%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 10:41:38 EDT 2022
% Result : Unsatisfiable 0.18s 0.36s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 48
% Syntax : Number of clauses : 173 ( 91 unt; 0 nHn; 83 RR)
% Number of literals : 293 ( 292 equ; 123 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 273 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),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_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( $equal(multiply(identity,a2),a2) )],[refute_0_18,prove_these_axioms_2]) ).
cnf(refute_0_20,plain,
inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity),
inference(subst,[],[inverse:[bind(A,$fot(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))))]]) ).
cnf(refute_0_21,plain,
double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(C),double_divide(A,identity)))]]) ).
cnf(refute_0_22,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),double_divide(A,identity))
| double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) ),[1,1],$fot(inverse(A))]]) ).
cnf(refute_0_23,plain,
( double_divide(A,identity) != inverse(A)
| double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(inverse(C),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)),
inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
double_divide(C,identity) = inverse(C),
inference(subst,[],[refute_0_4:[bind(A,$fot(C))]]) ).
cnf(refute_0_26,plain,
( identity != double_divide(A,inverse(A))
| double_divide(A,inverse(A)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(A,inverse(A))))]]) ).
cnf(refute_0_27,plain,
double_divide(A,inverse(A)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(A,inverse(A))) )],[identity,refute_0_26]) ).
cnf(refute_0_28,plain,
double_divide(D,inverse(D)) = identity,
inference(subst,[],[refute_0_27:[bind(A,$fot(D))]]) ).
cnf(refute_0_29,plain,
double_divide(D,identity) = inverse(D),
inference(subst,[],[refute_0_4:[bind(A,$fot(D))]]) ).
cnf(refute_0_30,plain,
double_divide(D,double_divide(D,identity)) = double_divide(D,double_divide(D,identity)),
introduced(tautology,[refl,[$fot(double_divide(D,double_divide(D,identity)))]]) ).
cnf(refute_0_31,plain,
( double_divide(D,double_divide(D,identity)) != double_divide(D,double_divide(D,identity))
| double_divide(D,identity) != inverse(D)
| double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,double_divide(D,identity))) ),[1,1],$fot(inverse(D))]]) ).
cnf(refute_0_32,plain,
( double_divide(D,identity) != inverse(D)
| double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)) ),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,double_divide(D,identity))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
double_divide(D,double_divide(D,identity)) = double_divide(D,inverse(D)),
inference(resolve,[$cnf( $equal(double_divide(D,identity),inverse(D)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
( double_divide(D,double_divide(D,identity)) != double_divide(D,inverse(D))
| double_divide(D,inverse(D)) != identity
| double_divide(D,double_divide(D,identity)) = identity ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(D,double_divide(D,identity)))),bind(Y,$fot(double_divide(D,inverse(D)))),bind(Z,$fot(identity))]]) ).
cnf(refute_0_37,plain,
( double_divide(D,inverse(D)) != identity
| double_divide(D,double_divide(D,identity)) = identity ),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),double_divide(D,inverse(D))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
double_divide(D,double_divide(D,identity)) = identity,
inference(resolve,[$cnf( $equal(double_divide(D,inverse(D)),identity) )],[refute_0_28,refute_0_37]) ).
cnf(refute_0_39,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,double_divide(D,double_divide(D,identity))),
introduced(tautology,[refl,[$fot(double_divide(C,double_divide(D,double_divide(D,identity))))]]) ).
cnf(refute_0_40,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != double_divide(C,double_divide(D,double_divide(D,identity)))
| double_divide(D,double_divide(D,identity)) != identity
| double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,double_divide(D,double_divide(D,identity)))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_41,plain,
( double_divide(D,double_divide(D,identity)) != identity
| double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity) ),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,double_divide(D,double_divide(D,identity)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = double_divide(C,identity),
inference(resolve,[$cnf( $equal(double_divide(D,double_divide(D,identity)),identity) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != double_divide(C,identity)
| double_divide(C,identity) != inverse(C)
| double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(C,double_divide(D,double_divide(D,identity))))),bind(Y,$fot(double_divide(C,identity))),bind(Z,$fot(inverse(C)))]]) ).
cnf(refute_0_44,plain,
( double_divide(C,identity) != inverse(C)
| double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C) ),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(C,identity)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
double_divide(C,double_divide(D,double_divide(D,identity))) = inverse(C),
inference(resolve,[$cnf( $equal(double_divide(C,identity),inverse(C)) )],[refute_0_25,refute_0_44]) ).
cnf(refute_0_46,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))]]) ).
cnf(refute_0_47,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != inverse(C)
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),[1,0],$fot(inverse(C))]]) ).
cnf(refute_0_48,plain,
( double_divide(C,double_divide(D,double_divide(D,identity))) != inverse(C)
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),double_divide(A,identity)),
inference(resolve,[$cnf( $equal(double_divide(C,double_divide(D,double_divide(D,identity))),inverse(C)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),double_divide(A,identity))
| double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))),bind(Y,$fot(double_divide(inverse(C),double_divide(A,identity)))),bind(Z,$fot(double_divide(inverse(C),inverse(A))))]]) ).
cnf(refute_0_51,plain,
( double_divide(inverse(C),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(inverse(C),double_divide(A,identity))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) = double_divide(inverse(C),inverse(A)),
inference(resolve,[$cnf( $equal(double_divide(inverse(C),double_divide(A,identity)),double_divide(inverse(C),inverse(A))) )],[refute_0_24,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))]]) ).
cnf(refute_0_54,plain,
( double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) ),[1,1],$fot(double_divide(inverse(C),inverse(A)))]]) ).
cnf(refute_0_55,plain,
( double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)) != double_divide(inverse(C),inverse(A))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)),double_divide(inverse(C),inverse(A))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
double_divide(B,identity) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_58,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(B,identity)),
introduced(tautology,[refl,[$fot(double_divide(A,double_divide(B,identity)))]]) ).
cnf(refute_0_59,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,double_divide(B,identity))
| double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_60,plain,
( double_divide(B,identity) != inverse(B)
| double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,double_divide(B,identity))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(double_divide(B,identity),inverse(B)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))]]) ).
cnf(refute_0_63,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) ),[1,0],$fot(double_divide(A,inverse(B)))]]) ).
cnf(refute_0_64,plain,
( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),
inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,inverse(B))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))
| double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))),bind(Y,$fot(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))))),bind(Z,$fot(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))))]]) ).
cnf(refute_0_67,plain,
( double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity)))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) = double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,inverse(B)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))) )],[refute_0_56,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B))]]) ).
cnf(refute_0_70,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)) ),[1,0],$fot(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))))]]) ).
cnf(refute_0_71,plain,
( double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))) != double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A)))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != C
| double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B)
| double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),C) ),[0],$fot(double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B))]]) ).
cnf(refute_0_74,plain,
( double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) != C
| double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
double_divide(double_divide(double_divide(A,inverse(B)),double_divide(inverse(C),inverse(A))),B) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B),C) )],[single_axiom,refute_0_74]) ).
cnf(refute_0_76,plain,
double_divide(double_divide(double_divide(X_11,inverse(X_11)),double_divide(inverse(X_12),inverse(X_11))),X_11) = X_12,
inference(subst,[],[refute_0_75:[bind(A,$fot(X_11)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_77,plain,
identity = double_divide(X_11,inverse(X_11)),
inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).
cnf(refute_0_78,plain,
( identity != double_divide(X_11,inverse(X_11))
| double_divide(X_11,inverse(X_11)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_11,inverse(X_11))))]]) ).
cnf(refute_0_79,plain,
double_divide(X_11,inverse(X_11)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( double_divide(X_11,inverse(X_11)) != identity
| double_divide(double_divide(double_divide(X_11,inverse(X_11)),double_divide(inverse(X_12),inverse(X_11))),X_11) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),X_11) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(X_11,inverse(X_11)),double_divide(inverse(X_12),inverse(X_11))),X_11),X_12) ),[0,0,0],$fot(identity)]]) ).
cnf(refute_0_81,plain,
( double_divide(double_divide(double_divide(X_11,inverse(X_11)),double_divide(inverse(X_12),inverse(X_11))),X_11) != X_12
| double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),X_11) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
double_divide(double_divide(identity,double_divide(inverse(X_12),inverse(X_11))),X_11) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(X_11,inverse(X_11)),double_divide(inverse(X_12),inverse(X_11))),X_11),X_12) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity) = X_22,
inference(subst,[],[refute_0_82:[bind(X_11,$fot(identity)),bind(X_12,$fot(X_22))]]) ).
cnf(refute_0_84,plain,
( double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity) != X_22
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity)
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = X_22 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity)) ),[1],$fot(X_22)]]) ).
cnf(refute_0_85,plain,
( inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity)
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = X_22 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity),X_22) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = X_22,
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),double_divide(double_divide(identity,double_divide(inverse(X_22),inverse(identity))),identity)) )],[refute_0_20,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(X_15),inverse(identity)) = inverse(double_divide(inverse(identity),inverse(X_15))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_15))),bind(B,$fot(inverse(identity)))]]) ).
cnf(refute_0_88,plain,
double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),double_divide(inverse(X_12),inverse(inverse(X_12)))),X_11) = X_12,
inference(subst,[],[refute_0_75:[bind(A,$fot(inverse(X_12))),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_89,plain,
identity = double_divide(inverse(X_12),inverse(inverse(X_12))),
inference(subst,[],[identity:[bind(A,$fot(inverse(X_12)))]]) ).
cnf(refute_0_90,plain,
( identity != double_divide(inverse(X_12),inverse(inverse(X_12)))
| double_divide(inverse(X_12),inverse(inverse(X_12))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(inverse(X_12),inverse(inverse(X_12)))))]]) ).
cnf(refute_0_91,plain,
double_divide(inverse(X_12),inverse(inverse(X_12))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(X_12),inverse(inverse(X_12)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),double_divide(inverse(X_12),inverse(inverse(X_12)))),X_11) != X_12
| double_divide(inverse(X_12),inverse(inverse(X_12))) != identity
| double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),double_divide(inverse(X_12),inverse(inverse(X_12)))),X_11),X_12) ),[0,0,1],$fot(identity)]]) ).
cnf(refute_0_93,plain,
( double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),double_divide(inverse(X_12),inverse(inverse(X_12)))),X_11) != X_12
| double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_12),inverse(inverse(X_12))),identity) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),double_divide(inverse(X_12),inverse(inverse(X_12)))),X_11),X_12) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_96,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_95]) ).
cnf(refute_0_97,plain,
inverse(double_divide(inverse(X_12),inverse(X_11))) = multiply(inverse(X_11),inverse(X_12)),
inference(subst,[],[refute_0_96:[bind(A,$fot(inverse(X_11))),bind(B,$fot(inverse(X_12)))]]) ).
cnf(refute_0_98,plain,
double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) = inverse(double_divide(inverse(X_12),inverse(X_11))),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(inverse(X_12),inverse(X_11))))]]) ).
cnf(refute_0_99,plain,
( double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) != inverse(double_divide(inverse(X_12),inverse(X_11)))
| inverse(double_divide(inverse(X_12),inverse(X_11))) != multiply(inverse(X_11),inverse(X_12))
| double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) = multiply(inverse(X_11),inverse(X_12)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity))),bind(Y,$fot(inverse(double_divide(inverse(X_12),inverse(X_11))))),bind(Z,$fot(multiply(inverse(X_11),inverse(X_12))))]]) ).
cnf(refute_0_100,plain,
( inverse(double_divide(inverse(X_12),inverse(X_11))) != multiply(inverse(X_11),inverse(X_12))
| double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) = multiply(inverse(X_11),inverse(X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),inverse(double_divide(inverse(X_12),inverse(X_11)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) = multiply(inverse(X_11),inverse(X_12)),
inference(resolve,[$cnf( $equal(inverse(double_divide(inverse(X_12),inverse(X_11))),multiply(inverse(X_11),inverse(X_12))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11))]]) ).
cnf(refute_0_103,plain,
( double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) != double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11)
| double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) != multiply(inverse(X_11),inverse(X_12))
| double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = double_divide(multiply(inverse(X_11),inverse(X_12)),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11)) ),[1,0],$fot(multiply(inverse(X_11),inverse(X_12)))]]) ).
cnf(refute_0_104,plain,
( double_divide(double_divide(inverse(X_12),inverse(X_11)),identity) != multiply(inverse(X_11),inverse(X_12))
| double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = double_divide(multiply(inverse(X_11),inverse(X_12)),X_11) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) = double_divide(multiply(inverse(X_11),inverse(X_12)),X_11),
inference(resolve,[$cnf( $equal(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),multiply(inverse(X_11),inverse(X_12))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) != X_12
| double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) != double_divide(multiply(inverse(X_11),inverse(X_12)),X_11)
| double_divide(multiply(inverse(X_11),inverse(X_12)),X_11) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),X_12) ),[0],$fot(double_divide(multiply(inverse(X_11),inverse(X_12)),X_11))]]) ).
cnf(refute_0_107,plain,
( double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11) != X_12
| double_divide(multiply(inverse(X_11),inverse(X_12)),X_11) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),double_divide(multiply(inverse(X_11),inverse(X_12)),X_11)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
double_divide(multiply(inverse(X_11),inverse(X_12)),X_11) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(inverse(X_12),inverse(X_11)),identity),X_11),X_12) )],[refute_0_94,refute_0_107]) ).
cnf(refute_0_109,plain,
double_divide(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(X_14)) = X_14,
inference(subst,[],[refute_0_108:[bind(X_11,$fot(inverse(X_14))),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_110,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_111,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_112,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_113,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_115,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_110,refute_0_115]) ).
cnf(refute_0_117,plain,
multiply(inverse(inverse(X_14)),inverse(X_14)) = inverse(identity),
inference(subst,[],[refute_0_116:[bind(X_3,$fot(inverse(X_14)))]]) ).
cnf(refute_0_118,plain,
( multiply(inverse(inverse(X_14)),inverse(X_14)) != inverse(identity)
| double_divide(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(X_14)) != X_14
| double_divide(inverse(identity),inverse(X_14)) = X_14 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(X_14)),X_14) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_119,plain,
( double_divide(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(X_14)) != X_14
| double_divide(inverse(identity),inverse(X_14)) = X_14 ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(identity)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
double_divide(inverse(identity),inverse(X_14)) = X_14,
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(inverse(X_14)),inverse(X_14)),inverse(X_14)),X_14) )],[refute_0_109,refute_0_119]) ).
cnf(refute_0_121,plain,
double_divide(inverse(identity),inverse(X_15)) = X_15,
inference(subst,[],[refute_0_120:[bind(X_14,$fot(X_15))]]) ).
cnf(refute_0_122,plain,
( multiply(inverse(X_15),inverse(identity)) != inverse(double_divide(inverse(identity),inverse(X_15)))
| double_divide(inverse(identity),inverse(X_15)) != X_15
| multiply(inverse(X_15),inverse(identity)) = inverse(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),inverse(double_divide(inverse(identity),inverse(X_15)))) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_123,plain,
( multiply(inverse(X_15),inverse(identity)) != inverse(double_divide(inverse(identity),inverse(X_15)))
| multiply(inverse(X_15),inverse(identity)) = inverse(X_15) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(X_15)),X_15) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(inverse(X_15),inverse(identity)) = inverse(X_15),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),inverse(double_divide(inverse(identity),inverse(X_15)))) )],[refute_0_87,refute_0_123]) ).
cnf(refute_0_125,plain,
identity = double_divide(inverse(identity),inverse(inverse(identity))),
inference(subst,[],[identity:[bind(A,$fot(inverse(identity)))]]) ).
cnf(refute_0_126,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_120:[bind(X_14,$fot(inverse(identity)))]]) ).
cnf(refute_0_127,plain,
( double_divide(inverse(identity),inverse(inverse(identity))) != inverse(identity)
| identity != double_divide(inverse(identity),inverse(inverse(identity)))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_128,plain,
( identity != double_divide(inverse(identity),inverse(inverse(identity)))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(inverse(identity),inverse(inverse(identity)))) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_131,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(inverse(X_15),inverse(identity)) = multiply(inverse(X_15),inverse(identity)),
introduced(tautology,[refl,[$fot(multiply(inverse(X_15),inverse(identity)))]]) ).
cnf(refute_0_133,plain,
( multiply(inverse(X_15),inverse(identity)) != multiply(inverse(X_15),inverse(identity))
| inverse(identity) != identity
| multiply(inverse(X_15),inverse(identity)) = multiply(inverse(X_15),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),multiply(inverse(X_15),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_134,plain,
( inverse(identity) != identity
| multiply(inverse(X_15),inverse(identity)) = multiply(inverse(X_15),identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),multiply(inverse(X_15),inverse(identity))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiply(inverse(X_15),inverse(identity)) = multiply(inverse(X_15),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( multiply(inverse(X_15),inverse(identity)) != multiply(inverse(X_15),identity)
| multiply(inverse(X_15),inverse(identity)) != inverse(X_15)
| multiply(inverse(X_15),identity) = inverse(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),inverse(X_15)) ),[0],$fot(multiply(inverse(X_15),identity))]]) ).
cnf(refute_0_137,plain,
( multiply(inverse(X_15),inverse(identity)) != inverse(X_15)
| multiply(inverse(X_15),identity) = inverse(X_15) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),multiply(inverse(X_15),identity)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
multiply(inverse(X_15),identity) = inverse(X_15),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),inverse(identity)),inverse(X_15)) )],[refute_0_124,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(inverse(inverse(X_22)),identity) = inverse(inverse(X_22)),
inference(subst,[],[refute_0_138:[bind(X_15,$fot(inverse(X_22)))]]) ).
cnf(refute_0_140,plain,
double_divide(inverse(X_22),identity) = inverse(inverse(X_22)),
inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_22)))]]) ).
cnf(refute_0_141,plain,
double_divide(inverse(X_22),inverse(identity)) = double_divide(inverse(X_22),inverse(identity)),
introduced(tautology,[refl,[$fot(double_divide(inverse(X_22),inverse(identity)))]]) ).
cnf(refute_0_142,plain,
( double_divide(inverse(X_22),inverse(identity)) != double_divide(inverse(X_22),inverse(identity))
| inverse(identity) != identity
| double_divide(inverse(X_22),inverse(identity)) = double_divide(inverse(X_22),identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_22),inverse(identity)),double_divide(inverse(X_22),inverse(identity))) ),[1,1],$fot(identity)]]) ).
cnf(refute_0_143,plain,
( inverse(identity) != identity
| double_divide(inverse(X_22),inverse(identity)) = double_divide(inverse(X_22),identity) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_22),inverse(identity)),double_divide(inverse(X_22),inverse(identity))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
double_divide(inverse(X_22),inverse(identity)) = double_divide(inverse(X_22),identity),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_131,refute_0_143]) ).
cnf(refute_0_145,plain,
( double_divide(inverse(X_22),identity) != inverse(inverse(X_22))
| double_divide(inverse(X_22),inverse(identity)) != double_divide(inverse(X_22),identity)
| double_divide(inverse(X_22),inverse(identity)) = inverse(inverse(X_22)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(double_divide(inverse(X_22),inverse(identity)))),bind(Y,$fot(double_divide(inverse(X_22),identity))),bind(Z,$fot(inverse(inverse(X_22))))]]) ).
cnf(refute_0_146,plain,
( double_divide(inverse(X_22),identity) != inverse(inverse(X_22))
| double_divide(inverse(X_22),inverse(identity)) = inverse(inverse(X_22)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_22),inverse(identity)),double_divide(inverse(X_22),identity)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
double_divide(inverse(X_22),inverse(identity)) = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_22),identity),inverse(inverse(X_22))) )],[refute_0_140,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(double_divide(inverse(X_22),inverse(identity)),identity) = multiply(double_divide(inverse(X_22),inverse(identity)),identity),
introduced(tautology,[refl,[$fot(multiply(double_divide(inverse(X_22),inverse(identity)),identity))]]) ).
cnf(refute_0_149,plain,
( multiply(double_divide(inverse(X_22),inverse(identity)),identity) != multiply(double_divide(inverse(X_22),inverse(identity)),identity)
| double_divide(inverse(X_22),inverse(identity)) != inverse(inverse(X_22))
| multiply(double_divide(inverse(X_22),inverse(identity)),identity) = multiply(inverse(inverse(X_22)),identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(inverse(X_22),inverse(identity)),identity),multiply(double_divide(inverse(X_22),inverse(identity)),identity)) ),[1,0],$fot(inverse(inverse(X_22)))]]) ).
cnf(refute_0_150,plain,
( double_divide(inverse(X_22),inverse(identity)) != inverse(inverse(X_22))
| multiply(double_divide(inverse(X_22),inverse(identity)),identity) = multiply(inverse(inverse(X_22)),identity) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(X_22),inverse(identity)),identity),multiply(double_divide(inverse(X_22),inverse(identity)),identity)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(double_divide(inverse(X_22),inverse(identity)),identity) = multiply(inverse(inverse(X_22)),identity),
inference(resolve,[$cnf( $equal(double_divide(inverse(X_22),inverse(identity)),inverse(inverse(X_22))) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(double_divide(inverse(X_22),inverse(identity)),identity) != multiply(inverse(inverse(X_22)),identity)
| multiply(inverse(inverse(X_22)),identity) != inverse(inverse(X_22))
| multiply(double_divide(inverse(X_22),inverse(identity)),identity) = inverse(inverse(X_22)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(multiply(double_divide(inverse(X_22),inverse(identity)),identity))),bind(Y,$fot(multiply(inverse(inverse(X_22)),identity))),bind(Z,$fot(inverse(inverse(X_22))))]]) ).
cnf(refute_0_153,plain,
( multiply(inverse(inverse(X_22)),identity) != inverse(inverse(X_22))
| multiply(double_divide(inverse(X_22),inverse(identity)),identity) = inverse(inverse(X_22)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(X_22),inverse(identity)),identity),multiply(inverse(inverse(X_22)),identity)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(double_divide(inverse(X_22),inverse(identity)),identity) = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),identity),inverse(inverse(X_22))) )],[refute_0_139,refute_0_153]) ).
cnf(refute_0_155,plain,
inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = multiply(double_divide(inverse(X_22),inverse(identity)),identity),
inference(subst,[],[refute_0_96:[bind(A,$fot(double_divide(inverse(X_22),inverse(identity)))),bind(B,$fot(identity))]]) ).
cnf(refute_0_156,plain,
( multiply(double_divide(inverse(X_22),inverse(identity)),identity) != inverse(inverse(X_22))
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != multiply(double_divide(inverse(X_22),inverse(identity)),identity)
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = inverse(inverse(X_22)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))))),bind(Y,$fot(multiply(double_divide(inverse(X_22),inverse(identity)),identity))),bind(Z,$fot(inverse(inverse(X_22))))]]) ).
cnf(refute_0_157,plain,
( multiply(double_divide(inverse(X_22),inverse(identity)),identity) != inverse(inverse(X_22))
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = inverse(inverse(X_22)) ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),multiply(double_divide(inverse(X_22),inverse(identity)),identity)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) = inverse(inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(double_divide(inverse(X_22),inverse(identity)),identity),inverse(inverse(X_22))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
( inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != X_22
| inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != inverse(inverse(X_22))
| inverse(inverse(X_22)) = X_22 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),X_22) ),[0],$fot(inverse(inverse(X_22)))]]) ).
cnf(refute_0_160,plain,
( inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))) != X_22
| inverse(inverse(X_22)) = X_22 ),
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),inverse(inverse(X_22))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
inverse(inverse(X_22)) = X_22,
inference(resolve,[$cnf( $equal(inverse(double_divide(identity,double_divide(inverse(X_22),inverse(identity)))),X_22) )],[refute_0_86,refute_0_160]) ).
cnf(refute_0_162,plain,
inverse(inverse(a2)) = a2,
inference(subst,[],[refute_0_161:[bind(X_22,$fot(a2))]]) ).
cnf(refute_0_163,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_164,plain,
( a2 != a2
| inverse(inverse(a2)) = a2 ),
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_164,refute_0_19]) ).
cnf(refute_0_166,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_167,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_166,refute_0_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP482-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:21:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.36
% 0.18/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.40
%------------------------------------------------------------------------------