%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:41:41 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 122
% Number of leaves : 186
% Syntax : Number of clauses : 644 ( 325 unt; 0 nHn; 350 RR)
% Number of literals : 1115 (1114 equ; 473 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 1082 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ).
cnf(multiply,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity) ).
cnf(inverse,axiom,
inverse(A) = double_divide(A,identity) ).
cnf(identity,axiom,
identity = double_divide(A,inverse(A)) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(double_divide(A,identity),double_divide(B,C)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,identity),double_divide(B,C)))]]) ).
cnf(refute_0_6,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(double_divide(A,identity),double_divide(B,C)) != double_divide(double_divide(A,identity),double_divide(B,C))
| double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(inverse(A),double_divide(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,identity),double_divide(B,C)),double_divide(double_divide(A,identity),double_divide(B,C))) ),[1,0],$fot(inverse(A))]]) ).
cnf(refute_0_7,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(inverse(A),double_divide(B,C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,identity),double_divide(B,C)),double_divide(double_divide(A,identity),double_divide(B,C))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(inverse(A),double_divide(B,C)),
inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) = double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))))]]) ).
cnf(refute_0_10,plain,
( double_divide(double_divide(A,identity),double_divide(B,C)) != double_divide(inverse(A),double_divide(B,C))
| double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) != double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C)))
| double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) = double_divide(identity,double_divide(inverse(A),double_divide(B,C))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C)))) ),[1,1],$fot(double_divide(inverse(A),double_divide(B,C)))]]) ).
cnf(refute_0_11,plain,
( double_divide(double_divide(A,identity),double_divide(B,C)) != double_divide(inverse(A),double_divide(B,C))
| double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) = double_divide(identity,double_divide(inverse(A),double_divide(B,C))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) = double_divide(identity,double_divide(inverse(A),double_divide(B,C))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,identity),double_divide(B,C)),double_divide(inverse(A),double_divide(B,C))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) = double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))]]) ).
cnf(refute_0_14,plain,
( double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) != double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)
| double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) != double_divide(identity,double_divide(inverse(A),double_divide(B,C)))
| double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) = double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) ),[1,0],$fot(double_divide(identity,double_divide(inverse(A),double_divide(B,C))))]]) ).
cnf(refute_0_15,plain,
( double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))) != double_divide(identity,double_divide(inverse(A),double_divide(B,C)))
| double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) = double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) = double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),double_divide(identity,double_divide(inverse(A),double_divide(B,C)))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)),
introduced(tautology,[refl,[$fot(inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)))]]) ).
cnf(refute_0_18,plain,
( double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) != double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)
| inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) != inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))
| inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)),inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))) ),[1,0],$fot(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))]]) ).
cnf(refute_0_19,plain,
( double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B) != double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)
| inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)),inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)))]]) ).
cnf(refute_0_22,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
( double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) != inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))
| inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) != inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))
| double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))),bind(Y,$fot(inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)))),bind(Z,$fot(inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))))]]) ).
cnf(refute_0_25,plain,
( inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)) != inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))
| double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity),inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) = inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B)),inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)))]]) ).
cnf(refute_0_28,plain,
( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) != double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))
| double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) != inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))
| double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))) ),[1,1],$fot(inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))]]) ).
cnf(refute_0_29,plain,
( double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity) != inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))
| double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity),inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) != C
| double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) != double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))
| double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),C) ),[0],$fot(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))))]]) ).
cnf(refute_0_32,plain,
( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) != C
| double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = C ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = C,
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)),C) )],[single_axiom,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_35,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| double_divide(double_divide(B,A),identity) != inverse(double_divide(B,A))
| multiply(A,B) = inverse(double_divide(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),inverse(double_divide(B,A))) ),[0],$fot(double_divide(double_divide(B,A),identity))]]) ).
cnf(refute_0_36,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_39,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) = multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C)))),
inference(subst,[],[refute_0_39:[bind(A,$fot(B)),bind(B,$fot(double_divide(identity,double_divide(inverse(A),double_divide(B,C)))))]]) ).
cnf(refute_0_41,plain,
double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),
introduced(tautology,[refl,[$fot(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))))]]) ).
cnf(refute_0_42,plain,
( double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) != double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))
| inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) != multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))
| double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))) ),[1,1],$fot(multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C)))))]]) ).
cnf(refute_0_43,plain,
( inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)) != multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))
| double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) ),
inference(resolve,[$cnf( $equal(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) = double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))),
inference(resolve,[$cnf( $equal(inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B)),multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) != C
| double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) != double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C)))))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),C) ),[0],$fot(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))))]]) ).
cnf(refute_0_46,plain,
( double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))) != C
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) = C ),
inference(resolve,[$cnf( $equal(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C)))))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,C))))) = C,
inference(resolve,[$cnf( $equal(double_divide(A,inverse(double_divide(double_divide(identity,double_divide(inverse(A),double_divide(B,C))),B))),C) )],[refute_0_33,refute_0_46]) ).
cnf(refute_0_48,plain,
double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(inverse(double_divide(B,A)),double_divide(X_11,X_12))))) = X_12,
inference(subst,[],[refute_0_47:[bind(A,$fot(double_divide(B,A))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_49,plain,
( double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(inverse(double_divide(B,A)),double_divide(X_11,X_12))))) != X_12
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(inverse(double_divide(B,A)),double_divide(X_11,X_12))))),X_12) ),[0,1,1,1,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(inverse(double_divide(B,A)),double_divide(X_11,X_12))))) != X_12
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = X_12 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_49]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(inverse(double_divide(B,A)),double_divide(X_11,X_12))))),X_12) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),multiply(A,B)),
inference(subst,[],[refute_0_39:[bind(A,$fot(double_divide(X_11,X_12))),bind(B,$fot(multiply(A,B)))]]) ).
cnf(refute_0_53,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,inverse(X_11)))))) = inverse(X_11),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(X_11)))]]) ).
cnf(refute_0_54,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_55,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_56,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,inverse(X_11)))))) != inverse(X_11)
| double_divide(X_11,inverse(X_11)) != identity
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,inverse(X_11)))))),inverse(X_11)) ),[0,1,1,1,1],$fot(identity)]]) ).
cnf(refute_0_58,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,inverse(X_11)))))) != inverse(X_11)
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,inverse(X_11)))))),inverse(X_11)) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(inverse(X_10),identity) = inverse(inverse(X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_61,plain,
double_divide(identity,double_divide(inverse(X_10),identity)) = double_divide(identity,double_divide(inverse(X_10),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(X_10),identity)))]]) ).
cnf(refute_0_62,plain,
( double_divide(identity,double_divide(inverse(X_10),identity)) != double_divide(identity,double_divide(inverse(X_10),identity))
| double_divide(inverse(X_10),identity) != inverse(inverse(X_10))
| double_divide(identity,double_divide(inverse(X_10),identity)) = double_divide(identity,inverse(inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_10),identity)),double_divide(identity,double_divide(inverse(X_10),identity))) ),[1,1],$fot(inverse(inverse(X_10)))]]) ).
cnf(refute_0_63,plain,
( double_divide(inverse(X_10),identity) != inverse(inverse(X_10))
| double_divide(identity,double_divide(inverse(X_10),identity)) = double_divide(identity,inverse(inverse(X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_10),identity)),double_divide(identity,double_divide(inverse(X_10),identity))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
double_divide(identity,double_divide(inverse(X_10),identity)) = double_divide(identity,inverse(inverse(X_10))),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),identity),inverse(inverse(X_10))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) = multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))),
introduced(tautology,[refl,[$fot(multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))))]]) ).
cnf(refute_0_66,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) != multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))
| double_divide(identity,double_divide(inverse(X_10),identity)) != double_divide(identity,inverse(inverse(X_10)))
| multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) = multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))),multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) ),[1,1],$fot(double_divide(identity,inverse(inverse(X_10))))]]) ).
cnf(refute_0_67,plain,
( double_divide(identity,double_divide(inverse(X_10),identity)) != double_divide(identity,inverse(inverse(X_10)))
| multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) = multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))),multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) = multiply(X_11,double_divide(identity,inverse(inverse(X_10)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_10),identity)),double_divide(identity,inverse(inverse(X_10)))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),
introduced(tautology,[refl,[$fot(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))))]]) ).
cnf(refute_0_70,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) != multiply(X_11,double_divide(identity,inverse(inverse(X_10))))
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) != double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))))
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))))) ),[1,1],$fot(multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_71,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))) != multiply(X_11,double_divide(identity,inverse(inverse(X_10))))
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) = double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity))),multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) != double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) != inverse(X_11)
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),inverse(X_11)) ),[0],$fot(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))))]]) ).
cnf(refute_0_74,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))) != inverse(X_11)
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),identity)))),inverse(X_11)) )],[refute_0_59,refute_0_74]) ).
cnf(refute_0_76,plain,
double_divide(identity,multiply(X_11,double_divide(identity,inverse(inverse(identity))))) = inverse(X_11),
inference(subst,[],[refute_0_75:[bind(X_10,$fot(identity))]]) ).
cnf(refute_0_77,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,identity))))) = identity,
inference(subst,[],[refute_0_47:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(identity))]]) ).
cnf(refute_0_78,plain,
inverse(X_11) = double_divide(X_11,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_79,plain,
( inverse(X_11) != double_divide(X_11,identity)
| double_divide(X_11,identity) = inverse(X_11) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(double_divide(X_11,identity)))]]) ).
cnf(refute_0_80,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),double_divide(X_11,identity)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,identity))))) != identity
| double_divide(X_11,identity) != inverse(X_11)
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,identity))))),identity) ),[0,1,1,1,1],$fot(inverse(X_11))]]) ).
cnf(refute_0_82,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,identity))))) != identity
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) = identity,
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),double_divide(X_11,identity))))),identity) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))))) = multiply(X_14,double_divide(identity,inverse(inverse(B)))),
inference(subst,[],[refute_0_47:[bind(C,$fot(multiply(X_14,double_divide(identity,inverse(inverse(B))))))]]) ).
cnf(refute_0_85,plain,
double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))) = inverse(X_14),
inference(subst,[],[refute_0_75:[bind(X_10,$fot(B)),bind(X_11,$fot(X_14))]]) ).
cnf(refute_0_86,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))))) != multiply(X_14,double_divide(identity,inverse(inverse(B))))
| double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))) != inverse(X_14)
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(X_14))))) = multiply(X_14,double_divide(identity,inverse(inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))))),multiply(X_14,double_divide(identity,inverse(inverse(B))))) ),[0,1,1,1,1],$fot(inverse(X_14))]]) ).
cnf(refute_0_87,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))))) != multiply(X_14,double_divide(identity,inverse(inverse(B))))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(X_14))))) = multiply(X_14,double_divide(identity,inverse(inverse(B)))) ),
inference(resolve,[$cnf( $equal(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))),inverse(X_14)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(X_14))))) = multiply(X_14,double_divide(identity,inverse(inverse(B)))),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))))),multiply(X_14,double_divide(identity,inverse(inverse(B))))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) = multiply(X_11,double_divide(identity,inverse(inverse(X_11)))),
inference(subst,[],[refute_0_88:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(X_14,$fot(X_11))]]) ).
cnf(refute_0_90,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) != multiply(X_11,double_divide(identity,inverse(inverse(X_11))))
| double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) != identity
| multiply(X_11,double_divide(identity,inverse(inverse(X_11)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))),identity) ),[0],$fot(multiply(X_11,double_divide(identity,inverse(inverse(X_11)))))]]) ).
cnf(refute_0_91,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))) != identity
| multiply(X_11,double_divide(identity,inverse(inverse(X_11)))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))),multiply(X_11,double_divide(identity,inverse(inverse(X_11))))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(X_11,double_divide(identity,inverse(inverse(X_11)))) = identity,
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,double_divide(inverse(X_10),inverse(X_11))))),identity) )],[refute_0_83,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(multiply(inverse(inverse(X_13)),identity))))) = identity,
inference(subst,[],[refute_0_92:[bind(X_11,$fot(multiply(inverse(inverse(X_13)),identity)))]]) ).
cnf(refute_0_94,plain,
double_divide(X_13,multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13))))) = inverse(multiply(inverse(inverse(X_13)),identity)),
inference(subst,[],[refute_0_75:[bind(X_10,$fot(X_13)),bind(X_11,$fot(multiply(inverse(inverse(X_13)),identity)))]]) ).
cnf(refute_0_95,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_37:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_96,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_97,plain,
( identity != double_divide(X_3,inverse(X_3))
| double_divide(X_3,inverse(X_3)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_3,inverse(X_3))))]]) ).
cnf(refute_0_98,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_100,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(inverse(double_divide(B,A)),double_divide(B,A)) = inverse(identity),
inference(subst,[],[refute_0_101:[bind(X_3,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(double_divide(B,A)),double_divide(B,A)) != inverse(identity)
| inverse(double_divide(B,A)) != multiply(A,B)
| multiply(multiply(A,B),double_divide(B,A)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(B,A)),double_divide(B,A)),inverse(identity)) ),[0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_104,plain,
( multiply(inverse(double_divide(B,A)),double_divide(B,A)) != inverse(identity)
| multiply(multiply(A,B),double_divide(B,A)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_103]) ).
cnf(refute_0_105,plain,
multiply(multiply(A,B),double_divide(B,A)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(B,A)),double_divide(B,A)),inverse(identity)) )],[refute_0_102,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13)))) = inverse(identity),
inference(subst,[],[refute_0_105:[bind(A,$fot(inverse(inverse(X_13)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_107,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13)))) != inverse(identity)
| double_divide(X_13,multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13))))) != inverse(multiply(inverse(inverse(X_13)),identity))
| double_divide(X_13,inverse(identity)) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_13,multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13))))),inverse(multiply(inverse(inverse(X_13)),identity))) ),[0,1],$fot(inverse(identity))]]) ).
cnf(refute_0_108,plain,
( double_divide(X_13,multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13))))) != inverse(multiply(inverse(inverse(X_13)),identity))
| double_divide(X_13,inverse(identity)) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13)))),inverse(identity)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
double_divide(X_13,inverse(identity)) = inverse(multiply(inverse(inverse(X_13)),identity)),
inference(resolve,[$cnf( $equal(double_divide(X_13,multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(X_13))))),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_94,refute_0_108]) ).
cnf(refute_0_110,plain,
( double_divide(X_13,inverse(identity)) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(multiply(inverse(inverse(X_13)),identity)) = double_divide(X_13,inverse(identity)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(double_divide(X_13,inverse(identity)))),bind(Y,$fot(inverse(multiply(inverse(inverse(X_13)),identity))))]]) ).
cnf(refute_0_111,plain,
inverse(multiply(inverse(inverse(X_13)),identity)) = double_divide(X_13,inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(identity)),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(multiply(inverse(inverse(X_13)),identity))))) != identity
| inverse(multiply(inverse(inverse(X_13)),identity)) != double_divide(X_13,inverse(identity))
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(multiply(inverse(inverse(X_13)),identity))))),identity) ),[0,1,1,0],$fot(double_divide(X_13,inverse(identity)))]]) ).
cnf(refute_0_113,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(multiply(inverse(inverse(X_13)),identity))))) != identity
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = identity ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X_13)),identity)),double_divide(X_13,inverse(identity))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(inverse(multiply(inverse(inverse(X_13)),identity))))),identity) )],[refute_0_93,refute_0_113]) ).
cnf(refute_0_115,plain,
inverse(double_divide(X_13,inverse(identity))) = multiply(inverse(identity),X_13),
inference(subst,[],[refute_0_39:[bind(A,$fot(inverse(identity))),bind(B,$fot(X_13))]]) ).
cnf(refute_0_116,plain,
double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) = double_divide(identity,inverse(double_divide(X_13,inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(double_divide(X_13,inverse(identity)))))]]) ).
cnf(refute_0_117,plain,
( double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) != double_divide(identity,inverse(double_divide(X_13,inverse(identity))))
| inverse(double_divide(X_13,inverse(identity))) != multiply(inverse(identity),X_13)
| double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) = double_divide(identity,multiply(inverse(identity),X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(double_divide(X_13,inverse(identity)))),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) ),[1,1],$fot(multiply(inverse(identity),X_13))]]) ).
cnf(refute_0_118,plain,
( inverse(double_divide(X_13,inverse(identity))) != multiply(inverse(identity),X_13)
| double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) = double_divide(identity,multiply(inverse(identity),X_13)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(double_divide(X_13,inverse(identity)))),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) = double_divide(identity,multiply(inverse(identity),X_13)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_13,inverse(identity))),multiply(inverse(identity),X_13)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))))]]) ).
cnf(refute_0_121,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) != multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity)))))
| double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) != double_divide(identity,multiply(inverse(identity),X_13))
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity)))))) ),[1,1],$fot(double_divide(identity,multiply(inverse(identity),X_13)))]]) ).
cnf(refute_0_122,plain,
( double_divide(identity,inverse(double_divide(X_13,inverse(identity)))) != double_divide(identity,multiply(inverse(identity),X_13))
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity)))))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) = multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(double_divide(X_13,inverse(identity)))),double_divide(identity,multiply(inverse(identity),X_13))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) != multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13)))
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) != identity
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),identity) ),[0],$fot(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))))]]) ).
cnf(refute_0_125,plain,
( multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))) != identity
| multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,multiply(inverse(identity),X_13))) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_13)),identity),double_divide(identity,inverse(double_divide(X_13,inverse(identity))))),identity) )],[refute_0_114,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))))) = identity,
inference(subst,[],[refute_0_126:[bind(X_13,$fot(double_divide(identity,inverse(inverse(inverse(identity))))))]]) ).
cnf(refute_0_128,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))) = identity,
inference(subst,[],[refute_0_92:[bind(X_11,$fot(inverse(identity)))]]) ).
cnf(refute_0_129,plain,
( multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))))) != identity
| multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))) != identity
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))))),identity) ),[0,1,1],$fot(identity)]]) ).
cnf(refute_0_130,plain,
( multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))))) != identity
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))),identity) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))))),identity) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_133,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)))]]) ).
cnf(refute_0_134,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_135,plain,
( double_divide(identity,identity) != inverse(identity)
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
inverse(multiply(inverse(inverse(inverse(identity))),identity)) = double_divide(inverse(identity),inverse(identity)),
inference(subst,[],[refute_0_111:[bind(X_13,$fot(inverse(identity)))]]) ).
cnf(refute_0_138,plain,
inverse(double_divide(identity,inverse(inverse(inverse(identity))))) = multiply(inverse(inverse(inverse(identity))),identity),
inference(subst,[],[refute_0_39:[bind(A,$fot(inverse(inverse(inverse(identity))))),bind(B,$fot(identity))]]) ).
cnf(refute_0_139,plain,
inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))))]]) ).
cnf(refute_0_140,plain,
( inverse(double_divide(identity,inverse(inverse(inverse(identity))))) != multiply(inverse(inverse(inverse(identity))),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) != inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity))))))
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = inverse(multiply(inverse(inverse(inverse(identity))),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity))))))) ),[1,0],$fot(multiply(inverse(inverse(inverse(identity))),identity))]]) ).
cnf(refute_0_141,plain,
( inverse(double_divide(identity,inverse(inverse(inverse(identity))))) != multiply(inverse(inverse(inverse(identity))),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = inverse(multiply(inverse(inverse(inverse(identity))),identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity))))))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = inverse(multiply(inverse(inverse(inverse(identity))),identity)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(inverse(identity))))),multiply(inverse(inverse(inverse(identity))),identity)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( inverse(multiply(inverse(inverse(inverse(identity))),identity)) != double_divide(inverse(identity),inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) != inverse(multiply(inverse(inverse(inverse(identity))),identity))
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = double_divide(inverse(identity),inverse(identity)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))))),bind(Y,$fot(inverse(multiply(inverse(inverse(inverse(identity))),identity)))),bind(Z,$fot(double_divide(inverse(identity),inverse(identity))))]]) ).
cnf(refute_0_144,plain,
( inverse(multiply(inverse(inverse(inverse(identity))),identity)) != double_divide(inverse(identity),inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = double_divide(inverse(identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),inverse(multiply(inverse(inverse(inverse(identity))),identity))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) = double_divide(inverse(identity),inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(inverse(identity))),identity)),double_divide(inverse(identity),inverse(identity))) )],[refute_0_137,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) = multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity))]]) ).
cnf(refute_0_147,plain,
( multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) != multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) != double_divide(inverse(identity),inverse(identity))
| multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) = multiply(double_divide(inverse(identity),inverse(identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity)) ),[1,0],$fot(double_divide(inverse(identity),inverse(identity)))]]) ).
cnf(refute_0_148,plain,
( inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))) != double_divide(inverse(identity),inverse(identity))
| multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) = multiply(double_divide(inverse(identity),inverse(identity)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) = multiply(double_divide(inverse(identity),inverse(identity)),identity),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),double_divide(inverse(identity),inverse(identity))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)))]]) ).
cnf(refute_0_151,plain,
( multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) != multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity))
| multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) != multiply(double_divide(inverse(identity),inverse(identity)),identity)
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity))) ),[1,0],$fot(multiply(double_divide(inverse(identity),inverse(identity)),identity))]]) ).
cnf(refute_0_152,plain,
( multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity) != multiply(double_divide(inverse(identity),inverse(identity)),identity)
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),multiply(double_divide(inverse(identity),inverse(identity)),identity)) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity))
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)))),bind(Y,$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)))),bind(Z,$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))))]]) ).
cnf(refute_0_155,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),double_divide(identity,identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))) )],[refute_0_136,refute_0_155]) ).
cnf(refute_0_157,plain,
( multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))
| multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) != identity
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),identity) ),[0],$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)))]]) ).
cnf(refute_0_158,plain,
( multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)) != identity
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(double_divide(identity,inverse(inverse(inverse(identity)))))),identity),double_divide(identity,identity)),identity) )],[refute_0_131,refute_0_158]) ).
cnf(refute_0_160,plain,
multiply(multiply(inverse(inverse(identity)),identity),double_divide(identity,multiply(inverse(identity),identity))) = identity,
inference(subst,[],[refute_0_126:[bind(X_13,$fot(identity))]]) ).
cnf(refute_0_161,plain,
double_divide(A,multiply(inverse(A),double_divide(identity,double_divide(inverse(A),double_divide(inverse(A),inverse(identity)))))) = inverse(identity),
inference(subst,[],[refute_0_47:[bind(B,$fot(inverse(A))),bind(C,$fot(inverse(identity)))]]) ).
cnf(refute_0_162,plain,
double_divide(X_13,multiply(identity,double_divide(identity,inverse(inverse(X_13))))) = inverse(identity),
inference(subst,[],[refute_0_75:[bind(X_10,$fot(X_13)),bind(X_11,$fot(identity))]]) ).
cnf(refute_0_163,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_37:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_164,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_165,plain,
( inverse(X_3) != double_divide(X_3,identity)
| double_divide(X_3,identity) = inverse(X_3) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(double_divide(X_3,identity)))]]) ).
cnf(refute_0_166,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_168,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_163,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(identity,double_divide(identity,inverse(inverse(X_13)))) = inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),
inference(subst,[],[refute_0_169:[bind(X_3,$fot(double_divide(identity,inverse(inverse(X_13)))))]]) ).
cnf(refute_0_171,plain,
( multiply(identity,double_divide(identity,inverse(inverse(X_13)))) != inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))
| double_divide(X_13,multiply(identity,double_divide(identity,inverse(inverse(X_13))))) != inverse(identity)
| double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_13,multiply(identity,double_divide(identity,inverse(inverse(X_13))))),inverse(identity)) ),[0,1],$fot(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))]]) ).
cnf(refute_0_172,plain,
( double_divide(X_13,multiply(identity,double_divide(identity,inverse(inverse(X_13))))) != inverse(identity)
| double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,double_divide(identity,inverse(inverse(X_13)))),inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(X_13,multiply(identity,double_divide(identity,inverse(inverse(X_13))))),inverse(identity)) )],[refute_0_162,refute_0_172]) ).
cnf(refute_0_174,plain,
inverse(double_divide(identity,inverse(inverse(X_13)))) = multiply(inverse(inverse(X_13)),identity),
inference(subst,[],[refute_0_39:[bind(A,$fot(inverse(inverse(X_13)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_175,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))]]) ).
cnf(refute_0_176,plain,
( inverse(double_divide(identity,inverse(inverse(X_13)))) != multiply(inverse(inverse(X_13)),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) != inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) ),[1,0],$fot(multiply(inverse(inverse(X_13)),identity))]]) ).
cnf(refute_0_177,plain,
( inverse(double_divide(identity,inverse(inverse(X_13)))) != multiply(inverse(inverse(X_13)),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = inverse(multiply(inverse(inverse(X_13)),identity)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_13)))),multiply(inverse(inverse(X_13)),identity)) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( inverse(multiply(inverse(inverse(X_13)),identity)) != double_divide(X_13,inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = double_divide(X_13,inverse(identity)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))),bind(Y,$fot(inverse(multiply(inverse(inverse(X_13)),identity)))),bind(Z,$fot(double_divide(X_13,inverse(identity))))]]) ).
cnf(refute_0_180,plain,
( inverse(multiply(inverse(inverse(X_13)),identity)) != double_divide(X_13,inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = double_divide(X_13,inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) = double_divide(X_13,inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X_13)),identity)),double_divide(X_13,inverse(identity))) )],[refute_0_111,refute_0_180]) ).
cnf(refute_0_182,plain,
double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),
introduced(tautology,[refl,[$fot(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))))]]) ).
cnf(refute_0_183,plain,
( double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) != double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))
| inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) != double_divide(X_13,inverse(identity))
| double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = double_divide(X_13,double_divide(X_13,inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))) ),[1,1],$fot(double_divide(X_13,inverse(identity)))]]) ).
cnf(refute_0_184,plain,
( inverse(inverse(double_divide(identity,inverse(inverse(X_13))))) != double_divide(X_13,inverse(identity))
| double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = double_divide(X_13,double_divide(X_13,inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13))))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) = double_divide(X_13,double_divide(X_13,inverse(identity))),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(X_13))))),double_divide(X_13,inverse(identity))) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
( double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) != double_divide(X_13,double_divide(X_13,inverse(identity)))
| double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) != inverse(identity)
| double_divide(X_13,double_divide(X_13,inverse(identity))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),inverse(identity)) ),[0],$fot(double_divide(X_13,double_divide(X_13,inverse(identity))))]]) ).
cnf(refute_0_187,plain,
( double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))) != inverse(identity)
| double_divide(X_13,double_divide(X_13,inverse(identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),double_divide(X_13,double_divide(X_13,inverse(identity)))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
double_divide(X_13,double_divide(X_13,inverse(identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(inverse(double_divide(identity,inverse(inverse(X_13)))))),inverse(identity)) )],[refute_0_173,refute_0_187]) ).
cnf(refute_0_189,plain,
double_divide(inverse(A),double_divide(inverse(A),inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_188:[bind(X_13,$fot(inverse(A)))]]) ).
cnf(refute_0_190,plain,
( double_divide(A,multiply(inverse(A),double_divide(identity,double_divide(inverse(A),double_divide(inverse(A),inverse(identity)))))) != inverse(identity)
| double_divide(inverse(A),double_divide(inverse(A),inverse(identity))) != inverse(identity)
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,double_divide(inverse(A),double_divide(inverse(A),inverse(identity)))))),inverse(identity)) ),[0,1,1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_191,plain,
( double_divide(A,multiply(inverse(A),double_divide(identity,double_divide(inverse(A),double_divide(inverse(A),inverse(identity)))))) != inverse(identity)
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(A),double_divide(inverse(A),inverse(identity))),inverse(identity)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,double_divide(inverse(A),double_divide(inverse(A),inverse(identity)))))),inverse(identity)) )],[refute_0_161,refute_0_191]) ).
cnf(refute_0_193,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_194,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_193]) ).
cnf(refute_0_195,plain,
double_divide(identity,inverse(identity)) = identity,
inference(subst,[],[refute_0_194:[bind(A,$fot(identity))]]) ).
cnf(refute_0_196,plain,
multiply(inverse(A),double_divide(identity,inverse(identity))) = multiply(inverse(A),double_divide(identity,inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(inverse(A),double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_197,plain,
( multiply(inverse(A),double_divide(identity,inverse(identity))) != multiply(inverse(A),double_divide(identity,inverse(identity)))
| double_divide(identity,inverse(identity)) != identity
| multiply(inverse(A),double_divide(identity,inverse(identity))) = multiply(inverse(A),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(A),double_divide(identity,inverse(identity))),multiply(inverse(A),double_divide(identity,inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_198,plain,
( double_divide(identity,inverse(identity)) != identity
| multiply(inverse(A),double_divide(identity,inverse(identity))) = multiply(inverse(A),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(A),double_divide(identity,inverse(identity))),multiply(inverse(A),double_divide(identity,inverse(identity)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(inverse(A),double_divide(identity,inverse(identity))) = multiply(inverse(A),identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))))]]) ).
cnf(refute_0_201,plain,
( multiply(inverse(A),double_divide(identity,inverse(identity))) != multiply(inverse(A),identity)
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) != double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity))))
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = double_divide(A,multiply(inverse(A),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity))))) ),[1,1],$fot(multiply(inverse(A),identity))]]) ).
cnf(refute_0_202,plain,
( multiply(inverse(A),double_divide(identity,inverse(identity))) != multiply(inverse(A),identity)
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = double_divide(A,multiply(inverse(A),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity))))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) = double_divide(A,multiply(inverse(A),identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(A),double_divide(identity,inverse(identity))),multiply(inverse(A),identity)) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) != double_divide(A,multiply(inverse(A),identity))
| double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) != inverse(identity)
| double_divide(A,multiply(inverse(A),identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),inverse(identity)) ),[0],$fot(double_divide(A,multiply(inverse(A),identity)))]]) ).
cnf(refute_0_205,plain,
( double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))) != inverse(identity)
| double_divide(A,multiply(inverse(A),identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),double_divide(A,multiply(inverse(A),identity))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
double_divide(A,multiply(inverse(A),identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(inverse(A),double_divide(identity,inverse(identity)))),inverse(identity)) )],[refute_0_192,refute_0_205]) ).
cnf(refute_0_207,plain,
double_divide(identity,multiply(inverse(identity),identity)) = inverse(identity),
inference(subst,[],[refute_0_206:[bind(A,$fot(identity))]]) ).
cnf(refute_0_208,plain,
( multiply(multiply(inverse(inverse(identity)),identity),double_divide(identity,multiply(inverse(identity),identity))) != identity
| double_divide(identity,multiply(inverse(identity),identity)) != inverse(identity)
| multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(identity)),identity),double_divide(identity,multiply(inverse(identity),identity))),identity) ),[0,1],$fot(inverse(identity))]]) ).
cnf(refute_0_209,plain,
( multiply(multiply(inverse(inverse(identity)),identity),double_divide(identity,multiply(inverse(identity),identity))) != identity
| multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(inverse(identity),identity)),inverse(identity)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(identity)),identity),double_divide(identity,multiply(inverse(identity),identity))),identity) )],[refute_0_160,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(multiply(inverse(B),identity),B) = inverse(double_divide(B,multiply(inverse(B),identity))),
inference(subst,[],[refute_0_37:[bind(A,$fot(multiply(inverse(B),identity)))]]) ).
cnf(refute_0_212,plain,
double_divide(B,multiply(inverse(B),identity)) = inverse(identity),
inference(subst,[],[refute_0_206:[bind(A,$fot(B))]]) ).
cnf(refute_0_213,plain,
( multiply(multiply(inverse(B),identity),B) != inverse(double_divide(B,multiply(inverse(B),identity)))
| double_divide(B,multiply(inverse(B),identity)) != inverse(identity)
| multiply(multiply(inverse(B),identity),B) = inverse(inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(B),identity),B),inverse(double_divide(B,multiply(inverse(B),identity)))) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_214,plain,
( multiply(multiply(inverse(B),identity),B) != inverse(double_divide(B,multiply(inverse(B),identity)))
| multiply(multiply(inverse(B),identity),B) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(B,multiply(inverse(B),identity)),inverse(identity)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(multiply(inverse(B),identity),B) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),identity),B),inverse(double_divide(B,multiply(inverse(B),identity)))) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) = inverse(inverse(identity)),
inference(subst,[],[refute_0_215:[bind(B,$fot(inverse(identity)))]]) ).
cnf(refute_0_217,plain,
( multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) != identity
| multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)),identity) ),[0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_218,plain,
( multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)) != identity
| inverse(inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
inverse(inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(identity)),identity),inverse(identity)),identity) )],[refute_0_210,refute_0_218]) ).
cnf(refute_0_220,plain,
inverse(inverse(inverse(identity))) = inverse(inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(inverse(inverse(inverse(identity))))]]) ).
cnf(refute_0_221,plain,
( inverse(inverse(identity)) != identity
| inverse(inverse(inverse(identity))) != inverse(inverse(inverse(identity)))
| inverse(inverse(inverse(identity))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(identity))),inverse(inverse(inverse(identity)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_222,plain,
( inverse(inverse(identity)) != identity
| inverse(inverse(inverse(identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(identity))),inverse(inverse(inverse(identity)))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
inverse(inverse(inverse(identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(identity,inverse(identity)) = inverse(inverse(inverse(identity))),
inference(subst,[],[refute_0_169:[bind(X_3,$fot(inverse(identity)))]]) ).
cnf(refute_0_225,plain,
( multiply(identity,inverse(identity)) != inverse(inverse(inverse(identity)))
| inverse(inverse(inverse(identity))) != inverse(identity)
| multiply(identity,inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(identity,inverse(identity)))),bind(Y,$fot(inverse(inverse(inverse(identity))))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_226,plain,
( inverse(inverse(inverse(identity))) != inverse(identity)
| multiply(identity,inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),inverse(inverse(inverse(identity)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(identity))),inverse(identity)) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(identity,identity) = inverse(inverse(identity)),
inference(subst,[],[refute_0_169:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_229,plain,
( multiply(identity,identity) != inverse(inverse(identity))
| inverse(inverse(identity)) != identity
| multiply(identity,identity) = identity ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(inverse(inverse(identity)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_230,plain,
( inverse(inverse(identity)) != identity
| multiply(identity,identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(identity,identity) = identity,
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_219,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(inverse(inverse(identity)),identity) = multiply(inverse(inverse(identity)),identity),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(identity)),identity))]]) ).
cnf(refute_0_233,plain,
( multiply(inverse(inverse(identity)),identity) != multiply(inverse(inverse(identity)),identity)
| inverse(inverse(identity)) != identity
| multiply(inverse(inverse(identity)),identity) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(identity)),identity),multiply(inverse(inverse(identity)),identity)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_234,plain,
( inverse(inverse(identity)) != identity
| multiply(inverse(inverse(identity)),identity) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(identity)),identity),multiply(inverse(inverse(identity)),identity)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(inverse(inverse(identity)),identity) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_219,refute_0_234]) ).
cnf(refute_0_236,plain,
( multiply(identity,identity) != identity
| multiply(inverse(inverse(identity)),identity) != multiply(identity,identity)
| multiply(inverse(inverse(identity)),identity) = identity ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(inverse(inverse(identity)),identity))),bind(Y,$fot(multiply(identity,identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_237,plain,
( multiply(identity,identity) != identity
| multiply(inverse(inverse(identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(identity)),identity),multiply(identity,identity)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
multiply(inverse(inverse(identity)),identity) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_231,refute_0_237]) ).
cnf(refute_0_239,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(inverse(B),identity)))))) = multiply(inverse(B),identity),
inference(subst,[],[refute_0_47:[bind(C,$fot(multiply(inverse(B),identity)))]]) ).
cnf(refute_0_240,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(inverse(B),identity)))))) != multiply(inverse(B),identity)
| double_divide(B,multiply(inverse(B),identity)) != inverse(identity)
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = multiply(inverse(B),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(inverse(B),identity)))))),multiply(inverse(B),identity)) ),[0,1,1,1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_241,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(inverse(B),identity)))))) != multiply(inverse(B),identity)
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = multiply(inverse(B),identity) ),
inference(resolve,[$cnf( $equal(double_divide(B,multiply(inverse(B),identity)),inverse(identity)) )],[refute_0_212,refute_0_240]) ).
cnf(refute_0_242,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = multiply(inverse(B),identity),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),double_divide(B,multiply(inverse(B),identity)))))),multiply(inverse(B),identity)) )],[refute_0_239,refute_0_241]) ).
cnf(refute_0_243,plain,
inverse(multiply(inverse(inverse(B)),identity)) = double_divide(B,inverse(identity)),
inference(subst,[],[refute_0_111:[bind(X_13,$fot(B))]]) ).
cnf(refute_0_244,plain,
inverse(double_divide(identity,inverse(inverse(B)))) = multiply(inverse(inverse(B)),identity),
inference(subst,[],[refute_0_39:[bind(A,$fot(inverse(inverse(B)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_245,plain,
inverse(inverse(double_divide(identity,inverse(inverse(B))))) = inverse(inverse(double_divide(identity,inverse(inverse(B))))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,inverse(inverse(B))))))]]) ).
cnf(refute_0_246,plain,
( inverse(double_divide(identity,inverse(inverse(B)))) != multiply(inverse(inverse(B)),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) != inverse(inverse(double_divide(identity,inverse(inverse(B)))))
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) = inverse(multiply(inverse(inverse(B)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(B))))),inverse(inverse(double_divide(identity,inverse(inverse(B)))))) ),[1,0],$fot(multiply(inverse(inverse(B)),identity))]]) ).
cnf(refute_0_247,plain,
( inverse(double_divide(identity,inverse(inverse(B)))) != multiply(inverse(inverse(B)),identity)
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) = inverse(multiply(inverse(inverse(B)),identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(B))))),inverse(inverse(double_divide(identity,inverse(inverse(B)))))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
inverse(inverse(double_divide(identity,inverse(inverse(B))))) = inverse(multiply(inverse(inverse(B)),identity)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(B)))),multiply(inverse(inverse(B)),identity)) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( inverse(multiply(inverse(inverse(B)),identity)) != double_divide(B,inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) != inverse(multiply(inverse(inverse(B)),identity))
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) = double_divide(B,inverse(identity)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(inverse(double_divide(identity,inverse(inverse(B))))))),bind(Y,$fot(inverse(multiply(inverse(inverse(B)),identity)))),bind(Z,$fot(double_divide(B,inverse(identity))))]]) ).
cnf(refute_0_250,plain,
( inverse(multiply(inverse(inverse(B)),identity)) != double_divide(B,inverse(identity))
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) = double_divide(B,inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(B))))),inverse(multiply(inverse(inverse(B)),identity))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
inverse(inverse(double_divide(identity,inverse(inverse(B))))) = double_divide(B,inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(B)),identity)),double_divide(B,inverse(identity))) )],[refute_0_243,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(identity,double_divide(identity,inverse(inverse(B)))) = inverse(inverse(double_divide(identity,inverse(inverse(B))))),
inference(subst,[],[refute_0_169:[bind(X_3,$fot(double_divide(identity,inverse(inverse(B)))))]]) ).
cnf(refute_0_253,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = multiply(identity,double_divide(identity,inverse(inverse(B)))),
inference(subst,[],[refute_0_88:[bind(X_14,$fot(identity))]]) ).
cnf(refute_0_254,plain,
( multiply(identity,double_divide(identity,inverse(inverse(B)))) != inverse(inverse(double_divide(identity,inverse(inverse(B)))))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) != multiply(identity,double_divide(identity,inverse(inverse(B))))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = inverse(inverse(double_divide(identity,inverse(inverse(B))))) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))))),bind(Y,$fot(multiply(identity,double_divide(identity,inverse(inverse(B)))))),bind(Z,$fot(inverse(inverse(double_divide(identity,inverse(inverse(B)))))))]]) ).
cnf(refute_0_255,plain,
( multiply(identity,double_divide(identity,inverse(inverse(B)))) != inverse(inverse(double_divide(identity,inverse(inverse(B)))))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = inverse(inverse(double_divide(identity,inverse(inverse(B))))) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))),multiply(identity,double_divide(identity,inverse(inverse(B))))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = inverse(inverse(double_divide(identity,inverse(inverse(B))))),
inference(resolve,[$cnf( $equal(multiply(identity,double_divide(identity,inverse(inverse(B)))),inverse(inverse(double_divide(identity,inverse(inverse(B)))))) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) != inverse(inverse(double_divide(identity,inverse(inverse(B)))))
| inverse(inverse(double_divide(identity,inverse(inverse(B))))) != double_divide(B,inverse(identity))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = double_divide(B,inverse(identity)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))))),bind(Y,$fot(inverse(inverse(double_divide(identity,inverse(inverse(B))))))),bind(Z,$fot(double_divide(B,inverse(identity))))]]) ).
cnf(refute_0_258,plain,
( inverse(inverse(double_divide(identity,inverse(inverse(B))))) != double_divide(B,inverse(identity))
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = double_divide(B,inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))),inverse(inverse(double_divide(identity,inverse(inverse(B)))))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) = double_divide(B,inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,inverse(inverse(B))))),double_divide(B,inverse(identity))) )],[refute_0_251,refute_0_258]) ).
cnf(refute_0_260,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) != multiply(inverse(B),identity)
| double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) != double_divide(B,inverse(identity))
| double_divide(B,inverse(identity)) = multiply(inverse(B),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))),multiply(inverse(B),identity)) ),[0],$fot(double_divide(B,inverse(identity)))]]) ).
cnf(refute_0_261,plain,
( double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))) != multiply(inverse(B),identity)
| double_divide(B,inverse(identity)) = multiply(inverse(B),identity) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))),double_divide(B,inverse(identity))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
double_divide(B,inverse(identity)) = multiply(inverse(B),identity),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(B,double_divide(identity,double_divide(inverse(A),inverse(identity))))),multiply(inverse(B),identity)) )],[refute_0_242,refute_0_261]) ).
cnf(refute_0_263,plain,
double_divide(inverse(identity),inverse(identity)) = multiply(inverse(inverse(identity)),identity),
inference(subst,[],[refute_0_262:[bind(B,$fot(inverse(identity)))]]) ).
cnf(refute_0_264,plain,
( multiply(inverse(inverse(identity)),identity) != identity
| double_divide(inverse(identity),inverse(identity)) != multiply(inverse(inverse(identity)),identity)
| double_divide(inverse(identity),inverse(identity)) = identity ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(inverse(identity),inverse(identity)))),bind(Y,$fot(multiply(inverse(inverse(identity)),identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_265,plain,
( multiply(inverse(inverse(identity)),identity) != identity
| double_divide(inverse(identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),multiply(inverse(inverse(identity)),identity)) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(identity)),identity),identity) )],[refute_0_238,refute_0_265]) ).
cnf(refute_0_267,plain,
multiply(double_divide(inverse(identity),inverse(identity)),identity) = multiply(double_divide(inverse(identity),inverse(identity)),identity),
introduced(tautology,[refl,[$fot(multiply(double_divide(inverse(identity),inverse(identity)),identity))]]) ).
cnf(refute_0_268,plain,
( multiply(double_divide(inverse(identity),inverse(identity)),identity) != multiply(double_divide(inverse(identity),inverse(identity)),identity)
| double_divide(inverse(identity),inverse(identity)) != identity
| multiply(double_divide(inverse(identity),inverse(identity)),identity) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(identity)),identity),multiply(double_divide(inverse(identity),inverse(identity)),identity)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_269,plain,
( double_divide(inverse(identity),inverse(identity)) != identity
| multiply(double_divide(inverse(identity),inverse(identity)),identity) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(identity)),identity),multiply(double_divide(inverse(identity),inverse(identity)),identity)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
multiply(double_divide(inverse(identity),inverse(identity)),identity) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),identity) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
( multiply(double_divide(inverse(identity),inverse(identity)),identity) != multiply(identity,identity)
| multiply(identity,identity) != identity
| multiply(double_divide(inverse(identity),inverse(identity)),identity) = identity ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(double_divide(inverse(identity),inverse(identity)),identity))),bind(Y,$fot(multiply(identity,identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_272,plain,
( multiply(identity,identity) != identity
| multiply(double_divide(inverse(identity),inverse(identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(identity)),identity),multiply(identity,identity)) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
multiply(double_divide(inverse(identity),inverse(identity)),identity) = identity,
inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_231,refute_0_272]) ).
cnf(refute_0_274,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)))]]) ).
cnf(refute_0_275,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) != multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))
| multiply(double_divide(inverse(identity),inverse(identity)),identity) != identity
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = multiply(identity,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_276,plain,
( multiply(double_divide(inverse(identity),inverse(identity)),identity) != identity
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = multiply(identity,inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = multiply(identity,inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(identity),inverse(identity)),identity),identity) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) != multiply(identity,inverse(identity))
| multiply(identity,inverse(identity)) != inverse(identity)
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)))),bind(Y,$fot(multiply(identity,inverse(identity)))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_279,plain,
( multiply(identity,inverse(identity)) != inverse(identity)
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),multiply(identity,inverse(identity))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),inverse(identity)) )],[refute_0_227,refute_0_279]) ).
cnf(refute_0_281,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) != identity
| multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_282,plain,
( multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),inverse(identity)) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(inverse(identity),inverse(identity)),identity),inverse(identity)),identity) )],[refute_0_159,refute_0_282]) ).
cnf(refute_0_284,plain,
( double_divide(identity,multiply(X_11,double_divide(identity,inverse(inverse(identity))))) != inverse(X_11)
| inverse(identity) != identity
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(inverse(identity))))),inverse(X_11)) ),[0,1,1,1,0],$fot(identity)]]) ).
cnf(refute_0_285,plain,
( double_divide(identity,multiply(X_11,double_divide(identity,inverse(inverse(identity))))) != inverse(X_11)
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(inverse(identity))))),inverse(X_11)) )],[refute_0_76,refute_0_285]) ).
cnf(refute_0_287,plain,
multiply(X_11,double_divide(identity,inverse(identity))) = multiply(X_11,double_divide(identity,inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(X_11,double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_288,plain,
( multiply(X_11,double_divide(identity,inverse(identity))) != multiply(X_11,double_divide(identity,inverse(identity)))
| double_divide(identity,inverse(identity)) != identity
| multiply(X_11,double_divide(identity,inverse(identity))) = multiply(X_11,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(identity))),multiply(X_11,double_divide(identity,inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_289,plain,
( double_divide(identity,inverse(identity)) != identity
| multiply(X_11,double_divide(identity,inverse(identity))) = multiply(X_11,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(identity))),multiply(X_11,double_divide(identity,inverse(identity)))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
multiply(X_11,double_divide(identity,inverse(identity))) = multiply(X_11,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_195,refute_0_289]) ).
cnf(refute_0_291,plain,
double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))))]]) ).
cnf(refute_0_292,plain,
( multiply(X_11,double_divide(identity,inverse(identity))) != multiply(X_11,identity)
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) != double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity))))
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = double_divide(identity,multiply(X_11,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity))))) ),[1,1],$fot(multiply(X_11,identity))]]) ).
cnf(refute_0_293,plain,
( multiply(X_11,double_divide(identity,inverse(identity))) != multiply(X_11,identity)
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = double_divide(identity,multiply(X_11,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity))))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) = double_divide(identity,multiply(X_11,identity)),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(identity))),multiply(X_11,identity)) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
( double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) != double_divide(identity,multiply(X_11,identity))
| double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) != inverse(X_11)
| double_divide(identity,multiply(X_11,identity)) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),inverse(X_11)) ),[0],$fot(double_divide(identity,multiply(X_11,identity)))]]) ).
cnf(refute_0_296,plain,
( double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))) != inverse(X_11)
| double_divide(identity,multiply(X_11,identity)) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),double_divide(identity,multiply(X_11,identity))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
double_divide(identity,multiply(X_11,identity)) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,double_divide(identity,inverse(identity)))),inverse(X_11)) )],[refute_0_286,refute_0_296]) ).
cnf(refute_0_298,plain,
multiply(multiply(X_23,identity),identity) = inverse(double_divide(identity,multiply(X_23,identity))),
inference(subst,[],[refute_0_37:[bind(A,$fot(multiply(X_23,identity))),bind(B,$fot(identity))]]) ).
cnf(refute_0_299,plain,
double_divide(identity,multiply(X_23,identity)) = inverse(X_23),
inference(subst,[],[refute_0_297:[bind(X_11,$fot(X_23))]]) ).
cnf(refute_0_300,plain,
( multiply(multiply(X_23,identity),identity) != inverse(double_divide(identity,multiply(X_23,identity)))
| double_divide(identity,multiply(X_23,identity)) != inverse(X_23)
| multiply(multiply(X_23,identity),identity) = inverse(inverse(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_23,identity),identity),inverse(double_divide(identity,multiply(X_23,identity)))) ),[1,0],$fot(inverse(X_23))]]) ).
cnf(refute_0_301,plain,
( multiply(multiply(X_23,identity),identity) != inverse(double_divide(identity,multiply(X_23,identity)))
| multiply(multiply(X_23,identity),identity) = inverse(inverse(X_23)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_23,identity)),inverse(X_23)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
multiply(multiply(X_23,identity),identity) = inverse(inverse(X_23)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_23,identity),identity),inverse(double_divide(identity,multiply(X_23,identity)))) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
double_divide(double_divide(B,A),inverse(identity)) = inverse(multiply(inverse(inverse(double_divide(B,A))),identity)),
inference(subst,[],[refute_0_109:[bind(X_13,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_304,plain,
( double_divide(double_divide(B,A),inverse(identity)) != inverse(multiply(inverse(inverse(double_divide(B,A))),identity))
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(double_divide(B,A),inverse(identity)) = inverse(multiply(inverse(multiply(A,B)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),inverse(multiply(inverse(inverse(double_divide(B,A))),identity))) ),[1,0,0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_305,plain,
( double_divide(double_divide(B,A),inverse(identity)) != inverse(multiply(inverse(inverse(double_divide(B,A))),identity))
| double_divide(double_divide(B,A),inverse(identity)) = inverse(multiply(inverse(multiply(A,B)),identity)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_304]) ).
cnf(refute_0_306,plain,
double_divide(double_divide(B,A),inverse(identity)) = inverse(multiply(inverse(multiply(A,B)),identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),inverse(multiply(inverse(inverse(double_divide(B,A))),identity))) )],[refute_0_303,refute_0_305]) ).
cnf(refute_0_307,plain,
multiply(inverse(double_divide(B,A)),identity) = multiply(inverse(double_divide(B,A)),identity),
introduced(tautology,[refl,[$fot(multiply(inverse(double_divide(B,A)),identity))]]) ).
cnf(refute_0_308,plain,
( multiply(inverse(double_divide(B,A)),identity) != multiply(inverse(double_divide(B,A)),identity)
| inverse(double_divide(B,A)) != multiply(A,B)
| multiply(inverse(double_divide(B,A)),identity) = multiply(multiply(A,B),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(B,A)),identity),multiply(inverse(double_divide(B,A)),identity)) ),[1,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_309,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| multiply(inverse(double_divide(B,A)),identity) = multiply(multiply(A,B),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(B,A)),identity),multiply(inverse(double_divide(B,A)),identity)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
multiply(inverse(double_divide(B,A)),identity) = multiply(multiply(A,B),identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_309]) ).
cnf(refute_0_311,plain,
double_divide(double_divide(B,A),inverse(identity)) = multiply(inverse(double_divide(B,A)),identity),
inference(subst,[],[refute_0_262:[bind(B,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_312,plain,
( multiply(inverse(double_divide(B,A)),identity) != multiply(multiply(A,B),identity)
| double_divide(double_divide(B,A),inverse(identity)) != multiply(inverse(double_divide(B,A)),identity)
| double_divide(double_divide(B,A),inverse(identity)) = multiply(multiply(A,B),identity) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(double_divide(B,A),inverse(identity)))),bind(Y,$fot(multiply(inverse(double_divide(B,A)),identity))),bind(Z,$fot(multiply(multiply(A,B),identity)))]]) ).
cnf(refute_0_313,plain,
( multiply(inverse(double_divide(B,A)),identity) != multiply(multiply(A,B),identity)
| double_divide(double_divide(B,A),inverse(identity)) = multiply(multiply(A,B),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),multiply(inverse(double_divide(B,A)),identity)) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
double_divide(double_divide(B,A),inverse(identity)) = multiply(multiply(A,B),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(B,A)),identity),multiply(multiply(A,B),identity)) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( double_divide(double_divide(B,A),inverse(identity)) != multiply(multiply(A,B),identity)
| double_divide(double_divide(B,A),inverse(identity)) != inverse(multiply(inverse(multiply(A,B)),identity))
| multiply(multiply(A,B),identity) = inverse(multiply(inverse(multiply(A,B)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),inverse(multiply(inverse(multiply(A,B)),identity))) ),[0],$fot(multiply(multiply(A,B),identity))]]) ).
cnf(refute_0_316,plain,
( double_divide(double_divide(B,A),inverse(identity)) != inverse(multiply(inverse(multiply(A,B)),identity))
| multiply(multiply(A,B),identity) = inverse(multiply(inverse(multiply(A,B)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),multiply(multiply(A,B),identity)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(multiply(A,B),identity) = inverse(multiply(inverse(multiply(A,B)),identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),inverse(identity)),inverse(multiply(inverse(multiply(A,B)),identity))) )],[refute_0_306,refute_0_316]) ).
cnf(refute_0_318,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_319,plain,
double_divide(B,inverse(identity)) = double_divide(B,inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(B,inverse(identity)))]]) ).
cnf(refute_0_320,plain,
( double_divide(B,inverse(identity)) != double_divide(B,inverse(identity))
| inverse(identity) != identity
| double_divide(B,inverse(identity)) = double_divide(B,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(B,inverse(identity)),double_divide(B,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_321,plain,
( inverse(identity) != identity
| double_divide(B,inverse(identity)) = double_divide(B,identity) ),
inference(resolve,[$cnf( $equal(double_divide(B,inverse(identity)),double_divide(B,inverse(identity))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
double_divide(B,inverse(identity)) = double_divide(B,identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_283,refute_0_321]) ).
cnf(refute_0_323,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(B,inverse(identity)) != double_divide(B,identity)
| double_divide(B,inverse(identity)) = inverse(B) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(B,inverse(identity)))),bind(Y,$fot(double_divide(B,identity))),bind(Z,$fot(inverse(B)))]]) ).
cnf(refute_0_324,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(B,inverse(identity)) = inverse(B) ),
inference(resolve,[$cnf( $equal(double_divide(B,inverse(identity)),double_divide(B,identity)) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
double_divide(B,inverse(identity)) = inverse(B),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_318,refute_0_324]) ).
cnf(refute_0_326,plain,
( double_divide(B,inverse(identity)) != multiply(inverse(B),identity)
| double_divide(B,inverse(identity)) != inverse(B)
| inverse(B) = multiply(inverse(B),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(B,inverse(identity)),multiply(inverse(B),identity)) ),[0],$fot(inverse(B))]]) ).
cnf(refute_0_327,plain,
( double_divide(B,inverse(identity)) != multiply(inverse(B),identity)
| inverse(B) = multiply(inverse(B),identity) ),
inference(resolve,[$cnf( $equal(double_divide(B,inverse(identity)),inverse(B)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
inverse(B) = multiply(inverse(B),identity),
inference(resolve,[$cnf( $equal(double_divide(B,inverse(identity)),multiply(inverse(B),identity)) )],[refute_0_262,refute_0_327]) ).
cnf(refute_0_329,plain,
( inverse(B) != multiply(inverse(B),identity)
| multiply(inverse(B),identity) = inverse(B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(B))),bind(Y,$fot(multiply(inverse(B),identity)))]]) ).
cnf(refute_0_330,plain,
multiply(inverse(B),identity) = inverse(B),
inference(resolve,[$cnf( $equal(inverse(B),multiply(inverse(B),identity)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(inverse(multiply(A,B)),identity) = inverse(multiply(A,B)),
inference(subst,[],[refute_0_330:[bind(B,$fot(multiply(A,B)))]]) ).
cnf(refute_0_332,plain,
inverse(multiply(inverse(multiply(A,B)),identity)) = inverse(multiply(inverse(multiply(A,B)),identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(multiply(A,B)),identity)))]]) ).
cnf(refute_0_333,plain,
( multiply(inverse(multiply(A,B)),identity) != inverse(multiply(A,B))
| inverse(multiply(inverse(multiply(A,B)),identity)) != inverse(multiply(inverse(multiply(A,B)),identity))
| inverse(multiply(inverse(multiply(A,B)),identity)) = inverse(inverse(multiply(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(multiply(A,B)),identity)),inverse(multiply(inverse(multiply(A,B)),identity))) ),[1,0],$fot(inverse(multiply(A,B)))]]) ).
cnf(refute_0_334,plain,
( multiply(inverse(multiply(A,B)),identity) != inverse(multiply(A,B))
| inverse(multiply(inverse(multiply(A,B)),identity)) = inverse(inverse(multiply(A,B))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(A,B)),identity)),inverse(multiply(inverse(multiply(A,B)),identity))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
inverse(multiply(inverse(multiply(A,B)),identity)) = inverse(inverse(multiply(A,B))),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(A,B)),identity),inverse(multiply(A,B))) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
( multiply(multiply(A,B),identity) != inverse(multiply(inverse(multiply(A,B)),identity))
| inverse(multiply(inverse(multiply(A,B)),identity)) != inverse(inverse(multiply(A,B)))
| multiply(multiply(A,B),identity) = inverse(inverse(multiply(A,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(A,B),identity),inverse(inverse(multiply(A,B)))) ),[0],$fot(inverse(multiply(inverse(multiply(A,B)),identity)))]]) ).
cnf(refute_0_337,plain,
( multiply(multiply(A,B),identity) != inverse(multiply(inverse(multiply(A,B)),identity))
| multiply(multiply(A,B),identity) = inverse(inverse(multiply(A,B))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(multiply(A,B)),identity)),inverse(inverse(multiply(A,B)))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
multiply(multiply(A,B),identity) = inverse(inverse(multiply(A,B))),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),identity),inverse(multiply(inverse(multiply(A,B)),identity))) )],[refute_0_317,refute_0_337]) ).
cnf(refute_0_339,plain,
double_divide(X_13,inverse(identity)) = multiply(inverse(X_13),identity),
inference(subst,[],[refute_0_262:[bind(B,$fot(X_13))]]) ).
cnf(refute_0_340,plain,
( double_divide(X_13,inverse(identity)) != multiply(inverse(X_13),identity)
| double_divide(X_13,inverse(identity)) != inverse(multiply(inverse(inverse(X_13)),identity))
| multiply(inverse(X_13),identity) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_13,inverse(identity)),inverse(multiply(inverse(inverse(X_13)),identity))) ),[0],$fot(multiply(inverse(X_13),identity))]]) ).
cnf(refute_0_341,plain,
( double_divide(X_13,inverse(identity)) != inverse(multiply(inverse(inverse(X_13)),identity))
| multiply(inverse(X_13),identity) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(identity)),multiply(inverse(X_13),identity)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
multiply(inverse(X_13),identity) = inverse(multiply(inverse(inverse(X_13)),identity)),
inference(resolve,[$cnf( $equal(double_divide(X_13,inverse(identity)),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_109,refute_0_341]) ).
cnf(refute_0_343,plain,
multiply(inverse(X_13),identity) = inverse(X_13),
inference(subst,[],[refute_0_330:[bind(B,$fot(X_13))]]) ).
cnf(refute_0_344,plain,
( multiply(inverse(X_13),identity) != inverse(X_13)
| multiply(inverse(X_13),identity) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(X_13) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_13),identity),inverse(multiply(inverse(inverse(X_13)),identity))) ),[0],$fot(inverse(X_13))]]) ).
cnf(refute_0_345,plain,
( multiply(inverse(X_13),identity) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(X_13) = inverse(multiply(inverse(inverse(X_13)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),identity),inverse(X_13)) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(inverse(inverse(X_13)),identity) = inverse(inverse(X_13)),
inference(subst,[],[refute_0_330:[bind(B,$fot(inverse(X_13)))]]) ).
cnf(refute_0_347,plain,
inverse(multiply(inverse(inverse(X_13)),identity)) = inverse(multiply(inverse(inverse(X_13)),identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(inverse(X_13)),identity)))]]) ).
cnf(refute_0_348,plain,
( multiply(inverse(inverse(X_13)),identity) != inverse(inverse(X_13))
| inverse(multiply(inverse(inverse(X_13)),identity)) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(multiply(inverse(inverse(X_13)),identity)) = inverse(inverse(inverse(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(inverse(X_13)),identity)),inverse(multiply(inverse(inverse(X_13)),identity))) ),[1,0],$fot(inverse(inverse(X_13)))]]) ).
cnf(refute_0_349,plain,
( multiply(inverse(inverse(X_13)),identity) != inverse(inverse(X_13))
| inverse(multiply(inverse(inverse(X_13)),identity)) = inverse(inverse(inverse(X_13))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X_13)),identity)),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
inverse(multiply(inverse(inverse(X_13)),identity)) = inverse(inverse(inverse(X_13))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_13)),identity),inverse(inverse(X_13))) )],[refute_0_346,refute_0_349]) ).
cnf(refute_0_351,plain,
( inverse(X_13) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(multiply(inverse(inverse(X_13)),identity)) != inverse(inverse(inverse(X_13)))
| inverse(X_13) = inverse(inverse(inverse(X_13))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(X_13),inverse(inverse(inverse(X_13)))) ),[0],$fot(inverse(multiply(inverse(inverse(X_13)),identity)))]]) ).
cnf(refute_0_352,plain,
( inverse(X_13) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(X_13) = inverse(inverse(inverse(X_13))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(inverse(X_13)),identity)),inverse(inverse(inverse(X_13)))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( multiply(inverse(X_13),identity) != inverse(multiply(inverse(inverse(X_13)),identity))
| inverse(X_13) = inverse(inverse(inverse(X_13))) ),
inference(resolve,[$cnf( $equal(inverse(X_13),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_345,refute_0_352]) ).
cnf(refute_0_354,plain,
inverse(X_13) = inverse(inverse(inverse(X_13))),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),identity),inverse(multiply(inverse(inverse(X_13)),identity))) )],[refute_0_342,refute_0_353]) ).
cnf(refute_0_355,plain,
inverse(double_divide(B,A)) = inverse(inverse(inverse(double_divide(B,A)))),
inference(subst,[],[refute_0_354:[bind(X_13,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_356,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| inverse(double_divide(B,A)) != inverse(inverse(inverse(double_divide(B,A))))
| inverse(double_divide(B,A)) = inverse(inverse(multiply(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(double_divide(B,A)),inverse(inverse(inverse(double_divide(B,A))))) ),[1,0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_357,plain,
( inverse(double_divide(B,A)) != inverse(inverse(inverse(double_divide(B,A))))
| inverse(double_divide(B,A)) = inverse(inverse(multiply(A,B))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_356]) ).
cnf(refute_0_358,plain,
inverse(double_divide(B,A)) = inverse(inverse(multiply(A,B))),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),inverse(inverse(inverse(double_divide(B,A))))) )],[refute_0_355,refute_0_357]) ).
cnf(refute_0_359,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| inverse(double_divide(B,A)) != inverse(inverse(multiply(A,B)))
| multiply(A,B) = inverse(inverse(multiply(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(double_divide(B,A)),inverse(inverse(multiply(A,B)))) ),[0],$fot(multiply(A,B))]]) ).
cnf(refute_0_360,plain,
( inverse(double_divide(B,A)) != inverse(inverse(multiply(A,B)))
| multiply(A,B) = inverse(inverse(multiply(A,B))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_359]) ).
cnf(refute_0_361,plain,
multiply(A,B) = inverse(inverse(multiply(A,B))),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),inverse(inverse(multiply(A,B)))) )],[refute_0_358,refute_0_360]) ).
cnf(refute_0_362,plain,
( multiply(A,B) != inverse(inverse(multiply(A,B)))
| inverse(inverse(multiply(A,B))) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(inverse(multiply(A,B)))))]]) ).
cnf(refute_0_363,plain,
inverse(inverse(multiply(A,B))) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(inverse(multiply(A,B)))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
( multiply(multiply(A,B),identity) != inverse(inverse(multiply(A,B)))
| inverse(inverse(multiply(A,B))) != multiply(A,B)
| multiply(multiply(A,B),identity) = multiply(A,B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(A,B),identity),multiply(A,B)) ),[0],$fot(inverse(inverse(multiply(A,B))))]]) ).
cnf(refute_0_365,plain,
( multiply(multiply(A,B),identity) != inverse(inverse(multiply(A,B)))
| multiply(multiply(A,B),identity) = multiply(A,B) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(A,B))),multiply(A,B)) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
multiply(multiply(A,B),identity) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),identity),inverse(inverse(multiply(A,B)))) )],[refute_0_338,refute_0_365]) ).
cnf(refute_0_367,plain,
multiply(multiply(X_23,identity),identity) = multiply(X_23,identity),
inference(subst,[],[refute_0_366:[bind(A,$fot(X_23)),bind(B,$fot(identity))]]) ).
cnf(refute_0_368,plain,
( multiply(multiply(X_23,identity),identity) != multiply(X_23,identity)
| multiply(multiply(X_23,identity),identity) != inverse(inverse(X_23))
| multiply(X_23,identity) = inverse(inverse(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_23,identity),identity),inverse(inverse(X_23))) ),[0],$fot(multiply(X_23,identity))]]) ).
cnf(refute_0_369,plain,
( multiply(multiply(X_23,identity),identity) != inverse(inverse(X_23))
| multiply(X_23,identity) = inverse(inverse(X_23)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_23,identity),identity),multiply(X_23,identity)) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(X_23,identity) = inverse(inverse(X_23)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_23,identity),identity),inverse(inverse(X_23))) )],[refute_0_302,refute_0_369]) ).
cnf(refute_0_371,plain,
multiply(X_11,identity) = inverse(inverse(X_11)),
inference(subst,[],[refute_0_370:[bind(X_23,$fot(X_11))]]) ).
cnf(refute_0_372,plain,
double_divide(identity,multiply(X_11,identity)) = double_divide(identity,multiply(X_11,identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(X_11,identity)))]]) ).
cnf(refute_0_373,plain,
( multiply(X_11,identity) != inverse(inverse(X_11))
| double_divide(identity,multiply(X_11,identity)) != double_divide(identity,multiply(X_11,identity))
| double_divide(identity,multiply(X_11,identity)) = double_divide(identity,inverse(inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_11,identity)),double_divide(identity,multiply(X_11,identity))) ),[1,1],$fot(inverse(inverse(X_11)))]]) ).
cnf(refute_0_374,plain,
( multiply(X_11,identity) != inverse(inverse(X_11))
| double_divide(identity,multiply(X_11,identity)) = double_divide(identity,inverse(inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,identity)),double_divide(identity,multiply(X_11,identity))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
double_divide(identity,multiply(X_11,identity)) = double_divide(identity,inverse(inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(X_11,identity),inverse(inverse(X_11))) )],[refute_0_371,refute_0_374]) ).
cnf(refute_0_376,plain,
( double_divide(identity,multiply(X_11,identity)) != double_divide(identity,inverse(inverse(X_11)))
| double_divide(identity,multiply(X_11,identity)) != inverse(X_11)
| double_divide(identity,inverse(inverse(X_11))) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_11,identity)),inverse(X_11)) ),[0],$fot(double_divide(identity,inverse(inverse(X_11))))]]) ).
cnf(refute_0_377,plain,
( double_divide(identity,multiply(X_11,identity)) != inverse(X_11)
| double_divide(identity,inverse(inverse(X_11))) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,identity)),double_divide(identity,inverse(inverse(X_11)))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
double_divide(identity,inverse(inverse(X_11))) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_11,identity)),inverse(X_11)) )],[refute_0_297,refute_0_377]) ).
cnf(refute_0_379,plain,
double_divide(X_10,multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) = X_12,
inference(subst,[],[refute_0_47:[bind(A,$fot(X_10)),bind(B,$fot(identity)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_380,plain,
multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))) = inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),
inference(subst,[],[refute_0_169:[bind(X_3,$fot(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))]]) ).
cnf(refute_0_381,plain,
( multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))) != inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))
| double_divide(X_10,multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) != X_12
| double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),X_12) ),[0,1],$fot(inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))))]]) ).
cnf(refute_0_382,plain,
( double_divide(X_10,multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) != X_12
| double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = X_12 ),
inference(resolve,[$cnf( $equal(multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))),inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(identity,double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),X_12) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))) = multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity),
inference(subst,[],[refute_0_39:[bind(A,$fot(double_divide(inverse(X_10),double_divide(identity,X_12)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_385,plain,
inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) = inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))))]]) ).
cnf(refute_0_386,plain,
( inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))) != multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)
| inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) != inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))
| inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) = inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) ),[1,0],$fot(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))]]) ).
cnf(refute_0_387,plain,
( inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))) != multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)
| inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) = inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) = inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))),multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) )],[refute_0_384,refute_0_387]) ).
cnf(refute_0_389,plain,
double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),
introduced(tautology,[refl,[$fot(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))))]]) ).
cnf(refute_0_390,plain,
( double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) != double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))))
| inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) != inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))
| double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))))) ),[1,1],$fot(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))]]) ).
cnf(refute_0_391,plain,
( inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))) != inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))
| double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) = double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12))))),inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
( double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) != X_12
| double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) != double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))
| double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),X_12) ),[0],$fot(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))))]]) ).
cnf(refute_0_394,plain,
( double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))) != X_12
| double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(inverse(double_divide(identity,double_divide(inverse(X_10),double_divide(identity,X_12)))))),X_12) )],[refute_0_383,refute_0_394]) ).
cnf(refute_0_396,plain,
inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) = multiply(double_divide(identity,X_12),inverse(X_10)),
inference(subst,[],[refute_0_363:[bind(A,$fot(double_divide(identity,X_12))),bind(B,$fot(inverse(X_10)))]]) ).
cnf(refute_0_397,plain,
inverse(double_divide(inverse(X_10),double_divide(identity,X_12))) = multiply(double_divide(identity,X_12),inverse(X_10)),
inference(subst,[],[refute_0_39:[bind(A,$fot(double_divide(identity,X_12))),bind(B,$fot(inverse(X_10)))]]) ).
cnf(refute_0_398,plain,
inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) = inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))))]]) ).
cnf(refute_0_399,plain,
( inverse(double_divide(inverse(X_10),double_divide(identity,X_12))) != multiply(double_divide(identity,X_12),inverse(X_10))
| inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) != inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))))
| inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))),inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))))) ),[1,0],$fot(multiply(double_divide(identity,X_12),inverse(X_10)))]]) ).
cnf(refute_0_400,plain,
( inverse(double_divide(inverse(X_10),double_divide(identity,X_12))) != multiply(double_divide(identity,X_12),inverse(X_10))
| inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))),inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))),multiply(double_divide(identity,X_12),inverse(X_10))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) = inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))),
inference(subst,[],[refute_0_370:[bind(X_23,$fot(double_divide(inverse(X_10),double_divide(identity,X_12))))]]) ).
cnf(refute_0_403,plain,
( multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) != inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))))
| inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) != inverse(multiply(double_divide(identity,X_12),inverse(X_10)))
| multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),bind(Y,$fot(inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))))),bind(Z,$fot(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))))]]) ).
cnf(refute_0_404,plain,
( inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))) != inverse(multiply(double_divide(identity,X_12),inverse(X_10)))
| multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity),inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12))))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) = inverse(multiply(double_divide(identity,X_12),inverse(X_10))),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(inverse(X_10),double_divide(identity,X_12)))),inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),
introduced(tautology,[refl,[$fot(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))]]) ).
cnf(refute_0_407,plain,
( multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) != inverse(multiply(double_divide(identity,X_12),inverse(X_10)))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) != inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) ),[1,0],$fot(inverse(multiply(double_divide(identity,X_12),inverse(X_10))))]]) ).
cnf(refute_0_408,plain,
( multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity) != inverse(multiply(double_divide(identity,X_12),inverse(X_10)))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity),inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
( inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) != inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10))))
| inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) != multiply(double_divide(identity,X_12),inverse(X_10))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = multiply(double_divide(identity,X_12),inverse(X_10)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))),bind(Y,$fot(inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))))),bind(Z,$fot(multiply(double_divide(identity,X_12),inverse(X_10))))]]) ).
cnf(refute_0_411,plain,
( inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))) != multiply(double_divide(identity,X_12),inverse(X_10))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = multiply(double_divide(identity,X_12),inverse(X_10)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10))))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) = multiply(double_divide(identity,X_12),inverse(X_10)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(double_divide(identity,X_12),inverse(X_10)))),multiply(double_divide(identity,X_12),inverse(X_10))) )],[refute_0_396,refute_0_411]) ).
cnf(refute_0_413,plain,
double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),
introduced(tautology,[refl,[$fot(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))))]]) ).
cnf(refute_0_414,plain,
( double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) != double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))
| inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) != multiply(double_divide(identity,X_12),inverse(X_10))
| double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))) ),[1,1],$fot(multiply(double_divide(identity,X_12),inverse(X_10)))]]) ).
cnf(refute_0_415,plain,
( inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)) != multiply(double_divide(identity,X_12),inverse(X_10))
| double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) = double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))),
inference(resolve,[$cnf( $equal(inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity)),multiply(double_divide(identity,X_12),inverse(X_10))) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
( double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) != X_12
| double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) != double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10)))
| double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),X_12) ),[0],$fot(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))))]]) ).
cnf(refute_0_418,plain,
( double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))) != X_12
| double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10)))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(multiply(double_divide(inverse(X_10),double_divide(identity,X_12)),identity))),X_12) )],[refute_0_395,refute_0_418]) ).
cnf(refute_0_420,plain,
multiply(X_12,identity) = inverse(inverse(X_12)),
inference(subst,[],[refute_0_370:[bind(X_23,$fot(X_12))]]) ).
cnf(refute_0_421,plain,
inverse(double_divide(identity,X_12)) = multiply(X_12,identity),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_12)),bind(B,$fot(identity))]]) ).
cnf(refute_0_422,plain,
( multiply(X_12,identity) != inverse(inverse(X_12))
| inverse(double_divide(identity,X_12)) != multiply(X_12,identity)
| inverse(double_divide(identity,X_12)) = inverse(inverse(X_12)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(inverse(double_divide(identity,X_12)))),bind(Y,$fot(multiply(X_12,identity))),bind(Z,$fot(inverse(inverse(X_12))))]]) ).
cnf(refute_0_423,plain,
( multiply(X_12,identity) != inverse(inverse(X_12))
| inverse(double_divide(identity,X_12)) = inverse(inverse(X_12)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,X_12)),multiply(X_12,identity)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
inverse(double_divide(identity,X_12)) = inverse(inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(X_12,identity),inverse(inverse(X_12))) )],[refute_0_420,refute_0_423]) ).
cnf(refute_0_425,plain,
double_divide(identity,inverse(inverse(X_10))) = inverse(X_10),
inference(subst,[],[refute_0_378:[bind(X_11,$fot(X_10))]]) ).
cnf(refute_0_426,plain,
multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) = multiply(X_11,double_divide(identity,inverse(inverse(X_10)))),
introduced(tautology,[refl,[$fot(multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_427,plain,
( multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) != multiply(X_11,double_divide(identity,inverse(inverse(X_10))))
| double_divide(identity,inverse(inverse(X_10))) != inverse(X_10)
| multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) = multiply(X_11,inverse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(inverse(X_10)))),multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) ),[1,1],$fot(inverse(X_10))]]) ).
cnf(refute_0_428,plain,
( double_divide(identity,inverse(inverse(X_10))) != inverse(X_10)
| multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) = multiply(X_11,inverse(X_10)) ),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(inverse(X_10)))),multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) = multiply(X_11,inverse(X_10)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_10))),inverse(X_10)) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),
introduced(tautology,[refl,[$fot(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))))]]) ).
cnf(refute_0_431,plain,
( multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) != multiply(X_11,inverse(X_10))
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) != double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = double_divide(X_10,multiply(X_11,inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))) ),[1,1],$fot(multiply(X_11,inverse(X_10)))]]) ).
cnf(refute_0_432,plain,
( multiply(X_11,double_divide(identity,inverse(inverse(X_10)))) != multiply(X_11,inverse(X_10))
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = double_divide(X_10,multiply(X_11,inverse(X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10)))))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) = double_divide(X_10,multiply(X_11,inverse(X_10))),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,inverse(inverse(X_10)))),multiply(X_11,inverse(X_10))) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) != double_divide(X_10,multiply(X_11,inverse(X_10)))
| double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) != inverse(X_11)
| double_divide(X_10,multiply(X_11,inverse(X_10))) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),inverse(X_11)) ),[0],$fot(double_divide(X_10,multiply(X_11,inverse(X_10))))]]) ).
cnf(refute_0_435,plain,
( double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))) != inverse(X_11)
| double_divide(X_10,multiply(X_11,inverse(X_10))) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),double_divide(X_10,multiply(X_11,inverse(X_10)))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
double_divide(X_10,multiply(X_11,inverse(X_10))) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(X_11,double_divide(identity,inverse(inverse(X_10))))),inverse(X_11)) )],[refute_0_75,refute_0_435]) ).
cnf(refute_0_437,plain,
double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = inverse(double_divide(identity,X_12)),
inference(subst,[],[refute_0_436:[bind(X_11,$fot(double_divide(identity,X_12)))]]) ).
cnf(refute_0_438,plain,
( double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) != inverse(double_divide(identity,X_12))
| inverse(double_divide(identity,X_12)) != inverse(inverse(X_12))
| double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = inverse(inverse(X_12)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))))),bind(Y,$fot(inverse(double_divide(identity,X_12)))),bind(Z,$fot(inverse(inverse(X_12))))]]) ).
cnf(refute_0_439,plain,
( inverse(double_divide(identity,X_12)) != inverse(inverse(X_12))
| double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = inverse(inverse(X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))),inverse(double_divide(identity,X_12))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) = inverse(inverse(X_12)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,X_12)),inverse(inverse(X_12))) )],[refute_0_424,refute_0_439]) ).
cnf(refute_0_441,plain,
( double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) != X_12
| double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) != inverse(inverse(X_12))
| inverse(inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))),X_12) ),[0],$fot(inverse(inverse(X_12)))]]) ).
cnf(refute_0_442,plain,
( double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))) != X_12
| inverse(inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))),inverse(inverse(X_12))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
inverse(inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(X_10,multiply(double_divide(identity,X_12),inverse(X_10))),X_12) )],[refute_0_419,refute_0_442]) ).
cnf(refute_0_444,plain,
inverse(inverse(X_11)) = X_11,
inference(subst,[],[refute_0_443:[bind(X_12,$fot(X_11))]]) ).
cnf(refute_0_445,plain,
double_divide(identity,inverse(inverse(X_11))) = double_divide(identity,inverse(inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(X_11))))]]) ).
cnf(refute_0_446,plain,
( double_divide(identity,inverse(inverse(X_11))) != double_divide(identity,inverse(inverse(X_11)))
| inverse(inverse(X_11)) != X_11
| double_divide(identity,inverse(inverse(X_11))) = double_divide(identity,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(X_11))),double_divide(identity,inverse(inverse(X_11)))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_447,plain,
( inverse(inverse(X_11)) != X_11
| double_divide(identity,inverse(inverse(X_11))) = double_divide(identity,X_11) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_11))),double_divide(identity,inverse(inverse(X_11)))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
double_divide(identity,inverse(inverse(X_11))) = double_divide(identity,X_11),
inference(resolve,[$cnf( $equal(inverse(inverse(X_11)),X_11) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( double_divide(identity,inverse(inverse(X_11))) != double_divide(identity,X_11)
| double_divide(identity,inverse(inverse(X_11))) != inverse(X_11)
| double_divide(identity,X_11) = inverse(X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(X_11))),inverse(X_11)) ),[0],$fot(double_divide(identity,X_11))]]) ).
cnf(refute_0_450,plain,
( double_divide(identity,inverse(inverse(X_11))) != inverse(X_11)
| double_divide(identity,X_11) = inverse(X_11) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_11))),double_divide(identity,X_11)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
double_divide(identity,X_11) = inverse(X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_11))),inverse(X_11)) )],[refute_0_378,refute_0_450]) ).
cnf(refute_0_452,plain,
double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) = inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))),
inference(subst,[],[refute_0_451:[bind(X_11,$fot(double_divide(multiply(A,B),double_divide(X_11,X_12))))]]) ).
cnf(refute_0_453,plain,
( double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) != inverse(double_divide(multiply(A,B),double_divide(X_11,X_12)))
| inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),multiply(A,B))
| double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),multiply(A,B)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),bind(Y,$fot(inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))))),bind(Z,$fot(multiply(double_divide(X_11,X_12),multiply(A,B))))]]) ).
cnf(refute_0_454,plain,
( inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),multiply(A,B))
| double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),multiply(A,B)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),inverse(double_divide(multiply(A,B),double_divide(X_11,X_12)))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),multiply(A,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(multiply(A,B),double_divide(X_11,X_12))),multiply(double_divide(X_11,X_12),multiply(A,B))) )],[refute_0_52,refute_0_454]) ).
cnf(refute_0_456,plain,
double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) = double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))]]) ).
cnf(refute_0_457,plain,
( double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) != double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)
| double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),multiply(A,B))
| double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) = double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) ),[1,0],$fot(multiply(double_divide(X_11,X_12),multiply(A,B)))]]) ).
cnf(refute_0_458,plain,
( double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),multiply(A,B))
| double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) = double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) = double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),multiply(double_divide(X_11,X_12),multiply(A,B))) )],[refute_0_455,refute_0_458]) ).
cnf(refute_0_460,plain,
multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) = multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)),
introduced(tautology,[refl,[$fot(multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)))]]) ).
cnf(refute_0_461,plain,
( multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) != multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))
| double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) != double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)
| multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)),multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))) ),[1,1],$fot(double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))]]) ).
cnf(refute_0_462,plain,
( double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11) != double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)
| multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)),multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = inverse(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B)))))),
inference(subst,[],[refute_0_37:[bind(A,$fot(multiply(X_14,double_divide(identity,inverse(inverse(B))))))]]) ).
cnf(refute_0_465,plain,
( multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != inverse(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))
| double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))) != inverse(X_14)
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = inverse(inverse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),inverse(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))) ),[1,0],$fot(inverse(X_14))]]) ).
cnf(refute_0_466,plain,
( multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != inverse(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = inverse(inverse(X_14)) ),
inference(resolve,[$cnf( $equal(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))),inverse(X_14)) )],[refute_0_85,refute_0_465]) ).
cnf(refute_0_467,plain,
multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = inverse(inverse(X_14)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),inverse(double_divide(B,multiply(X_14,double_divide(identity,inverse(inverse(B))))))) )],[refute_0_464,refute_0_466]) ).
cnf(refute_0_468,plain,
double_divide(identity,inverse(inverse(B))) = inverse(B),
inference(subst,[],[refute_0_378:[bind(X_11,$fot(B))]]) ).
cnf(refute_0_469,plain,
multiply(X_14,double_divide(identity,inverse(inverse(B)))) = multiply(X_14,double_divide(identity,inverse(inverse(B)))),
introduced(tautology,[refl,[$fot(multiply(X_14,double_divide(identity,inverse(inverse(B)))))]]) ).
cnf(refute_0_470,plain,
( multiply(X_14,double_divide(identity,inverse(inverse(B)))) != multiply(X_14,double_divide(identity,inverse(inverse(B))))
| double_divide(identity,inverse(inverse(B))) != inverse(B)
| multiply(X_14,double_divide(identity,inverse(inverse(B)))) = multiply(X_14,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_14,double_divide(identity,inverse(inverse(B)))),multiply(X_14,double_divide(identity,inverse(inverse(B))))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_471,plain,
( double_divide(identity,inverse(inverse(B))) != inverse(B)
| multiply(X_14,double_divide(identity,inverse(inverse(B)))) = multiply(X_14,inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(X_14,double_divide(identity,inverse(inverse(B)))),multiply(X_14,double_divide(identity,inverse(inverse(B))))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
multiply(X_14,double_divide(identity,inverse(inverse(B)))) = multiply(X_14,inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(B))),inverse(B)) )],[refute_0_468,refute_0_471]) ).
cnf(refute_0_473,plain,
multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),
introduced(tautology,[refl,[$fot(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B))]]) ).
cnf(refute_0_474,plain,
( multiply(X_14,double_divide(identity,inverse(inverse(B)))) != multiply(X_14,inverse(B))
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B)
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = multiply(multiply(X_14,inverse(B)),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B)) ),[1,0],$fot(multiply(X_14,inverse(B)))]]) ).
cnf(refute_0_475,plain,
( multiply(X_14,double_divide(identity,inverse(inverse(B)))) != multiply(X_14,inverse(B))
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = multiply(multiply(X_14,inverse(B)),B) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B)) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) = multiply(multiply(X_14,inverse(B)),B),
inference(resolve,[$cnf( $equal(multiply(X_14,double_divide(identity,inverse(inverse(B)))),multiply(X_14,inverse(B))) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
( multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != multiply(multiply(X_14,inverse(B)),B)
| multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != inverse(inverse(X_14))
| multiply(multiply(X_14,inverse(B)),B) = inverse(inverse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),inverse(inverse(X_14))) ),[0],$fot(multiply(multiply(X_14,inverse(B)),B))]]) ).
cnf(refute_0_478,plain,
( multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != inverse(inverse(X_14))
| multiply(multiply(X_14,inverse(B)),B) = inverse(inverse(X_14)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),multiply(multiply(X_14,inverse(B)),B)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
inverse(inverse(X_14)) = X_14,
inference(subst,[],[refute_0_443:[bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_480,plain,
( multiply(multiply(X_14,inverse(B)),B) != inverse(inverse(X_14))
| inverse(inverse(X_14)) != X_14
| multiply(multiply(X_14,inverse(B)),B) = X_14 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_14,inverse(B)),B),X_14) ),[0],$fot(inverse(inverse(X_14)))]]) ).
cnf(refute_0_481,plain,
( multiply(multiply(X_14,inverse(B)),B) != inverse(inverse(X_14))
| multiply(multiply(X_14,inverse(B)),B) = X_14 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_14)),X_14) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
( multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B) != inverse(inverse(X_14))
| multiply(multiply(X_14,inverse(B)),B) = X_14 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,inverse(B)),B),inverse(inverse(X_14))) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
multiply(multiply(X_14,inverse(B)),B) = X_14,
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,double_divide(identity,inverse(inverse(B)))),B),inverse(inverse(X_14))) )],[refute_0_467,refute_0_482]) ).
cnf(refute_0_484,plain,
multiply(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),B) = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),
inference(subst,[],[refute_0_483:[bind(X_14,$fot(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))))]]) ).
cnf(refute_0_485,plain,
multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = inverse(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))))),
inference(subst,[],[refute_0_37:[bind(A,$fot(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))))]]) ).
cnf(refute_0_486,plain,
double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))) = X_12,
inference(subst,[],[refute_0_47:[bind(A,$fot(B)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_487,plain,
( multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != inverse(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))))
| double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))) != X_12
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),inverse(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_488,plain,
( multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != inverse(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))))
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))),X_12) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),inverse(double_divide(B,multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))))) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
inverse(double_divide(inverse(B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),inverse(B)),
inference(subst,[],[refute_0_39:[bind(A,$fot(double_divide(X_11,X_12))),bind(B,$fot(inverse(B)))]]) ).
cnf(refute_0_491,plain,
double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) = inverse(double_divide(inverse(B),double_divide(X_11,X_12))),
inference(subst,[],[refute_0_451:[bind(X_11,$fot(double_divide(inverse(B),double_divide(X_11,X_12))))]]) ).
cnf(refute_0_492,plain,
( double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) != inverse(double_divide(inverse(B),double_divide(X_11,X_12)))
| inverse(double_divide(inverse(B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),inverse(B))
| double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),inverse(B)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))),bind(Y,$fot(inverse(double_divide(inverse(B),double_divide(X_11,X_12))))),bind(Z,$fot(multiply(double_divide(X_11,X_12),inverse(B))))]]) ).
cnf(refute_0_493,plain,
( inverse(double_divide(inverse(B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),inverse(B))
| double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))),inverse(double_divide(inverse(B),double_divide(X_11,X_12)))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) = multiply(double_divide(X_11,X_12),inverse(B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(B),double_divide(X_11,X_12))),multiply(double_divide(X_11,X_12),inverse(B))) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) = multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),
introduced(tautology,[refl,[$fot(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))))]]) ).
cnf(refute_0_496,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) != multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))
| double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),inverse(B))
| multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) = multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))) ),[1,1],$fot(multiply(double_divide(X_11,X_12),inverse(B)))]]) ).
cnf(refute_0_497,plain,
( double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))) != multiply(double_divide(X_11,X_12),inverse(B))
| multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) = multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))) ),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) = multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12))),multiply(double_divide(X_11,X_12),inverse(B))) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),
introduced(tautology,[refl,[$fot(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B))]]) ).
cnf(refute_0_500,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) != multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B)))
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B)
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B)) ),[1,0],$fot(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))))]]) ).
cnf(refute_0_501,plain,
( multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))) != multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B)))
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B)) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) = multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B),
inference(resolve,[$cnf( $equal(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B)))) )],[refute_0_498,refute_0_501]) ).
cnf(refute_0_503,plain,
( multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B)
| multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != inverse(X_12)
| multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),inverse(X_12)) ),[0],$fot(multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B))]]) ).
cnf(refute_0_504,plain,
( multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B) != inverse(X_12)
| multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B)) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
multiply(multiply(X_11,multiply(double_divide(X_11,X_12),inverse(B))),B) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,double_divide(identity,double_divide(inverse(B),double_divide(X_11,X_12)))),B),inverse(X_12)) )],[refute_0_489,refute_0_504]) ).
cnf(refute_0_506,plain,
multiply(multiply(X_41,multiply(double_divide(X_41,identity),inverse(X_40))),X_40) = inverse(identity),
inference(subst,[],[refute_0_505:[bind(B,$fot(X_40)),bind(X_11,$fot(X_41)),bind(X_12,$fot(identity))]]) ).
cnf(refute_0_507,plain,
inverse(X_41) = double_divide(X_41,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_41))]]) ).
cnf(refute_0_508,plain,
( inverse(X_41) != double_divide(X_41,identity)
| double_divide(X_41,identity) = inverse(X_41) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_41))),bind(Y,$fot(double_divide(X_41,identity)))]]) ).
cnf(refute_0_509,plain,
double_divide(X_41,identity) = inverse(X_41),
inference(resolve,[$cnf( $equal(inverse(X_41),double_divide(X_41,identity)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
( multiply(multiply(X_41,multiply(double_divide(X_41,identity),inverse(X_40))),X_40) != inverse(identity)
| double_divide(X_41,identity) != inverse(X_41)
| multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_41,multiply(double_divide(X_41,identity),inverse(X_40))),X_40),inverse(identity)) ),[0,0,1,0],$fot(inverse(X_41))]]) ).
cnf(refute_0_511,plain,
( multiply(multiply(X_41,multiply(double_divide(X_41,identity),inverse(X_40))),X_40) != inverse(identity)
| multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_41,identity),inverse(X_41)) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(multiply(X_41,multiply(double_divide(X_41,identity),inverse(X_40))),X_40),inverse(identity)) )],[refute_0_506,refute_0_511]) ).
cnf(refute_0_513,plain,
( multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) != inverse(identity)
| inverse(identity) != identity
| multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_514,plain,
( multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) != inverse(identity)
| multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_283,refute_0_513]) ).
cnf(refute_0_515,plain,
multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_41,multiply(inverse(X_41),inverse(X_40))),X_40),inverse(identity)) )],[refute_0_512,refute_0_514]) ).
cnf(refute_0_516,plain,
multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)) = identity,
inference(subst,[],[refute_0_515:[bind(X_40,$fot(inverse(B))),bind(X_41,$fot(X_44))]]) ).
cnf(refute_0_517,plain,
( multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)) != identity
| multiply(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),B) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| multiply(identity,B) = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),B),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_518,plain,
( multiply(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),B) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| multiply(identity,B) = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),identity) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
multiply(identity,B) = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),inverse(B)),B),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) )],[refute_0_484,refute_0_518]) ).
cnf(refute_0_520,plain,
inverse(inverse(X_3)) = X_3,
inference(subst,[],[refute_0_443:[bind(X_12,$fot(X_3))]]) ).
cnf(refute_0_521,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_522,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| multiply(identity,X_3) = X_3 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),X_3) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
multiply(identity,X_3) = X_3,
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(inverse(X_3))) )],[refute_0_169,refute_0_522]) ).
cnf(refute_0_524,plain,
multiply(identity,B) = B,
inference(subst,[],[refute_0_523:[bind(X_3,$fot(B))]]) ).
cnf(refute_0_525,plain,
( multiply(identity,B) != B
| multiply(identity,B) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| B = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,B),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) ),[0],$fot(B)]]) ).
cnf(refute_0_526,plain,
( multiply(identity,B) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| B = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) ),
inference(resolve,[$cnf( $equal(multiply(identity,B),B) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
inverse(inverse(B)) = B,
inference(subst,[],[refute_0_443:[bind(X_12,$fot(B))]]) ).
cnf(refute_0_528,plain,
multiply(inverse(X_44),inverse(inverse(B))) = multiply(inverse(X_44),inverse(inverse(B))),
introduced(tautology,[refl,[$fot(multiply(inverse(X_44),inverse(inverse(B))))]]) ).
cnf(refute_0_529,plain,
( multiply(inverse(X_44),inverse(inverse(B))) != multiply(inverse(X_44),inverse(inverse(B)))
| inverse(inverse(B)) != B
| multiply(inverse(X_44),inverse(inverse(B))) = multiply(inverse(X_44),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_44),inverse(inverse(B))),multiply(inverse(X_44),inverse(inverse(B)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_530,plain,
( inverse(inverse(B)) != B
| multiply(inverse(X_44),inverse(inverse(B))) = multiply(inverse(X_44),B) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),inverse(inverse(B))),multiply(inverse(X_44),inverse(inverse(B)))) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
multiply(inverse(X_44),inverse(inverse(B))) = multiply(inverse(X_44),B),
inference(resolve,[$cnf( $equal(inverse(inverse(B)),B) )],[refute_0_527,refute_0_530]) ).
cnf(refute_0_532,plain,
multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) = multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),
introduced(tautology,[refl,[$fot(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))))]]) ).
cnf(refute_0_533,plain,
( multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| multiply(inverse(X_44),inverse(inverse(B))) != multiply(inverse(X_44),B)
| multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) = multiply(X_44,multiply(inverse(X_44),B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) ),[1,1],$fot(multiply(inverse(X_44),B))]]) ).
cnf(refute_0_534,plain,
( multiply(inverse(X_44),inverse(inverse(B))) != multiply(inverse(X_44),B)
| multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) = multiply(X_44,multiply(inverse(X_44),B)) ),
inference(resolve,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) = multiply(X_44,multiply(inverse(X_44),B)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),inverse(inverse(B))),multiply(inverse(X_44),B)) )],[refute_0_531,refute_0_534]) ).
cnf(refute_0_536,plain,
( B != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))) != multiply(X_44,multiply(inverse(X_44),B))
| B = multiply(X_44,multiply(inverse(X_44),B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(B,multiply(X_44,multiply(inverse(X_44),B))) ),[0],$fot(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))))]]) ).
cnf(refute_0_537,plain,
( B != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| B = multiply(X_44,multiply(inverse(X_44),B)) ),
inference(resolve,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),inverse(inverse(B)))),multiply(X_44,multiply(inverse(X_44),B))) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
( multiply(identity,B) != multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))
| B = multiply(X_44,multiply(inverse(X_44),B)) ),
inference(resolve,[$cnf( $equal(B,multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) )],[refute_0_526,refute_0_537]) ).
cnf(refute_0_539,plain,
B = multiply(X_44,multiply(inverse(X_44),B)),
inference(resolve,[$cnf( $equal(multiply(identity,B),multiply(X_44,multiply(inverse(X_44),inverse(inverse(B))))) )],[refute_0_519,refute_0_538]) ).
cnf(refute_0_540,plain,
double_divide(inverse(X_44),X_48) = multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_48))),
inference(subst,[],[refute_0_539:[bind(B,$fot(double_divide(inverse(X_44),X_48)))]]) ).
cnf(refute_0_541,plain,
inverse(inverse(X_23)) = X_23,
inference(subst,[],[refute_0_443:[bind(X_12,$fot(X_23))]]) ).
cnf(refute_0_542,plain,
( multiply(X_23,identity) != inverse(inverse(X_23))
| inverse(inverse(X_23)) != X_23
| multiply(X_23,identity) = X_23 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_23,identity),X_23) ),[0],$fot(inverse(inverse(X_23)))]]) ).
cnf(refute_0_543,plain,
( multiply(X_23,identity) != inverse(inverse(X_23))
| multiply(X_23,identity) = X_23 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_23)),X_23) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
multiply(X_23,identity) = X_23,
inference(resolve,[$cnf( $equal(multiply(X_23,identity),inverse(inverse(X_23))) )],[refute_0_370,refute_0_543]) ).
cnf(refute_0_545,plain,
multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity) = multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),
inference(subst,[],[refute_0_544:[bind(X_23,$fot(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))))]]) ).
cnf(refute_0_546,plain,
multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity) = inverse(X_42),
inference(subst,[],[refute_0_505:[bind(B,$fot(identity)),bind(X_11,$fot(X_41)),bind(X_12,$fot(X_42))]]) ).
cnf(refute_0_547,plain,
( multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity) != multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))
| multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity) != inverse(X_42)
| inverse(X_42) = multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) ),[0],$fot(inverse(X_42))]]) ).
cnf(refute_0_548,plain,
( multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity) != multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))
| inverse(X_42) = multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity),inverse(X_42)) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
inverse(X_42) = multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),identity),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) )],[refute_0_545,refute_0_548]) ).
cnf(refute_0_550,plain,
multiply(double_divide(X_41,X_42),identity) = double_divide(X_41,X_42),
inference(subst,[],[refute_0_544:[bind(X_23,$fot(double_divide(X_41,X_42)))]]) ).
cnf(refute_0_551,plain,
multiply(double_divide(X_41,X_42),inverse(identity)) = multiply(double_divide(X_41,X_42),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(double_divide(X_41,X_42),inverse(identity)))]]) ).
cnf(refute_0_552,plain,
( multiply(double_divide(X_41,X_42),inverse(identity)) != multiply(double_divide(X_41,X_42),inverse(identity))
| inverse(identity) != identity
| multiply(double_divide(X_41,X_42),inverse(identity)) = multiply(double_divide(X_41,X_42),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_41,X_42),inverse(identity)),multiply(double_divide(X_41,X_42),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_553,plain,
( inverse(identity) != identity
| multiply(double_divide(X_41,X_42),inverse(identity)) = multiply(double_divide(X_41,X_42),identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_41,X_42),inverse(identity)),multiply(double_divide(X_41,X_42),inverse(identity))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
multiply(double_divide(X_41,X_42),inverse(identity)) = multiply(double_divide(X_41,X_42),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_283,refute_0_553]) ).
cnf(refute_0_555,plain,
( multiply(double_divide(X_41,X_42),identity) != double_divide(X_41,X_42)
| multiply(double_divide(X_41,X_42),inverse(identity)) != multiply(double_divide(X_41,X_42),identity)
| multiply(double_divide(X_41,X_42),inverse(identity)) = double_divide(X_41,X_42) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(double_divide(X_41,X_42),inverse(identity)))),bind(Y,$fot(multiply(double_divide(X_41,X_42),identity))),bind(Z,$fot(double_divide(X_41,X_42)))]]) ).
cnf(refute_0_556,plain,
( multiply(double_divide(X_41,X_42),identity) != double_divide(X_41,X_42)
| multiply(double_divide(X_41,X_42),inverse(identity)) = double_divide(X_41,X_42) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_41,X_42),inverse(identity)),multiply(double_divide(X_41,X_42),identity)) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
multiply(double_divide(X_41,X_42),inverse(identity)) = double_divide(X_41,X_42),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_41,X_42),identity),double_divide(X_41,X_42)) )],[refute_0_550,refute_0_556]) ).
cnf(refute_0_558,plain,
multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) = multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))))]]) ).
cnf(refute_0_559,plain,
( multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) != multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))
| multiply(double_divide(X_41,X_42),inverse(identity)) != double_divide(X_41,X_42)
| multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) = multiply(X_41,double_divide(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) ),[1,1],$fot(double_divide(X_41,X_42))]]) ).
cnf(refute_0_560,plain,
( multiply(double_divide(X_41,X_42),inverse(identity)) != double_divide(X_41,X_42)
| multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) = multiply(X_41,double_divide(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) = multiply(X_41,double_divide(X_41,X_42)),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_41,X_42),inverse(identity)),double_divide(X_41,X_42)) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))) != multiply(X_41,double_divide(X_41,X_42))
| inverse(X_42) != multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))
| inverse(X_42) = multiply(X_41,double_divide(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_42),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) ),[1],$fot(multiply(X_41,double_divide(X_41,X_42)))]]) ).
cnf(refute_0_563,plain,
( inverse(X_42) != multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))
| inverse(X_42) = multiply(X_41,double_divide(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity))),multiply(X_41,double_divide(X_41,X_42))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
inverse(X_42) = multiply(X_41,double_divide(X_41,X_42)),
inference(resolve,[$cnf( $equal(inverse(X_42),multiply(X_41,multiply(double_divide(X_41,X_42),inverse(identity)))) )],[refute_0_549,refute_0_563]) ).
cnf(refute_0_565,plain,
inverse(X_48) = multiply(inverse(X_44),double_divide(inverse(X_44),X_48)),
inference(subst,[],[refute_0_564:[bind(X_41,$fot(inverse(X_44))),bind(X_42,$fot(X_48))]]) ).
cnf(refute_0_566,plain,
( inverse(X_48) != multiply(inverse(X_44),double_divide(inverse(X_44),X_48))
| multiply(inverse(X_44),double_divide(inverse(X_44),X_48)) = inverse(X_48) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_48))),bind(Y,$fot(multiply(inverse(X_44),double_divide(inverse(X_44),X_48))))]]) ).
cnf(refute_0_567,plain,
multiply(inverse(X_44),double_divide(inverse(X_44),X_48)) = inverse(X_48),
inference(resolve,[$cnf( $equal(inverse(X_48),multiply(inverse(X_44),double_divide(inverse(X_44),X_48))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
( multiply(inverse(X_44),double_divide(inverse(X_44),X_48)) != inverse(X_48)
| double_divide(inverse(X_44),X_48) != multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_48)))
| double_divide(inverse(X_44),X_48) = multiply(X_44,inverse(X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_44),X_48),multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_48)))) ),[1,1],$fot(inverse(X_48))]]) ).
cnf(refute_0_569,plain,
( double_divide(inverse(X_44),X_48) != multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_48)))
| double_divide(inverse(X_44),X_48) = multiply(X_44,inverse(X_48)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),double_divide(inverse(X_44),X_48)),inverse(X_48)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
double_divide(inverse(X_44),X_48) = multiply(X_44,inverse(X_48)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_44),X_48),multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_48)))) )],[refute_0_540,refute_0_569]) ).
cnf(refute_0_571,plain,
double_divide(inverse(multiply(A,B)),X_50) = multiply(multiply(A,B),inverse(X_50)),
inference(subst,[],[refute_0_570:[bind(X_44,$fot(multiply(A,B))),bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_572,plain,
inverse(inverse(double_divide(B,A))) = double_divide(B,A),
inference(subst,[],[refute_0_443:[bind(X_12,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_573,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| inverse(inverse(double_divide(B,A))) != double_divide(B,A)
| inverse(multiply(A,B)) = double_divide(B,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(B,A))),double_divide(B,A)) ),[0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_574,plain,
( inverse(inverse(double_divide(B,A))) != double_divide(B,A)
| inverse(multiply(A,B)) = double_divide(B,A) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_39,refute_0_573]) ).
cnf(refute_0_575,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(B,A))),double_divide(B,A)) )],[refute_0_572,refute_0_574]) ).
cnf(refute_0_576,plain,
( double_divide(inverse(multiply(A,B)),X_50) != multiply(multiply(A,B),inverse(X_50))
| inverse(multiply(A,B)) != double_divide(B,A)
| double_divide(double_divide(B,A),X_50) = multiply(multiply(A,B),inverse(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(multiply(A,B)),X_50),multiply(multiply(A,B),inverse(X_50))) ),[0,0],$fot(double_divide(B,A))]]) ).
cnf(refute_0_577,plain,
( double_divide(inverse(multiply(A,B)),X_50) != multiply(multiply(A,B),inverse(X_50))
| double_divide(double_divide(B,A),X_50) = multiply(multiply(A,B),inverse(X_50)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,B)),double_divide(B,A)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
double_divide(double_divide(B,A),X_50) = multiply(multiply(A,B),inverse(X_50)),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(A,B)),X_50),multiply(multiply(A,B),inverse(X_50))) )],[refute_0_571,refute_0_577]) ).
cnf(refute_0_579,plain,
double_divide(double_divide(X_64,X_63),multiply(A,B)) = multiply(multiply(X_63,X_64),inverse(multiply(A,B))),
inference(subst,[],[refute_0_578:[bind(A,$fot(X_63)),bind(B,$fot(X_64)),bind(X_50,$fot(multiply(A,B)))]]) ).
cnf(refute_0_580,plain,
( double_divide(double_divide(X_64,X_63),multiply(A,B)) != multiply(multiply(X_63,X_64),inverse(multiply(A,B)))
| inverse(multiply(A,B)) != double_divide(B,A)
| double_divide(double_divide(X_64,X_63),multiply(A,B)) = multiply(multiply(X_63,X_64),double_divide(B,A)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_64,X_63),multiply(A,B)),multiply(multiply(X_63,X_64),inverse(multiply(A,B)))) ),[1,1],$fot(double_divide(B,A))]]) ).
cnf(refute_0_581,plain,
( double_divide(double_divide(X_64,X_63),multiply(A,B)) != multiply(multiply(X_63,X_64),inverse(multiply(A,B)))
| double_divide(double_divide(X_64,X_63),multiply(A,B)) = multiply(multiply(X_63,X_64),double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(A,B)),double_divide(B,A)) )],[refute_0_575,refute_0_580]) ).
cnf(refute_0_582,plain,
double_divide(double_divide(X_64,X_63),multiply(A,B)) = multiply(multiply(X_63,X_64),double_divide(B,A)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_64,X_63),multiply(A,B)),multiply(multiply(X_63,X_64),inverse(multiply(A,B)))) )],[refute_0_579,refute_0_581]) ).
cnf(refute_0_583,plain,
double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)),
inference(subst,[],[refute_0_582:[bind(A,$fot(X_11)),bind(B,$fot(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),bind(X_63,$fot(A)),bind(X_64,$fot(B))]]) ).
cnf(refute_0_584,plain,
( multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) != multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) != multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))))),bind(Y,$fot(multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)))),bind(Z,$fot(multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))))]]) ).
cnf(refute_0_585,plain,
( multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)) != multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) = multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)),
inference(resolve,[$cnf( $equal(multiply(multiply(A,B),double_divide(double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))),X_11)),multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))) )],[refute_0_463,refute_0_585]) ).
cnf(refute_0_587,plain,
( double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) != X_12
| double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) != multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))
| multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),X_12) ),[0],$fot(multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)))]]) ).
cnf(refute_0_588,plain,
( double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))) != X_12
| multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
multiply(multiply(A,B),double_divide(multiply(double_divide(X_11,X_12),multiply(A,B)),X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),multiply(X_11,double_divide(identity,double_divide(multiply(A,B),double_divide(X_11,X_12))))),X_12) )],[refute_0_51,refute_0_588]) ).
cnf(refute_0_590,plain,
multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_78)) = X_79,
inference(subst,[],[refute_0_589:[bind(A,$fot(inverse(double_divide(X_78,X_79)))),bind(B,$fot(X_77)),bind(X_11,$fot(X_78)),bind(X_12,$fot(X_79))]]) ).
cnf(refute_0_591,plain,
X_77 = multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),
inference(subst,[],[refute_0_539:[bind(B,$fot(X_77)),bind(X_44,$fot(double_divide(X_78,X_79)))]]) ).
cnf(refute_0_592,plain,
( X_77 != multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77))
| multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)) = X_77 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_77)),bind(Y,$fot(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77))))]]) ).
cnf(refute_0_593,plain,
multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)) = X_77,
inference(resolve,[$cnf( $equal(X_77,multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
( multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_78)) != X_79
| multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)) != X_77
| multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = X_79 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_78)),X_79) ),[0,1,0],$fot(X_77)]]) ).
cnf(refute_0_595,plain,
( multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_78)) != X_79
| multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = X_79 ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_77) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = X_79,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(multiply(double_divide(X_78,X_79),multiply(inverse(double_divide(X_78,X_79)),X_77)),X_78)),X_79) )],[refute_0_590,refute_0_595]) ).
cnf(refute_0_597,plain,
inverse(double_divide(X_78,X_79)) = multiply(X_79,X_78),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_79)),bind(B,$fot(X_78))]]) ).
cnf(refute_0_598,plain,
multiply(inverse(double_divide(X_78,X_79)),X_77) = multiply(inverse(double_divide(X_78,X_79)),X_77),
introduced(tautology,[refl,[$fot(multiply(inverse(double_divide(X_78,X_79)),X_77))]]) ).
cnf(refute_0_599,plain,
( multiply(inverse(double_divide(X_78,X_79)),X_77) != multiply(inverse(double_divide(X_78,X_79)),X_77)
| inverse(double_divide(X_78,X_79)) != multiply(X_79,X_78)
| multiply(inverse(double_divide(X_78,X_79)),X_77) = multiply(multiply(X_79,X_78),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(X_78,X_79)),X_77),multiply(inverse(double_divide(X_78,X_79)),X_77)) ),[1,0],$fot(multiply(X_79,X_78))]]) ).
cnf(refute_0_600,plain,
( inverse(double_divide(X_78,X_79)) != multiply(X_79,X_78)
| multiply(inverse(double_divide(X_78,X_79)),X_77) = multiply(multiply(X_79,X_78),X_77) ),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(X_78,X_79)),X_77),multiply(inverse(double_divide(X_78,X_79)),X_77)) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
multiply(inverse(double_divide(X_78,X_79)),X_77) = multiply(multiply(X_79,X_78),X_77),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_78,X_79)),multiply(X_79,X_78)) )],[refute_0_597,refute_0_600]) ).
cnf(refute_0_602,plain,
multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)))]]) ).
cnf(refute_0_603,plain,
( multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) != multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78))
| multiply(inverse(double_divide(X_78,X_79)),X_77) != multiply(multiply(X_79,X_78),X_77)
| multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78))) ),[1,0],$fot(multiply(multiply(X_79,X_78),X_77))]]) ).
cnf(refute_0_604,plain,
( multiply(inverse(double_divide(X_78,X_79)),X_77) != multiply(multiply(X_79,X_78),X_77)
| multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) = multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(X_78,X_79)),X_77),multiply(multiply(X_79,X_78),X_77)) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) != X_79
| multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) != multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78))
| multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)) = X_79 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),X_79) ),[0],$fot(multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)))]]) ).
cnf(refute_0_607,plain,
( multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)) != X_79
| multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)) = X_79 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
multiply(multiply(multiply(X_79,X_78),X_77),double_divide(X_77,X_78)) = X_79,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(double_divide(X_78,X_79)),X_77),double_divide(X_77,X_78)),X_79) )],[refute_0_596,refute_0_607]) ).
cnf(refute_0_609,plain,
multiply(multiply(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(multiply(X_85,X_84),X_83),
inference(subst,[],[refute_0_608:[bind(X_78,$fot(double_divide(X_83,X_84))),bind(X_79,$fot(multiply(multiply(X_85,X_84),X_83)))]]) ).
cnf(refute_0_610,plain,
multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)) = X_85,
inference(subst,[],[refute_0_608:[bind(X_77,$fot(X_83)),bind(X_78,$fot(X_84)),bind(X_79,$fot(X_85))]]) ).
cnf(refute_0_611,plain,
( multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)) != X_85
| multiply(multiply(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(multiply(X_85,X_84),X_83)
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(multiply(X_85,X_84),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(multiply(X_85,X_84),X_83)) ),[0,0,0],$fot(X_85)]]) ).
cnf(refute_0_612,plain,
( multiply(multiply(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(multiply(X_85,X_84),X_83)
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(multiply(X_85,X_84),X_83) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_85) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(multiply(X_85,X_84),X_83),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_85,X_84),X_83),double_divide(X_83,X_84)),X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(multiply(X_85,X_84),X_83)) )],[refute_0_609,refute_0_612]) ).
cnf(refute_0_614,plain,
inverse(double_divide(X_83,X_84)) = multiply(X_84,X_83),
inference(subst,[],[refute_0_39:[bind(A,$fot(X_84)),bind(B,$fot(X_83))]]) ).
cnf(refute_0_615,plain,
multiply(X_85,inverse(double_divide(X_83,X_84))) = multiply(X_85,inverse(double_divide(X_83,X_84))),
introduced(tautology,[refl,[$fot(multiply(X_85,inverse(double_divide(X_83,X_84))))]]) ).
cnf(refute_0_616,plain,
( multiply(X_85,inverse(double_divide(X_83,X_84))) != multiply(X_85,inverse(double_divide(X_83,X_84)))
| inverse(double_divide(X_83,X_84)) != multiply(X_84,X_83)
| multiply(X_85,inverse(double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_85,inverse(double_divide(X_83,X_84))),multiply(X_85,inverse(double_divide(X_83,X_84)))) ),[1,1],$fot(multiply(X_84,X_83))]]) ).
cnf(refute_0_617,plain,
( inverse(double_divide(X_83,X_84)) != multiply(X_84,X_83)
| multiply(X_85,inverse(double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(multiply(X_85,inverse(double_divide(X_83,X_84))),multiply(X_85,inverse(double_divide(X_83,X_84)))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
multiply(X_85,inverse(double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_83,X_84)),multiply(X_84,X_83)) )],[refute_0_614,refute_0_617]) ).
cnf(refute_0_619,plain,
multiply(multiply(multiply(multiply(X_14,inverse(X_84)),X_84),X_83),double_divide(X_83,X_84)) = multiply(X_14,inverse(X_84)),
inference(subst,[],[refute_0_608:[bind(X_77,$fot(X_83)),bind(X_78,$fot(X_84)),bind(X_79,$fot(multiply(X_14,inverse(X_84))))]]) ).
cnf(refute_0_620,plain,
multiply(multiply(X_14,inverse(X_84)),X_84) = X_14,
inference(subst,[],[refute_0_483:[bind(B,$fot(X_84))]]) ).
cnf(refute_0_621,plain,
( multiply(multiply(X_14,inverse(X_84)),X_84) != X_14
| multiply(multiply(multiply(multiply(X_14,inverse(X_84)),X_84),X_83),double_divide(X_83,X_84)) != multiply(X_14,inverse(X_84))
| multiply(multiply(X_14,X_83),double_divide(X_83,X_84)) = multiply(X_14,inverse(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(X_14,inverse(X_84)),X_84),X_83),double_divide(X_83,X_84)),multiply(X_14,inverse(X_84))) ),[0,0,0],$fot(X_14)]]) ).
cnf(refute_0_622,plain,
( multiply(multiply(multiply(multiply(X_14,inverse(X_84)),X_84),X_83),double_divide(X_83,X_84)) != multiply(X_14,inverse(X_84))
| multiply(multiply(X_14,X_83),double_divide(X_83,X_84)) = multiply(X_14,inverse(X_84)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,inverse(X_84)),X_84),X_14) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
multiply(multiply(X_14,X_83),double_divide(X_83,X_84)) = multiply(X_14,inverse(X_84)),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(X_14,inverse(X_84)),X_84),X_83),double_divide(X_83,X_84)),multiply(X_14,inverse(X_84))) )],[refute_0_619,refute_0_622]) ).
cnf(refute_0_624,plain,
multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(X_85,inverse(double_divide(X_83,X_84))),
inference(subst,[],[refute_0_623:[bind(X_14,$fot(X_85)),bind(X_83,$fot(X_77)),bind(X_84,$fot(double_divide(X_83,X_84)))]]) ).
cnf(refute_0_625,plain,
( multiply(X_85,inverse(double_divide(X_83,X_84))) != multiply(X_85,multiply(X_84,X_83))
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(X_85,inverse(double_divide(X_83,X_84)))
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))))),bind(Y,$fot(multiply(X_85,inverse(double_divide(X_83,X_84))))),bind(Z,$fot(multiply(X_85,multiply(X_84,X_83))))]]) ).
cnf(refute_0_626,plain,
( multiply(X_85,inverse(double_divide(X_83,X_84))) != multiply(X_85,multiply(X_84,X_83))
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(X_85,inverse(double_divide(X_83,X_84)))) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) = multiply(X_85,multiply(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_85,inverse(double_divide(X_83,X_84))),multiply(X_85,multiply(X_84,X_83))) )],[refute_0_618,refute_0_626]) ).
cnf(refute_0_628,plain,
( multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(X_85,multiply(X_84,X_83))
| multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(multiply(X_85,X_84),X_83)
| multiply(X_85,multiply(X_84,X_83)) = multiply(multiply(X_85,X_84),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(multiply(X_85,X_84),X_83)) ),[0],$fot(multiply(X_85,multiply(X_84,X_83)))]]) ).
cnf(refute_0_629,plain,
( multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))) != multiply(multiply(X_85,X_84),X_83)
| multiply(X_85,multiply(X_84,X_83)) = multiply(multiply(X_85,X_84),X_83) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(X_85,multiply(X_84,X_83))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
multiply(X_85,multiply(X_84,X_83)) = multiply(multiply(X_85,X_84),X_83),
inference(resolve,[$cnf( $equal(multiply(multiply(X_85,X_77),double_divide(X_77,double_divide(X_83,X_84))),multiply(multiply(X_85,X_84),X_83)) )],[refute_0_613,refute_0_629]) ).
cnf(refute_0_631,plain,
( multiply(X_85,multiply(X_84,X_83)) != multiply(multiply(X_85,X_84),X_83)
| multiply(multiply(X_85,X_84),X_83) = multiply(X_85,multiply(X_84,X_83)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_85,multiply(X_84,X_83)))),bind(Y,$fot(multiply(multiply(X_85,X_84),X_83)))]]) ).
cnf(refute_0_632,plain,
multiply(multiply(X_85,X_84),X_83) = multiply(X_85,multiply(X_84,X_83)),
inference(resolve,[$cnf( $equal(multiply(X_85,multiply(X_84,X_83)),multiply(multiply(X_85,X_84),X_83)) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_632:[bind(X_83,$fot(c3)),bind(X_84,$fot(b3)),bind(X_85,$fot(a3))]]) ).
cnf(refute_0_634,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_635,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_635,prove_these_axioms_3]) ).
cnf(refute_0_637,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_638,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_637,refute_0_636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : GRP489-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.09 % Command : metis --show proof --show saturation %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Tue Jun 14 10:28:57 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.08/0.28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.46
%------------------------------------------------------------------------------