%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 10:41:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 116
% Syntax : Number of clauses : 421 ( 218 unt; 0 nHn; 200 RR)
% Number of literals : 718 ( 717 equ; 299 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 822 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ).
cnf(multiply,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity) ).
cnf(inverse,axiom,
inverse(A) = double_divide(A,identity) ).
cnf(identity,axiom,
identity = double_divide(A,inverse(A)) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_6,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| double_divide(double_divide(B,A),identity) != inverse(double_divide(B,A))
| multiply(A,B) = inverse(double_divide(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),inverse(double_divide(B,A))) ),[0],$fot(double_divide(double_divide(B,A),identity))]]) ).
cnf(refute_0_7,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = inverse(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11))),
inference(subst,[],[refute_0_8:[bind(A,$fot(multiply(double_divide(X_12,X_10),X_11))),bind(B,$fot(double_divide(identity,double_divide(X_10,inverse(X_11)))))]]) ).
cnf(refute_0_10,plain,
double_divide(double_divide(B,double_divide(C,A)),identity) = inverse(double_divide(B,double_divide(C,A))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,double_divide(C,A))))]]) ).
cnf(refute_0_11,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).
cnf(refute_0_12,plain,
( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,1],$fot(inverse(double_divide(B,double_divide(C,A))))]]) ).
cnf(refute_0_13,plain,
( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,double_divide(C,A)),identity),inverse(double_divide(B,double_divide(C,A)))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_16,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(B,identity)))]]) ).
cnf(refute_0_17,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,double_divide(B,identity))
| double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_18,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,double_divide(B,identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(A,double_divide(B,identity))))]]) ).
cnf(refute_0_21,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,double_divide(B,identity)))
| double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) ),[1,1],$fot(double_divide(A,inverse(B)))]]) ).
cnf(refute_0_22,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,inverse(B))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,0],$fot(double_divide(identity,double_divide(A,inverse(B))))]]) ).
cnf(refute_0_26,plain,
( double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,inverse(B)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_28]) ).
cnf(refute_0_30,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Y,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Z,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))))]]) ).
cnf(refute_0_31,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
| double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).
cnf(refute_0_34,plain,
( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) )],[single_axiom,refute_0_34]) ).
cnf(refute_0_36,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_37,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(double_divide(B,double_divide(C,A))) = multiply(double_divide(C,A),B),
inference(subst,[],[refute_0_37:[bind(A,$fot(double_divide(C,A)))]]) ).
cnf(refute_0_39,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).
cnf(refute_0_40,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
| inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) ),[1,1],$fot(multiply(double_divide(C,A),B))]]) ).
cnf(refute_0_41,plain,
( inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,double_divide(C,A))),multiply(double_divide(C,A),B)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)))]]) ).
cnf(refute_0_44,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) )],[refute_0_35,refute_0_44]) ).
cnf(refute_0_46,plain,
double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_47,plain,
( multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != inverse(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)))
| double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)) != X_12
| multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),inverse(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_48,plain,
( multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != inverse(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)))
| multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)),X_12) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),inverse(double_divide(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(double_divide(X_12,X_10),X_11)))) )],[refute_0_9,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(double_divide(X_10,inverse(X_11))) = multiply(inverse(X_11),X_10),
inference(subst,[],[refute_0_37:[bind(A,$fot(inverse(X_11))),bind(B,$fot(X_10))]]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),B)) = double_divide(identity,double_divide(identity,inverse(X_20))),
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(inverse(X_20)))),bind(C,$fot(double_divide(identity,double_divide(identity,inverse(X_20)))))]]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_53,plain,
inverse(X_12) = double_divide(X_12,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_54,plain,
( inverse(X_12) != double_divide(X_12,identity)
| double_divide(X_12,identity) = inverse(X_12) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(double_divide(X_12,identity)))]]) ).
cnf(refute_0_55,plain,
double_divide(X_12,identity) = inverse(X_12),
inference(resolve,[$cnf( $equal(inverse(X_12),double_divide(X_12,identity)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( double_divide(X_12,identity) != inverse(X_12)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) != X_12
| double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)),X_12) ),[0,1,0],$fot(inverse(X_12))]]) ).
cnf(refute_0_57,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) != X_12
| double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,identity),inverse(X_12)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)),X_12) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(identity),X_16)) = identity,
inference(subst,[],[refute_0_58:[bind(X_11,$fot(X_16)),bind(X_12,$fot(identity))]]) ).
cnf(refute_0_60,plain,
identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
inference(subst,[],[identity:[bind(A,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_61,plain,
multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_62,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_63,plain,
inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$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_65,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( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
identity = double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),
inference(subst,[],[refute_0_66:[bind(X_2,$fot(double_divide(inverse(identity),inverse(identity)))),bind(X_3,$fot(identity))]]) ).
cnf(refute_0_68,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) = inverse(identity),
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(identity))),bind(B,$fot(identity)),bind(C,$fot(inverse(identity)))]]) ).
cnf(refute_0_69,plain,
( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) != inverse(identity)
| identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_70,plain,
( identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),inverse(identity)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_73,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(identity),X_16)) != identity
| inverse(identity) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(identity),X_16)),identity) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_75,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(identity),X_16)) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(identity),X_16)),identity) )],[refute_0_59,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_78,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_79,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_80,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_82,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(identity,X_16) = inverse(inverse(X_16)),
inference(subst,[],[refute_0_83:[bind(X_3,$fot(X_16))]]) ).
cnf(refute_0_85,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)))]]) ).
cnf(refute_0_86,plain,
( multiply(identity,X_16) != inverse(inverse(X_16))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) != double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16))) ),[1,1],$fot(inverse(inverse(X_16)))]]) ).
cnf(refute_0_87,plain,
( multiply(identity,X_16) != inverse(inverse(X_16))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))),
inference(resolve,[$cnf( $equal(multiply(identity,X_16),inverse(inverse(X_16))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) != double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16)))
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),identity) ),[0],$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))))]]) ).
cnf(refute_0_90,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),inverse(inverse(X_16))) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(identity,X_16)),identity) )],[refute_0_76,refute_0_90]) ).
cnf(refute_0_92,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))) = identity,
inference(subst,[],[refute_0_91:[bind(X_16,$fot(X_20))]]) ).
cnf(refute_0_93,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))) != identity
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),B)) != double_divide(identity,double_divide(identity,inverse(X_20)))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(identity,double_divide(identity,inverse(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),B)),double_divide(identity,double_divide(identity,inverse(X_20)))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_94,plain,
( double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),B)) != double_divide(identity,double_divide(identity,inverse(X_20)))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(identity,double_divide(identity,inverse(X_20))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),identity) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(identity,double_divide(identity,inverse(X_20))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(double_divide(double_divide(identity,double_divide(identity,inverse(X_20))),inverse(inverse(X_20))),B)),double_divide(identity,double_divide(identity,inverse(X_20)))) )],[refute_0_51,refute_0_94]) ).
cnf(refute_0_96,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(double_divide(X_12,inverse(X_12)),X_11)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(X_12))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_97,plain,
identity = double_divide(X_12,inverse(X_12)),
inference(subst,[],[identity:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_98,plain,
( identity != double_divide(X_12,inverse(X_12))
| double_divide(X_12,inverse(X_12)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_12,inverse(X_12))))]]) ).
cnf(refute_0_99,plain,
double_divide(X_12,inverse(X_12)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_12,inverse(X_12))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( double_divide(X_12,inverse(X_12)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(double_divide(X_12,inverse(X_12)),X_11)) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(double_divide(X_12,inverse(X_12)),X_11)),X_12) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_101,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(double_divide(X_12,inverse(X_12)),X_11)) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,inverse(X_12)),identity) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(double_divide(X_12,inverse(X_12)),X_11)),X_12) )],[refute_0_96,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(identity,X_11) = inverse(inverse(X_11)),
inference(subst,[],[refute_0_83:[bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_104,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)))]]) ).
cnf(refute_0_105,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) != double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11))
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11))) ),[1,1],$fot(inverse(inverse(X_11)))]]) ).
cnf(refute_0_106,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(identity,X_11),inverse(inverse(X_11))) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) != double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11)))
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),X_12) ),[0],$fot(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))))]]) ).
cnf(refute_0_109,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),multiply(identity,X_11)),X_12) )],[refute_0_102,refute_0_109]) ).
cnf(refute_0_111,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))) = inverse(X_20),
inference(subst,[],[refute_0_110:[bind(X_11,$fot(B)),bind(X_12,$fot(inverse(X_20)))]]) ).
cnf(refute_0_112,plain,
multiply(identity,B) = inverse(inverse(B)),
inference(subst,[],[refute_0_83:[bind(X_3,$fot(B))]]) ).
cnf(refute_0_113,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)))]]) ).
cnf(refute_0_114,plain,
( multiply(identity,B) != inverse(inverse(B))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) != double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B))) ),[1,1],$fot(inverse(inverse(B)))]]) ).
cnf(refute_0_115,plain,
( multiply(identity,B) != inverse(inverse(B))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))),
inference(resolve,[$cnf( $equal(multiply(identity,B),inverse(inverse(B))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) != double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B)))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))) != inverse(X_20)
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = inverse(X_20) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)))),bind(Y,$fot(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))))),bind(Z,$fot(inverse(X_20)))]]) ).
cnf(refute_0_118,plain,
( double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))) != inverse(X_20)
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = inverse(X_20) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) = inverse(X_20),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),inverse(inverse(B))),inverse(X_20)) )],[refute_0_111,refute_0_118]) ).
cnf(refute_0_120,plain,
( double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) != double_divide(identity,double_divide(identity,inverse(X_20)))
| double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) != inverse(X_20)
| inverse(X_20) = double_divide(identity,double_divide(identity,inverse(X_20))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),double_divide(identity,double_divide(identity,inverse(X_20)))) ),[0],$fot(inverse(X_20))]]) ).
cnf(refute_0_121,plain,
( double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)) != double_divide(identity,double_divide(identity,inverse(X_20)))
| inverse(X_20) = double_divide(identity,double_divide(identity,inverse(X_20))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),inverse(X_20)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
inverse(X_20) = double_divide(identity,double_divide(identity,inverse(X_20))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(inverse(X_20)),inverse(B))),multiply(identity,B)),double_divide(identity,double_divide(identity,inverse(X_20)))) )],[refute_0_95,refute_0_121]) ).
cnf(refute_0_123,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(double_divide(identity,inverse(inverse(A))),A),B)) = double_divide(identity,inverse(inverse(A))),
inference(subst,[],[refute_0_45:[bind(C,$fot(double_divide(identity,inverse(inverse(A)))))]]) ).
cnf(refute_0_124,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) = identity,
inference(subst,[],[refute_0_45:[bind(A,$fot(inverse(X_18))),bind(B,$fot(identity)),bind(C,$fot(identity))]]) ).
cnf(refute_0_125,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(X_16),X_16)) = X_16,
inference(subst,[],[refute_0_58:[bind(X_11,$fot(X_16)),bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_126,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_127,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_128,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_129,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_131,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_126,refute_0_131]) ).
cnf(refute_0_133,plain,
( multiply(inverse(X_3),X_3) != inverse(identity)
| inverse(identity) != identity
| multiply(inverse(X_3),X_3) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_3),X_3),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_134,plain,
( multiply(inverse(X_3),X_3) != inverse(identity)
| multiply(inverse(X_3),X_3) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_73,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_3),X_3) = identity,
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(identity)) )],[refute_0_132,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(inverse(X_16),X_16) = identity,
inference(subst,[],[refute_0_135:[bind(X_3,$fot(X_16))]]) ).
cnf(refute_0_137,plain,
( multiply(inverse(X_16),X_16) != identity
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(X_16),X_16)) != X_16
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(X_16),X_16)),X_16) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_138,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(X_16),X_16)) != X_16
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = X_16 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_16),X_16),identity) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = X_16,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),multiply(inverse(X_16),X_16)),X_16) )],[refute_0_125,refute_0_138]) ).
cnf(refute_0_140,plain,
inverse(double_divide(identity,double_divide(identity,inverse(X_16)))) = multiply(double_divide(identity,inverse(X_16)),identity),
inference(subst,[],[refute_0_37:[bind(A,$fot(double_divide(identity,inverse(X_16)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_141,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = inverse(double_divide(identity,double_divide(identity,inverse(X_16)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,double_divide(identity,inverse(X_16)))))]]) ).
cnf(refute_0_142,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_16))))
| inverse(double_divide(identity,double_divide(identity,inverse(X_16)))) != multiply(double_divide(identity,inverse(X_16)),identity)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = multiply(double_divide(identity,inverse(X_16)),identity) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity))),bind(Y,$fot(inverse(double_divide(identity,double_divide(identity,inverse(X_16)))))),bind(Z,$fot(multiply(double_divide(identity,inverse(X_16)),identity)))]]) ).
cnf(refute_0_143,plain,
( inverse(double_divide(identity,double_divide(identity,inverse(X_16)))) != multiply(double_divide(identity,inverse(X_16)),identity)
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = multiply(double_divide(identity,inverse(X_16)),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_16))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) = multiply(double_divide(identity,inverse(X_16)),identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(identity,inverse(X_16)))),multiply(double_divide(identity,inverse(X_16)),identity)) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) != X_16
| double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) != multiply(double_divide(identity,inverse(X_16)),identity)
| multiply(double_divide(identity,inverse(X_16)),identity) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity),X_16) ),[0],$fot(multiply(double_divide(identity,inverse(X_16)),identity))]]) ).
cnf(refute_0_146,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity) != X_16
| multiply(double_divide(identity,inverse(X_16)),identity) = X_16 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity),multiply(double_divide(identity,inverse(X_16)),identity)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
multiply(double_divide(identity,inverse(X_16)),identity) = X_16,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_16))),identity),X_16) )],[refute_0_139,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(double_divide(identity,inverse(X_18)),identity) = X_18,
inference(subst,[],[refute_0_147:[bind(X_16,$fot(X_18))]]) ).
cnf(refute_0_149,plain,
( multiply(double_divide(identity,inverse(X_18)),identity) != X_18
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)),identity) ),[0,1],$fot(X_18)]]) ).
cnf(refute_0_150,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_18)),identity),X_18) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),multiply(double_divide(identity,inverse(X_18)),identity)),identity) )],[refute_0_124,refute_0_150]) ).
cnf(refute_0_152,plain,
double_divide(inverse(X_18),identity) = inverse(inverse(X_18)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_18)))]]) ).
cnf(refute_0_153,plain,
double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_18),inverse(identity)))]]) ).
cnf(refute_0_154,plain,
( double_divide(inverse(X_18),inverse(identity)) != double_divide(inverse(X_18),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_155,plain,
( inverse(identity) != identity
| double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),inverse(identity))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
double_divide(inverse(X_18),inverse(identity)) = double_divide(inverse(X_18),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_73,refute_0_155]) ).
cnf(refute_0_157,plain,
( double_divide(inverse(X_18),identity) != inverse(inverse(X_18))
| double_divide(inverse(X_18),inverse(identity)) != double_divide(inverse(X_18),identity)
| double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(inverse(X_18),inverse(identity)))),bind(Y,$fot(double_divide(inverse(X_18),identity))),bind(Z,$fot(inverse(inverse(X_18))))]]) ).
cnf(refute_0_158,plain,
( double_divide(inverse(X_18),identity) != inverse(inverse(X_18))
| double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),double_divide(inverse(X_18),identity)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
double_divide(inverse(X_18),inverse(identity)) = inverse(inverse(X_18)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),identity),inverse(inverse(X_18))) )],[refute_0_152,refute_0_158]) ).
cnf(refute_0_160,plain,
double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,double_divide(inverse(X_18),inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(X_18),inverse(identity))))]]) ).
cnf(refute_0_161,plain,
( double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,double_divide(inverse(X_18),inverse(identity)))
| double_divide(inverse(X_18),inverse(identity)) != inverse(inverse(X_18))
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,double_divide(inverse(X_18),inverse(identity)))) ),[1,1],$fot(inverse(inverse(X_18)))]]) ).
cnf(refute_0_162,plain,
( double_divide(inverse(X_18),inverse(identity)) != inverse(inverse(X_18))
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,double_divide(inverse(X_18),inverse(identity)))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
double_divide(identity,double_divide(inverse(X_18),inverse(identity))) = double_divide(identity,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_18),inverse(identity)),inverse(inverse(X_18))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18))]]) ).
cnf(refute_0_165,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)
| double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,inverse(inverse(X_18)))
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_18))))]]) ).
cnf(refute_0_166,plain,
( double_divide(identity,double_divide(inverse(X_18),inverse(identity))) != double_divide(identity,inverse(inverse(X_18)))
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) = double_divide(double_divide(identity,inverse(inverse(X_18))),X_18),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),double_divide(identity,inverse(inverse(X_18)))) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != double_divide(double_divide(identity,inverse(inverse(X_18))),X_18)
| double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != identity
| double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),identity) ),[0],$fot(double_divide(double_divide(identity,inverse(inverse(X_18))),X_18))]]) ).
cnf(refute_0_169,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18) != identity
| double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),double_divide(double_divide(identity,inverse(inverse(X_18))),X_18)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
double_divide(double_divide(identity,inverse(inverse(X_18))),X_18) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_18),inverse(identity))),X_18),identity) )],[refute_0_151,refute_0_169]) ).
cnf(refute_0_171,plain,
double_divide(double_divide(identity,inverse(inverse(A))),A) = identity,
inference(subst,[],[refute_0_170:[bind(X_18,$fot(A))]]) ).
cnf(refute_0_172,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(double_divide(identity,inverse(inverse(A))),A),B)) != double_divide(identity,inverse(inverse(A)))
| double_divide(double_divide(identity,inverse(inverse(A))),A) != identity
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(identity,inverse(inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(double_divide(identity,inverse(inverse(A))),A),B)),double_divide(identity,inverse(inverse(A)))) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_173,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(double_divide(identity,inverse(inverse(A))),A),B)) != double_divide(identity,inverse(inverse(A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(identity,inverse(inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(A))),A),identity) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(identity,inverse(inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(double_divide(identity,inverse(inverse(A))),A),B)),double_divide(identity,inverse(inverse(A)))) )],[refute_0_123,refute_0_173]) ).
cnf(refute_0_175,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)))]]) ).
cnf(refute_0_176,plain,
( multiply(identity,B) != inverse(inverse(B))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B))) ),[1,1],$fot(inverse(inverse(B)))]]) ).
cnf(refute_0_177,plain,
( multiply(identity,B) != inverse(inverse(B))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))),
inference(resolve,[$cnf( $equal(multiply(identity,B),inverse(inverse(B))) )],[refute_0_112,refute_0_177]) ).
cnf(refute_0_179,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) != double_divide(identity,inverse(inverse(A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))) = double_divide(identity,inverse(inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),double_divide(identity,inverse(inverse(A)))) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))))]]) ).
cnf(refute_0_180,plain,
( double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)) != double_divide(identity,inverse(inverse(A)))
| double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))) = double_divide(identity,inverse(inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B)))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(inverse(B))) = double_divide(identity,inverse(inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(identity,B)),double_divide(identity,inverse(inverse(A)))) )],[refute_0_174,refute_0_180]) ).
cnf(refute_0_182,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) = double_divide(identity,inverse(inverse(inverse(X_12)))),
inference(subst,[],[refute_0_181:[bind(A,$fot(inverse(X_12))),bind(B,$fot(X_11))]]) ).
cnf(refute_0_183,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) != double_divide(identity,inverse(inverse(inverse(X_12))))
| double_divide(identity,inverse(inverse(inverse(X_12)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))),X_12) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(X_12)))))]]) ).
cnf(refute_0_184,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))) != X_12
| double_divide(identity,inverse(inverse(inverse(X_12)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))),double_divide(identity,inverse(inverse(inverse(X_12))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
double_divide(identity,inverse(inverse(inverse(X_12)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),inverse(inverse(X_11))),X_12) )],[refute_0_110,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(double_divide(identity,inverse(X_22)),identity) = inverse(double_divide(identity,double_divide(identity,inverse(X_22)))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(identity,inverse(X_22)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_187,plain,
inverse(X_22) = double_divide(identity,double_divide(identity,inverse(X_22))),
inference(subst,[],[refute_0_122:[bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_188,plain,
( inverse(X_22) != double_divide(identity,double_divide(identity,inverse(X_22)))
| double_divide(identity,double_divide(identity,inverse(X_22))) = inverse(X_22) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_22))),bind(Y,$fot(double_divide(identity,double_divide(identity,inverse(X_22)))))]]) ).
cnf(refute_0_189,plain,
double_divide(identity,double_divide(identity,inverse(X_22))) = inverse(X_22),
inference(resolve,[$cnf( $equal(inverse(X_22),double_divide(identity,double_divide(identity,inverse(X_22)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
( multiply(double_divide(identity,inverse(X_22)),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_22))))
| double_divide(identity,double_divide(identity,inverse(X_22))) != inverse(X_22)
| multiply(double_divide(identity,inverse(X_22)),identity) = inverse(inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_22)),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_22))))) ),[1,0],$fot(inverse(X_22))]]) ).
cnf(refute_0_191,plain,
( multiply(double_divide(identity,inverse(X_22)),identity) != inverse(double_divide(identity,double_divide(identity,inverse(X_22))))
| multiply(double_divide(identity,inverse(X_22)),identity) = inverse(inverse(X_22)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_22))),inverse(X_22)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(double_divide(identity,inverse(X_22)),identity) = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_22)),identity),inverse(double_divide(identity,double_divide(identity,inverse(X_22))))) )],[refute_0_186,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(double_divide(identity,inverse(X_22)),identity) = X_22,
inference(subst,[],[refute_0_147:[bind(X_16,$fot(X_22))]]) ).
cnf(refute_0_194,plain,
( multiply(double_divide(identity,inverse(X_22)),identity) != X_22
| multiply(double_divide(identity,inverse(X_22)),identity) != inverse(inverse(X_22))
| X_22 = inverse(inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_22)),identity),inverse(inverse(X_22))) ),[0],$fot(X_22)]]) ).
cnf(refute_0_195,plain,
( multiply(double_divide(identity,inverse(X_22)),identity) != inverse(inverse(X_22))
| X_22 = inverse(inverse(X_22)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_22)),identity),X_22) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
X_22 = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_22)),identity),inverse(inverse(X_22))) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
( X_22 != inverse(inverse(X_22))
| inverse(inverse(X_22)) = X_22 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_22)),bind(Y,$fot(inverse(inverse(X_22))))]]) ).
cnf(refute_0_198,plain,
inverse(inverse(X_22)) = X_22,
inference(resolve,[$cnf( $equal(X_22,inverse(inverse(X_22))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
inverse(inverse(inverse(X_12))) = inverse(X_12),
inference(subst,[],[refute_0_198:[bind(X_22,$fot(inverse(X_12)))]]) ).
cnf(refute_0_200,plain,
double_divide(identity,inverse(inverse(inverse(X_12)))) = double_divide(identity,inverse(inverse(inverse(X_12)))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(inverse(X_12)))))]]) ).
cnf(refute_0_201,plain,
( double_divide(identity,inverse(inverse(inverse(X_12)))) != double_divide(identity,inverse(inverse(inverse(X_12))))
| inverse(inverse(inverse(X_12))) != inverse(X_12)
| double_divide(identity,inverse(inverse(inverse(X_12)))) = double_divide(identity,inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_12)))),double_divide(identity,inverse(inverse(inverse(X_12))))) ),[1,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_202,plain,
( inverse(inverse(inverse(X_12))) != inverse(X_12)
| double_divide(identity,inverse(inverse(inverse(X_12)))) = double_divide(identity,inverse(X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_12)))),double_divide(identity,inverse(inverse(inverse(X_12))))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
double_divide(identity,inverse(inverse(inverse(X_12)))) = double_divide(identity,inverse(X_12)),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(X_12))),inverse(X_12)) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( double_divide(identity,inverse(inverse(inverse(X_12)))) != X_12
| double_divide(identity,inverse(inverse(inverse(X_12)))) != double_divide(identity,inverse(X_12))
| double_divide(identity,inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_12)))),X_12) ),[0],$fot(double_divide(identity,inverse(X_12)))]]) ).
cnf(refute_0_205,plain,
( double_divide(identity,inverse(inverse(inverse(X_12)))) != X_12
| double_divide(identity,inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_12)))),double_divide(identity,inverse(X_12))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
double_divide(identity,inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_12)))),X_12) )],[refute_0_185,refute_0_205]) ).
cnf(refute_0_207,plain,
double_divide(identity,inverse(X_20)) = X_20,
inference(subst,[],[refute_0_206:[bind(X_12,$fot(X_20))]]) ).
cnf(refute_0_208,plain,
double_divide(identity,double_divide(identity,inverse(X_20))) = double_divide(identity,double_divide(identity,inverse(X_20))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(identity,inverse(X_20))))]]) ).
cnf(refute_0_209,plain,
( double_divide(identity,double_divide(identity,inverse(X_20))) != double_divide(identity,double_divide(identity,inverse(X_20)))
| double_divide(identity,inverse(X_20)) != X_20
| double_divide(identity,double_divide(identity,inverse(X_20))) = double_divide(identity,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_20))),double_divide(identity,double_divide(identity,inverse(X_20)))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_210,plain,
( double_divide(identity,inverse(X_20)) != X_20
| double_divide(identity,double_divide(identity,inverse(X_20))) = double_divide(identity,X_20) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_20))),double_divide(identity,double_divide(identity,inverse(X_20)))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
double_divide(identity,double_divide(identity,inverse(X_20))) = double_divide(identity,X_20),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(X_20)),X_20) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( double_divide(identity,double_divide(identity,inverse(X_20))) != double_divide(identity,X_20)
| inverse(X_20) != double_divide(identity,double_divide(identity,inverse(X_20)))
| inverse(X_20) = double_divide(identity,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(X_20),double_divide(identity,double_divide(identity,inverse(X_20)))) ),[1],$fot(double_divide(identity,X_20))]]) ).
cnf(refute_0_213,plain,
( inverse(X_20) != double_divide(identity,double_divide(identity,inverse(X_20)))
| inverse(X_20) = double_divide(identity,X_20) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_20))),double_divide(identity,X_20)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
inverse(X_20) = double_divide(identity,X_20),
inference(resolve,[$cnf( $equal(inverse(X_20),double_divide(identity,double_divide(identity,inverse(X_20)))) )],[refute_0_122,refute_0_213]) ).
cnf(refute_0_215,plain,
( inverse(X_20) != double_divide(identity,X_20)
| double_divide(identity,X_20) = inverse(X_20) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_20))),bind(Y,$fot(double_divide(identity,X_20)))]]) ).
cnf(refute_0_216,plain,
double_divide(identity,X_20) = inverse(X_20),
inference(resolve,[$cnf( $equal(inverse(X_20),double_divide(identity,X_20)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
double_divide(identity,double_divide(X_10,inverse(X_11))) = inverse(double_divide(X_10,inverse(X_11))),
inference(subst,[],[refute_0_216:[bind(X_20,$fot(double_divide(X_10,inverse(X_11))))]]) ).
cnf(refute_0_218,plain,
( double_divide(identity,double_divide(X_10,inverse(X_11))) != inverse(double_divide(X_10,inverse(X_11)))
| inverse(double_divide(X_10,inverse(X_11))) != multiply(inverse(X_11),X_10)
| double_divide(identity,double_divide(X_10,inverse(X_11))) = multiply(inverse(X_11),X_10) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(identity,double_divide(X_10,inverse(X_11))))),bind(Y,$fot(inverse(double_divide(X_10,inverse(X_11))))),bind(Z,$fot(multiply(inverse(X_11),X_10)))]]) ).
cnf(refute_0_219,plain,
( inverse(double_divide(X_10,inverse(X_11))) != multiply(inverse(X_11),X_10)
| double_divide(identity,double_divide(X_10,inverse(X_11))) = multiply(inverse(X_11),X_10) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_10,inverse(X_11))),inverse(double_divide(X_10,inverse(X_11)))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
double_divide(identity,double_divide(X_10,inverse(X_11))) = multiply(inverse(X_11),X_10),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,inverse(X_11))),multiply(inverse(X_11),X_10)) )],[refute_0_50,refute_0_219]) ).
cnf(refute_0_221,plain,
multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),
introduced(tautology,[refl,[$fot(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))))]]) ).
cnf(refute_0_222,plain,
( multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11))))
| double_divide(identity,double_divide(X_10,inverse(X_11))) != multiply(inverse(X_11),X_10)
| multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11))))) ),[1,1],$fot(multiply(inverse(X_11),X_10))]]) ).
cnf(refute_0_223,plain,
( double_divide(identity,double_divide(X_10,inverse(X_11))) != multiply(inverse(X_11),X_10)
| multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11))))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) = multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_10,inverse(X_11))),multiply(inverse(X_11),X_10)) )],[refute_0_220,refute_0_223]) ).
cnf(refute_0_225,plain,
( multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10))
| multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != inverse(X_12)
| multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),inverse(X_12)) ),[0],$fot(multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)))]]) ).
cnf(refute_0_226,plain,
( multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))) != inverse(X_12)
| multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
multiply(multiply(double_divide(X_12,X_10),X_11),multiply(inverse(X_11),X_10)) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_10),X_11),double_divide(identity,double_divide(X_10,inverse(X_11)))),inverse(X_12)) )],[refute_0_49,refute_0_226]) ).
cnf(refute_0_228,plain,
multiply(multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)),
inference(subst,[],[refute_0_227:[bind(X_10,$fot(multiply(X_2,X_3))),bind(X_11,$fot(X_38)),bind(X_12,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_229,plain,
( identity != double_divide(double_divide(X_3,X_2),multiply(X_2,X_3))
| double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3))))]]) ).
cnf(refute_0_230,plain,
double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),multiply(X_2,X_3))) )],[refute_0_66,refute_0_229]) ).
cnf(refute_0_231,plain,
( multiply(multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) != identity
| multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_38),multiply(inverse(X_38),multiply(X_2,X_3))),inverse(double_divide(X_3,X_2))) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_232,plain,
( multiply(multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),identity) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_38),multiply(inverse(X_38),multiply(X_2,X_3))),inverse(double_divide(X_3,X_2))) )],[refute_0_228,refute_0_232]) ).
cnf(refute_0_234,plain,
inverse(inverse(X_3)) = X_3,
inference(subst,[],[refute_0_198:[bind(X_22,$fot(X_3))]]) ).
cnf(refute_0_235,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_236,plain,
( multiply(identity,X_3) != inverse(inverse(X_3))
| multiply(identity,X_3) = X_3 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_3)),X_3) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
multiply(identity,X_3) = X_3,
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(inverse(X_3))) )],[refute_0_83,refute_0_236]) ).
cnf(refute_0_238,plain,
multiply(identity,X_38) = X_38,
inference(subst,[],[refute_0_237:[bind(X_3,$fot(X_38))]]) ).
cnf(refute_0_239,plain,
multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),
introduced(tautology,[refl,[$fot(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))))]]) ).
cnf(refute_0_240,plain,
( multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3)))
| multiply(identity,X_38) != X_38
| multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3)))) ),[1,0],$fot(X_38)]]) ).
cnf(refute_0_241,plain,
( multiply(identity,X_38) != X_38
| multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))),
inference(resolve,[$cnf( $equal(multiply(identity,X_38),X_38) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
( multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3)))
| multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),inverse(double_divide(X_3,X_2))) ),[0],$fot(multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))))]]) ).
cnf(refute_0_244,plain,
( multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = inverse(double_divide(X_3,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3)))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
( multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
| multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_2,X_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))),multiply(X_2,X_3)) ),[0],$fot(inverse(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_246,plain,
( multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_2,X_3) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_63,refute_0_245]) ).
cnf(refute_0_247,plain,
( multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))) != inverse(double_divide(X_3,X_2))
| multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_2,X_3) ),
inference(resolve,[$cnf( $equal(multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))),inverse(double_divide(X_3,X_2))) )],[refute_0_244,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(X_38,multiply(inverse(X_38),multiply(X_2,X_3))) = multiply(X_2,X_3),
inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_38),multiply(inverse(X_38),multiply(X_2,X_3))),inverse(double_divide(X_3,X_2))) )],[refute_0_233,refute_0_247]) ).
cnf(refute_0_249,plain,
multiply(X_42,multiply(inverse(X_42),multiply(identity,X_41))) = multiply(identity,X_41),
inference(subst,[],[refute_0_248:[bind(X_2,$fot(identity)),bind(X_3,$fot(X_41)),bind(X_38,$fot(X_42))]]) ).
cnf(refute_0_250,plain,
multiply(identity,X_41) = X_41,
inference(subst,[],[refute_0_237:[bind(X_3,$fot(X_41))]]) ).
cnf(refute_0_251,plain,
( multiply(X_42,multiply(inverse(X_42),multiply(identity,X_41))) != multiply(identity,X_41)
| multiply(identity,X_41) != X_41
| multiply(X_42,multiply(inverse(X_42),X_41)) = multiply(identity,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_42,multiply(inverse(X_42),multiply(identity,X_41))),multiply(identity,X_41)) ),[0,1,1],$fot(X_41)]]) ).
cnf(refute_0_252,plain,
( multiply(X_42,multiply(inverse(X_42),multiply(identity,X_41))) != multiply(identity,X_41)
| multiply(X_42,multiply(inverse(X_42),X_41)) = multiply(identity,X_41) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_41),X_41) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
multiply(X_42,multiply(inverse(X_42),X_41)) = multiply(identity,X_41),
inference(resolve,[$cnf( $equal(multiply(X_42,multiply(inverse(X_42),multiply(identity,X_41))),multiply(identity,X_41)) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
( multiply(X_42,multiply(inverse(X_42),X_41)) != multiply(identity,X_41)
| multiply(identity,X_41) != X_41
| multiply(X_42,multiply(inverse(X_42),X_41)) = X_41 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_42,multiply(inverse(X_42),X_41)),X_41) ),[0],$fot(multiply(identity,X_41))]]) ).
cnf(refute_0_255,plain,
( multiply(X_42,multiply(inverse(X_42),X_41)) != multiply(identity,X_41)
| multiply(X_42,multiply(inverse(X_42),X_41)) = X_41 ),
inference(resolve,[$cnf( $equal(multiply(identity,X_41),X_41) )],[refute_0_250,refute_0_254]) ).
cnf(refute_0_256,plain,
multiply(X_42,multiply(inverse(X_42),X_41)) = X_41,
inference(resolve,[$cnf( $equal(multiply(X_42,multiply(inverse(X_42),X_41)),multiply(identity,X_41)) )],[refute_0_253,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(multiply(X_53,X_54),multiply(inverse(multiply(X_53,X_54)),X_41)) = X_41,
inference(subst,[],[refute_0_256:[bind(X_42,$fot(multiply(X_53,X_54)))]]) ).
cnf(refute_0_258,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_11)) = double_divide(X_3,X_2),
inference(subst,[],[refute_0_45:[bind(A,$fot(multiply(X_2,X_3))),bind(B,$fot(X_11)),bind(C,$fot(double_divide(X_3,X_2)))]]) ).
cnf(refute_0_259,plain,
( double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) != identity
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_11)) != double_divide(X_3,X_2)
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_11)),double_divide(X_3,X_2)) ),[0,1,0],$fot(identity)]]) ).
cnf(refute_0_260,plain,
( double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_11)) != double_divide(X_3,X_2)
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),identity) )],[refute_0_230,refute_0_259]) ).
cnf(refute_0_261,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(X_3,X_2),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),X_11)),double_divide(X_3,X_2)) )],[refute_0_258,refute_0_260]) ).
cnf(refute_0_262,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)))]]) ).
cnf(refute_0_263,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) != double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11))
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11))) ),[1,1],$fot(inverse(inverse(X_11)))]]) ).
cnf(refute_0_264,plain,
( multiply(identity,X_11) != inverse(inverse(X_11))
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) = double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))),
inference(resolve,[$cnf( $equal(multiply(identity,X_11),inverse(inverse(X_11))) )],[refute_0_103,refute_0_264]) ).
cnf(refute_0_266,plain,
( double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) != double_divide(X_3,X_2)
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) != double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11)))
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) = double_divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),double_divide(X_3,X_2)) ),[0],$fot(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))))]]) ).
cnf(refute_0_267,plain,
( double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)) != double_divide(X_3,X_2)
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) = double_divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11)))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) = double_divide(X_3,X_2),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),multiply(identity,X_11)),double_divide(X_3,X_2)) )],[refute_0_261,refute_0_267]) ).
cnf(refute_0_269,plain,
double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) = double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),
inference(subst,[],[refute_0_181:[bind(A,$fot(multiply(X_2,X_3))),bind(B,$fot(X_11))]]) ).
cnf(refute_0_270,plain,
( double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) != double_divide(X_3,X_2)
| double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) != double_divide(identity,inverse(inverse(multiply(X_2,X_3))))
| double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))),double_divide(X_3,X_2)) ),[0],$fot(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))))]]) ).
cnf(refute_0_271,plain,
( double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))) != double_divide(X_3,X_2)
| double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))),double_divide(identity,inverse(inverse(multiply(X_2,X_3))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(X_3,X_2),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(multiply(X_2,X_3),inverse(X_11))),inverse(inverse(X_11))),double_divide(X_3,X_2)) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
inverse(inverse(multiply(X_2,X_3))) = multiply(X_2,X_3),
inference(subst,[],[refute_0_198:[bind(X_22,$fot(multiply(X_2,X_3)))]]) ).
cnf(refute_0_274,plain,
double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))))]]) ).
cnf(refute_0_275,plain,
( double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) != double_divide(identity,inverse(inverse(multiply(X_2,X_3))))
| inverse(inverse(multiply(X_2,X_3))) != multiply(X_2,X_3)
| double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(identity,multiply(X_2,X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),double_divide(identity,inverse(inverse(multiply(X_2,X_3))))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_276,plain,
( inverse(inverse(multiply(X_2,X_3))) != multiply(X_2,X_3)
| double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(identity,multiply(X_2,X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),double_divide(identity,inverse(inverse(multiply(X_2,X_3))))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) = double_divide(identity,multiply(X_2,X_3)),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_2,X_3))),multiply(X_2,X_3)) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) != double_divide(X_3,X_2)
| double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) != double_divide(identity,multiply(X_2,X_3))
| double_divide(identity,multiply(X_2,X_3)) = double_divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),double_divide(X_3,X_2)) ),[0],$fot(double_divide(identity,multiply(X_2,X_3)))]]) ).
cnf(refute_0_279,plain,
( double_divide(identity,inverse(inverse(multiply(X_2,X_3)))) != double_divide(X_3,X_2)
| double_divide(identity,multiply(X_2,X_3)) = double_divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),double_divide(identity,multiply(X_2,X_3))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
double_divide(identity,multiply(X_2,X_3)) = double_divide(X_3,X_2),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(X_2,X_3)))),double_divide(X_3,X_2)) )],[refute_0_272,refute_0_279]) ).
cnf(refute_0_281,plain,
double_divide(identity,multiply(X_2,X_3)) = inverse(multiply(X_2,X_3)),
inference(subst,[],[refute_0_216:[bind(X_20,$fot(multiply(X_2,X_3)))]]) ).
cnf(refute_0_282,plain,
( double_divide(identity,multiply(X_2,X_3)) != double_divide(X_3,X_2)
| double_divide(identity,multiply(X_2,X_3)) != inverse(multiply(X_2,X_3))
| inverse(multiply(X_2,X_3)) = double_divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(X_2,X_3)),double_divide(X_3,X_2)) ),[0],$fot(inverse(multiply(X_2,X_3)))]]) ).
cnf(refute_0_283,plain,
( double_divide(identity,multiply(X_2,X_3)) != double_divide(X_3,X_2)
| inverse(multiply(X_2,X_3)) = double_divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_2,X_3)),inverse(multiply(X_2,X_3))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
inverse(multiply(X_2,X_3)) = double_divide(X_3,X_2),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(X_2,X_3)),double_divide(X_3,X_2)) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
inverse(multiply(X_53,X_54)) = double_divide(X_54,X_53),
inference(subst,[],[refute_0_284:[bind(X_2,$fot(X_53)),bind(X_3,$fot(X_54))]]) ).
cnf(refute_0_286,plain,
( multiply(multiply(X_53,X_54),multiply(inverse(multiply(X_53,X_54)),X_41)) != X_41
| inverse(multiply(X_53,X_54)) != double_divide(X_54,X_53)
| multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),X_41)) = X_41 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_53,X_54),multiply(inverse(multiply(X_53,X_54)),X_41)),X_41) ),[0,1,0],$fot(double_divide(X_54,X_53))]]) ).
cnf(refute_0_287,plain,
( multiply(multiply(X_53,X_54),multiply(inverse(multiply(X_53,X_54)),X_41)) != X_41
| multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),X_41)) = X_41 ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_53,X_54)),double_divide(X_54,X_53)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),X_41)) = X_41,
inference(resolve,[$cnf( $equal(multiply(multiply(X_53,X_54),multiply(inverse(multiply(X_53,X_54)),X_41)),X_41) )],[refute_0_257,refute_0_287]) ).
cnf(refute_0_289,plain,
multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73)))) = multiply(X_53,multiply(X_54,X_73)),
inference(subst,[],[refute_0_288:[bind(X_41,$fot(multiply(X_53,multiply(X_54,X_73))))]]) ).
cnf(refute_0_290,plain,
double_divide(double_divide(identity,double_divide(X_10,inverse(double_divide(B,A)))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(X_10)),bind(B,$fot(double_divide(B,A))),bind(C,$fot(X_12))]]) ).
cnf(refute_0_291,plain,
( double_divide(double_divide(identity,double_divide(X_10,inverse(double_divide(B,A)))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| inverse(double_divide(B,A)) != multiply(A,B)
| double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,inverse(double_divide(B,A)))),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) ),[0,0,1,1],$fot(multiply(A,B))]]) ).
cnf(refute_0_292,plain,
( double_divide(double_divide(identity,double_divide(X_10,inverse(double_divide(B,A)))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_37,refute_0_291]) ).
cnf(refute_0_293,plain,
double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,inverse(double_divide(B,A)))),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) )],[refute_0_290,refute_0_292]) ).
cnf(refute_0_294,plain,
inverse(double_divide(X_10,multiply(A,B))) = multiply(multiply(A,B),X_10),
inference(subst,[],[refute_0_37:[bind(A,$fot(multiply(A,B))),bind(B,$fot(X_10))]]) ).
cnf(refute_0_295,plain,
double_divide(identity,double_divide(X_10,multiply(A,B))) = inverse(double_divide(X_10,multiply(A,B))),
inference(subst,[],[refute_0_216:[bind(X_20,$fot(double_divide(X_10,multiply(A,B))))]]) ).
cnf(refute_0_296,plain,
( double_divide(identity,double_divide(X_10,multiply(A,B))) != inverse(double_divide(X_10,multiply(A,B)))
| inverse(double_divide(X_10,multiply(A,B))) != multiply(multiply(A,B),X_10)
| double_divide(identity,double_divide(X_10,multiply(A,B))) = multiply(multiply(A,B),X_10) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(identity,double_divide(X_10,multiply(A,B))))),bind(Y,$fot(inverse(double_divide(X_10,multiply(A,B))))),bind(Z,$fot(multiply(multiply(A,B),X_10)))]]) ).
cnf(refute_0_297,plain,
( inverse(double_divide(X_10,multiply(A,B))) != multiply(multiply(A,B),X_10)
| double_divide(identity,double_divide(X_10,multiply(A,B))) = multiply(multiply(A,B),X_10) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_10,multiply(A,B))),inverse(double_divide(X_10,multiply(A,B)))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
double_divide(identity,double_divide(X_10,multiply(A,B))) = multiply(multiply(A,B),X_10),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_10,multiply(A,B))),multiply(multiply(A,B),X_10)) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))))]]) ).
cnf(refute_0_300,plain,
( double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A)))
| double_divide(identity,double_divide(X_10,multiply(A,B))) != multiply(multiply(A,B),X_10)
| double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A)))) ),[1,0],$fot(multiply(multiply(A,B),X_10))]]) ).
cnf(refute_0_301,plain,
( double_divide(identity,double_divide(X_10,multiply(A,B))) != multiply(multiply(A,B),X_10)
| double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) = double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(multiply(A,B),X_10)) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
( double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A)))
| double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) ),[0],$fot(double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))))]]) ).
cnf(refute_0_304,plain,
( double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A)))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_10,multiply(A,B))),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) )],[refute_0_293,refute_0_304]) ).
cnf(refute_0_306,plain,
multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_28))) = double_divide(inverse(X_44),X_28),
inference(subst,[],[refute_0_256:[bind(X_41,$fot(double_divide(inverse(X_44),X_28))),bind(X_42,$fot(X_44))]]) ).
cnf(refute_0_307,plain,
multiply(double_divide(X_26,B),B) = inverse(double_divide(B,double_divide(X_26,B))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(X_26,B)))]]) ).
cnf(refute_0_308,plain,
double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) = X_12,
inference(subst,[],[refute_0_45:[bind(A,$fot(X_11)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_309,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_310,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_311,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)),X_12) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_313,plain,
( double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)),X_12) )],[refute_0_308,refute_0_313]) ).
cnf(refute_0_315,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_316,plain,
( double_divide(identity,identity) != inverse(identity)
| inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(identity,identity))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_317,plain,
( inverse(identity) != identity
| double_divide(identity,identity) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
double_divide(identity,identity) = identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_73,refute_0_317]) ).
cnf(refute_0_319,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)))]]) ).
cnf(refute_0_320,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))
| double_divide(identity,identity) != identity
| double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_321,plain,
( double_divide(identity,identity) != identity
| double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),identity) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != double_divide(identity,multiply(double_divide(X_12,X_11),X_11))
| double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),X_12) ),[0],$fot(double_divide(identity,multiply(double_divide(X_12,X_11),X_11)))]]) ).
cnf(refute_0_324,plain,
( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(identity,multiply(double_divide(X_12,X_11),X_11))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),X_12) )],[refute_0_314,refute_0_324]) ).
cnf(refute_0_326,plain,
double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = double_divide(X_11,double_divide(X_12,X_11)),
inference(subst,[],[refute_0_280:[bind(X_2,$fot(double_divide(X_12,X_11))),bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_327,plain,
( double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) != double_divide(X_11,double_divide(X_12,X_11))
| double_divide(X_11,double_divide(X_12,X_11)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_12,X_11),X_11)),X_12) ),[0],$fot(double_divide(X_11,double_divide(X_12,X_11)))]]) ).
cnf(refute_0_328,plain,
( double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) != X_12
| double_divide(X_11,double_divide(X_12,X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_12,X_11),X_11)),double_divide(X_11,double_divide(X_12,X_11))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
double_divide(X_11,double_divide(X_12,X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_12,X_11),X_11)),X_12) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
double_divide(B,double_divide(X_26,B)) = X_26,
inference(subst,[],[refute_0_329:[bind(X_11,$fot(B)),bind(X_12,$fot(X_26))]]) ).
cnf(refute_0_331,plain,
( multiply(double_divide(X_26,B),B) != inverse(double_divide(B,double_divide(X_26,B)))
| double_divide(B,double_divide(X_26,B)) != X_26
| multiply(double_divide(X_26,B),B) = inverse(X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_26,B),B),inverse(double_divide(B,double_divide(X_26,B)))) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_332,plain,
( multiply(double_divide(X_26,B),B) != inverse(double_divide(B,double_divide(X_26,B)))
| multiply(double_divide(X_26,B),B) = inverse(X_26) ),
inference(resolve,[$cnf( $equal(double_divide(B,double_divide(X_26,B)),X_26) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
multiply(double_divide(X_26,B),B) = inverse(X_26),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_26,B),B),inverse(double_divide(B,double_divide(X_26,B)))) )],[refute_0_307,refute_0_332]) ).
cnf(refute_0_334,plain,
multiply(double_divide(X_28,double_divide(X_12,X_28)),double_divide(X_12,X_28)) = inverse(X_28),
inference(subst,[],[refute_0_333:[bind(B,$fot(double_divide(X_12,X_28))),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_335,plain,
double_divide(X_28,double_divide(X_12,X_28)) = X_12,
inference(subst,[],[refute_0_329:[bind(X_11,$fot(X_28))]]) ).
cnf(refute_0_336,plain,
( multiply(double_divide(X_28,double_divide(X_12,X_28)),double_divide(X_12,X_28)) != inverse(X_28)
| double_divide(X_28,double_divide(X_12,X_28)) != X_12
| multiply(X_12,double_divide(X_12,X_28)) = inverse(X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_28,double_divide(X_12,X_28)),double_divide(X_12,X_28)),inverse(X_28)) ),[0,0],$fot(X_12)]]) ).
cnf(refute_0_337,plain,
( multiply(double_divide(X_28,double_divide(X_12,X_28)),double_divide(X_12,X_28)) != inverse(X_28)
| multiply(X_12,double_divide(X_12,X_28)) = inverse(X_28) ),
inference(resolve,[$cnf( $equal(double_divide(X_28,double_divide(X_12,X_28)),X_12) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
multiply(X_12,double_divide(X_12,X_28)) = inverse(X_28),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_28,double_divide(X_12,X_28)),double_divide(X_12,X_28)),inverse(X_28)) )],[refute_0_334,refute_0_337]) ).
cnf(refute_0_339,plain,
multiply(inverse(X_44),double_divide(inverse(X_44),X_28)) = inverse(X_28),
inference(subst,[],[refute_0_338:[bind(X_12,$fot(inverse(X_44)))]]) ).
cnf(refute_0_340,plain,
( multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_28))) != double_divide(inverse(X_44),X_28)
| multiply(inverse(X_44),double_divide(inverse(X_44),X_28)) != inverse(X_28)
| multiply(X_44,inverse(X_28)) = double_divide(inverse(X_44),X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_28))),double_divide(inverse(X_44),X_28)) ),[0,1],$fot(inverse(X_28))]]) ).
cnf(refute_0_341,plain,
( multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_28))) != double_divide(inverse(X_44),X_28)
| multiply(X_44,inverse(X_28)) = double_divide(inverse(X_44),X_28) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_44),double_divide(inverse(X_44),X_28)),inverse(X_28)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
multiply(X_44,inverse(X_28)) = double_divide(inverse(X_44),X_28),
inference(resolve,[$cnf( $equal(multiply(X_44,multiply(inverse(X_44),double_divide(inverse(X_44),X_28))),double_divide(inverse(X_44),X_28)) )],[refute_0_306,refute_0_341]) ).
cnf(refute_0_343,plain,
multiply(inverse(X_22),inverse(X_45)) = double_divide(inverse(inverse(X_22)),X_45),
inference(subst,[],[refute_0_342:[bind(X_28,$fot(X_45)),bind(X_44,$fot(inverse(X_22)))]]) ).
cnf(refute_0_344,plain,
( multiply(inverse(X_22),inverse(X_45)) != double_divide(inverse(inverse(X_22)),X_45)
| inverse(inverse(X_22)) != X_22
| multiply(inverse(X_22),inverse(X_45)) = double_divide(X_22,X_45) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_22),inverse(X_45)),double_divide(inverse(inverse(X_22)),X_45)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_345,plain,
( multiply(inverse(X_22),inverse(X_45)) != double_divide(inverse(inverse(X_22)),X_45)
| multiply(inverse(X_22),inverse(X_45)) = double_divide(X_22,X_45) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_22)),X_22) )],[refute_0_198,refute_0_344]) ).
cnf(refute_0_346,plain,
multiply(inverse(X_22),inverse(X_45)) = double_divide(X_22,X_45),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),inverse(X_45)),double_divide(inverse(inverse(X_22)),X_45)) )],[refute_0_343,refute_0_345]) ).
cnf(refute_0_347,plain,
multiply(inverse(X_22),inverse(multiply(X_53,X_54))) = double_divide(X_22,multiply(X_53,X_54)),
inference(subst,[],[refute_0_346:[bind(X_45,$fot(multiply(X_53,X_54)))]]) ).
cnf(refute_0_348,plain,
( multiply(inverse(X_22),inverse(multiply(X_53,X_54))) != double_divide(X_22,multiply(X_53,X_54))
| inverse(multiply(X_53,X_54)) != double_divide(X_54,X_53)
| multiply(inverse(X_22),double_divide(X_54,X_53)) = double_divide(X_22,multiply(X_53,X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_22),inverse(multiply(X_53,X_54))),double_divide(X_22,multiply(X_53,X_54))) ),[0,1],$fot(double_divide(X_54,X_53))]]) ).
cnf(refute_0_349,plain,
( multiply(inverse(X_22),inverse(multiply(X_53,X_54))) != double_divide(X_22,multiply(X_53,X_54))
| multiply(inverse(X_22),double_divide(X_54,X_53)) = double_divide(X_22,multiply(X_53,X_54)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_53,X_54)),double_divide(X_54,X_53)) )],[refute_0_285,refute_0_348]) ).
cnf(refute_0_350,plain,
multiply(inverse(X_22),double_divide(X_54,X_53)) = double_divide(X_22,multiply(X_53,X_54)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_22),inverse(multiply(X_53,X_54))),double_divide(X_22,multiply(X_53,X_54))) )],[refute_0_347,refute_0_349]) ).
cnf(refute_0_351,plain,
multiply(inverse(multiply(X_2,X_3)),double_divide(X_57,X_56)) = double_divide(multiply(X_2,X_3),multiply(X_56,X_57)),
inference(subst,[],[refute_0_350:[bind(X_22,$fot(multiply(X_2,X_3))),bind(X_53,$fot(X_56)),bind(X_54,$fot(X_57))]]) ).
cnf(refute_0_352,plain,
( multiply(inverse(multiply(X_2,X_3)),double_divide(X_57,X_56)) != double_divide(multiply(X_2,X_3),multiply(X_56,X_57))
| inverse(multiply(X_2,X_3)) != double_divide(X_3,X_2)
| multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)) = double_divide(multiply(X_2,X_3),multiply(X_56,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(multiply(X_2,X_3)),double_divide(X_57,X_56)),double_divide(multiply(X_2,X_3),multiply(X_56,X_57))) ),[0,0],$fot(double_divide(X_3,X_2))]]) ).
cnf(refute_0_353,plain,
( multiply(inverse(multiply(X_2,X_3)),double_divide(X_57,X_56)) != double_divide(multiply(X_2,X_3),multiply(X_56,X_57))
| multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)) = double_divide(multiply(X_2,X_3),multiply(X_56,X_57)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_2,X_3)),double_divide(X_3,X_2)) )],[refute_0_284,refute_0_352]) ).
cnf(refute_0_354,plain,
multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)) = double_divide(multiply(X_2,X_3),multiply(X_56,X_57)),
inference(resolve,[$cnf( $equal(multiply(inverse(multiply(X_2,X_3)),double_divide(X_57,X_56)),double_divide(multiply(X_2,X_3),multiply(X_56,X_57))) )],[refute_0_351,refute_0_353]) ).
cnf(refute_0_355,plain,
( multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)) != double_divide(multiply(X_2,X_3),multiply(X_56,X_57))
| double_divide(multiply(X_2,X_3),multiply(X_56,X_57)) = multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)))),bind(Y,$fot(double_divide(multiply(X_2,X_3),multiply(X_56,X_57))))]]) ).
cnf(refute_0_356,plain,
double_divide(multiply(X_2,X_3),multiply(X_56,X_57)) = multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_3,X_2),double_divide(X_57,X_56)),double_divide(multiply(X_2,X_3),multiply(X_56,X_57))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) = multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10))),
inference(subst,[],[refute_0_356:[bind(X_2,$fot(multiply(A,B))),bind(X_3,$fot(X_10)),bind(X_56,$fot(double_divide(X_12,X_10))),bind(X_57,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_358,plain,
( double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) != multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10)))
| multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) ),[0],$fot(multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10))))]]) ).
cnf(refute_0_359,plain,
( double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))) != X_12
| multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))),multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10)))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
multiply(double_divide(X_10,multiply(A,B)),double_divide(double_divide(B,A),double_divide(X_12,X_10))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(multiply(multiply(A,B),X_10),multiply(double_divide(X_12,X_10),double_divide(B,A))),X_12) )],[refute_0_305,refute_0_359]) ).
cnf(refute_0_361,plain,
multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(double_divide(identity,X_67),double_divide(X_70,X_69))) = X_70,
inference(subst,[],[refute_0_360:[bind(A,$fot(X_67)),bind(B,$fot(identity)),bind(X_10,$fot(X_69)),bind(X_12,$fot(X_70))]]) ).
cnf(refute_0_362,plain,
inverse(X_67) = double_divide(identity,X_67),
inference(subst,[],[refute_0_214:[bind(X_20,$fot(X_67))]]) ).
cnf(refute_0_363,plain,
( inverse(X_67) != double_divide(identity,X_67)
| double_divide(identity,X_67) = inverse(X_67) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_67))),bind(Y,$fot(double_divide(identity,X_67)))]]) ).
cnf(refute_0_364,plain,
double_divide(identity,X_67) = inverse(X_67),
inference(resolve,[$cnf( $equal(inverse(X_67),double_divide(identity,X_67)) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
( multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(double_divide(identity,X_67),double_divide(X_70,X_69))) != X_70
| double_divide(identity,X_67) != inverse(X_67)
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = X_70 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(double_divide(identity,X_67),double_divide(X_70,X_69))),X_70) ),[0,1,0],$fot(inverse(X_67))]]) ).
cnf(refute_0_366,plain,
( multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(double_divide(identity,X_67),double_divide(X_70,X_69))) != X_70
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = X_70 ),
inference(resolve,[$cnf( $equal(double_divide(identity,X_67),inverse(X_67)) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = X_70,
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(double_divide(identity,X_67),double_divide(X_70,X_69))),X_70) )],[refute_0_361,refute_0_366]) ).
cnf(refute_0_368,plain,
inverse(double_divide(X_70,X_69)) = multiply(X_69,X_70),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_69)),bind(B,$fot(X_70))]]) ).
cnf(refute_0_369,plain,
multiply(X_67,inverse(double_divide(X_70,X_69))) = multiply(X_67,inverse(double_divide(X_70,X_69))),
introduced(tautology,[refl,[$fot(multiply(X_67,inverse(double_divide(X_70,X_69))))]]) ).
cnf(refute_0_370,plain,
( multiply(X_67,inverse(double_divide(X_70,X_69))) != multiply(X_67,inverse(double_divide(X_70,X_69)))
| inverse(double_divide(X_70,X_69)) != multiply(X_69,X_70)
| multiply(X_67,inverse(double_divide(X_70,X_69))) = multiply(X_67,multiply(X_69,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_67,inverse(double_divide(X_70,X_69))),multiply(X_67,inverse(double_divide(X_70,X_69)))) ),[1,1],$fot(multiply(X_69,X_70))]]) ).
cnf(refute_0_371,plain,
( inverse(double_divide(X_70,X_69)) != multiply(X_69,X_70)
| multiply(X_67,inverse(double_divide(X_70,X_69))) = multiply(X_67,multiply(X_69,X_70)) ),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(double_divide(X_70,X_69))),multiply(X_67,inverse(double_divide(X_70,X_69)))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
multiply(X_67,inverse(double_divide(X_70,X_69))) = multiply(X_67,multiply(X_69,X_70)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_70,X_69)),multiply(X_69,X_70)) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
( multiply(X_44,inverse(X_28)) != double_divide(inverse(X_44),X_28)
| double_divide(inverse(X_44),X_28) = multiply(X_44,inverse(X_28)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_44,inverse(X_28)))),bind(Y,$fot(double_divide(inverse(X_44),X_28)))]]) ).
cnf(refute_0_374,plain,
double_divide(inverse(X_44),X_28) = multiply(X_44,inverse(X_28)),
inference(resolve,[$cnf( $equal(multiply(X_44,inverse(X_28)),double_divide(inverse(X_44),X_28)) )],[refute_0_342,refute_0_373]) ).
cnf(refute_0_375,plain,
double_divide(inverse(X_67),double_divide(X_70,X_69)) = multiply(X_67,inverse(double_divide(X_70,X_69))),
inference(subst,[],[refute_0_374:[bind(X_28,$fot(double_divide(X_70,X_69))),bind(X_44,$fot(X_67))]]) ).
cnf(refute_0_376,plain,
( multiply(X_67,inverse(double_divide(X_70,X_69))) != multiply(X_67,multiply(X_69,X_70))
| double_divide(inverse(X_67),double_divide(X_70,X_69)) != multiply(X_67,inverse(double_divide(X_70,X_69)))
| double_divide(inverse(X_67),double_divide(X_70,X_69)) = multiply(X_67,multiply(X_69,X_70)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(double_divide(inverse(X_67),double_divide(X_70,X_69)))),bind(Y,$fot(multiply(X_67,inverse(double_divide(X_70,X_69))))),bind(Z,$fot(multiply(X_67,multiply(X_69,X_70))))]]) ).
cnf(refute_0_377,plain,
( multiply(X_67,inverse(double_divide(X_70,X_69))) != multiply(X_67,multiply(X_69,X_70))
| double_divide(inverse(X_67),double_divide(X_70,X_69)) = multiply(X_67,multiply(X_69,X_70)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_67),double_divide(X_70,X_69)),multiply(X_67,inverse(double_divide(X_70,X_69)))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
double_divide(inverse(X_67),double_divide(X_70,X_69)) = multiply(X_67,multiply(X_69,X_70)),
inference(resolve,[$cnf( $equal(multiply(X_67,inverse(double_divide(X_70,X_69))),multiply(X_67,multiply(X_69,X_70))) )],[refute_0_372,refute_0_377]) ).
cnf(refute_0_379,plain,
multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))),
introduced(tautology,[refl,[$fot(multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))))]]) ).
cnf(refute_0_380,plain,
( multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69)))
| double_divide(inverse(X_67),double_divide(X_70,X_69)) != multiply(X_67,multiply(X_69,X_70))
| multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69)))) ),[1,1],$fot(multiply(X_67,multiply(X_69,X_70)))]]) ).
cnf(refute_0_381,plain,
( double_divide(inverse(X_67),double_divide(X_70,X_69)) != multiply(X_67,multiply(X_69,X_70))
| multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69)))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_67),double_divide(X_70,X_69)),multiply(X_67,multiply(X_69,X_70))) )],[refute_0_378,refute_0_381]) ).
cnf(refute_0_383,plain,
double_divide(identity,inverse(X_16)) = X_16,
inference(subst,[],[refute_0_206:[bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_384,plain,
multiply(double_divide(identity,inverse(X_16)),identity) = multiply(double_divide(identity,inverse(X_16)),identity),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(X_16)),identity))]]) ).
cnf(refute_0_385,plain,
( multiply(double_divide(identity,inverse(X_16)),identity) != multiply(double_divide(identity,inverse(X_16)),identity)
| double_divide(identity,inverse(X_16)) != X_16
| multiply(double_divide(identity,inverse(X_16)),identity) = multiply(X_16,identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_16)),identity),multiply(double_divide(identity,inverse(X_16)),identity)) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_386,plain,
( double_divide(identity,inverse(X_16)) != X_16
| multiply(double_divide(identity,inverse(X_16)),identity) = multiply(X_16,identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_16)),identity),multiply(double_divide(identity,inverse(X_16)),identity)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
multiply(double_divide(identity,inverse(X_16)),identity) = multiply(X_16,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(X_16)),X_16) )],[refute_0_383,refute_0_386]) ).
cnf(refute_0_388,plain,
( multiply(double_divide(identity,inverse(X_16)),identity) != X_16
| multiply(double_divide(identity,inverse(X_16)),identity) != multiply(X_16,identity)
| multiply(X_16,identity) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(X_16)),identity),X_16) ),[0],$fot(multiply(X_16,identity))]]) ).
cnf(refute_0_389,plain,
( multiply(double_divide(identity,inverse(X_16)),identity) != X_16
| multiply(X_16,identity) = X_16 ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_16)),identity),multiply(X_16,identity)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
multiply(X_16,identity) = X_16,
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(X_16)),identity),X_16) )],[refute_0_147,refute_0_389]) ).
cnf(refute_0_391,plain,
multiply(X_67,identity) = X_67,
inference(subst,[],[refute_0_390:[bind(X_16,$fot(X_67))]]) ).
cnf(refute_0_392,plain,
double_divide(X_69,multiply(X_67,identity)) = double_divide(X_69,multiply(X_67,identity)),
introduced(tautology,[refl,[$fot(double_divide(X_69,multiply(X_67,identity)))]]) ).
cnf(refute_0_393,plain,
( multiply(X_67,identity) != X_67
| double_divide(X_69,multiply(X_67,identity)) != double_divide(X_69,multiply(X_67,identity))
| double_divide(X_69,multiply(X_67,identity)) = double_divide(X_69,X_67) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_69,multiply(X_67,identity)),double_divide(X_69,multiply(X_67,identity))) ),[1,1],$fot(X_67)]]) ).
cnf(refute_0_394,plain,
( multiply(X_67,identity) != X_67
| double_divide(X_69,multiply(X_67,identity)) = double_divide(X_69,X_67) ),
inference(resolve,[$cnf( $equal(double_divide(X_69,multiply(X_67,identity)),double_divide(X_69,multiply(X_67,identity))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
double_divide(X_69,multiply(X_67,identity)) = double_divide(X_69,X_67),
inference(resolve,[$cnf( $equal(multiply(X_67,identity),X_67) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),
introduced(tautology,[refl,[$fot(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))))]]) ).
cnf(refute_0_397,plain,
( multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69)))
| double_divide(X_69,multiply(X_67,identity)) != double_divide(X_69,X_67)
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69)))) ),[1,0],$fot(double_divide(X_69,X_67))]]) ).
cnf(refute_0_398,plain,
( double_divide(X_69,multiply(X_67,identity)) != double_divide(X_69,X_67)
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69)))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))),
inference(resolve,[$cnf( $equal(double_divide(X_69,multiply(X_67,identity)),double_divide(X_69,X_67)) )],[refute_0_395,refute_0_398]) ).
cnf(refute_0_400,plain,
( multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69)))
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))))),bind(Y,$fot(multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))))),bind(Z,$fot(multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))))]]) ).
cnf(refute_0_401,plain,
( multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69)))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) = multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,X_67),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))) )],[refute_0_382,refute_0_401]) ).
cnf(refute_0_403,plain,
( multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) != X_70
| multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) != multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))
| multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) = X_70 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),X_70) ),[0],$fot(multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))))]]) ).
cnf(refute_0_404,plain,
( multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))) != X_70
| multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) = X_70 ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70)))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
multiply(double_divide(X_69,X_67),multiply(X_67,multiply(X_69,X_70))) = X_70,
inference(resolve,[$cnf( $equal(multiply(double_divide(X_69,multiply(X_67,identity)),double_divide(inverse(X_67),double_divide(X_70,X_69))),X_70) )],[refute_0_367,refute_0_404]) ).
cnf(refute_0_406,plain,
multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73))) = X_73,
inference(subst,[],[refute_0_405:[bind(X_67,$fot(X_53)),bind(X_69,$fot(X_54)),bind(X_70,$fot(X_73))]]) ).
cnf(refute_0_407,plain,
( multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73)))) != multiply(X_53,multiply(X_54,X_73))
| multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73))) != X_73
| multiply(multiply(X_53,X_54),X_73) = multiply(X_53,multiply(X_54,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73)))),multiply(X_53,multiply(X_54,X_73))) ),[0,1],$fot(X_73)]]) ).
cnf(refute_0_408,plain,
( multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73)))) != multiply(X_53,multiply(X_54,X_73))
| multiply(multiply(X_53,X_54),X_73) = multiply(X_53,multiply(X_54,X_73)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73))),X_73) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
multiply(multiply(X_53,X_54),X_73) = multiply(X_53,multiply(X_54,X_73)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_53,X_54),multiply(double_divide(X_54,X_53),multiply(X_53,multiply(X_54,X_73)))),multiply(X_53,multiply(X_54,X_73))) )],[refute_0_289,refute_0_408]) ).
cnf(refute_0_410,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_409:[bind(X_53,$fot(a3)),bind(X_54,$fot(b3)),bind(X_73,$fot(c3))]]) ).
cnf(refute_0_411,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_412,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_412,prove_these_axioms_3]) ).
cnf(refute_0_414,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_415,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_414,refute_0_413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP498-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 15:15:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.50
%------------------------------------------------------------------------------