%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:42:23 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 75
% Syntax : Number of clauses : 233 ( 120 unt; 0 nHn; 132 RR)
% Number of literals : 399 ( 398 equ; 169 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 261 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B ).
cnf(multiply,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity) ).
cnf(inverse,axiom,
inverse(A) = double_divide(A,identity) ).
cnf(identity,axiom,
identity = double_divide(A,inverse(A)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != double_divide(A,identity)
| double_divide(A,identity) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).
cnf(refute_0_4,plain,
double_divide(A,identity) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).
cnf(refute_0_6,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| double_divide(double_divide(B,A),identity) != inverse(double_divide(B,A))
| multiply(A,B) = inverse(double_divide(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),inverse(double_divide(B,A))) ),[0],$fot(double_divide(double_divide(B,A),identity))]]) ).
cnf(refute_0_7,plain,
( multiply(A,B) != double_divide(double_divide(B,A),identity)
| multiply(A,B) = inverse(double_divide(B,A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_10,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_11,plain,
( inverse(X_3) != double_divide(X_3,identity)
| double_divide(X_3,identity) = inverse(X_3) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(double_divide(X_3,identity)))]]) ).
cnf(refute_0_12,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_14,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(a2))]]) ).
cnf(refute_0_17,plain,
( multiply(identity,a2) != inverse(inverse(a2))
| inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).
cnf(refute_0_18,plain,
( inverse(inverse(a2)) != a2
| multiply(identity,a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(identity,a2),inverse(inverse(a2))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(inverse(a2)) != a2,
inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_18,prove_these_axioms_2]) ).
cnf(refute_0_20,plain,
double_divide(identity,identity) = inverse(identity),
inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)))]]) ).
cnf(refute_0_22,plain,
( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))) ),[1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_23,plain,
( double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) != B
| double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) != double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity))
| double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)) = B ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),B) ),[0],$fot(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)))]]) ).
cnf(refute_0_26,plain,
( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) != B
| double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)) = B ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),inverse(identity)) = B,
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)),B) )],[single_axiom,refute_0_26]) ).
cnf(refute_0_28,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,inverse(X_10))),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11,
inference(subst,[],[refute_0_27:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(inverse(X_10)))]]) ).
cnf(refute_0_29,plain,
identity = double_divide(X_10,inverse(X_10)),
inference(subst,[],[identity:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_30,plain,
( identity != double_divide(X_10,inverse(X_10))
| double_divide(X_10,inverse(X_10)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_10,inverse(X_10))))]]) ).
cnf(refute_0_31,plain,
double_divide(X_10,inverse(X_10)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_10,inverse(X_10))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( double_divide(X_10,inverse(X_10)) != identity
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,inverse(X_10))),double_divide(identity,inverse(X_10)))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,inverse(X_10))),double_divide(identity,inverse(X_10)))),inverse(identity)),X_11) ),[0,0,1,0,1],$fot(identity)]]) ).
cnf(refute_0_33,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,inverse(X_10))),double_divide(identity,inverse(X_10)))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(X_10,inverse(X_10)),identity) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,inverse(X_10))),double_divide(identity,inverse(X_10)))),inverse(identity)),X_11) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
double_divide(X_11,identity) = inverse(X_11),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_36,plain,
double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) = double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))))]]) ).
cnf(refute_0_37,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) != double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))
| double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) = double_divide(inverse(X_11),double_divide(identity,inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))),double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) ),[1,0],$fot(inverse(X_11))]]) ).
cnf(refute_0_38,plain,
( double_divide(X_11,identity) != inverse(X_11)
| double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) = double_divide(inverse(X_11),double_divide(identity,inverse(X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))),double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) = double_divide(inverse(X_11),double_divide(identity,inverse(X_10))),
inference(resolve,[$cnf( $equal(double_divide(X_11,identity),inverse(X_11)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) = double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))))]]) ).
cnf(refute_0_41,plain,
( double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) != double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))))
| double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) != double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))
| double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) = double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))))) ),[1,1],$fot(double_divide(inverse(X_11),double_divide(identity,inverse(X_10))))]]) ).
cnf(refute_0_42,plain,
( double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))) != double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))
| double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) = double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) = double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10))),double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)))]]) ).
cnf(refute_0_45,plain,
( double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) != double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10))))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity))) ),[1,0],$fot(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))))]]) ).
cnf(refute_0_46,plain,
( double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))) != double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10))))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10))))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),X_11) ),[0],$fot(double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)))]]) ).
cnf(refute_0_49,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
double_divide(double_divide(X_10,double_divide(inverse(X_11),double_divide(identity,inverse(X_10)))),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,identity),double_divide(identity,inverse(X_10)))),inverse(identity)),X_11) )],[refute_0_34,refute_0_49]) ).
cnf(refute_0_51,plain,
double_divide(double_divide(identity,double_divide(inverse(X_14),double_divide(identity,inverse(identity)))),inverse(identity)) = X_14,
inference(subst,[],[refute_0_50:[bind(X_10,$fot(identity)),bind(X_11,$fot(X_14))]]) ).
cnf(refute_0_52,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_53,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_54,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_14),double_divide(identity,inverse(identity)))),inverse(identity)) != X_14
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),double_divide(identity,inverse(identity)))),inverse(identity)),X_14) ),[0,0,1,1],$fot(identity)]]) ).
cnf(refute_0_56,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_14),double_divide(identity,inverse(identity)))),inverse(identity)) != X_14
| double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),double_divide(identity,inverse(identity)))),inverse(identity)),X_14) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
double_divide(inverse(X_14),identity) = inverse(inverse(X_14)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_14)))]]) ).
cnf(refute_0_59,plain,
double_divide(identity,double_divide(inverse(X_14),identity)) = double_divide(identity,double_divide(inverse(X_14),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(X_14),identity)))]]) ).
cnf(refute_0_60,plain,
( double_divide(identity,double_divide(inverse(X_14),identity)) != double_divide(identity,double_divide(inverse(X_14),identity))
| double_divide(inverse(X_14),identity) != inverse(inverse(X_14))
| double_divide(identity,double_divide(inverse(X_14),identity)) = double_divide(identity,inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_14),identity)),double_divide(identity,double_divide(inverse(X_14),identity))) ),[1,1],$fot(inverse(inverse(X_14)))]]) ).
cnf(refute_0_61,plain,
( double_divide(inverse(X_14),identity) != inverse(inverse(X_14))
| double_divide(identity,double_divide(inverse(X_14),identity)) = double_divide(identity,inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_14),identity)),double_divide(identity,double_divide(inverse(X_14),identity))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(identity,double_divide(inverse(X_14),identity)) = double_divide(identity,inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_14),identity),inverse(inverse(X_14))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)))]]) ).
cnf(refute_0_64,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) != double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity))
| double_divide(identity,double_divide(inverse(X_14),identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity))) ),[1,0],$fot(double_divide(identity,inverse(inverse(X_14))))]]) ).
cnf(refute_0_65,plain,
( double_divide(identity,double_divide(inverse(X_14),identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) = double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(X_14),identity)),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) != X_14
| double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) != double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity))
| double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),X_14) ),[0],$fot(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)))]]) ).
cnf(refute_0_68,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)) != X_14
| double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_14),identity)),inverse(identity)),X_14) )],[refute_0_57,refute_0_68]) ).
cnf(refute_0_70,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),double_divide(identity,identity))),inverse(identity)) = X_11,
inference(subst,[],[refute_0_27:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(identity))]]) ).
cnf(refute_0_71,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),double_divide(identity,identity))),inverse(identity)) != X_11
| double_divide(identity,identity) != inverse(identity)
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),double_divide(identity,identity))),inverse(identity)),X_11) ),[0,0,1,1],$fot(inverse(identity))]]) ).
cnf(refute_0_72,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),double_divide(identity,identity))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_20,refute_0_71]) ).
cnf(refute_0_73,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),double_divide(identity,identity))),inverse(identity)),X_11) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
double_divide(X_10,identity) = inverse(X_10),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_10))]]) ).
cnf(refute_0_75,plain,
double_divide(X_11,double_divide(X_10,identity)) = double_divide(X_11,double_divide(X_10,identity)),
introduced(tautology,[refl,[$fot(double_divide(X_11,double_divide(X_10,identity)))]]) ).
cnf(refute_0_76,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_11,double_divide(X_10,identity)) != double_divide(X_11,double_divide(X_10,identity))
| double_divide(X_11,double_divide(X_10,identity)) = double_divide(X_11,inverse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_11,double_divide(X_10,identity)),double_divide(X_11,double_divide(X_10,identity))) ),[1,1],$fot(inverse(X_10))]]) ).
cnf(refute_0_77,plain,
( double_divide(X_10,identity) != inverse(X_10)
| double_divide(X_11,double_divide(X_10,identity)) = double_divide(X_11,inverse(X_10)) ),
inference(resolve,[$cnf( $equal(double_divide(X_11,double_divide(X_10,identity)),double_divide(X_11,double_divide(X_10,identity))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
double_divide(X_11,double_divide(X_10,identity)) = double_divide(X_11,inverse(X_10)),
inference(resolve,[$cnf( $equal(double_divide(X_10,identity),inverse(X_10)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) = double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)))]]) ).
cnf(refute_0_80,plain,
( double_divide(X_11,double_divide(X_10,identity)) != double_divide(X_11,inverse(X_10))
| double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) != double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))
| double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) = double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)),double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) ),[1,0],$fot(double_divide(X_11,inverse(X_10)))]]) ).
cnf(refute_0_81,plain,
( double_divide(X_11,double_divide(X_10,identity)) != double_divide(X_11,inverse(X_10))
| double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) = double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)),double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) = double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_11,double_divide(X_10,identity)),double_divide(X_11,inverse(X_10))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) = double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))))]]) ).
cnf(refute_0_84,plain,
( double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) != double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)))
| double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) != double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))
| double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) = double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)))) ),[1,1],$fot(double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)))]]) ).
cnf(refute_0_85,plain,
( double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)) != double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))
| double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) = double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) = double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity)),double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)))]]) ).
cnf(refute_0_88,plain,
( double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) != double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity))) ),[1,0],$fot(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))))]]) ).
cnf(refute_0_89,plain,
( double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))) != double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) = double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity)))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) != double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity))
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),X_11) ),[0],$fot(double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)))]]) ).
cnf(refute_0_92,plain,
( double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)) != X_11
| double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)) = X_11 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
double_divide(double_divide(X_10,double_divide(double_divide(X_11,inverse(X_10)),inverse(identity))),inverse(identity)) = X_11,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_10,double_divide(double_divide(X_11,double_divide(X_10,identity)),inverse(identity))),inverse(identity)),X_11) )],[refute_0_73,refute_0_92]) ).
cnf(refute_0_94,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_14))),
inference(subst,[],[refute_0_93:[bind(X_10,$fot(identity)),bind(X_11,$fot(double_divide(identity,inverse(inverse(X_14)))))]]) ).
cnf(refute_0_95,plain,
( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) != X_14
| double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_14)))) ),[0,0,1,0],$fot(X_14)]]) ).
cnf(refute_0_96,plain,
( double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),X_14) )],[refute_0_69,refute_0_95]) ).
cnf(refute_0_97,plain,
double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
double_divide(double_divide(identity,double_divide(inverse(X_19),inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(X_19)))),
inference(subst,[],[refute_0_97:[bind(X_14,$fot(inverse(X_19)))]]) ).
cnf(refute_0_99,plain,
double_divide(double_divide(X_19,double_divide(double_divide(X_19,inverse(X_19)),inverse(identity))),inverse(identity)) = X_19,
inference(subst,[],[refute_0_93:[bind(X_10,$fot(X_19)),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_100,plain,
identity = double_divide(X_19,inverse(X_19)),
inference(subst,[],[identity:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_101,plain,
( identity != double_divide(X_19,inverse(X_19))
| double_divide(X_19,inverse(X_19)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_19,inverse(X_19))))]]) ).
cnf(refute_0_102,plain,
double_divide(X_19,inverse(X_19)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_19,inverse(X_19))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( double_divide(X_19,inverse(X_19)) != identity
| double_divide(double_divide(X_19,double_divide(double_divide(X_19,inverse(X_19)),inverse(identity))),inverse(identity)) != X_19
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(double_divide(X_19,inverse(X_19)),inverse(identity))),inverse(identity)),X_19) ),[0,0,1,0],$fot(identity)]]) ).
cnf(refute_0_104,plain,
( double_divide(double_divide(X_19,double_divide(double_divide(X_19,inverse(X_19)),inverse(identity))),inverse(identity)) != X_19
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = X_19 ),
inference(resolve,[$cnf( $equal(double_divide(X_19,inverse(X_19)),identity) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = X_19,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(double_divide(X_19,inverse(X_19)),inverse(identity))),inverse(identity)),X_19) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
double_divide(X_19,identity) = inverse(X_19),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_107,plain,
double_divide(X_19,double_divide(identity,inverse(identity))) = double_divide(X_19,double_divide(identity,inverse(identity))),
introduced(tautology,[refl,[$fot(double_divide(X_19,double_divide(identity,inverse(identity))))]]) ).
cnf(refute_0_108,plain,
( double_divide(X_19,double_divide(identity,inverse(identity))) != double_divide(X_19,double_divide(identity,inverse(identity)))
| double_divide(identity,inverse(identity)) != identity
| double_divide(X_19,double_divide(identity,inverse(identity))) = double_divide(X_19,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(X_19,double_divide(identity,inverse(identity))),double_divide(X_19,double_divide(identity,inverse(identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_109,plain,
( double_divide(identity,inverse(identity)) != identity
| double_divide(X_19,double_divide(identity,inverse(identity))) = double_divide(X_19,identity) ),
inference(resolve,[$cnf( $equal(double_divide(X_19,double_divide(identity,inverse(identity))),double_divide(X_19,double_divide(identity,inverse(identity)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
double_divide(X_19,double_divide(identity,inverse(identity))) = double_divide(X_19,identity),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_54,refute_0_109]) ).
cnf(refute_0_111,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_112,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_111]) ).
cnf(refute_0_113,plain,
( double_divide(X_19,double_divide(identity,inverse(identity))) != double_divide(X_19,identity)
| double_divide(X_19,identity) != inverse(X_19)
| double_divide(X_19,double_divide(identity,inverse(identity))) = inverse(X_19) ),
inference(subst,[],[refute_0_112:[bind(X,$fot(double_divide(X_19,double_divide(identity,inverse(identity))))),bind(Y,$fot(double_divide(X_19,identity))),bind(Z,$fot(inverse(X_19)))]]) ).
cnf(refute_0_114,plain,
( double_divide(X_19,identity) != inverse(X_19)
| double_divide(X_19,double_divide(identity,inverse(identity))) = inverse(X_19) ),
inference(resolve,[$cnf( $equal(double_divide(X_19,double_divide(identity,inverse(identity))),double_divide(X_19,identity)) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
double_divide(X_19,double_divide(identity,inverse(identity))) = inverse(X_19),
inference(resolve,[$cnf( $equal(double_divide(X_19,identity),inverse(X_19)) )],[refute_0_106,refute_0_114]) ).
cnf(refute_0_116,plain,
double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)))]]) ).
cnf(refute_0_117,plain,
( double_divide(X_19,double_divide(identity,inverse(identity))) != inverse(X_19)
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) != double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity))
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(inverse(X_19),inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity))) ),[1,0],$fot(inverse(X_19))]]) ).
cnf(refute_0_118,plain,
( double_divide(X_19,double_divide(identity,inverse(identity))) != inverse(X_19)
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(inverse(X_19),inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(inverse(X_19),inverse(identity)),
inference(resolve,[$cnf( $equal(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(X_19)) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
( double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) != X_19
| double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) != double_divide(inverse(X_19),inverse(identity))
| double_divide(inverse(X_19),inverse(identity)) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),X_19) ),[0],$fot(double_divide(inverse(X_19),inverse(identity)))]]) ).
cnf(refute_0_121,plain,
( double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)) != X_19
| double_divide(inverse(X_19),inverse(identity)) = X_19 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),double_divide(inverse(X_19),inverse(identity))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
double_divide(inverse(X_19),inverse(identity)) = X_19,
inference(resolve,[$cnf( $equal(double_divide(double_divide(X_19,double_divide(identity,inverse(identity))),inverse(identity)),X_19) )],[refute_0_105,refute_0_121]) ).
cnf(refute_0_123,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_19),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(inverse(X_19))))
| double_divide(inverse(X_19),inverse(identity)) != X_19
| double_divide(double_divide(identity,X_19),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_19),inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(inverse(X_19))))) ),[0,0,1],$fot(X_19)]]) ).
cnf(refute_0_124,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_19),inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(inverse(X_19))))
| double_divide(double_divide(identity,X_19),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(X_19)))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_19),inverse(identity)),X_19) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
double_divide(double_divide(identity,X_19),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(X_19)))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_19),inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(inverse(X_19))))) )],[refute_0_98,refute_0_124]) ).
cnf(refute_0_126,plain,
double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))),
inference(subst,[],[refute_0_125:[bind(X_19,$fot(inverse(inverse(X_14))))]]) ).
cnf(refute_0_127,plain,
( double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) != X_14
| double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) != double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14))))))
| double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),X_14) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))))]]) ).
cnf(refute_0_128,plain,
( double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)) != X_14
| double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14))))))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) = X_14,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_14))),inverse(identity)),X_14) )],[refute_0_69,refute_0_128]) ).
cnf(refute_0_130,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_131,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_130]) ).
cnf(refute_0_132,plain,
inverse(double_divide(X_14,inverse(identity))) = multiply(inverse(identity),X_14),
inference(subst,[],[refute_0_131:[bind(A,$fot(inverse(identity))),bind(B,$fot(X_14))]]) ).
cnf(refute_0_133,plain,
inverse(inverse(double_divide(X_14,inverse(identity)))) = inverse(inverse(double_divide(X_14,inverse(identity)))),
introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(X_14,inverse(identity)))))]]) ).
cnf(refute_0_134,plain,
( inverse(double_divide(X_14,inverse(identity))) != multiply(inverse(identity),X_14)
| inverse(inverse(double_divide(X_14,inverse(identity)))) != inverse(inverse(double_divide(X_14,inverse(identity))))
| inverse(inverse(double_divide(X_14,inverse(identity)))) = inverse(multiply(inverse(identity),X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(X_14,inverse(identity)))),inverse(inverse(double_divide(X_14,inverse(identity))))) ),[1,0],$fot(multiply(inverse(identity),X_14))]]) ).
cnf(refute_0_135,plain,
( inverse(double_divide(X_14,inverse(identity))) != multiply(inverse(identity),X_14)
| inverse(inverse(double_divide(X_14,inverse(identity)))) = inverse(multiply(inverse(identity),X_14)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(X_14,inverse(identity)))),inverse(inverse(double_divide(X_14,inverse(identity))))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
inverse(inverse(double_divide(X_14,inverse(identity)))) = inverse(multiply(inverse(identity),X_14)),
inference(resolve,[$cnf( $equal(inverse(double_divide(X_14,inverse(identity))),multiply(inverse(identity),X_14)) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) = inverse(inverse(inverse(double_divide(X_14,inverse(identity))))),
introduced(tautology,[refl,[$fot(inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))]]) ).
cnf(refute_0_138,plain,
( inverse(inverse(double_divide(X_14,inverse(identity)))) != inverse(multiply(inverse(identity),X_14))
| inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) != inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))
| inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) = inverse(inverse(multiply(inverse(identity),X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(inverse(double_divide(X_14,inverse(identity))))),inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) ),[1,0],$fot(inverse(multiply(inverse(identity),X_14)))]]) ).
cnf(refute_0_139,plain,
( inverse(inverse(double_divide(X_14,inverse(identity)))) != inverse(multiply(inverse(identity),X_14))
| inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) = inverse(inverse(multiply(inverse(identity),X_14))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(double_divide(X_14,inverse(identity))))),inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) = inverse(inverse(multiply(inverse(identity),X_14))),
inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(X_14,inverse(identity)))),inverse(multiply(inverse(identity),X_14))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) = double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))))]]) ).
cnf(refute_0_142,plain,
( double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) != double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))
| inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) != inverse(inverse(multiply(inverse(identity),X_14)))
| double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))),double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))) ),[1,1],$fot(inverse(inverse(multiply(inverse(identity),X_14))))]]) ).
cnf(refute_0_143,plain,
( inverse(inverse(inverse(double_divide(X_14,inverse(identity))))) != inverse(inverse(multiply(inverse(identity),X_14)))
| double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))),double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),
inference(resolve,[$cnf( $equal(inverse(inverse(inverse(double_divide(X_14,inverse(identity))))),inverse(inverse(multiply(inverse(identity),X_14)))) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))),
inference(subst,[],[refute_0_125:[bind(X_19,$fot(double_divide(X_14,inverse(identity))))]]) ).
cnf(refute_0_146,plain,
( double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))
| double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) != double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))
| double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) ),
inference(subst,[],[refute_0_112:[bind(X,$fot(double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)))),bind(Y,$fot(double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))))),bind(Z,$fot(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))))]]) ).
cnf(refute_0_147,plain,
( double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))) != double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))
| double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity))))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(double_divide(X_14,inverse(identity)))))),double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
( double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))
| double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_14)))) ),[0],$fot(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))))]]) ).
cnf(refute_0_150,plain,
( double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_14,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_97,refute_0_150]) ).
cnf(refute_0_152,plain,
multiply(identity,X_14) = inverse(inverse(X_14)),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(X_14))]]) ).
cnf(refute_0_153,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = inverse(identity),
inference(subst,[],[refute_0_122:[bind(X_19,$fot(inverse(identity)))]]) ).
cnf(refute_0_154,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) = inverse(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(identity))),bind(B,$fot(double_divide(identity,inverse(inverse(X_15)))))]]) ).
cnf(refute_0_155,plain,
double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)) = X_15,
inference(subst,[],[refute_0_69:[bind(X_14,$fot(X_15))]]) ).
cnf(refute_0_156,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) != inverse(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)))
| double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)) != X_15
| multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) = inverse(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))),inverse(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)))) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_157,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) != inverse(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)))
| multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) = inverse(X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)),X_15) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))) = inverse(X_15),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(X_15)))),inverse(double_divide(double_divide(identity,inverse(inverse(X_15))),inverse(identity)))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))) = inverse(inverse(identity)),
inference(subst,[],[refute_0_158:[bind(X_15,$fot(inverse(identity)))]]) ).
cnf(refute_0_160,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(identity,inverse(inverse(identity))),
inference(subst,[],[refute_0_97:[bind(X_14,$fot(identity))]]) ).
cnf(refute_0_161,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,inverse(identity)) != identity
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(identity)))) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)) != double_divide(identity,inverse(inverse(identity)))
| double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_54,refute_0_161]) ).
cnf(refute_0_163,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_160,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = double_divide(identity,inverse(inverse(inverse(identity)))),
inference(subst,[],[refute_0_125:[bind(X_19,$fot(identity))]]) ).
cnf(refute_0_165,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(identity,inverse(inverse(identity)))
| double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(identity,inverse(inverse(inverse(identity))))
| double_divide(identity,inverse(inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(identity,inverse(inverse(identity)))) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(identity)))))]]) ).
cnf(refute_0_166,plain,
( double_divide(double_divide(identity,identity),inverse(identity)) != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,inverse(inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(identity,inverse(inverse(inverse(identity))))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
double_divide(identity,inverse(inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))) != inverse(inverse(identity))
| double_divide(identity,inverse(inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = inverse(inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))),inverse(inverse(identity))) ),[0,1],$fot(double_divide(identity,inverse(inverse(identity))))]]) ).
cnf(refute_0_169,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))) != inverse(inverse(identity))
| multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(inverse(identity))))),inverse(inverse(identity))) )],[refute_0_159,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(subst,[],[refute_0_158:[bind(X_15,$fot(identity))]]) ).
cnf(refute_0_172,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != inverse(inverse(identity))
| inverse(identity) = inverse(inverse(identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))),inverse(inverse(identity))) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != inverse(inverse(identity))
| inverse(identity) = inverse(inverse(identity)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))),inverse(identity)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
inverse(identity) = inverse(inverse(identity)),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),double_divide(identity,inverse(inverse(identity)))),inverse(inverse(identity))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( inverse(identity) != inverse(inverse(identity))
| inverse(inverse(identity)) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(identity))),bind(Y,$fot(inverse(inverse(identity))))]]) ).
cnf(refute_0_176,plain,
inverse(inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),inverse(inverse(identity))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
( double_divide(inverse(inverse(identity)),inverse(identity)) != inverse(identity)
| inverse(inverse(identity)) != inverse(identity)
| double_divide(inverse(identity),inverse(identity)) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(inverse(identity)),inverse(identity)),inverse(identity)) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_178,plain,
( double_divide(inverse(inverse(identity)),inverse(identity)) != inverse(identity)
| double_divide(inverse(identity),inverse(identity)) = inverse(identity) ),
inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(identity)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(identity)),inverse(identity)),inverse(identity)) )],[refute_0_153,refute_0_178]) ).
cnf(refute_0_180,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(subst,[],[refute_0_122:[bind(X_19,$fot(identity))]]) ).
cnf(refute_0_181,plain,
( double_divide(inverse(identity),inverse(identity)) != identity
| double_divide(inverse(identity),inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(identity)) ),[0],$fot(identity)]]) ).
cnf(refute_0_182,plain,
( double_divide(inverse(identity),inverse(identity)) != inverse(identity)
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),identity) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(identity)),inverse(identity)) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_185,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
multiply(inverse(identity),X_14) = multiply(inverse(identity),X_14),
introduced(tautology,[refl,[$fot(multiply(inverse(identity),X_14))]]) ).
cnf(refute_0_187,plain,
( multiply(inverse(identity),X_14) != multiply(inverse(identity),X_14)
| inverse(identity) != identity
| multiply(inverse(identity),X_14) = multiply(identity,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),X_14),multiply(inverse(identity),X_14)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_188,plain,
( inverse(identity) != identity
| multiply(inverse(identity),X_14) = multiply(identity,X_14) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_14),multiply(inverse(identity),X_14)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(inverse(identity),X_14) = multiply(identity,X_14),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( multiply(identity,X_14) != inverse(inverse(X_14))
| multiply(inverse(identity),X_14) != multiply(identity,X_14)
| multiply(inverse(identity),X_14) = inverse(inverse(X_14)) ),
inference(subst,[],[refute_0_112:[bind(X,$fot(multiply(inverse(identity),X_14))),bind(Y,$fot(multiply(identity,X_14))),bind(Z,$fot(inverse(inverse(X_14))))]]) ).
cnf(refute_0_191,plain,
( multiply(identity,X_14) != inverse(inverse(X_14))
| multiply(inverse(identity),X_14) = inverse(inverse(X_14)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_14),multiply(identity,X_14)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(inverse(identity),X_14) = inverse(inverse(X_14)),
inference(resolve,[$cnf( $equal(multiply(identity,X_14),inverse(inverse(X_14))) )],[refute_0_152,refute_0_191]) ).
cnf(refute_0_193,plain,
inverse(multiply(inverse(identity),X_14)) = inverse(multiply(inverse(identity),X_14)),
introduced(tautology,[refl,[$fot(inverse(multiply(inverse(identity),X_14)))]]) ).
cnf(refute_0_194,plain,
( multiply(inverse(identity),X_14) != inverse(inverse(X_14))
| inverse(multiply(inverse(identity),X_14)) != inverse(multiply(inverse(identity),X_14))
| inverse(multiply(inverse(identity),X_14)) = inverse(inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(identity),X_14)),inverse(multiply(inverse(identity),X_14))) ),[1,0],$fot(inverse(inverse(X_14)))]]) ).
cnf(refute_0_195,plain,
( multiply(inverse(identity),X_14) != inverse(inverse(X_14))
| inverse(multiply(inverse(identity),X_14)) = inverse(inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(identity),X_14)),inverse(multiply(inverse(identity),X_14))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
inverse(multiply(inverse(identity),X_14)) = inverse(inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(multiply(inverse(identity),X_14),inverse(inverse(X_14))) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
inverse(inverse(multiply(inverse(identity),X_14))) = inverse(inverse(multiply(inverse(identity),X_14))),
introduced(tautology,[refl,[$fot(inverse(inverse(multiply(inverse(identity),X_14))))]]) ).
cnf(refute_0_198,plain,
( inverse(multiply(inverse(identity),X_14)) != inverse(inverse(inverse(X_14)))
| inverse(inverse(multiply(inverse(identity),X_14))) != inverse(inverse(multiply(inverse(identity),X_14)))
| inverse(inverse(multiply(inverse(identity),X_14))) = inverse(inverse(inverse(inverse(X_14)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(inverse(identity),X_14))),inverse(inverse(multiply(inverse(identity),X_14)))) ),[1,0],$fot(inverse(inverse(inverse(X_14))))]]) ).
cnf(refute_0_199,plain,
( inverse(multiply(inverse(identity),X_14)) != inverse(inverse(inverse(X_14)))
| inverse(inverse(multiply(inverse(identity),X_14))) = inverse(inverse(inverse(inverse(X_14)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(inverse(identity),X_14))),inverse(inverse(multiply(inverse(identity),X_14)))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
inverse(inverse(multiply(inverse(identity),X_14))) = inverse(inverse(inverse(inverse(X_14)))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(identity),X_14)),inverse(inverse(inverse(X_14)))) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),
introduced(tautology,[refl,[$fot(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))))]]) ).
cnf(refute_0_202,plain,
( double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) != double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))
| inverse(inverse(multiply(inverse(identity),X_14))) != inverse(inverse(inverse(inverse(X_14))))
| double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))) ),[1,1],$fot(inverse(inverse(inverse(inverse(X_14)))))]]) ).
cnf(refute_0_203,plain,
( inverse(inverse(multiply(inverse(identity),X_14))) != inverse(inverse(inverse(inverse(X_14))))
| double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14))))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) = double_divide(identity,inverse(inverse(inverse(inverse(X_14))))),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(inverse(identity),X_14))),inverse(inverse(inverse(inverse(X_14))))) )],[refute_0_200,refute_0_203]) ).
cnf(refute_0_205,plain,
( double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) != double_divide(identity,inverse(inverse(inverse(inverse(X_14)))))
| double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) = double_divide(identity,inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),double_divide(identity,inverse(inverse(X_14)))) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(inverse(X_14))))))]]) ).
cnf(refute_0_206,plain,
( double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) = double_divide(identity,inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),double_divide(identity,inverse(inverse(inverse(inverse(X_14)))))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) = double_divide(identity,inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(multiply(inverse(identity),X_14)))),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_151,refute_0_206]) ).
cnf(refute_0_208,plain,
double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) = double_divide(identity,inverse(inverse(inverse(X_14)))),
inference(subst,[],[refute_0_207:[bind(X_14,$fot(inverse(X_14)))]]) ).
cnf(refute_0_209,plain,
( double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) != X_14
| double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) != double_divide(identity,inverse(inverse(inverse(X_14))))
| double_divide(identity,inverse(inverse(inverse(X_14)))) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))),X_14) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(X_14)))))]]) ).
cnf(refute_0_210,plain,
( double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))) != X_14
| double_divide(identity,inverse(inverse(inverse(X_14)))) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))),double_divide(identity,inverse(inverse(inverse(X_14))))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
double_divide(identity,inverse(inverse(inverse(X_14)))) = X_14,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(inverse(X_14)))))),X_14) )],[refute_0_129,refute_0_210]) ).
cnf(refute_0_212,plain,
double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) = inverse(X_14),
inference(subst,[],[refute_0_211:[bind(X_14,$fot(inverse(X_14)))]]) ).
cnf(refute_0_213,plain,
( double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) != inverse(X_14)
| inverse(X_14) = double_divide(identity,inverse(inverse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(X_14))))),double_divide(identity,inverse(inverse(X_14)))) ),[0],$fot(inverse(X_14))]]) ).
cnf(refute_0_214,plain,
( double_divide(identity,inverse(inverse(inverse(inverse(X_14))))) != double_divide(identity,inverse(inverse(X_14)))
| inverse(X_14) = double_divide(identity,inverse(inverse(X_14))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(X_14))))),inverse(X_14)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
inverse(X_14) = double_divide(identity,inverse(inverse(X_14))),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(inverse(X_14))))),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_207,refute_0_214]) ).
cnf(refute_0_216,plain,
( inverse(X_14) != double_divide(identity,inverse(inverse(X_14)))
| double_divide(identity,inverse(inverse(X_14))) = inverse(X_14) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_14))),bind(Y,$fot(double_divide(identity,inverse(inverse(X_14)))))]]) ).
cnf(refute_0_217,plain,
double_divide(identity,inverse(inverse(X_14))) = inverse(X_14),
inference(resolve,[$cnf( $equal(inverse(X_14),double_divide(identity,inverse(inverse(X_14)))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
double_divide(identity,inverse(inverse(inverse(X_14)))) = inverse(inverse(X_14)),
inference(subst,[],[refute_0_217:[bind(X_14,$fot(inverse(X_14)))]]) ).
cnf(refute_0_219,plain,
( double_divide(identity,inverse(inverse(inverse(X_14)))) != X_14
| double_divide(identity,inverse(inverse(inverse(X_14)))) != inverse(inverse(X_14))
| inverse(inverse(X_14)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_14)))),X_14) ),[0],$fot(inverse(inverse(X_14)))]]) ).
cnf(refute_0_220,plain,
( double_divide(identity,inverse(inverse(inverse(X_14)))) != X_14
| inverse(inverse(X_14)) = X_14 ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_14)))),inverse(inverse(X_14))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
inverse(inverse(X_14)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_14)))),X_14) )],[refute_0_211,refute_0_220]) ).
cnf(refute_0_222,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_221:[bind(X_14,$fot(a2))]]) ).
cnf(refute_0_223,plain,
( a2 != a2
| inverse(inverse(a2)) != a2
| inverse(inverse(a2)) = a2 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(a2)),a2) ),[0,0,0],$fot(a2)]]) ).
cnf(refute_0_224,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_224,refute_0_19]) ).
cnf(refute_0_226,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_227,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_226,refute_0_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP566-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:37:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.39
% 0.21/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.44
%------------------------------------------------------------------------------