TSTP Solution File: GRP580-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:42:36 EDT 2022
% Result : Unsatisfiable 0.13s 0.33s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 107
% Syntax : Number of clauses : 416 ( 207 unt; 0 nHn; 222 RR)
% Number of literals : 722 ( 721 equ; 308 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 544 ( 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_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
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( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_6,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,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
introduced(tautology,[equality,[$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_8,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( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_11,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,[$fot(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))]]) ).
cnf(refute_0_12,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))
| double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),inverse(B)) ),
introduced(tautology,[equality,[$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_13,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( $equal(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(B,A),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))))]]) ).
cnf(refute_0_16,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_17,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( $equal(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity)),double_divide(double_divide(double_divide(B,A),C),inverse(B))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),
introduced(tautology,[refl,[$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_20,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_21,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( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$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_26,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( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))) )],[refute_0_9,refute_0_26]) ).
cnf(refute_0_28,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) = C ),
introduced(tautology,[equality,[$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_29,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( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),inverse(B))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)),C) )],[single_axiom,refute_0_29]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)),
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(double_divide(X_11,X_10))))]]) ).
cnf(refute_0_32,plain,
identity = double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_11,X_10)))]]) ).
cnf(refute_0_33,plain,
( identity != double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))
| double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))))]]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))) != identity
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)) ),
introduced(tautology,[equality,[$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_36,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( $equal(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),identity) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_11,X_10)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),inverse(double_divide(X_11,X_10))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_11,X_10))) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_39,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_40,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_43,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
inverse(double_divide(X_11,X_10)) = multiply(X_10,X_11),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_45,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_11,X_10))
| inverse(double_divide(X_11,X_10)) != multiply(X_10,X_11)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_10,X_11) ),
introduced(tautology,[equality,[$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_46,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( $equal(inverse(double_divide(X_11,X_10)),multiply(X_10,X_11)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_10,X_11),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),inverse(double_divide(X_11,X_10))) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))) = multiply(double_divide(identity,inverse(X_11)),X_10),
inference(subst,[],[refute_0_43:[bind(A,$fot(double_divide(identity,inverse(X_11)))),bind(B,$fot(X_10))]]) ).
cnf(refute_0_49,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) = inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(X_10,double_divide(identity,inverse(X_11)))))]]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) != inverse(double_divide(X_10,double_divide(identity,inverse(X_11))))
| inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))) != multiply(double_divide(identity,inverse(X_11)),X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) = multiply(double_divide(identity,inverse(X_11)),X_10) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity))),bind(Y,$fot(inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))))),bind(Z,$fot(multiply(double_divide(identity,inverse(X_11)),X_10)))]]) ).
cnf(refute_0_51,plain,
( inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))) != multiply(double_divide(identity,inverse(X_11)),X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) = multiply(double_divide(identity,inverse(X_11)),X_10) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity),inverse(double_divide(X_10,double_divide(identity,inverse(X_11))))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) = multiply(double_divide(identity,inverse(X_11)),X_10),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,double_divide(identity,inverse(X_11)))),multiply(double_divide(identity,inverse(X_11)),X_10)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_30:[bind(A,$fot(inverse(X_11))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_54,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_55,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_56,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(inverse(X_11),double_divide(double_divide(identity,X_12),inverse(X_11))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$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_58,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( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(double_divide(inverse(X_11),double_divide(double_divide(identity,X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_11),double_divide(double_divide(double_divide(X_11,inverse(X_11)),X_12),inverse(X_11))),inverse(identity)),X_12) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity))),inverse(identity)) = double_divide(multiply(identity,X_11),inverse(X_11)),
inference(subst,[],[refute_0_59:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(multiply(identity,X_11),inverse(X_11))))]]) ).
cnf(refute_0_61,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),identity),inverse(X_11))),inverse(identity)) = identity,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(identity))]]) ).
cnf(refute_0_62,plain,
inverse(double_divide(X_11,X_10)) = double_divide(double_divide(X_11,X_10),identity),
inference(subst,[],[inverse:[bind(A,$fot(double_divide(X_11,X_10)))]]) ).
cnf(refute_0_63,plain,
( inverse(double_divide(X_11,X_10)) != double_divide(double_divide(X_11,X_10),identity)
| double_divide(double_divide(X_11,X_10),identity) = inverse(double_divide(X_11,X_10)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(double_divide(X_11,X_10)))),bind(Y,$fot(double_divide(double_divide(X_11,X_10),identity)))]]) ).
cnf(refute_0_64,plain,
double_divide(double_divide(X_11,X_10),identity) = inverse(double_divide(X_11,X_10)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_11,X_10)),double_divide(double_divide(X_11,X_10),identity)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),identity),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_11,X_10),identity) != inverse(double_divide(X_11,X_10))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),identity),inverse(X_11))),inverse(identity)),identity) ),[0,0,1,0],$fot(inverse(double_divide(X_11,X_10)))]]) ).
cnf(refute_0_66,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),identity),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,X_10),identity),inverse(double_divide(X_11,X_10))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_11,X_10),identity),inverse(X_11))),inverse(identity)),identity) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) = double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)))]]) ).
cnf(refute_0_69,plain,
( double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) != double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))
| inverse(double_divide(X_11,X_10)) != multiply(X_10,X_11)
| double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) = double_divide(multiply(X_10,X_11),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)),double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) ),[1,0],$fot(multiply(X_10,X_11))]]) ).
cnf(refute_0_70,plain,
( inverse(double_divide(X_11,X_10)) != multiply(X_10,X_11)
| double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) = double_divide(multiply(X_10,X_11),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)),double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) = double_divide(multiply(X_10,X_11),inverse(X_11)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_11,X_10)),multiply(X_10,X_11)) )],[refute_0_44,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) = double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))))]]) ).
cnf(refute_0_73,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) != double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)))
| double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) != double_divide(multiply(X_10,X_11),inverse(X_11))
| double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)))) ),[1,1],$fot(double_divide(multiply(X_10,X_11),inverse(X_11)))]]) ).
cnf(refute_0_74,plain,
( double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)) != double_divide(multiply(X_10,X_11),inverse(X_11))
| double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11)),double_divide(multiply(X_10,X_11),inverse(X_11))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_77,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) != double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11)))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity))) ),[1,0],$fot(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))))]]) ).
cnf(refute_0_78,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))) != double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11)))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11)))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),identity) ),[0],$fot(double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_81,plain,
( double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(double_divide(X_10,double_divide(multiply(X_10,X_11),inverse(X_11))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_11,X_10)),inverse(X_11))),inverse(identity)),identity) )],[refute_0_67,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity)) = identity,
inference(subst,[],[refute_0_82:[bind(X_10,$fot(identity))]]) ).
cnf(refute_0_84,plain,
( double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(multiply(identity,X_11),inverse(X_11))
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(multiply(identity,X_11),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(multiply(identity,X_11),inverse(X_11))) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_85,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(multiply(identity,X_11),inverse(X_11))
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(multiply(identity,X_11),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity)),identity) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(multiply(identity,X_11),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(multiply(identity,X_11),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(multiply(identity,X_11),inverse(X_11))) )],[refute_0_60,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_41:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_88,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_89,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_90,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_92,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(subst,[],[refute_0_93:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_95,plain,
double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(X_15,identity),
inference(subst,[],[refute_0_47:[bind(X_10,$fot(X_15)),bind(X_11,$fot(identity))]]) ).
cnf(refute_0_96,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_97,plain,
( identity != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_98,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(X_15,identity)
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(X_15,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)),multiply(X_15,identity)) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_100,plain,
( double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(X_15,identity)
| double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(X_15,identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(X_15,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)),multiply(X_15,identity)) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(X_15,identity) = inverse(X_15),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_103,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(double_divide(X_15,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_15,identity),inverse(identity)))]]) ).
cnf(refute_0_104,plain,
( double_divide(X_15,identity) != inverse(X_15)
| double_divide(double_divide(X_15,identity),inverse(identity)) != double_divide(double_divide(X_15,identity),inverse(identity))
| double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(inverse(X_15),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),double_divide(double_divide(X_15,identity),inverse(identity))) ),[1,0],$fot(inverse(X_15))]]) ).
cnf(refute_0_105,plain,
( double_divide(X_15,identity) != inverse(X_15)
| double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(inverse(X_15),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),double_divide(double_divide(X_15,identity),inverse(identity))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(inverse(X_15),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_15,identity),inverse(X_15)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( double_divide(double_divide(X_15,identity),inverse(identity)) != multiply(X_15,identity)
| double_divide(double_divide(X_15,identity),inverse(identity)) != double_divide(inverse(X_15),inverse(identity))
| double_divide(inverse(X_15),inverse(identity)) = multiply(X_15,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),multiply(X_15,identity)) ),[0],$fot(double_divide(inverse(X_15),inverse(identity)))]]) ).
cnf(refute_0_108,plain,
( double_divide(double_divide(X_15,identity),inverse(identity)) != multiply(X_15,identity)
| double_divide(inverse(X_15),inverse(identity)) = multiply(X_15,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),double_divide(inverse(X_15),inverse(identity))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
double_divide(inverse(X_15),inverse(identity)) = multiply(X_15,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),multiply(X_15,identity)) )],[refute_0_101,refute_0_108]) ).
cnf(refute_0_110,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = multiply(inverse(identity),identity),
inference(subst,[],[refute_0_109:[bind(X_15,$fot(inverse(identity)))]]) ).
cnf(refute_0_111,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| double_divide(inverse(inverse(identity)),inverse(identity)) != multiply(inverse(identity),identity)
| double_divide(inverse(inverse(identity)),inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(inverse(identity)),inverse(identity)))),bind(Y,$fot(multiply(inverse(identity),identity))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_112,plain,
( multiply(inverse(identity),identity) != inverse(identity)
| double_divide(inverse(inverse(identity)),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),inverse(identity)),multiply(inverse(identity),identity)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),identity),inverse(identity)) )],[refute_0_94,refute_0_112]) ).
cnf(refute_0_114,plain,
double_divide(inverse(identity),identity) = inverse(inverse(identity)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_115,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(double_divide(inverse(identity),identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(identity),identity),inverse(identity)))]]) ).
cnf(refute_0_116,plain,
( double_divide(double_divide(inverse(identity),identity),inverse(identity)) != double_divide(double_divide(inverse(identity),identity),inverse(identity))
| double_divide(inverse(identity),identity) != inverse(inverse(identity))
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(double_divide(inverse(identity),identity),inverse(identity))) ),[1,0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_117,plain,
( double_divide(inverse(identity),identity) != inverse(inverse(identity))
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(double_divide(inverse(identity),identity),inverse(identity))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),identity),inverse(inverse(identity))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( double_divide(double_divide(inverse(identity),identity),inverse(identity)) != double_divide(inverse(inverse(identity)),inverse(identity))
| double_divide(inverse(inverse(identity)),inverse(identity)) != inverse(identity)
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(identity),identity),inverse(identity)))),bind(Y,$fot(double_divide(inverse(inverse(identity)),inverse(identity)))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_120,plain,
( double_divide(inverse(inverse(identity)),inverse(identity)) != inverse(identity)
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(inverse(inverse(identity)),inverse(identity))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),inverse(identity)),inverse(identity)) )],[refute_0_113,refute_0_120]) ).
cnf(refute_0_122,plain,
( double_divide(double_divide(inverse(identity),identity),inverse(identity)) != double_divide(multiply(identity,X_11),inverse(X_11))
| double_divide(double_divide(inverse(identity),identity),inverse(identity)) != inverse(identity)
| inverse(identity) = double_divide(multiply(identity,X_11),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(multiply(identity,X_11),inverse(X_11))) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_123,plain,
( double_divide(double_divide(inverse(identity),identity),inverse(identity)) != double_divide(multiply(identity,X_11),inverse(X_11))
| inverse(identity) = double_divide(multiply(identity,X_11),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),inverse(identity)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_41:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_125,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_126,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_127,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_129,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_124,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(identity,X_11) = inverse(inverse(X_11)),
inference(subst,[],[refute_0_130:[bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_132,plain,
double_divide(multiply(identity,X_11),inverse(X_11)) = double_divide(multiply(identity,X_11),inverse(X_11)),
introduced(tautology,[refl,[$fot(double_divide(multiply(identity,X_11),inverse(X_11)))]]) ).
cnf(refute_0_133,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(multiply(identity,X_11),inverse(X_11)) != double_divide(multiply(identity,X_11),inverse(X_11))
| double_divide(multiply(identity,X_11),inverse(X_11)) = double_divide(inverse(inverse(X_11)),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(identity,X_11),inverse(X_11)),double_divide(multiply(identity,X_11),inverse(X_11))) ),[1,0],$fot(inverse(inverse(X_11)))]]) ).
cnf(refute_0_134,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(multiply(identity,X_11),inverse(X_11)) = double_divide(inverse(inverse(X_11)),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_11),inverse(X_11)),double_divide(multiply(identity,X_11),inverse(X_11))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
double_divide(multiply(identity,X_11),inverse(X_11)) = double_divide(inverse(inverse(X_11)),inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(identity,X_11),inverse(inverse(X_11))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( double_divide(multiply(identity,X_11),inverse(X_11)) != double_divide(inverse(inverse(X_11)),inverse(X_11))
| inverse(identity) != double_divide(multiply(identity,X_11),inverse(X_11))
| inverse(identity) = double_divide(inverse(inverse(X_11)),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),double_divide(multiply(identity,X_11),inverse(X_11))) ),[1],$fot(double_divide(inverse(inverse(X_11)),inverse(X_11)))]]) ).
cnf(refute_0_137,plain,
( inverse(identity) != double_divide(multiply(identity,X_11),inverse(X_11))
| inverse(identity) = double_divide(inverse(inverse(X_11)),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_11),inverse(X_11)),double_divide(inverse(inverse(X_11)),inverse(X_11))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
( double_divide(double_divide(inverse(identity),identity),inverse(identity)) != double_divide(multiply(identity,X_11),inverse(X_11))
| inverse(identity) = double_divide(inverse(inverse(X_11)),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(multiply(identity,X_11),inverse(X_11))) )],[refute_0_123,refute_0_137]) ).
cnf(refute_0_139,plain,
inverse(identity) = double_divide(inverse(inverse(X_11)),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(multiply(identity,X_11),inverse(X_11))) )],[refute_0_86,refute_0_138]) ).
cnf(refute_0_140,plain,
inverse(identity) = double_divide(inverse(inverse(inverse(identity))),inverse(inverse(identity))),
inference(subst,[],[refute_0_139:[bind(X_11,$fot(inverse(identity)))]]) ).
cnf(refute_0_141,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_30:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_142,plain,
inverse(X_11) = double_divide(X_11,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_143,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_144,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(resolve,[$cnf( $equal(inverse(X_11),double_divide(X_11,identity)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(identity,double_divide(double_divide(inverse(X_11),X_12),inverse(X_11))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$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_146,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( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
double_divide(double_divide(identity,double_divide(double_divide(inverse(X_11),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(X_11,identity),X_12),inverse(X_11))),inverse(identity)),X_12) )],[refute_0_141,refute_0_146]) ).
cnf(refute_0_148,plain,
double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity))),inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)),
inference(subst,[],[refute_0_147:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(multiply(inverse(identity),X_11),inverse(X_11))))]]) ).
cnf(refute_0_149,plain,
double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity)) = identity,
inference(subst,[],[refute_0_82:[bind(X_10,$fot(inverse(identity)))]]) ).
cnf(refute_0_150,plain,
( double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(multiply(inverse(identity),X_11),inverse(X_11))
| double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(multiply(inverse(identity),X_11),inverse(X_11))) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_151,plain,
( double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(multiply(inverse(identity),X_11),inverse(X_11))
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity)),identity) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),X_11),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(multiply(inverse(identity),X_11),inverse(X_11))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(identity,identity) = inverse(inverse(identity)),
inference(subst,[],[refute_0_130:[bind(X_3,$fot(identity))]]) ).
cnf(refute_0_154,plain,
double_divide(inverse(identity),inverse(identity)) = multiply(identity,identity),
inference(subst,[],[refute_0_109:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_155,plain,
( multiply(identity,identity) != inverse(inverse(identity))
| double_divide(inverse(identity),inverse(identity)) != multiply(identity,identity)
| double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(identity),inverse(identity)))),bind(Y,$fot(multiply(identity,identity))),bind(Z,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_156,plain,
( multiply(identity,identity) != inverse(inverse(identity))
| double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),multiply(identity,identity)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(double_divide(identity,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),inverse(identity)))]]) ).
cnf(refute_0_159,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(double_divide(identity,identity),inverse(identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(double_divide(identity,identity),inverse(identity))) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_160,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(double_divide(identity,identity),inverse(identity))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_160]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(inverse(identity),inverse(identity))
| double_divide(inverse(identity),inverse(identity)) != inverse(inverse(identity))
| double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(identity,identity),inverse(identity)))),bind(Y,$fot(double_divide(inverse(identity),inverse(identity)))),bind(Z,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_163,plain,
( double_divide(inverse(identity),inverse(identity)) != inverse(inverse(identity))
| double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(inverse(identity),inverse(identity))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_157,refute_0_163]) ).
cnf(refute_0_165,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(multiply(inverse(identity),X_11),inverse(X_11))
| double_divide(double_divide(identity,identity),inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(multiply(inverse(identity),X_11),inverse(X_11))) ),[0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_166,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(multiply(inverse(identity),X_11),inverse(X_11))
| inverse(inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
inverse(inverse(identity)) = double_divide(multiply(inverse(identity),X_11),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(multiply(inverse(identity),X_11),inverse(X_11))) )],[refute_0_152,refute_0_166]) ).
cnf(refute_0_168,plain,
inverse(inverse(identity)) = double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity)))),
inference(subst,[],[refute_0_167:[bind(X_11,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_169,plain,
multiply(inverse(X_25),inverse(inverse(X_25))) = inverse(double_divide(inverse(inverse(X_25)),inverse(X_25))),
inference(subst,[],[refute_0_41:[bind(A,$fot(inverse(X_25))),bind(B,$fot(inverse(inverse(X_25))))]]) ).
cnf(refute_0_170,plain,
inverse(identity) = double_divide(inverse(inverse(X_25)),inverse(X_25)),
inference(subst,[],[refute_0_139:[bind(X_11,$fot(X_25))]]) ).
cnf(refute_0_171,plain,
( inverse(identity) != double_divide(inverse(inverse(X_25)),inverse(X_25))
| double_divide(inverse(inverse(X_25)),inverse(X_25)) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(identity))),bind(Y,$fot(double_divide(inverse(inverse(X_25)),inverse(X_25))))]]) ).
cnf(refute_0_172,plain,
double_divide(inverse(inverse(X_25)),inverse(X_25)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(inverse(inverse(X_25)),inverse(X_25))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( multiply(inverse(X_25),inverse(inverse(X_25))) != inverse(double_divide(inverse(inverse(X_25)),inverse(X_25)))
| double_divide(inverse(inverse(X_25)),inverse(X_25)) != inverse(identity)
| multiply(inverse(X_25),inverse(inverse(X_25))) = inverse(inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_25),inverse(inverse(X_25))),inverse(double_divide(inverse(inverse(X_25)),inverse(X_25)))) ),[1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_174,plain,
( multiply(inverse(X_25),inverse(inverse(X_25))) != inverse(double_divide(inverse(inverse(X_25)),inverse(X_25)))
| multiply(inverse(X_25),inverse(inverse(X_25))) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(X_25)),inverse(X_25)),inverse(identity)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(inverse(X_25),inverse(inverse(X_25))) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_25),inverse(inverse(X_25))),inverse(double_divide(inverse(inverse(X_25)),inverse(X_25)))) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(inverse(identity),inverse(inverse(identity))) = inverse(inverse(identity)),
inference(subst,[],[refute_0_175:[bind(X_25,$fot(identity))]]) ).
cnf(refute_0_177,plain,
( multiply(inverse(identity),inverse(inverse(identity))) != inverse(inverse(identity))
| inverse(inverse(identity)) != double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))
| inverse(inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))) ),[1,0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_178,plain,
( inverse(inverse(identity)) != double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))
| inverse(inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(identity))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
inverse(inverse(identity)) = double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))) )],[refute_0_168,refute_0_178]) ).
cnf(refute_0_180,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_181,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_180]) ).
cnf(refute_0_182,plain,
double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))) = identity,
inference(subst,[],[refute_0_181:[bind(A,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_183,plain,
( double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))) != identity
| inverse(inverse(identity)) != double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))
| inverse(inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))) ),[1],$fot(identity)]]) ).
cnf(refute_0_184,plain,
( inverse(inverse(identity)) != double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))
| inverse(inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))),identity) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
inverse(inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))) )],[refute_0_179,refute_0_184]) ).
cnf(refute_0_186,plain,
( inverse(identity) != double_divide(inverse(inverse(inverse(identity))),inverse(inverse(identity)))
| inverse(inverse(identity)) != identity
| inverse(identity) = double_divide(inverse(identity),inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),double_divide(inverse(inverse(inverse(identity))),inverse(inverse(identity)))) ),[1,0,0],$fot(identity)]]) ).
cnf(refute_0_187,plain,
( inverse(identity) != double_divide(inverse(inverse(inverse(identity))),inverse(inverse(identity)))
| inverse(identity) = double_divide(inverse(identity),inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
inverse(identity) = double_divide(inverse(identity),inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(inverse(inverse(inverse(identity))),inverse(inverse(identity)))) )],[refute_0_140,refute_0_187]) ).
cnf(refute_0_189,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = identity,
inference(subst,[],[refute_0_181:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_190,plain,
( double_divide(inverse(identity),inverse(inverse(identity))) != identity
| inverse(identity) != double_divide(inverse(identity),inverse(inverse(identity)))
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),double_divide(inverse(identity),inverse(inverse(identity)))) ),[1],$fot(identity)]]) ).
cnf(refute_0_191,plain,
( inverse(identity) != double_divide(inverse(identity),inverse(inverse(identity)))
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),identity) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(inverse(identity),inverse(inverse(identity)))) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_194,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity))
| inverse(identity) != identity
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_195,plain,
( inverse(identity) != identity
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) != multiply(double_divide(identity,inverse(X_11)),X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(double_divide(identity,inverse(X_11)),X_10) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity))),bind(Z,$fot(multiply(double_divide(identity,inverse(X_11)),X_10)))]]) ).
cnf(refute_0_198,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity) != multiply(double_divide(identity,inverse(X_11)),X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(double_divide(identity,inverse(X_11)),X_10) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(double_divide(identity,inverse(X_11)),X_10),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),identity),multiply(double_divide(identity,inverse(X_11)),X_10)) )],[refute_0_52,refute_0_198]) ).
cnf(refute_0_200,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(X_10,X_11)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(double_divide(identity,inverse(X_11)),X_10)
| multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_10,X_11)) ),[0],$fot(multiply(double_divide(identity,inverse(X_11)),X_10))]]) ).
cnf(refute_0_201,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(X_10,X_11)
| multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_10,X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(double_divide(identity,inverse(X_11)),X_10)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_10,X_11),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_10,X_11)) )],[refute_0_47,refute_0_201]) ).
cnf(refute_0_203,plain,
double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)) = double_divide(identity,inverse(X_11)),
inference(subst,[],[refute_0_147:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_204,plain,
double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(inverse(identity),X_11),
inference(subst,[],[refute_0_47:[bind(X_10,$fot(inverse(identity)))]]) ).
cnf(refute_0_205,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_206,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( $equal(double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity)),multiply(inverse(identity),X_11)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(identity,inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(inverse(identity),double_divide(identity,inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(identity,inverse(X_11))) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(X_17)))),inverse(identity)) = C,
inference(subst,[],[refute_0_30:[bind(A,$fot(inverse(identity))),bind(B,$fot(inverse(X_17)))]]) ).
cnf(refute_0_209,plain,
double_divide(inverse(X_17),inverse(identity)) = multiply(X_17,identity),
inference(subst,[],[refute_0_109:[bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_210,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(X_17)))),inverse(identity)) != C
| double_divide(inverse(X_17),inverse(identity)) != multiply(X_17,identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(X_17)))),inverse(identity)),C) ),[0,0,1,0,0],$fot(multiply(X_17,identity))]]) ).
cnf(refute_0_211,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(X_17)))),inverse(identity)) != C
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),inverse(identity)),multiply(X_17,identity)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(X_17)))),inverse(identity)),C) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(identity)))),inverse(identity)) = multiply(X_10,inverse(identity)),
inference(subst,[],[refute_0_47:[bind(X_11,$fot(inverse(identity)))]]) ).
cnf(refute_0_214,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(identity)))),inverse(identity)) != multiply(X_10,inverse(identity))
| inverse(inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),multiply(X_10,inverse(identity))) ),[0,0,1,1],$fot(identity)]]) ).
cnf(refute_0_215,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(identity)))),inverse(identity)) != multiply(X_10,inverse(identity))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(identity)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_185,refute_0_214]) ).
cnf(refute_0_216,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = multiply(X_10,inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),multiply(X_10,inverse(identity))) )],[refute_0_213,refute_0_215]) ).
cnf(refute_0_217,plain,
double_divide(inverse(X_10),identity) = inverse(inverse(X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_10)))]]) ).
cnf(refute_0_218,plain,
double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_10),inverse(identity)))]]) ).
cnf(refute_0_219,plain,
( double_divide(inverse(X_10),inverse(identity)) != double_divide(inverse(X_10),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_220,plain,
( inverse(identity) != identity
| double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
double_divide(inverse(X_10),inverse(identity)) = double_divide(inverse(X_10),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_220]) ).
cnf(refute_0_222,plain,
double_divide(X_10,identity) = inverse(X_10),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_223,plain,
( double_divide(identity,identity) != inverse(identity)
| inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(identity,identity))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_224,plain,
( inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_223]) ).
cnf(refute_0_225,plain,
double_divide(identity,identity) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_224]) ).
cnf(refute_0_226,plain,
double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(identity,identity)))]]) ).
cnf(refute_0_227,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_228,plain,
( double_divide(identity,identity) != identity
| double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),double_divide(X_10,double_divide(identity,identity))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
double_divide(X_10,double_divide(identity,identity)) = double_divide(X_10,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),identity) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
( double_divide(X_10,double_divide(identity,identity)) != double_divide(X_10,identity)
| double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_10,double_divide(identity,identity)) = inverse(X_10) ),
inference(subst,[],[refute_0_24:[bind(X,$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_231,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_10,double_divide(identity,identity)) = inverse(X_10) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),double_divide(X_10,identity)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
double_divide(X_10,double_divide(identity,identity)) = inverse(X_10),
inference(resolve,[$cnf( $equal(double_divide(X_10,identity),inverse(X_10)) )],[refute_0_222,refute_0_231]) ).
cnf(refute_0_233,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)))]]) ).
cnf(refute_0_234,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_235,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( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,identity)),inverse(X_10)) )],[refute_0_232,refute_0_235]) ).
cnf(refute_0_237,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != double_divide(inverse(X_10),inverse(identity))
| double_divide(inverse(X_10),inverse(identity)) != double_divide(inverse(X_10),identity)
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$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_238,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( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(inverse(X_10),inverse(identity))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = double_divide(inverse(X_10),identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),inverse(identity)),double_divide(inverse(X_10),identity)) )],[refute_0_221,refute_0_238]) ).
cnf(refute_0_240,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != double_divide(inverse(X_10),identity)
| double_divide(inverse(X_10),identity) != inverse(inverse(X_10))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X_10)) ),
inference(subst,[],[refute_0_24:[bind(X,$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_241,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( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),double_divide(inverse(X_10),identity)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X_10)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_10),identity),inverse(inverse(X_10))) )],[refute_0_217,refute_0_241]) ).
cnf(refute_0_243,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(identity))
| double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != inverse(inverse(X_10))
| inverse(inverse(X_10)) = multiply(X_10,inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),multiply(X_10,inverse(identity))) ),[0],$fot(inverse(inverse(X_10)))]]) ).
cnf(refute_0_244,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(identity))
| inverse(inverse(X_10)) = multiply(X_10,inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),inverse(inverse(X_10))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
multiply(X_10,inverse(identity)) = multiply(X_10,inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(X_10,inverse(identity)))]]) ).
cnf(refute_0_246,plain,
( multiply(X_10,inverse(identity)) != multiply(X_10,inverse(identity))
| inverse(identity) != identity
| multiply(X_10,inverse(identity)) = multiply(X_10,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_10,inverse(identity)),multiply(X_10,inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_247,plain,
( inverse(identity) != identity
| multiply(X_10,inverse(identity)) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_10,inverse(identity)),multiply(X_10,inverse(identity))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(X_10,inverse(identity)) = multiply(X_10,identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_247]) ).
cnf(refute_0_249,plain,
( multiply(X_10,inverse(identity)) != multiply(X_10,identity)
| inverse(inverse(X_10)) != multiply(X_10,inverse(identity))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,inverse(identity))) ),[1],$fot(multiply(X_10,identity))]]) ).
cnf(refute_0_250,plain,
( inverse(inverse(X_10)) != multiply(X_10,inverse(identity))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(multiply(X_10,inverse(identity)),multiply(X_10,identity)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)) != multiply(X_10,inverse(identity))
| inverse(inverse(X_10)) = multiply(X_10,identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,inverse(identity))) )],[refute_0_244,refute_0_250]) ).
cnf(refute_0_252,plain,
inverse(inverse(X_10)) = multiply(X_10,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,identity)),inverse(identity)),multiply(X_10,inverse(identity))) )],[refute_0_216,refute_0_251]) ).
cnf(refute_0_253,plain,
( inverse(inverse(X_10)) != multiply(X_10,identity)
| multiply(X_10,identity) = inverse(inverse(X_10)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(inverse(X_10)))),bind(Y,$fot(multiply(X_10,identity)))]]) ).
cnf(refute_0_254,plain,
multiply(X_10,identity) = inverse(inverse(X_10)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),multiply(X_10,identity)) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
multiply(inverse(inverse(C)),identity) = inverse(inverse(inverse(inverse(C)))),
inference(subst,[],[refute_0_254:[bind(X_10,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_256,plain,
inverse(double_divide(identity,inverse(inverse(C)))) = multiply(inverse(inverse(C)),identity),
inference(subst,[],[refute_0_43:[bind(A,$fot(inverse(inverse(C)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_257,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_24:[bind(X,$fot(inverse(double_divide(identity,inverse(inverse(C)))))),bind(Y,$fot(multiply(inverse(inverse(C)),identity))),bind(Z,$fot(inverse(inverse(inverse(inverse(C))))))]]) ).
cnf(refute_0_258,plain,
( multiply(inverse(inverse(C)),identity) != inverse(inverse(inverse(inverse(C))))
| inverse(double_divide(identity,inverse(inverse(C)))) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(C)))),multiply(inverse(inverse(C)),identity)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
inverse(double_divide(identity,inverse(inverse(C)))) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(C)),identity),inverse(inverse(inverse(inverse(C))))) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(double_divide(identity,inverse(inverse(C)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,inverse(inverse(C)))))]]) ).
cnf(refute_0_261,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_24:[bind(X,$fot(double_divide(double_divide(identity,inverse(inverse(C))),identity))),bind(Y,$fot(inverse(double_divide(identity,inverse(inverse(C)))))),bind(Z,$fot(inverse(inverse(inverse(inverse(C))))))]]) ).
cnf(refute_0_262,plain,
( inverse(double_divide(identity,inverse(inverse(C)))) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),identity),inverse(double_divide(identity,inverse(inverse(C))))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
double_divide(double_divide(identity,inverse(inverse(C))),identity) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(C)))),inverse(inverse(inverse(inverse(C))))) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)))]]) ).
cnf(refute_0_265,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_266,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( $equal(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_266]) ).
cnf(refute_0_268,plain,
multiply(C,identity) = inverse(inverse(C)),
inference(subst,[],[refute_0_254:[bind(X_10,$fot(C))]]) ).
cnf(refute_0_269,plain,
inverse(double_divide(identity,C)) = multiply(C,identity),
inference(subst,[],[refute_0_43:[bind(A,$fot(C)),bind(B,$fot(identity))]]) ).
cnf(refute_0_270,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_24:[bind(X,$fot(inverse(double_divide(identity,C)))),bind(Y,$fot(multiply(C,identity))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_271,plain,
( multiply(C,identity) != inverse(inverse(C))
| inverse(double_divide(identity,C)) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,C)),multiply(C,identity)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
inverse(double_divide(identity,C)) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(multiply(C,identity),inverse(inverse(C))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
double_divide(double_divide(identity,C),identity) = inverse(double_divide(identity,C)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,C)))]]) ).
cnf(refute_0_274,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_24:[bind(X,$fot(double_divide(double_divide(identity,C),identity))),bind(Y,$fot(inverse(double_divide(identity,C)))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_275,plain,
( inverse(double_divide(identity,C)) != inverse(inverse(C))
| double_divide(double_divide(identity,C),identity) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),inverse(double_divide(identity,C))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
double_divide(double_divide(identity,C),identity) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,C)),inverse(inverse(C))) )],[refute_0_272,refute_0_275]) ).
cnf(refute_0_277,plain,
double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,C),inverse(identity)))]]) ).
cnf(refute_0_278,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_279,plain,
( inverse(identity) != identity
| double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(identity)),double_divide(double_divide(identity,C),inverse(identity))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
double_divide(double_divide(identity,C),inverse(identity)) = double_divide(double_divide(identity,C),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_279]) ).
cnf(refute_0_281,plain,
double_divide(inverse(identity),C) = double_divide(inverse(identity),C),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),C))]]) ).
cnf(refute_0_282,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_283,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),C) = double_divide(identity,C) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),C),double_divide(inverse(identity),C)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
double_divide(inverse(identity),C) = double_divide(identity,C),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_283]) ).
cnf(refute_0_285,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))]]) ).
cnf(refute_0_286,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_287,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( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(inverse(identity),C),inverse(identity))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),C),double_divide(identity,C)) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
( double_divide(double_divide(identity,C),inverse(identity)) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(identity,C),inverse(identity))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$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_290,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( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(identity,C),inverse(identity))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(identity,C),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(identity)),double_divide(double_divide(identity,C),identity)) )],[refute_0_280,refute_0_290]) ).
cnf(refute_0_292,plain,
( double_divide(double_divide(identity,C),identity) != inverse(inverse(C))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_24:[bind(X,$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_293,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( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(identity,C),identity)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),inverse(inverse(C))) )],[refute_0_276,refute_0_293]) ).
cnf(refute_0_295,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
inference(subst,[],[refute_0_59:[bind(X_11,$fot(identity)),bind(X_12,$fot(double_divide(double_divide(double_divide(B,identity),C),inverse(B))))]]) ).
cnf(refute_0_296,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity)) = C,
inference(subst,[],[refute_0_30:[bind(A,$fot(identity))]]) ).
cnf(refute_0_297,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_298,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( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity)),C) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(double_divide(B,identity),C),inverse(B))),inverse(identity))),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
double_divide(double_divide(B,identity),C) = double_divide(double_divide(B,identity),C),
introduced(tautology,[refl,[$fot(double_divide(double_divide(B,identity),C))]]) ).
cnf(refute_0_301,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_302,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(B,identity),C) = double_divide(inverse(B),C) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,identity),C),double_divide(double_divide(B,identity),C)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
double_divide(double_divide(B,identity),C) = double_divide(inverse(B),C),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_10,refute_0_302]) ).
cnf(refute_0_304,plain,
double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(double_divide(B,identity),C),inverse(B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(B,identity),C),inverse(B)))]]) ).
cnf(refute_0_305,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_306,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( $equal(double_divide(double_divide(double_divide(B,identity),C),inverse(B)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
double_divide(double_divide(double_divide(B,identity),C),inverse(B)) = double_divide(double_divide(inverse(B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,identity),C),double_divide(inverse(B),C)) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
( double_divide(double_divide(double_divide(B,identity),C),inverse(B)) != double_divide(double_divide(inverse(B),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(double_divide(B,identity),C),inverse(B))
| double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(B),C),inverse(B)) ),
introduced(tautology,[equality,[$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_309,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( $equal(double_divide(double_divide(double_divide(B,identity),C),inverse(B)),double_divide(double_divide(inverse(B),C),inverse(B))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
double_divide(double_divide(inverse(identity),C),inverse(identity)) = double_divide(double_divide(inverse(B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(double_divide(B,identity),C),inverse(B))) )],[refute_0_299,refute_0_309]) ).
cnf(refute_0_311,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != double_divide(double_divide(inverse(B),C),inverse(B))
| double_divide(double_divide(inverse(B),C),inverse(B)) = double_divide(double_divide(inverse(identity),C),inverse(identity)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(inverse(B),C),inverse(B))))]]) ).
cnf(refute_0_312,plain,
double_divide(double_divide(inverse(B),C),inverse(B)) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),double_divide(double_divide(inverse(B),C),inverse(B))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) = double_divide(double_divide(inverse(identity),C),inverse(identity)),
inference(subst,[],[refute_0_312:[bind(B,$fot(inverse(X_17)))]]) ).
cnf(refute_0_314,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != inverse(inverse(C))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) != double_divide(double_divide(inverse(identity),C),inverse(identity))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))))),bind(Y,$fot(double_divide(double_divide(inverse(identity),C),inverse(identity)))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_315,plain,
( double_divide(double_divide(inverse(identity),C),inverse(identity)) != inverse(inverse(C))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))),double_divide(double_divide(inverse(identity),C),inverse(identity))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),C),inverse(identity)),inverse(inverse(C))) )],[refute_0_294,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(X_17,identity) = inverse(inverse(X_17)),
inference(subst,[],[refute_0_254:[bind(X_10,$fot(X_17))]]) ).
cnf(refute_0_318,plain,
double_divide(multiply(X_17,identity),C) = double_divide(multiply(X_17,identity),C),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_17,identity),C))]]) ).
cnf(refute_0_319,plain,
( multiply(X_17,identity) != inverse(inverse(X_17))
| double_divide(multiply(X_17,identity),C) != double_divide(multiply(X_17,identity),C)
| double_divide(multiply(X_17,identity),C) = double_divide(inverse(inverse(X_17)),C) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_17,identity),C),double_divide(multiply(X_17,identity),C)) ),[1,0],$fot(inverse(inverse(X_17)))]]) ).
cnf(refute_0_320,plain,
( multiply(X_17,identity) != inverse(inverse(X_17))
| double_divide(multiply(X_17,identity),C) = double_divide(inverse(inverse(X_17)),C) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_17,identity),C),double_divide(multiply(X_17,identity),C)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
double_divide(multiply(X_17,identity),C) = double_divide(inverse(inverse(X_17)),C),
inference(resolve,[$cnf( $equal(multiply(X_17,identity),inverse(inverse(X_17))) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))]]) ).
cnf(refute_0_323,plain,
( double_divide(multiply(X_17,identity),C) != double_divide(inverse(inverse(X_17)),C)
| double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) != double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))
| double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) ),[1,0],$fot(double_divide(inverse(inverse(X_17)),C))]]) ).
cnf(refute_0_324,plain,
( double_divide(multiply(X_17,identity),C) != double_divide(inverse(inverse(X_17)),C)
| double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_17,identity),C),double_divide(inverse(inverse(X_17)),C)) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
( double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) != double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17)))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) != inverse(inverse(C))
| double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = inverse(inverse(C)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))),bind(Y,$fot(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))))),bind(Z,$fot(inverse(inverse(C))))]]) ).
cnf(refute_0_327,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))) != inverse(inverse(C))
| double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = inverse(inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17)))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) = inverse(inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(X_17))),inverse(inverse(C))) )],[refute_0_316,refute_0_327]) ).
cnf(refute_0_329,plain,
double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))))]]) ).
cnf(refute_0_330,plain,
( double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) != inverse(inverse(C))
| double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))
| double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))) ),[1,1],$fot(inverse(inverse(C)))]]) ).
cnf(refute_0_331,plain,
( double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))) != inverse(inverse(C))
| double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))),inverse(inverse(C))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))))]]) ).
cnf(refute_0_334,plain,
( double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))
| inverse(identity) != identity
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_335,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_335]) ).
cnf(refute_0_337,plain,
( double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))))),bind(Y,$fot(double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))))),bind(Z,$fot(double_divide(identity,inverse(inverse(C)))))]]) ).
cnf(refute_0_338,plain,
( double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17))))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) = double_divide(identity,inverse(inverse(C))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(identity,inverse(inverse(C)))) )],[refute_0_332,refute_0_338]) ).
cnf(refute_0_340,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)))]]) ).
cnf(refute_0_341,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity))
| double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity))) ),[1,0],$fot(double_divide(identity,inverse(inverse(C))))]]) ).
cnf(refute_0_342,plain,
( double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))) != double_divide(identity,inverse(inverse(C)))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),double_divide(identity,inverse(inverse(C)))) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),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_345,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_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(C))),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),identity)) )],[refute_0_267,refute_0_345]) ).
cnf(refute_0_347,plain,
( double_divide(double_divide(identity,inverse(inverse(C))),identity) != inverse(inverse(inverse(inverse(C))))
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(C))),identity)
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),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_348,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_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(C))),identity)) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) = inverse(inverse(inverse(inverse(C)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(C))),identity),inverse(inverse(inverse(inverse(C))))) )],[refute_0_263,refute_0_348]) ).
cnf(refute_0_350,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != C
| double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != inverse(inverse(inverse(inverse(C))))
| inverse(inverse(inverse(inverse(C)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),C) ),[0],$fot(inverse(inverse(inverse(inverse(C)))))]]) ).
cnf(refute_0_351,plain,
( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)) != C
| inverse(inverse(inverse(inverse(C)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),inverse(inverse(inverse(inverse(C))))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
inverse(inverse(inverse(inverse(C)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(X_17,identity),C),inverse(inverse(X_17)))),inverse(identity)),C) )],[refute_0_212,refute_0_351]) ).
cnf(refute_0_353,plain,
inverse(inverse(inverse(inverse(X_11)))) = X_11,
inference(subst,[],[refute_0_352:[bind(C,$fot(X_11))]]) ).
cnf(refute_0_354,plain,
multiply(inverse(inverse(X_11)),identity) = inverse(inverse(inverse(inverse(X_11)))),
inference(subst,[],[refute_0_254:[bind(X_10,$fot(inverse(inverse(X_11))))]]) ).
cnf(refute_0_355,plain,
( multiply(inverse(inverse(X_11)),identity) != inverse(inverse(inverse(inverse(X_11))))
| inverse(inverse(inverse(inverse(X_11)))) != X_11
| multiply(inverse(inverse(X_11)),identity) = X_11 ),
inference(subst,[],[refute_0_24:[bind(X,$fot(multiply(inverse(inverse(X_11)),identity))),bind(Y,$fot(inverse(inverse(inverse(inverse(X_11)))))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_356,plain,
( inverse(inverse(inverse(inverse(X_11)))) != X_11
| multiply(inverse(inverse(X_11)),identity) = X_11 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),identity),inverse(inverse(inverse(inverse(X_11))))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
multiply(inverse(inverse(X_11)),identity) = X_11,
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(X_11)))),X_11) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
inverse(double_divide(identity,inverse(inverse(X_11)))) = multiply(inverse(inverse(X_11)),identity),
inference(subst,[],[refute_0_43:[bind(A,$fot(inverse(inverse(X_11)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_359,plain,
( multiply(inverse(inverse(X_11)),identity) != X_11
| inverse(double_divide(identity,inverse(inverse(X_11)))) != multiply(inverse(inverse(X_11)),identity)
| inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11 ),
inference(subst,[],[refute_0_24:[bind(X,$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_360,plain,
( multiply(inverse(inverse(X_11)),identity) != X_11
| inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_11)))),multiply(inverse(inverse(X_11)),identity)) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
inverse(double_divide(identity,inverse(inverse(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_11)),identity),X_11) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = inverse(double_divide(identity,inverse(inverse(X_11)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,inverse(inverse(X_11)))))]]) ).
cnf(refute_0_363,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_24:[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,$fot(X_11))]]) ).
cnf(refute_0_364,plain,
( inverse(double_divide(identity,inverse(inverse(X_11)))) != X_11
| double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),identity),inverse(double_divide(identity,inverse(inverse(X_11))))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),identity) = X_11,
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_11)))),X_11) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_367,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_368,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( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_368]) ).
cnf(refute_0_370,plain,
multiply(inverse(identity),X_11) = multiply(inverse(identity),X_11),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),X_11))]]) ).
cnf(refute_0_371,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_372,plain,
( inverse(identity) != identity
| multiply(inverse(identity),X_11) = multiply(identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),multiply(inverse(identity),X_11)) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
multiply(inverse(identity),X_11) = multiply(identity,X_11),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_192,refute_0_372]) ).
cnf(refute_0_374,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| multiply(inverse(identity),X_11) != multiply(identity,X_11)
| multiply(inverse(identity),X_11) = inverse(inverse(X_11)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(multiply(inverse(identity),X_11))),bind(Y,$fot(multiply(identity,X_11))),bind(Z,$fot(inverse(inverse(X_11))))]]) ).
cnf(refute_0_375,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| multiply(inverse(identity),X_11) = inverse(inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),multiply(identity,X_11)) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
multiply(inverse(identity),X_11) = inverse(inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(identity,X_11),inverse(inverse(X_11))) )],[refute_0_131,refute_0_375]) ).
cnf(refute_0_377,plain,
double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,multiply(inverse(identity),X_11)),
introduced(tautology,[refl,[$fot(double_divide(identity,multiply(inverse(identity),X_11)))]]) ).
cnf(refute_0_378,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_379,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( $equal(double_divide(identity,multiply(inverse(identity),X_11)),double_divide(identity,multiply(inverse(identity),X_11))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
double_divide(identity,multiply(inverse(identity),X_11)) = double_divide(identity,inverse(inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_11),inverse(inverse(X_11))) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)))]]) ).
cnf(refute_0_382,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_383,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( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(inverse(identity),X_11)),double_divide(identity,inverse(inverse(X_11)))) )],[refute_0_380,refute_0_383]) ).
cnf(refute_0_385,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))
| double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),identity)
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$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_386,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( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_11))),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),identity)) )],[refute_0_369,refute_0_386]) ).
cnf(refute_0_388,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_11))),identity)
| double_divide(double_divide(identity,inverse(inverse(X_11))),identity) != X_11
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = X_11 ),
inference(subst,[],[refute_0_24:[bind(X,$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_389,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( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_11))),identity)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_11))),identity),X_11) )],[refute_0_365,refute_0_389]) ).
cnf(refute_0_391,plain,
( double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != X_11
| double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)) != double_divide(identity,inverse(X_11))
| X_11 = double_divide(identity,inverse(X_11)) ),
introduced(tautology,[equality,[$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_392,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( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),X_11) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
X_11 = double_divide(identity,inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(identity),X_11)),inverse(identity)),double_divide(identity,inverse(X_11))) )],[refute_0_207,refute_0_392]) ).
cnf(refute_0_394,plain,
( X_11 != double_divide(identity,inverse(X_11))
| double_divide(identity,inverse(X_11)) = X_11 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_11)),bind(Y,$fot(double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_395,plain,
double_divide(identity,inverse(X_11)) = X_11,
inference(resolve,[$cnf( $equal(X_11,double_divide(identity,inverse(X_11))) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(double_divide(identity,inverse(X_11)),X_10),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(X_11)),X_10))]]) ).
cnf(refute_0_397,plain,
( multiply(double_divide(identity,inverse(X_11)),X_10) != multiply(double_divide(identity,inverse(X_11)),X_10)
| double_divide(identity,inverse(X_11)) != X_11
| multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_11)),X_10),multiply(double_divide(identity,inverse(X_11)),X_10)) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_398,plain,
( double_divide(identity,inverse(X_11)) != X_11
| multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_11)),X_10),multiply(double_divide(identity,inverse(X_11)),X_10)) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
multiply(double_divide(identity,inverse(X_11)),X_10) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(X_11)),X_11) )],[refute_0_395,refute_0_398]) ).
cnf(refute_0_400,plain,
( multiply(double_divide(identity,inverse(X_11)),X_10) != multiply(X_10,X_11)
| multiply(double_divide(identity,inverse(X_11)),X_10) != multiply(X_11,X_10)
| multiply(X_11,X_10) = multiply(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_11)),X_10),multiply(X_10,X_11)) ),[0],$fot(multiply(X_11,X_10))]]) ).
cnf(refute_0_401,plain,
( multiply(double_divide(identity,inverse(X_11)),X_10) != multiply(X_10,X_11)
| multiply(X_11,X_10) = multiply(X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_11)),X_10),multiply(X_11,X_10)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
multiply(X_11,X_10) = multiply(X_10,X_11),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_11)),X_10),multiply(X_10,X_11)) )],[refute_0_202,refute_0_401]) ).
cnf(refute_0_403,plain,
( multiply(X_11,X_10) != multiply(X_10,X_11)
| multiply(X_10,X_11) = multiply(X_11,X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_11,X_10))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_404,plain,
multiply(X_10,X_11) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(multiply(X_11,X_10),multiply(X_10,X_11)) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(b,a) = multiply(a,b),
inference(subst,[],[refute_0_404:[bind(X_10,$fot(b)),bind(X_11,$fot(a))]]) ).
cnf(refute_0_406,plain,
( multiply(a,b) != multiply(a,b)
| multiply(b,a) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,b),multiply(b,a)) ),[1],$fot(multiply(a,b))]]) ).
cnf(refute_0_407,plain,
( multiply(a,b) != multiply(a,b)
| multiply(a,b) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(b,a),multiply(a,b)) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
multiply(a,b) != multiply(a,b),
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(b,a)) )],[refute_0_407,prove_these_axioms_4]) ).
cnf(refute_0_409,plain,
multiply(a,b) = multiply(a,b),
introduced(tautology,[refl,[$fot(multiply(a,b))]]) ).
cnf(refute_0_410,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a,b),multiply(a,b)) )],[refute_0_409,refute_0_408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.09/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jun 13 20:10:27 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33
% 0.13/0.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------