%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP080-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 10:34:34 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 142
% Syntax : Number of clauses : 522 ( 265 unt; 0 nHn; 271 RR)
% Number of literals : 900 ( 899 equ; 384 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 820 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = Z ).
cnf(multiply,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity) ).
cnf(inverse,axiom,
inverse(X) = double_divide(X,identity) ).
cnf(identity,axiom,
identity = double_divide(X,inverse(X)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(X) != double_divide(X,identity)
| double_divide(X,identity) = inverse(X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X))),bind(Y0,$fot(double_divide(X,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(X,identity) = inverse(X),
inference(resolve,[$cnf( $equal(inverse(X),double_divide(X,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(double_divide(Y,X),identity) = inverse(double_divide(Y,X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(double_divide(Y,X)))]]) ).
cnf(refute_0_6,plain,
( multiply(X,Y) != double_divide(double_divide(Y,X),identity)
| double_divide(double_divide(Y,X),identity) != inverse(double_divide(Y,X))
| multiply(X,Y) = inverse(double_divide(Y,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,Y),inverse(double_divide(Y,X))) ),[0],$fot(double_divide(double_divide(Y,X),identity))]]) ).
cnf(refute_0_7,plain,
( multiply(X,Y) != double_divide(double_divide(Y,X),identity)
| multiply(X,Y) = inverse(double_divide(Y,X)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(Y,X),identity),inverse(double_divide(Y,X))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(X,Y) = inverse(double_divide(Y,X)),
inference(resolve,[$cnf( $equal(multiply(X,Y),double_divide(double_divide(Y,X),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_10,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_11,plain,
( identity != double_divide(X_3,inverse(X_3))
| double_divide(X_3,inverse(X_3)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(double_divide(X_3,inverse(X_3))))]]) ).
cnf(refute_0_12,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_14,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| multiply(inverse(X_3),X_3) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
double_divide(double_divide(Y,double_divide(Z,X)),identity) = inverse(double_divide(Y,double_divide(Z,X))),
inference(subst,[],[refute_0_4:[bind(X,$fot(double_divide(Y,double_divide(Z,X))))]]) ).
cnf(refute_0_17,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)))]]) ).
cnf(refute_0_18,plain,
( double_divide(double_divide(Y,double_divide(Z,X)),identity) != inverse(double_divide(Y,double_divide(Z,X)))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity))) ),[1,1],$fot(inverse(double_divide(Y,double_divide(Z,X))))]]) ).
cnf(refute_0_19,plain,
( double_divide(double_divide(Y,double_divide(Z,X)),identity) != inverse(double_divide(Y,double_divide(Z,X)))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(Y,double_divide(Z,X)),identity),inverse(double_divide(Y,double_divide(Z,X)))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
double_divide(Y,identity) = inverse(Y),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y))]]) ).
cnf(refute_0_22,plain,
double_divide(X,double_divide(Y,identity)) = double_divide(X,double_divide(Y,identity)),
introduced(tautology,[refl,[$fot(double_divide(X,double_divide(Y,identity)))]]) ).
cnf(refute_0_23,plain,
( double_divide(X,double_divide(Y,identity)) != double_divide(X,double_divide(Y,identity))
| double_divide(Y,identity) != inverse(Y)
| double_divide(X,double_divide(Y,identity)) = double_divide(X,inverse(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X,double_divide(Y,identity)),double_divide(X,double_divide(Y,identity))) ),[1,1],$fot(inverse(Y))]]) ).
cnf(refute_0_24,plain,
( double_divide(Y,identity) != inverse(Y)
| double_divide(X,double_divide(Y,identity)) = double_divide(X,inverse(Y)) ),
inference(resolve,[$cnf( $equal(double_divide(X,double_divide(Y,identity)),double_divide(X,double_divide(Y,identity))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
double_divide(X,double_divide(Y,identity)) = double_divide(X,inverse(Y)),
inference(resolve,[$cnf( $equal(double_divide(Y,identity),inverse(Y)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
double_divide(identity,double_divide(X,double_divide(Y,identity))) = double_divide(identity,double_divide(X,double_divide(Y,identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(X,double_divide(Y,identity))))]]) ).
cnf(refute_0_27,plain,
( double_divide(X,double_divide(Y,identity)) != double_divide(X,inverse(Y))
| double_divide(identity,double_divide(X,double_divide(Y,identity))) != double_divide(identity,double_divide(X,double_divide(Y,identity)))
| double_divide(identity,double_divide(X,double_divide(Y,identity))) = double_divide(identity,double_divide(X,inverse(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(identity,double_divide(X,double_divide(Y,identity)))) ),[1,1],$fot(double_divide(X,inverse(Y)))]]) ).
cnf(refute_0_28,plain,
( double_divide(X,double_divide(Y,identity)) != double_divide(X,inverse(Y))
| double_divide(identity,double_divide(X,double_divide(Y,identity))) = double_divide(identity,double_divide(X,inverse(Y))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(identity,double_divide(X,double_divide(Y,identity)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
double_divide(identity,double_divide(X,double_divide(Y,identity))) = double_divide(identity,double_divide(X,inverse(Y))),
inference(resolve,[$cnf( $equal(double_divide(X,double_divide(Y,identity)),double_divide(X,inverse(Y))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)))]]) ).
cnf(refute_0_31,plain,
( double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity))
| double_divide(identity,double_divide(X,double_divide(Y,identity))) != double_divide(identity,double_divide(X,inverse(Y)))
| double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity))) ),[1,0],$fot(double_divide(identity,double_divide(X,inverse(Y))))]]) ).
cnf(refute_0_32,plain,
( double_divide(identity,double_divide(X,double_divide(Y,identity))) != double_divide(identity,double_divide(X,inverse(Y)))
| double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(identity,double_divide(X,inverse(Y)))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
( double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))
| double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)))),bind(Y0,$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)))),bind(Z0,$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))))]]) ).
cnf(refute_0_37,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))
| double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))) )],[refute_0_20,refute_0_37]) ).
cnf(refute_0_39,plain,
( double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != Z
| double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),Z) ),[0],$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))))]]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)) != Z
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,double_divide(Y,identity))),double_divide(double_divide(Y,double_divide(Z,X)),identity)),Z) )],[single_axiom,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(X,Y) != inverse(double_divide(Y,X))
| inverse(double_divide(Y,X)) = multiply(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(inverse(double_divide(Y,X))))]]) ).
cnf(refute_0_43,plain,
inverse(double_divide(Y,X)) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),inverse(double_divide(Y,X))) )],[refute_0_8,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(double_divide(Y,double_divide(Z,X))) = multiply(double_divide(Z,X),Y),
inference(subst,[],[refute_0_43:[bind(X,$fot(double_divide(Z,X)))]]) ).
cnf(refute_0_45,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))))]]) ).
cnf(refute_0_46,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))
| inverse(double_divide(Y,double_divide(Z,X))) != multiply(double_divide(Z,X),Y)
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))) ),[1,1],$fot(multiply(double_divide(Z,X),Y))]]) ).
cnf(refute_0_47,plain,
( inverse(double_divide(Y,double_divide(Z,X))) != multiply(double_divide(Z,X),Y)
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X))))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)),
inference(resolve,[$cnf( $equal(inverse(double_divide(Y,double_divide(Z,X))),multiply(double_divide(Z,X),Y)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) != Z
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) != double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)) = Z ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),Z) ),[0],$fot(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)))]]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) != Z
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)) = Z ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(Z,X),Y)) = Z,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))),Z) )],[refute_0_41,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(identity,double_divide(X_9,inverse(X_9))),multiply(double_divide(X_10,X_9),X_9)) = X_10,
inference(subst,[],[refute_0_51:[bind(X,$fot(X_9)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_53,plain,
identity = double_divide(X_9,inverse(X_9)),
inference(subst,[],[identity:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_54,plain,
( identity != double_divide(X_9,inverse(X_9))
| double_divide(X_9,inverse(X_9)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(double_divide(X_9,inverse(X_9))))]]) ).
cnf(refute_0_55,plain,
double_divide(X_9,inverse(X_9)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_9,inverse(X_9))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( double_divide(X_9,inverse(X_9)) != identity
| double_divide(double_divide(identity,double_divide(X_9,inverse(X_9))),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_9,inverse(X_9))),multiply(double_divide(X_10,X_9),X_9)),X_10) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_57,plain,
( double_divide(double_divide(identity,double_divide(X_9,inverse(X_9))),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(X_9,inverse(X_9)),identity) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_9,inverse(X_9))),multiply(double_divide(X_10,X_9),X_9)),X_10) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(X,$fot(identity))]]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_61,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) != double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9))) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_62,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) != double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9))
| double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),X_10) ),[0],$fot(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_65,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_10,X_9),X_9)),X_10) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(inverse(identity),multiply(double_divide(inverse(identity),inverse(identity)),inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_66:[bind(X_10,$fot(inverse(identity))),bind(X_9,$fot(inverse(identity)))]]) ).
cnf(refute_0_68,plain,
double_divide(inverse(identity),multiply(double_divide(X_11,identity),identity)) = X_11,
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_11)),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_69,plain,
inverse(X_11) = double_divide(X_11,identity),
inference(subst,[],[inverse:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_70,plain,
( inverse(X_11) != double_divide(X_11,identity)
| double_divide(X_11,identity) = inverse(X_11) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_11))),bind(Y0,$fot(double_divide(X_11,identity)))]]) ).
cnf(refute_0_71,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),double_divide(X_11,identity)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(inverse(identity),multiply(double_divide(X_11,identity),identity)) != X_11
| double_divide(inverse(identity),multiply(inverse(X_11),identity)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_11,identity),identity)),X_11) ),[0,1,0],$fot(inverse(X_11))]]) ).
cnf(refute_0_73,plain,
( double_divide(inverse(identity),multiply(double_divide(X_11,identity),identity)) != X_11
| double_divide(inverse(identity),multiply(inverse(X_11),identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
double_divide(inverse(identity),multiply(inverse(X_11),identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_11,identity),identity)),X_11) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(inverse(identity),multiply(inverse(identity),identity)) = identity,
inference(subst,[],[refute_0_74:[bind(X_11,$fot(identity))]]) ).
cnf(refute_0_76,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| double_divide(inverse(identity),multiply(inverse(identity),identity)) != identity
| double_divide(inverse(identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(inverse(identity),identity)),identity) ),[0,1],$fot(inverse(identity))]]) ).
cnf(refute_0_78,plain,
( double_divide(inverse(identity),multiply(inverse(identity),identity)) != identity
| double_divide(inverse(identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(inverse(identity),identity)),identity) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( double_divide(inverse(identity),multiply(double_divide(inverse(identity),inverse(identity)),inverse(identity))) != inverse(identity)
| double_divide(inverse(identity),inverse(identity)) != identity
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(inverse(identity),inverse(identity)),inverse(identity))),inverse(identity)) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_81,plain,
( double_divide(inverse(identity),multiply(double_divide(inverse(identity),inverse(identity)),inverse(identity))) != inverse(identity)
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),identity) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(inverse(identity),multiply(identity,inverse(identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(inverse(identity),inverse(identity)),inverse(identity))),inverse(identity)) )],[refute_0_67,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(inverse(identity),multiply(double_divide(X_11,inverse(X_11)),inverse(X_11))) = X_11,
inference(subst,[],[refute_0_66:[bind(X_10,$fot(X_11)),bind(X_9,$fot(inverse(X_11)))]]) ).
cnf(refute_0_84,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_85,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_86,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(inverse(identity),multiply(double_divide(X_11,inverse(X_11)),inverse(X_11))) != X_11
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_11,inverse(X_11)),inverse(X_11))),X_11) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_88,plain,
( double_divide(inverse(identity),multiply(double_divide(X_11,inverse(X_11)),inverse(X_11))) != X_11
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
double_divide(inverse(identity),multiply(identity,inverse(X_11))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_11,inverse(X_11)),inverse(X_11))),X_11) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(X,$fot(identity)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_91,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_92,plain,
( inverse(X_3) != double_divide(X_3,identity)
| double_divide(X_3,identity) = inverse(X_3) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_3))),bind(Y0,$fot(double_divide(X_3,identity)))]]) ).
cnf(refute_0_93,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_95,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(identity,inverse(X_11)) = inverse(inverse(inverse(X_11))),
inference(subst,[],[refute_0_96:[bind(X_3,$fot(inverse(X_11)))]]) ).
cnf(refute_0_98,plain,
double_divide(inverse(identity),multiply(identity,inverse(X_11))) = double_divide(inverse(identity),multiply(identity,inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),multiply(identity,inverse(X_11))))]]) ).
cnf(refute_0_99,plain,
( multiply(identity,inverse(X_11)) != inverse(inverse(inverse(X_11)))
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) != double_divide(inverse(identity),multiply(identity,inverse(X_11)))
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) = double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(X_11))),double_divide(inverse(identity),multiply(identity,inverse(X_11)))) ),[1,1],$fot(inverse(inverse(inverse(X_11))))]]) ).
cnf(refute_0_100,plain,
( multiply(identity,inverse(X_11)) != inverse(inverse(inverse(X_11)))
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) = double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(X_11))),double_divide(inverse(identity),multiply(identity,inverse(X_11)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
double_divide(inverse(identity),multiply(identity,inverse(X_11))) = double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_11)),inverse(inverse(inverse(X_11)))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( double_divide(inverse(identity),multiply(identity,inverse(X_11))) != X_11
| double_divide(inverse(identity),multiply(identity,inverse(X_11))) != double_divide(inverse(identity),inverse(inverse(inverse(X_11))))
| double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(X_11))),X_11) ),[0],$fot(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))))]]) ).
cnf(refute_0_103,plain,
( double_divide(inverse(identity),multiply(identity,inverse(X_11))) != X_11
| double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(X_11))),double_divide(inverse(identity),inverse(inverse(inverse(X_11))))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(X_11))),X_11) )],[refute_0_89,refute_0_103]) ).
cnf(refute_0_105,plain,
double_divide(inverse(identity),inverse(inverse(inverse(identity)))) = identity,
inference(subst,[],[refute_0_104:[bind(X_11,$fot(identity))]]) ).
cnf(refute_0_106,plain,
multiply(identity,inverse(identity)) = inverse(inverse(inverse(identity))),
inference(subst,[],[refute_0_96:[bind(X_3,$fot(inverse(identity)))]]) ).
cnf(refute_0_107,plain,
double_divide(inverse(identity),multiply(identity,inverse(identity))) = double_divide(inverse(identity),multiply(identity,inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),multiply(identity,inverse(identity))))]]) ).
cnf(refute_0_108,plain,
( multiply(identity,inverse(identity)) != inverse(inverse(inverse(identity)))
| double_divide(inverse(identity),multiply(identity,inverse(identity))) != double_divide(inverse(identity),multiply(identity,inverse(identity)))
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = double_divide(inverse(identity),inverse(inverse(inverse(identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),double_divide(inverse(identity),multiply(identity,inverse(identity)))) ),[1,1],$fot(inverse(inverse(inverse(identity))))]]) ).
cnf(refute_0_109,plain,
( multiply(identity,inverse(identity)) != inverse(inverse(inverse(identity)))
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = double_divide(inverse(identity),inverse(inverse(inverse(identity)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),double_divide(inverse(identity),multiply(identity,inverse(identity)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
double_divide(inverse(identity),multiply(identity,inverse(identity))) = double_divide(inverse(identity),inverse(inverse(inverse(identity)))),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),inverse(inverse(inverse(identity)))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( double_divide(inverse(identity),multiply(identity,inverse(identity))) != double_divide(inverse(identity),inverse(inverse(inverse(identity))))
| double_divide(inverse(identity),inverse(inverse(inverse(identity)))) != identity
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = identity ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(inverse(identity),multiply(identity,inverse(identity))))),bind(Y0,$fot(double_divide(inverse(identity),inverse(inverse(inverse(identity)))))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_112,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(identity)))) != identity
| double_divide(inverse(identity),multiply(identity,inverse(identity))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),double_divide(inverse(identity),inverse(inverse(inverse(identity))))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
double_divide(inverse(identity),multiply(identity,inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(identity)))),identity) )],[refute_0_105,refute_0_112]) ).
cnf(refute_0_114,plain,
( double_divide(inverse(identity),multiply(identity,inverse(identity))) != identity
| double_divide(inverse(identity),multiply(identity,inverse(identity))) != inverse(identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),inverse(identity)) ),[0],$fot(identity)]]) ).
cnf(refute_0_115,plain,
( double_divide(inverse(identity),multiply(identity,inverse(identity))) != inverse(identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),identity) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(identity,inverse(identity))),inverse(identity)) )],[refute_0_82,refute_0_115]) ).
cnf(refute_0_117,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(inverse(identity)))]]) ).
cnf(refute_0_118,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiply(inverse(X_3),X_3) != inverse(identity)
| inverse(identity) != identity
| multiply(inverse(X_3),X_3) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_3),X_3),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_120,plain,
( multiply(inverse(X_3),X_3) != inverse(identity)
| multiply(inverse(X_3),X_3) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(inverse(X_3),X_3) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(identity)) )],[refute_0_15,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(inverse(a1),a1) = identity,
inference(subst,[],[refute_0_121:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_123,plain,
( multiply(inverse(a1),a1) != identity
| identity != identity
| multiply(inverse(a1),a1) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),identity) ),[0],$fot(identity)]]) ).
cnf(refute_0_124,plain,
( identity != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_124,prove_these_axioms]) ).
cnf(refute_0_126,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(double_divide(X_10,identity),X_9)) = X_10,
inference(subst,[],[refute_0_51:[bind(X,$fot(identity)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_127,plain,
inverse(X_10) = double_divide(X_10,identity),
inference(subst,[],[inverse:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_128,plain,
( inverse(X_10) != double_divide(X_10,identity)
| double_divide(X_10,identity) = inverse(X_10) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(inverse(X_10))),bind(Y0,$fot(double_divide(X_10,identity)))]]) ).
cnf(refute_0_129,plain,
double_divide(X_10,identity) = inverse(X_10),
inference(resolve,[$cnf( $equal(inverse(X_10),double_divide(X_10,identity)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(double_divide(X_10,identity),X_9)) != X_10
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(double_divide(X_10,identity),X_9)),X_10) ),[0,1,0],$fot(inverse(X_10))]]) ).
cnf(refute_0_131,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(double_divide(X_10,identity),X_9)) != X_10
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,identity),inverse(X_10)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(double_divide(X_10,identity),X_9)),X_10) )],[refute_0_126,refute_0_131]) ).
cnf(refute_0_133,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),Y)) = double_divide(identity,double_divide(identity,inverse(X))),
inference(subst,[],[refute_0_51:[bind(Z,$fot(double_divide(identity,double_divide(identity,inverse(X)))))]]) ).
cnf(refute_0_134,plain,
identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
inference(subst,[],[identity:[bind(X,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_135,plain,
multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_136,plain,
( multiply(X_2,X_3) != inverse(double_divide(X_3,X_2))
| inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_2,X_3))),bind(Y0,$fot(inverse(double_divide(X_3,X_2))))]]) ).
cnf(refute_0_137,plain,
inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_139,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_134,refute_0_139]) ).
cnf(refute_0_141,plain,
identity = double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(double_divide(identity,inverse(X_17)),identity)),
inference(subst,[],[refute_0_140:[bind(X_2,$fot(double_divide(identity,inverse(X_17)))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_142,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(inverse(X_17),X_17)) = X_17,
inference(subst,[],[refute_0_132:[bind(X_10,$fot(X_17)),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_143,plain,
multiply(inverse(X_17),X_17) = identity,
inference(subst,[],[refute_0_121:[bind(X_3,$fot(X_17))]]) ).
cnf(refute_0_144,plain,
( multiply(inverse(X_17),X_17) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(inverse(X_17),X_17)) != X_17
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(inverse(X_17),X_17)),X_17) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_145,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(inverse(X_17),X_17)) != X_17
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = X_17 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_17),X_17),identity) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = X_17,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(inverse(X_17),X_17)),X_17) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
inverse(double_divide(identity,double_divide(identity,inverse(X_17)))) = multiply(double_divide(identity,inverse(X_17)),identity),
inference(subst,[],[refute_0_43:[bind(X,$fot(double_divide(identity,inverse(X_17)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_148,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = inverse(double_divide(identity,double_divide(identity,inverse(X_17)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(double_divide(identity,double_divide(identity,inverse(X_17)))))]]) ).
cnf(refute_0_149,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_17))))
| inverse(double_divide(identity,double_divide(identity,inverse(X_17)))) != multiply(double_divide(identity,inverse(X_17)),identity)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = multiply(double_divide(identity,inverse(X_17)),identity) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity))),bind(Y0,$fot(inverse(double_divide(identity,double_divide(identity,inverse(X_17)))))),bind(Z0,$fot(multiply(double_divide(identity,inverse(X_17)),identity)))]]) ).
cnf(refute_0_150,plain,
( inverse(double_divide(identity,double_divide(identity,inverse(X_17)))) != multiply(double_divide(identity,inverse(X_17)),identity)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = multiply(double_divide(identity,inverse(X_17)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_17))))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) = multiply(double_divide(identity,inverse(X_17)),identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(identity,inverse(X_17)))),multiply(double_divide(identity,inverse(X_17)),identity)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) != X_17
| double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) != multiply(double_divide(identity,inverse(X_17)),identity)
| multiply(double_divide(identity,inverse(X_17)),identity) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity),X_17) ),[0],$fot(multiply(double_divide(identity,inverse(X_17)),identity))]]) ).
cnf(refute_0_153,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity) != X_17
| multiply(double_divide(identity,inverse(X_17)),identity) = X_17 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity),multiply(double_divide(identity,inverse(X_17)),identity)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(double_divide(identity,inverse(X_17)),identity) = X_17,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),identity),X_17) )],[refute_0_146,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(double_divide(identity,inverse(X_17)),identity) != X_17
| identity != double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(double_divide(identity,inverse(X_17)),identity))
| identity = double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(double_divide(identity,inverse(X_17)),identity))) ),[1,1],$fot(X_17)]]) ).
cnf(refute_0_156,plain,
( identity != double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(double_divide(identity,inverse(X_17)),identity))
| identity = double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),X_17) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_17)),identity),X_17) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
identity = double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),X_17),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(identity,inverse(X_17))),multiply(double_divide(identity,inverse(X_17)),identity))) )],[refute_0_141,refute_0_156]) ).
cnf(refute_0_158,plain,
identity = double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),
inference(subst,[],[refute_0_157:[bind(X_17,$fot(X))]]) ).
cnf(refute_0_159,plain,
( identity != double_divide(double_divide(identity,double_divide(identity,inverse(X))),X)
| double_divide(double_divide(identity,double_divide(identity,inverse(X))),X) = identity ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(identity)),bind(Y0,$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X)))]]) ).
cnf(refute_0_160,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),X) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(identity,inverse(X))),X)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),Y)) != double_divide(identity,double_divide(identity,inverse(X)))
| double_divide(double_divide(identity,double_divide(identity,inverse(X))),X) != identity
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,double_divide(identity,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),Y)),double_divide(identity,double_divide(identity,inverse(X)))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),Y)) != double_divide(identity,double_divide(identity,inverse(X)))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,double_divide(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),identity) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,double_divide(identity,inverse(X))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X))),X),Y)),double_divide(identity,double_divide(identity,inverse(X)))) )],[refute_0_133,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,inverse(inverse(X))),X),Y)) = double_divide(identity,inverse(inverse(X))),
inference(subst,[],[refute_0_51:[bind(Z,$fot(double_divide(identity,inverse(inverse(X)))))]]) ).
cnf(refute_0_165,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) = identity,
inference(subst,[],[refute_0_51:[bind(X,$fot(inverse(X_18))),bind(Y,$fot(identity)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_166,plain,
multiply(double_divide(identity,inverse(X_18)),identity) = X_18,
inference(subst,[],[refute_0_154:[bind(X_17,$fot(X_18))]]) ).
cnf(refute_0_167,plain,
( multiply(double_divide(identity,inverse(X_18)),identity) != X_18
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)),identity) ),[0,1],$fot(X_18)]]) ).
cnf(refute_0_168,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_18)),identity),X_18) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)),identity) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
double_divide(inverse(X_18),identity) = inverse(inverse(X_18)),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(X_18)))]]) ).
cnf(refute_0_171,plain,
double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_18),inverse(identity)))]]) ).
cnf(refute_0_172,plain,
( double_divide(inverse(X_18),inverse(identity)) != double_divide(inverse(X_18),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_173,plain,
( inverse(identity) != identity
| double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),inverse(identity))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_173]) ).
cnf(refute_0_175,plain,
( double_divide(inverse(X_18),identity) != inverse(inverse(X_18))
| double_divide(inverse(X_18),inverse(identity)) != double_divide(inverse(X_18),identity)
| double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(inverse(X_18),inverse(identity)))),bind(Y0,$fot(double_divide(inverse(X_18),identity))),bind(Z0,$fot(inverse(inverse(X_18))))]]) ).
cnf(refute_0_176,plain,
( double_divide(inverse(X_18),identity) != inverse(inverse(X_18))
| double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),identity)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),identity),inverse(inverse(X_18))) )],[refute_0_170,refute_0_176]) ).
cnf(refute_0_178,plain,
double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,double_divide(inverse(X_18),inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(X_18),inverse(identity))))]]) ).
cnf(refute_0_179,plain,
( double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,double_divide(inverse(X_18),inverse(identity)))
| double_divide(inverse(X_18),inverse(identity)) != inverse(inverse(X_18))
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,double_divide(inverse(X_18),inverse(identity)))) ),[1,1],$fot(inverse(inverse(X_18)))]]) ).
cnf(refute_0_180,plain,
( double_divide(inverse(X_18),inverse(identity)) != inverse(inverse(X_18))
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,double_divide(inverse(X_18),inverse(identity)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),inverse(inverse(X_18))) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18))]]) ).
cnf(refute_0_183,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,inverse(inverse(X_18)))
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_18))))]]) ).
cnf(refute_0_184,plain,
( double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,inverse(inverse(X_18)))
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,inverse(inverse(X_18)))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != double_divide(double_divide(identity,inverse(inverse(X_18))),X_18)
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != identity
| double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),identity) ),[0],$fot(double_divide(double_divide(identity,inverse(inverse(X_18))),X_18))]]) ).
cnf(refute_0_187,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != identity
| double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,inverse(inverse(X_18))),X_18)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),identity) )],[refute_0_169,refute_0_187]) ).
cnf(refute_0_189,plain,
double_divide(double_divide(identity,inverse(inverse(X))),X) = identity,
inference(subst,[],[refute_0_188:[bind(X_18,$fot(X))]]) ).
cnf(refute_0_190,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,inverse(inverse(X))),X),Y)) != double_divide(identity,inverse(inverse(X)))
| double_divide(double_divide(identity,inverse(inverse(X))),X) != identity
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,inverse(inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,inverse(inverse(X))),X),Y)),double_divide(identity,inverse(inverse(X)))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_191,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,inverse(inverse(X))),X),Y)) != double_divide(identity,inverse(inverse(X)))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,inverse(inverse(X))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X))),X),identity) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) = double_divide(identity,inverse(inverse(X))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(double_divide(double_divide(identity,inverse(inverse(X))),X),Y)),double_divide(identity,inverse(inverse(X)))) )],[refute_0_164,refute_0_191]) ).
cnf(refute_0_193,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) != double_divide(identity,double_divide(identity,inverse(X)))
| double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) != double_divide(identity,inverse(inverse(X)))
| double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(identity,inverse(X))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)),double_divide(identity,double_divide(identity,inverse(X)))) ),[0],$fot(double_divide(identity,inverse(inverse(X))))]]) ).
cnf(refute_0_194,plain,
( double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)) != double_divide(identity,double_divide(identity,inverse(X)))
| double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(identity,inverse(X))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)),double_divide(identity,inverse(inverse(X)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(identity,inverse(X))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X,inverse(Y))),multiply(identity,Y)),double_divide(identity,double_divide(identity,inverse(X)))) )],[refute_0_163,refute_0_194]) ).
cnf(refute_0_196,plain,
( double_divide(identity,inverse(inverse(X))) != double_divide(identity,double_divide(identity,inverse(X)))
| double_divide(identity,double_divide(identity,inverse(X))) = double_divide(identity,inverse(inverse(X))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(double_divide(identity,inverse(inverse(X))))),bind(Y0,$fot(double_divide(identity,double_divide(identity,inverse(X)))))]]) ).
cnf(refute_0_197,plain,
double_divide(identity,double_divide(identity,inverse(X))) = double_divide(identity,inverse(inverse(X))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X))),double_divide(identity,double_divide(identity,inverse(X)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
double_divide(identity,double_divide(identity,inverse(X_9))) = double_divide(identity,inverse(inverse(X_9))),
inference(subst,[],[refute_0_197:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_199,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)))]]) ).
cnf(refute_0_200,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) != double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9))
| double_divide(identity,double_divide(identity,inverse(X_9))) != double_divide(identity,inverse(inverse(X_9)))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9))) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_9))))]]) ).
cnf(refute_0_201,plain,
( double_divide(identity,double_divide(identity,inverse(X_9))) != double_divide(identity,inverse(inverse(X_9)))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_9))),double_divide(identity,inverse(inverse(X_9)))) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) != X_10
| double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) != double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9))
| double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),X_10) ),[0],$fot(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)))]]) ).
cnf(refute_0_204,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)) != X_10
| double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_9))),multiply(inverse(X_10),X_9)),X_10) )],[refute_0_132,refute_0_204]) ).
cnf(refute_0_206,plain,
double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(X_24)),identity)) = inverse(X_24),
inference(subst,[],[refute_0_205:[bind(X_10,$fot(inverse(X_24))),bind(X_9,$fot(identity))]]) ).
cnf(refute_0_207,plain,
multiply(double_divide(identity,inverse(X_24)),identity) = inverse(double_divide(identity,double_divide(identity,inverse(X_24)))),
inference(subst,[],[refute_0_8:[bind(X,$fot(double_divide(identity,inverse(X_24)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_208,plain,
double_divide(identity,inverse(inverse(X_24))) = double_divide(identity,double_divide(identity,inverse(X_24))),
inference(subst,[],[refute_0_195:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_209,plain,
( double_divide(identity,inverse(inverse(X_24))) != double_divide(identity,double_divide(identity,inverse(X_24)))
| double_divide(identity,double_divide(identity,inverse(X_24))) = double_divide(identity,inverse(inverse(X_24))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(double_divide(identity,inverse(inverse(X_24))))),bind(Y0,$fot(double_divide(identity,double_divide(identity,inverse(X_24)))))]]) ).
cnf(refute_0_210,plain,
double_divide(identity,double_divide(identity,inverse(X_24))) = double_divide(identity,inverse(inverse(X_24))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_24))),double_divide(identity,double_divide(identity,inverse(X_24)))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( multiply(double_divide(identity,inverse(X_24)),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_24))))
| double_divide(identity,double_divide(identity,inverse(X_24))) != double_divide(identity,inverse(inverse(X_24)))
| multiply(double_divide(identity,inverse(X_24)),identity) = inverse(double_divide(identity,inverse(inverse(X_24)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_24)),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_24))))) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_24))))]]) ).
cnf(refute_0_212,plain,
( multiply(double_divide(identity,inverse(X_24)),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_24))))
| multiply(double_divide(identity,inverse(X_24)),identity) = inverse(double_divide(identity,inverse(inverse(X_24)))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_24))),double_divide(identity,inverse(inverse(X_24)))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
multiply(double_divide(identity,inverse(X_24)),identity) = inverse(double_divide(identity,inverse(inverse(X_24)))),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_24)),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_24))))) )],[refute_0_207,refute_0_212]) ).
cnf(refute_0_214,plain,
multiply(double_divide(identity,inverse(X_24)),identity) = X_24,
inference(subst,[],[refute_0_154:[bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_215,plain,
( multiply(double_divide(identity,inverse(X_24)),identity) != X_24
| multiply(double_divide(identity,inverse(X_24)),identity) != inverse(double_divide(identity,inverse(inverse(X_24))))
| X_24 = inverse(double_divide(identity,inverse(inverse(X_24)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_24)),identity),inverse(double_divide(identity,inverse(inverse(X_24))))) ),[0],$fot(X_24)]]) ).
cnf(refute_0_216,plain,
( multiply(double_divide(identity,inverse(X_24)),identity) != inverse(double_divide(identity,inverse(inverse(X_24))))
| X_24 = inverse(double_divide(identity,inverse(inverse(X_24)))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_24)),identity),X_24) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
inverse(double_divide(identity,inverse(inverse(X_24)))) = multiply(inverse(inverse(X_24)),identity),
inference(subst,[],[refute_0_43:[bind(X,$fot(inverse(inverse(X_24)))),bind(Y,$fot(identity))]]) ).
cnf(refute_0_218,plain,
( X_24 != inverse(double_divide(identity,inverse(inverse(X_24))))
| inverse(double_divide(identity,inverse(inverse(X_24)))) != multiply(inverse(inverse(X_24)),identity)
| X_24 = multiply(inverse(inverse(X_24)),identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,multiply(inverse(inverse(X_24)),identity)) ),[0],$fot(inverse(double_divide(identity,inverse(inverse(X_24)))))]]) ).
cnf(refute_0_219,plain,
( X_24 != inverse(double_divide(identity,inverse(inverse(X_24))))
| X_24 = multiply(inverse(inverse(X_24)),identity) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_24)))),multiply(inverse(inverse(X_24)),identity)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
( multiply(double_divide(identity,inverse(X_24)),identity) != inverse(double_divide(identity,inverse(inverse(X_24))))
| X_24 = multiply(inverse(inverse(X_24)),identity) ),
inference(resolve,[$cnf( $equal(X_24,inverse(double_divide(identity,inverse(inverse(X_24))))) )],[refute_0_216,refute_0_219]) ).
cnf(refute_0_221,plain,
X_24 = multiply(inverse(inverse(X_24)),identity),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_24)),identity),inverse(double_divide(identity,inverse(inverse(X_24))))) )],[refute_0_213,refute_0_220]) ).
cnf(refute_0_222,plain,
( X_24 != multiply(inverse(inverse(X_24)),identity)
| multiply(inverse(inverse(X_24)),identity) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_24)),bind(Y0,$fot(multiply(inverse(inverse(X_24)),identity)))]]) ).
cnf(refute_0_223,plain,
multiply(inverse(inverse(X_24)),identity) = X_24,
inference(resolve,[$cnf( $equal(X_24,multiply(inverse(inverse(X_24)),identity)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( multiply(inverse(inverse(X_24)),identity) != X_24
| double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(X_24)),identity)) != inverse(X_24)
| double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = inverse(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(X_24)),identity)),inverse(X_24)) ),[0,1],$fot(X_24)]]) ).
cnf(refute_0_225,plain,
( double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(X_24)),identity)) != inverse(X_24)
| double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = inverse(X_24) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_24)),identity),X_24) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = inverse(X_24),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(X_24)),identity)),inverse(X_24)) )],[refute_0_206,refute_0_225]) ).
cnf(refute_0_227,plain,
( double_divide(identity,identity) != inverse(identity)
| inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(identity,identity))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_228,plain,
( inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_59,refute_0_227]) ).
cnf(refute_0_229,plain,
double_divide(identity,identity) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_228]) ).
cnf(refute_0_230,plain,
inverse(inverse(identity)) = inverse(inverse(identity)),
introduced(tautology,[refl,[$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_231,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_232,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
inverse(inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_232]) ).
cnf(refute_0_234,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) != inverse(identity)
| inverse(inverse(identity)) = identity ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(inverse(inverse(identity)))),bind(Y0,$fot(inverse(identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_235,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(identity)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
inverse(inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_235]) ).
cnf(refute_0_237,plain,
double_divide(identity,inverse(inverse(identity))) = double_divide(identity,inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(identity))))]]) ).
cnf(refute_0_238,plain,
( double_divide(identity,inverse(inverse(identity))) != double_divide(identity,inverse(inverse(identity)))
| inverse(inverse(identity)) != identity
| double_divide(identity,inverse(inverse(identity))) = double_divide(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),double_divide(identity,inverse(inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_239,plain,
( inverse(inverse(identity)) != identity
| double_divide(identity,inverse(inverse(identity))) = double_divide(identity,identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
double_divide(identity,inverse(inverse(identity))) = double_divide(identity,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( double_divide(identity,identity) != identity
| double_divide(identity,inverse(inverse(identity))) != double_divide(identity,identity)
| double_divide(identity,inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(identity,inverse(inverse(identity))))),bind(Y0,$fot(double_divide(identity,identity))),bind(Z0,$fot(identity))]]) ).
cnf(refute_0_242,plain,
( double_divide(identity,identity) != identity
| double_divide(identity,inverse(inverse(identity))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),double_divide(identity,identity)) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
double_divide(identity,inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(double_divide(identity,identity),identity) )],[refute_0_229,refute_0_242]) ).
cnf(refute_0_244,plain,
double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = double_divide(double_divide(identity,inverse(inverse(identity))),X_24),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(identity))),X_24))]]) ).
cnf(refute_0_245,plain,
( double_divide(double_divide(identity,inverse(inverse(identity))),X_24) != double_divide(double_divide(identity,inverse(inverse(identity))),X_24)
| double_divide(identity,inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = double_divide(identity,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),X_24),double_divide(double_divide(identity,inverse(inverse(identity))),X_24)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_246,plain,
( double_divide(identity,inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = double_divide(identity,X_24) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),X_24),double_divide(double_divide(identity,inverse(inverse(identity))),X_24)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
double_divide(double_divide(identity,inverse(inverse(identity))),X_24) = double_divide(identity,X_24),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),identity) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
( double_divide(double_divide(identity,inverse(inverse(identity))),X_24) != double_divide(identity,X_24)
| double_divide(double_divide(identity,inverse(inverse(identity))),X_24) != inverse(X_24)
| double_divide(identity,X_24) = inverse(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),X_24),inverse(X_24)) ),[0],$fot(double_divide(identity,X_24))]]) ).
cnf(refute_0_249,plain,
( double_divide(double_divide(identity,inverse(inverse(identity))),X_24) != inverse(X_24)
| double_divide(identity,X_24) = inverse(X_24) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),X_24),double_divide(identity,X_24)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
double_divide(identity,X_24) = inverse(X_24),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(identity))),X_24),inverse(X_24)) )],[refute_0_226,refute_0_249]) ).
cnf(refute_0_251,plain,
double_divide(identity,inverse(inverse(X_9))) = inverse(inverse(inverse(X_9))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(inverse(inverse(X_9))))]]) ).
cnf(refute_0_252,plain,
double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)))]]) ).
cnf(refute_0_253,plain,
( double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) != double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9))
| double_divide(identity,inverse(inverse(X_9))) != inverse(inverse(inverse(X_9)))
| double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9))) ),[1,0],$fot(inverse(inverse(inverse(X_9))))]]) ).
cnf(refute_0_254,plain,
( double_divide(identity,inverse(inverse(X_9))) != inverse(inverse(inverse(X_9)))
| double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_9))),inverse(inverse(inverse(X_9)))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
( double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) != X_10
| double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) != double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9))
| double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),X_10) ),[0],$fot(double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)))]]) ).
cnf(refute_0_257,plain,
( double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) != X_10
| double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
double_divide(inverse(inverse(inverse(X_9))),multiply(inverse(X_10),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_9))),multiply(inverse(X_10),X_9)),X_10) )],[refute_0_205,refute_0_257]) ).
cnf(refute_0_259,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),multiply(inverse(X_38),inverse(inverse(X_38)))) = X_38,
inference(subst,[],[refute_0_258:[bind(X_10,$fot(X_38)),bind(X_9,$fot(inverse(inverse(X_38))))]]) ).
cnf(refute_0_260,plain,
multiply(X,inverse(X)) = inverse(double_divide(inverse(X),X)),
inference(subst,[],[refute_0_8:[bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_261,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(inverse(identity),X_27)) = identity,
inference(subst,[],[refute_0_205:[bind(X_10,$fot(identity)),bind(X_9,$fot(X_27))]]) ).
cnf(refute_0_262,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(inverse(identity),X_27)) != identity
| inverse(identity) != identity
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(inverse(identity),X_27)),identity) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_263,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(inverse(identity),X_27)) != identity
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_262]) ).
cnf(refute_0_264,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(inverse(identity),X_27)),identity) )],[refute_0_261,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(identity,X_27) = inverse(inverse(X_27)),
inference(subst,[],[refute_0_96:[bind(X_3,$fot(X_27))]]) ).
cnf(refute_0_266,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)))]]) ).
cnf(refute_0_267,plain,
( multiply(identity,X_27) != inverse(inverse(X_27))
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) != double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27))
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27))) ),[1,1],$fot(inverse(inverse(X_27)))]]) ).
cnf(refute_0_268,plain,
( multiply(identity,X_27) != inverse(inverse(X_27))
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) = double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),
inference(resolve,[$cnf( $equal(multiply(identity,X_27),inverse(inverse(X_27))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) != double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27)))
| double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) != identity
| double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),identity) ),[0],$fot(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))))]]) ).
cnf(refute_0_271,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)) != identity
| double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),multiply(identity,X_27)),identity) )],[refute_0_264,refute_0_271]) ).
cnf(refute_0_273,plain,
double_divide(identity,inverse(inverse(X_27))) = inverse(inverse(inverse(X_27))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(inverse(inverse(X_27))))]]) ).
cnf(refute_0_274,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))))]]) ).
cnf(refute_0_275,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) != double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27)))
| double_divide(identity,inverse(inverse(X_27))) != inverse(inverse(inverse(X_27)))
| double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27)))) ),[1,0],$fot(inverse(inverse(inverse(X_27))))]]) ).
cnf(refute_0_276,plain,
( double_divide(identity,inverse(inverse(X_27))) != inverse(inverse(inverse(X_27)))
| double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27)))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) = double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(inverse(X_27)))) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) != double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27)))
| double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) != identity
| double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),identity) ),[0],$fot(double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))))]]) ).
cnf(refute_0_279,plain,
( double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))) != identity
| double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27)))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
double_divide(inverse(inverse(inverse(X_27))),inverse(inverse(X_27))) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_27))),inverse(inverse(X_27))),identity) )],[refute_0_272,refute_0_279]) ).
cnf(refute_0_281,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(inverse(inverse(inverse(X_11))))) = identity,
inference(subst,[],[refute_0_280:[bind(X_27,$fot(inverse(inverse(X_11))))]]) ).
cnf(refute_0_282,plain,
double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))))]]) ).
cnf(refute_0_283,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) != double_divide(inverse(identity),inverse(inverse(inverse(X_11))))
| inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = double_divide(identity,inverse(inverse(inverse(X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),double_divide(inverse(identity),inverse(inverse(inverse(X_11))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_284,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = double_divide(identity,inverse(inverse(inverse(X_11)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),double_divide(inverse(identity),inverse(inverse(inverse(X_11))))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) = double_divide(identity,inverse(inverse(inverse(X_11)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_284]) ).
cnf(refute_0_286,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) != X_11
| double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) != double_divide(identity,inverse(inverse(inverse(X_11))))
| double_divide(identity,inverse(inverse(inverse(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),X_11) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(X_11)))))]]) ).
cnf(refute_0_287,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(X_11)))) != X_11
| double_divide(identity,inverse(inverse(inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),double_divide(identity,inverse(inverse(inverse(X_11))))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
double_divide(identity,inverse(inverse(inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(X_11)))),X_11) )],[refute_0_104,refute_0_287]) ).
cnf(refute_0_289,plain,
double_divide(identity,inverse(inverse(inverse(X_11)))) = inverse(inverse(inverse(inverse(X_11)))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(inverse(inverse(inverse(X_11)))))]]) ).
cnf(refute_0_290,plain,
( double_divide(identity,inverse(inverse(inverse(X_11)))) != X_11
| double_divide(identity,inverse(inverse(inverse(X_11)))) != inverse(inverse(inverse(inverse(X_11))))
| inverse(inverse(inverse(inverse(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_11)))),X_11) ),[0],$fot(inverse(inverse(inverse(inverse(X_11)))))]]) ).
cnf(refute_0_291,plain,
( double_divide(identity,inverse(inverse(inverse(X_11)))) != X_11
| inverse(inverse(inverse(inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_11)))),inverse(inverse(inverse(inverse(X_11))))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
inverse(inverse(inverse(inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_11)))),X_11) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(inverse(inverse(inverse(X_11))))) != identity
| inverse(inverse(inverse(inverse(X_11)))) != X_11
| double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(inverse(inverse(inverse(X_11))))),identity) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_294,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(inverse(inverse(inverse(X_11))))) != identity
| double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(X_11)))),X_11) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = identity,
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(inverse(inverse(inverse(X_11))))),identity) )],[refute_0_281,refute_0_294]) ).
cnf(refute_0_296,plain,
inverse(inverse(inverse(inverse(inverse(X_11))))) = inverse(X_11),
inference(subst,[],[refute_0_292:[bind(X_11,$fot(inverse(X_11)))]]) ).
cnf(refute_0_297,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),
introduced(tautology,[refl,[$fot(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11))]]) ).
cnf(refute_0_298,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) != double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11)
| inverse(inverse(inverse(inverse(inverse(X_11))))) != inverse(X_11)
| double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = double_divide(inverse(X_11),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11)) ),[1,0],$fot(inverse(X_11))]]) ).
cnf(refute_0_299,plain,
( inverse(inverse(inverse(inverse(inverse(X_11))))) != inverse(X_11)
| double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = double_divide(inverse(X_11),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) = double_divide(inverse(X_11),X_11),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(inverse(X_11))))),inverse(X_11)) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) != double_divide(inverse(X_11),X_11)
| double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) != identity
| double_divide(inverse(X_11),X_11) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),identity) ),[0],$fot(double_divide(inverse(X_11),X_11))]]) ).
cnf(refute_0_302,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11) != identity
| double_divide(inverse(X_11),X_11) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),double_divide(inverse(X_11),X_11)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
double_divide(inverse(X_11),X_11) = identity,
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_11))))),X_11),identity) )],[refute_0_295,refute_0_302]) ).
cnf(refute_0_304,plain,
double_divide(inverse(X),X) = identity,
inference(subst,[],[refute_0_303:[bind(X_11,$fot(X))]]) ).
cnf(refute_0_305,plain,
( multiply(X,inverse(X)) != inverse(double_divide(inverse(X),X))
| double_divide(inverse(X),X) != identity
| multiply(X,inverse(X)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(X)),inverse(double_divide(inverse(X),X))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_306,plain,
( multiply(X,inverse(X)) != inverse(double_divide(inverse(X),X))
| multiply(X,inverse(X)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X),X),identity) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
multiply(X,inverse(X)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(X,inverse(X)),inverse(double_divide(inverse(X),X))) )],[refute_0_260,refute_0_306]) ).
cnf(refute_0_308,plain,
( multiply(X,inverse(X)) != inverse(identity)
| inverse(identity) != identity
| multiply(X,inverse(X)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,inverse(X)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_309,plain,
( multiply(X,inverse(X)) != inverse(identity)
| multiply(X,inverse(X)) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_308]) ).
cnf(refute_0_310,plain,
multiply(X,inverse(X)) = identity,
inference(resolve,[$cnf( $equal(multiply(X,inverse(X)),inverse(identity)) )],[refute_0_307,refute_0_309]) ).
cnf(refute_0_311,plain,
multiply(inverse(X_38),inverse(inverse(X_38))) = identity,
inference(subst,[],[refute_0_310:[bind(X,$fot(inverse(X_38)))]]) ).
cnf(refute_0_312,plain,
( multiply(inverse(X_38),inverse(inverse(X_38))) != identity
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),multiply(inverse(X_38),inverse(inverse(X_38)))) != X_38
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = X_38 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),multiply(inverse(X_38),inverse(inverse(X_38)))),X_38) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_313,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),multiply(inverse(X_38),inverse(inverse(X_38)))) != X_38
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = X_38 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),inverse(inverse(X_38))),identity) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = X_38,
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),multiply(inverse(X_38),inverse(inverse(X_38)))),X_38) )],[refute_0_259,refute_0_313]) ).
cnf(refute_0_315,plain,
inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))) = inverse(inverse(X_38)),
inference(subst,[],[refute_0_292:[bind(X_11,$fot(inverse(inverse(X_38))))]]) ).
cnf(refute_0_316,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))),
inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(inverse(inverse(inverse(inverse(X_38)))))))]]) ).
cnf(refute_0_317,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) != inverse(inverse(inverse(inverse(inverse(inverse(X_38))))))
| inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))) != inverse(inverse(X_38))
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = inverse(inverse(X_38)) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity))),bind(Y0,$fot(inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))))),bind(Z0,$fot(inverse(inverse(X_38))))]]) ).
cnf(refute_0_318,plain,
( inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))) != inverse(inverse(X_38))
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = inverse(inverse(X_38)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity),inverse(inverse(inverse(inverse(inverse(inverse(X_38))))))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) = inverse(inverse(X_38)),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(inverse(inverse(X_38)))))),inverse(inverse(X_38))) )],[refute_0_315,refute_0_318]) ).
cnf(refute_0_320,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) != X_38
| double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) != inverse(inverse(X_38))
| inverse(inverse(X_38)) = X_38 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity),X_38) ),[0],$fot(inverse(inverse(X_38)))]]) ).
cnf(refute_0_321,plain,
( double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity) != X_38
| inverse(inverse(X_38)) = X_38 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity),inverse(inverse(X_38))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
inverse(inverse(X_38)) = X_38,
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(inverse(inverse(X_38))))),identity),X_38) )],[refute_0_314,refute_0_321]) ).
cnf(refute_0_323,plain,
inverse(inverse(X_3)) = X_3,
inference(subst,[],[refute_0_322:[bind(X_38,$fot(X_3))]]) ).
cnf(refute_0_324,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| inverse(inverse(X_3)) != X_3
| multiply(identity,X_3) = X_3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,X_3),X_3) ),[0],$fot(inverse(inverse(X_3)))]]) ).
cnf(refute_0_325,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| multiply(identity,X_3) = X_3 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),X_3) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
multiply(identity,X_3) = X_3,
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(inverse(X_3))) )],[refute_0_96,refute_0_325]) ).
cnf(refute_0_327,plain,
multiply(identity,a2) = a2,
inference(subst,[],[refute_0_326:[bind(X_3,$fot(a2))]]) ).
cnf(refute_0_328,plain,
( multiply(identity,a2) != a2
| a2 != a2
| multiply(identity,a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_329,plain,
( a2 != a2
| multiply(identity,a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_329,refute_0_125]) ).
cnf(refute_0_331,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_332,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| identity != identity ),
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_331,refute_0_330]) ).
cnf(refute_0_333,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_334,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_333,refute_0_332]) ).
cnf(refute_0_335,plain,
multiply(X,multiply(X_98,X_97)) = inverse(double_divide(multiply(X_98,X_97),X)),
inference(subst,[],[refute_0_8:[bind(Y,$fot(multiply(X_98,X_97)))]]) ).
cnf(refute_0_336,plain,
double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_337,plain,
( double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) != double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9))
| inverse(identity) != identity
| double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_338,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) = double_divide(identity,multiply(double_divide(X_10,X_9),X_9)),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_338]) ).
cnf(refute_0_340,plain,
( double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) != double_divide(identity,multiply(double_divide(X_10,X_9),X_9))
| double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),X_10) ),[0],$fot(double_divide(identity,multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_341,plain,
( double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),double_divide(identity,multiply(double_divide(X_10,X_9),X_9))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),multiply(double_divide(X_10,X_9),X_9)),X_10) )],[refute_0_66,refute_0_341]) ).
cnf(refute_0_343,plain,
double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) = inverse(multiply(double_divide(X_10,X_9),X_9)),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_344,plain,
( double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) != inverse(multiply(double_divide(X_10,X_9),X_9))
| inverse(multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_10,X_9),X_9)),X_10) ),[0],$fot(inverse(multiply(double_divide(X_10,X_9),X_9)))]]) ).
cnf(refute_0_345,plain,
( double_divide(identity,multiply(double_divide(X_10,X_9),X_9)) != X_10
| inverse(multiply(double_divide(X_10,X_9),X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_10,X_9),X_9)),inverse(multiply(double_divide(X_10,X_9),X_9))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
inverse(multiply(double_divide(X_10,X_9),X_9)) = X_10,
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_10,X_9),X_9)),X_10) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
double_divide(inverse(identity),inverse(inverse(inverse(double_divide(Y,X))))) = double_divide(Y,X),
inference(subst,[],[refute_0_104:[bind(X_11,$fot(double_divide(Y,X)))]]) ).
cnf(refute_0_348,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(double_divide(Y,X))))) != double_divide(Y,X)
| inverse(double_divide(Y,X)) != multiply(X,Y)
| double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(double_divide(Y,X))))),double_divide(Y,X)) ),[0,1,0,0],$fot(multiply(X,Y))]]) ).
cnf(refute_0_349,plain,
( double_divide(inverse(identity),inverse(inverse(inverse(double_divide(Y,X))))) != double_divide(Y,X)
| double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(Y,X)),multiply(X,Y)) )],[refute_0_43,refute_0_348]) ).
cnf(refute_0_350,plain,
double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(Y,X),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(inverse(double_divide(Y,X))))),double_divide(Y,X)) )],[refute_0_347,refute_0_349]) ).
cnf(refute_0_351,plain,
double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_352,plain,
( double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) != double_divide(inverse(identity),inverse(inverse(multiply(X,Y))))
| inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(identity,inverse(inverse(multiply(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),double_divide(inverse(identity),inverse(inverse(multiply(X,Y))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_353,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(identity,inverse(inverse(multiply(X,Y)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),double_divide(inverse(identity),inverse(inverse(multiply(X,Y))))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) = double_divide(identity,inverse(inverse(multiply(X,Y)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_353]) ).
cnf(refute_0_355,plain,
( double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) != double_divide(identity,inverse(inverse(multiply(X,Y))))
| double_divide(identity,inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) ),[0],$fot(double_divide(identity,inverse(inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_356,plain,
( double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| double_divide(identity,inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),double_divide(identity,inverse(inverse(multiply(X,Y))))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
double_divide(identity,inverse(inverse(multiply(X,Y)))) = double_divide(Y,X),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) )],[refute_0_350,refute_0_356]) ).
cnf(refute_0_358,plain,
double_divide(identity,inverse(inverse(multiply(X,Y)))) = inverse(inverse(inverse(multiply(X,Y)))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(inverse(inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_359,plain,
( double_divide(identity,inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| double_divide(identity,inverse(inverse(multiply(X,Y)))) != inverse(inverse(inverse(multiply(X,Y))))
| inverse(inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) ),[0],$fot(inverse(inverse(inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_360,plain,
( double_divide(identity,inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| inverse(inverse(inverse(multiply(X,Y)))) = double_divide(Y,X) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X,Y)))),inverse(inverse(inverse(multiply(X,Y))))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
inverse(inverse(inverse(multiply(X,Y)))) = double_divide(Y,X),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
inverse(inverse(inverse(multiply(X,Y)))) = inverse(multiply(X,Y)),
inference(subst,[],[refute_0_322:[bind(X_38,$fot(inverse(multiply(X,Y))))]]) ).
cnf(refute_0_363,plain,
( inverse(inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| inverse(inverse(inverse(multiply(X,Y)))) != inverse(multiply(X,Y))
| inverse(multiply(X,Y)) = double_divide(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) ),[0],$fot(inverse(multiply(X,Y)))]]) ).
cnf(refute_0_364,plain,
( inverse(inverse(inverse(multiply(X,Y)))) != double_divide(Y,X)
| inverse(multiply(X,Y)) = double_divide(Y,X) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(multiply(X,Y)))),inverse(multiply(X,Y))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
inverse(multiply(X,Y)) = double_divide(Y,X),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(multiply(X,Y)))),double_divide(Y,X)) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
inverse(multiply(double_divide(X_10,X_9),X_9)) = double_divide(X_9,double_divide(X_10,X_9)),
inference(subst,[],[refute_0_365:[bind(X,$fot(double_divide(X_10,X_9))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_367,plain,
( inverse(multiply(double_divide(X_10,X_9),X_9)) != X_10
| inverse(multiply(double_divide(X_10,X_9),X_9)) != double_divide(X_9,double_divide(X_10,X_9))
| double_divide(X_9,double_divide(X_10,X_9)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(double_divide(X_10,X_9),X_9)),X_10) ),[0],$fot(double_divide(X_9,double_divide(X_10,X_9)))]]) ).
cnf(refute_0_368,plain,
( inverse(multiply(double_divide(X_10,X_9),X_9)) != X_10
| double_divide(X_9,double_divide(X_10,X_9)) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(multiply(double_divide(X_10,X_9),X_9)),double_divide(X_9,double_divide(X_10,X_9))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
double_divide(X_9,double_divide(X_10,X_9)) = X_10,
inference(resolve,[$cnf( $equal(inverse(multiply(double_divide(X_10,X_9),X_9)),X_10) )],[refute_0_346,refute_0_368]) ).
cnf(refute_0_370,plain,
double_divide(double_divide(X_62,X_10),double_divide(X_10,double_divide(X_62,X_10))) = X_10,
inference(subst,[],[refute_0_369:[bind(X_9,$fot(double_divide(X_62,X_10)))]]) ).
cnf(refute_0_371,plain,
double_divide(X_10,double_divide(X_62,X_10)) = X_62,
inference(subst,[],[refute_0_369:[bind(X_10,$fot(X_62)),bind(X_9,$fot(X_10))]]) ).
cnf(refute_0_372,plain,
( double_divide(X_10,double_divide(X_62,X_10)) != X_62
| double_divide(double_divide(X_62,X_10),double_divide(X_10,double_divide(X_62,X_10))) != X_10
| double_divide(double_divide(X_62,X_10),X_62) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_62,X_10),double_divide(X_10,double_divide(X_62,X_10))),X_10) ),[0,1],$fot(X_62)]]) ).
cnf(refute_0_373,plain,
( double_divide(double_divide(X_62,X_10),double_divide(X_10,double_divide(X_62,X_10))) != X_10
| double_divide(double_divide(X_62,X_10),X_62) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(X_62,X_10)),X_62) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
double_divide(double_divide(X_62,X_10),X_62) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_62,X_10),double_divide(X_10,double_divide(X_62,X_10))),X_10) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
double_divide(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),multiply(X_93,X_95)) = double_divide(multiply(X_95,X_94),X_93),
inference(subst,[],[refute_0_374:[bind(X_10,$fot(double_divide(multiply(X_95,X_94),X_93))),bind(X_62,$fot(multiply(X_93,X_95)))]]) ).
cnf(refute_0_376,plain,
double_divide(double_divide(identity,double_divide(X_8,inverse(double_divide(Y,X)))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10,
inference(subst,[],[refute_0_51:[bind(X,$fot(X_8)),bind(Y,$fot(double_divide(Y,X))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_377,plain,
( double_divide(double_divide(identity,double_divide(X_8,inverse(double_divide(Y,X)))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != X_10
| inverse(double_divide(Y,X)) != multiply(X,Y)
| double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,inverse(double_divide(Y,X)))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),X_10) ),[0,0,1,1],$fot(multiply(X,Y))]]) ).
cnf(refute_0_378,plain,
( double_divide(double_divide(identity,double_divide(X_8,inverse(double_divide(Y,X)))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != X_10
| double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(Y,X)),multiply(X,Y)) )],[refute_0_43,refute_0_377]) ).
cnf(refute_0_379,plain,
double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,inverse(double_divide(Y,X)))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),X_10) )],[refute_0_376,refute_0_378]) ).
cnf(refute_0_380,plain,
inverse(double_divide(X_8,multiply(X,Y))) = multiply(multiply(X,Y),X_8),
inference(subst,[],[refute_0_43:[bind(X,$fot(multiply(X,Y))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_381,plain,
double_divide(identity,double_divide(X_8,multiply(X,Y))) = inverse(double_divide(X_8,multiply(X,Y))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(double_divide(X_8,multiply(X,Y))))]]) ).
cnf(refute_0_382,plain,
( double_divide(identity,double_divide(X_8,multiply(X,Y))) != inverse(double_divide(X_8,multiply(X,Y)))
| inverse(double_divide(X_8,multiply(X,Y))) != multiply(multiply(X,Y),X_8)
| double_divide(identity,double_divide(X_8,multiply(X,Y))) = multiply(multiply(X,Y),X_8) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(identity,double_divide(X_8,multiply(X,Y))))),bind(Y0,$fot(inverse(double_divide(X_8,multiply(X,Y))))),bind(Z0,$fot(multiply(multiply(X,Y),X_8)))]]) ).
cnf(refute_0_383,plain,
( inverse(double_divide(X_8,multiply(X,Y))) != multiply(multiply(X,Y),X_8)
| double_divide(identity,double_divide(X_8,multiply(X,Y))) = multiply(multiply(X,Y),X_8) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_8,multiply(X,Y))),inverse(double_divide(X_8,multiply(X,Y)))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
double_divide(identity,double_divide(X_8,multiply(X,Y))) = multiply(multiply(X,Y),X_8),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_8,multiply(X,Y))),multiply(multiply(X,Y),X_8)) )],[refute_0_380,refute_0_383]) ).
cnf(refute_0_385,plain,
double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))))]]) ).
cnf(refute_0_386,plain,
( double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X)))
| double_divide(identity,double_divide(X_8,multiply(X,Y))) != multiply(multiply(X,Y),X_8)
| double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X)))) ),[1,0],$fot(multiply(multiply(X,Y),X_8))]]) ).
cnf(refute_0_387,plain,
( double_divide(identity,double_divide(X_8,multiply(X,Y))) != multiply(multiply(X,Y),X_8)
| double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X)))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(multiply(X,Y),X_8)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
( double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != X_10
| double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X)))
| double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),X_10) ),[0],$fot(double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))))]]) ).
cnf(refute_0_390,plain,
( double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))) != X_10
| double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X)))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
double_divide(multiply(multiply(X,Y),X_8),multiply(double_divide(X_10,X_8),double_divide(Y,X))) = X_10,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,multiply(X,Y))),multiply(double_divide(X_10,X_8),double_divide(Y,X))),X_10) )],[refute_0_379,refute_0_390]) ).
cnf(refute_0_392,plain,
double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),double_divide(identity,X_83))) = X_85,
inference(subst,[],[refute_0_391:[bind(X,$fot(X_83)),bind(Y,$fot(identity)),bind(X_10,$fot(X_85)),bind(X_8,$fot(X_86))]]) ).
cnf(refute_0_393,plain,
double_divide(identity,X_83) = inverse(X_83),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(X_83))]]) ).
cnf(refute_0_394,plain,
( double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),double_divide(identity,X_83))) != X_85
| double_divide(identity,X_83) != inverse(X_83)
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = X_85 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),double_divide(identity,X_83))),X_85) ),[0,1,1],$fot(inverse(X_83))]]) ).
cnf(refute_0_395,plain,
( double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),double_divide(identity,X_83))) != X_85
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = X_85 ),
inference(resolve,[$cnf( $equal(double_divide(identity,X_83),inverse(X_83)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = X_85,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),double_divide(identity,X_83))),X_85) )],[refute_0_392,refute_0_395]) ).
cnf(refute_0_397,plain,
multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = inverse(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9))),
inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(double_divide(X_10,X_8),X_9))),bind(Y,$fot(double_divide(identity,double_divide(X_8,inverse(X_9)))))]]) ).
cnf(refute_0_398,plain,
double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)) = X_10,
inference(subst,[],[refute_0_51:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_399,plain,
( multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != inverse(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)))
| double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)) != X_10
| multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),inverse(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_400,plain,
( multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != inverse(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)))
| multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = inverse(X_10) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)),X_10) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),inverse(double_divide(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(double_divide(X_10,X_8),X_9)))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
inverse(double_divide(X_8,inverse(X_9))) = multiply(inverse(X_9),X_8),
inference(subst,[],[refute_0_43:[bind(X,$fot(inverse(X_9))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_403,plain,
double_divide(identity,double_divide(X_8,inverse(X_9))) = inverse(double_divide(X_8,inverse(X_9))),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(double_divide(X_8,inverse(X_9))))]]) ).
cnf(refute_0_404,plain,
( double_divide(identity,double_divide(X_8,inverse(X_9))) != inverse(double_divide(X_8,inverse(X_9)))
| inverse(double_divide(X_8,inverse(X_9))) != multiply(inverse(X_9),X_8)
| double_divide(identity,double_divide(X_8,inverse(X_9))) = multiply(inverse(X_9),X_8) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(identity,double_divide(X_8,inverse(X_9))))),bind(Y0,$fot(inverse(double_divide(X_8,inverse(X_9))))),bind(Z0,$fot(multiply(inverse(X_9),X_8)))]]) ).
cnf(refute_0_405,plain,
( inverse(double_divide(X_8,inverse(X_9))) != multiply(inverse(X_9),X_8)
| double_divide(identity,double_divide(X_8,inverse(X_9))) = multiply(inverse(X_9),X_8) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_8,inverse(X_9))),inverse(double_divide(X_8,inverse(X_9)))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
double_divide(identity,double_divide(X_8,inverse(X_9))) = multiply(inverse(X_9),X_8),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_8,inverse(X_9))),multiply(inverse(X_9),X_8)) )],[refute_0_402,refute_0_405]) ).
cnf(refute_0_407,plain,
multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),
introduced(tautology,[refl,[$fot(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))))]]) ).
cnf(refute_0_408,plain,
( multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9))))
| double_divide(identity,double_divide(X_8,inverse(X_9))) != multiply(inverse(X_9),X_8)
| multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9))))) ),[1,1],$fot(multiply(inverse(X_9),X_8))]]) ).
cnf(refute_0_409,plain,
( double_divide(identity,double_divide(X_8,inverse(X_9))) != multiply(inverse(X_9),X_8)
| multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9))))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) = multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_8,inverse(X_9))),multiply(inverse(X_9),X_8)) )],[refute_0_406,refute_0_409]) ).
cnf(refute_0_411,plain,
( multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8))
| multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != inverse(X_10)
| multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)) = inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),inverse(X_10)) ),[0],$fot(multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)))]]) ).
cnf(refute_0_412,plain,
( multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))) != inverse(X_10)
| multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)) = inverse(X_10) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
multiply(multiply(double_divide(X_10,X_8),X_9),multiply(inverse(X_9),X_8)) = inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_10,X_8),X_9),double_divide(identity,double_divide(X_8,inverse(X_9)))),inverse(X_10)) )],[refute_0_401,refute_0_412]) ).
cnf(refute_0_414,plain,
multiply(multiply(double_divide(inverse(X_46),X_46),X_47),multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)),
inference(subst,[],[refute_0_413:[bind(X_10,$fot(inverse(X_46))),bind(X_8,$fot(X_46)),bind(X_9,$fot(X_47))]]) ).
cnf(refute_0_415,plain,
double_divide(inverse(X_46),X_46) = identity,
inference(subst,[],[refute_0_303:[bind(X_11,$fot(X_46))]]) ).
cnf(refute_0_416,plain,
( multiply(multiply(double_divide(inverse(X_46),X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| double_divide(inverse(X_46),X_46) != identity
| multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(inverse(X_46),X_46),X_47),multiply(inverse(X_47),X_46)),inverse(inverse(X_46))) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_417,plain,
( multiply(multiply(double_divide(inverse(X_46),X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_46),X_46),identity) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(X_46),X_46),X_47),multiply(inverse(X_47),X_46)),inverse(inverse(X_46))) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
multiply(identity,X_47) = X_47,
inference(subst,[],[refute_0_326:[bind(X_3,$fot(X_47))]]) ).
cnf(refute_0_420,plain,
multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),
introduced(tautology,[refl,[$fot(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)))]]) ).
cnf(refute_0_421,plain,
( multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) != multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46))
| multiply(identity,X_47) != X_47
| multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = multiply(X_47,multiply(inverse(X_47),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46))) ),[1,0],$fot(X_47)]]) ).
cnf(refute_0_422,plain,
( multiply(identity,X_47) != X_47
| multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = multiply(X_47,multiply(inverse(X_47),X_46)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) = multiply(X_47,multiply(inverse(X_47),X_46)),
inference(resolve,[$cnf( $equal(multiply(identity,X_47),X_47) )],[refute_0_419,refute_0_422]) ).
cnf(refute_0_424,plain,
( multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) != multiply(X_47,multiply(inverse(X_47),X_46))
| multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| multiply(X_47,multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),inverse(inverse(X_46))) ),[0],$fot(multiply(X_47,multiply(inverse(X_47),X_46)))]]) ).
cnf(refute_0_425,plain,
( multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| multiply(X_47,multiply(inverse(X_47),X_46)) = inverse(inverse(X_46)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),multiply(X_47,multiply(inverse(X_47),X_46))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
inverse(inverse(X_46)) = X_46,
inference(subst,[],[refute_0_322:[bind(X_38,$fot(X_46))]]) ).
cnf(refute_0_427,plain,
( multiply(X_47,multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| inverse(inverse(X_46)) != X_46
| multiply(X_47,multiply(inverse(X_47),X_46)) = X_46 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_47,multiply(inverse(X_47),X_46)),X_46) ),[0],$fot(inverse(inverse(X_46)))]]) ).
cnf(refute_0_428,plain,
( multiply(X_47,multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| multiply(X_47,multiply(inverse(X_47),X_46)) = X_46 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_46)),X_46) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
( multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)) != inverse(inverse(X_46))
| multiply(X_47,multiply(inverse(X_47),X_46)) = X_46 ),
inference(resolve,[$cnf( $equal(multiply(X_47,multiply(inverse(X_47),X_46)),inverse(inverse(X_46))) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
multiply(X_47,multiply(inverse(X_47),X_46)) = X_46,
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_47),multiply(inverse(X_47),X_46)),inverse(inverse(X_46))) )],[refute_0_418,refute_0_429]) ).
cnf(refute_0_431,plain,
multiply(inverse(X_38),multiply(inverse(inverse(X_38)),X_50)) = X_50,
inference(subst,[],[refute_0_430:[bind(X_46,$fot(X_50)),bind(X_47,$fot(inverse(X_38)))]]) ).
cnf(refute_0_432,plain,
( multiply(inverse(X_38),multiply(inverse(inverse(X_38)),X_50)) != X_50
| inverse(inverse(X_38)) != X_38
| multiply(inverse(X_38),multiply(X_38,X_50)) = X_50 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_38),multiply(inverse(inverse(X_38)),X_50)),X_50) ),[0,1,0],$fot(X_38)]]) ).
cnf(refute_0_433,plain,
( multiply(inverse(X_38),multiply(inverse(inverse(X_38)),X_50)) != X_50
| multiply(inverse(X_38),multiply(X_38,X_50)) = X_50 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_38)),X_38) )],[refute_0_322,refute_0_432]) ).
cnf(refute_0_434,plain,
multiply(inverse(X_38),multiply(X_38,X_50)) = X_50,
inference(resolve,[$cnf( $equal(multiply(inverse(X_38),multiply(inverse(inverse(X_38)),X_50)),X_50) )],[refute_0_431,refute_0_433]) ).
cnf(refute_0_435,plain,
multiply(inverse(multiply(X_38,X_49)),multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38)))) = multiply(inverse(X_49),inverse(X_38)),
inference(subst,[],[refute_0_434:[bind(X_38,$fot(multiply(X_38,X_49))),bind(X_50,$fot(multiply(inverse(X_49),inverse(X_38))))]]) ).
cnf(refute_0_436,plain,
multiply(multiply(double_divide(identity,X_46),X_47),multiply(inverse(X_47),X_46)) = inverse(identity),
inference(subst,[],[refute_0_413:[bind(X_10,$fot(identity)),bind(X_8,$fot(X_46)),bind(X_9,$fot(X_47))]]) ).
cnf(refute_0_437,plain,
double_divide(identity,X_46) = inverse(X_46),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(X_46))]]) ).
cnf(refute_0_438,plain,
( multiply(multiply(double_divide(identity,X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(identity)
| double_divide(identity,X_46) != inverse(X_46)
| multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(identity,X_46),X_47),multiply(inverse(X_47),X_46)),inverse(identity)) ),[0,0,0],$fot(inverse(X_46))]]) ).
cnf(refute_0_439,plain,
( multiply(multiply(double_divide(identity,X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(identity)
| multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,X_46),inverse(X_46)) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(identity,X_46),X_47),multiply(inverse(X_47),X_46)),inverse(identity)) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
( multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(identity)
| inverse(identity) != identity
| multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_442,plain,
( multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) != inverse(identity)
| multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_118,refute_0_441]) ).
cnf(refute_0_443,plain,
multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_46),X_47),multiply(inverse(X_47),X_46)),inverse(identity)) )],[refute_0_440,refute_0_442]) ).
cnf(refute_0_444,plain,
multiply(multiply(inverse(inverse(X_38)),X_49),multiply(inverse(X_49),inverse(X_38))) = identity,
inference(subst,[],[refute_0_443:[bind(X_46,$fot(inverse(X_38))),bind(X_47,$fot(X_49))]]) ).
cnf(refute_0_445,plain,
( multiply(multiply(inverse(inverse(X_38)),X_49),multiply(inverse(X_49),inverse(X_38))) != identity
| inverse(inverse(X_38)) != X_38
| multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_38)),X_49),multiply(inverse(X_49),inverse(X_38))),identity) ),[0,0,0],$fot(X_38)]]) ).
cnf(refute_0_446,plain,
( multiply(multiply(inverse(inverse(X_38)),X_49),multiply(inverse(X_49),inverse(X_38))) != identity
| multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38))) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_38)),X_38) )],[refute_0_322,refute_0_445]) ).
cnf(refute_0_447,plain,
multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_38)),X_49),multiply(inverse(X_49),inverse(X_38))),identity) )],[refute_0_444,refute_0_446]) ).
cnf(refute_0_448,plain,
( multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38))) != identity
| multiply(inverse(multiply(X_38,X_49)),multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38)))) != multiply(inverse(X_49),inverse(X_38))
| multiply(inverse(multiply(X_38,X_49)),identity) = multiply(inverse(X_49),inverse(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38)))),multiply(inverse(X_49),inverse(X_38))) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_449,plain,
( multiply(inverse(multiply(X_38,X_49)),multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38)))) != multiply(inverse(X_49),inverse(X_38))
| multiply(inverse(multiply(X_38,X_49)),identity) = multiply(inverse(X_49),inverse(X_38)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38))),identity) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
multiply(inverse(multiply(X_38,X_49)),identity) = multiply(inverse(X_49),inverse(X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),multiply(multiply(X_38,X_49),multiply(inverse(X_49),inverse(X_38)))),multiply(inverse(X_49),inverse(X_38))) )],[refute_0_435,refute_0_449]) ).
cnf(refute_0_451,plain,
inverse(multiply(X_38,X_49)) = double_divide(X_49,X_38),
inference(subst,[],[refute_0_365:[bind(X,$fot(X_38)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_452,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(subst,[],[refute_0_8:[bind(Y,$fot(identity))]]) ).
cnf(refute_0_453,plain,
double_divide(identity,X) = inverse(X),
inference(subst,[],[refute_0_250:[bind(X_24,$fot(X))]]) ).
cnf(refute_0_454,plain,
( multiply(X,identity) != inverse(double_divide(identity,X))
| double_divide(identity,X) != inverse(X)
| multiply(X,identity) = inverse(inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,identity),inverse(double_divide(identity,X))) ),[1,0],$fot(inverse(X))]]) ).
cnf(refute_0_455,plain,
( multiply(X,identity) != inverse(double_divide(identity,X))
| multiply(X,identity) = inverse(inverse(X)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,X),inverse(X)) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(resolve,[$cnf( $equal(multiply(X,identity),inverse(double_divide(identity,X))) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
inverse(inverse(X)) = X,
inference(subst,[],[refute_0_322:[bind(X_38,$fot(X))]]) ).
cnf(refute_0_458,plain,
( multiply(X,identity) != inverse(inverse(X))
| inverse(inverse(X)) != X
| multiply(X,identity) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,identity),X) ),[0],$fot(inverse(inverse(X)))]]) ).
cnf(refute_0_459,plain,
( multiply(X,identity) != inverse(inverse(X))
| multiply(X,identity) = X ),
inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
multiply(X,identity) = X,
inference(resolve,[$cnf( $equal(multiply(X,identity),inverse(inverse(X))) )],[refute_0_456,refute_0_459]) ).
cnf(refute_0_461,plain,
multiply(inverse(multiply(X_38,X_49)),identity) = inverse(multiply(X_38,X_49)),
inference(subst,[],[refute_0_460:[bind(X,$fot(inverse(multiply(X_38,X_49))))]]) ).
cnf(refute_0_462,plain,
( multiply(inverse(multiply(X_38,X_49)),identity) != inverse(multiply(X_38,X_49))
| inverse(multiply(X_38,X_49)) != double_divide(X_49,X_38)
| multiply(inverse(multiply(X_38,X_49)),identity) = double_divide(X_49,X_38) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(multiply(inverse(multiply(X_38,X_49)),identity))),bind(Y0,$fot(inverse(multiply(X_38,X_49)))),bind(Z0,$fot(double_divide(X_49,X_38)))]]) ).
cnf(refute_0_463,plain,
( inverse(multiply(X_38,X_49)) != double_divide(X_49,X_38)
| multiply(inverse(multiply(X_38,X_49)),identity) = double_divide(X_49,X_38) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),identity),inverse(multiply(X_38,X_49))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
multiply(inverse(multiply(X_38,X_49)),identity) = double_divide(X_49,X_38),
inference(resolve,[$cnf( $equal(inverse(multiply(X_38,X_49)),double_divide(X_49,X_38)) )],[refute_0_451,refute_0_463]) ).
cnf(refute_0_465,plain,
( multiply(inverse(multiply(X_38,X_49)),identity) != multiply(inverse(X_49),inverse(X_38))
| multiply(inverse(multiply(X_38,X_49)),identity) != double_divide(X_49,X_38)
| double_divide(X_49,X_38) = multiply(inverse(X_49),inverse(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),identity),multiply(inverse(X_49),inverse(X_38))) ),[0],$fot(double_divide(X_49,X_38))]]) ).
cnf(refute_0_466,plain,
( multiply(inverse(multiply(X_38,X_49)),identity) != multiply(inverse(X_49),inverse(X_38))
| double_divide(X_49,X_38) = multiply(inverse(X_49),inverse(X_38)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),identity),double_divide(X_49,X_38)) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
double_divide(X_49,X_38) = multiply(inverse(X_49),inverse(X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_38,X_49)),identity),multiply(inverse(X_49),inverse(X_38))) )],[refute_0_450,refute_0_466]) ).
cnf(refute_0_468,plain,
double_divide(multiply(X_70,X_71),X_38) = multiply(inverse(multiply(X_70,X_71)),inverse(X_38)),
inference(subst,[],[refute_0_467:[bind(X_49,$fot(multiply(X_70,X_71)))]]) ).
cnf(refute_0_469,plain,
inverse(multiply(X_70,X_71)) = double_divide(X_71,X_70),
inference(subst,[],[refute_0_365:[bind(X,$fot(X_70)),bind(Y,$fot(X_71))]]) ).
cnf(refute_0_470,plain,
( double_divide(multiply(X_70,X_71),X_38) != multiply(inverse(multiply(X_70,X_71)),inverse(X_38))
| inverse(multiply(X_70,X_71)) != double_divide(X_71,X_70)
| double_divide(multiply(X_70,X_71),X_38) = multiply(double_divide(X_71,X_70),inverse(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_70,X_71),X_38),multiply(inverse(multiply(X_70,X_71)),inverse(X_38))) ),[1,0],$fot(double_divide(X_71,X_70))]]) ).
cnf(refute_0_471,plain,
( double_divide(multiply(X_70,X_71),X_38) != multiply(inverse(multiply(X_70,X_71)),inverse(X_38))
| double_divide(multiply(X_70,X_71),X_38) = multiply(double_divide(X_71,X_70),inverse(X_38)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_70,X_71)),double_divide(X_71,X_70)) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
double_divide(multiply(X_70,X_71),X_38) = multiply(double_divide(X_71,X_70),inverse(X_38)),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_70,X_71),X_38),multiply(inverse(multiply(X_70,X_71)),inverse(X_38))) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
( double_divide(multiply(X_70,X_71),X_38) != multiply(double_divide(X_71,X_70),inverse(X_38))
| multiply(double_divide(X_71,X_70),inverse(X_38)) = double_divide(multiply(X_70,X_71),X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(double_divide(multiply(X_70,X_71),X_38))),bind(Y0,$fot(multiply(double_divide(X_71,X_70),inverse(X_38))))]]) ).
cnf(refute_0_474,plain,
multiply(double_divide(X_71,X_70),inverse(X_38)) = double_divide(multiply(X_70,X_71),X_38),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_70,X_71),X_38),multiply(double_divide(X_71,X_70),inverse(X_38))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
multiply(double_divide(X_85,X_86),inverse(X_83)) = double_divide(multiply(X_86,X_85),X_83),
inference(subst,[],[refute_0_474:[bind(X_38,$fot(X_83)),bind(X_70,$fot(X_86)),bind(X_71,$fot(X_85))]]) ).
cnf(refute_0_476,plain,
double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))))]]) ).
cnf(refute_0_477,plain,
( multiply(double_divide(X_85,X_86),inverse(X_83)) != double_divide(multiply(X_86,X_85),X_83)
| double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))
| double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))) ),[1,1],$fot(double_divide(multiply(X_86,X_85),X_83))]]) ).
cnf(refute_0_478,plain,
( multiply(double_divide(X_85,X_86),inverse(X_83)) != double_divide(multiply(X_86,X_85),X_83)
| double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_85,X_86),inverse(X_83)),double_divide(multiply(X_86,X_85),X_83)) )],[refute_0_475,refute_0_478]) ).
cnf(refute_0_480,plain,
multiply(X_83,identity) = X_83,
inference(subst,[],[refute_0_460:[bind(X,$fot(X_83))]]) ).
cnf(refute_0_481,plain,
multiply(multiply(X_83,identity),X_86) = multiply(multiply(X_83,identity),X_86),
introduced(tautology,[refl,[$fot(multiply(multiply(X_83,identity),X_86))]]) ).
cnf(refute_0_482,plain,
( multiply(X_83,identity) != X_83
| multiply(multiply(X_83,identity),X_86) != multiply(multiply(X_83,identity),X_86)
| multiply(multiply(X_83,identity),X_86) = multiply(X_83,X_86) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_83,identity),X_86),multiply(multiply(X_83,identity),X_86)) ),[1,0],$fot(X_83)]]) ).
cnf(refute_0_483,plain,
( multiply(X_83,identity) != X_83
| multiply(multiply(X_83,identity),X_86) = multiply(X_83,X_86) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_83,identity),X_86),multiply(multiply(X_83,identity),X_86)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
multiply(multiply(X_83,identity),X_86) = multiply(X_83,X_86),
inference(resolve,[$cnf( $equal(multiply(X_83,identity),X_83) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),
introduced(tautology,[refl,[$fot(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))))]]) ).
cnf(refute_0_486,plain,
( multiply(multiply(X_83,identity),X_86) != multiply(X_83,X_86)
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))) ),[1,0],$fot(multiply(X_83,X_86))]]) ).
cnf(refute_0_487,plain,
( multiply(multiply(X_83,identity),X_86) != multiply(X_83,X_86)
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_83,identity),X_86),multiply(X_83,X_86)) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
( double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))))),bind(Y0,$fot(double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))))),bind(Z0,$fot(double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))))]]) ).
cnf(refute_0_490,plain,
( double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83)))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) = double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_83,X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))) )],[refute_0_479,refute_0_490]) ).
cnf(refute_0_492,plain,
( double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != X_85
| double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))
| double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) = X_85 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),X_85) ),[0],$fot(double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)))]]) ).
cnf(refute_0_493,plain,
( double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))) != X_85
| double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) = X_85 ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
double_divide(multiply(X_83,X_86),double_divide(multiply(X_86,X_85),X_83)) = X_85,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(X_83,identity),X_86),multiply(double_divide(X_85,X_86),inverse(X_83))),X_85) )],[refute_0_396,refute_0_493]) ).
cnf(refute_0_495,plain,
double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)) = X_94,
inference(subst,[],[refute_0_494:[bind(X_83,$fot(X_93)),bind(X_85,$fot(X_94)),bind(X_86,$fot(X_95))]]) ).
cnf(refute_0_496,plain,
( double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)) != X_94
| double_divide(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),multiply(X_93,X_95)) != double_divide(multiply(X_95,X_94),X_93)
| double_divide(X_94,multiply(X_93,X_95)) = double_divide(multiply(X_95,X_94),X_93) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),multiply(X_93,X_95)),double_divide(multiply(X_95,X_94),X_93)) ),[0,0],$fot(X_94)]]) ).
cnf(refute_0_497,plain,
( double_divide(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),multiply(X_93,X_95)) != double_divide(multiply(X_95,X_94),X_93)
| double_divide(X_94,multiply(X_93,X_95)) = double_divide(multiply(X_95,X_94),X_93) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),X_94) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
double_divide(X_94,multiply(X_93,X_95)) = double_divide(multiply(X_95,X_94),X_93),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_93,X_95),double_divide(multiply(X_95,X_94),X_93)),multiply(X_93,X_95)),double_divide(multiply(X_95,X_94),X_93)) )],[refute_0_375,refute_0_497]) ).
cnf(refute_0_499,plain,
double_divide(X_97,multiply(X,X_98)) = double_divide(multiply(X_98,X_97),X),
inference(subst,[],[refute_0_498:[bind(X_93,$fot(X)),bind(X_94,$fot(X_97)),bind(X_95,$fot(X_98))]]) ).
cnf(refute_0_500,plain,
( double_divide(X_97,multiply(X,X_98)) != double_divide(multiply(X_98,X_97),X)
| double_divide(multiply(X_98,X_97),X) = double_divide(X_97,multiply(X,X_98)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(double_divide(X_97,multiply(X,X_98)))),bind(Y0,$fot(double_divide(multiply(X_98,X_97),X)))]]) ).
cnf(refute_0_501,plain,
double_divide(multiply(X_98,X_97),X) = double_divide(X_97,multiply(X,X_98)),
inference(resolve,[$cnf( $equal(double_divide(X_97,multiply(X,X_98)),double_divide(multiply(X_98,X_97),X)) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
( multiply(X,multiply(X_98,X_97)) != inverse(double_divide(multiply(X_98,X_97),X))
| double_divide(multiply(X_98,X_97),X) != double_divide(X_97,multiply(X,X_98))
| multiply(X,multiply(X_98,X_97)) = inverse(double_divide(X_97,multiply(X,X_98))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiply(X_98,X_97)),inverse(double_divide(multiply(X_98,X_97),X))) ),[1,0],$fot(double_divide(X_97,multiply(X,X_98)))]]) ).
cnf(refute_0_503,plain,
( multiply(X,multiply(X_98,X_97)) != inverse(double_divide(multiply(X_98,X_97),X))
| multiply(X,multiply(X_98,X_97)) = inverse(double_divide(X_97,multiply(X,X_98))) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_98,X_97),X),double_divide(X_97,multiply(X,X_98))) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
multiply(X,multiply(X_98,X_97)) = inverse(double_divide(X_97,multiply(X,X_98))),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_98,X_97)),inverse(double_divide(multiply(X_98,X_97),X))) )],[refute_0_335,refute_0_503]) ).
cnf(refute_0_505,plain,
inverse(double_divide(X_97,multiply(X,X_98))) = multiply(multiply(X,X_98),X_97),
inference(subst,[],[refute_0_43:[bind(X,$fot(multiply(X,X_98))),bind(Y,$fot(X_97))]]) ).
cnf(refute_0_506,plain,
( multiply(X,multiply(X_98,X_97)) != inverse(double_divide(X_97,multiply(X,X_98)))
| inverse(double_divide(X_97,multiply(X,X_98))) != multiply(multiply(X,X_98),X_97)
| multiply(X,multiply(X_98,X_97)) = multiply(multiply(X,X_98),X_97) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,multiply(X_98,X_97)),multiply(multiply(X,X_98),X_97)) ),[0],$fot(inverse(double_divide(X_97,multiply(X,X_98))))]]) ).
cnf(refute_0_507,plain,
( multiply(X,multiply(X_98,X_97)) != inverse(double_divide(X_97,multiply(X,X_98)))
| multiply(X,multiply(X_98,X_97)) = multiply(multiply(X,X_98),X_97) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_97,multiply(X,X_98))),multiply(multiply(X,X_98),X_97)) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
multiply(X,multiply(X_98,X_97)) = multiply(multiply(X,X_98),X_97),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_98,X_97)),inverse(double_divide(X_97,multiply(X,X_98)))) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
( multiply(X,multiply(X_98,X_97)) != multiply(multiply(X,X_98),X_97)
| multiply(multiply(X,X_98),X_97) = multiply(X,multiply(X_98,X_97)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,multiply(X_98,X_97)))),bind(Y0,$fot(multiply(multiply(X,X_98),X_97)))]]) ).
cnf(refute_0_510,plain,
multiply(multiply(X,X_98),X_97) = multiply(X,multiply(X_98,X_97)),
inference(resolve,[$cnf( $equal(multiply(X,multiply(X_98,X_97)),multiply(multiply(X,X_98),X_97)) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_510:[bind(X,$fot(a3)),bind(X_97,$fot(c3)),bind(X_98,$fot(b3))]]) ).
cnf(refute_0_512,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_513,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_513,refute_0_334]) ).
cnf(refute_0_515,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_516,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_515,refute_0_514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP080-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 12:09:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.53
%------------------------------------------------------------------------------