y),inverse(double_divide(Z,double_divide(U,Z))))),X) = double_divide(inverse(Y),inverse(U)),
inference('REWRITE',[status(thm)],[2315,4226,theory(equality)]) ).
cnf(4290,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(double_divide(Z,double_divide(U,Z)),double_divide(Y,inverse(double_divide(X,double_divide(V,double_divide(U,V)))))),
inference('REWRITE',[status(thm)],[1895,4232,theory(equality)]) ).
cnf(4291,plain,
double_divide(X,double_divide(Y,inverse(double_divide(Z,X)))) = double_divide(inverse(Z),inverse(Y)),
inference('REWRITE',[status(thm)],[1845,4290,theory(equality)]) ).
cnf(4292,plain,
double_divide(inverse(inverse(inverse(X))),inverse(inverse(double_divide(Y,double_divide(Z,Y))))) = double_divide(inverse(X),Z),
inference('REWRITE',[status(thm)],[4155,4291,theory(equality)]) ).
cnf(4297,plain,
double_divide(inverse(inverse(X)),inverse(inverse(double_divide(Y,inverse(Z))))) = double_divide(inverse(double_divide(X,Z)),inverse(Y)),
inference('REWRITE',[status(thm)],[3652,4291,theory(equality)]) ).
cnf(4300,plain,
double_divide(inverse(inverse(inverse(double_divide(X,inverse(X))))),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[3323,4291,theory(equality)]) ).
cnf(4301,plain,
double_divide(X,Y) = double_divide(Z,double_divide(double_divide(double_divide(U,double_divide(X,U)),Y),Z)),
inference('REWRITE',[status(thm)],[3228,4300,theory(equality)]) ).
cnf(4302,plain,
double_divide(X,Y) = double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),inverse(double_divide(X,Y))),
inference('REWRITE',[status(thm)],[3094,4301,theory(equality)]) ).
cnf(4305,plain,
double_divide(double_divide(inverse(double_divide(X,double_divide(Y,X))),Z),inverse(double_divide(U,double_divide(Y,U)))) = Z,
inference('REWRITE',[status(thm)],[3248,4302,theory(equality)]) ).
cnf(4307,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(Y,Z),
inference('REWRITE',[status(thm)],[1828,4305,theory(equality)]) ).
cnf(4308,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(Z,double_divide(Y,inverse(double_divide(X,double_divide(U,double_divide(Z,U)))))),
inference('REWRITE',[status(thm)],[4290,4307,theory(equality)]) ).
cnf(4310,plain,
double_divide(inverse(X),inverse(inverse(double_divide(Y,double_divide(Z,Y))))) = double_divide(inverse(X),inverse(inverse(Z))),
inference('REWRITE',[status(thm)],[4068,4308,theory(equality)]) ).
cnf(4311,plain,
double_divide(inverse(inverse(inverse(X))),inverse(inverse(Y))) = double_divide(inverse(X),Y),
inference('REWRITE',[status(thm)],[4292,4310,theory(equality)]) ).
cnf(4321,plain,
double_divide(inverse(double_divide(inverse(X),X)),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[4199,4311,theory(equality)]) ).
cnf(4322,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('REWRITE',[status(thm)],[4145,4321,theory(equality)]) ).
cnf(4323,plain,
double_divide(X,double_divide(Y,double_divide(Z,double_divide(U,double_divide(Y,U))))) = double_divide(X,Z),
inference('REWRITE',[status(thm)],[1767,4322,theory(equality)]) ).
cnf(4324,plain,
double_divide(inverse(X),Y) = double_divide(inverse(double_divide(Z,double_divide(X,Z))),Y),
inference('REWRITE',[status(thm)],[4014,4323,theory(equality)]) ).
cnf(4327,plain,
double_divide(double_divide(inverse(double_divide(X,inverse(Y))),inverse(Z)),X) = double_divide(Z,inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[4176,4324,theory(equality)]) ).
cnf(4332,plain,
inverse(inverse(X)) = double_divide(Y,inverse(inverse(double_divide(X,Y)))),
inference('REWRITE',[status(thm)],[3832,4327,theory(equality)]) ).
cnf(4333,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(inverse(U),inverse(double_divide(U,Z)))))),
inference('REWRITE',[status(thm)],[3397,4327,theory(equality)]) ).
cnf(4339,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,inverse(double_divide(Z,double_divide(inverse(Y),Z)))),
inference('REWRITE',[status(thm)],[644,4333,theory(equality)]) ).
cnf(4352,plain,
double_divide(inverse(double_divide(double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X),Z)),inverse(inverse(U))) = double_divide(Y,U),
inference('REWRITE',[status(thm)],[3365,4339,theory(equality)]) ).
cnf(4355,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('REWRITE',[status(thm)],[2819,4227,4297,4339,theory(equality)]) ).
cnf(4358,plain,
inverse(double_divide(inverse(double_divide(inverse(inverse(double_divide(X,inverse(X)))),Y)),Z)) = inverse(double_divide(Y,Z)),
inference('REWRITE',[status(thm)],[4090,4355,theory(equality)]) ).
cnf(4365,plain,
double_divide(inverse(inverse(double_divide(X,Y))),inverse(inverse(Z))) = double_divide(double_divide(X,Y),Z),
inference('REWRITE',[status(thm)],[4211,4358,theory(equality)]) ).
cnf(4369,plain,
double_divide(double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X),U) = double_divide(double_divide(Z,inverse(Y)),U),
inference('REWRITE',[status(thm)],[4200,4365,theory(equality)]) ).
cnf(4371,plain,
double_divide(inverse(inverse(X)),inverse(inverse(Y))) = double_divide(X,Y),
inference('REWRITE',[status(thm)],[4352,4322,4369,theory(equality)]) ).
cnf(4379,plain,
inverse(double_divide(double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),Z))),Y)) = inverse(Z),
inference('REWRITE',[status(thm)],[4064,4355,theory(equality)]) ).
cnf(4380,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X) = double_divide(Z,inverse(Y)),
inference('REWRITE',[status(thm)],[3433,4379,theory(equality)]) ).
cnf(4389,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(Z),inverse(double_divide(Z,double_divide(Y,X)))),
inference('REWRITE',[status(thm)],[3343,4380,theory(equality)]) ).
cnf(4390,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(double_divide(inverse(double_divide(Z,Y)),X),Z),
inference('REWRITE',[status(thm)],[642,4371,4389,theory(equality)]) ).
cnf(4391,plain,
double_divide(inverse(inverse(X)),inverse(Y)) = double_divide(X,inverse(Y)),
inference('REWRITE',[status(thm)],[4380,4390,theory(equality)]) ).
cnf(4395,plain,
double_divide(inverse(double_divide(X,inverse(X))),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[4300,4391,theory(equality)]) ).
cnf(4397,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(X,Y))),inverse(Z)) = inverse(double_divide(Z,Y)),
inference('REWRITE',[status(thm)],[3109,4395,theory(equality)]) ).
cnf(4398,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),Z))),Y) = Z,
inference('REWRITE',[status(thm)],[628,4397,theory(equality)]) ).
cnf(4399,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(Y,inverse(double_divide(X,Z))),
inference('REWRITE',[status(thm)],[2896,4398,theory(equality)]) ).
cnf(4400,plain,
double_divide(X,Y) = double_divide(inverse(Z),inverse(double_divide(inverse(double_divide(Z,X)),Y))),
inference('REWRITE',[status(thm)],[185,4398,theory(equality)]) ).
cnf(4403,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Y))),Z))) = double_divide(X,Z),
inference('REWRITE',[status(thm)],[3080,4400,theory(equality)]) ).
cnf(4404,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = double_divide(inverse(double_divide(Y,Z)),inverse(Z)),
inference('REWRITE',[status(thm)],[3129,4403,theory(equality)]) ).
cnf(4412,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,Y),
inference('REWRITE',[status(thm)],[4371,4391,theory(equality)]) ).
cnf(4417,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4332,4355,4412,theory(equality)]) ).
cnf(4437,plain,
double_divide(inverse(double_divide(X,Y)),inverse(Y)) = inverse(X),
inference('REWRITE',[status(thm)],[3657,4417,4355,theory(equality)]) ).
cnf(4438,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[4404,4437,theory(equality)]) ).
cnf(4439,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[4389,4438,theory(equality)]) ).
cnf(4458,plain,
double_divide(inverse(double_divide(X,Y)),Z) = double_divide(X,inverse(double_divide(Y,Z))),
inference('REWRITE',[status(thm)],[4399,4439,theory(equality)]) ).
cnf(4459,plain,
$false,
inference('REWRITE',[status(thm)],[4,4458,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP504-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.12 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 12:04:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.45 #<PACKAGE "SNARK-USER">
% 0.19/0.45 *
% 0.19/0.45 SNARK-TPTP-OPTIONS
% 0.19/0.45 *
% 0.19/0.45 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.45 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.45 (USE-FACTORING :POS)
% 0.19/0.45 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.45 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.45 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.45 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.45 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.45 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.45 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.45 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.45 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.45 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.45 *
% 0.19/0.45 "."
% 0.19/0.45 *
% 0.19/0.45 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T12:04:22
% 0.19/0.45 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-13T12:04:22
% 2.68/2.85
% 2.68/2.85
% 2.68/2.85 #||
% 2.68/2.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.68/2.85 % SZS output start Refutation
% See solution above
% 2.73/2.90 ||#
% 2.73/2.90
% 2.73/2.90 ; Summary of computation:
% 2.73/2.90 ; 13722 formulas have been input or derived (from 50 formulas).
% 2.73/2.90 ; 4459 (32%) were retained. Of these,
% 2.73/2.90 ; 4424 (99%) were simplified or subsumed later,
% 2.73/2.90 ; 35 ( 1%) are still being kept.
% 2.73/2.90 ;
% 2.73/2.90 ; Run time in seconds excluding printing time:
% 2.73/2.90 ; 0.001 0% Read assertion file (1 call)
% 2.73/2.90 ; 0.000 0% Assert (3 calls)
% 2.73/2.90 ; 0.673 28% Process new row (10,248 calls)
% 2.73/2.90 ; 0.011 0% Resolution (98 calls)
% 2.73/2.90 ; 0.223 9% Paramodulation (49 calls)
% 2.73/2.90 ; 0.668 28% Forward simplification (9,816 calls)
% 2.73/2.90 ; 0.673 28% Backward simplification (4,458 calls)
% 2.73/2.90 ; 0.088 4% Ordering (22,188 calls)
% 2.73/2.90 ; 0.000 0% Sortal reasoning (32 calls)
% 2.73/2.90 ; 0.000 0% Purity testing (1 call)
% 2.73/2.90 ; 0.061 3% Other
% 2.73/2.90 ; 2.398 Total
% 2.73/2.90 ; 2.447 Real time
% 2.73/2.90 ;
% 2.73/2.90 ; Term-hash-array has 17,637 terms in all.
% 2.73/2.90 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.73/2.90 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.73/2.90 ; Path-index has 149 entries (14,187 at peak, 17,935 added, 17,786 deleted).
% 2.73/2.90 ; Path-index has 11,102 nodes (16,310 at peak, 17,931 added, 6,829 deleted).
% 2.73/2.90 ; Trie-index has 149 entries (14,187 at peak, 17,935 added, 17,786 deleted).
% 2.73/2.90 ; Trie-index has 599 nodes (70,500 at peak, 89,455 added, 88,856 deleted).
% 2.73/2.90 ; Retrieved 24,580 generalization terms in 100,033 calls.
% 2.73/2.90 ; Retrieved 31,289 instance terms in 4,596 calls.
% 2.73/2.90 ; Retrieved 120,117 unifiable terms in 504 calls.
% 2.73/2.90 ;
% 2.73/2.90 ; The agenda of backward simplifiable rows to process has 3292 entries:
% 2.73/2.90 ; 3292 with value 0
% 2.73/2.90 ; The agenda of rows to process has 104 entries:
% 2.73/2.90 ; 14 with value 38 8 with value 42 5 with value 46
% 2.73/2.90 ; 24 with value 39 6 with value 43 1 with value 47
% 2.73/2.90 ; 14 with value 40 3 with value 44 1 with value 48
% 2.73/2.90 ; 23 with value 41 5 with value 45
% 2.73/2.90 ; The agenda of rows to give has 33 entries:
% 2.73/2.90 ; 1 with value (4 16) 3 with value (4 26) 3 with value (4 32)
% 2.73/2.90 ; 2 with value (4 18) 5 with value (4 27) 2 with value (4 33)
% 2.73/2.90 ; 1 with value (4 21) 1 with value (4 28) 1 with value (4 35)
% 2.73/2.90 ; 3 with value (4 22) 2 with value (4 29) 1 with value (4 37)
% 2.73/2.90 ; 2 with value (4 23) 1 with value (4 30) 1 with value (4 38)
% 2.73/2.90 ; 2 with value (4 25) 2 with value (4 31)
% 2.73/2.90 Evaluation took:
% 2.73/2.90 2.448 seconds of real time
% 2.73/2.90 2.272034 seconds of user run time
% 2.73/2.90 0.176285 seconds of system run time
% 2.73/2.90 [Run times include 0.411 seconds GC run time.]
% 2.73/2.90 0 calls to %EVAL
% 2.73/2.90 0 page faults and
% 2.73/2.90 190,730,280 bytes consed.
% 2.73/2.90 :PROOF-FOUND
% 2.73/2.90 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T12:04:24
% 2.73/2.90 :PROOF-FOUND
% 2.73/2.90 *
%------------------------------------------------------------------------------