TSTP Solution File: GRP486-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:41:39 EDT 2022
% Result : Unsatisfiable 0.22s 0.47s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 161
% Syntax : Number of clauses : 592 ( 302 unt; 0 nHn; 288 RR)
% Number of literals : 1014 (1013 equ; 424 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 1005 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),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_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_6,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)))]]) ).
cnf(refute_0_7,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) ),[1,1],$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(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)),
inference(resolve,[$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(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))]]) ).
cnf(refute_0_12,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_13,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,B),C),inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))))]]) ).
cnf(refute_0_16,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))
| double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))) ),[1,1],$fot(double_divide(double_divide(double_divide(A,B),C),inverse(B)))]]) ).
cnf(refute_0_17,plain,
( double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) != double_divide(double_divide(double_divide(A,B),C),inverse(B))
| double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) = double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)),double_divide(double_divide(double_divide(A,B),C),inverse(B))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)))]]) ).
cnf(refute_0_20,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))) ),[1,0],$fot(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))))]]) ).
cnf(refute_0_21,plain,
( double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))) != double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)))),bind(Y,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)))),bind(Z,$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))))]]) ).
cnf(refute_0_26,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))) )],[refute_0_9,refute_0_26]) ).
cnf(refute_0_28,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),C) ),[0],$fot(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)))]]) ).
cnf(refute_0_29,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) != C
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),inverse(B))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)),C) )],[single_axiom,refute_0_29]) ).
cnf(refute_0_31,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,identity),X_12),inverse(identity))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(identity)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_32,plain,
inverse(X_10) = double_divide(X_10,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_33,plain,
( inverse(X_10) != double_divide(X_10,identity)
| double_divide(X_10,identity) = inverse(X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_10))),bind(Y,$fot(double_divide(X_10,identity)))]]) ).
cnf(refute_0_34,plain,
double_divide(X_10,identity) = inverse(X_10),
inference(resolve,[$cnf( $equal(inverse(X_10),double_divide(X_10,identity)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,identity),X_12),inverse(identity))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,identity),X_12),inverse(identity))),inverse(identity)),X_12) ),[0,0,1,0,0],$fot(inverse(X_10))]]) ).
cnf(refute_0_36,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,identity),X_12),inverse(identity))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,identity),inverse(X_10)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,identity),X_12),inverse(identity))),inverse(identity)),X_12) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)),
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(double_divide(X_10,X_11))))]]) ).
cnf(refute_0_39,plain,
identity = double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_40,plain,
( identity != double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))
| double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))))]]) ).
cnf(refute_0_41,plain,
double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))) != identity
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_43,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),identity) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = inverse(double_divide(X_10,X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),inverse(double_divide(X_10,X_11))),inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_46,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_47,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_50,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
inverse(double_divide(X_10,X_11)) = multiply(X_11,X_10),
inference(subst,[],[refute_0_50:[bind(A,$fot(X_11)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_52,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| inverse(double_divide(X_10,X_11)) != multiply(X_11,X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_11,X_10)) ),[0],$fot(inverse(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_53,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,X_11)),multiply(X_11,X_10)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),inverse(double_divide(X_10,X_11))) )],[refute_0_44,refute_0_53]) ).
cnf(refute_0_55,plain,
double_divide(double_divide(inverse(X_17),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) = C,
inference(subst,[],[refute_0_30:[bind(A,$fot(inverse(X_17))),bind(B,$fot(inverse(identity)))]]) ).
cnf(refute_0_56,plain,
double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(identity,X_15),
inference(subst,[],[refute_0_54:[bind(X_10,$fot(X_15)),bind(X_11,$fot(identity))]]) ).
cnf(refute_0_57,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_58,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_59,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(identity,X_15)
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)),multiply(identity,X_15)) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_61,plain,
( double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)) != multiply(identity,X_15)
| double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = multiply(identity,X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,double_divide(identity,inverse(identity))),inverse(identity)),multiply(identity,X_15)) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
double_divide(X_15,identity) = inverse(X_15),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_64,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(double_divide(X_15,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_15,identity),inverse(identity)))]]) ).
cnf(refute_0_65,plain,
( double_divide(X_15,identity) != inverse(X_15)
| double_divide(double_divide(X_15,identity),inverse(identity)) != double_divide(double_divide(X_15,identity),inverse(identity))
| double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(inverse(X_15),inverse(identity)) ),
introduced(tautology,[equality,[$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_66,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( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),double_divide(double_divide(X_15,identity),inverse(identity))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
double_divide(double_divide(X_15,identity),inverse(identity)) = double_divide(inverse(X_15),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_15,identity),inverse(X_15)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( double_divide(double_divide(X_15,identity),inverse(identity)) != multiply(identity,X_15)
| double_divide(double_divide(X_15,identity),inverse(identity)) != double_divide(inverse(X_15),inverse(identity))
| double_divide(inverse(X_15),inverse(identity)) = multiply(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),multiply(identity,X_15)) ),[0],$fot(double_divide(inverse(X_15),inverse(identity)))]]) ).
cnf(refute_0_69,plain,
( double_divide(double_divide(X_15,identity),inverse(identity)) != multiply(identity,X_15)
| double_divide(inverse(X_15),inverse(identity)) = multiply(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),double_divide(inverse(X_15),inverse(identity))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_48:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_71,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_72,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_73,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_75,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_70,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(identity,X_15) = inverse(inverse(X_15)),
inference(subst,[],[refute_0_76:[bind(X_3,$fot(X_15))]]) ).
cnf(refute_0_78,plain,
( multiply(identity,X_15) != inverse(inverse(X_15))
| double_divide(inverse(X_15),inverse(identity)) != multiply(identity,X_15)
| double_divide(inverse(X_15),inverse(identity)) = inverse(inverse(X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_15),inverse(identity)),multiply(identity,X_15)) ),[1],$fot(inverse(inverse(X_15)))]]) ).
cnf(refute_0_79,plain,
( double_divide(inverse(X_15),inverse(identity)) != multiply(identity,X_15)
| double_divide(inverse(X_15),inverse(identity)) = inverse(inverse(X_15)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_15),inverse(inverse(X_15))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( double_divide(double_divide(X_15,identity),inverse(identity)) != multiply(identity,X_15)
| double_divide(inverse(X_15),inverse(identity)) = inverse(inverse(X_15)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_15),inverse(identity)),multiply(identity,X_15)) )],[refute_0_69,refute_0_79]) ).
cnf(refute_0_81,plain,
double_divide(inverse(X_15),inverse(identity)) = inverse(inverse(X_15)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_15,identity),inverse(identity)),multiply(identity,X_15)) )],[refute_0_62,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(inverse(X_17),inverse(identity)) = inverse(inverse(X_17)),
inference(subst,[],[refute_0_81:[bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_83,plain,
( double_divide(double_divide(inverse(X_17),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(inverse(X_17),inverse(identity)) != inverse(inverse(X_17))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)),C) ),[0,0,1,0,0],$fot(inverse(inverse(X_17)))]]) ).
cnf(refute_0_84,plain,
( double_divide(double_divide(inverse(X_17),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),inverse(identity)),inverse(inverse(X_17))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(double_divide(inverse(X_17),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)),C) )],[refute_0_55,refute_0_84]) ).
cnf(refute_0_86,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity))),inverse(identity)) = double_divide(identity,inverse(X_16)),
inference(subst,[],[refute_0_30:[bind(B,$fot(identity)),bind(C,$fot(double_divide(identity,inverse(X_16))))]]) ).
cnf(refute_0_87,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity)) = multiply(X_16,double_divide(A,identity)),
inference(subst,[],[refute_0_54:[bind(X_10,$fot(double_divide(A,identity))),bind(X_11,$fot(X_16))]]) ).
cnf(refute_0_88,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(X_16))
| double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity)) != multiply(X_16,double_divide(A,identity))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(identity,inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity))),inverse(identity)),double_divide(identity,inverse(X_16))) ),[0,0,1],$fot(multiply(X_16,double_divide(A,identity)))]]) ).
cnf(refute_0_89,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(X_16))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(identity,inverse(X_16)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity)),multiply(X_16,double_divide(A,identity))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(identity,inverse(X_16)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(identity,inverse(X_16))),inverse(identity))),inverse(identity)),double_divide(identity,inverse(X_16))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(X_16,double_divide(A,identity)) = multiply(X_16,double_divide(A,identity)),
introduced(tautology,[refl,[$fot(multiply(X_16,double_divide(A,identity)))]]) ).
cnf(refute_0_92,plain,
( multiply(X_16,double_divide(A,identity)) != multiply(X_16,double_divide(A,identity))
| double_divide(A,identity) != inverse(A)
| multiply(X_16,double_divide(A,identity)) = multiply(X_16,inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_16,double_divide(A,identity)),multiply(X_16,double_divide(A,identity))) ),[1,1],$fot(inverse(A))]]) ).
cnf(refute_0_93,plain,
( double_divide(A,identity) != inverse(A)
| multiply(X_16,double_divide(A,identity)) = multiply(X_16,inverse(A)) ),
inference(resolve,[$cnf( $equal(multiply(X_16,double_divide(A,identity)),multiply(X_16,double_divide(A,identity))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(X_16,double_divide(A,identity)) = multiply(X_16,inverse(A)),
inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_4,refute_0_93]) ).
cnf(refute_0_95,plain,
double_divide(A,multiply(X_16,double_divide(A,identity))) = double_divide(A,multiply(X_16,double_divide(A,identity))),
introduced(tautology,[refl,[$fot(double_divide(A,multiply(X_16,double_divide(A,identity))))]]) ).
cnf(refute_0_96,plain,
( multiply(X_16,double_divide(A,identity)) != multiply(X_16,inverse(A))
| double_divide(A,multiply(X_16,double_divide(A,identity))) != double_divide(A,multiply(X_16,double_divide(A,identity)))
| double_divide(A,multiply(X_16,double_divide(A,identity))) = double_divide(A,multiply(X_16,inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,multiply(X_16,double_divide(A,identity))),double_divide(A,multiply(X_16,double_divide(A,identity)))) ),[1,1],$fot(multiply(X_16,inverse(A)))]]) ).
cnf(refute_0_97,plain,
( multiply(X_16,double_divide(A,identity)) != multiply(X_16,inverse(A))
| double_divide(A,multiply(X_16,double_divide(A,identity))) = double_divide(A,multiply(X_16,inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(X_16,double_divide(A,identity))),double_divide(A,multiply(X_16,double_divide(A,identity)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
double_divide(A,multiply(X_16,double_divide(A,identity))) = double_divide(A,multiply(X_16,inverse(A))),
inference(resolve,[$cnf( $equal(multiply(X_16,double_divide(A,identity)),multiply(X_16,inverse(A))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)))]]) ).
cnf(refute_0_100,plain,
( double_divide(A,multiply(X_16,double_divide(A,identity))) != double_divide(A,multiply(X_16,inverse(A)))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) != double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity))) ),[1,0],$fot(double_divide(A,multiply(X_16,inverse(A))))]]) ).
cnf(refute_0_101,plain,
( double_divide(A,multiply(X_16,double_divide(A,identity))) != double_divide(A,multiply(X_16,inverse(A)))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) = double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(A,multiply(X_16,double_divide(A,identity))),double_divide(A,multiply(X_16,inverse(A)))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) != double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity))
| double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) != double_divide(identity,inverse(X_16))
| double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)) = double_divide(identity,inverse(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),double_divide(identity,inverse(X_16))) ),[0],$fot(double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)))]]) ).
cnf(refute_0_104,plain,
( double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)) != double_divide(identity,inverse(X_16))
| double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)) = double_divide(identity,inverse(X_16)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
double_divide(double_divide(A,multiply(X_16,inverse(A))),inverse(identity)) = double_divide(identity,inverse(X_16)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,multiply(X_16,double_divide(A,identity))),inverse(identity)),double_divide(identity,inverse(X_16))) )],[refute_0_90,refute_0_104]) ).
cnf(refute_0_106,plain,
double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)) = double_divide(identity,inverse(C)),
inference(subst,[],[refute_0_105:[bind(A,$fot(inverse(X_17))),bind(X_16,$fot(C))]]) ).
cnf(refute_0_107,plain,
inverse(double_divide(inverse(inverse(X_17)),C)) = multiply(C,inverse(inverse(X_17))),
inference(subst,[],[refute_0_50:[bind(A,$fot(C)),bind(B,$fot(inverse(inverse(X_17))))]]) ).
cnf(refute_0_108,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),identity) = inverse(double_divide(inverse(inverse(X_17)),C)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(inverse(inverse(X_17)),C)))]]) ).
cnf(refute_0_109,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),identity) != inverse(double_divide(inverse(inverse(X_17)),C))
| inverse(double_divide(inverse(inverse(X_17)),C)) != multiply(C,inverse(inverse(X_17)))
| double_divide(double_divide(inverse(inverse(X_17)),C),identity) = multiply(C,inverse(inverse(X_17))) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(inverse(X_17)),C),identity))),bind(Y,$fot(inverse(double_divide(inverse(inverse(X_17)),C)))),bind(Z,$fot(multiply(C,inverse(inverse(X_17)))))]]) ).
cnf(refute_0_110,plain,
( inverse(double_divide(inverse(inverse(X_17)),C)) != multiply(C,inverse(inverse(X_17)))
| double_divide(double_divide(inverse(inverse(X_17)),C),identity) = multiply(C,inverse(inverse(X_17))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),identity),inverse(double_divide(inverse(inverse(X_17)),C))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),identity) = multiply(C,inverse(inverse(X_17))),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(inverse(X_17)),C)),multiply(C,inverse(inverse(X_17)))) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),identity),inverse(X_11))),inverse(identity)) = identity,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(identity))]]) ).
cnf(refute_0_113,plain,
inverse(double_divide(X_10,X_11)) = double_divide(double_divide(X_10,X_11),identity),
inference(subst,[],[inverse:[bind(A,$fot(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_114,plain,
( inverse(double_divide(X_10,X_11)) != double_divide(double_divide(X_10,X_11),identity)
| double_divide(double_divide(X_10,X_11),identity) = inverse(double_divide(X_10,X_11)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(double_divide(X_10,X_11)))),bind(Y,$fot(double_divide(double_divide(X_10,X_11),identity)))]]) ).
cnf(refute_0_115,plain,
double_divide(double_divide(X_10,X_11),identity) = inverse(double_divide(X_10,X_11)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,X_11)),double_divide(double_divide(X_10,X_11),identity)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( double_divide(double_divide(X_10,X_11),identity) != inverse(double_divide(X_10,X_11))
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),identity),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),identity),inverse(X_11))),inverse(identity)),identity) ),[0,0,1,0],$fot(inverse(double_divide(X_10,X_11)))]]) ).
cnf(refute_0_117,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),identity),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,X_11),identity),inverse(double_divide(X_10,X_11))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,X_11),identity),inverse(X_11))),inverse(identity)),identity) )],[refute_0_112,refute_0_117]) ).
cnf(refute_0_119,plain,
double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) = double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)))]]) ).
cnf(refute_0_120,plain,
( double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) != double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))
| inverse(double_divide(X_10,X_11)) != multiply(X_11,X_10)
| double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) = double_divide(multiply(X_11,X_10),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)),double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) ),[1,0],$fot(multiply(X_11,X_10))]]) ).
cnf(refute_0_121,plain,
( inverse(double_divide(X_10,X_11)) != multiply(X_11,X_10)
| double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) = double_divide(multiply(X_11,X_10),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)),double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) = double_divide(multiply(X_11,X_10),inverse(X_11)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,X_11)),multiply(X_11,X_10)) )],[refute_0_51,refute_0_121]) ).
cnf(refute_0_123,plain,
double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) = double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))))]]) ).
cnf(refute_0_124,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) != double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)))
| double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) != double_divide(multiply(X_11,X_10),inverse(X_11))
| double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)))) ),[1,1],$fot(double_divide(multiply(X_11,X_10),inverse(X_11)))]]) ).
cnf(refute_0_125,plain,
( double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)) != double_divide(multiply(X_11,X_10),inverse(X_11))
| double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) = double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11)),double_divide(multiply(X_11,X_10),inverse(X_11))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_128,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) != double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11)))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity))) ),[1,0],$fot(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))))]]) ).
cnf(refute_0_129,plain,
( double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))) != double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11)))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11)))) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
( double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),identity) ),[0],$fot(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_132,plain,
( double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(inverse(double_divide(X_10,X_11)),inverse(X_11))),inverse(identity)),identity) )],[refute_0_118,refute_0_132]) ).
cnf(refute_0_134,plain,
double_divide(double_divide(X_13,double_divide(multiply(inverse(X_13),X_13),inverse(inverse(X_13)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_133:[bind(X_10,$fot(X_13)),bind(X_11,$fot(inverse(X_13)))]]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_48:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_136,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_137,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_138,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_140,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_135,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(inverse(X_13),X_13) = inverse(identity),
inference(subst,[],[refute_0_141:[bind(X_3,$fot(X_13))]]) ).
cnf(refute_0_143,plain,
( multiply(inverse(X_13),X_13) != inverse(identity)
| double_divide(double_divide(X_13,double_divide(multiply(inverse(X_13),X_13),inverse(inverse(X_13)))),inverse(identity)) != identity
| double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(multiply(inverse(X_13),X_13),inverse(inverse(X_13)))),inverse(identity)),identity) ),[0,0,1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_144,plain,
( double_divide(double_divide(X_13,double_divide(multiply(inverse(X_13),X_13),inverse(inverse(X_13)))),inverse(identity)) != identity
| double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),X_13),inverse(identity)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
double_divide(double_divide(X_13,double_divide(inverse(identity),inverse(inverse(X_13)))),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_13,double_divide(multiply(inverse(X_13),X_13),inverse(inverse(X_13)))),inverse(identity)),identity) )],[refute_0_134,refute_0_144]) ).
cnf(refute_0_146,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_145:[bind(X_13,$fot(identity))]]) ).
cnf(refute_0_147,plain,
identity = double_divide(inverse(identity),inverse(inverse(identity))),
inference(subst,[],[identity:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_148,plain,
( identity != double_divide(inverse(identity),inverse(inverse(identity)))
| double_divide(inverse(identity),inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(inverse(identity),inverse(inverse(identity)))))]]) ).
cnf(refute_0_149,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)),identity) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_151,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),identity) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)),identity) )],[refute_0_146,refute_0_151]) ).
cnf(refute_0_153,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)),
inference(subst,[],[refute_0_81:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_154,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(double_divide(identity,identity),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),inverse(identity)))]]) ).
cnf(refute_0_155,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(double_divide(identity,identity),inverse(identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
introduced(tautology,[equality,[$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_156,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(double_divide(identity,identity),inverse(identity))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(inverse(identity),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_5,refute_0_156]) ).
cnf(refute_0_158,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(inverse(identity),inverse(identity))
| double_divide(inverse(identity),inverse(identity)) != inverse(inverse(identity))
| double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(subst,[],[refute_0_24:[bind(X,$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_159,plain,
( double_divide(inverse(identity),inverse(identity)) != inverse(inverse(identity))
| double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(inverse(identity),inverse(identity))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_153,refute_0_159]) ).
cnf(refute_0_161,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) != inverse(inverse(identity))
| inverse(inverse(identity)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),identity) ),[0],$fot(inverse(inverse(identity)))]]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != identity
| inverse(inverse(identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),inverse(inverse(identity))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
inverse(inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),identity) )],[refute_0_152,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))))]]) ).
cnf(refute_0_165,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) != double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))
| inverse(inverse(identity)) != identity
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = double_divide(double_divide(inverse(inverse(X_17)),C),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_166,plain,
( inverse(inverse(identity)) != identity
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = double_divide(double_divide(inverse(inverse(X_17)),C),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = double_divide(double_divide(inverse(inverse(X_17)),C),identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),identity) != multiply(C,inverse(inverse(X_17)))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) != double_divide(double_divide(inverse(inverse(X_17)),C),identity)
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = multiply(C,inverse(inverse(X_17))) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))))),bind(Y,$fot(double_divide(double_divide(inverse(inverse(X_17)),C),identity))),bind(Z,$fot(multiply(C,inverse(inverse(X_17)))))]]) ).
cnf(refute_0_169,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),identity) != multiply(C,inverse(inverse(X_17)))
| double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = multiply(C,inverse(inverse(X_17))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))),double_divide(double_divide(inverse(inverse(X_17)),C),identity)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) = multiply(C,inverse(inverse(X_17))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),identity),multiply(C,inverse(inverse(X_17)))) )],[refute_0_111,refute_0_169]) ).
cnf(refute_0_171,plain,
double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) = double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))))]]) ).
cnf(refute_0_172,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) != multiply(C,inverse(inverse(X_17)))
| double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) != double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))))
| double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) = double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))))) ),[1,1],$fot(multiply(C,inverse(inverse(X_17))))]]) ).
cnf(refute_0_173,plain,
( double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))) != multiply(C,inverse(inverse(X_17)))
| double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) = double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) = double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity))),multiply(C,inverse(inverse(X_17)))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)))]]) ).
cnf(refute_0_176,plain,
( double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) != double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity))
| double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) != double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17))))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity))) ),[1,0],$fot(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))))]]) ).
cnf(refute_0_177,plain,
( double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))) != double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17))))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17))))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)) != double_divide(identity,inverse(C))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) != double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(identity,inverse(C)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)))),bind(Z,$fot(double_divide(identity,inverse(C))))]]) ).
cnf(refute_0_180,plain,
( double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)) != double_divide(identity,inverse(C))
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(identity,inverse(C)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) = double_divide(identity,inverse(C)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),multiply(C,inverse(inverse(X_17)))),inverse(identity)),double_divide(identity,inverse(C))) )],[refute_0_106,refute_0_180]) ).
cnf(refute_0_182,plain,
( double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) != double_divide(identity,inverse(C))
| double_divide(identity,inverse(C)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),C) ),[0],$fot(double_divide(identity,inverse(C)))]]) ).
cnf(refute_0_183,plain,
( double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(identity,inverse(C)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),double_divide(identity,inverse(C))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
double_divide(identity,inverse(C)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_17),double_divide(double_divide(inverse(inverse(X_17)),C),inverse(inverse(identity)))),inverse(identity)),C) )],[refute_0_85,refute_0_183]) ).
cnf(refute_0_185,plain,
double_divide(identity,inverse(X_11)) = X_11,
inference(subst,[],[refute_0_184:[bind(C,$fot(X_11))]]) ).
cnf(refute_0_186,plain,
double_divide(X_10,double_divide(identity,inverse(X_11))) = double_divide(X_10,double_divide(identity,inverse(X_11))),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(identity,inverse(X_11))))]]) ).
cnf(refute_0_187,plain,
( double_divide(X_10,double_divide(identity,inverse(X_11))) != double_divide(X_10,double_divide(identity,inverse(X_11)))
| double_divide(identity,inverse(X_11)) != X_11
| double_divide(X_10,double_divide(identity,inverse(X_11))) = double_divide(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(identity,inverse(X_11))),double_divide(X_10,double_divide(identity,inverse(X_11)))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_188,plain,
( double_divide(identity,inverse(X_11)) != X_11
| double_divide(X_10,double_divide(identity,inverse(X_11))) = double_divide(X_10,X_11) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,inverse(X_11))),double_divide(X_10,double_divide(identity,inverse(X_11)))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
double_divide(X_10,double_divide(identity,inverse(X_11))) = double_divide(X_10,X_11),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(X_11)),X_11) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)))]]) ).
cnf(refute_0_191,plain,
( double_divide(X_10,double_divide(identity,inverse(X_11))) != double_divide(X_10,X_11)
| 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))
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,X_11),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity))) ),[1,0],$fot(double_divide(X_10,X_11))]]) ).
cnf(refute_0_192,plain,
( double_divide(X_10,double_divide(identity,inverse(X_11))) != double_divide(X_10,X_11)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,X_11),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) = double_divide(double_divide(X_10,X_11),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(identity,inverse(X_11))),double_divide(X_10,X_11)) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(X_11,X_10)
| double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != double_divide(double_divide(X_10,X_11),inverse(identity))
| double_divide(double_divide(X_10,X_11),inverse(identity)) = multiply(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_11,X_10)) ),[0],$fot(double_divide(double_divide(X_10,X_11),inverse(identity)))]]) ).
cnf(refute_0_195,plain,
( double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)) != multiply(X_11,X_10)
| double_divide(double_divide(X_10,X_11),inverse(identity)) = multiply(X_11,X_10) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),double_divide(double_divide(X_10,X_11),inverse(identity))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
double_divide(double_divide(X_10,X_11),inverse(identity)) = multiply(X_11,X_10),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(identity,inverse(X_11))),inverse(identity)),multiply(X_11,X_10)) )],[refute_0_54,refute_0_195]) ).
cnf(refute_0_197,plain,
double_divide(double_divide(inverse(X_10),X_12),inverse(identity)) = multiply(X_12,inverse(X_10)),
inference(subst,[],[refute_0_196:[bind(X_10,$fot(inverse(X_10))),bind(X_11,$fot(X_12))]]) ).
cnf(refute_0_198,plain,
multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) = multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10),
introduced(tautology,[refl,[$fot(multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10))]]) ).
cnf(refute_0_199,plain,
( multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) != multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10)
| double_divide(double_divide(inverse(X_10),X_12),inverse(identity)) != multiply(X_12,inverse(X_10))
| multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) = multiply(multiply(X_12,inverse(X_10)),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10),multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10)) ),[1,0],$fot(multiply(X_12,inverse(X_10)))]]) ).
cnf(refute_0_200,plain,
( double_divide(double_divide(inverse(X_10),X_12),inverse(identity)) != multiply(X_12,inverse(X_10))
| multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) = multiply(multiply(X_12,inverse(X_10)),X_10) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10),multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) = multiply(multiply(X_12,inverse(X_10)),X_10),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),multiply(X_12,inverse(X_10))) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10),
inference(subst,[],[refute_0_196:[bind(X_11,$fot(double_divide(double_divide(inverse(X_10),X_12),inverse(identity))))]]) ).
cnf(refute_0_203,plain,
( multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) != multiply(multiply(X_12,inverse(X_10)),X_10)
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) != multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10)
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = multiply(multiply(X_12,inverse(X_10)),X_10) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)))),bind(Y,$fot(multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10))),bind(Z,$fot(multiply(multiply(X_12,inverse(X_10)),X_10)))]]) ).
cnf(refute_0_204,plain,
( multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10) != multiply(multiply(X_12,inverse(X_10)),X_10)
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = multiply(multiply(X_12,inverse(X_10)),X_10) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)),multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) = multiply(multiply(X_12,inverse(X_10)),X_10),
inference(resolve,[$cnf( $equal(multiply(double_divide(double_divide(inverse(X_10),X_12),inverse(identity)),X_10),multiply(multiply(X_12,inverse(X_10)),X_10)) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) != multiply(multiply(X_12,inverse(X_10)),X_10)
| multiply(multiply(X_12,inverse(X_10)),X_10) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)),X_12) ),[0],$fot(multiply(multiply(X_12,inverse(X_10)),X_10))]]) ).
cnf(refute_0_207,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)) != X_12
| multiply(multiply(X_12,inverse(X_10)),X_10) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)),multiply(multiply(X_12,inverse(X_10)),X_10)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(multiply(X_12,inverse(X_10)),X_10) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(inverse(X_10),X_12),inverse(identity))),inverse(identity)),X_12) )],[refute_0_37,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),X_10) = multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),
inference(subst,[],[refute_0_208:[bind(X_12,$fot(multiply(X_85,multiply(X_83,inverse(inverse(X_10))))))]]) ).
cnf(refute_0_210,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity))),inverse(identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),
inference(subst,[],[refute_0_30:[bind(B,$fot(identity)),bind(C,$fot(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))))]]) ).
cnf(refute_0_211,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_30:[bind(A,$fot(double_divide(A,identity))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_212,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))
| double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity)) != X_12
| double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))) ),[0,0,1],$fot(X_12)]]) ).
cnf(refute_0_213,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity))),inverse(identity)) != double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))
| double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity)),X_12) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))),inverse(identity))),inverse(identity)),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
double_divide(double_divide(A,identity),X_11) = double_divide(double_divide(A,identity),X_11),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,identity),X_11))]]) ).
cnf(refute_0_216,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(double_divide(A,identity),X_11) != double_divide(double_divide(A,identity),X_11)
| double_divide(double_divide(A,identity),X_11) = double_divide(inverse(A),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,identity),X_11),double_divide(double_divide(A,identity),X_11)) ),[1,0],$fot(inverse(A))]]) ).
cnf(refute_0_217,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(double_divide(A,identity),X_11) = double_divide(inverse(A),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,identity),X_11),double_divide(double_divide(A,identity),X_11)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
double_divide(double_divide(A,identity),X_11) = double_divide(inverse(A),X_11),
inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_4,refute_0_217]) ).
cnf(refute_0_219,plain,
double_divide(double_divide(double_divide(A,identity),X_11),X_12) = double_divide(double_divide(double_divide(A,identity),X_11),X_12),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,identity),X_11),X_12))]]) ).
cnf(refute_0_220,plain,
( double_divide(double_divide(A,identity),X_11) != double_divide(inverse(A),X_11)
| double_divide(double_divide(double_divide(A,identity),X_11),X_12) != double_divide(double_divide(double_divide(A,identity),X_11),X_12)
| double_divide(double_divide(double_divide(A,identity),X_11),X_12) = double_divide(double_divide(inverse(A),X_11),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,identity),X_11),X_12),double_divide(double_divide(double_divide(A,identity),X_11),X_12)) ),[1,0],$fot(double_divide(inverse(A),X_11))]]) ).
cnf(refute_0_221,plain,
( double_divide(double_divide(A,identity),X_11) != double_divide(inverse(A),X_11)
| double_divide(double_divide(double_divide(A,identity),X_11),X_12) = double_divide(double_divide(inverse(A),X_11),X_12) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,identity),X_11),X_12),double_divide(double_divide(double_divide(A,identity),X_11),X_12)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
double_divide(double_divide(double_divide(A,identity),X_11),X_12) = double_divide(double_divide(inverse(A),X_11),X_12),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,identity),X_11),double_divide(inverse(A),X_11)) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) = double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)))]]) ).
cnf(refute_0_224,plain,
( double_divide(double_divide(double_divide(A,identity),X_11),X_12) != double_divide(double_divide(inverse(A),X_11),X_12)
| double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) != double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))
| double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))) ),[1,0],$fot(double_divide(double_divide(inverse(A),X_11),X_12))]]) ).
cnf(refute_0_225,plain,
( double_divide(double_divide(double_divide(A,identity),X_11),X_12) != double_divide(double_divide(inverse(A),X_11),X_12)
| double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,identity),X_11),X_12),double_divide(double_divide(inverse(A),X_11),X_12)) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
( double_divide(double_divide(A,X_12),inverse(identity)) != double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))
| double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(double_divide(A,X_12),inverse(identity)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) ),[0],$fot(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)))]]) ).
cnf(refute_0_228,plain,
( double_divide(double_divide(A,X_12),inverse(identity)) != double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))
| double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
double_divide(double_divide(A,X_12),inverse(identity)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,X_12),inverse(identity)),double_divide(double_divide(double_divide(double_divide(A,identity),X_11),X_12),inverse(X_11))) )],[refute_0_214,refute_0_228]) ).
cnf(refute_0_230,plain,
double_divide(double_divide(A,X_12),inverse(identity)) = multiply(X_12,A),
inference(subst,[],[refute_0_196:[bind(X_10,$fot(A)),bind(X_11,$fot(X_12))]]) ).
cnf(refute_0_231,plain,
( double_divide(double_divide(A,X_12),inverse(identity)) != multiply(X_12,A)
| double_divide(double_divide(A,X_12),inverse(identity)) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| multiply(X_12,A) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,X_12),inverse(identity)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) ),[0],$fot(multiply(X_12,A))]]) ).
cnf(refute_0_232,plain,
( double_divide(double_divide(A,X_12),inverse(identity)) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| multiply(X_12,A) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,X_12),inverse(identity)),multiply(X_12,A)) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
multiply(X_12,A) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,X_12),inverse(identity)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
multiply(multiply(X_12,inverse(inverse(X_32))),inverse(X_32)) = X_12,
inference(subst,[],[refute_0_208:[bind(X_10,$fot(inverse(X_32)))]]) ).
cnf(refute_0_235,plain,
multiply(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_10) = multiply(X_23,inverse(inverse(X_10))),
inference(subst,[],[refute_0_208:[bind(X_12,$fot(multiply(X_23,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_236,plain,
multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)) = X_23,
inference(subst,[],[refute_0_208:[bind(X_10,$fot(inverse(X_10))),bind(X_12,$fot(X_23))]]) ).
cnf(refute_0_237,plain,
( multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)) != X_23
| multiply(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_10) != multiply(X_23,inverse(inverse(X_10)))
| multiply(X_23,X_10) = multiply(X_23,inverse(inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_10),multiply(X_23,inverse(inverse(X_10)))) ),[0,0],$fot(X_23)]]) ).
cnf(refute_0_238,plain,
( multiply(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_10) != multiply(X_23,inverse(inverse(X_10)))
| multiply(X_23,X_10) = multiply(X_23,inverse(inverse(X_10))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_23) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
multiply(X_23,X_10) = multiply(X_23,inverse(inverse(X_10))),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_23,inverse(inverse(X_10))),inverse(X_10)),X_10),multiply(X_23,inverse(inverse(X_10)))) )],[refute_0_235,refute_0_238]) ).
cnf(refute_0_240,plain,
multiply(X_12,X_32) = multiply(X_12,inverse(inverse(X_32))),
inference(subst,[],[refute_0_239:[bind(X_10,$fot(X_32)),bind(X_23,$fot(X_12))]]) ).
cnf(refute_0_241,plain,
( multiply(X_12,X_32) != multiply(X_12,inverse(inverse(X_32)))
| multiply(X_12,inverse(inverse(X_32))) = multiply(X_12,X_32) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_12,X_32))),bind(Y,$fot(multiply(X_12,inverse(inverse(X_32)))))]]) ).
cnf(refute_0_242,plain,
multiply(X_12,inverse(inverse(X_32))) = multiply(X_12,X_32),
inference(resolve,[$cnf( $equal(multiply(X_12,X_32),multiply(X_12,inverse(inverse(X_32)))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
( multiply(X_12,inverse(inverse(X_32))) != multiply(X_12,X_32)
| multiply(multiply(X_12,inverse(inverse(X_32))),inverse(X_32)) != X_12
| multiply(multiply(X_12,X_32),inverse(X_32)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_12,inverse(inverse(X_32))),inverse(X_32)),X_12) ),[0,0],$fot(multiply(X_12,X_32))]]) ).
cnf(refute_0_244,plain,
( multiply(multiply(X_12,inverse(inverse(X_32))),inverse(X_32)) != X_12
| multiply(multiply(X_12,X_32),inverse(X_32)) = X_12 ),
inference(resolve,[$cnf( $equal(multiply(X_12,inverse(inverse(X_32))),multiply(X_12,X_32)) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
multiply(multiply(X_12,X_32),inverse(X_32)) = X_12,
inference(resolve,[$cnf( $equal(multiply(multiply(X_12,inverse(inverse(X_32))),inverse(X_32)),X_12) )],[refute_0_234,refute_0_244]) ).
cnf(refute_0_246,plain,
multiply(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),inverse(X_35)) = double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),
inference(subst,[],[refute_0_245:[bind(X_12,$fot(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))))),bind(X_32,$fot(X_35))]]) ).
cnf(refute_0_247,plain,
double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12,
inference(subst,[],[refute_0_30:[bind(A,$fot(X_10)),bind(B,$fot(inverse(X_10))),bind(C,$fot(X_12))]]) ).
cnf(refute_0_248,plain,
identity = double_divide(X_10,inverse(X_10)),
inference(subst,[],[identity:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_249,plain,
( identity != double_divide(X_10,inverse(X_10))
| double_divide(X_10,inverse(X_10)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_10,inverse(X_10))))]]) ).
cnf(refute_0_250,plain,
double_divide(X_10,inverse(X_10)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_10,inverse(X_10))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( double_divide(X_10,inverse(X_10)) != identity
| double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) ),[0,0,1,0,0],$fot(identity)]]) ).
cnf(refute_0_252,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(X_10)),identity) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(double_divide(X_10,inverse(X_10)),X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) )],[refute_0_247,refute_0_252]) ).
cnf(refute_0_254,plain,
double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) = multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10),
inference(subst,[],[refute_0_196:[bind(X_11,$fot(double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))))]]) ).
cnf(refute_0_255,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) != multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10)
| multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) ),[0],$fot(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10))]]) ).
cnf(refute_0_256,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)) != X_12
| multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)),multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_10))),X_10) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(identity,X_12),inverse(inverse(X_10)))),inverse(identity)),X_12) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35) = X_12,
inference(subst,[],[refute_0_257:[bind(X_10,$fot(X_35))]]) ).
cnf(refute_0_259,plain,
( multiply(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),inverse(X_35)) != double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))
| multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35) != X_12
| multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),inverse(X_35)),double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))) ),[0,0],$fot(X_12)]]) ).
cnf(refute_0_260,plain,
( multiply(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),inverse(X_35)) != double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))
| multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),X_12) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),X_35),inverse(X_35)),double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))) )],[refute_0_246,refute_0_260]) ).
cnf(refute_0_262,plain,
multiply(multiply(X_12,inverse(X_12)),inverse(inverse(X_12))) = X_12,
inference(subst,[],[refute_0_245:[bind(X_32,$fot(inverse(X_12)))]]) ).
cnf(refute_0_263,plain,
multiply(A,inverse(A)) = inverse(double_divide(inverse(A),A)),
inference(subst,[],[refute_0_48:[bind(B,$fot(inverse(A)))]]) ).
cnf(refute_0_264,plain,
identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_265,plain,
multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_48:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_266,plain,
( multiply(X_2,X_3) != inverse(double_divide(X_3,X_2))
| inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,X_3))),bind(Y,$fot(inverse(double_divide(X_3,X_2))))]]) ).
cnf(refute_0_267,plain,
inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_269,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_264,refute_0_269]) ).
cnf(refute_0_271,plain,
identity = double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),multiply(multiply(X_23,inverse(X_3)),X_3)),
inference(subst,[],[refute_0_270:[bind(X_2,$fot(multiply(X_23,inverse(X_3))))]]) ).
cnf(refute_0_272,plain,
multiply(multiply(X_23,inverse(X_3)),X_3) = X_23,
inference(subst,[],[refute_0_208:[bind(X_10,$fot(X_3)),bind(X_12,$fot(X_23))]]) ).
cnf(refute_0_273,plain,
( multiply(multiply(X_23,inverse(X_3)),X_3) != X_23
| identity != double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),multiply(multiply(X_23,inverse(X_3)),X_3))
| identity = double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),multiply(multiply(X_23,inverse(X_3)),X_3))) ),[1,1],$fot(X_23)]]) ).
cnf(refute_0_274,plain,
( identity != double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),multiply(multiply(X_23,inverse(X_3)),X_3))
| identity = double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),X_23) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_23,inverse(X_3)),X_3),X_23) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
identity = double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),X_23),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,multiply(X_23,inverse(X_3))),multiply(multiply(X_23,inverse(X_3)),X_3))) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
identity = double_divide(double_divide(inverse(X_32),multiply(X_23,inverse(inverse(X_32)))),X_23),
inference(subst,[],[refute_0_275:[bind(X_3,$fot(inverse(X_32)))]]) ).
cnf(refute_0_277,plain,
multiply(X_23,X_32) = multiply(X_23,inverse(inverse(X_32))),
inference(subst,[],[refute_0_239:[bind(X_10,$fot(X_32))]]) ).
cnf(refute_0_278,plain,
( multiply(X_23,X_32) != multiply(X_23,inverse(inverse(X_32)))
| multiply(X_23,inverse(inverse(X_32))) = multiply(X_23,X_32) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_23,X_32))),bind(Y,$fot(multiply(X_23,inverse(inverse(X_32)))))]]) ).
cnf(refute_0_279,plain,
multiply(X_23,inverse(inverse(X_32))) = multiply(X_23,X_32),
inference(resolve,[$cnf( $equal(multiply(X_23,X_32),multiply(X_23,inverse(inverse(X_32)))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
( multiply(X_23,inverse(inverse(X_32))) != multiply(X_23,X_32)
| identity != double_divide(double_divide(inverse(X_32),multiply(X_23,inverse(inverse(X_32)))),X_23)
| identity = double_divide(double_divide(inverse(X_32),multiply(X_23,X_32)),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(inverse(X_32),multiply(X_23,inverse(inverse(X_32)))),X_23)) ),[1,0,1],$fot(multiply(X_23,X_32))]]) ).
cnf(refute_0_281,plain,
( identity != double_divide(double_divide(inverse(X_32),multiply(X_23,inverse(inverse(X_32)))),X_23)
| identity = double_divide(double_divide(inverse(X_32),multiply(X_23,X_32)),X_23) ),
inference(resolve,[$cnf( $equal(multiply(X_23,inverse(inverse(X_32))),multiply(X_23,X_32)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
identity = double_divide(double_divide(inverse(X_32),multiply(X_23,X_32)),X_23),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(inverse(X_32),multiply(X_23,inverse(inverse(X_32)))),X_23)) )],[refute_0_276,refute_0_281]) ).
cnf(refute_0_283,plain,
identity = double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),multiply(X_38,double_divide(identity,multiply(X_38,identity)))),X_38),
inference(subst,[],[refute_0_282:[bind(X_23,$fot(X_38)),bind(X_32,$fot(double_divide(identity,multiply(X_38,identity))))]]) ).
cnf(refute_0_284,plain,
multiply(A,double_divide(identity,multiply(A,identity))) = inverse(double_divide(double_divide(identity,multiply(A,identity)),A)),
inference(subst,[],[refute_0_48:[bind(B,$fot(double_divide(identity,multiply(A,identity))))]]) ).
cnf(refute_0_285,plain,
identity = double_divide(double_divide(identity,multiply(X_24,inverse(identity))),X_24),
inference(subst,[],[refute_0_275:[bind(X_23,$fot(X_24)),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_286,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) = inverse(identity),
inference(subst,[],[refute_0_30:[bind(B,$fot(double_divide(multiply(X_14,A),inverse(X_14)))),bind(C,$fot(inverse(identity)))]]) ).
cnf(refute_0_287,plain,
double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)) = identity,
inference(subst,[],[refute_0_133:[bind(X_10,$fot(A)),bind(X_11,$fot(X_14))]]) ).
cnf(refute_0_288,plain,
( double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)) != identity
| double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) != inverse(identity)
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)),inverse(identity)) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_289,plain,
( double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) != inverse(identity)
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),identity) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(multiply(X_14,A),inverse(X_14))),inverse(identity)),inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)),inverse(identity)) )],[refute_0_286,refute_0_289]) ).
cnf(refute_0_291,plain,
double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) = multiply(double_divide(multiply(X_14,A),inverse(X_14)),A),
inference(subst,[],[refute_0_54:[bind(X_10,$fot(A)),bind(X_11,$fot(double_divide(multiply(X_14,A),inverse(X_14))))]]) ).
cnf(refute_0_292,plain,
( double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) != multiply(double_divide(multiply(X_14,A),inverse(X_14)),A)
| double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) != inverse(identity)
| multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)),inverse(identity)) ),[0],$fot(multiply(double_divide(multiply(X_14,A),inverse(X_14)),A))]]) ).
cnf(refute_0_293,plain,
( double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)) != inverse(identity)
| multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)),multiply(double_divide(multiply(X_14,A),inverse(X_14)),A)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(identity,inverse(double_divide(multiply(X_14,A),inverse(X_14))))),inverse(identity)),inverse(identity)) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10) = inverse(identity),
inference(subst,[],[refute_0_294:[bind(A,$fot(X_10)),bind(X_14,$fot(X_11))]]) ).
cnf(refute_0_296,plain,
double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10),
inference(subst,[],[refute_0_196:[bind(X_11,$fot(double_divide(multiply(X_11,X_10),inverse(X_11))))]]) ).
cnf(refute_0_297,plain,
( multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10) != inverse(identity)
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) != multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10)
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)))),bind(Y,$fot(multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10))),bind(Z,$fot(inverse(identity)))]]) ).
cnf(refute_0_298,plain,
( multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10) != inverse(identity)
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)),multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(double_divide(multiply(X_11,X_10),inverse(X_11)),X_10),inverse(identity)) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
( double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) != identity
| double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) != inverse(identity)
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_301,plain,
( double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)) != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)),inverse(identity)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(multiply(X_11,X_10),inverse(X_11))),inverse(identity)),identity) )],[refute_0_133,refute_0_301]) ).
cnf(refute_0_303,plain,
( identity != double_divide(double_divide(identity,multiply(X_24,inverse(identity))),X_24)
| inverse(identity) != identity
| identity = double_divide(double_divide(identity,multiply(X_24,identity)),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(X_24,inverse(identity))),X_24)) ),[1,0,1,1],$fot(identity)]]) ).
cnf(refute_0_304,plain,
( identity != double_divide(double_divide(identity,multiply(X_24,inverse(identity))),X_24)
| identity = double_divide(double_divide(identity,multiply(X_24,identity)),X_24) ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
identity = double_divide(double_divide(identity,multiply(X_24,identity)),X_24),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(X_24,inverse(identity))),X_24)) )],[refute_0_285,refute_0_304]) ).
cnf(refute_0_306,plain,
identity = double_divide(double_divide(identity,multiply(A,identity)),A),
inference(subst,[],[refute_0_305:[bind(X_24,$fot(A))]]) ).
cnf(refute_0_307,plain,
( identity != double_divide(double_divide(identity,multiply(A,identity)),A)
| double_divide(double_divide(identity,multiply(A,identity)),A) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(identity,multiply(A,identity)),A)))]]) ).
cnf(refute_0_308,plain,
double_divide(double_divide(identity,multiply(A,identity)),A) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(A,identity)),A)) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
( multiply(A,double_divide(identity,multiply(A,identity))) != inverse(double_divide(double_divide(identity,multiply(A,identity)),A))
| double_divide(double_divide(identity,multiply(A,identity)),A) != identity
| multiply(A,double_divide(identity,multiply(A,identity))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,double_divide(identity,multiply(A,identity))),inverse(double_divide(double_divide(identity,multiply(A,identity)),A))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_310,plain,
( multiply(A,double_divide(identity,multiply(A,identity))) != inverse(double_divide(double_divide(identity,multiply(A,identity)),A))
| multiply(A,double_divide(identity,multiply(A,identity))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(A,identity)),A),identity) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
multiply(A,double_divide(identity,multiply(A,identity))) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(A,double_divide(identity,multiply(A,identity))),inverse(double_divide(double_divide(identity,multiply(A,identity)),A))) )],[refute_0_284,refute_0_310]) ).
cnf(refute_0_312,plain,
( multiply(A,double_divide(identity,multiply(A,identity))) != inverse(identity)
| inverse(identity) != identity
| multiply(A,double_divide(identity,multiply(A,identity))) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,double_divide(identity,multiply(A,identity))),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_313,plain,
( multiply(A,double_divide(identity,multiply(A,identity))) != inverse(identity)
| multiply(A,double_divide(identity,multiply(A,identity))) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_312]) ).
cnf(refute_0_314,plain,
multiply(A,double_divide(identity,multiply(A,identity))) = identity,
inference(resolve,[$cnf( $equal(multiply(A,double_divide(identity,multiply(A,identity))),inverse(identity)) )],[refute_0_311,refute_0_313]) ).
cnf(refute_0_315,plain,
multiply(X_38,double_divide(identity,multiply(X_38,identity))) = identity,
inference(subst,[],[refute_0_314:[bind(A,$fot(X_38))]]) ).
cnf(refute_0_316,plain,
( multiply(X_38,double_divide(identity,multiply(X_38,identity))) != identity
| identity != double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),multiply(X_38,double_divide(identity,multiply(X_38,identity)))),X_38)
| identity = double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),multiply(X_38,double_divide(identity,multiply(X_38,identity)))),X_38)) ),[1,0,1],$fot(identity)]]) ).
cnf(refute_0_317,plain,
( identity != double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),multiply(X_38,double_divide(identity,multiply(X_38,identity)))),X_38)
| identity = double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) ),
inference(resolve,[$cnf( $equal(multiply(X_38,double_divide(identity,multiply(X_38,identity))),identity) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
identity = double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),multiply(X_38,double_divide(identity,multiply(X_38,identity)))),X_38)) )],[refute_0_283,refute_0_317]) ).
cnf(refute_0_319,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) = C,
inference(subst,[],[refute_0_30:[bind(A,$fot(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))))),bind(B,$fot(inverse(identity)))]]) ).
cnf(refute_0_320,plain,
double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)) = identity,
inference(subst,[],[refute_0_145:[bind(X_13,$fot(X_20))]]) ).
cnf(refute_0_321,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)) != identity
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)),C) ),[0,0,1,0,0],$fot(identity)]]) ).
cnf(refute_0_322,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),identity) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),inverse(identity)),C),inverse(inverse(identity)))),inverse(identity)),C) )],[refute_0_319,refute_0_322]) ).
cnf(refute_0_324,plain,
inverse(double_divide(identity,C)) = multiply(C,identity),
inference(subst,[],[refute_0_50:[bind(A,$fot(C)),bind(B,$fot(identity))]]) ).
cnf(refute_0_325,plain,
double_divide(double_divide(identity,C),identity) = inverse(double_divide(identity,C)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,C)))]]) ).
cnf(refute_0_326,plain,
( double_divide(double_divide(identity,C),identity) != inverse(double_divide(identity,C))
| inverse(double_divide(identity,C)) != multiply(C,identity)
| double_divide(double_divide(identity,C),identity) = multiply(C,identity) ),
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,$fot(multiply(C,identity)))]]) ).
cnf(refute_0_327,plain,
( inverse(double_divide(identity,C)) != multiply(C,identity)
| double_divide(double_divide(identity,C),identity) = multiply(C,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),inverse(double_divide(identity,C))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
double_divide(double_divide(identity,C),identity) = multiply(C,identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,C)),multiply(C,identity)) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
double_divide(double_divide(identity,C),inverse(inverse(identity))) = double_divide(double_divide(identity,C),inverse(inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,C),inverse(inverse(identity))))]]) ).
cnf(refute_0_330,plain,
( double_divide(double_divide(identity,C),inverse(inverse(identity))) != double_divide(double_divide(identity,C),inverse(inverse(identity)))
| inverse(inverse(identity)) != identity
| double_divide(double_divide(identity,C),inverse(inverse(identity))) = double_divide(double_divide(identity,C),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(inverse(identity))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_331,plain,
( inverse(inverse(identity)) != identity
| double_divide(double_divide(identity,C),inverse(inverse(identity))) = double_divide(double_divide(identity,C),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(inverse(identity))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
double_divide(double_divide(identity,C),inverse(inverse(identity))) = double_divide(double_divide(identity,C),identity),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_163,refute_0_331]) ).
cnf(refute_0_333,plain,
( double_divide(double_divide(identity,C),identity) != multiply(C,identity)
| double_divide(double_divide(identity,C),inverse(inverse(identity))) != double_divide(double_divide(identity,C),identity)
| double_divide(double_divide(identity,C),inverse(inverse(identity))) = multiply(C,identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(identity,C),inverse(inverse(identity))))),bind(Y,$fot(double_divide(double_divide(identity,C),identity))),bind(Z,$fot(multiply(C,identity)))]]) ).
cnf(refute_0_334,plain,
( double_divide(double_divide(identity,C),identity) != multiply(C,identity)
| double_divide(double_divide(identity,C),inverse(inverse(identity))) = multiply(C,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(inverse(identity))),double_divide(double_divide(identity,C),identity)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
double_divide(double_divide(identity,C),inverse(inverse(identity))) = multiply(C,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),identity),multiply(C,identity)) )],[refute_0_328,refute_0_334]) ).
cnf(refute_0_336,plain,
double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) = double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))))]]) ).
cnf(refute_0_337,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) != double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity))))
| double_divide(double_divide(identity,C),inverse(inverse(identity))) != multiply(C,identity)
| double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) = double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity))))) ),[1,1],$fot(multiply(C,identity))]]) ).
cnf(refute_0_338,plain,
( double_divide(double_divide(identity,C),inverse(inverse(identity))) != multiply(C,identity)
| double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) = double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity))))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) = double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,C),inverse(inverse(identity))),multiply(C,identity)) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)))]]) ).
cnf(refute_0_341,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) != double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) != double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity))) ),[1,0],$fot(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)))]]) ).
cnf(refute_0_342,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))) != double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) = double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) != double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),C) ),[0],$fot(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)))]]) ).
cnf(refute_0_345,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)) != C
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(double_divide(identity,C),inverse(inverse(identity)))),inverse(identity)),C) )],[refute_0_323,refute_0_345]) ).
cnf(refute_0_347,plain,
inverse(double_divide(identity,multiply(C,identity))) = multiply(multiply(C,identity),identity),
inference(subst,[],[refute_0_50:[bind(A,$fot(multiply(C,identity))),bind(B,$fot(identity))]]) ).
cnf(refute_0_348,plain,
double_divide(double_divide(identity,multiply(C,identity)),identity) = inverse(double_divide(identity,multiply(C,identity))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,multiply(C,identity))))]]) ).
cnf(refute_0_349,plain,
( double_divide(double_divide(identity,multiply(C,identity)),identity) != inverse(double_divide(identity,multiply(C,identity)))
| inverse(double_divide(identity,multiply(C,identity))) != multiply(multiply(C,identity),identity)
| double_divide(double_divide(identity,multiply(C,identity)),identity) = multiply(multiply(C,identity),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(identity,multiply(C,identity)),identity))),bind(Y,$fot(inverse(double_divide(identity,multiply(C,identity))))),bind(Z,$fot(multiply(multiply(C,identity),identity)))]]) ).
cnf(refute_0_350,plain,
( inverse(double_divide(identity,multiply(C,identity))) != multiply(multiply(C,identity),identity)
| double_divide(double_divide(identity,multiply(C,identity)),identity) = multiply(multiply(C,identity),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(C,identity)),identity),inverse(double_divide(identity,multiply(C,identity)))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
double_divide(double_divide(identity,multiply(C,identity)),identity) = multiply(multiply(C,identity),identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,multiply(C,identity))),multiply(multiply(C,identity),identity)) )],[refute_0_347,refute_0_350]) ).
cnf(refute_0_352,plain,
double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)))]]) ).
cnf(refute_0_353,plain,
( double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(C,identity)),inverse(identity))
| inverse(identity) != identity
| double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)),double_divide(double_divide(identity,multiply(C,identity)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_354,plain,
( inverse(identity) != identity
| double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)),double_divide(double_divide(identity,multiply(C,identity)),inverse(identity))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_354]) ).
cnf(refute_0_356,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_357,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_356]) ).
cnf(refute_0_358,plain,
double_divide(X_20,inverse(X_20)) = identity,
inference(subst,[],[refute_0_357:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_359,plain,
double_divide(identity,inverse(inverse(X_20))) = inverse(X_20),
inference(subst,[],[refute_0_184:[bind(C,$fot(inverse(X_20)))]]) ).
cnf(refute_0_360,plain,
double_divide(inverse(identity),inverse(inverse(X_20))) = double_divide(inverse(identity),inverse(inverse(X_20))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),inverse(inverse(X_20))))]]) ).
cnf(refute_0_361,plain,
( double_divide(inverse(identity),inverse(inverse(X_20))) != double_divide(inverse(identity),inverse(inverse(X_20)))
| inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(X_20))) = double_divide(identity,inverse(inverse(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(X_20))),double_divide(inverse(identity),inverse(inverse(X_20)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_362,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),inverse(inverse(X_20))) = double_divide(identity,inverse(inverse(X_20))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(X_20))),double_divide(inverse(identity),inverse(inverse(X_20)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
double_divide(inverse(identity),inverse(inverse(X_20))) = double_divide(identity,inverse(inverse(X_20))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_362]) ).
cnf(refute_0_364,plain,
( double_divide(identity,inverse(inverse(X_20))) != inverse(X_20)
| double_divide(inverse(identity),inverse(inverse(X_20))) != double_divide(identity,inverse(inverse(X_20)))
| double_divide(inverse(identity),inverse(inverse(X_20))) = inverse(X_20) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(identity),inverse(inverse(X_20))))),bind(Y,$fot(double_divide(identity,inverse(inverse(X_20))))),bind(Z,$fot(inverse(X_20)))]]) ).
cnf(refute_0_365,plain,
( double_divide(identity,inverse(inverse(X_20))) != inverse(X_20)
| double_divide(inverse(identity),inverse(inverse(X_20))) = inverse(X_20) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(X_20))),double_divide(identity,inverse(inverse(X_20)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
double_divide(inverse(identity),inverse(inverse(X_20))) = inverse(X_20),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(X_20))),inverse(X_20)) )],[refute_0_359,refute_0_365]) ).
cnf(refute_0_367,plain,
double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),
introduced(tautology,[refl,[$fot(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))))]]) ).
cnf(refute_0_368,plain,
( double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) != double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20))))
| double_divide(inverse(identity),inverse(inverse(X_20))) != inverse(X_20)
| double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = double_divide(X_20,inverse(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20))))) ),[1,1],$fot(inverse(X_20))]]) ).
cnf(refute_0_369,plain,
( double_divide(inverse(identity),inverse(inverse(X_20))) != inverse(X_20)
| double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = double_divide(X_20,inverse(X_20)) ),
inference(resolve,[$cnf( $equal(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20))))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = double_divide(X_20,inverse(X_20)),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(X_20))),inverse(X_20)) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
( double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) != double_divide(X_20,inverse(X_20))
| double_divide(X_20,inverse(X_20)) != identity
| double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = identity ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))))),bind(Y,$fot(double_divide(X_20,inverse(X_20)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_372,plain,
( double_divide(X_20,inverse(X_20)) != identity
| double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),double_divide(X_20,inverse(X_20))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) = identity,
inference(resolve,[$cnf( $equal(double_divide(X_20,inverse(X_20)),identity) )],[refute_0_358,refute_0_372]) ).
cnf(refute_0_374,plain,
double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) = double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)))]]) ).
cnf(refute_0_375,plain,
( double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) != identity
| double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) != double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))
| double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) = double_divide(identity,multiply(C,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_376,plain,
( double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))) != identity
| double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) = double_divide(identity,multiply(C,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) = double_divide(identity,multiply(C,identity)),
inference(resolve,[$cnf( $equal(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),identity) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)))]]) ).
cnf(refute_0_379,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) != double_divide(identity,multiply(C,identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity))) ),[1,0],$fot(double_divide(identity,multiply(C,identity)))]]) ).
cnf(refute_0_380,plain,
( double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)) != double_divide(identity,multiply(C,identity))
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),double_divide(identity,multiply(C,identity))) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(C,identity)),inverse(identity))
| double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(C,identity)),identity)
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)))),bind(Z,$fot(double_divide(double_divide(identity,multiply(C,identity)),identity)))]]) ).
cnf(refute_0_383,plain,
( double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(C,identity)),identity)
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),double_divide(double_divide(identity,multiply(C,identity)),inverse(identity))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = double_divide(double_divide(identity,multiply(C,identity)),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(C,identity)),inverse(identity)),double_divide(double_divide(identity,multiply(C,identity)),identity)) )],[refute_0_355,refute_0_383]) ).
cnf(refute_0_385,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != double_divide(double_divide(identity,multiply(C,identity)),identity)
| double_divide(double_divide(identity,multiply(C,identity)),identity) != multiply(multiply(C,identity),identity)
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = multiply(multiply(C,identity),identity) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)))),bind(Y,$fot(double_divide(double_divide(identity,multiply(C,identity)),identity))),bind(Z,$fot(multiply(multiply(C,identity),identity)))]]) ).
cnf(refute_0_386,plain,
( double_divide(double_divide(identity,multiply(C,identity)),identity) != multiply(multiply(C,identity),identity)
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = multiply(multiply(C,identity),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),double_divide(double_divide(identity,multiply(C,identity)),identity)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) = multiply(multiply(C,identity),identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(C,identity)),identity),multiply(multiply(C,identity),identity)) )],[refute_0_351,refute_0_386]) ).
cnf(refute_0_388,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != C
| double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != multiply(multiply(C,identity),identity)
| multiply(multiply(C,identity),identity) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),C) ),[0],$fot(multiply(multiply(C,identity),identity))]]) ).
cnf(refute_0_389,plain,
( double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)) != C
| multiply(multiply(C,identity),identity) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),multiply(multiply(C,identity),identity)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
multiply(multiply(C,identity),identity) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_20,double_divide(inverse(identity),inverse(inverse(X_20)))),multiply(C,identity)),inverse(identity)),C) )],[refute_0_346,refute_0_389]) ).
cnf(refute_0_391,plain,
multiply(multiply(X_38,identity),identity) = X_38,
inference(subst,[],[refute_0_390:[bind(C,$fot(X_38))]]) ).
cnf(refute_0_392,plain,
inverse(double_divide(identity,multiply(X_38,identity))) = multiply(multiply(X_38,identity),identity),
inference(subst,[],[refute_0_50:[bind(A,$fot(multiply(X_38,identity))),bind(B,$fot(identity))]]) ).
cnf(refute_0_393,plain,
( multiply(multiply(X_38,identity),identity) != X_38
| inverse(double_divide(identity,multiply(X_38,identity))) != multiply(multiply(X_38,identity),identity)
| inverse(double_divide(identity,multiply(X_38,identity))) = X_38 ),
inference(subst,[],[refute_0_24:[bind(X,$fot(inverse(double_divide(identity,multiply(X_38,identity))))),bind(Y,$fot(multiply(multiply(X_38,identity),identity))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_394,plain,
( multiply(multiply(X_38,identity),identity) != X_38
| inverse(double_divide(identity,multiply(X_38,identity))) = X_38 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,multiply(X_38,identity))),multiply(multiply(X_38,identity),identity)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
inverse(double_divide(identity,multiply(X_38,identity))) = X_38,
inference(resolve,[$cnf( $equal(multiply(multiply(X_38,identity),identity),X_38) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
inverse(inverse(double_divide(identity,multiply(X_38,identity)))) = inverse(inverse(double_divide(identity,multiply(X_38,identity)))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(identity,multiply(X_38,identity)))))]]) ).
cnf(refute_0_397,plain,
( inverse(double_divide(identity,multiply(X_38,identity))) != X_38
| inverse(inverse(double_divide(identity,multiply(X_38,identity)))) != inverse(inverse(double_divide(identity,multiply(X_38,identity))))
| inverse(inverse(double_divide(identity,multiply(X_38,identity)))) = inverse(X_38) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(identity,multiply(X_38,identity)))),inverse(inverse(double_divide(identity,multiply(X_38,identity))))) ),[1,0],$fot(X_38)]]) ).
cnf(refute_0_398,plain,
( inverse(double_divide(identity,multiply(X_38,identity))) != X_38
| inverse(inverse(double_divide(identity,multiply(X_38,identity)))) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,multiply(X_38,identity)))),inverse(inverse(double_divide(identity,multiply(X_38,identity))))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
inverse(inverse(double_divide(identity,multiply(X_38,identity)))) = inverse(X_38),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,multiply(X_38,identity))),X_38) )],[refute_0_395,refute_0_398]) ).
cnf(refute_0_400,plain,
double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) = inverse(inverse(double_divide(identity,multiply(X_38,identity)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(double_divide(identity,multiply(X_38,identity)))))]]) ).
cnf(refute_0_401,plain,
( double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) != inverse(inverse(double_divide(identity,multiply(X_38,identity))))
| inverse(inverse(double_divide(identity,multiply(X_38,identity)))) != inverse(X_38)
| double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) = inverse(X_38) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity))),bind(Y,$fot(inverse(inverse(double_divide(identity,multiply(X_38,identity)))))),bind(Z,$fot(inverse(X_38)))]]) ).
cnf(refute_0_402,plain,
( inverse(inverse(double_divide(identity,multiply(X_38,identity)))) != inverse(X_38)
| double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) = inverse(X_38) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),inverse(inverse(double_divide(identity,multiply(X_38,identity))))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) = inverse(X_38),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(identity,multiply(X_38,identity)))),inverse(X_38)) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) = double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38))]]) ).
cnf(refute_0_405,plain,
( double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) != double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)
| double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) != inverse(X_38)
| double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) = double_divide(inverse(X_38),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38),double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)) ),[1,0],$fot(inverse(X_38))]]) ).
cnf(refute_0_406,plain,
( double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity) != inverse(X_38)
| double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) = double_divide(inverse(X_38),X_38) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38),double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) = double_divide(inverse(X_38),X_38),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),inverse(X_38)) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
( double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38) != double_divide(inverse(X_38),X_38)
| identity != double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)
| identity = double_divide(inverse(X_38),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)) ),[1],$fot(double_divide(inverse(X_38),X_38))]]) ).
cnf(refute_0_409,plain,
( identity != double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)
| identity = double_divide(inverse(X_38),X_38) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38),double_divide(inverse(X_38),X_38)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
identity = double_divide(inverse(X_38),X_38),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(inverse(double_divide(identity,multiply(X_38,identity))),identity),X_38)) )],[refute_0_318,refute_0_409]) ).
cnf(refute_0_411,plain,
identity = double_divide(inverse(A),A),
inference(subst,[],[refute_0_410:[bind(X_38,$fot(A))]]) ).
cnf(refute_0_412,plain,
( identity != double_divide(inverse(A),A)
| double_divide(inverse(A),A) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(inverse(A),A)))]]) ).
cnf(refute_0_413,plain,
double_divide(inverse(A),A) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(A),A)) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
( multiply(A,inverse(A)) != inverse(double_divide(inverse(A),A))
| double_divide(inverse(A),A) != identity
| multiply(A,inverse(A)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(A,inverse(A)),inverse(double_divide(inverse(A),A))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_415,plain,
( multiply(A,inverse(A)) != inverse(double_divide(inverse(A),A))
| multiply(A,inverse(A)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(A),A),identity) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
multiply(A,inverse(A)) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(A,inverse(A)),inverse(double_divide(inverse(A),A))) )],[refute_0_263,refute_0_415]) ).
cnf(refute_0_417,plain,
( multiply(A,inverse(A)) != inverse(identity)
| inverse(identity) != identity
| multiply(A,inverse(A)) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,inverse(A)),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_418,plain,
( multiply(A,inverse(A)) != inverse(identity)
| multiply(A,inverse(A)) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_417]) ).
cnf(refute_0_419,plain,
multiply(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(multiply(A,inverse(A)),inverse(identity)) )],[refute_0_416,refute_0_418]) ).
cnf(refute_0_420,plain,
multiply(X_12,inverse(X_12)) = identity,
inference(subst,[],[refute_0_419:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_421,plain,
( multiply(X_12,inverse(X_12)) != identity
| multiply(multiply(X_12,inverse(X_12)),inverse(inverse(X_12))) != X_12
| multiply(identity,inverse(inverse(X_12))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_12,inverse(X_12)),inverse(inverse(X_12))),X_12) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_422,plain,
( multiply(multiply(X_12,inverse(X_12)),inverse(inverse(X_12))) != X_12
| multiply(identity,inverse(inverse(X_12))) = X_12 ),
inference(resolve,[$cnf( $equal(multiply(X_12,inverse(X_12)),identity) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
multiply(identity,inverse(inverse(X_12))) = X_12,
inference(resolve,[$cnf( $equal(multiply(multiply(X_12,inverse(X_12)),inverse(inverse(X_12))),X_12) )],[refute_0_262,refute_0_422]) ).
cnf(refute_0_424,plain,
multiply(identity,X_12) = inverse(inverse(X_12)),
inference(subst,[],[refute_0_76:[bind(X_3,$fot(X_12))]]) ).
cnf(refute_0_425,plain,
( multiply(X_23,X_10) != multiply(X_23,inverse(inverse(X_10)))
| multiply(X_23,inverse(inverse(X_10))) = multiply(X_23,X_10) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_23,X_10))),bind(Y,$fot(multiply(X_23,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_426,plain,
multiply(X_23,inverse(inverse(X_10))) = multiply(X_23,X_10),
inference(resolve,[$cnf( $equal(multiply(X_23,X_10),multiply(X_23,inverse(inverse(X_10)))) )],[refute_0_239,refute_0_425]) ).
cnf(refute_0_427,plain,
multiply(identity,inverse(inverse(X_12))) = multiply(identity,X_12),
inference(subst,[],[refute_0_426:[bind(X_10,$fot(X_12)),bind(X_23,$fot(identity))]]) ).
cnf(refute_0_428,plain,
( multiply(identity,X_12) != inverse(inverse(X_12))
| multiply(identity,inverse(inverse(X_12))) != multiply(identity,X_12)
| multiply(identity,inverse(inverse(X_12))) = inverse(inverse(X_12)) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(multiply(identity,inverse(inverse(X_12))))),bind(Y,$fot(multiply(identity,X_12))),bind(Z,$fot(inverse(inverse(X_12))))]]) ).
cnf(refute_0_429,plain,
( multiply(identity,X_12) != inverse(inverse(X_12))
| multiply(identity,inverse(inverse(X_12))) = inverse(inverse(X_12)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(inverse(X_12))),multiply(identity,X_12)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
multiply(identity,inverse(inverse(X_12))) = inverse(inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(identity,X_12),inverse(inverse(X_12))) )],[refute_0_424,refute_0_429]) ).
cnf(refute_0_431,plain,
( multiply(identity,inverse(inverse(X_12))) != X_12
| multiply(identity,inverse(inverse(X_12))) != inverse(inverse(X_12))
| inverse(inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(inverse(X_12))),X_12) ),[0],$fot(inverse(inverse(X_12)))]]) ).
cnf(refute_0_432,plain,
( multiply(identity,inverse(inverse(X_12))) != X_12
| inverse(inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(inverse(X_12))),inverse(inverse(X_12))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
inverse(inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(multiply(identity,inverse(inverse(X_12))),X_12) )],[refute_0_423,refute_0_432]) ).
cnf(refute_0_434,plain,
inverse(inverse(X_35)) = X_35,
inference(subst,[],[refute_0_433:[bind(X_12,$fot(X_35))]]) ).
cnf(refute_0_435,plain,
double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) = double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))))]]) ).
cnf(refute_0_436,plain,
( double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) != double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))
| inverse(inverse(X_35)) != X_35
| double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) = double_divide(double_divide(identity,X_12),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_437,plain,
( inverse(inverse(X_35)) != X_35
| double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) = double_divide(double_divide(identity,X_12),X_35) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) = double_divide(double_divide(identity,X_12),X_35),
inference(resolve,[$cnf( $equal(inverse(inverse(X_35)),X_35) )],[refute_0_434,refute_0_437]) ).
cnf(refute_0_439,plain,
( multiply(X_12,inverse(X_35)) != double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))
| double_divide(double_divide(identity,X_12),inverse(inverse(X_35))) != double_divide(double_divide(identity,X_12),X_35)
| multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_12,inverse(X_35)),double_divide(double_divide(identity,X_12),X_35)) ),[0],$fot(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))))]]) ).
cnf(refute_0_440,plain,
( multiply(X_12,inverse(X_35)) != double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))
| multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),X_35) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_12),inverse(inverse(X_35))),double_divide(double_divide(identity,X_12),X_35)) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
multiply(X_12,inverse(X_35)) = double_divide(double_divide(identity,X_12),X_35),
inference(resolve,[$cnf( $equal(multiply(X_12,inverse(X_35)),double_divide(double_divide(identity,X_12),inverse(inverse(X_35)))) )],[refute_0_261,refute_0_440]) ).
cnf(refute_0_442,plain,
inverse(inverse(double_divide(B,A))) = double_divide(B,A),
inference(subst,[],[refute_0_433:[bind(X_12,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_443,plain,
( inverse(double_divide(B,A)) != multiply(A,B)
| inverse(inverse(double_divide(B,A))) != double_divide(B,A)
| inverse(multiply(A,B)) = double_divide(B,A) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(B,A))),double_divide(B,A)) ),[0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_444,plain,
( inverse(inverse(double_divide(B,A))) != double_divide(B,A)
| inverse(multiply(A,B)) = double_divide(B,A) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_50,refute_0_443]) ).
cnf(refute_0_445,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(B,A))),double_divide(B,A)) )],[refute_0_442,refute_0_444]) ).
cnf(refute_0_446,plain,
inverse(multiply(X_54,identity)) = double_divide(identity,X_54),
inference(subst,[],[refute_0_445:[bind(A,$fot(X_54)),bind(B,$fot(identity))]]) ).
cnf(refute_0_447,plain,
multiply(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),X_28) = multiply(inverse(inverse(X_28)),inverse(identity)),
inference(subst,[],[refute_0_257:[bind(X_10,$fot(X_28)),bind(X_12,$fot(multiply(inverse(inverse(X_28)),inverse(identity))))]]) ).
cnf(refute_0_448,plain,
identity = double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),
inference(subst,[],[refute_0_275:[bind(X_23,$fot(inverse(inverse(X_28)))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_449,plain,
( identity != double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28)))
| double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28)))))]]) ).
cnf(refute_0_450,plain,
double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28)))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
( multiply(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),X_28) != multiply(inverse(inverse(X_28)),inverse(identity))
| double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))) != identity
| multiply(identity,X_28) = multiply(inverse(inverse(X_28)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),X_28),multiply(inverse(inverse(X_28)),inverse(identity))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_452,plain,
( multiply(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),X_28) != multiply(inverse(inverse(X_28)),inverse(identity))
| multiply(identity,X_28) = multiply(inverse(inverse(X_28)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),identity) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
multiply(identity,X_28) = multiply(inverse(inverse(X_28)),inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(double_divide(double_divide(identity,multiply(inverse(inverse(X_28)),inverse(identity))),inverse(inverse(X_28))),X_28),multiply(inverse(inverse(X_28)),inverse(identity))) )],[refute_0_447,refute_0_452]) ).
cnf(refute_0_454,plain,
multiply(identity,X_28) = inverse(inverse(X_28)),
inference(subst,[],[refute_0_76:[bind(X_3,$fot(X_28))]]) ).
cnf(refute_0_455,plain,
( multiply(identity,X_28) != multiply(inverse(inverse(X_28)),inverse(identity))
| multiply(identity,X_28) != inverse(inverse(X_28))
| inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_28),multiply(inverse(inverse(X_28)),inverse(identity))) ),[0],$fot(inverse(inverse(X_28)))]]) ).
cnf(refute_0_456,plain,
( multiply(identity,X_28) != multiply(inverse(inverse(X_28)),inverse(identity))
| inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_28),inverse(inverse(X_28))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
multiply(inverse(inverse(X_28)),inverse(identity)) = multiply(inverse(inverse(X_28)),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_28)),inverse(identity)))]]) ).
cnf(refute_0_458,plain,
( multiply(inverse(inverse(X_28)),inverse(identity)) != multiply(inverse(inverse(X_28)),inverse(identity))
| inverse(identity) != identity
| multiply(inverse(inverse(X_28)),inverse(identity)) = multiply(inverse(inverse(X_28)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_28)),inverse(identity)),multiply(inverse(inverse(X_28)),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_459,plain,
( inverse(identity) != identity
| multiply(inverse(inverse(X_28)),inverse(identity)) = multiply(inverse(inverse(X_28)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_28)),inverse(identity)),multiply(inverse(inverse(X_28)),inverse(identity))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
multiply(inverse(inverse(X_28)),inverse(identity)) = multiply(inverse(inverse(X_28)),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_459]) ).
cnf(refute_0_461,plain,
( multiply(inverse(inverse(X_28)),inverse(identity)) != multiply(inverse(inverse(X_28)),identity)
| inverse(inverse(X_28)) != multiply(inverse(inverse(X_28)),inverse(identity))
| inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_28)),multiply(inverse(inverse(X_28)),inverse(identity))) ),[1],$fot(multiply(inverse(inverse(X_28)),identity))]]) ).
cnf(refute_0_462,plain,
( inverse(inverse(X_28)) != multiply(inverse(inverse(X_28)),inverse(identity))
| inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_28)),inverse(identity)),multiply(inverse(inverse(X_28)),identity)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
( multiply(identity,X_28) != multiply(inverse(inverse(X_28)),inverse(identity))
| inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_28)),multiply(inverse(inverse(X_28)),inverse(identity))) )],[refute_0_456,refute_0_462]) ).
cnf(refute_0_464,plain,
inverse(inverse(X_28)) = multiply(inverse(inverse(X_28)),identity),
inference(resolve,[$cnf( $equal(multiply(identity,X_28),multiply(inverse(inverse(X_28)),inverse(identity))) )],[refute_0_453,refute_0_463]) ).
cnf(refute_0_465,plain,
inverse(inverse(X_28)) = X_28,
inference(subst,[],[refute_0_433:[bind(X_12,$fot(X_28))]]) ).
cnf(refute_0_466,plain,
( inverse(inverse(X_28)) != X_28
| inverse(inverse(X_28)) != multiply(inverse(inverse(X_28)),identity)
| X_28 = multiply(inverse(inverse(X_28)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_28)),multiply(inverse(inverse(X_28)),identity)) ),[0],$fot(X_28)]]) ).
cnf(refute_0_467,plain,
( inverse(inverse(X_28)) != multiply(inverse(inverse(X_28)),identity)
| X_28 = multiply(inverse(inverse(X_28)),identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_28)),X_28) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
multiply(inverse(inverse(X_28)),identity) = multiply(inverse(inverse(X_28)),identity),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_28)),identity))]]) ).
cnf(refute_0_469,plain,
( multiply(inverse(inverse(X_28)),identity) != multiply(inverse(inverse(X_28)),identity)
| inverse(inverse(X_28)) != X_28
| multiply(inverse(inverse(X_28)),identity) = multiply(X_28,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_28)),identity),multiply(inverse(inverse(X_28)),identity)) ),[1,0],$fot(X_28)]]) ).
cnf(refute_0_470,plain,
( inverse(inverse(X_28)) != X_28
| multiply(inverse(inverse(X_28)),identity) = multiply(X_28,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_28)),identity),multiply(inverse(inverse(X_28)),identity)) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
multiply(inverse(inverse(X_28)),identity) = multiply(X_28,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_28)),X_28) )],[refute_0_465,refute_0_470]) ).
cnf(refute_0_472,plain,
( X_28 != multiply(inverse(inverse(X_28)),identity)
| multiply(inverse(inverse(X_28)),identity) != multiply(X_28,identity)
| X_28 = multiply(X_28,identity) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_28,multiply(X_28,identity)) ),[0],$fot(multiply(inverse(inverse(X_28)),identity))]]) ).
cnf(refute_0_473,plain,
( X_28 != multiply(inverse(inverse(X_28)),identity)
| X_28 = multiply(X_28,identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_28)),identity),multiply(X_28,identity)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
( inverse(inverse(X_28)) != multiply(inverse(inverse(X_28)),identity)
| X_28 = multiply(X_28,identity) ),
inference(resolve,[$cnf( $equal(X_28,multiply(inverse(inverse(X_28)),identity)) )],[refute_0_467,refute_0_473]) ).
cnf(refute_0_475,plain,
X_28 = multiply(X_28,identity),
inference(resolve,[$cnf( $equal(inverse(inverse(X_28)),multiply(inverse(inverse(X_28)),identity)) )],[refute_0_464,refute_0_474]) ).
cnf(refute_0_476,plain,
X_54 = multiply(X_54,identity),
inference(subst,[],[refute_0_475:[bind(X_28,$fot(X_54))]]) ).
cnf(refute_0_477,plain,
( X_54 != multiply(X_54,identity)
| multiply(X_54,identity) = X_54 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_54)),bind(Y,$fot(multiply(X_54,identity)))]]) ).
cnf(refute_0_478,plain,
multiply(X_54,identity) = X_54,
inference(resolve,[$cnf( $equal(X_54,multiply(X_54,identity)) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
( multiply(X_54,identity) != X_54
| inverse(multiply(X_54,identity)) != double_divide(identity,X_54)
| inverse(X_54) = double_divide(identity,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_54,identity)),double_divide(identity,X_54)) ),[0,0],$fot(X_54)]]) ).
cnf(refute_0_480,plain,
( inverse(multiply(X_54,identity)) != double_divide(identity,X_54)
| inverse(X_54) = double_divide(identity,X_54) ),
inference(resolve,[$cnf( $equal(multiply(X_54,identity),X_54) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
inverse(X_54) = double_divide(identity,X_54),
inference(resolve,[$cnf( $equal(inverse(multiply(X_54,identity)),double_divide(identity,X_54)) )],[refute_0_446,refute_0_480]) ).
cnf(refute_0_482,plain,
( inverse(X_54) != double_divide(identity,X_54)
| double_divide(identity,X_54) = inverse(X_54) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_54))),bind(Y,$fot(double_divide(identity,X_54)))]]) ).
cnf(refute_0_483,plain,
double_divide(identity,X_54) = inverse(X_54),
inference(resolve,[$cnf( $equal(inverse(X_54),double_divide(identity,X_54)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
double_divide(identity,X_12) = inverse(X_12),
inference(subst,[],[refute_0_483:[bind(X_54,$fot(X_12))]]) ).
cnf(refute_0_485,plain,
double_divide(double_divide(identity,X_12),X_35) = double_divide(double_divide(identity,X_12),X_35),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_12),X_35))]]) ).
cnf(refute_0_486,plain,
( double_divide(double_divide(identity,X_12),X_35) != double_divide(double_divide(identity,X_12),X_35)
| double_divide(identity,X_12) != inverse(X_12)
| double_divide(double_divide(identity,X_12),X_35) = double_divide(inverse(X_12),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_12),X_35),double_divide(double_divide(identity,X_12),X_35)) ),[1,0],$fot(inverse(X_12))]]) ).
cnf(refute_0_487,plain,
( double_divide(identity,X_12) != inverse(X_12)
| double_divide(double_divide(identity,X_12),X_35) = double_divide(inverse(X_12),X_35) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_12),X_35),double_divide(double_divide(identity,X_12),X_35)) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
double_divide(double_divide(identity,X_12),X_35) = double_divide(inverse(X_12),X_35),
inference(resolve,[$cnf( $equal(double_divide(identity,X_12),inverse(X_12)) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
( multiply(X_12,inverse(X_35)) != double_divide(double_divide(identity,X_12),X_35)
| double_divide(double_divide(identity,X_12),X_35) != double_divide(inverse(X_12),X_35)
| multiply(X_12,inverse(X_35)) = double_divide(inverse(X_12),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_12,inverse(X_35)),double_divide(inverse(X_12),X_35)) ),[0],$fot(double_divide(double_divide(identity,X_12),X_35))]]) ).
cnf(refute_0_490,plain,
( multiply(X_12,inverse(X_35)) != double_divide(double_divide(identity,X_12),X_35)
| multiply(X_12,inverse(X_35)) = double_divide(inverse(X_12),X_35) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_12),X_35),double_divide(inverse(X_12),X_35)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
multiply(X_12,inverse(X_35)) = double_divide(inverse(X_12),X_35),
inference(resolve,[$cnf( $equal(multiply(X_12,inverse(X_35)),double_divide(double_divide(identity,X_12),X_35)) )],[refute_0_441,refute_0_490]) ).
cnf(refute_0_492,plain,
( multiply(X_12,inverse(X_35)) != double_divide(inverse(X_12),X_35)
| double_divide(inverse(X_12),X_35) = multiply(X_12,inverse(X_35)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_12,inverse(X_35)))),bind(Y,$fot(double_divide(inverse(X_12),X_35)))]]) ).
cnf(refute_0_493,plain,
double_divide(inverse(X_12),X_35) = multiply(X_12,inverse(X_35)),
inference(resolve,[$cnf( $equal(multiply(X_12,inverse(X_35)),double_divide(inverse(X_12),X_35)) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
double_divide(inverse(A),X_11) = multiply(A,inverse(X_11)),
inference(subst,[],[refute_0_493:[bind(X_12,$fot(A)),bind(X_35,$fot(X_11))]]) ).
cnf(refute_0_495,plain,
double_divide(double_divide(inverse(A),X_11),X_12) = double_divide(double_divide(inverse(A),X_11),X_12),
introduced(tautology,[refl,[$fot(double_divide(double_divide(inverse(A),X_11),X_12))]]) ).
cnf(refute_0_496,plain,
( double_divide(double_divide(inverse(A),X_11),X_12) != double_divide(double_divide(inverse(A),X_11),X_12)
| double_divide(inverse(A),X_11) != multiply(A,inverse(X_11))
| double_divide(double_divide(inverse(A),X_11),X_12) = double_divide(multiply(A,inverse(X_11)),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(inverse(A),X_11),X_12),double_divide(double_divide(inverse(A),X_11),X_12)) ),[1,0],$fot(multiply(A,inverse(X_11)))]]) ).
cnf(refute_0_497,plain,
( double_divide(inverse(A),X_11) != multiply(A,inverse(X_11))
| double_divide(double_divide(inverse(A),X_11),X_12) = double_divide(multiply(A,inverse(X_11)),X_12) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(A),X_11),X_12),double_divide(double_divide(inverse(A),X_11),X_12)) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
double_divide(double_divide(inverse(A),X_11),X_12) = double_divide(multiply(A,inverse(X_11)),X_12),
inference(resolve,[$cnf( $equal(double_divide(inverse(A),X_11),multiply(A,inverse(X_11))) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) = double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)))]]) ).
cnf(refute_0_500,plain,
( double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| double_divide(double_divide(inverse(A),X_11),X_12) != double_divide(multiply(A,inverse(X_11)),X_12)
| double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) ),[1,0],$fot(double_divide(multiply(A,inverse(X_11)),X_12))]]) ).
cnf(refute_0_501,plain,
( double_divide(double_divide(inverse(A),X_11),X_12) != double_divide(multiply(A,inverse(X_11)),X_12)
| double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(A),X_11),X_12),double_divide(multiply(A,inverse(X_11)),X_12)) )],[refute_0_498,refute_0_501]) ).
cnf(refute_0_503,plain,
( multiply(X_12,A) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)) != double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))
| multiply(X_12,A) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_12,A),double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))) ),[0],$fot(double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)))]]) ).
cnf(refute_0_504,plain,
( multiply(X_12,A) != double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))
| multiply(X_12,A) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11)),double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
multiply(X_12,A) = double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)),
inference(resolve,[$cnf( $equal(multiply(X_12,A),double_divide(double_divide(double_divide(inverse(A),X_11),X_12),inverse(X_11))) )],[refute_0_233,refute_0_504]) ).
cnf(refute_0_506,plain,
inverse(double_divide(multiply(A,inverse(X_11)),X_12)) = multiply(X_12,multiply(A,inverse(X_11))),
inference(subst,[],[refute_0_50:[bind(A,$fot(X_12)),bind(B,$fot(multiply(A,inverse(X_11))))]]) ).
cnf(refute_0_507,plain,
multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) = multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11),
introduced(tautology,[refl,[$fot(multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11))]]) ).
cnf(refute_0_508,plain,
( multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) != multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11)
| inverse(double_divide(multiply(A,inverse(X_11)),X_12)) != multiply(X_12,multiply(A,inverse(X_11)))
| multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11),multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11)) ),[1,0],$fot(multiply(X_12,multiply(A,inverse(X_11))))]]) ).
cnf(refute_0_509,plain,
( inverse(double_divide(multiply(A,inverse(X_11)),X_12)) != multiply(X_12,multiply(A,inverse(X_11)))
| multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11),multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11),
inference(resolve,[$cnf( $equal(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),multiply(X_12,multiply(A,inverse(X_11)))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
multiply(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),inverse(X_32)) = double_divide(multiply(X_47,X_32),inverse(X_47)),
inference(subst,[],[refute_0_245:[bind(X_12,$fot(double_divide(multiply(X_47,X_32),inverse(X_47))))]]) ).
cnf(refute_0_512,plain,
( multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) != inverse(identity)
| inverse(identity) != identity
| multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(double_divide(multiply(X_14,A),inverse(X_14)),A),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_513,plain,
( multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) != inverse(identity)
| multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_302,refute_0_512]) ).
cnf(refute_0_514,plain,
multiply(double_divide(multiply(X_14,A),inverse(X_14)),A) = identity,
inference(resolve,[$cnf( $equal(multiply(double_divide(multiply(X_14,A),inverse(X_14)),A),inverse(identity)) )],[refute_0_294,refute_0_513]) ).
cnf(refute_0_515,plain,
multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32) = identity,
inference(subst,[],[refute_0_514:[bind(A,$fot(X_32)),bind(X_14,$fot(X_47))]]) ).
cnf(refute_0_516,plain,
( multiply(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),inverse(X_32)) != double_divide(multiply(X_47,X_32),inverse(X_47))
| multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32) != identity
| multiply(identity,inverse(X_32)) = double_divide(multiply(X_47,X_32),inverse(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),inverse(X_32)),double_divide(multiply(X_47,X_32),inverse(X_47))) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_517,plain,
( multiply(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),inverse(X_32)) != double_divide(multiply(X_47,X_32),inverse(X_47))
| multiply(identity,inverse(X_32)) = double_divide(multiply(X_47,X_32),inverse(X_47)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),identity) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
multiply(identity,inverse(X_32)) = double_divide(multiply(X_47,X_32),inverse(X_47)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(multiply(X_47,X_32),inverse(X_47)),X_32),inverse(X_32)),double_divide(multiply(X_47,X_32),inverse(X_47))) )],[refute_0_511,refute_0_517]) ).
cnf(refute_0_519,plain,
inverse(inverse(X_3)) = X_3,
inference(subst,[],[refute_0_433:[bind(X_12,$fot(X_3))]]) ).
cnf(refute_0_520,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| inverse(inverse(X_3)) != X_3
| multiply(identity,X_3) = X_3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,X_3),X_3) ),[0],$fot(inverse(inverse(X_3)))]]) ).
cnf(refute_0_521,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| multiply(identity,X_3) = X_3 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),X_3) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
multiply(identity,X_3) = X_3,
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(inverse(X_3))) )],[refute_0_76,refute_0_521]) ).
cnf(refute_0_523,plain,
multiply(identity,inverse(X_32)) = inverse(X_32),
inference(subst,[],[refute_0_522:[bind(X_3,$fot(inverse(X_32)))]]) ).
cnf(refute_0_524,plain,
( multiply(identity,inverse(X_32)) != double_divide(multiply(X_47,X_32),inverse(X_47))
| multiply(identity,inverse(X_32)) != inverse(X_32)
| inverse(X_32) = double_divide(multiply(X_47,X_32),inverse(X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,inverse(X_32)),double_divide(multiply(X_47,X_32),inverse(X_47))) ),[0],$fot(inverse(X_32))]]) ).
cnf(refute_0_525,plain,
( multiply(identity,inverse(X_32)) != double_divide(multiply(X_47,X_32),inverse(X_47))
| inverse(X_32) = double_divide(multiply(X_47,X_32),inverse(X_47)) ),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_32)),inverse(X_32)) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
inverse(X_32) = double_divide(multiply(X_47,X_32),inverse(X_47)),
inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_32)),double_divide(multiply(X_47,X_32),inverse(X_47))) )],[refute_0_518,refute_0_525]) ).
cnf(refute_0_527,plain,
inverse(inverse(X_32)) = double_divide(multiply(multiply(X_12,X_32),inverse(X_32)),inverse(multiply(X_12,X_32))),
inference(subst,[],[refute_0_526:[bind(X_32,$fot(inverse(X_32))),bind(X_47,$fot(multiply(X_12,X_32)))]]) ).
cnf(refute_0_528,plain,
( multiply(multiply(X_12,X_32),inverse(X_32)) != X_12
| inverse(inverse(X_32)) != double_divide(multiply(multiply(X_12,X_32),inverse(X_32)),inverse(multiply(X_12,X_32)))
| inverse(inverse(X_32)) = double_divide(X_12,inverse(multiply(X_12,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_32)),double_divide(multiply(multiply(X_12,X_32),inverse(X_32)),inverse(multiply(X_12,X_32)))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_529,plain,
( inverse(inverse(X_32)) != double_divide(multiply(multiply(X_12,X_32),inverse(X_32)),inverse(multiply(X_12,X_32)))
| inverse(inverse(X_32)) = double_divide(X_12,inverse(multiply(X_12,X_32))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_12,X_32),inverse(X_32)),X_12) )],[refute_0_245,refute_0_528]) ).
cnf(refute_0_530,plain,
inverse(inverse(X_32)) = double_divide(X_12,inverse(multiply(X_12,X_32))),
inference(resolve,[$cnf( $equal(inverse(inverse(X_32)),double_divide(multiply(multiply(X_12,X_32),inverse(X_32)),inverse(multiply(X_12,X_32)))) )],[refute_0_527,refute_0_529]) ).
cnf(refute_0_531,plain,
inverse(inverse(X_32)) = X_32,
inference(subst,[],[refute_0_433:[bind(X_12,$fot(X_32))]]) ).
cnf(refute_0_532,plain,
( inverse(inverse(X_32)) != X_32
| inverse(inverse(X_32)) != double_divide(X_12,inverse(multiply(X_12,X_32)))
| X_32 = double_divide(X_12,inverse(multiply(X_12,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_32)),double_divide(X_12,inverse(multiply(X_12,X_32)))) ),[0],$fot(X_32)]]) ).
cnf(refute_0_533,plain,
( inverse(inverse(X_32)) != double_divide(X_12,inverse(multiply(X_12,X_32)))
| X_32 = double_divide(X_12,inverse(multiply(X_12,X_32))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_32)),X_32) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
inverse(multiply(X_12,X_32)) = double_divide(X_32,X_12),
inference(subst,[],[refute_0_445:[bind(A,$fot(X_12)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_535,plain,
double_divide(X_12,inverse(multiply(X_12,X_32))) = double_divide(X_12,inverse(multiply(X_12,X_32))),
introduced(tautology,[refl,[$fot(double_divide(X_12,inverse(multiply(X_12,X_32))))]]) ).
cnf(refute_0_536,plain,
( double_divide(X_12,inverse(multiply(X_12,X_32))) != double_divide(X_12,inverse(multiply(X_12,X_32)))
| inverse(multiply(X_12,X_32)) != double_divide(X_32,X_12)
| double_divide(X_12,inverse(multiply(X_12,X_32))) = double_divide(X_12,double_divide(X_32,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_12,inverse(multiply(X_12,X_32))),double_divide(X_12,inverse(multiply(X_12,X_32)))) ),[1,1],$fot(double_divide(X_32,X_12))]]) ).
cnf(refute_0_537,plain,
( inverse(multiply(X_12,X_32)) != double_divide(X_32,X_12)
| double_divide(X_12,inverse(multiply(X_12,X_32))) = double_divide(X_12,double_divide(X_32,X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(X_12,inverse(multiply(X_12,X_32))),double_divide(X_12,inverse(multiply(X_12,X_32)))) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
double_divide(X_12,inverse(multiply(X_12,X_32))) = double_divide(X_12,double_divide(X_32,X_12)),
inference(resolve,[$cnf( $equal(inverse(multiply(X_12,X_32)),double_divide(X_32,X_12)) )],[refute_0_534,refute_0_537]) ).
cnf(refute_0_539,plain,
( X_32 != double_divide(X_12,inverse(multiply(X_12,X_32)))
| double_divide(X_12,inverse(multiply(X_12,X_32))) != double_divide(X_12,double_divide(X_32,X_12))
| X_32 = double_divide(X_12,double_divide(X_32,X_12)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_32,double_divide(X_12,double_divide(X_32,X_12))) ),[0],$fot(double_divide(X_12,inverse(multiply(X_12,X_32))))]]) ).
cnf(refute_0_540,plain,
( X_32 != double_divide(X_12,inverse(multiply(X_12,X_32)))
| X_32 = double_divide(X_12,double_divide(X_32,X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(X_12,inverse(multiply(X_12,X_32))),double_divide(X_12,double_divide(X_32,X_12))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
( inverse(inverse(X_32)) != double_divide(X_12,inverse(multiply(X_12,X_32)))
| X_32 = double_divide(X_12,double_divide(X_32,X_12)) ),
inference(resolve,[$cnf( $equal(X_32,double_divide(X_12,inverse(multiply(X_12,X_32)))) )],[refute_0_533,refute_0_540]) ).
cnf(refute_0_542,plain,
X_32 = double_divide(X_12,double_divide(X_32,X_12)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_32)),double_divide(X_12,inverse(multiply(X_12,X_32)))) )],[refute_0_530,refute_0_541]) ).
cnf(refute_0_543,plain,
multiply(inverse(X_12),X_67) = double_divide(X_12,double_divide(multiply(inverse(X_12),X_67),X_12)),
inference(subst,[],[refute_0_542:[bind(X_32,$fot(multiply(inverse(X_12),X_67)))]]) ).
cnf(refute_0_544,plain,
inverse(X_48) = double_divide(multiply(inverse(X_12),X_48),inverse(inverse(X_12))),
inference(subst,[],[refute_0_526:[bind(X_32,$fot(X_48)),bind(X_47,$fot(inverse(X_12)))]]) ).
cnf(refute_0_545,plain,
( inverse(X_48) != double_divide(multiply(inverse(X_12),X_48),inverse(inverse(X_12)))
| inverse(inverse(X_12)) != X_12
| inverse(X_48) = double_divide(multiply(inverse(X_12),X_48),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_48),double_divide(multiply(inverse(X_12),X_48),inverse(inverse(X_12)))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_546,plain,
( inverse(X_48) != double_divide(multiply(inverse(X_12),X_48),inverse(inverse(X_12)))
| inverse(X_48) = double_divide(multiply(inverse(X_12),X_48),X_12) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_12)),X_12) )],[refute_0_433,refute_0_545]) ).
cnf(refute_0_547,plain,
inverse(X_48) = double_divide(multiply(inverse(X_12),X_48),X_12),
inference(resolve,[$cnf( $equal(inverse(X_48),double_divide(multiply(inverse(X_12),X_48),inverse(inverse(X_12)))) )],[refute_0_544,refute_0_546]) ).
cnf(refute_0_548,plain,
inverse(X_67) = double_divide(multiply(inverse(X_12),X_67),X_12),
inference(subst,[],[refute_0_547:[bind(X_48,$fot(X_67))]]) ).
cnf(refute_0_549,plain,
( inverse(X_67) != double_divide(multiply(inverse(X_12),X_67),X_12)
| double_divide(multiply(inverse(X_12),X_67),X_12) = inverse(X_67) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(double_divide(multiply(inverse(X_12),X_67),X_12)))]]) ).
cnf(refute_0_550,plain,
double_divide(multiply(inverse(X_12),X_67),X_12) = inverse(X_67),
inference(resolve,[$cnf( $equal(inverse(X_67),double_divide(multiply(inverse(X_12),X_67),X_12)) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
( multiply(inverse(X_12),X_67) != double_divide(X_12,double_divide(multiply(inverse(X_12),X_67),X_12))
| double_divide(multiply(inverse(X_12),X_67),X_12) != inverse(X_67)
| multiply(inverse(X_12),X_67) = double_divide(X_12,inverse(X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_12),X_67),double_divide(X_12,double_divide(multiply(inverse(X_12),X_67),X_12))) ),[1,1],$fot(inverse(X_67))]]) ).
cnf(refute_0_552,plain,
( multiply(inverse(X_12),X_67) != double_divide(X_12,double_divide(multiply(inverse(X_12),X_67),X_12))
| multiply(inverse(X_12),X_67) = double_divide(X_12,inverse(X_67)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_12),X_67),X_12),inverse(X_67)) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
multiply(inverse(X_12),X_67) = double_divide(X_12,inverse(X_67)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_67),double_divide(X_12,double_divide(multiply(inverse(X_12),X_67),X_12))) )],[refute_0_543,refute_0_552]) ).
cnf(refute_0_554,plain,
( multiply(inverse(X_12),X_67) != double_divide(X_12,inverse(X_67))
| double_divide(X_12,inverse(X_67)) = multiply(inverse(X_12),X_67) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(inverse(X_12),X_67))),bind(Y,$fot(double_divide(X_12,inverse(X_67))))]]) ).
cnf(refute_0_555,plain,
double_divide(X_12,inverse(X_67)) = multiply(inverse(X_12),X_67),
inference(resolve,[$cnf( $equal(multiply(inverse(X_12),X_67),double_divide(X_12,inverse(X_67))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) = multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11),
inference(subst,[],[refute_0_555:[bind(X_12,$fot(double_divide(multiply(A,inverse(X_11)),X_12))),bind(X_67,$fot(X_11))]]) ).
cnf(refute_0_557,plain,
( multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) != multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)
| double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) != multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11)
| double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)))),bind(Y,$fot(multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11))),bind(Z,$fot(multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)))]]) ).
cnf(refute_0_558,plain,
( multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11) != multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)
| double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)),multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11)) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(multiply(A,inverse(X_11)),X_12)),X_11),multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)) )],[refute_0_510,refute_0_558]) ).
cnf(refute_0_560,plain,
( multiply(X_12,A) != double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))
| double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)) != multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)
| multiply(X_12,A) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_12,A),multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)) ),[0],$fot(double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)))]]) ).
cnf(refute_0_561,plain,
( multiply(X_12,A) != double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))
| multiply(X_12,A) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11)),multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11)) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
multiply(X_12,A) = multiply(multiply(X_12,multiply(A,inverse(X_11))),X_11),
inference(resolve,[$cnf( $equal(multiply(X_12,A),double_divide(double_divide(multiply(A,inverse(X_11)),X_12),inverse(X_11))) )],[refute_0_505,refute_0_561]) ).
cnf(refute_0_563,plain,
multiply(X_85,X_83) = multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),
inference(subst,[],[refute_0_562:[bind(A,$fot(X_83)),bind(X_11,$fot(inverse(X_10))),bind(X_12,$fot(X_85))]]) ).
cnf(refute_0_564,plain,
( multiply(X_85,X_83) != multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10))
| multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)) = multiply(X_85,X_83) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_85,X_83))),bind(Y,$fot(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10))))]]) ).
cnf(refute_0_565,plain,
multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)) = multiply(X_85,X_83),
inference(resolve,[$cnf( $equal(multiply(X_85,X_83),multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10))) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
( multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)) != multiply(X_85,X_83)
| multiply(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),X_10) != multiply(X_85,multiply(X_83,inverse(inverse(X_10))))
| multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),X_10),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) ),[0,0],$fot(multiply(X_85,X_83))]]) ).
cnf(refute_0_567,plain,
( multiply(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),X_10) != multiply(X_85,multiply(X_83,inverse(inverse(X_10))))
| multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),multiply(X_85,X_83)) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),inverse(X_10)),X_10),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) )],[refute_0_209,refute_0_567]) ).
cnf(refute_0_569,plain,
inverse(inverse(X_10)) = X_10,
inference(subst,[],[refute_0_433:[bind(X_12,$fot(X_10))]]) ).
cnf(refute_0_570,plain,
multiply(X_83,inverse(inverse(X_10))) = multiply(X_83,inverse(inverse(X_10))),
introduced(tautology,[refl,[$fot(multiply(X_83,inverse(inverse(X_10))))]]) ).
cnf(refute_0_571,plain,
( multiply(X_83,inverse(inverse(X_10))) != multiply(X_83,inverse(inverse(X_10)))
| inverse(inverse(X_10)) != X_10
| multiply(X_83,inverse(inverse(X_10))) = multiply(X_83,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_83,inverse(inverse(X_10))),multiply(X_83,inverse(inverse(X_10)))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_572,plain,
( inverse(inverse(X_10)) != X_10
| multiply(X_83,inverse(inverse(X_10))) = multiply(X_83,X_10) ),
inference(resolve,[$cnf( $equal(multiply(X_83,inverse(inverse(X_10))),multiply(X_83,inverse(inverse(X_10)))) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
multiply(X_83,inverse(inverse(X_10))) = multiply(X_83,X_10),
inference(resolve,[$cnf( $equal(inverse(inverse(X_10)),X_10) )],[refute_0_569,refute_0_572]) ).
cnf(refute_0_574,plain,
multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) = multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),
introduced(tautology,[refl,[$fot(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))))]]) ).
cnf(refute_0_575,plain,
( multiply(X_83,inverse(inverse(X_10))) != multiply(X_83,X_10)
| multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) != multiply(X_85,multiply(X_83,inverse(inverse(X_10))))
| multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) = multiply(X_85,multiply(X_83,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) ),[1,1],$fot(multiply(X_83,X_10))]]) ).
cnf(refute_0_576,plain,
( multiply(X_83,inverse(inverse(X_10))) != multiply(X_83,X_10)
| multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) = multiply(X_85,multiply(X_83,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) = multiply(X_85,multiply(X_83,X_10)),
inference(resolve,[$cnf( $equal(multiply(X_83,inverse(inverse(X_10))),multiply(X_83,X_10)) )],[refute_0_573,refute_0_576]) ).
cnf(refute_0_578,plain,
( multiply(X_85,multiply(X_83,inverse(inverse(X_10)))) != multiply(X_85,multiply(X_83,X_10))
| multiply(multiply(X_85,X_83),X_10) != multiply(X_85,multiply(X_83,inverse(inverse(X_10))))
| multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_85,X_83),X_10),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) ),[1],$fot(multiply(X_85,multiply(X_83,X_10)))]]) ).
cnf(refute_0_579,plain,
( multiply(multiply(X_85,X_83),X_10) != multiply(X_85,multiply(X_83,inverse(inverse(X_10))))
| multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(X_85,multiply(X_83,inverse(inverse(X_10)))),multiply(X_85,multiply(X_83,X_10))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
multiply(multiply(X_85,X_83),X_10) = multiply(X_85,multiply(X_83,X_10)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_85,X_83),X_10),multiply(X_85,multiply(X_83,inverse(inverse(X_10))))) )],[refute_0_568,refute_0_579]) ).
cnf(refute_0_581,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_580:[bind(X_10,$fot(c3)),bind(X_83,$fot(b3)),bind(X_85,$fot(a3))]]) ).
cnf(refute_0_582,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),[0],$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_583,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_581,refute_0_582]) ).
cnf(refute_0_584,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_583,prove_these_axioms_3]) ).
cnf(refute_0_585,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_586,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_585,refute_0_584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 10:24:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.47
% 0.22/0.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.42/0.56
%------------------------------------------------------------------------------