TSTP Solution File: GRP083-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n032.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 11:36:04 EDT 2022
% Result : Unsatisfiable 3.53s 3.70s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 3
% Syntax : Number of clauses : 201 ( 197 unt; 0 nHn; 7 RR)
% Number of literals : 208 ( 207 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 758 ( 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/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(4,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| 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,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(928,plain,
double_divide(double_divide(X,Y),double_divide(double_divide(inverse(Z),inverse(U)),double_divide(X,Z))) = double_divide(inverse(Y),inverse(double_divide(V,double_divide(U,V)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[786,37,theory(equality)]),870,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(2064,plain,
double_divide(double_divide(X,double_divide(Y,inverse(double_divide(Z,U)))),X) = double_divide(double_divide(double_divide(V,double_divide(inverse(Z),inverse(double_divide(W,double_divide(Y,W))))),V),U),
inference('PARAMODULATE',[status(thm)],[1325,single_axiom,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(3079,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Y))),double_divide(Z,X)))) = inverse(double_divide(inverse(double_divide(U,inverse(U))),Z)),
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(3220,plain,
double_divide(X,inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),double_divide(Z,X)))) = inverse(double_divide(inverse(double_divide(U,inverse(U))),Z)),
inference('PARAMODULATE',[status(thm)],[3067,2804,theory(equality)]) ).
cnf(3223,plain,
double_divide(X,inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),double_divide(Z,X)))) = inverse(double_divide(inverse(inverse(double_divide(U,inverse(U)))),Z)),
inference('PARAMODULATE',[status(thm)],[3067,3067,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(3254,plain,
double_divide(double_divide(X,double_divide(Y,inverse(double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),U)))),X) = double_divide(Y,U),
inference('PARAMODULATE',[status(thm)],[1324,3067,theory(equality)]) ).
cnf(3270,plain,
inverse(X) = double_divide(X,inverse(double_divide(double_divide(inverse(inverse(inverse(double_divide(Y,inverse(Y))))),inverse(Z)),inverse(Z)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2223,3067,theory(equality)]),949,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(3425,plain,
double_divide(double_divide(inverse(inverse(double_divide(X,double_divide(Y,X)))),inverse(Z)),double_divide(U,inverse(Y))) = double_divide(Z,inverse(double_divide(V,double_divide(U,V)))),
inference('PARAMODULATE',[status(thm)],[2793,2414,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(3538,plain,
double_divide(double_divide(inverse(X),inverse(Y)),double_divide(Z,X)) = double_divide(Y,inverse(double_divide(U,double_divide(inverse(double_divide(inverse(inverse(double_divide(V,inverse(V)))),Z)),U)))),
inference('PARAMODULATE',[status(thm)],[2793,3067,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(4234,plain,
double_divide(double_divide(X,double_divide(Y,inverse(double_divide(Z,U)))),X) = double_divide(double_divide(inverse(Z),inverse(Y)),U),
inference('REWRITE',[status(thm)],[2064,4232,theory(equality)]) ).
cnf(4252,plain,
double_divide(double_divide(inverse(inverse(inverse(double_divide(X,inverse(X))))),inverse(Y)),Z) = double_divide(Y,Z),
inference('REWRITE',[status(thm)],[3254,4234,theory(equality)]) ).
cnf(4253,plain,
inverse(X) = double_divide(X,inverse(double_divide(Y,inverse(Y)))),
inference('REWRITE',[status(thm)],[3270,4252,theory(equality)]) ).
cnf(4270,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(inverse(a2)) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[4,4253,theory(equality)]) ).
cnf(4291,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(4292,plain,
double_divide(X,double_divide(Y,inverse(double_divide(Z,X)))) = double_divide(inverse(Z),inverse(Y)),
inference('REWRITE',[status(thm)],[1845,4291,theory(equality)]) ).
cnf(4293,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)],[4155,4292,theory(equality)]) ).
cnf(4298,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)],[3652,4292,theory(equality)]) ).
cnf(4301,plain,
double_divide(inverse(inverse(inverse(double_divide(X,inverse(X))))),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[3323,4292,theory(equality)]) ).
cnf(4302,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)],[3228,4301,theory(equality)]) ).
cnf(4303,plain,
double_divide(X,Y) = double_divide(inverse(inverse(double_divide(Z,inverse(Z)))),inverse(double_divide(X,Y))),
inference('REWRITE',[status(thm)],[3094,4302,theory(equality)]) ).
cnf(4306,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)],[3248,4303,theory(equality)]) ).
cnf(4308,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(Y,Z),
inference('REWRITE',[status(thm)],[1828,4306,theory(equality)]) ).
cnf(4309,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)],[4291,4308,theory(equality)]) ).
cnf(4311,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)],[4068,4309,theory(equality)]) ).
cnf(4312,plain,
double_divide(inverse(inverse(inverse(X))),inverse(inverse(Y))) = double_divide(inverse(X),Y),
inference('REWRITE',[status(thm)],[4293,4311,theory(equality)]) ).
cnf(4322,plain,
double_divide(inverse(double_divide(inverse(X),X)),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[4199,4312,theory(equality)]) ).
cnf(4323,plain,
double_divide(double_divide(X,Y),X) = Y,
inference('REWRITE',[status(thm)],[4145,4322,theory(equality)]) ).
cnf(4324,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)],[1767,4323,theory(equality)]) ).
cnf(4325,plain,
double_divide(inverse(X),Y) = double_divide(inverse(double_divide(Z,double_divide(X,Z))),Y),
inference('REWRITE',[status(thm)],[4014,4324,theory(equality)]) ).
cnf(4328,plain,
double_divide(double_divide(inverse(double_divide(X,inverse(Y))),inverse(Z)),X) = double_divide(Z,inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[4176,4325,theory(equality)]) ).
cnf(4333,plain,
inverse(inverse(X)) = double_divide(Y,inverse(inverse(double_divide(X,Y)))),
inference('REWRITE',[status(thm)],[3832,4328,theory(equality)]) ).
cnf(4334,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)],[3397,4328,theory(equality)]) ).
cnf(4340,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,inverse(double_divide(Z,double_divide(inverse(Y),Z)))),
inference('REWRITE',[status(thm)],[644,4334,theory(equality)]) ).
cnf(4344,plain,
double_divide(double_divide(inverse(X),inverse(Y)),double_divide(Z,X)) = double_divide(Y,inverse(inverse(double_divide(inverse(inverse(double_divide(U,inverse(U)))),Z)))),
inference('REWRITE',[status(thm)],[3538,4340,theory(equality)]) ).
cnf(4353,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)],[3365,4340,theory(equality)]) ).
cnf(4356,plain,
X = double_divide(Y,double_divide(X,Y)),
inference('REWRITE',[status(thm)],[2819,4227,4298,4340,theory(equality)]) ).
cnf(4359,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)],[4090,4356,theory(equality)]) ).
cnf(4366,plain,
double_divide(inverse(inverse(double_divide(X,Y))),inverse(inverse(Z))) = double_divide(double_divide(X,Y),Z),
inference('REWRITE',[status(thm)],[4211,4359,theory(equality)]) ).
cnf(4370,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)],[4200,4366,theory(equality)]) ).
cnf(4372,plain,
double_divide(inverse(inverse(X)),inverse(inverse(Y))) = double_divide(X,Y),
inference('REWRITE',[status(thm)],[4353,4323,4370,theory(equality)]) ).
cnf(4380,plain,
inverse(double_divide(double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),Z))),Y)) = inverse(Z),
inference('REWRITE',[status(thm)],[4064,4356,theory(equality)]) ).
cnf(4381,plain,
double_divide(double_divide(inverse(double_divide(X,Y)),inverse(Z)),X) = double_divide(Z,inverse(Y)),
inference('REWRITE',[status(thm)],[3433,4380,theory(equality)]) ).
cnf(4390,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(Z),inverse(double_divide(Z,double_divide(Y,X)))),
inference('REWRITE',[status(thm)],[3343,4381,theory(equality)]) ).
cnf(4391,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(double_divide(inverse(double_divide(Z,Y)),X),Z),
inference('REWRITE',[status(thm)],[642,4372,4390,theory(equality)]) ).
cnf(4392,plain,
double_divide(inverse(inverse(X)),inverse(Y)) = double_divide(X,inverse(Y)),
inference('REWRITE',[status(thm)],[4381,4391,theory(equality)]) ).
cnf(4396,plain,
double_divide(inverse(double_divide(X,inverse(X))),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[4301,4392,theory(equality)]) ).
cnf(4398,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(X,Y))),inverse(Z)) = inverse(double_divide(Z,Y)),
inference('REWRITE',[status(thm)],[3109,4396,theory(equality)]) ).
cnf(4399,plain,
double_divide(double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),Z))),Y) = Z,
inference('REWRITE',[status(thm)],[628,4398,theory(equality)]) ).
cnf(4400,plain,
double_divide(double_divide(inverse(X),inverse(Y)),Z) = double_divide(Y,inverse(double_divide(X,Z))),
inference('REWRITE',[status(thm)],[2896,4399,theory(equality)]) ).
cnf(4401,plain,
double_divide(X,Y) = double_divide(inverse(Z),inverse(double_divide(inverse(double_divide(Z,X)),Y))),
inference('REWRITE',[status(thm)],[185,4399,theory(equality)]) ).
cnf(4404,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Y))),Z))) = double_divide(X,Z),
inference('REWRITE',[status(thm)],[3080,4401,theory(equality)]) ).
cnf(4405,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = double_divide(inverse(double_divide(Y,Z)),inverse(Z)),
inference('REWRITE',[status(thm)],[3129,4404,theory(equality)]) ).
cnf(4406,plain,
X = inverse(double_divide(inverse(double_divide(Y,inverse(Y))),X)),
inference('REWRITE',[status(thm)],[3079,4356,4404,theory(equality)]) ).
cnf(4410,plain,
double_divide(X,inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),double_divide(Z,X)))) = Z,
inference('REWRITE',[status(thm)],[3220,4406,theory(equality)]) ).
cnf(4411,plain,
X = inverse(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),X)),
inference('REWRITE',[status(thm)],[3223,4410,theory(equality)]) ).
cnf(4412,plain,
double_divide(double_divide(inverse(X),inverse(Y)),double_divide(Z,X)) = double_divide(Y,inverse(Z)),
inference('REWRITE',[status(thm)],[4344,4411,theory(equality)]) ).
cnf(4413,plain,
double_divide(X,inverse(inverse(Y))) = double_divide(X,Y),
inference('REWRITE',[status(thm)],[4372,4392,theory(equality)]) ).
cnf(4418,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4333,4356,4413,theory(equality)]) ).
cnf(4419,plain,
X = inverse(double_divide(double_divide(Y,inverse(Y)),X)),
inference('REWRITE',[status(thm)],[4411,4418,theory(equality)]) ).
cnf(4422,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[4270,4418,theory(equality)]) ).
cnf(4439,plain,
double_divide(inverse(double_divide(X,Y)),inverse(Y)) = inverse(X),
inference('REWRITE',[status(thm)],[3657,4418,4356,theory(equality)]) ).
cnf(4440,plain,
double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
inference('REWRITE',[status(thm)],[4405,4439,theory(equality)]) ).
cnf(4441,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('REWRITE',[status(thm)],[4390,4440,theory(equality)]) ).
cnf(4460,plain,
double_divide(inverse(double_divide(X,Y)),Z) = double_divide(X,inverse(double_divide(Y,Z))),
inference('REWRITE',[status(thm)],[4400,4441,theory(equality)]) ).
cnf(4461,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference('REWRITE',[status(thm)],[4422,4460,theory(equality)]) ).
cnf(4462,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)) = double_divide(X,inverse(Z)),
inference('REWRITE',[status(thm)],[4412,4441,theory(equality)]) ).
cnf(4473,plain,
double_divide(double_divide(X,Y),double_divide(Z,inverse(X))) = inverse(double_divide(Z,Y)),
inference('REWRITE',[status(thm)],[928,4462,4441,4356,theory(equality)]) ).
cnf(4487,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(Y,inverse(X)),
inference('REWRITE',[status(thm)],[3425,4473,4418,4356,theory(equality)]) ).
cnf(4488,plain,
double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)),
inference('REWRITE',[status(thm)],[4461,4487,theory(equality)]) ).
cnf(4598,plain,
inverse(X) = double_divide(double_divide(Y,inverse(Y)),X),
inference('PARAMODULATE',[status(thm)],[4418,4419,theory(equality)]) ).
cnf(4625,plain,
double_divide(X,inverse(X)) = double_divide(Y,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[4356,4598,theory(equality)]) ).
cnf(4626,plain,
$false,
inference('REWRITE',[status(thm)],[4488,4625,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP083-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 03:19:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.45 #<PACKAGE "SNARK-USER">
% 0.18/0.45 *
% 0.18/0.45 SNARK-TPTP-OPTIONS
% 0.18/0.45 *
% 0.18/0.45 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.45 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.45 (USE-FACTORING :POS)
% 0.18/0.45 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.45 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.45 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.45 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.45 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.45 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.45 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.45 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.45 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.45 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.45 *
% 0.18/0.45 "."
% 0.18/0.45 *
% 0.18/0.45 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T03:19:12
% 0.18/0.45 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-14T03:19:12
% 3.53/3.70
% 3.53/3.70
% 3.53/3.70 #||
% 3.53/3.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.54/3.70 % SZS output start Refutation
% See solution above
% 3.55/3.74 ||#
% 3.55/3.74
% 3.55/3.74 ; Summary of computation:
% 3.55/3.74 ; 13932 formulas have been input or derived (from 63 formulas).
% 3.55/3.74 ; 4626 (33%) were retained. Of these,
% 3.55/3.74 ; 4474 (97%) were simplified or subsumed later,
% 3.55/3.74 ; 152 ( 3%) are still being kept.
% 3.55/3.74 ;
% 3.55/3.74 ; Run time in seconds excluding printing time:
% 3.55/3.74 ; 0.001 0% Read assertion file (1 call)
% 3.55/3.74 ; 0.000 0% Assert (3 calls)
% 3.55/3.74 ; 0.865 27% Process new row (13,837 calls)
% 3.55/3.74 ; 0.015 0% Resolution (124 calls)
% 3.55/3.74 ; 0.288 9% Paramodulation (62 calls)
% 3.55/3.74 ; 0.000 0% Condensing (3 calls)
% 3.55/3.74 ; 0.000 0% Forward subsumption (3 calls)
% 3.55/3.74 ; 0.000 0% Backward subsumption (3 calls)
% 3.55/3.74 ; 0.952 29% Forward simplification (13,297 calls)
% 3.55/3.74 ; 0.751 23% Backward simplification (4,625 calls)
% 3.55/3.74 ; 0.313 10% Ordering (66,379 calls)
% 3.55/3.74 ; 0.000 0% Sortal reasoning (32 calls)
% 3.55/3.74 ; 0.000 0% Purity testing (1 call)
% 3.55/3.74 ; 0.059 2% Other
% 3.55/3.74 ; 3.244 Total
% 3.55/3.74 ; 3.289 Real time
% 3.55/3.74 ;
% 3.55/3.74 ; Term-hash-array has 18,148 terms in all.
% 3.55/3.74 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 3.55/3.74 ; Feature-vector-row-index has 1 node (30 at peak, 79 added, 78 deleted).
% 3.55/3.74 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 3.55/3.74 ; Retrieved 0 possibly backward subsumed rows in 3 calls.
% 3.55/3.74 ; Path-index has 609 entries (14,204 at peak, 18,668 added, 18,059 deleted).
% 3.55/3.74 ; Path-index has 11,386 nodes (16,344 at peak, 18,495 added, 7,109 deleted).
% 3.55/3.74 ; Trie-index has 609 entries (14,204 at peak, 18,668 added, 18,059 deleted).
% 3.55/3.74 ; Trie-index has 2,770 nodes (70,552 at peak, 92,592 added, 89,822 deleted).
% 3.55/3.74 ; Retrieved 83,116 generalization terms in 151,997 calls.
% 3.55/3.74 ; Retrieved 32,793 instance terms in 4,907 calls.
% 3.55/3.74 ; Retrieved 122,617 unifiable terms in 607 calls.
% 3.55/3.74 ;
% 3.55/3.74 ; The agenda of rows to process has 16 entries:
% 3.55/3.74 ; 1 with value 23 2 with value 26 2 with value 30
% 3.55/3.74 ; 1 with value 24 2 with value 27 2 with value 32
% 3.55/3.74 ; 3 with value 25 1 with value 28 2 with value 34
% 3.55/3.74 ; The agenda of rows to give has 140 entries:
% 3.55/3.74 ; 2 with value (4 22) 10 with value (4 30) 8 with value (4 37)
% 3.55/3.74 ; 2 with value (4 23) 13 with value (4 31) 6 with value (4 38)
% 3.55/3.74 ; 2 with value (4 24) 17 with value (4 32) 3 with value (4 39)
% 3.55/3.74 ; 3 with value (4 25) 12 with value (4 33) 2 with value (4 40)
% 3.55/3.74 ; 8 with value (4 26) 16 with value (4 34) 1 with value (4 42)
% 3.55/3.74 ; 4 with value (4 27) 5 with value (4 35) 1 with value (4 43)
% 3.55/3.74 ; 8 with value (4 28) 6 with value (4 36) 1 with value (4 44)
% 3.55/3.74 ; 10 with value (4 29)
% 3.55/3.74 Evaluation took:
% 3.55/3.74 3.29 seconds of real time
% 3.55/3.74 3.049102 seconds of user run time
% 3.55/3.74 0.240751 seconds of system run time
% 3.55/3.74 [Run times include 0.514 seconds GC run time.]
% 3.55/3.74 0 calls to %EVAL
% 3.55/3.74 0 page faults and
% 3.55/3.74 225,204,152 bytes consed.
% 3.55/3.74 :PROOF-FOUND
% 3.55/3.74 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T03:19:16
% 3.55/3.74 :PROOF-FOUND
% 3.55/3.74 *
%------------------------------------------------------------------------------