%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:41:42 EDT 2022
% Result : Unsatisfiable 0.21s 0.38s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 59
% Syntax : Number of clauses : 181 ( 95 unt; 0 nHn; 102 RR)
% Number of literals : 306 ( 305 equ; 128 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 : 276 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C ).
cnf(multiply,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity) ).
cnf(inverse,axiom,
inverse(A) = double_divide(A,identity) ).
cnf(identity,axiom,
identity = double_divide(A,inverse(A)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity ).
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( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(inverse(X_3),X_3) = inverse(double_divide(X_3,inverse(X_3))),
inference(subst,[],[refute_0_8:[bind(A,$fot(inverse(X_3))),bind(B,$fot(X_3))]]) ).
cnf(refute_0_10,plain,
identity = double_divide(X_3,inverse(X_3)),
inference(subst,[],[identity:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_11,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_12,plain,
double_divide(X_3,inverse(X_3)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_3,inverse(X_3))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(inverse(X_3),X_3) != inverse(double_divide(X_3,inverse(X_3)))
| double_divide(X_3,inverse(X_3)) != identity
| multiply(inverse(X_3),X_3) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_14,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( $equal(double_divide(X_3,inverse(X_3)),identity) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(inverse(X_3),X_3) = inverse(identity),
inference(resolve,[$cnf( $equal(multiply(inverse(X_3),X_3),inverse(double_divide(X_3,inverse(X_3)))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(inverse(a1),a1) = inverse(identity),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(a1))]]) ).
cnf(refute_0_17,plain,
( multiply(inverse(a1),a1) != inverse(identity)
| inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),identity) ),[0],$fot(inverse(identity))]]) ).
cnf(refute_0_18,plain,
( inverse(identity) != identity
| multiply(inverse(a1),a1) = identity ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),inverse(identity)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(identity) != identity,
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),identity) )],[refute_0_18,prove_these_axioms_1]) ).
cnf(refute_0_20,plain,
double_divide(double_divide(A,B),identity) = inverse(double_divide(A,B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(A,B)))]]) ).
cnf(refute_0_21,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),
introduced(tautology,[refl,[$fot(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))]]) ).
cnf(refute_0_22,plain,
( double_divide(double_divide(A,B),identity) != inverse(double_divide(A,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) ),[1,0],$fot(inverse(double_divide(A,B)))]]) ).
cnf(refute_0_23,plain,
( double_divide(double_divide(A,B),identity) != inverse(double_divide(A,B))
| double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)),
inference(resolve,[$cnf( $equal(double_divide(double_divide(A,B),identity),inverse(double_divide(A,B))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))]]) ).
cnf(refute_0_26,plain,
( double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) ),[1,1],$fot(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))]]) ).
cnf(refute_0_27,plain,
( double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))))]]) ).
cnf(refute_0_30,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))
| double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))]]) ).
cnf(refute_0_31,plain,
( double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),C) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))))]]) ).
cnf(refute_0_34,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))),C) )],[single_axiom,refute_0_34]) ).
cnf(refute_0_36,plain,
( multiply(A,B) != inverse(double_divide(B,A))
| inverse(double_divide(B,A)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(inverse(double_divide(B,A))))]]) ).
cnf(refute_0_37,plain,
inverse(double_divide(B,A)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),inverse(double_divide(B,A))) )],[refute_0_8,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(subst,[],[refute_0_37:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_39,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(inverse(double_divide(A,B)),double_divide(C,B)),
introduced(tautology,[refl,[$fot(double_divide(inverse(double_divide(A,B)),double_divide(C,B)))]]) ).
cnf(refute_0_40,plain,
( double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(inverse(double_divide(A,B)),double_divide(C,B))
| inverse(double_divide(A,B)) != multiply(B,A)
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) ),[1,0],$fot(multiply(B,A))]]) ).
cnf(refute_0_41,plain,
( inverse(double_divide(A,B)) != multiply(B,A)
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(inverse(double_divide(A,B)),double_divide(C,B))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
double_divide(inverse(double_divide(A,B)),double_divide(C,B)) = double_divide(multiply(B,A),double_divide(C,B)),
inference(resolve,[$cnf( $equal(inverse(double_divide(A,B)),multiply(B,A)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))]]) ).
cnf(refute_0_44,plain,
( double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))
| double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(multiply(B,A),double_divide(C,B))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) ),[1,1],$fot(double_divide(multiply(B,A),double_divide(C,B)))]]) ).
cnf(refute_0_45,plain,
( double_divide(inverse(double_divide(A,B)),double_divide(C,B)) != double_divide(multiply(B,A),double_divide(C,B))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))),
inference(resolve,[$cnf( $equal(double_divide(inverse(double_divide(A,B)),double_divide(C,B)),double_divide(multiply(B,A),double_divide(C,B))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))))]]) ).
cnf(refute_0_48,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))
| double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) ),[1,1],$fot(double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))]]) ).
cnf(refute_0_49,plain,
( double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))) != double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B))),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),C) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))))]]) ).
cnf(refute_0_52,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))) != C
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B))))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(B,A),double_divide(C,B)))) = C,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(double_divide(A,B)),double_divide(C,B)))),C) )],[refute_0_35,refute_0_52]) ).
cnf(refute_0_54,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) = X_12,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_10)),bind(B,$fot(inverse(X_12))),bind(C,$fot(X_12))]]) ).
cnf(refute_0_55,plain,
identity = double_divide(X_12,inverse(X_12)),
inference(subst,[],[identity:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_56,plain,
( identity != double_divide(X_12,inverse(X_12))
| double_divide(X_12,inverse(X_12)) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_12,inverse(X_12))))]]) ).
cnf(refute_0_57,plain,
double_divide(X_12,inverse(X_12)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(X_12,inverse(X_12))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( double_divide(X_12,inverse(X_12)) != identity
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))),X_12) ),[0,1,1,1],$fot(identity)]]) ).
cnf(refute_0_59,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,inverse(X_12)),identity) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),double_divide(X_12,inverse(X_12))))),X_12) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
double_divide(multiply(inverse(X_12),X_10),identity) = inverse(multiply(inverse(X_12),X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(inverse(X_12),X_10)))]]) ).
cnf(refute_0_62,plain,
double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))]]) ).
cnf(refute_0_63,plain,
( double_divide(multiply(inverse(X_12),X_10),identity) != inverse(multiply(inverse(X_12),X_10))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) ),[1,1],$fot(inverse(multiply(inverse(X_12),X_10)))]]) ).
cnf(refute_0_64,plain,
( double_divide(multiply(inverse(X_12),X_10),identity) != inverse(multiply(inverse(X_12),X_10))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) = double_divide(identity,inverse(multiply(inverse(X_12),X_10))),
inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_12),X_10),identity),inverse(multiply(inverse(X_12),X_10))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))))]]) ).
cnf(refute_0_67,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))
| double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,inverse(multiply(inverse(X_12),X_10)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))) ),[1,1],$fot(double_divide(identity,inverse(multiply(inverse(X_12),X_10))))]]) ).
cnf(refute_0_68,plain,
( double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)) != double_divide(identity,inverse(multiply(inverse(X_12),X_10)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) = double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity)),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10))))
| double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),X_12) ),[0],$fot(double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))))]]) ).
cnf(refute_0_71,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10))))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,inverse(multiply(inverse(X_12),X_10)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(inverse(X_12),X_10),identity))),X_12) )],[refute_0_60,refute_0_71]) ).
cnf(refute_0_73,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) = X_13,
inference(subst,[],[refute_0_72:[bind(X_10,$fot(X_13)),bind(X_12,$fot(X_13))]]) ).
cnf(refute_0_74,plain,
multiply(inverse(X_13),X_13) = inverse(identity),
inference(subst,[],[refute_0_15:[bind(X_3,$fot(X_13))]]) ).
cnf(refute_0_75,plain,
( multiply(inverse(X_13),X_13) != inverse(identity)
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) != X_13
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))),X_13) ),[0,1,1,0],$fot(inverse(identity))]]) ).
cnf(refute_0_76,plain,
( double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))) != X_13
| double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_13),X_13),inverse(identity)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
double_divide(double_divide(identity,X_13),double_divide(identity,inverse(inverse(identity)))) = X_13,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_13),double_divide(identity,inverse(multiply(inverse(X_13),X_13)))),X_13) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(subst,[],[refute_0_77:[bind(X_13,$fot(double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_79,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(subst,[],[refute_0_77:[bind(X_13,$fot(inverse(identity)))]]) ).
cnf(refute_0_80,plain,
identity = double_divide(identity,inverse(identity)),
inference(subst,[],[identity:[bind(A,$fot(identity))]]) ).
cnf(refute_0_81,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_82,plain,
double_divide(identity,inverse(identity)) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(identity))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(identity,inverse(identity)) != identity
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))),inverse(identity)) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_84,plain,
( double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(identity)),identity) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))),inverse(identity)) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,double_divide(identity,inverse(inverse(identity)))) != inverse(identity)
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_87,plain,
( double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_78,refute_0_87]) ).
cnf(refute_0_89,plain,
double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(subst,[],[refute_0_77:[bind(X_13,$fot(identity))]]) ).
cnf(refute_0_90,plain,
inverse(identity) = double_divide(identity,identity),
inference(subst,[],[inverse:[bind(A,$fot(identity))]]) ).
cnf(refute_0_91,plain,
( inverse(identity) != double_divide(identity,identity)
| double_divide(identity,identity) = inverse(identity) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(identity))),bind(Y,$fot(double_divide(identity,identity)))]]) ).
cnf(refute_0_92,plain,
double_divide(identity,identity) = inverse(identity),
inference(resolve,[$cnf( $equal(inverse(identity),double_divide(identity,identity)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) != identity
| double_divide(identity,identity) != inverse(identity)
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))),identity) ),[0,0],$fot(inverse(identity))]]) ).
cnf(refute_0_94,plain,
( double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) != identity
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity ),
inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))),identity) )],[refute_0_89,refute_0_94]) ).
cnf(refute_0_96,plain,
( double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != identity
| identity = double_divide(identity,inverse(inverse(identity))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) ),[0],$fot(identity)]]) ).
cnf(refute_0_97,plain,
( double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) != double_divide(identity,inverse(inverse(identity)))
| identity = double_divide(identity,inverse(inverse(identity))) ),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(resolve,[$cnf( $equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) )],[refute_0_88,refute_0_97]) ).
cnf(refute_0_99,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) = X_12,
inference(subst,[],[refute_0_53:[bind(A,$fot(X_10)),bind(B,$fot(identity)),bind(C,$fot(X_12))]]) ).
cnf(refute_0_100,plain,
inverse(X_12) = double_divide(X_12,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_12))]]) ).
cnf(refute_0_101,plain,
( inverse(X_12) != double_divide(X_12,identity)
| double_divide(X_12,identity) = inverse(X_12) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_12))),bind(Y,$fot(double_divide(X_12,identity)))]]) ).
cnf(refute_0_102,plain,
double_divide(X_12,identity) = inverse(X_12),
inference(resolve,[$cnf( $equal(inverse(X_12),double_divide(X_12,identity)) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( double_divide(X_12,identity) != inverse(X_12)
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))),X_12) ),[0,1,1,1],$fot(inverse(X_12))]]) ).
cnf(refute_0_104,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(X_12,identity),inverse(X_12)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),double_divide(X_12,identity)))),X_12) )],[refute_0_99,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).
cnf(refute_0_107,plain,
inverse(X_3) = double_divide(X_3,identity),
inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_108,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_109,plain,
double_divide(X_3,identity) = inverse(X_3),
inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| double_divide(X_3,identity) != inverse(X_3)
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).
cnf(refute_0_111,plain,
( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
| multiply(identity,X_3) = inverse(inverse(X_3)) ),
inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(identity,X_3) = inverse(inverse(X_3)),
inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
multiply(identity,X_10) = inverse(inverse(X_10)),
inference(subst,[],[refute_0_112:[bind(X_3,$fot(X_10))]]) ).
cnf(refute_0_114,plain,
double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(multiply(identity,X_10),inverse(X_12)),
introduced(tautology,[refl,[$fot(double_divide(multiply(identity,X_10),inverse(X_12)))]]) ).
cnf(refute_0_115,plain,
( multiply(identity,X_10) != inverse(inverse(X_10))
| double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(multiply(identity,X_10),inverse(X_12))
| double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(multiply(identity,X_10),inverse(X_12))) ),[1,0],$fot(inverse(inverse(X_10)))]]) ).
cnf(refute_0_116,plain,
( multiply(identity,X_10) != inverse(inverse(X_10))
| double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(multiply(identity,X_10),inverse(X_12))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
double_divide(multiply(identity,X_10),inverse(X_12)) = double_divide(inverse(inverse(X_10)),inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(identity,X_10),inverse(inverse(X_10))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))]]) ).
cnf(refute_0_119,plain,
( double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(inverse(inverse(X_10)),inverse(X_12))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) ),[1,1],$fot(double_divide(inverse(inverse(X_10)),inverse(X_12)))]]) ).
cnf(refute_0_120,plain,
( double_divide(multiply(identity,X_10),inverse(X_12)) != double_divide(inverse(inverse(X_10)),inverse(X_12))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) = double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))),
inference(resolve,[$cnf( $equal(double_divide(multiply(identity,X_10),inverse(X_12)),double_divide(inverse(inverse(X_10)),inverse(X_12))) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))))]]) ).
cnf(refute_0_123,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))
| double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))]]) ).
cnf(refute_0_124,plain,
( double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))) != double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) = double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12))),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),X_12) ),[0],$fot(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))))]]) ).
cnf(refute_0_127,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12))))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(multiply(identity,X_10),inverse(X_12)))),X_12) )],[refute_0_105,refute_0_127]) ).
cnf(refute_0_129,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) = double_divide(identity,X_15),
inference(subst,[],[refute_0_53:[bind(B,$fot(double_divide(identity,inverse(inverse(identity))))),bind(C,$fot(double_divide(identity,X_15)))]]) ).
cnf(refute_0_130,plain,
double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))) = X_15,
inference(subst,[],[refute_0_77:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_131,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))) != X_15
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))),double_divide(identity,X_15)) ),[0,1,1,1],$fot(X_15)]]) ).
cnf(refute_0_132,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity)))),X_15) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(identity,X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),double_divide(double_divide(identity,X_15),double_divide(identity,inverse(inverse(identity))))))),double_divide(identity,X_15)) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
multiply(identity,A) = inverse(inverse(A)),
inference(subst,[],[refute_0_112:[bind(X_3,$fot(A))]]) ).
cnf(refute_0_135,plain,
( identity != double_divide(identity,inverse(inverse(identity)))
| double_divide(identity,inverse(inverse(identity))) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(identity,inverse(inverse(identity)))))]]) ).
cnf(refute_0_136,plain,
double_divide(identity,inverse(inverse(identity))) = identity,
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) )],[refute_0_98,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(double_divide(identity,inverse(inverse(identity))),A),
introduced(tautology,[refl,[$fot(multiply(double_divide(identity,inverse(inverse(identity))),A))]]) ).
cnf(refute_0_138,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != multiply(double_divide(identity,inverse(inverse(identity))),A)
| double_divide(identity,inverse(inverse(identity))) != identity
| multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(double_divide(identity,inverse(inverse(identity))),A)) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_139,plain,
( double_divide(identity,inverse(inverse(identity))) != identity
| multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(double_divide(identity,inverse(inverse(identity))),A)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = multiply(identity,A),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),identity) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_142,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_141]) ).
cnf(refute_0_143,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != multiply(identity,A)
| multiply(identity,A) != inverse(inverse(A))
| multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)) ),
inference(subst,[],[refute_0_142:[bind(X,$fot(multiply(double_divide(identity,inverse(inverse(identity))),A))),bind(Y,$fot(multiply(identity,A))),bind(Z,$fot(inverse(inverse(A))))]]) ).
cnf(refute_0_144,plain,
( multiply(identity,A) != inverse(inverse(A))
| multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)) ),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),multiply(identity,A)) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(double_divide(identity,inverse(inverse(identity))),A) = inverse(inverse(A)),
inference(resolve,[$cnf( $equal(multiply(identity,A),inverse(inverse(A))) )],[refute_0_134,refute_0_144]) ).
cnf(refute_0_146,plain,
double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),
introduced(tautology,[refl,[$fot(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))]]) ).
cnf(refute_0_147,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != inverse(inverse(A))
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) ),[1,0],$fot(inverse(inverse(A)))]]) ).
cnf(refute_0_148,plain,
( multiply(double_divide(identity,inverse(inverse(identity))),A) != inverse(inverse(A))
| double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15) ),
inference(resolve,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) = double_divide(inverse(inverse(A)),X_15),
inference(resolve,[$cnf( $equal(multiply(double_divide(identity,inverse(inverse(identity))),A),inverse(inverse(A))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),
introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))]]) ).
cnf(refute_0_151,plain,
( double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(inverse(inverse(A)),X_15)
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) ),[1,1],$fot(double_divide(inverse(inverse(A)),X_15))]]) ).
cnf(refute_0_152,plain,
( double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15) != double_divide(inverse(inverse(A)),X_15)
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)) ),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) = double_divide(identity,double_divide(inverse(inverse(A)),X_15)),
inference(resolve,[$cnf( $equal(double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15),double_divide(inverse(inverse(A)),X_15)) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),
introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))))]]) ).
cnf(refute_0_155,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))
| double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(inverse(inverse(A)),X_15))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))) ),[1,1],$fot(double_divide(identity,double_divide(inverse(inverse(A)),X_15)))]]) ).
cnf(refute_0_156,plain,
( double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)) != double_divide(identity,double_divide(inverse(inverse(A)),X_15))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) = double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))),
inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15)),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15)))
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(identity,X_15)) ),[0],$fot(double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))))]]) ).
cnf(refute_0_159,plain,
( double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))) != double_divide(identity,X_15)
| double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15) ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15)))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(inverse(inverse(A)),X_15))) = double_divide(identity,X_15),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,A),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),A),X_15))),double_divide(identity,X_15)) )],[refute_0_133,refute_0_159]) ).
cnf(refute_0_161,plain,
double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) = double_divide(identity,inverse(X_12)),
inference(subst,[],[refute_0_160:[bind(A,$fot(X_10)),bind(X_15,$fot(inverse(X_12)))]]) ).
cnf(refute_0_162,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != X_12
| double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != double_divide(identity,inverse(X_12))
| double_divide(identity,inverse(X_12)) = X_12 ),
introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),X_12) ),[0],$fot(double_divide(identity,inverse(X_12)))]]) ).
cnf(refute_0_163,plain,
( double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))) != X_12
| double_divide(identity,inverse(X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),double_divide(identity,inverse(X_12))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
double_divide(identity,inverse(X_12)) = X_12,
inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,X_10),double_divide(identity,double_divide(inverse(inverse(X_10)),inverse(X_12)))),X_12) )],[refute_0_128,refute_0_163]) ).
cnf(refute_0_165,plain,
double_divide(identity,inverse(inverse(identity))) = inverse(identity),
inference(subst,[],[refute_0_164:[bind(X_12,$fot(inverse(identity)))]]) ).
cnf(refute_0_166,plain,
( double_divide(identity,inverse(inverse(identity))) != inverse(identity)
| identity != double_divide(identity,inverse(inverse(identity)))
| identity = inverse(identity) ),
introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) ),[1],$fot(inverse(identity))]]) ).
cnf(refute_0_167,plain,
( identity != double_divide(identity,inverse(inverse(identity)))
| identity = inverse(identity) ),
inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(identity))),inverse(identity)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
identity = inverse(identity),
inference(resolve,[$cnf( $equal(identity,double_divide(identity,inverse(inverse(identity)))) )],[refute_0_98,refute_0_167]) ).
cnf(refute_0_169,plain,
( identity != inverse(identity)
| inverse(identity) = identity ),
inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).
cnf(refute_0_170,plain,
inverse(identity) = identity,
inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( identity != identity
| inverse(identity) != identity
| inverse(identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(inverse(identity),identity) ),[0,0],$fot(identity)]]) ).
cnf(refute_0_172,plain,
( identity != identity
| inverse(identity) = identity ),
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
identity != identity,
inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_172,refute_0_19]) ).
cnf(refute_0_174,plain,
identity = identity,
introduced(tautology,[refl,[$fot(identity)]]) ).
cnf(refute_0_175,plain,
$false,
inference(resolve,[$cnf( $equal(identity,identity) )],[refute_0_174,refute_0_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP490-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n008.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 11:20:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.38
% 0.21/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.42
%------------------------------------------------------------------------------