TSTP Solution File: GRP504-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  * 
%------------------------------------------------------------------------------