TSTP Solution File: GRP492-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:41:42 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 110
% Syntax : Number of clauses : 369 ( 193 unt; 0 nHn; 186 RR)
% Number of literals : 628 ( 627 equ; 261 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 653 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = 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( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(double_divide(X_26,B),B) = inverse(double_divide(B,double_divide(X_26,B))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(X_26,B)))]]) ).
cnf(refute_0_10,plain,
double_divide(double_divide(A,B),identity) = inverse(double_divide(A,B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(A,B)))]]) ).
cnf(refute_0_11,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))]]) ).
cnf(refute_0_12,plain,
( double_divide(double_divide(A,B),identity) != inverse(double_divide(A,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) ),[1,0],$fot(inverse(double_divide(A,B)))]]) ).
cnf(refute_0_13,plain,
( double_divide(double_divide(A,B),identity) != inverse(double_divide(A,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,B),identity),inverse(double_divide(A,B))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))]]) ).
cnf(refute_0_16,plain,
( double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) ),[1,1],$fot(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))]]) ).
cnf(refute_0_17,plain,
( double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))))]]) ).
cnf(refute_0_20,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))]]) ).
cnf(refute_0_21,plain,
( double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),C) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))))]]) ).
cnf(refute_0_24,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),C) )],[single_axiom,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_27,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_26]) ).
cnf(refute_0_28,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(subst,[],[refute_0_27:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_29,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))]]) ).
cnf(refute_0_30,plain,
( double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| inverse(double_divide(A,B)) != multiply(B,A)
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),[1,0],$fot(multiply(B,A))]]) ).
cnf(refute_0_31,plain,
( inverse(double_divide(A,B)) != multiply(B,A)
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,B)),multiply(B,A)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))]]) ).
cnf(refute_0_34,plain,
( double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(multiply(B,A),double_divide(C,B))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),[1,1],$fot(double_divide(multiply(B,A),double_divide(C,B)))]]) ).
cnf(refute_0_35,plain,
( double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(multiply(B,A),double_divide(C,B))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(multiply(B,A),double_divide(C,B))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))))]]) ).
cnf(refute_0_38,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) ),[1,1],$fot(double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))]]) ).
cnf(refute_0_39,plain,
( double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),C) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))))]]) ).
cnf(refute_0_42,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),C) )],[refute_0_25,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(double_divide(identity,identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = X_12,
inference(subst,[],[refute_0_43:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_45,plain,
inverse(identity) = double_divide(identity,identity),
inference(subst,[],[inverse:[bind(A,$fot(identity))]]) ).
cnf(refute_0_46,plain,
( inverse(identity) != double_divide(identity,identity)
| double_divide(identity,identity) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(identity))),bind(Y,$fot(double_divide(identity,identity)))]]) ).
cnf(refute_0_47,plain,
double_divide(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(identity,identity)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != X_12
| double_divide(identity,identity) != inverse(identity)
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),X_12) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_49,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != X_12
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),X_12) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) = X_12,
inference(subst,[],[refute_0_43:[bind(A,$fot(X_10)),bind(B,$fot(inverse(X_12))),bind(C,$fot(X_12))]]) ).
cnf(refute_0_52,plain,
identity = double_divide(X_12,inverse(X_12)),
inference(subst,[],[identity:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_53,plain,
( identity != double_divide(X_12,inverse(X_12))
| double_divide(X_12,inverse(X_12)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_12,inverse(X_12))))]]) ).
cnf(refute_0_54,plain,
double_divide(X_12,inverse(X_12)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_12,inverse(X_12))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( double_divide(X_12,inverse(X_12)) != identity
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))),X_12) ),[0,1,1,1],$fot(identity)]]) ).
cnf(refute_0_56,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,inverse(X_12)),identity) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))),X_12) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(multiply(inverse(X_12),X_10),identity) = inverse(multiply(inverse(X_12),X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(inverse(X_12),X_10)))]]) ).
cnf(refute_0_59,plain,
double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))]]) ).
cnf(refute_0_60,plain,
( double_divide(multiply(inverse(X_12),X_10),identity) != inverse(multiply(inverse(X_12),X_10))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) ),[1,1],$fot(inverse(multiply(inverse(X_12),X_10)))]]) ).
cnf(refute_0_61,plain,
( double_divide(multiply(inverse(X_12),X_10),identity) != inverse(multiply(inverse(X_12),X_10))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_12),X_10),identity),inverse(multiply(inverse(X_12),X_10))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))))]]) ).
cnf(refute_0_64,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,inverse(multiply(inverse(X_12),X_10)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))) ),[1,1],$fot(double_divide(identity,inverse(multiply(inverse(X_12),X_10))))]]) ).
cnf(refute_0_65,plain,
( double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,inverse(multiply(inverse(X_12),X_10)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10))))
| double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),X_12) ),[0],$fot(double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))))]]) ).
cnf(refute_0_68,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10))))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),X_12) )],[refute_0_57,refute_0_68]) ).
cnf(refute_0_70,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) = X_13,
inference(subst,[],[refute_0_69:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X_13))]]) ).
cnf(refute_0_71,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_72,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_73,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_74,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_76,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_71,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(X_13),X_13) = inverse(identity),
inference(subst,[],[refute_0_77:[bind(X_3,$fot(X_13))]]) ).
cnf(refute_0_79,plain,
( multiply(inverse(X_13),X_13) != inverse(identity)
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) != X_13
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))),X_13) ),[0,1,1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_80,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) != X_13
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),X_13),inverse(identity)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))),X_13) )],[refute_0_70,refute_0_80]) ).
cnf(refute_0_82,plain,
inverse(double_divide(identity,X_13)) = multiply(X_13,identity),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_13)),bind(B,$fot(identity))]]) ).
cnf(refute_0_83,plain,
double_divide(double_divide(identity,X_13),identity) = inverse(double_divide(identity,X_13)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,X_13)))]]) ).
cnf(refute_0_84,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_85,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_84]) ).
cnf(refute_0_86,plain,
( double_divide(double_divide(identity,X_13),identity) != inverse(double_divide(identity,X_13))
| inverse(double_divide(identity,X_13)) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(double_divide(double_divide(identity,X_13),identity))),bind(Y,$fot(inverse(double_divide(identity,X_13)))),bind(Z,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_87,plain,
( inverse(double_divide(identity,X_13)) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),identity),inverse(double_divide(identity,X_13))) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
double_divide(double_divide(identity,X_13),identity) = multiply(X_13,identity),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,X_13)),multiply(X_13,identity)) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(subst,[],[refute_0_81:[bind(X_13,$fot(double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_90,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(subst,[],[refute_0_81:[bind(X_13,$fot(inverse(identity)))]]) ).
cnf(refute_0_91,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_92,plain,
( identity != double_divide(identity,inverse(identity))
| double_divide(identity,inverse(identity)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_93,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(identity,inverse(identity)) != identity
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))),inverse(identity)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_95,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))),inverse(identity)) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_98,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_89,refute_0_98]) ).
cnf(refute_0_100,plain,
double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(subst,[],[refute_0_81:[bind(X_13,$fot(identity))]]) ).
cnf(refute_0_101,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) != identity
| double_divide(identity,identity) != inverse(identity)
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))),identity) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_102,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) != identity
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_47,refute_0_101]) ).
cnf(refute_0_103,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))),identity) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
( double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != identity
| identity = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_105,plain,
( double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| identity = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_99,refute_0_105]) ).
cnf(refute_0_107,plain,
( identity != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_108,plain,
double_divide(identity,inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_110,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) != double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity))))
| double_divide(identity,inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,X_13),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity))))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_111,plain,
( double_divide(identity,inverse(inverse(identity))) != identity
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,X_13),identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity))))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,X_13),identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),identity) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) != double_divide(double_divide(identity,X_13),identity)
| double_divide(double_divide(identity,X_13),identity) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = multiply(X_13,identity) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))))),bind(Y,$fot(double_divide(double_divide(identity,X_13),identity))),bind(Z,$fot(multiply(X_13,identity)))]]) ).
cnf(refute_0_114,plain,
( double_divide(double_divide(identity,X_13),identity) != multiply(X_13,identity)
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = multiply(X_13,identity) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),double_divide(double_divide(identity,X_13),identity)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = multiply(X_13,identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),identity),multiply(X_13,identity)) )],[refute_0_88,refute_0_114]) ).
cnf(refute_0_116,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) != X_13
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) != multiply(X_13,identity)
| multiply(X_13,identity) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),X_13) ),[0],$fot(multiply(X_13,identity))]]) ).
cnf(refute_0_117,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) != X_13
| multiply(X_13,identity) = X_13 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),multiply(X_13,identity)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(X_13,identity) = X_13,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))),X_13) )],[refute_0_81,refute_0_117]) ).
cnf(refute_0_119,plain,
multiply(X_11,identity) = X_11,
inference(subst,[],[refute_0_118:[bind(X_13,$fot(X_11))]]) ).
cnf(refute_0_120,plain,
double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) = double_divide(multiply(X_11,identity),double_divide(X_12,X_11)),
introduced(tautology,[refl,[$fot(double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))]]) ).
cnf(refute_0_121,plain,
( multiply(X_11,identity) != X_11
| double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) != double_divide(multiply(X_11,identity),double_divide(X_12,X_11))
| double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) = double_divide(X_11,double_divide(X_12,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(X_11,identity),double_divide(X_12,X_11)),double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_122,plain,
( multiply(X_11,identity) != X_11
| double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) = double_divide(X_11,double_divide(X_12,X_11)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_11,identity),double_divide(X_12,X_11)),double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) = double_divide(X_11,double_divide(X_12,X_11)),
inference(resolve,[$cnf( $equal(multiply(X_11,identity),X_11) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) = double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))))]]) ).
cnf(refute_0_125,plain,
( double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) != double_divide(X_11,double_divide(X_12,X_11))
| double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) != double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))
| double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) = double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) ),[1,1],$fot(double_divide(X_11,double_divide(X_12,X_11)))]]) ).
cnf(refute_0_126,plain,
( double_divide(multiply(X_11,identity),double_divide(X_12,X_11)) != double_divide(X_11,double_divide(X_12,X_11))
| double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) = double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) = double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))),
inference(resolve,[$cnf( $equal(double_divide(multiply(X_11,identity),double_divide(X_12,X_11)),double_divide(X_11,double_divide(X_12,X_11))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))))]]) ).
cnf(refute_0_129,plain,
( double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) != double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))))
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))))) ),[1,1],$fot(double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))]]) ).
cnf(refute_0_130,plain,
( double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))) != double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) = double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11))),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
( double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != X_12
| double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))
| double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),X_12) ),[0],$fot(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))))]]) ).
cnf(refute_0_133,plain,
( double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))) != X_12
| double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X_11,identity),double_divide(X_12,X_11)))),X_12) )],[refute_0_50,refute_0_133]) ).
cnf(refute_0_135,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) = X_12,
inference(subst,[],[refute_0_43:[bind(A,$fot(X_10)),bind(B,$fot(identity)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_136,plain,
inverse(X_12) = double_divide(X_12,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_137,plain,
( inverse(X_12) != double_divide(X_12,identity)
| double_divide(X_12,identity) = inverse(X_12) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(double_divide(X_12,identity)))]]) ).
cnf(refute_0_138,plain,
double_divide(X_12,identity) = inverse(X_12),
inference(resolve,[$cnf( $equal(inverse(X_12),double_divide(X_12,identity)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( double_divide(X_12,identity) != inverse(X_12)
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))),X_12) ),[0,1,1,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_140,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,identity),inverse(X_12)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))),X_12) )],[refute_0_135,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_143,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_144,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_145,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_147,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_142,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(identity,X_10) = inverse(inverse(X_10)),
inference(subst,[],[refute_0_148:[bind(X_3,$fot(X_10))]]) ).
cnf(refute_0_150,plain,
double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(multiply(identity,X_10),inverse(X_12)),
introduced(tautology,[refl,[$fot(double_divide(multiply(identity,X_10),inverse(X_12)))]]) ).
cnf(refute_0_151,plain,
( multiply(identity,X_10) != inverse(inverse(X_10))
| double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(multiply(identity,X_10),inverse(X_12))
| double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(multiply(identity,X_10),inverse(X_12))) ),[1,0],$fot(inverse(inverse(X_10)))]]) ).
cnf(refute_0_152,plain,
( multiply(identity,X_10) != inverse(inverse(X_10))
| double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(multiply(identity,X_10),inverse(X_12))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(identity,X_10),inverse(inverse(X_10))) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))]]) ).
cnf(refute_0_155,plain,
( double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(inverse(inverse(X_10)),inverse(X_12))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) ),[1,1],$fot(double_divide(inverse(inverse(X_10)),inverse(X_12)))]]) ).
cnf(refute_0_156,plain,
( double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(inverse(inverse(X_10)),inverse(X_12))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(inverse(inverse(X_10)),inverse(X_12))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))))]]) ).
cnf(refute_0_159,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))]]) ).
cnf(refute_0_160,plain,
( double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),X_12) ),[0],$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))))]]) ).
cnf(refute_0_163,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),X_12) )],[refute_0_141,refute_0_163]) ).
cnf(refute_0_165,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) = double_divide(identity,X_15),
inference(subst,[],[refute_0_43:[bind(B,$fot(double_divide(identity,inverse(inverse(identity))))),bind(C,$fot(double_divide(identity,X_15)))]]) ).
cnf(refute_0_166,plain,
double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))) = X_15,
inference(subst,[],[refute_0_81:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_167,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))) != X_15
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))),double_divide(identity,X_15)) ),[0,1,1,1],$fot(X_15)]]) ).
cnf(refute_0_168,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))),X_15) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))),double_divide(identity,X_15)) )],[refute_0_165,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(identity,A) = inverse(inverse(A)),
inference(subst,[],[refute_0_148:[bind(X_3,$fot(A))]]) ).
cnf(refute_0_171,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(double_divide(identity,inverse(inverse(identity))),A),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(inverse(identity))),A))]]) ).
cnf(refute_0_172,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != multiply(double_divide(identity,inverse(inverse(identity))),A)
| double_divide(identity,inverse(inverse(identity))) != identity
| multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(double_divide(identity,inverse(inverse(identity))),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_173,plain,
( double_divide(identity,inverse(inverse(identity))) != identity
| multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(double_divide(identity,inverse(inverse(identity))),A)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),identity) )],[refute_0_108,refute_0_173]) ).
cnf(refute_0_175,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != multiply(identity,A)
| multiply(identity,A) != inverse(inverse(A))
| multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(multiply(double_divide(identity,inverse(inverse(identity))),A))),bind(Y,$fot(multiply(identity,A))),bind(Z,$fot(inverse(inverse(A))))]]) ).
cnf(refute_0_176,plain,
( multiply(identity,A) != inverse(inverse(A))
| multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(identity,A)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)),
inference(resolve,[$cnf( $equal(multiply(identity,A),inverse(inverse(A))) )],[refute_0_170,refute_0_176]) ).
cnf(refute_0_178,plain,
double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),
introduced(tautology,[refl,[$fot(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))]]) ).
cnf(refute_0_179,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != inverse(inverse(A))
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) ),[1,0],$fot(inverse(inverse(A)))]]) ).
cnf(refute_0_180,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != inverse(inverse(A))
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),inverse(inverse(A))) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))]]) ).
cnf(refute_0_183,plain,
( double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(inverse(inverse(A)),X_15)
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) ),[1,1],$fot(double_divide(inverse(inverse(A)),X_15))]]) ).
cnf(refute_0_184,plain,
( double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(inverse(inverse(A)),X_15)
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)),
inference(resolve,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(inverse(inverse(A)),X_15)) )],[refute_0_181,refute_0_184]) ).
cnf(refute_0_186,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))))]]) ).
cnf(refute_0_187,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(inverse(inverse(A)),X_15))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(inverse(A)),X_15)))]]) ).
cnf(refute_0_188,plain,
( double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(inverse(inverse(A)),X_15))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(identity,X_15)) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))))]]) ).
cnf(refute_0_191,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(identity,X_15)) )],[refute_0_169,refute_0_191]) ).
cnf(refute_0_193,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = double_divide(identity,inverse(X_12)),
inference(subst,[],[refute_0_192:[bind(A,$fot(X_10)),bind(X_15,$fot(inverse(X_12)))]]) ).
cnf(refute_0_194,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != double_divide(identity,inverse(X_12))
| double_divide(identity,inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),X_12) ),[0],$fot(double_divide(identity,inverse(X_12)))]]) ).
cnf(refute_0_195,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != X_12
| double_divide(identity,inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),double_divide(identity,inverse(X_12))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
double_divide(identity,inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),X_12) )],[refute_0_164,refute_0_195]) ).
cnf(refute_0_197,plain,
double_divide(identity,inverse(inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_196:[bind(X_12,$fot(inverse(identity)))]]) ).
cnf(refute_0_198,plain,
( double_divide(identity,inverse(inverse(identity))) != inverse(identity)
| identity != double_divide(identity,inverse(inverse(identity)))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_199,plain,
( identity != double_divide(identity,inverse(inverse(identity)))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),inverse(identity)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) )],[refute_0_106,refute_0_199]) ).
cnf(refute_0_201,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_202,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),
introduced(tautology,[refl,[$fot(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))))]]) ).
cnf(refute_0_204,plain,
( double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))
| inverse(identity) != identity
| double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_205,plain,
( inverse(identity) != identity
| double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
( double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != X_12
| double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))
| double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),X_12) ),[0],$fot(double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))))]]) ).
cnf(refute_0_208,plain,
( double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != X_12
| double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11))))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),X_12) )],[refute_0_134,refute_0_208]) ).
cnf(refute_0_210,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X_21,identity)))) = X_21,
inference(subst,[],[refute_0_209:[bind(X_11,$fot(identity)),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_211,plain,
inverse(X_21) = double_divide(X_21,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_212,plain,
( inverse(X_21) != double_divide(X_21,identity)
| double_divide(X_21,identity) = inverse(X_21) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_21))),bind(Y,$fot(double_divide(X_21,identity)))]]) ).
cnf(refute_0_213,plain,
double_divide(X_21,identity) = inverse(X_21),
inference(resolve,[$cnf( $equal(inverse(X_21),double_divide(X_21,identity)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
( double_divide(X_21,identity) != inverse(X_21)
| double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X_21,identity)))) != X_21
| double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X_21,identity)))),X_21) ),[0,1,1,1],$fot(inverse(X_21))]]) ).
cnf(refute_0_215,plain,
( double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X_21,identity)))) != X_21
| double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = X_21 ),
inference(resolve,[$cnf( $equal(double_divide(X_21,identity),inverse(X_21)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = X_21,
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X_21,identity)))),X_21) )],[refute_0_210,refute_0_215]) ).
cnf(refute_0_217,plain,
double_divide(identity,inverse(X_21)) = X_21,
inference(subst,[],[refute_0_196:[bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_218,plain,
double_divide(identity,double_divide(identity,inverse(X_21))) = double_divide(identity,double_divide(identity,inverse(X_21))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(identity,inverse(X_21))))]]) ).
cnf(refute_0_219,plain,
( double_divide(identity,double_divide(identity,inverse(X_21))) != double_divide(identity,double_divide(identity,inverse(X_21)))
| double_divide(identity,inverse(X_21)) != X_21
| double_divide(identity,double_divide(identity,inverse(X_21))) = double_divide(identity,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_21))),double_divide(identity,double_divide(identity,inverse(X_21)))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_220,plain,
( double_divide(identity,inverse(X_21)) != X_21
| double_divide(identity,double_divide(identity,inverse(X_21))) = double_divide(identity,X_21) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_21))),double_divide(identity,double_divide(identity,inverse(X_21)))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
double_divide(identity,double_divide(identity,inverse(X_21))) = double_divide(identity,X_21),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(X_21)),X_21) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))))]]) ).
cnf(refute_0_223,plain,
( double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) != double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21))))
| double_divide(identity,double_divide(identity,inverse(X_21))) != double_divide(identity,X_21)
| double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = double_divide(identity,double_divide(identity,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21))))) ),[1,1],$fot(double_divide(identity,X_21))]]) ).
cnf(refute_0_224,plain,
( double_divide(identity,double_divide(identity,inverse(X_21))) != double_divide(identity,X_21)
| double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = double_divide(identity,double_divide(identity,X_21)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21))))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) = double_divide(identity,double_divide(identity,X_21)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_21))),double_divide(identity,X_21)) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) != X_21
| double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) != double_divide(identity,double_divide(identity,X_21))
| double_divide(identity,double_divide(identity,X_21)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),X_21) ),[0],$fot(double_divide(identity,double_divide(identity,X_21)))]]) ).
cnf(refute_0_227,plain,
( double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))) != X_21
| double_divide(identity,double_divide(identity,X_21)) = X_21 ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),double_divide(identity,double_divide(identity,X_21))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
double_divide(identity,double_divide(identity,X_21)) = X_21,
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(X_21)))),X_21) )],[refute_0_216,refute_0_227]) ).
cnf(refute_0_229,plain,
double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) = double_divide(X_11,double_divide(X_12,X_11)),
inference(subst,[],[refute_0_228:[bind(X_21,$fot(double_divide(X_11,double_divide(X_12,X_11))))]]) ).
cnf(refute_0_230,plain,
( double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != X_12
| double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,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( $equal(double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),X_12) ),[0],$fot(double_divide(X_11,double_divide(X_12,X_11)))]]) ).
cnf(refute_0_231,plain,
( double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))) != X_12
| double_divide(X_11,double_divide(X_12,X_11)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),double_divide(X_11,double_divide(X_12,X_11))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
double_divide(X_11,double_divide(X_12,X_11)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(X_11,double_divide(X_12,X_11)))),X_12) )],[refute_0_209,refute_0_231]) ).
cnf(refute_0_233,plain,
double_divide(B,double_divide(X_26,B)) = X_26,
inference(subst,[],[refute_0_232:[bind(X_11,$fot(B)),bind(X_12,$fot(X_26))]]) ).
cnf(refute_0_234,plain,
( multiply(double_divide(X_26,B),B) != inverse(double_divide(B,double_divide(X_26,B)))
| double_divide(B,double_divide(X_26,B)) != X_26
| multiply(double_divide(X_26,B),B) = inverse(X_26) ),
introduced(tautology,[equality,[$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_235,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( $equal(double_divide(B,double_divide(X_26,B)),X_26) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
multiply(double_divide(X_26,B),B) = inverse(X_26),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_26,B),B),inverse(double_divide(B,double_divide(X_26,B)))) )],[refute_0_9,refute_0_235]) ).
cnf(refute_0_237,plain,
multiply(double_divide(double_divide(multiply(X_84,B),X_82),B),B) = inverse(double_divide(multiply(X_84,B),X_82)),
inference(subst,[],[refute_0_236:[bind(X_26,$fot(double_divide(multiply(X_84,B),X_82)))]]) ).
cnf(refute_0_238,plain,
multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = inverse(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))))),bind(B,$fot(double_divide(identity,X_10)))]]) ).
cnf(refute_0_239,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))) = X_12,
inference(subst,[],[refute_0_43:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_240,plain,
( multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != inverse(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))) != X_12
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),inverse(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_241,plain,
( multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != inverse(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))),X_12) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),inverse(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))))) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) = inverse(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))))),bind(B,$fot(identity))]]) ).
cnf(refute_0_244,plain,
double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))) = X_21,
inference(subst,[],[refute_0_209:[bind(X_11,$fot(X_20)),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_245,plain,
( multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) != inverse(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))))
| double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))) != X_21
| multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) = inverse(X_21) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity),inverse(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))))) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_246,plain,
( multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) != inverse(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))))
| multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) = inverse(X_21) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))),X_21) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) = inverse(X_21),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity),inverse(double_divide(identity,double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))))) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) = double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),
inference(subst,[],[refute_0_118:[bind(X_13,$fot(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))))]]) ).
cnf(refute_0_249,plain,
( multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) != double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))
| multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) != inverse(X_21)
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = inverse(X_21) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity),inverse(X_21)) ),[0],$fot(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))))]]) ).
cnf(refute_0_250,plain,
( multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity) != inverse(X_21)
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = inverse(X_21) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity),double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = inverse(X_21),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),identity),inverse(X_21)) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
double_divide(X_20,double_divide(X_21,X_20)) = X_21,
inference(subst,[],[refute_0_232:[bind(X_11,$fot(X_20)),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_253,plain,
double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))))]]) ).
cnf(refute_0_254,plain,
( double_divide(X_20,double_divide(X_21,X_20)) != X_21
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) != double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = double_divide(identity,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_255,plain,
( double_divide(X_20,double_divide(X_21,X_20)) != X_21
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = double_divide(identity,X_21) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),double_divide(identity,double_divide(X_20,double_divide(X_21,X_20)))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) = double_divide(identity,X_21),
inference(resolve,[$cnf( $equal(double_divide(X_20,double_divide(X_21,X_20)),X_21) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
( double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) != double_divide(identity,X_21)
| double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) != inverse(X_21)
| double_divide(identity,X_21) = inverse(X_21) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),inverse(X_21)) ),[0],$fot(double_divide(identity,X_21))]]) ).
cnf(refute_0_258,plain,
( double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))) != inverse(X_21)
| double_divide(identity,X_21) = inverse(X_21) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),double_divide(identity,X_21)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
double_divide(identity,X_21) = inverse(X_21),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(X_20,double_divide(X_21,X_20))),inverse(X_21)) )],[refute_0_251,refute_0_258]) ).
cnf(refute_0_260,plain,
double_divide(identity,X_10) = inverse(X_10),
inference(subst,[],[refute_0_259:[bind(X_21,$fot(X_10))]]) ).
cnf(refute_0_261,plain,
multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)),
introduced(tautology,[refl,[$fot(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)))]]) ).
cnf(refute_0_262,plain,
( multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) != multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10))
| double_divide(identity,X_10) != inverse(X_10)
| multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)),multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10))) ),[1,1],$fot(inverse(X_10))]]) ).
cnf(refute_0_263,plain,
( double_divide(identity,X_10) != inverse(X_10)
| multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)),multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)),
inference(resolve,[$cnf( $equal(double_divide(identity,X_10),inverse(X_10)) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) = multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),
inference(subst,[],[refute_0_27:[bind(A,$fot(double_divide(X_12,X_11))),bind(B,$fot(multiply(X_11,X_10)))]]) ).
cnf(refute_0_266,plain,
double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) = inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),
inference(subst,[],[refute_0_259:[bind(X_21,$fot(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))))]]) ).
cnf(refute_0_267,plain,
( double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) != inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))
| inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) != multiply(double_divide(X_12,X_11),multiply(X_11,X_10))
| double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) = multiply(double_divide(X_12,X_11),multiply(X_11,X_10)) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))))),bind(Y,$fot(inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))))),bind(Z,$fot(multiply(double_divide(X_12,X_11),multiply(X_11,X_10))))]]) ).
cnf(refute_0_268,plain,
( inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) != multiply(double_divide(X_12,X_11),multiply(X_11,X_10))
| double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) = multiply(double_divide(X_12,X_11),multiply(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) = multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),
inference(resolve,[$cnf( $equal(inverse(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),multiply(double_divide(X_12,X_11),multiply(X_11,X_10))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)))]]) ).
cnf(refute_0_271,plain,
( multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10))
| double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) != multiply(double_divide(X_12,X_11),multiply(X_11,X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10))) ),[1,0],$fot(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)))]]) ).
cnf(refute_0_272,plain,
( double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))) != multiply(double_divide(X_12,X_11),multiply(X_11,X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),multiply(double_divide(X_12,X_11),multiply(X_11,X_10))) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
( multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) != multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)))),bind(Y,$fot(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)))),bind(Z,$fot(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))))]]) ).
cnf(refute_0_275,plain,
( multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)) != multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) = multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),double_divide(identity,X_10)),multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))) )],[refute_0_264,refute_0_275]) ).
cnf(refute_0_277,plain,
( multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))
| multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != inverse(X_12)
| multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),inverse(X_12)) ),[0],$fot(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)))]]) ).
cnf(refute_0_278,plain,
( multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)) != inverse(X_12)
| multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,double_divide(multiply(X_11,X_10),double_divide(X_12,X_11))),double_divide(identity,X_10)),inverse(X_12)) )],[refute_0_242,refute_0_278]) ).
cnf(refute_0_280,plain,
multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = inverse(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13))))),
inference(subst,[],[refute_0_8:[bind(A,$fot(double_divide(identity,inverse(multiply(inverse(X_14),X_13))))),bind(B,$fot(double_divide(identity,X_13)))]]) ).
cnf(refute_0_281,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))) = X_14,
inference(subst,[],[refute_0_69:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_282,plain,
( multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != inverse(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))))
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))) != X_14
| multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = inverse(X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),inverse(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))))) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_283,plain,
( multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != inverse(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))))
| multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = inverse(X_14) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))),X_14) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = inverse(X_14),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),inverse(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_14),X_13)))))) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
double_divide(identity,inverse(multiply(inverse(X_14),X_13))) = multiply(inverse(X_14),X_13),
inference(subst,[],[refute_0_196:[bind(X_12,$fot(multiply(inverse(X_14),X_13)))]]) ).
cnf(refute_0_286,plain,
multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)))]]) ).
cnf(refute_0_287,plain,
( multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13))
| double_divide(identity,inverse(multiply(inverse(X_14),X_13))) != multiply(inverse(X_14),X_13)
| multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13))) ),[1,0],$fot(multiply(inverse(X_14),X_13))]]) ).
cnf(refute_0_288,plain,
( double_divide(identity,inverse(multiply(inverse(X_14),X_13))) != multiply(inverse(X_14),X_13)
| multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),multiply(inverse(X_14),X_13)) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
( multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13))
| multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != inverse(X_14)
| multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = inverse(X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),inverse(X_14)) ),[0],$fot(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)))]]) ).
cnf(refute_0_291,plain,
( multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)) != inverse(X_14)
| multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = inverse(X_14) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = inverse(X_14),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(multiply(inverse(X_14),X_13))),double_divide(identity,X_13)),inverse(X_14)) )],[refute_0_284,refute_0_291]) ).
cnf(refute_0_293,plain,
double_divide(identity,X_13) = inverse(X_13),
inference(subst,[],[refute_0_259:[bind(X_21,$fot(X_13))]]) ).
cnf(refute_0_294,plain,
multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)))]]) ).
cnf(refute_0_295,plain,
( multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) != multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13))
| double_divide(identity,X_13) != inverse(X_13)
| multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),inverse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13))) ),[1,1],$fot(inverse(X_13))]]) ).
cnf(refute_0_296,plain,
( double_divide(identity,X_13) != inverse(X_13)
| multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),inverse(X_13)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) = multiply(multiply(inverse(X_14),X_13),inverse(X_13)),
inference(resolve,[$cnf( $equal(double_divide(identity,X_13),inverse(X_13)) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
( multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) != multiply(multiply(inverse(X_14),X_13),inverse(X_13))
| multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) != inverse(X_14)
| multiply(multiply(inverse(X_14),X_13),inverse(X_13)) = inverse(X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),inverse(X_14)) ),[0],$fot(multiply(multiply(inverse(X_14),X_13),inverse(X_13)))]]) ).
cnf(refute_0_299,plain,
( multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)) != inverse(X_14)
| multiply(multiply(inverse(X_14),X_13),inverse(X_13)) = inverse(X_14) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),multiply(multiply(inverse(X_14),X_13),inverse(X_13))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
multiply(multiply(inverse(X_14),X_13),inverse(X_13)) = inverse(X_14),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_14),X_13),double_divide(identity,X_13)),inverse(X_14)) )],[refute_0_292,refute_0_299]) ).
cnf(refute_0_301,plain,
multiply(multiply(inverse(inverse(X_21)),X_36),inverse(X_36)) = inverse(inverse(X_21)),
inference(subst,[],[refute_0_300:[bind(X_13,$fot(X_36)),bind(X_14,$fot(inverse(X_21)))]]) ).
cnf(refute_0_302,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(X_21),double_divide(X_21,inverse(X_21))))) = X_21,
inference(subst,[],[refute_0_209:[bind(X_11,$fot(inverse(X_21))),bind(X_12,$fot(X_21))]]) ).
cnf(refute_0_303,plain,
identity = double_divide(X_21,inverse(X_21)),
inference(subst,[],[identity:[bind(A,$fot(X_21))]]) ).
cnf(refute_0_304,plain,
( identity != double_divide(X_21,inverse(X_21))
| double_divide(X_21,inverse(X_21)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_21,inverse(X_21))))]]) ).
cnf(refute_0_305,plain,
double_divide(X_21,inverse(X_21)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_21,inverse(X_21))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
( double_divide(X_21,inverse(X_21)) != identity
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),double_divide(X_21,inverse(X_21))))) != X_21
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),double_divide(X_21,inverse(X_21))))),X_21) ),[0,1,1,1],$fot(identity)]]) ).
cnf(refute_0_307,plain,
( double_divide(identity,double_divide(identity,double_divide(inverse(X_21),double_divide(X_21,inverse(X_21))))) != X_21
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = X_21 ),
inference(resolve,[$cnf( $equal(double_divide(X_21,inverse(X_21)),identity) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = X_21,
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),double_divide(X_21,inverse(X_21))))),X_21) )],[refute_0_302,refute_0_307]) ).
cnf(refute_0_309,plain,
double_divide(inverse(X_21),identity) = inverse(inverse(X_21)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_21)))]]) ).
cnf(refute_0_310,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = double_divide(inverse(X_21),identity),
inference(subst,[],[refute_0_228:[bind(X_21,$fot(double_divide(inverse(X_21),identity)))]]) ).
cnf(refute_0_311,plain,
( double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) != double_divide(inverse(X_21),identity)
| double_divide(inverse(X_21),identity) != inverse(inverse(X_21))
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = inverse(inverse(X_21)) ),
inference(subst,[],[refute_0_85:[bind(X,$fot(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))))),bind(Y,$fot(double_divide(inverse(X_21),identity))),bind(Z,$fot(inverse(inverse(X_21))))]]) ).
cnf(refute_0_312,plain,
( double_divide(inverse(X_21),identity) != inverse(inverse(X_21))
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = inverse(inverse(X_21)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))),double_divide(inverse(X_21),identity)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) = inverse(inverse(X_21)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_21),identity),inverse(inverse(X_21))) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) != X_21
| double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) != inverse(inverse(X_21))
| inverse(inverse(X_21)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))),X_21) ),[0],$fot(inverse(inverse(X_21)))]]) ).
cnf(refute_0_315,plain,
( double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))) != X_21
| inverse(inverse(X_21)) = X_21 ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))),inverse(inverse(X_21))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
inverse(inverse(X_21)) = X_21,
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,double_divide(inverse(X_21),identity))),X_21) )],[refute_0_308,refute_0_315]) ).
cnf(refute_0_317,plain,
( multiply(multiply(inverse(inverse(X_21)),X_36),inverse(X_36)) != inverse(inverse(X_21))
| inverse(inverse(X_21)) != X_21
| multiply(multiply(X_21,X_36),inverse(X_36)) = inverse(inverse(X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_21)),X_36),inverse(X_36)),inverse(inverse(X_21))) ),[0,0,0],$fot(X_21)]]) ).
cnf(refute_0_318,plain,
( multiply(multiply(inverse(inverse(X_21)),X_36),inverse(X_36)) != inverse(inverse(X_21))
| multiply(multiply(X_21,X_36),inverse(X_36)) = inverse(inverse(X_21)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_21)),X_21) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
multiply(multiply(X_21,X_36),inverse(X_36)) = inverse(inverse(X_21)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_21)),X_36),inverse(X_36)),inverse(inverse(X_21))) )],[refute_0_301,refute_0_318]) ).
cnf(refute_0_320,plain,
( multiply(multiply(X_21,X_36),inverse(X_36)) != inverse(inverse(X_21))
| inverse(inverse(X_21)) != X_21
| multiply(multiply(X_21,X_36),inverse(X_36)) = X_21 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_21,X_36),inverse(X_36)),X_21) ),[0],$fot(inverse(inverse(X_21)))]]) ).
cnf(refute_0_321,plain,
( multiply(multiply(X_21,X_36),inverse(X_36)) != inverse(inverse(X_21))
| multiply(multiply(X_21,X_36),inverse(X_36)) = X_21 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_21)),X_21) )],[refute_0_316,refute_0_320]) ).
cnf(refute_0_322,plain,
multiply(multiply(X_21,X_36),inverse(X_36)) = X_21,
inference(resolve,[$cnf( $equal(multiply(multiply(X_21,X_36),inverse(X_36)),inverse(inverse(X_21))) )],[refute_0_319,refute_0_321]) ).
cnf(refute_0_323,plain,
multiply(multiply(double_divide(X_26,X_39),X_39),inverse(X_39)) = double_divide(X_26,X_39),
inference(subst,[],[refute_0_322:[bind(X_21,$fot(double_divide(X_26,X_39))),bind(X_36,$fot(X_39))]]) ).
cnf(refute_0_324,plain,
multiply(double_divide(X_26,X_39),X_39) = inverse(X_26),
inference(subst,[],[refute_0_236:[bind(B,$fot(X_39))]]) ).
cnf(refute_0_325,plain,
( multiply(multiply(double_divide(X_26,X_39),X_39),inverse(X_39)) != double_divide(X_26,X_39)
| multiply(double_divide(X_26,X_39),X_39) != inverse(X_26)
| multiply(inverse(X_26),inverse(X_39)) = double_divide(X_26,X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_26,X_39),X_39),inverse(X_39)),double_divide(X_26,X_39)) ),[0,0],$fot(inverse(X_26))]]) ).
cnf(refute_0_326,plain,
( multiply(multiply(double_divide(X_26,X_39),X_39),inverse(X_39)) != double_divide(X_26,X_39)
| multiply(inverse(X_26),inverse(X_39)) = double_divide(X_26,X_39) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(X_26,X_39),X_39),inverse(X_26)) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
multiply(inverse(X_26),inverse(X_39)) = double_divide(X_26,X_39),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_26,X_39),X_39),inverse(X_39)),double_divide(X_26,X_39)) )],[refute_0_323,refute_0_326]) ).
cnf(refute_0_328,plain,
multiply(inverse(double_divide(B,A)),inverse(X_43)) = double_divide(double_divide(B,A),X_43),
inference(subst,[],[refute_0_327:[bind(X_26,$fot(double_divide(B,A))),bind(X_39,$fot(X_43))]]) ).
cnf(refute_0_329,plain,
( multiply(inverse(double_divide(B,A)),inverse(X_43)) != double_divide(double_divide(B,A),X_43)
| inverse(double_divide(B,A)) != multiply(A,B)
| multiply(multiply(A,B),inverse(X_43)) = double_divide(double_divide(B,A),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(double_divide(B,A)),inverse(X_43)),double_divide(double_divide(B,A),X_43)) ),[0,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_330,plain,
( multiply(inverse(double_divide(B,A)),inverse(X_43)) != double_divide(double_divide(B,A),X_43)
| multiply(multiply(A,B),inverse(X_43)) = double_divide(double_divide(B,A),X_43) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(B,A)),multiply(A,B)) )],[refute_0_27,refute_0_329]) ).
cnf(refute_0_331,plain,
multiply(multiply(A,B),inverse(X_43)) = double_divide(double_divide(B,A),X_43),
inference(resolve,[$cnf( $equal(multiply(inverse(double_divide(B,A)),inverse(X_43)),double_divide(double_divide(B,A),X_43)) )],[refute_0_328,refute_0_330]) ).
cnf(refute_0_332,plain,
multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) = double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10),
inference(subst,[],[refute_0_331:[bind(A,$fot(double_divide(X_12,X_11))),bind(B,$fot(multiply(X_11,X_10))),bind(X_43,$fot(X_10))]]) ).
cnf(refute_0_333,plain,
( multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) != double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10)
| multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) != inverse(X_12)
| double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)),inverse(X_12)) ),[0],$fot(double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10))]]) ).
cnf(refute_0_334,plain,
( multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)) != inverse(X_12)
| double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)),double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
double_divide(double_divide(multiply(X_11,X_10),double_divide(X_12,X_11)),X_10) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(double_divide(X_12,X_11),multiply(X_11,X_10)),inverse(X_10)),inverse(X_12)) )],[refute_0_279,refute_0_334]) ).
cnf(refute_0_336,plain,
double_divide(double_divide(multiply(X_80,X_79),double_divide(double_divide(X_80,X_12),X_80)),X_79) = inverse(double_divide(X_80,X_12)),
inference(subst,[],[refute_0_335:[bind(X_10,$fot(X_79)),bind(X_11,$fot(X_80)),bind(X_12,$fot(double_divide(X_80,X_12)))]]) ).
cnf(refute_0_337,plain,
double_divide(double_divide(X_26,X_12),double_divide(X_12,double_divide(X_26,X_12))) = X_12,
inference(subst,[],[refute_0_232:[bind(X_11,$fot(double_divide(X_26,X_12)))]]) ).
cnf(refute_0_338,plain,
double_divide(X_12,double_divide(X_26,X_12)) = X_26,
inference(subst,[],[refute_0_232:[bind(X_11,$fot(X_12)),bind(X_12,$fot(X_26))]]) ).
cnf(refute_0_339,plain,
( double_divide(X_12,double_divide(X_26,X_12)) != X_26
| double_divide(double_divide(X_26,X_12),double_divide(X_12,double_divide(X_26,X_12))) != X_12
| double_divide(double_divide(X_26,X_12),X_26) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_26,X_12),double_divide(X_12,double_divide(X_26,X_12))),X_12) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_340,plain,
( double_divide(double_divide(X_26,X_12),double_divide(X_12,double_divide(X_26,X_12))) != X_12
| double_divide(double_divide(X_26,X_12),X_26) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,double_divide(X_26,X_12)),X_26) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
double_divide(double_divide(X_26,X_12),X_26) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_26,X_12),double_divide(X_12,double_divide(X_26,X_12))),X_12) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
double_divide(double_divide(X_80,X_12),X_80) = X_12,
inference(subst,[],[refute_0_341:[bind(X_26,$fot(X_80))]]) ).
cnf(refute_0_343,plain,
( double_divide(double_divide(X_80,X_12),X_80) != X_12
| double_divide(double_divide(multiply(X_80,X_79),double_divide(double_divide(X_80,X_12),X_80)),X_79) != inverse(double_divide(X_80,X_12))
| double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = inverse(double_divide(X_80,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(multiply(X_80,X_79),double_divide(double_divide(X_80,X_12),X_80)),X_79),inverse(double_divide(X_80,X_12))) ),[0,0,1],$fot(X_12)]]) ).
cnf(refute_0_344,plain,
( double_divide(double_divide(multiply(X_80,X_79),double_divide(double_divide(X_80,X_12),X_80)),X_79) != inverse(double_divide(X_80,X_12))
| double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = inverse(double_divide(X_80,X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_80,X_12),X_80),X_12) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = inverse(double_divide(X_80,X_12)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_80,X_79),double_divide(double_divide(X_80,X_12),X_80)),X_79),inverse(double_divide(X_80,X_12))) )],[refute_0_336,refute_0_344]) ).
cnf(refute_0_346,plain,
inverse(double_divide(X_80,X_12)) = multiply(X_12,X_80),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_12)),bind(B,$fot(X_80))]]) ).
cnf(refute_0_347,plain,
( double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) != inverse(double_divide(X_80,X_12))
| inverse(double_divide(X_80,X_12)) != multiply(X_12,X_80)
| double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = multiply(X_12,X_80) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double_divide(double_divide(multiply(X_80,X_79),X_12),X_79),multiply(X_12,X_80)) ),[0],$fot(inverse(double_divide(X_80,X_12)))]]) ).
cnf(refute_0_348,plain,
( double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) != inverse(double_divide(X_80,X_12))
| double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = multiply(X_12,X_80) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_80,X_12)),multiply(X_12,X_80)) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
double_divide(double_divide(multiply(X_80,X_79),X_12),X_79) = multiply(X_12,X_80),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_80,X_79),X_12),X_79),inverse(double_divide(X_80,X_12))) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
double_divide(double_divide(multiply(X_84,B),X_82),B) = multiply(X_82,X_84),
inference(subst,[],[refute_0_349:[bind(X_12,$fot(X_82)),bind(X_79,$fot(B)),bind(X_80,$fot(X_84))]]) ).
cnf(refute_0_351,plain,
( multiply(double_divide(double_divide(multiply(X_84,B),X_82),B),B) != inverse(double_divide(multiply(X_84,B),X_82))
| double_divide(double_divide(multiply(X_84,B),X_82),B) != multiply(X_82,X_84)
| multiply(multiply(X_82,X_84),B) = inverse(double_divide(multiply(X_84,B),X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(double_divide(multiply(X_84,B),X_82),B),B),inverse(double_divide(multiply(X_84,B),X_82))) ),[0,0],$fot(multiply(X_82,X_84))]]) ).
cnf(refute_0_352,plain,
( multiply(double_divide(double_divide(multiply(X_84,B),X_82),B),B) != inverse(double_divide(multiply(X_84,B),X_82))
| multiply(multiply(X_82,X_84),B) = inverse(double_divide(multiply(X_84,B),X_82)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(multiply(X_84,B),X_82),B),multiply(X_82,X_84)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
multiply(multiply(X_82,X_84),B) = inverse(double_divide(multiply(X_84,B),X_82)),
inference(resolve,[$cnf( $equal(multiply(double_divide(double_divide(multiply(X_84,B),X_82),B),B),inverse(double_divide(multiply(X_84,B),X_82))) )],[refute_0_237,refute_0_352]) ).
cnf(refute_0_354,plain,
inverse(double_divide(multiply(X_84,B),X_82)) = multiply(X_82,multiply(X_84,B)),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_82)),bind(B,$fot(multiply(X_84,B)))]]) ).
cnf(refute_0_355,plain,
( multiply(multiply(X_82,X_84),B) != inverse(double_divide(multiply(X_84,B),X_82))
| inverse(double_divide(multiply(X_84,B),X_82)) != multiply(X_82,multiply(X_84,B))
| multiply(multiply(X_82,X_84),B) = multiply(X_82,multiply(X_84,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_82,X_84),B),multiply(X_82,multiply(X_84,B))) ),[0],$fot(inverse(double_divide(multiply(X_84,B),X_82)))]]) ).
cnf(refute_0_356,plain,
( multiply(multiply(X_82,X_84),B) != inverse(double_divide(multiply(X_84,B),X_82))
| multiply(multiply(X_82,X_84),B) = multiply(X_82,multiply(X_84,B)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(multiply(X_84,B),X_82)),multiply(X_82,multiply(X_84,B))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
multiply(multiply(X_82,X_84),B) = multiply(X_82,multiply(X_84,B)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_82,X_84),B),inverse(double_divide(multiply(X_84,B),X_82))) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(subst,[],[refute_0_357:[bind(B,$fot(c3)),bind(X_82,$fot(a3)),bind(X_84,$fot(b3))]]) ).
cnf(refute_0_359,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_360,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolve,[$cnf( $equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) )],[refute_0_360,prove_these_axioms_3]) ).
cnf(refute_0_362,plain,
multiply(a3,multiply(b3,c3)) = multiply(a3,multiply(b3,c3)),
introduced(tautology,[refl,[$fot(multiply(a3,multiply(b3,c3)))]]) ).
cnf(refute_0_363,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) )],[refute_0_362,refute_0_361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 04:25:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44
% 0.19/0.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.51
%------------------------------------------------------------------------------