TSTP Solution File: GRP578-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 10:42:29 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 99
% Number of leaves : 121
% Syntax : Number of clauses : 481 ( 236 unt; 0 nHn; 282 RR)
% Number of literals : 839 ( 838 equ; 361 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 514 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,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_2,negated_conjecture,
multiply(identity,a2) != a2 ).
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( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_6,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_7,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_10,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_11,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_12,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_14,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(a2))]]) ).
cnf(refute_0_17,plain,
( multiply(identity,a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),inverse(inverse(a2))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_18,prove_these_axioms_2]) ).
cnf(refute_0_20,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)))]]) ).
cnf(refute_0_22,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_23,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_26,plain,
double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))]]) ).
cnf(refute_0_27,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_28,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))))]]) ).
cnf(refute_0_31,plain,
( double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(B,A),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))) ),[1,1],$fot(double_divide(double_divide(double_divide(B,A),C),inverse(B)))]]) ).
cnf(refute_0_32,plain,
( double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(B,A),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),double_divide(double_divide(double_divide(B,A),C),inverse(B))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)))]]) ).
cnf(refute_0_35,plain,
( double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))) ),[1,0],$fot(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))))]]) ).
cnf(refute_0_36,plain,
( double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B)))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_39,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_38]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)))),bind(Y,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)))),bind(Z,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))))]]) ).
cnf(refute_0_41,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))) )],[refute_0_24,refute_0_41]) ).
cnf(refute_0_43,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),C) ),[0],$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)))]]) ).
cnf(refute_0_44,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),C) )],[single_axiom,refute_0_44]) ).
cnf(refute_0_46,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_15),inverse(identity)),C),inverse(inverse(X_15)))),inverse(identity)) = C,
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(identity))),bind(B,$fot(inverse(X_15)))]]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)),
inference(subst,[],[refute_0_45:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(double_divide(X_11,X_10))))]]) ).
cnf(refute_0_48,plain,
identity = double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_11,X_10)))]]) ).
cnf(refute_0_49,plain,
( identity != double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))
| double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))))]]) ).
cnf(refute_0_50,plain,
double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) != identity
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_11,X_10))) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_52,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),identity) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_11,X_10))) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_55,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_54]) ).
cnf(refute_0_56,plain,
inverse(double_divide(X_11,X_10)) = multiply(X_10,X_11),
inference(subst,[],[refute_0_55:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_57,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| inverse(double_divide(X_11,X_10)) != multiply(X_10,X_11)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_10,X_11)) ),[0],$fot(inverse(double_divide(X_11,X_10)))]]) ).
cnf(refute_0_58,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_10,X_11) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_11,X_10)),multiply(X_10,X_11)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_10,X_11),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),inverse(double_divide(X_11,X_10))) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(X_13,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(X_13,identity),
inference(subst,[],[refute_0_59:[bind(X_10,$fot(X_13)),bind(X_11,$fot(identity))]]) ).
cnf(refute_0_61,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_62,plain,
( identity != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_63,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( double_divide(double_divide(X_13,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(X_13,identity)
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(X_13,identity),inverse(identity)) = multiply(X_13,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(identity,inverse(identity))),inverse(identity)),multiply(X_13,identity)) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_65,plain,
( double_divide(double_divide(X_13,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(X_13,identity)
| double_divide(double_divide(X_13,identity),inverse(identity)) = multiply(X_13,identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(double_divide(X_13,identity),inverse(identity)) = multiply(X_13,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(identity,inverse(identity))),inverse(identity)),multiply(X_13,identity)) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(X_13,identity) = inverse(X_13),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_13))]]) ).
cnf(refute_0_68,plain,
double_divide(double_divide(X_13,identity),inverse(identity)) = double_divide(double_divide(X_13,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_13,identity),inverse(identity)))]]) ).
cnf(refute_0_69,plain,
( double_divide(X_13,identity) != inverse(X_13)
| double_divide(double_divide(X_13,identity),inverse(identity)) != double_divide(double_divide(X_13,identity),inverse(identity))
| double_divide(double_divide(X_13,identity),inverse(identity)) = double_divide(inverse(X_13),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_13,identity),inverse(identity)),double_divide(double_divide(X_13,identity),inverse(identity))) ),[1,0],$fot(inverse(X_13))]]) ).
cnf(refute_0_70,plain,
( double_divide(X_13,identity) != inverse(X_13)
| double_divide(double_divide(X_13,identity),inverse(identity)) = double_divide(inverse(X_13),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,identity),inverse(identity)),double_divide(double_divide(X_13,identity),inverse(identity))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
double_divide(double_divide(X_13,identity),inverse(identity)) = double_divide(inverse(X_13),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_13,identity),inverse(X_13)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( double_divide(double_divide(X_13,identity),inverse(identity)) != multiply(X_13,identity)
| double_divide(double_divide(X_13,identity),inverse(identity)) != double_divide(inverse(X_13),inverse(identity))
| double_divide(inverse(X_13),inverse(identity)) = multiply(X_13,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_13,identity),inverse(identity)),multiply(X_13,identity)) ),[0],$fot(double_divide(inverse(X_13),inverse(identity)))]]) ).
cnf(refute_0_73,plain,
( double_divide(double_divide(X_13,identity),inverse(identity)) != multiply(X_13,identity)
| double_divide(inverse(X_13),inverse(identity)) = multiply(X_13,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,identity),inverse(identity)),double_divide(inverse(X_13),inverse(identity))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
double_divide(inverse(X_13),inverse(identity)) = multiply(X_13,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,identity),inverse(identity)),multiply(X_13,identity)) )],[refute_0_66,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(inverse(X_15),inverse(identity)) = multiply(X_15,identity),
inference(subst,[],[refute_0_74:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_76,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_15),inverse(identity)),C),inverse(inverse(X_15)))),inverse(identity)) != C
| double_divide(inverse(X_15),inverse(identity)) != multiply(X_15,identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_15),inverse(identity)),C),inverse(inverse(X_15)))),inverse(identity)),C) ),[0,0,1,0,0],$fot(multiply(X_15,identity))]]) ).
cnf(refute_0_77,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_15),inverse(identity)),C),inverse(inverse(X_15)))),inverse(identity)) != C
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_15),inverse(identity)),multiply(X_15,identity)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_15),inverse(identity)),C),inverse(inverse(X_15)))),inverse(identity)),C) )],[refute_0_46,refute_0_77]) ).
cnf(refute_0_79,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(inverse(identity))))),inverse(identity)) = multiply(X_10,inverse(inverse(identity))),
inference(subst,[],[refute_0_59:[bind(X_11,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_80,plain,
identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_81,plain,
multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_82,plain,
( multiply(X_2,X_3) != inverse(double_divide(X_3,X_2))
| inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,X_3))),bind(Y,$fot(inverse(double_divide(X_3,X_2))))]]) ).
cnf(refute_0_83,plain,
inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_85,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
identity = double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(identity)),identity)),
inference(subst,[],[refute_0_86:[bind(X_2,$fot(inverse(inverse(identity)))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_88,plain,
double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(X_11))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_89,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_90,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_91,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(inverse(X_11),double_divide(double_divide(identity,X_12),inverse(X_11))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)),X_12) ),[0,0,1,0,0],$fot(identity)]]) ).
cnf(refute_0_93,plain,
( double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(inverse(X_11),double_divide(double_divide(identity,X_12),inverse(X_11))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
double_divide(double_divide(inverse(X_11),double_divide(double_divide(identity,X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)),X_12) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
double_divide(double_divide(inverse(double_divide(identity,X_19)),double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))),inverse(identity)) = X_19,
inference(subst,[],[refute_0_94:[bind(X_11,$fot(double_divide(identity,X_19))),bind(X_12,$fot(X_19))]]) ).
cnf(refute_0_96,plain,
identity = double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(identity,X_19)))]]) ).
cnf(refute_0_97,plain,
( identity != double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))
| double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))))]]) ).
cnf(refute_0_98,plain,
double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19))) != identity
| double_divide(double_divide(inverse(double_divide(identity,X_19)),double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))),inverse(identity)) != X_19
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))),inverse(identity)),X_19) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_100,plain,
( double_divide(double_divide(inverse(double_divide(identity,X_19)),double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))),inverse(identity)) != X_19
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = X_19 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19))),identity) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = X_19,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),double_divide(double_divide(identity,X_19),inverse(double_divide(identity,X_19)))),inverse(identity)),X_19) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(inverse(multiply(X_19,identity)),inverse(identity)) = multiply(multiply(X_19,identity),identity),
inference(subst,[],[refute_0_74:[bind(X_13,$fot(multiply(X_19,identity)))]]) ).
cnf(refute_0_103,plain,
inverse(double_divide(identity,X_19)) = multiply(X_19,identity),
inference(subst,[],[refute_0_55:[bind(A,$fot(X_19)),bind(B,$fot(identity))]]) ).
cnf(refute_0_104,plain,
inverse(inverse(double_divide(identity,X_19))) = inverse(inverse(double_divide(identity,X_19))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,X_19))))]]) ).
cnf(refute_0_105,plain,
( inverse(double_divide(identity,X_19)) != multiply(X_19,identity)
| inverse(inverse(double_divide(identity,X_19))) != inverse(inverse(double_divide(identity,X_19)))
| inverse(inverse(double_divide(identity,X_19))) = inverse(multiply(X_19,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,X_19))),inverse(inverse(double_divide(identity,X_19)))) ),[1,0],$fot(multiply(X_19,identity))]]) ).
cnf(refute_0_106,plain,
( inverse(double_divide(identity,X_19)) != multiply(X_19,identity)
| inverse(inverse(double_divide(identity,X_19))) = inverse(multiply(X_19,identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,X_19))),inverse(inverse(double_divide(identity,X_19)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
inverse(inverse(double_divide(identity,X_19))) = inverse(multiply(X_19,identity)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,X_19)),multiply(X_19,identity)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
double_divide(inverse(double_divide(identity,X_19)),identity) = inverse(inverse(double_divide(identity,X_19))),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(double_divide(identity,X_19))))]]) ).
cnf(refute_0_109,plain,
( double_divide(inverse(double_divide(identity,X_19)),identity) != inverse(inverse(double_divide(identity,X_19)))
| inverse(inverse(double_divide(identity,X_19))) != inverse(multiply(X_19,identity))
| double_divide(inverse(double_divide(identity,X_19)),identity) = inverse(multiply(X_19,identity)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(inverse(double_divide(identity,X_19)),identity))),bind(Y,$fot(inverse(inverse(double_divide(identity,X_19))))),bind(Z,$fot(inverse(multiply(X_19,identity))))]]) ).
cnf(refute_0_110,plain,
( inverse(inverse(double_divide(identity,X_19))) != inverse(multiply(X_19,identity))
| double_divide(inverse(double_divide(identity,X_19)),identity) = inverse(multiply(X_19,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(inverse(double_divide(identity,X_19)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
double_divide(inverse(double_divide(identity,X_19)),identity) = inverse(multiply(X_19,identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,X_19))),inverse(multiply(X_19,identity))) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)))]]) ).
cnf(refute_0_113,plain,
( double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) != double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity))
| double_divide(inverse(double_divide(identity,X_19)),identity) != inverse(multiply(X_19,identity))
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = double_divide(inverse(multiply(X_19,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity))) ),[1,0],$fot(inverse(multiply(X_19,identity)))]]) ).
cnf(refute_0_114,plain,
( double_divide(inverse(double_divide(identity,X_19)),identity) != inverse(multiply(X_19,identity))
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = double_divide(inverse(multiply(X_19,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = double_divide(inverse(multiply(X_19,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(multiply(X_19,identity))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
( double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) != double_divide(inverse(multiply(X_19,identity)),inverse(identity))
| double_divide(inverse(multiply(X_19,identity)),inverse(identity)) != multiply(multiply(X_19,identity),identity)
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = multiply(multiply(X_19,identity),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)))),bind(Y,$fot(double_divide(inverse(multiply(X_19,identity)),inverse(identity)))),bind(Z,$fot(multiply(multiply(X_19,identity),identity)))]]) ).
cnf(refute_0_117,plain,
( double_divide(inverse(multiply(X_19,identity)),inverse(identity)) != multiply(multiply(X_19,identity),identity)
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = multiply(multiply(X_19,identity),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),double_divide(inverse(multiply(X_19,identity)),inverse(identity))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) = multiply(multiply(X_19,identity),identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(multiply(X_19,identity)),inverse(identity)),multiply(multiply(X_19,identity),identity)) )],[refute_0_102,refute_0_117]) ).
cnf(refute_0_119,plain,
( double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) != X_19
| double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) != multiply(multiply(X_19,identity),identity)
| multiply(multiply(X_19,identity),identity) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),X_19) ),[0],$fot(multiply(multiply(X_19,identity),identity))]]) ).
cnf(refute_0_120,plain,
( double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)) != X_19
| multiply(multiply(X_19,identity),identity) = X_19 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),multiply(multiply(X_19,identity),identity)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
multiply(multiply(X_19,identity),identity) = X_19,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,X_19)),identity),inverse(identity)),X_19) )],[refute_0_101,refute_0_120]) ).
cnf(refute_0_122,plain,
multiply(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),
inference(subst,[],[refute_0_121:[bind(X_19,$fot(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))))]]) ).
cnf(refute_0_123,plain,
double_divide(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11),
inference(subst,[],[refute_0_59:[bind(X_10,$fot(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity))))]]) ).
cnf(refute_0_124,plain,
identity = double_divide(double_divide(identity,multiply(X_20,identity)),multiply(multiply(X_20,identity),identity)),
inference(subst,[],[refute_0_86:[bind(X_2,$fot(multiply(X_20,identity))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_125,plain,
multiply(multiply(X_20,identity),identity) = X_20,
inference(subst,[],[refute_0_121:[bind(X_19,$fot(X_20))]]) ).
cnf(refute_0_126,plain,
( multiply(multiply(X_20,identity),identity) != X_20
| identity != double_divide(double_divide(identity,multiply(X_20,identity)),multiply(multiply(X_20,identity),identity))
| identity = double_divide(double_divide(identity,multiply(X_20,identity)),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(X_20,identity)),multiply(multiply(X_20,identity),identity))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_127,plain,
( identity != double_divide(double_divide(identity,multiply(X_20,identity)),multiply(multiply(X_20,identity),identity))
| identity = double_divide(double_divide(identity,multiply(X_20,identity)),X_20) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_20,identity),identity),X_20) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
identity = double_divide(double_divide(identity,multiply(X_20,identity)),X_20),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(X_20,identity)),multiply(multiply(X_20,identity),identity))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
identity = double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),
inference(subst,[],[refute_0_128:[bind(X_20,$fot(double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_130,plain,
( identity != double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11)))
| double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11)))))]]) ).
cnf(refute_0_131,plain,
double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11)))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( double_divide(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)
| double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))) != identity
| double_divide(identity,inverse(identity)) = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),inverse(identity)),multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_133,plain,
( double_divide(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)
| double_divide(identity,inverse(identity)) = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),identity) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
double_divide(identity,inverse(identity)) = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),double_divide(identity,inverse(X_11))),inverse(identity)),multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)) )],[refute_0_123,refute_0_133]) ).
cnf(refute_0_135,plain,
( double_divide(identity,inverse(identity)) != multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)
| double_divide(identity,inverse(identity)) != identity
| identity = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(identity)),multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)) ),[0],$fot(identity)]]) ).
cnf(refute_0_136,plain,
( double_divide(identity,inverse(identity)) != multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)
| identity = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_63,refute_0_135]) ).
cnf(refute_0_137,plain,
identity = multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),multiply(double_divide(identity,multiply(double_divide(identity,inverse(X_11)),identity)),X_11)) )],[refute_0_134,refute_0_136]) ).
cnf(refute_0_138,plain,
identity = multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),
inference(subst,[],[refute_0_137:[bind(X_11,$fot(identity))]]) ).
cnf(refute_0_139,plain,
( identity != multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity)
| multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity)))]]) ).
cnf(refute_0_140,plain,
multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity) = identity,
inference(resolve,[$cnf( $equal(identity,multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( multiply(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity) != identity
| multiply(identity,identity) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_142,plain,
( multiply(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| multiply(identity,identity) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(identity,identity) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),identity),identity),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) )],[refute_0_122,refute_0_142]) ).
cnf(refute_0_144,plain,
multiply(identity,identity) = inverse(inverse(identity)),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_145,plain,
( multiply(identity,identity) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| multiply(identity,identity) != inverse(inverse(identity))
| inverse(inverse(identity)) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,identity),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) ),[0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_146,plain,
( multiply(identity,identity) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| inverse(inverse(identity)) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(double_divide(identity,inverse(identity)),identity) = multiply(double_divide(identity,inverse(identity)),identity),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(identity)),identity))]]) ).
cnf(refute_0_148,plain,
( multiply(double_divide(identity,inverse(identity)),identity) != multiply(double_divide(identity,inverse(identity)),identity)
| double_divide(identity,inverse(identity)) != identity
| multiply(double_divide(identity,inverse(identity)),identity) = multiply(identity,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(identity)),identity),multiply(double_divide(identity,inverse(identity)),identity)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_149,plain,
( double_divide(identity,inverse(identity)) != identity
| multiply(double_divide(identity,inverse(identity)),identity) = multiply(identity,identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(identity)),identity),multiply(double_divide(identity,inverse(identity)),identity)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
multiply(double_divide(identity,inverse(identity)),identity) = multiply(identity,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_63,refute_0_149]) ).
cnf(refute_0_151,plain,
( multiply(double_divide(identity,inverse(identity)),identity) != multiply(identity,identity)
| multiply(identity,identity) != inverse(inverse(identity))
| multiply(double_divide(identity,inverse(identity)),identity) = inverse(inverse(identity)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(double_divide(identity,inverse(identity)),identity))),bind(Y,$fot(multiply(identity,identity))),bind(Z,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_152,plain,
( multiply(identity,identity) != inverse(inverse(identity))
| multiply(double_divide(identity,inverse(identity)),identity) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(identity)),identity),multiply(identity,identity)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(double_divide(identity,inverse(identity)),identity) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_144,refute_0_152]) ).
cnf(refute_0_154,plain,
double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) = double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)))]]) ).
cnf(refute_0_155,plain,
( multiply(double_divide(identity,inverse(identity)),identity) != inverse(inverse(identity))
| double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) ),[1,1],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_156,plain,
( multiply(double_divide(identity,inverse(identity)),identity) != inverse(inverse(identity))
| double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(identity)),identity),inverse(inverse(identity))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)) != double_divide(identity,inverse(inverse(identity)))
| inverse(inverse(identity)) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| inverse(inverse(identity)) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) ),[1],$fot(double_divide(identity,inverse(inverse(identity))))]]) ).
cnf(refute_0_159,plain,
( inverse(inverse(identity)) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| inverse(inverse(identity)) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity)),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( multiply(identity,identity) != double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))
| inverse(inverse(identity)) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) )],[refute_0_146,refute_0_159]) ).
cnf(refute_0_161,plain,
inverse(inverse(identity)) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(multiply(identity,identity),double_divide(identity,multiply(double_divide(identity,inverse(identity)),identity))) )],[refute_0_143,refute_0_160]) ).
cnf(refute_0_162,plain,
( inverse(inverse(identity)) != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,inverse(inverse(identity))) = inverse(inverse(identity)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(inverse(identity)))),bind(Y,$fot(double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_163,plain,
double_divide(identity,inverse(inverse(identity))) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( double_divide(identity,inverse(inverse(identity))) != inverse(inverse(identity))
| identity != double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(identity)),identity))
| identity = double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(identity)),identity))) ),[1,0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_165,plain,
( identity != double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(identity)),identity))
| identity = double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
identity = double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,inverse(inverse(identity))),multiply(inverse(inverse(identity)),identity))) )],[refute_0_87,refute_0_165]) ).
cnf(refute_0_167,plain,
double_divide(inverse(inverse(identity)),identity) = inverse(inverse(inverse(identity))),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_168,plain,
multiply(multiply(identity,identity),identity) = identity,
inference(subst,[],[refute_0_121:[bind(X_19,$fot(identity))]]) ).
cnf(refute_0_169,plain,
( multiply(multiply(identity,identity),identity) != identity
| multiply(identity,identity) != inverse(inverse(identity))
| multiply(inverse(inverse(identity)),identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,identity),identity),identity) ),[0,0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_170,plain,
( multiply(multiply(identity,identity),identity) != identity
| multiply(inverse(inverse(identity)),identity) = identity ),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_144,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(inverse(inverse(identity)),identity) = identity,
inference(resolve,[$cnf( $equal(multiply(multiply(identity,identity),identity),identity) )],[refute_0_168,refute_0_170]) ).
cnf(refute_0_172,plain,
double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)))]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(inverse(identity)),identity) != identity
| double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) != double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))
| double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = double_divide(inverse(inverse(identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_174,plain,
( multiply(inverse(inverse(identity)),identity) != identity
| double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = double_divide(inverse(inverse(identity)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = double_divide(inverse(inverse(identity)),identity),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(identity)),identity),identity) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) != double_divide(inverse(inverse(identity)),identity)
| double_divide(inverse(inverse(identity)),identity) != inverse(inverse(inverse(identity)))
| double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = inverse(inverse(inverse(identity))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)))),bind(Y,$fot(double_divide(inverse(inverse(identity)),identity))),bind(Z,$fot(inverse(inverse(inverse(identity)))))]]) ).
cnf(refute_0_177,plain,
( double_divide(inverse(inverse(identity)),identity) != inverse(inverse(inverse(identity)))
| double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = inverse(inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),double_divide(inverse(inverse(identity)),identity)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) = inverse(inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))) )],[refute_0_167,refute_0_177]) ).
cnf(refute_0_179,plain,
( double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)) != inverse(inverse(inverse(identity)))
| identity != double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))
| identity = inverse(inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))) ),[1],$fot(inverse(inverse(inverse(identity))))]]) ).
cnf(refute_0_180,plain,
( identity != double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))
| identity = inverse(inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity)),inverse(inverse(inverse(identity)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
identity = inverse(inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(inverse(identity)),multiply(inverse(inverse(identity)),identity))) )],[refute_0_166,refute_0_180]) ).
cnf(refute_0_182,plain,
( identity != inverse(inverse(inverse(identity)))
| inverse(inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(inverse(inverse(identity)))))]]) ).
cnf(refute_0_183,plain,
inverse(inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(inverse(inverse(identity)))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(inverse(identity))))),inverse(identity)) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(inverse(identity))) != identity
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(inverse(identity))))),inverse(identity)),multiply(X_10,inverse(inverse(identity)))) ),[0,0,1,1],$fot(identity)]]) ).
cnf(refute_0_185,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(inverse(identity))))),inverse(identity)) != multiply(X_10,inverse(inverse(identity)))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(identity))),identity) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(inverse(identity))))),inverse(identity)),multiply(X_10,inverse(inverse(identity)))) )],[refute_0_79,refute_0_185]) ).
cnf(refute_0_187,plain,
double_divide(inverse(X_10),identity) = inverse(inverse(X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_188,plain,
identity = multiply(double_divide(identity,multiply(double_divide(identity,inverse(inverse(inverse(identity)))),identity)),inverse(inverse(identity))),
inference(subst,[],[refute_0_137:[bind(X_11,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_189,plain,
( identity != multiply(double_divide(identity,multiply(double_divide(identity,inverse(inverse(inverse(identity)))),identity)),inverse(inverse(identity)))
| inverse(inverse(inverse(identity))) != identity
| identity = multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(double_divide(identity,multiply(double_divide(identity,inverse(inverse(inverse(identity)))),identity)),inverse(inverse(identity)))) ),[1,0,1,0,1],$fot(identity)]]) ).
cnf(refute_0_190,plain,
( identity != multiply(double_divide(identity,multiply(double_divide(identity,inverse(inverse(inverse(identity)))),identity)),inverse(inverse(identity)))
| identity = multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(identity))),identity) )],[refute_0_183,refute_0_189]) ).
cnf(refute_0_191,plain,
identity = multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(identity,multiply(double_divide(identity,multiply(double_divide(identity,inverse(inverse(inverse(identity)))),identity)),inverse(inverse(identity)))) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
inverse(inverse(inverse(inverse(identity)))) = inverse(inverse(inverse(inverse(identity)))),
introduced(tautology,[refl,[$fot(inverse(inverse(inverse(inverse(identity)))))]]) ).
cnf(refute_0_193,plain,
( inverse(inverse(inverse(identity))) != identity
| inverse(inverse(inverse(inverse(identity)))) != inverse(inverse(inverse(inverse(identity))))
| inverse(inverse(inverse(inverse(identity)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(inverse(identity)))),inverse(inverse(inverse(inverse(identity))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_194,plain,
( inverse(inverse(inverse(identity))) != identity
| inverse(inverse(inverse(inverse(identity)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(identity)))),inverse(inverse(inverse(inverse(identity))))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
inverse(inverse(inverse(inverse(identity)))) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(identity))),identity) )],[refute_0_183,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(identity,inverse(inverse(identity))) = inverse(inverse(inverse(inverse(identity)))),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_197,plain,
( multiply(identity,inverse(inverse(identity))) != inverse(inverse(inverse(inverse(identity))))
| inverse(inverse(inverse(inverse(identity)))) != inverse(identity)
| multiply(identity,inverse(inverse(identity))) = inverse(identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(identity,inverse(inverse(identity))))),bind(Y,$fot(inverse(inverse(inverse(inverse(identity)))))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_198,plain,
( inverse(inverse(inverse(inverse(identity)))) != inverse(identity)
| multiply(identity,inverse(inverse(identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(inverse(identity))),inverse(inverse(inverse(inverse(identity))))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(identity,inverse(inverse(identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_201,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_202,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_203,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_205,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_200,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(subst,[],[refute_0_206:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_208,plain,
multiply(double_divide(identity,identity),identity) = multiply(double_divide(identity,identity),identity),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,identity),identity))]]) ).
cnf(refute_0_209,plain,
( multiply(double_divide(identity,identity),identity) != multiply(double_divide(identity,identity),identity)
| double_divide(identity,identity) != inverse(identity)
| multiply(double_divide(identity,identity),identity) = multiply(inverse(identity),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,identity),identity),multiply(double_divide(identity,identity),identity)) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_210,plain,
( double_divide(identity,identity) != inverse(identity)
| multiply(double_divide(identity,identity),identity) = multiply(inverse(identity),identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,identity),identity),multiply(double_divide(identity,identity),identity)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
multiply(double_divide(identity,identity),identity) = multiply(inverse(identity),identity),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_20,refute_0_210]) ).
cnf(refute_0_212,plain,
( multiply(double_divide(identity,identity),identity) != multiply(inverse(identity),identity)
| multiply(inverse(identity),identity) != inverse(identity)
| multiply(double_divide(identity,identity),identity) = inverse(identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(double_divide(identity,identity),identity))),bind(Y,$fot(multiply(inverse(identity),identity))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_213,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| multiply(double_divide(identity,identity),identity) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,identity),identity),multiply(inverse(identity),identity)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
multiply(double_divide(identity,identity),identity) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_207,refute_0_213]) ).
cnf(refute_0_215,plain,
double_divide(identity,multiply(double_divide(identity,identity),identity)) = double_divide(identity,multiply(double_divide(identity,identity),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(double_divide(identity,identity),identity)))]]) ).
cnf(refute_0_216,plain,
( multiply(double_divide(identity,identity),identity) != inverse(identity)
| double_divide(identity,multiply(double_divide(identity,identity),identity)) != double_divide(identity,multiply(double_divide(identity,identity),identity))
| double_divide(identity,multiply(double_divide(identity,identity),identity)) = double_divide(identity,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,identity),identity)),double_divide(identity,multiply(double_divide(identity,identity),identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_217,plain,
( multiply(double_divide(identity,identity),identity) != inverse(identity)
| double_divide(identity,multiply(double_divide(identity,identity),identity)) = double_divide(identity,inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,identity),identity)),double_divide(identity,multiply(double_divide(identity,identity),identity))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
double_divide(identity,multiply(double_divide(identity,identity),identity)) = double_divide(identity,inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,identity),identity),inverse(identity)) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
( double_divide(identity,multiply(double_divide(identity,identity),identity)) != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) != identity
| double_divide(identity,multiply(double_divide(identity,identity),identity)) = identity ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(identity,multiply(double_divide(identity,identity),identity)))),bind(Y,$fot(double_divide(identity,inverse(identity)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_220,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(identity,multiply(double_divide(identity,identity),identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,identity),identity)),double_divide(identity,inverse(identity))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
double_divide(identity,multiply(double_divide(identity,identity),identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_63,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))))]]) ).
cnf(refute_0_223,plain,
( multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) != multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))
| double_divide(identity,multiply(double_divide(identity,identity),identity)) != identity
| multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = multiply(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_224,plain,
( double_divide(identity,multiply(double_divide(identity,identity),identity)) != identity
| multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = multiply(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = multiply(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(identity,identity),identity)),identity) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) != multiply(identity,inverse(inverse(identity)))
| multiply(identity,inverse(inverse(identity))) != inverse(identity)
| multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = inverse(identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))))),bind(Y,$fot(multiply(identity,inverse(inverse(identity))))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_227,plain,
( multiply(identity,inverse(inverse(identity))) != inverse(identity)
| multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),multiply(identity,inverse(inverse(identity)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(inverse(identity))),inverse(identity)) )],[refute_0_199,refute_0_227]) ).
cnf(refute_0_229,plain,
( multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))) != inverse(identity)
| identity != multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_230,plain,
( identity != multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity))),inverse(identity)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,multiply(double_divide(identity,multiply(double_divide(identity,identity),identity)),inverse(inverse(identity)))) )],[refute_0_191,refute_0_230]) ).
cnf(refute_0_232,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_233,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_10),inverse(identity)))]]) ).
cnf(refute_0_235,plain,
( double_divide(inverse(X_10),inverse(identity)) != double_divide(inverse(X_10),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_236,plain,
( inverse(identity) != identity
| double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
double_divide(X_10,identity) = inverse(X_10),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_239,plain,
( double_divide(identity,identity) != inverse(identity)
| inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(identity,identity))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_240,plain,
( inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_20,refute_0_239]) ).
cnf(refute_0_241,plain,
double_divide(identity,identity) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_240]) ).
cnf(refute_0_242,plain,
double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(identity,identity)))]]) ).
cnf(refute_0_243,plain,
( double_divide(X_10,double_divide(identity,identity)) != double_divide(X_10,double_divide(identity,identity))
| double_divide(identity,identity) != identity
| double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),double_divide(X_10,double_divide(identity,identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_244,plain,
( double_divide(identity,identity) != identity
| double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),double_divide(X_10,double_divide(identity,identity))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),identity) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
( double_divide(X_10,double_divide(identity,identity)) != double_divide(X_10,identity)
| double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_10,double_divide(identity,identity)) = inverse(X_10) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(X_10,double_divide(identity,identity)))),bind(Y,$fot(double_divide(X_10,identity))),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_247,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_10,double_divide(identity,identity)) = inverse(X_10) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),double_divide(X_10,identity)) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
double_divide(X_10,double_divide(identity,identity)) = inverse(X_10),
inference(resolve,[$cnf( $equal(double_divide(X_10,identity),inverse(X_10)) )],[refute_0_238,refute_0_247]) ).
cnf(refute_0_249,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)))]]) ).
cnf(refute_0_250,plain,
( double_divide(X_10,double_divide(identity,identity)) != inverse(X_10)
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity))) ),[1,0],$fot(inverse(X_10))]]) ).
cnf(refute_0_251,plain,
( double_divide(X_10,double_divide(identity,identity)) != inverse(X_10)
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),inverse(X_10)) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != double_divide(inverse(X_10),inverse(identity))
| double_divide(inverse(X_10),inverse(identity)) != double_divide(inverse(X_10),identity)
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)))),bind(Y,$fot(double_divide(inverse(X_10),inverse(identity)))),bind(Z,$fot(double_divide(inverse(X_10),identity)))]]) ).
cnf(refute_0_254,plain,
( double_divide(inverse(X_10),inverse(identity)) != double_divide(inverse(X_10),identity)
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),identity)) )],[refute_0_237,refute_0_254]) ).
cnf(refute_0_256,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != double_divide(inverse(X_10),identity)
| double_divide(inverse(X_10),identity) != inverse(inverse(X_10))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X_10)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)))),bind(Y,$fot(double_divide(inverse(X_10),identity))),bind(Z,$fot(inverse(inverse(X_10))))]]) ).
cnf(refute_0_257,plain,
( double_divide(inverse(X_10),identity) != inverse(inverse(X_10))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X_10)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(inverse(X_10),identity)) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X_10)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),identity),inverse(inverse(X_10))) )],[refute_0_187,refute_0_257]) ).
cnf(refute_0_259,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(inverse(identity)))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != inverse(inverse(X_10))
| inverse(inverse(X_10)) = multiply(X_10,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),multiply(X_10,inverse(inverse(identity)))) ),[0],$fot(inverse(inverse(X_10)))]]) ).
cnf(refute_0_260,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(X_10)) = multiply(X_10,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),inverse(inverse(X_10))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
inverse(inverse(identity)) = inverse(inverse(identity)),
introduced(tautology,[refl,[$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_262,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_263,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
inverse(inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_263]) ).
cnf(refute_0_265,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) != inverse(identity)
| inverse(inverse(identity)) = identity ),
inference(subst,[],[refute_0_39:[bind(X,$fot(inverse(inverse(identity)))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_266,plain,
( inverse(identity) != identity
| inverse(inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(identity)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
inverse(inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_266]) ).
cnf(refute_0_268,plain,
multiply(X_10,inverse(inverse(identity))) = multiply(X_10,inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(multiply(X_10,inverse(inverse(identity))))]]) ).
cnf(refute_0_269,plain,
( multiply(X_10,inverse(inverse(identity))) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(identity)) != identity
| multiply(X_10,inverse(inverse(identity))) = multiply(X_10,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_10,inverse(inverse(identity))),multiply(X_10,inverse(inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_270,plain,
( inverse(inverse(identity)) != identity
| multiply(X_10,inverse(inverse(identity))) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_10,inverse(inverse(identity))),multiply(X_10,inverse(inverse(identity)))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
multiply(X_10,inverse(inverse(identity))) = multiply(X_10,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_267,refute_0_270]) ).
cnf(refute_0_272,plain,
( multiply(X_10,inverse(inverse(identity))) != multiply(X_10,identity)
| inverse(inverse(X_10)) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,inverse(inverse(identity)))) ),[1],$fot(multiply(X_10,identity))]]) ).
cnf(refute_0_273,plain,
( inverse(inverse(X_10)) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_10,inverse(inverse(identity))),multiply(X_10,identity)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(inverse(identity)))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,inverse(inverse(identity)))) )],[refute_0_260,refute_0_273]) ).
cnf(refute_0_275,plain,
inverse(inverse(X_10)) = multiply(X_10,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),multiply(X_10,inverse(inverse(identity)))) )],[refute_0_186,refute_0_274]) ).
cnf(refute_0_276,plain,
( inverse(inverse(X_10)) != multiply(X_10,identity)
| multiply(X_10,identity) = inverse(inverse(X_10)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(inverse(X_10)))),bind(Y,$fot(multiply(X_10,identity)))]]) ).
cnf(refute_0_277,plain,
multiply(X_10,identity) = inverse(inverse(X_10)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,identity)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
multiply(inverse(inverse(C)),identity) = inverse(inverse(inverse(inverse(C)))),
inference(subst,[],[refute_0_277:[bind(X_10,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_279,plain,
inverse(double_divide(identity,inverse(inverse(C)))) = multiply(inverse(inverse(C)),identity),
inference(subst,[],[refute_0_55:[bind(A,$fot(inverse(inverse(C)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_280,plain,
( multiply(inverse(inverse(C)),identity) != inverse(inverse(inverse(inverse(C))))
| inverse(double_divide(identity,inverse(inverse(C)))) != multiply(inverse(inverse(C)),identity)
| inverse(double_divide(identity,inverse(inverse(C)))) = inverse(inverse(inverse(inverse(C)))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(inverse(double_divide(identity,inverse(inverse(C)))))),bind(Y,$fot(multiply(inverse(inverse(C)),identity))),bind(Z,$fot(inverse(inverse(inverse(inverse(C))))))]]) ).
cnf(refute_0_281,plain,
( multiply(inverse(inverse(C)),identity) != inverse(inverse(inverse(inverse(C))))
| inverse(double_divide(identity,inverse(inverse(C)))) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(C)))),multiply(inverse(inverse(C)),identity)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
inverse(double_divide(identity,inverse(inverse(C)))) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(C)),identity),inverse(inverse(inverse(inverse(C))))) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(double_divide(identity,inverse(inverse(C)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,inverse(inverse(C)))))]]) ).
cnf(refute_0_284,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),identity) != inverse(double_divide(identity,inverse(inverse(C))))
| inverse(double_divide(identity,inverse(inverse(C)))) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(inverse(inverse(inverse(C)))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(inverse(C))),identity))),bind(Y,$fot(inverse(double_divide(identity,inverse(inverse(C)))))),bind(Z,$fot(inverse(inverse(inverse(inverse(C))))))]]) ).
cnf(refute_0_285,plain,
( inverse(double_divide(identity,inverse(inverse(C)))) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),identity),inverse(double_divide(identity,inverse(inverse(C))))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(C)))),inverse(inverse(inverse(inverse(C))))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)))]]) ).
cnf(refute_0_288,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))
| inverse(identity) != identity
| double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_289,plain,
( inverse(identity) != identity
| double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_289]) ).
cnf(refute_0_291,plain,
multiply(C,identity) = inverse(inverse(C)),
inference(subst,[],[refute_0_277:[bind(X_10,$fot(C))]]) ).
cnf(refute_0_292,plain,
inverse(double_divide(identity,C)) = multiply(C,identity),
inference(subst,[],[refute_0_55:[bind(A,$fot(C)),bind(B,$fot(identity))]]) ).
cnf(refute_0_293,plain,
( multiply(C,identity) != inverse(inverse(C))
| inverse(double_divide(identity,C)) != multiply(C,identity)
| inverse(double_divide(identity,C)) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(inverse(double_divide(identity,C)))),bind(Y,$fot(multiply(C,identity))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_294,plain,
( multiply(C,identity) != inverse(inverse(C))
| inverse(double_divide(identity,C)) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,C)),multiply(C,identity)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
inverse(double_divide(identity,C)) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(multiply(C,identity),inverse(inverse(C))) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
double_divide(double_divide(identity,C),identity) = inverse(double_divide(identity,C)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,C)))]]) ).
cnf(refute_0_297,plain,
( double_divide(double_divide(identity,C),identity) != inverse(double_divide(identity,C))
| inverse(double_divide(identity,C)) != inverse(inverse(C))
| double_divide(double_divide(identity,C),identity) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,C),identity))),bind(Y,$fot(inverse(double_divide(identity,C)))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_298,plain,
( inverse(double_divide(identity,C)) != inverse(inverse(C))
| double_divide(double_divide(identity,C),identity) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),inverse(double_divide(identity,C))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
double_divide(double_divide(identity,C),identity) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,C)),inverse(inverse(C))) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,C),inverse(identity)))]]) ).
cnf(refute_0_301,plain,
( double_divide(double_divide(identity,C),inverse(identity)) != double_divide(double_divide(identity,C),inverse(identity))
| inverse(identity) != identity
| double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(identity)),double_divide(double_divide(identity,C),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_302,plain,
( inverse(identity) != identity
| double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(identity)),double_divide(double_divide(identity,C),inverse(identity))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_302]) ).
cnf(refute_0_304,plain,
double_divide(inverse(identity),C) = double_divide(inverse(identity),C),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),C))]]) ).
cnf(refute_0_305,plain,
( double_divide(inverse(identity),C) != double_divide(inverse(identity),C)
| inverse(identity) != identity
| double_divide(inverse(identity),C) = double_divide(identity,C) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),C),double_divide(inverse(identity),C)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_306,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),C) = double_divide(identity,C) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),C),double_divide(inverse(identity),C)) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
double_divide(inverse(identity),C) = double_divide(identity,C),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_306]) ).
cnf(refute_0_308,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))]]) ).
cnf(refute_0_309,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(inverse(identity),C),inverse(identity))
| double_divide(inverse(identity),C) != double_divide(identity,C)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(inverse(identity),C),inverse(identity))) ),[1,0],$fot(double_divide(identity,C))]]) ).
cnf(refute_0_310,plain,
( double_divide(inverse(identity),C) != double_divide(identity,C)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(inverse(identity),C),inverse(identity))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),C),double_divide(identity,C)) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
( double_divide(double_divide(identity,C),inverse(identity)) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(identity,C),inverse(identity))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,C),inverse(identity)))),bind(Z,$fot(double_divide(double_divide(identity,C),identity)))]]) ).
cnf(refute_0_313,plain,
( double_divide(double_divide(identity,C),inverse(identity)) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(identity,C),inverse(identity))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(identity)),double_divide(double_divide(identity,C),identity)) )],[refute_0_303,refute_0_313]) ).
cnf(refute_0_315,plain,
( double_divide(double_divide(identity,C),identity) != inverse(inverse(C))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,C),identity))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_316,plain,
( double_divide(double_divide(identity,C),identity) != inverse(inverse(C))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(identity,C),identity)) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),inverse(inverse(C))) )],[refute_0_299,refute_0_316]) ).
cnf(refute_0_318,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
inference(subst,[],[refute_0_94:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(double_divide(double_divide(B,identity),C),inverse(B))))]]) ).
cnf(refute_0_319,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity)) = C,
inference(subst,[],[refute_0_45:[bind(A,$fot(identity))]]) ).
cnf(refute_0_320,plain,
( double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity)) != C
| double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) ),[0,0,1],$fot(C)]]) ).
cnf(refute_0_321,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity)),C) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
double_divide(double_divide(B,identity),C) = double_divide(double_divide(B,identity),C),
introduced(tautology,[refl,[$fot(double_divide(double_divide(B,identity),C))]]) ).
cnf(refute_0_324,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(B,identity),C) != double_divide(double_divide(B,identity),C)
| double_divide(double_divide(B,identity),C) = double_divide(inverse(B),C) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(B,identity),C),double_divide(double_divide(B,identity),C)) ),[1,0],$fot(inverse(B))]]) ).
cnf(refute_0_325,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(B,identity),C) = double_divide(inverse(B),C) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,identity),C),double_divide(double_divide(B,identity),C)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
double_divide(double_divide(B,identity),C) = double_divide(inverse(B),C),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_25,refute_0_325]) ).
cnf(refute_0_327,plain,
double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(B,identity),C),inverse(B)))]]) ).
cnf(refute_0_328,plain,
( double_divide(double_divide(B,identity),C) != double_divide(inverse(B),C)
| double_divide(double_divide(double_divide(B,identity),C),inverse(B)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(inverse(B),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(B,identity),C),inverse(B)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) ),[1,0],$fot(double_divide(inverse(B),C))]]) ).
cnf(refute_0_329,plain,
( double_divide(double_divide(B,identity),C) != double_divide(inverse(B),C)
| double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(inverse(B),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,identity),C),inverse(B)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(inverse(B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,identity),C),double_divide(inverse(B),C)) )],[refute_0_326,refute_0_329]) ).
cnf(refute_0_331,plain,
( double_divide(double_divide(double_divide(B,identity),C),inverse(B)) != double_divide(double_divide(inverse(B),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(B),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) ),[1],$fot(double_divide(double_divide(inverse(B),C),inverse(B)))]]) ).
cnf(refute_0_332,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(B),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,identity),C),inverse(B)),double_divide(double_divide(inverse(B),C),inverse(B))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_322,refute_0_332]) ).
cnf(refute_0_334,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(inverse(B),C),inverse(B))
| double_divide(double_divide(inverse(B),C),inverse(B)) = double_divide(double_divide(inverse(identity),C),inverse(identity)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(inverse(B),C),inverse(B))))]]) ).
cnf(refute_0_335,plain,
double_divide(double_divide(inverse(B),C),inverse(B)) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(inverse(B),C),inverse(B))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
inference(subst,[],[refute_0_335:[bind(B,$fot(inverse(X_15)))]]) ).
cnf(refute_0_337,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != inverse(inverse(C))
| double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) != double_divide(double_divide(inverse(identity),C),inverse(identity))
| double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))))),bind(Y,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_338,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != inverse(inverse(C))
| double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))),double_divide(double_divide(inverse(identity),C),inverse(identity))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),inverse(inverse(C))) )],[refute_0_317,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(X_15,identity) = inverse(inverse(X_15)),
inference(subst,[],[refute_0_277:[bind(X_10,$fot(X_15))]]) ).
cnf(refute_0_341,plain,
double_divide(multiply(X_15,identity),C) = double_divide(multiply(X_15,identity),C),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_15,identity),C))]]) ).
cnf(refute_0_342,plain,
( multiply(X_15,identity) != inverse(inverse(X_15))
| double_divide(multiply(X_15,identity),C) != double_divide(multiply(X_15,identity),C)
| double_divide(multiply(X_15,identity),C) = double_divide(inverse(inverse(X_15)),C) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_15,identity),C),double_divide(multiply(X_15,identity),C)) ),[1,0],$fot(inverse(inverse(X_15)))]]) ).
cnf(refute_0_343,plain,
( multiply(X_15,identity) != inverse(inverse(X_15))
| double_divide(multiply(X_15,identity),C) = double_divide(inverse(inverse(X_15)),C) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_15,identity),C),double_divide(multiply(X_15,identity),C)) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
double_divide(multiply(X_15,identity),C) = double_divide(inverse(inverse(X_15)),C),
inference(resolve,[$cnf( $equal(multiply(X_15,identity),inverse(inverse(X_15))) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))]]) ).
cnf(refute_0_346,plain,
( double_divide(multiply(X_15,identity),C) != double_divide(inverse(inverse(X_15)),C)
| double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) != double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))
| double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) ),[1,0],$fot(double_divide(inverse(inverse(X_15)),C))]]) ).
cnf(refute_0_347,plain,
( double_divide(multiply(X_15,identity),C) != double_divide(inverse(inverse(X_15)),C)
| double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_15,identity),C),double_divide(inverse(inverse(X_15)),C)) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
( double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) != double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15)))
| double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) != inverse(inverse(C))
| double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))),bind(Y,$fot(double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_350,plain,
( double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))) != inverse(inverse(C))
| double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))),double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15)))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_15)),C),inverse(inverse(X_15))),inverse(inverse(C))) )],[refute_0_339,refute_0_350]) ).
cnf(refute_0_352,plain,
double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))))]]) ).
cnf(refute_0_353,plain,
( double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) != inverse(inverse(C))
| double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))
| double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))) ),[1,1],$fot(inverse(inverse(C)))]]) ).
cnf(refute_0_354,plain,
( double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))) != inverse(inverse(C))
| double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))),inverse(inverse(C))) )],[refute_0_351,refute_0_354]) ).
cnf(refute_0_356,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))))]]) ).
cnf(refute_0_357,plain,
( double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))
| inverse(identity) != identity
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_358,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_358]) ).
cnf(refute_0_360,plain,
( double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))))),bind(Y,$fot(double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))))),bind(Z,$fot(double_divide(identity,inverse(inverse(C)))))]]) ).
cnf(refute_0_361,plain,
( double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15))))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) = double_divide(identity,inverse(inverse(C))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(identity,inverse(inverse(C)))) )],[refute_0_355,refute_0_361]) ).
cnf(refute_0_363,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)))]]) ).
cnf(refute_0_364,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity))) ),[1,0],$fot(double_divide(identity,inverse(inverse(C))))]]) ).
cnf(refute_0_365,plain,
( double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),double_divide(identity,inverse(inverse(C)))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)))),bind(Z,$fot(double_divide(double_divide(identity,inverse(inverse(C))),identity)))]]) ).
cnf(refute_0_368,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),identity)) )],[refute_0_290,refute_0_368]) ).
cnf(refute_0_370,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),identity) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,inverse(inverse(C))),identity))),bind(Z,$fot(inverse(inverse(inverse(inverse(C))))))]]) ).
cnf(refute_0_371,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),identity) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),identity)) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),identity),inverse(inverse(inverse(inverse(C))))) )],[refute_0_286,refute_0_371]) ).
cnf(refute_0_373,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != C
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != inverse(inverse(inverse(inverse(C))))
| inverse(inverse(inverse(inverse(C)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),C) ),[0],$fot(inverse(inverse(inverse(inverse(C)))))]]) ).
cnf(refute_0_374,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)) != C
| inverse(inverse(inverse(inverse(C)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),inverse(inverse(inverse(inverse(C))))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
inverse(inverse(inverse(inverse(C)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_15,identity),C),inverse(inverse(X_15)))),inverse(identity)),C) )],[refute_0_78,refute_0_374]) ).
cnf(refute_0_376,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_377,plain,
inverse(X_11) = double_divide(X_11,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_378,plain,
( inverse(X_11) != double_divide(X_11,identity)
| double_divide(X_11,identity) = inverse(X_11) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(double_divide(X_11,identity)))]]) ).
cnf(refute_0_379,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),double_divide(X_11,identity)) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(identity,double_divide(double_divide(inverse(X_11),X_12),inverse(X_11))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)),X_12) ),[0,0,1,0,0],$fot(inverse(X_11))]]) ).
cnf(refute_0_381,plain,
( double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(identity,double_divide(double_divide(inverse(X_11),X_12),inverse(X_11))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
double_divide(double_divide(identity,double_divide(double_divide(inverse(X_11),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)),X_12) )],[refute_0_376,refute_0_381]) ).
cnf(refute_0_383,plain,
double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)) = double_divide(identity,inverse(X_11)),
inference(subst,[],[refute_0_382:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_384,plain,
double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(inverse(identity),X_11),
inference(subst,[],[refute_0_59:[bind(X_10,$fot(inverse(identity)))]]) ).
cnf(refute_0_385,plain,
( double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(X_11))
| double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(inverse(identity),X_11)
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(identity,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(identity,inverse(X_11))) ),[0,0,1],$fot(multiply(inverse(identity),X_11))]]) ).
cnf(refute_0_386,plain,
( double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(X_11))
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(identity,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity)),multiply(inverse(identity),X_11)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(identity,inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(identity,inverse(X_11))) )],[refute_0_383,refute_0_386]) ).
cnf(refute_0_388,plain,
double_divide(double_divide(identity,multiply(inverse(identity),inverse(X_15))),inverse(identity)) = double_divide(identity,inverse(inverse(X_15))),
inference(subst,[],[refute_0_387:[bind(X_11,$fot(inverse(X_15)))]]) ).
cnf(refute_0_389,plain,
multiply(inverse(identity),inverse(X_15)) = inverse(double_divide(inverse(X_15),inverse(identity))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(identity))),bind(B,$fot(inverse(X_15)))]]) ).
cnf(refute_0_390,plain,
( multiply(inverse(identity),inverse(X_15)) != inverse(double_divide(inverse(X_15),inverse(identity)))
| double_divide(inverse(X_15),inverse(identity)) != multiply(X_15,identity)
| multiply(inverse(identity),inverse(X_15)) = inverse(multiply(X_15,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),inverse(X_15)),inverse(double_divide(inverse(X_15),inverse(identity)))) ),[1,0],$fot(multiply(X_15,identity))]]) ).
cnf(refute_0_391,plain,
( multiply(inverse(identity),inverse(X_15)) != inverse(double_divide(inverse(X_15),inverse(identity)))
| multiply(inverse(identity),inverse(X_15)) = inverse(multiply(X_15,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_15),inverse(identity)),multiply(X_15,identity)) )],[refute_0_75,refute_0_390]) ).
cnf(refute_0_392,plain,
multiply(inverse(identity),inverse(X_15)) = inverse(multiply(X_15,identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),inverse(X_15)),inverse(double_divide(inverse(X_15),inverse(identity)))) )],[refute_0_389,refute_0_391]) ).
cnf(refute_0_393,plain,
( multiply(inverse(identity),inverse(X_15)) != inverse(multiply(X_15,identity))
| double_divide(double_divide(identity,multiply(inverse(identity),inverse(X_15))),inverse(identity)) != double_divide(identity,inverse(inverse(X_15)))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),inverse(X_15))),inverse(identity)),double_divide(identity,inverse(inverse(X_15)))) ),[0,0,1],$fot(inverse(multiply(X_15,identity)))]]) ).
cnf(refute_0_394,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),inverse(X_15))),inverse(identity)) != double_divide(identity,inverse(inverse(X_15)))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_15))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),inverse(X_15)),inverse(multiply(X_15,identity))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_15))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),inverse(X_15))),inverse(identity)),double_divide(identity,inverse(inverse(X_15)))) )],[refute_0_388,refute_0_394]) ).
cnf(refute_0_396,plain,
double_divide(inverse(inverse(X_15)),identity) = inverse(inverse(inverse(X_15))),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(inverse(X_15))))]]) ).
cnf(refute_0_397,plain,
double_divide(inverse(inverse(X_15)),inverse(identity)) = double_divide(inverse(inverse(X_15)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(inverse(X_15)),inverse(identity)))]]) ).
cnf(refute_0_398,plain,
( double_divide(inverse(inverse(X_15)),inverse(identity)) != double_divide(inverse(inverse(X_15)),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(inverse(X_15)),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(X_15)),inverse(identity)),double_divide(inverse(inverse(X_15)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_399,plain,
( inverse(identity) != identity
| double_divide(inverse(inverse(X_15)),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_15)),inverse(identity)),double_divide(inverse(inverse(X_15)),inverse(identity))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
double_divide(inverse(inverse(X_15)),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_399]) ).
cnf(refute_0_401,plain,
inverse(inverse(inverse(inverse(X_11)))) = X_11,
inference(subst,[],[refute_0_375:[bind(C,$fot(X_11))]]) ).
cnf(refute_0_402,plain,
multiply(inverse(inverse(X_11)),identity) = inverse(inverse(inverse(inverse(X_11)))),
inference(subst,[],[refute_0_277:[bind(X_10,$fot(inverse(inverse(X_11))))]]) ).
cnf(refute_0_403,plain,
( multiply(inverse(inverse(X_11)),identity) != inverse(inverse(inverse(inverse(X_11))))
| inverse(inverse(inverse(inverse(X_11)))) != X_11
| multiply(inverse(inverse(X_11)),identity) = X_11 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(inverse(inverse(X_11)),identity))),bind(Y,$fot(inverse(inverse(inverse(inverse(X_11)))))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_404,plain,
( inverse(inverse(inverse(inverse(X_11)))) != X_11
| multiply(inverse(inverse(X_11)),identity) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),identity),inverse(inverse(inverse(inverse(X_11))))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(inverse(inverse(X_11)),identity) = X_11,
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(X_11)))),X_11) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
inverse(double_divide(identity,inverse(inverse(X_11)))) = multiply(inverse(inverse(X_11)),identity),
inference(subst,[],[refute_0_55:[bind(A,$fot(inverse(inverse(X_11)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_407,plain,
( multiply(inverse(inverse(X_11)),identity) != X_11
| inverse(double_divide(identity,inverse(inverse(X_11)))) != multiply(inverse(inverse(X_11)),identity)
| inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(inverse(double_divide(identity,inverse(inverse(X_11)))))),bind(Y,$fot(multiply(inverse(inverse(X_11)),identity))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_408,plain,
( multiply(inverse(inverse(X_11)),identity) != X_11
| inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_11)))),multiply(inverse(inverse(X_11)),identity)) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),identity),X_11) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = inverse(double_divide(identity,inverse(inverse(X_11)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,inverse(inverse(X_11)))))]]) ).
cnf(refute_0_411,plain,
( double_divide(double_divide(identity,inverse(inverse(X_11))),identity) != inverse(double_divide(identity,inverse(inverse(X_11))))
| inverse(double_divide(identity,inverse(inverse(X_11)))) != X_11
| double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = X_11 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),identity))),bind(Y,$fot(inverse(double_divide(identity,inverse(inverse(X_11)))))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_412,plain,
( inverse(double_divide(identity,inverse(inverse(X_11)))) != X_11
| double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),identity),inverse(double_divide(identity,inverse(inverse(X_11))))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = X_11,
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_11)))),X_11) )],[refute_0_409,refute_0_412]) ).
cnf(refute_0_414,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_415,plain,
( double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))
| inverse(identity) != identity
| double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_416,plain,
( inverse(identity) != identity
| double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_416]) ).
cnf(refute_0_418,plain,
multiply(identity,X_11) = inverse(inverse(X_11)),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_419,plain,
multiply(inverse(identity),X_11) = multiply(inverse(identity),X_11),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),X_11))]]) ).
cnf(refute_0_420,plain,
( multiply(inverse(identity),X_11) != multiply(inverse(identity),X_11)
| inverse(identity) != identity
| multiply(inverse(identity),X_11) = multiply(identity,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),X_11),multiply(inverse(identity),X_11)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_421,plain,
( inverse(identity) != identity
| multiply(inverse(identity),X_11) = multiply(identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),multiply(inverse(identity),X_11)) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
multiply(inverse(identity),X_11) = multiply(identity,X_11),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_233,refute_0_421]) ).
cnf(refute_0_423,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| multiply(inverse(identity),X_11) != multiply(identity,X_11)
| multiply(inverse(identity),X_11) = inverse(inverse(X_11)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(inverse(identity),X_11))),bind(Y,$fot(multiply(identity,X_11))),bind(Z,$fot(inverse(inverse(X_11))))]]) ).
cnf(refute_0_424,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| multiply(inverse(identity),X_11) = inverse(inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),multiply(identity,X_11)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
multiply(inverse(identity),X_11) = inverse(inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(identity,X_11),inverse(inverse(X_11))) )],[refute_0_418,refute_0_424]) ).
cnf(refute_0_426,plain,
double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,multiply(inverse(identity),X_11)),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(inverse(identity),X_11)))]]) ).
cnf(refute_0_427,plain,
( multiply(inverse(identity),X_11) != inverse(inverse(X_11))
| double_divide(identity,multiply(inverse(identity),X_11)) != double_divide(identity,multiply(inverse(identity),X_11))
| double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,inverse(inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(inverse(identity),X_11)),double_divide(identity,multiply(inverse(identity),X_11))) ),[1,1],$fot(inverse(inverse(X_11)))]]) ).
cnf(refute_0_428,plain,
( multiply(inverse(identity),X_11) != inverse(inverse(X_11))
| double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,inverse(inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(inverse(identity),X_11)),double_divide(identity,multiply(inverse(identity),X_11))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,inverse(inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),inverse(inverse(X_11))) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)))]]) ).
cnf(refute_0_431,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity))
| double_divide(identity,multiply(inverse(identity),X_11)) != double_divide(identity,inverse(inverse(X_11)))
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity))) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_11))))]]) ).
cnf(refute_0_432,plain,
( double_divide(identity,multiply(inverse(identity),X_11)) != double_divide(identity,inverse(inverse(X_11)))
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(inverse(identity),X_11)),double_divide(identity,inverse(inverse(X_11)))) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))
| double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),identity)
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)))),bind(Z,$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),identity)))]]) ).
cnf(refute_0_435,plain,
( double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),identity)
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),identity)) )],[refute_0_417,refute_0_435]) ).
cnf(refute_0_437,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),identity)
| double_divide(double_divide(identity,inverse(inverse(X_11))),identity) != X_11
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = X_11 ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),identity))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_438,plain,
( double_divide(double_divide(identity,inverse(inverse(X_11))),identity) != X_11
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),identity)) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),identity),X_11) )],[refute_0_413,refute_0_438]) ).
cnf(refute_0_440,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != X_11
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(identity,inverse(X_11))
| X_11 = double_divide(identity,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(identity,inverse(X_11))) ),[0],$fot(X_11)]]) ).
cnf(refute_0_441,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(identity,inverse(X_11))
| X_11 = double_divide(identity,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),X_11) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
X_11 = double_divide(identity,inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(identity,inverse(X_11))) )],[refute_0_387,refute_0_441]) ).
cnf(refute_0_443,plain,
( X_11 != double_divide(identity,inverse(X_11))
| double_divide(identity,inverse(X_11)) = X_11 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_11)),bind(Y,$fot(double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_444,plain,
double_divide(identity,inverse(X_11)) = X_11,
inference(resolve,[$cnf( $equal(X_11,double_divide(identity,inverse(X_11))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
double_divide(identity,inverse(multiply(X_15,identity))) = multiply(X_15,identity),
inference(subst,[],[refute_0_444:[bind(X_11,$fot(multiply(X_15,identity)))]]) ).
cnf(refute_0_446,plain,
( multiply(X_15,identity) != inverse(inverse(X_15))
| double_divide(identity,inverse(multiply(X_15,identity))) != multiply(X_15,identity)
| double_divide(identity,inverse(multiply(X_15,identity))) = inverse(inverse(X_15)) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(identity,inverse(multiply(X_15,identity))))),bind(Y,$fot(multiply(X_15,identity))),bind(Z,$fot(inverse(inverse(X_15))))]]) ).
cnf(refute_0_447,plain,
( multiply(X_15,identity) != inverse(inverse(X_15))
| double_divide(identity,inverse(multiply(X_15,identity))) = inverse(inverse(X_15)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(multiply(X_15,identity))),multiply(X_15,identity)) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
double_divide(identity,inverse(multiply(X_15,identity))) = inverse(inverse(X_15)),
inference(resolve,[$cnf( $equal(multiply(X_15,identity),inverse(inverse(X_15))) )],[refute_0_340,refute_0_447]) ).
cnf(refute_0_449,plain,
double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)))]]) ).
cnf(refute_0_450,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity))
| double_divide(identity,inverse(multiply(X_15,identity))) != inverse(inverse(X_15))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity))) ),[1,0],$fot(inverse(inverse(X_15)))]]) ).
cnf(refute_0_451,plain,
( double_divide(identity,inverse(multiply(X_15,identity))) != inverse(inverse(X_15))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(multiply(X_15,identity))),inverse(inverse(X_15))) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(inverse(inverse(X_15)),inverse(identity))
| double_divide(inverse(inverse(X_15)),inverse(identity)) != double_divide(inverse(inverse(X_15)),identity)
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)))),bind(Y,$fot(double_divide(inverse(inverse(X_15)),inverse(identity)))),bind(Z,$fot(double_divide(inverse(inverse(X_15)),identity)))]]) ).
cnf(refute_0_454,plain,
( double_divide(inverse(inverse(X_15)),inverse(identity)) != double_divide(inverse(inverse(X_15)),identity)
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(inverse(inverse(X_15)),inverse(identity))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = double_divide(inverse(inverse(X_15)),identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_15)),inverse(identity)),double_divide(inverse(inverse(X_15)),identity)) )],[refute_0_400,refute_0_454]) ).
cnf(refute_0_456,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(inverse(inverse(X_15)),identity)
| double_divide(inverse(inverse(X_15)),identity) != inverse(inverse(inverse(X_15)))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = inverse(inverse(inverse(X_15))) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)))),bind(Y,$fot(double_divide(inverse(inverse(X_15)),identity))),bind(Z,$fot(inverse(inverse(inverse(X_15)))))]]) ).
cnf(refute_0_457,plain,
( double_divide(inverse(inverse(X_15)),identity) != inverse(inverse(inverse(X_15)))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = inverse(inverse(inverse(X_15))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(inverse(inverse(X_15)),identity)) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) = inverse(inverse(inverse(X_15))),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_15)),identity),inverse(inverse(inverse(X_15)))) )],[refute_0_396,refute_0_457]) ).
cnf(refute_0_459,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_15)))
| double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != inverse(inverse(inverse(X_15)))
| inverse(inverse(inverse(X_15))) = double_divide(identity,inverse(inverse(X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_15)))) ),[0],$fot(inverse(inverse(inverse(X_15))))]]) ).
cnf(refute_0_460,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_15)))
| inverse(inverse(inverse(X_15))) = double_divide(identity,inverse(inverse(X_15))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),inverse(inverse(inverse(X_15)))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
double_divide(identity,inverse(inverse(X_15))) = inverse(X_15),
inference(subst,[],[refute_0_444:[bind(X_11,$fot(inverse(X_15)))]]) ).
cnf(refute_0_462,plain,
( double_divide(identity,inverse(inverse(X_15))) != inverse(X_15)
| inverse(inverse(inverse(X_15))) != double_divide(identity,inverse(inverse(X_15)))
| inverse(inverse(inverse(X_15))) = inverse(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(X_15))),double_divide(identity,inverse(inverse(X_15)))) ),[1],$fot(inverse(X_15))]]) ).
cnf(refute_0_463,plain,
( inverse(inverse(inverse(X_15))) != double_divide(identity,inverse(inverse(X_15)))
| inverse(inverse(inverse(X_15))) = inverse(X_15) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_15))),inverse(X_15)) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
( double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_15)))
| inverse(inverse(inverse(X_15))) = inverse(X_15) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(X_15))),double_divide(identity,inverse(inverse(X_15)))) )],[refute_0_460,refute_0_463]) ).
cnf(refute_0_465,plain,
inverse(inverse(inverse(X_15))) = inverse(X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(multiply(X_15,identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_15)))) )],[refute_0_395,refute_0_464]) ).
cnf(refute_0_466,plain,
inverse(inverse(inverse(inverse(C)))) = inverse(inverse(C)),
inference(subst,[],[refute_0_465:[bind(X_15,$fot(inverse(C)))]]) ).
cnf(refute_0_467,plain,
( inverse(inverse(inverse(inverse(C)))) != C
| inverse(inverse(inverse(inverse(C)))) != inverse(inverse(C))
| inverse(inverse(C)) = C ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(inverse(C)))),C) ),[0],$fot(inverse(inverse(C)))]]) ).
cnf(refute_0_468,plain,
( inverse(inverse(inverse(inverse(C)))) != C
| inverse(inverse(C)) = C ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(C)))),inverse(inverse(C))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
inverse(inverse(C)) = C,
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(C)))),C) )],[refute_0_375,refute_0_468]) ).
cnf(refute_0_470,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_469:[bind(C,$fot(a2))]]) ).
cnf(refute_0_471,plain,
( a2 != a2
| inverse(inverse(a2)) != a2
| inverse(inverse(a2)) = a2 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a2)),a2) ),[0,0,0],$fot(a2)]]) ).
cnf(refute_0_472,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_472,refute_0_19]) ).
cnf(refute_0_474,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_475,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_474,refute_0_473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 23:56:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.50
%------------------------------------------------------------------------------