%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 10:41:44 EDT 2022

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   51
%            Number of leaves      :   75
% Syntax   : Number of clauses     :  270 ( 139 unt;   0 nHn; 141 RR)
%            Number of literals    :  462 ( 461 equ; 195 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   :  378 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C ).

cnf(multiply,axiom,
    multiply(A,B) = double_divide(double_divide(B,A),identity) ).

cnf(inverse,axiom,
    inverse(A) = double_divide(A,identity) ).

cnf(identity,axiom,
    identity = double_divide(A,inverse(A)) ).

cnf(prove_these_axioms_2,negated_conjecture,
    multiply(identity,a2) != a2 ).

cnf(refute_0_0,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_1,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_2,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( inverse(A) != double_divide(A,identity)
    | double_divide(A,identity) = inverse(A) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(double_divide(A,identity)))]]) ).

cnf(refute_0_4,plain,
    double_divide(A,identity) = inverse(A),
    inference(resolve,[$cnf( $equal(inverse(A),double_divide(A,identity)) )],[inverse,refute_0_3]) ).

cnf(refute_0_5,plain,
    double_divide(double_divide(B,A),identity) = inverse(double_divide(B,A)),
    inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,A)))]]) ).

cnf(refute_0_6,plain,
    ( multiply(A,B) != double_divide(double_divide(B,A),identity)
    | double_divide(double_divide(B,A),identity) != inverse(double_divide(B,A))
    | multiply(A,B) = inverse(double_divide(B,A)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),inverse(double_divide(B,A))) ),[0],$fot(double_divide(double_divide(B,A),identity))]]) ).

cnf(refute_0_7,plain,
    ( multiply(A,B) != double_divide(double_divide(B,A),identity)
    | multiply(A,B) = inverse(double_divide(B,A)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(B,A),identity),inverse(double_divide(B,A))) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    multiply(A,B) = inverse(double_divide(B,A)),
    inference(resolve,[$cnf( $equal(multiply(A,B),double_divide(double_divide(B,A),identity)) )],[multiply,refute_0_7]) ).

cnf(refute_0_9,plain,
    multiply(identity,X_3) = inverse(double_divide(X_3,identity)),
    inference(subst,[],[refute_0_8:[bind(A,$fot(identity)),bind(B,$fot(X_3))]]) ).

cnf(refute_0_10,plain,
    inverse(X_3) = double_divide(X_3,identity),
    inference(subst,[],[inverse:[bind(A,$fot(X_3))]]) ).

cnf(refute_0_11,plain,
    ( inverse(X_3) != double_divide(X_3,identity)
    | double_divide(X_3,identity) = inverse(X_3) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_3))),bind(Y,$fot(double_divide(X_3,identity)))]]) ).

cnf(refute_0_12,plain,
    double_divide(X_3,identity) = inverse(X_3),
    inference(resolve,[$cnf( $equal(inverse(X_3),double_divide(X_3,identity)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
    | double_divide(X_3,identity) != inverse(X_3)
    | multiply(identity,X_3) = inverse(inverse(X_3)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) ),[1,0],$fot(inverse(X_3))]]) ).

cnf(refute_0_14,plain,
    ( multiply(identity,X_3) != inverse(double_divide(X_3,identity))
    | multiply(identity,X_3) = inverse(inverse(X_3)) ),
    inference(resolve,[$cnf( $equal(double_divide(X_3,identity),inverse(X_3)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    multiply(identity,X_3) = inverse(inverse(X_3)),
    inference(resolve,[$cnf( $equal(multiply(identity,X_3),inverse(double_divide(X_3,identity))) )],[refute_0_9,refute_0_14]) ).

cnf(refute_0_16,plain,
    multiply(identity,a2) = inverse(inverse(a2)),
    inference(subst,[],[refute_0_15:[bind(X_3,$fot(a2))]]) ).

cnf(refute_0_17,plain,
    ( multiply(identity,a2) != inverse(inverse(a2))
    | inverse(inverse(a2)) != a2
    | multiply(identity,a2) = a2 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(identity,a2),a2) ),[0],$fot(inverse(inverse(a2)))]]) ).

cnf(refute_0_18,plain,
    ( inverse(inverse(a2)) != a2
    | multiply(identity,a2) = a2 ),
    inference(resolve,[$cnf( $equal(multiply(identity,a2),inverse(inverse(a2))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    inverse(inverse(a2)) != a2,
    inference(resolve,[$cnf( $equal(multiply(identity,a2),a2) )],[refute_0_18,prove_these_axioms_2]) ).

cnf(refute_0_20,plain,
    double_divide(double_divide(B,double_divide(C,A)),identity) = inverse(double_divide(B,double_divide(C,A))),
    inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(B,double_divide(C,A))))]]) ).

cnf(refute_0_21,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).

cnf(refute_0_22,plain,
    ( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,1],$fot(inverse(double_divide(B,double_divide(C,A))))]]) ).

cnf(refute_0_23,plain,
    ( double_divide(double_divide(B,double_divide(C,A)),identity) != inverse(double_divide(B,double_divide(C,A)))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(B,double_divide(C,A)),identity),inverse(double_divide(B,double_divide(C,A)))) )],[refute_0_20,refute_0_23]) ).

cnf(refute_0_25,plain,
    double_divide(B,identity) = inverse(B),
    inference(subst,[],[refute_0_4:[bind(A,$fot(B))]]) ).

cnf(refute_0_26,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_27,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_28,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_26,refute_0_27]) ).

cnf(refute_0_29,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_25,refute_0_28]) ).

cnf(refute_0_30,plain,
    double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,double_divide(B,identity))),
    introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(A,double_divide(B,identity))))]]) ).

cnf(refute_0_31,plain,
    ( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
    | double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,double_divide(B,identity)))
    | double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) ),[1,1],$fot(double_divide(A,inverse(B)))]]) ).

cnf(refute_0_32,plain,
    ( double_divide(A,double_divide(B,identity)) != double_divide(A,inverse(B))
    | double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))) ),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,double_divide(B,identity)))) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(A,inverse(B))),
    inference(resolve,[$cnf( $equal(double_divide(A,double_divide(B,identity)),double_divide(A,inverse(B))) )],[refute_0_29,refute_0_32]) ).

cnf(refute_0_34,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))]]) ).

cnf(refute_0_35,plain,
    ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))
    | double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
    | double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) ),[1,0],$fot(double_divide(identity,double_divide(A,inverse(B))))]]) ).

cnf(refute_0_36,plain,
    ( double_divide(identity,double_divide(A,double_divide(B,identity))) != double_divide(identity,double_divide(A,inverse(B)))
    | double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(A,inverse(B)))) )],[refute_0_33,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_39,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
    | double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Y,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)))),bind(Z,$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))))]]) ).

cnf(refute_0_41,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
    | double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity))) )],[refute_0_37,refute_0_40]) ).

cnf(refute_0_42,plain,
    double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_24,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
    | double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).

cnf(refute_0_44,plain,
    ( double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) != C
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = C,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)),C) )],[single_axiom,refute_0_44]) ).

cnf(refute_0_46,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_47,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_46]) ).

cnf(refute_0_48,plain,
    inverse(double_divide(B,double_divide(C,A))) = multiply(double_divide(C,A),B),
    inference(subst,[],[refute_0_47:[bind(A,$fot(double_divide(C,A)))]]) ).

cnf(refute_0_49,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))))]]) ).

cnf(refute_0_50,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))
    | inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) ),[1,1],$fot(multiply(double_divide(C,A),B))]]) ).

cnf(refute_0_51,plain,
    ( inverse(double_divide(B,double_divide(C,A))) != multiply(double_divide(C,A),B)
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A))))) )],[refute_0_49,refute_0_50]) ).

cnf(refute_0_52,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) = double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)),
    inference(resolve,[$cnf( $equal(inverse(double_divide(B,double_divide(C,A))),multiply(double_divide(C,A),B)) )],[refute_0_48,refute_0_51]) ).

cnf(refute_0_53,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) ),[0],$fot(double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)))]]) ).

cnf(refute_0_54,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))) != C
    | double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B))) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(B))),multiply(double_divide(C,A),B)) = C,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(B))),inverse(double_divide(B,double_divide(C,A)))),C) )],[refute_0_45,refute_0_54]) ).

cnf(refute_0_56,plain,
    double_divide(double_divide(identity,double_divide(A,inverse(identity))),multiply(double_divide(C,A),identity)) = C,
    inference(subst,[],[refute_0_55:[bind(B,$fot(identity))]]) ).

cnf(refute_0_57,plain,
    identity = double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2))),
    inference(subst,[],[identity:[bind(A,$fot(double_divide(X_3,X_2)))]]) ).

cnf(refute_0_58,plain,
    multiply(X_2,X_3) = inverse(double_divide(X_3,X_2)),
    inference(subst,[],[refute_0_8:[bind(A,$fot(X_2)),bind(B,$fot(X_3))]]) ).

cnf(refute_0_59,plain,
    ( multiply(X_2,X_3) != inverse(double_divide(X_3,X_2))
    | inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,X_3))),bind(Y,$fot(inverse(double_divide(X_3,X_2))))]]) ).

cnf(refute_0_60,plain,
    inverse(double_divide(X_3,X_2)) = multiply(X_2,X_3),
    inference(resolve,[$cnf( $equal(multiply(X_2,X_3),inverse(double_divide(X_3,X_2))) )],[refute_0_58,refute_0_59]) ).

cnf(refute_0_61,plain,
    ( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
    | inverse(double_divide(X_3,X_2)) != multiply(X_2,X_3)
    | identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) ),[1,1],$fot(multiply(X_2,X_3))]]) ).

cnf(refute_0_62,plain,
    ( identity != double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))
    | identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)) ),
    inference(resolve,[$cnf( $equal(inverse(double_divide(X_3,X_2)),multiply(X_2,X_3)) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    identity = double_divide(double_divide(X_3,X_2),multiply(X_2,X_3)),
    inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(X_3,X_2),inverse(double_divide(X_3,X_2)))) )],[refute_0_57,refute_0_62]) ).

cnf(refute_0_64,plain,
    identity = double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),
    inference(subst,[],[refute_0_63:[bind(X_2,$fot(double_divide(inverse(identity),inverse(identity)))),bind(X_3,$fot(identity))]]) ).

cnf(refute_0_65,plain,
    double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) = inverse(identity),
    inference(subst,[],[refute_0_55:[bind(A,$fot(inverse(identity))),bind(B,$fot(identity)),bind(C,$fot(inverse(identity)))]]) ).

cnf(refute_0_66,plain,
    ( double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) != inverse(identity)
    | identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
    | identity = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) ),[1],$fot(inverse(identity))]]) ).

cnf(refute_0_67,plain,
    ( identity != double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))
    | identity = inverse(identity) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),inverse(identity)) )],[refute_0_65,refute_0_66]) ).

cnf(refute_0_68,plain,
    identity = inverse(identity),
    inference(resolve,[$cnf( $equal(identity,double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity))) )],[refute_0_64,refute_0_67]) ).

cnf(refute_0_69,plain,
    ( identity != inverse(identity)
    | inverse(identity) = identity ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(inverse(identity)))]]) ).

cnf(refute_0_70,plain,
    inverse(identity) = identity,
    inference(resolve,[$cnf( $equal(identity,inverse(identity)) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(identity))),multiply(double_divide(C,A),identity)) != C
    | inverse(identity) != identity
    | double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = C ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(identity))),multiply(double_divide(C,A),identity)),C) ),[0,0,1,1],$fot(identity)]]) ).

cnf(refute_0_72,plain,
    ( double_divide(double_divide(identity,double_divide(A,inverse(identity))),multiply(double_divide(C,A),identity)) != C
    | double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = C ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = C,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,inverse(identity))),multiply(double_divide(C,A),identity)),C) )],[refute_0_56,refute_0_72]) ).

cnf(refute_0_74,plain,
    double_divide(identity,double_divide(A,identity)) = double_divide(identity,double_divide(A,identity)),
    introduced(tautology,[refl,[$fot(double_divide(identity,double_divide(A,identity)))]]) ).

cnf(refute_0_75,plain,
    ( double_divide(A,identity) != inverse(A)
    | double_divide(identity,double_divide(A,identity)) != double_divide(identity,double_divide(A,identity))
    | double_divide(identity,double_divide(A,identity)) = double_divide(identity,inverse(A)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(A,identity))) ),[1,1],$fot(inverse(A))]]) ).

cnf(refute_0_76,plain,
    ( double_divide(A,identity) != inverse(A)
    | double_divide(identity,double_divide(A,identity)) = double_divide(identity,inverse(A)) ),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(A,identity))) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    double_divide(identity,double_divide(A,identity)) = double_divide(identity,inverse(A)),
    inference(resolve,[$cnf( $equal(double_divide(A,identity),inverse(A)) )],[refute_0_4,refute_0_76]) ).

cnf(refute_0_78,plain,
    double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)))]]) ).

cnf(refute_0_79,plain,
    ( double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) != double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity))
    | double_divide(identity,double_divide(A,identity)) != double_divide(identity,inverse(A))
    | double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity))) ),[1,0],$fot(double_divide(identity,inverse(A)))]]) ).

cnf(refute_0_80,plain,
    ( double_divide(identity,double_divide(A,identity)) != double_divide(identity,inverse(A))
    | double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity))) )],[refute_0_78,refute_0_79]) ).

cnf(refute_0_81,plain,
    double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) = double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(A,identity)),double_divide(identity,inverse(A))) )],[refute_0_77,refute_0_80]) ).

cnf(refute_0_82,plain,
    ( double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) != C
    | double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) != double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity))
    | double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)) = C ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),C) ),[0],$fot(double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)))]]) ).

cnf(refute_0_83,plain,
    ( double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)) != C
    | double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)) = C ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    double_divide(double_divide(identity,inverse(A)),multiply(double_divide(C,A),identity)) = C,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(A,identity)),multiply(double_divide(C,A),identity)),C) )],[refute_0_73,refute_0_83]) ).

cnf(refute_0_85,plain,
    double_divide(double_divide(identity,inverse(inverse(inverse(X_17)))),multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = X_21,
    inference(subst,[],[refute_0_84:[bind(A,$fot(inverse(inverse(X_17)))),bind(C,$fot(X_21))]]) ).

cnf(refute_0_86,plain,
    double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) = X_12,
    inference(subst,[],[refute_0_55:[bind(A,$fot(X_11)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).

cnf(refute_0_87,plain,
    identity = double_divide(X_11,inverse(X_11)),
    inference(subst,[],[identity:[bind(A,$fot(X_11))]]) ).

cnf(refute_0_88,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_89,plain,
    double_divide(X_11,inverse(X_11)) = identity,
    inference(resolve,[$cnf( $equal(identity,double_divide(X_11,inverse(X_11))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( double_divide(X_11,inverse(X_11)) != identity
    | double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) != X_12
    | double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)),X_12) ),[0,0,1],$fot(identity)]]) ).

cnf(refute_0_91,plain,
    ( double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)) != X_12
    | double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
    inference(resolve,[$cnf( $equal(double_divide(X_11,inverse(X_11)),identity) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = X_12,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(X_11,inverse(X_11))),multiply(double_divide(X_12,X_11),X_11)),X_12) )],[refute_0_86,refute_0_91]) ).

cnf(refute_0_93,plain,
    double_divide(identity,identity) = inverse(identity),
    inference(subst,[],[refute_0_4:[bind(A,$fot(identity))]]) ).

cnf(refute_0_94,plain,
    ( double_divide(identity,identity) != inverse(identity)
    | inverse(identity) != identity
    | double_divide(identity,identity) = identity ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(identity,identity))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).

cnf(refute_0_95,plain,
    ( inverse(identity) != identity
    | double_divide(identity,identity) = identity ),
    inference(resolve,[$cnf( $equal(double_divide(identity,identity),inverse(identity)) )],[refute_0_93,refute_0_94]) ).

cnf(refute_0_96,plain,
    double_divide(identity,identity) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_95]) ).

cnf(refute_0_97,plain,
    double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)))]]) ).

cnf(refute_0_98,plain,
    ( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))
    | double_divide(identity,identity) != identity
    | double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_99,plain,
    ( double_divide(identity,identity) != identity
    | double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11))) )],[refute_0_97,refute_0_98]) ).

cnf(refute_0_100,plain,
    double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) = double_divide(identity,multiply(double_divide(X_12,X_11),X_11)),
    inference(resolve,[$cnf( $equal(double_divide(identity,identity),identity) )],[refute_0_96,refute_0_99]) ).

cnf(refute_0_101,plain,
    ( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != X_12
    | double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != double_divide(identity,multiply(double_divide(X_12,X_11),X_11))
    | double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),X_12) ),[0],$fot(double_divide(identity,multiply(double_divide(X_12,X_11),X_11)))]]) ).

cnf(refute_0_102,plain,
    ( double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)) != X_12
    | double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12 ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),double_divide(identity,multiply(double_divide(X_12,X_11),X_11))) )],[refute_0_100,refute_0_101]) ).

cnf(refute_0_103,plain,
    double_divide(identity,multiply(double_divide(X_12,X_11),X_11)) = X_12,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,identity),multiply(double_divide(X_12,X_11),X_11)),X_12) )],[refute_0_92,refute_0_102]) ).

cnf(refute_0_104,plain,
    double_divide(identity,multiply(double_divide(X_17,inverse(X_17)),inverse(X_17))) = X_17,
    inference(subst,[],[refute_0_103:[bind(X_11,$fot(inverse(X_17))),bind(X_12,$fot(X_17))]]) ).

cnf(refute_0_105,plain,
    identity = double_divide(X_17,inverse(X_17)),
    inference(subst,[],[identity:[bind(A,$fot(X_17))]]) ).

cnf(refute_0_106,plain,
    ( identity != double_divide(X_17,inverse(X_17))
    | double_divide(X_17,inverse(X_17)) = identity ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_17,inverse(X_17))))]]) ).

cnf(refute_0_107,plain,
    double_divide(X_17,inverse(X_17)) = identity,
    inference(resolve,[$cnf( $equal(identity,double_divide(X_17,inverse(X_17))) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    ( double_divide(X_17,inverse(X_17)) != identity
    | double_divide(identity,multiply(double_divide(X_17,inverse(X_17)),inverse(X_17))) != X_17
    | double_divide(identity,multiply(identity,inverse(X_17))) = X_17 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_17,inverse(X_17)),inverse(X_17))),X_17) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_109,plain,
    ( double_divide(identity,multiply(double_divide(X_17,inverse(X_17)),inverse(X_17))) != X_17
    | double_divide(identity,multiply(identity,inverse(X_17))) = X_17 ),
    inference(resolve,[$cnf( $equal(double_divide(X_17,inverse(X_17)),identity) )],[refute_0_107,refute_0_108]) ).

cnf(refute_0_110,plain,
    double_divide(identity,multiply(identity,inverse(X_17))) = X_17,
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_17,inverse(X_17)),inverse(X_17))),X_17) )],[refute_0_104,refute_0_109]) ).

cnf(refute_0_111,plain,
    multiply(identity,inverse(X_17)) = inverse(inverse(inverse(X_17))),
    inference(subst,[],[refute_0_15:[bind(X_3,$fot(inverse(X_17)))]]) ).

cnf(refute_0_112,plain,
    double_divide(identity,multiply(identity,inverse(X_17))) = double_divide(identity,multiply(identity,inverse(X_17))),
    introduced(tautology,[refl,[$fot(double_divide(identity,multiply(identity,inverse(X_17))))]]) ).

cnf(refute_0_113,plain,
    ( multiply(identity,inverse(X_17)) != inverse(inverse(inverse(X_17)))
    | double_divide(identity,multiply(identity,inverse(X_17))) != double_divide(identity,multiply(identity,inverse(X_17)))
    | double_divide(identity,multiply(identity,inverse(X_17))) = double_divide(identity,inverse(inverse(inverse(X_17)))) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(identity,inverse(X_17))),double_divide(identity,multiply(identity,inverse(X_17)))) ),[1,1],$fot(inverse(inverse(inverse(X_17))))]]) ).

cnf(refute_0_114,plain,
    ( multiply(identity,inverse(X_17)) != inverse(inverse(inverse(X_17)))
    | double_divide(identity,multiply(identity,inverse(X_17))) = double_divide(identity,inverse(inverse(inverse(X_17)))) ),
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(identity,inverse(X_17))),double_divide(identity,multiply(identity,inverse(X_17)))) )],[refute_0_112,refute_0_113]) ).

cnf(refute_0_115,plain,
    double_divide(identity,multiply(identity,inverse(X_17))) = double_divide(identity,inverse(inverse(inverse(X_17)))),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(X_17)),inverse(inverse(inverse(X_17)))) )],[refute_0_111,refute_0_114]) ).

cnf(refute_0_116,plain,
    ( double_divide(identity,multiply(identity,inverse(X_17))) != X_17
    | double_divide(identity,multiply(identity,inverse(X_17))) != double_divide(identity,inverse(inverse(inverse(X_17))))
    | double_divide(identity,inverse(inverse(inverse(X_17)))) = X_17 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(identity,inverse(X_17))),X_17) ),[0],$fot(double_divide(identity,inverse(inverse(inverse(X_17)))))]]) ).

cnf(refute_0_117,plain,
    ( double_divide(identity,multiply(identity,inverse(X_17))) != X_17
    | double_divide(identity,inverse(inverse(inverse(X_17)))) = X_17 ),
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(identity,inverse(X_17))),double_divide(identity,inverse(inverse(inverse(X_17))))) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    double_divide(identity,inverse(inverse(inverse(X_17)))) = X_17,
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(identity,inverse(X_17))),X_17) )],[refute_0_110,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( double_divide(double_divide(identity,inverse(inverse(inverse(X_17)))),multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != X_21
    | double_divide(identity,inverse(inverse(inverse(X_17)))) != X_17
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = X_21 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(inverse(X_17)))),multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),X_21) ),[0,0],$fot(X_17)]]) ).

cnf(refute_0_120,plain,
    ( double_divide(double_divide(identity,inverse(inverse(inverse(X_17)))),multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != X_21
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = X_21 ),
    inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_17)))),X_17) )],[refute_0_118,refute_0_119]) ).

cnf(refute_0_121,plain,
    double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = X_21,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(inverse(X_17)))),multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),X_21) )],[refute_0_85,refute_0_120]) ).

cnf(refute_0_122,plain,
    inverse(double_divide(X_21,inverse(inverse(X_17)))) = multiply(inverse(inverse(X_17)),X_21),
    inference(subst,[],[refute_0_47:[bind(A,$fot(inverse(inverse(X_17)))),bind(B,$fot(X_21))]]) ).

cnf(refute_0_123,plain,
    inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) = inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))),
    introduced(tautology,[refl,[$fot(inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))))]]) ).

cnf(refute_0_124,plain,
    ( inverse(double_divide(X_21,inverse(inverse(X_17)))) != multiply(inverse(inverse(X_17)),X_21)
    | inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) != inverse(inverse(double_divide(X_21,inverse(inverse(X_17)))))
    | inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) = inverse(multiply(inverse(inverse(X_17)),X_21)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))),inverse(inverse(double_divide(X_21,inverse(inverse(X_17)))))) ),[1,0],$fot(multiply(inverse(inverse(X_17)),X_21))]]) ).

cnf(refute_0_125,plain,
    ( inverse(double_divide(X_21,inverse(inverse(X_17)))) != multiply(inverse(inverse(X_17)),X_21)
    | inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) = inverse(multiply(inverse(inverse(X_17)),X_21)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))),inverse(inverse(double_divide(X_21,inverse(inverse(X_17)))))) )],[refute_0_123,refute_0_124]) ).

cnf(refute_0_126,plain,
    inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) = inverse(multiply(inverse(inverse(X_17)),X_21)),
    inference(resolve,[$cnf( $equal(inverse(double_divide(X_21,inverse(inverse(X_17)))),multiply(inverse(inverse(X_17)),X_21)) )],[refute_0_122,refute_0_125]) ).

cnf(refute_0_127,plain,
    multiply(A,identity) = inverse(double_divide(identity,A)),
    inference(subst,[],[refute_0_8:[bind(B,$fot(identity))]]) ).

cnf(refute_0_128,plain,
    double_divide(identity,multiply(double_divide(X_17,identity),identity)) = X_17,
    inference(subst,[],[refute_0_103:[bind(X_11,$fot(identity)),bind(X_12,$fot(X_17))]]) ).

cnf(refute_0_129,plain,
    inverse(X_17) = double_divide(X_17,identity),
    inference(subst,[],[inverse:[bind(A,$fot(X_17))]]) ).

cnf(refute_0_130,plain,
    ( inverse(X_17) != double_divide(X_17,identity)
    | double_divide(X_17,identity) = inverse(X_17) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_17))),bind(Y,$fot(double_divide(X_17,identity)))]]) ).

cnf(refute_0_131,plain,
    double_divide(X_17,identity) = inverse(X_17),
    inference(resolve,[$cnf( $equal(inverse(X_17),double_divide(X_17,identity)) )],[refute_0_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    ( double_divide(X_17,identity) != inverse(X_17)
    | double_divide(identity,multiply(double_divide(X_17,identity),identity)) != X_17
    | double_divide(identity,multiply(inverse(X_17),identity)) = X_17 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_17,identity),identity)),X_17) ),[0,1,0],$fot(inverse(X_17))]]) ).

cnf(refute_0_133,plain,
    ( double_divide(identity,multiply(double_divide(X_17,identity),identity)) != X_17
    | double_divide(identity,multiply(inverse(X_17),identity)) = X_17 ),
    inference(resolve,[$cnf( $equal(double_divide(X_17,identity),inverse(X_17)) )],[refute_0_131,refute_0_132]) ).

cnf(refute_0_134,plain,
    double_divide(identity,multiply(inverse(X_17),identity)) = X_17,
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(double_divide(X_17,identity),identity)),X_17) )],[refute_0_128,refute_0_133]) ).

cnf(refute_0_135,plain,
    double_divide(identity,multiply(inverse(inverse(X_22)),identity)) = inverse(X_22),
    inference(subst,[],[refute_0_134:[bind(X_17,$fot(inverse(X_22)))]]) ).

cnf(refute_0_136,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(double_divide(X_21,inverse(X_21)),identity)) = X_21,
    inference(subst,[],[refute_0_84:[bind(A,$fot(inverse(X_21))),bind(C,$fot(X_21))]]) ).

cnf(refute_0_137,plain,
    identity = double_divide(X_21,inverse(X_21)),
    inference(subst,[],[identity:[bind(A,$fot(X_21))]]) ).

cnf(refute_0_138,plain,
    ( identity != double_divide(X_21,inverse(X_21))
    | double_divide(X_21,inverse(X_21)) = identity ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(identity)),bind(Y,$fot(double_divide(X_21,inverse(X_21))))]]) ).

cnf(refute_0_139,plain,
    double_divide(X_21,inverse(X_21)) = identity,
    inference(resolve,[$cnf( $equal(identity,double_divide(X_21,inverse(X_21))) )],[refute_0_137,refute_0_138]) ).

cnf(refute_0_140,plain,
    ( double_divide(X_21,inverse(X_21)) != identity
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(double_divide(X_21,inverse(X_21)),identity)) != X_21
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = X_21 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(double_divide(X_21,inverse(X_21)),identity)),X_21) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_141,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(double_divide(X_21,inverse(X_21)),identity)) != X_21
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = X_21 ),
    inference(resolve,[$cnf( $equal(double_divide(X_21,inverse(X_21)),identity) )],[refute_0_139,refute_0_140]) ).

cnf(refute_0_142,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = X_21,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(double_divide(X_21,inverse(X_21)),identity)),X_21) )],[refute_0_136,refute_0_141]) ).

cnf(refute_0_143,plain,
    inverse(double_divide(identity,inverse(inverse(X_21)))) = multiply(inverse(inverse(X_21)),identity),
    inference(subst,[],[refute_0_47:[bind(A,$fot(inverse(inverse(X_21)))),bind(B,$fot(identity))]]) ).

cnf(refute_0_144,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),identity) = inverse(double_divide(identity,inverse(inverse(X_21)))),
    inference(subst,[],[refute_0_4:[bind(A,$fot(double_divide(identity,inverse(inverse(X_21)))))]]) ).

cnf(refute_0_145,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),identity) != inverse(double_divide(identity,inverse(inverse(X_21))))
    | inverse(double_divide(identity,inverse(inverse(X_21)))) != multiply(inverse(inverse(X_21)),identity)
    | double_divide(double_divide(identity,inverse(inverse(X_21))),identity) = multiply(inverse(inverse(X_21)),identity) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(inverse(X_21))),identity))),bind(Y,$fot(inverse(double_divide(identity,inverse(inverse(X_21)))))),bind(Z,$fot(multiply(inverse(inverse(X_21)),identity)))]]) ).

cnf(refute_0_146,plain,
    ( inverse(double_divide(identity,inverse(inverse(X_21)))) != multiply(inverse(inverse(X_21)),identity)
    | double_divide(double_divide(identity,inverse(inverse(X_21))),identity) = multiply(inverse(inverse(X_21)),identity) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),identity),inverse(double_divide(identity,inverse(inverse(X_21))))) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),identity) = multiply(inverse(inverse(X_21)),identity),
    inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(inverse(X_21)))),multiply(inverse(inverse(X_21)),identity)) )],[refute_0_143,refute_0_146]) ).

cnf(refute_0_148,plain,
    inverse(inverse(identity)) = inverse(inverse(identity)),
    introduced(tautology,[refl,[$fot(inverse(inverse(identity)))]]) ).

cnf(refute_0_149,plain,
    ( inverse(identity) != identity
    | inverse(inverse(identity)) != inverse(inverse(identity))
    | inverse(inverse(identity)) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_150,plain,
    ( inverse(identity) != identity
    | inverse(inverse(identity)) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(inverse(identity))) )],[refute_0_148,refute_0_149]) ).

cnf(refute_0_151,plain,
    inverse(inverse(identity)) = inverse(identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_150]) ).

cnf(refute_0_152,plain,
    ( inverse(identity) != identity
    | inverse(inverse(identity)) != inverse(identity)
    | inverse(inverse(identity)) = identity ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(inverse(inverse(identity)))),bind(Y,$fot(inverse(identity))),bind(Z,$fot(identity))]]) ).

cnf(refute_0_153,plain,
    ( inverse(identity) != identity
    | inverse(inverse(identity)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(identity)),inverse(identity)) )],[refute_0_151,refute_0_152]) ).

cnf(refute_0_154,plain,
    inverse(inverse(identity)) = identity,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_153]) ).

cnf(refute_0_155,plain,
    multiply(identity,identity) = inverse(inverse(identity)),
    inference(subst,[],[refute_0_15:[bind(X_3,$fot(identity))]]) ).

cnf(refute_0_156,plain,
    ( multiply(identity,identity) != inverse(inverse(identity))
    | inverse(inverse(identity)) != identity
    | multiply(identity,identity) = identity ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(identity,identity))),bind(Y,$fot(inverse(inverse(identity)))),bind(Z,$fot(identity))]]) ).

cnf(refute_0_157,plain,
    ( inverse(inverse(identity)) != identity
    | multiply(identity,identity) = identity ),
    inference(resolve,[$cnf( $equal(multiply(identity,identity),inverse(inverse(identity))) )],[refute_0_155,refute_0_156]) ).

cnf(refute_0_158,plain,
    multiply(identity,identity) = identity,
    inference(resolve,[$cnf( $equal(inverse(inverse(identity)),identity) )],[refute_0_154,refute_0_157]) ).

cnf(refute_0_159,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)))]]) ).

cnf(refute_0_160,plain,
    ( multiply(identity,identity) != identity
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) != double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity))
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = double_divide(double_divide(identity,inverse(inverse(X_21))),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_161,plain,
    ( multiply(identity,identity) != identity
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = double_divide(double_divide(identity,inverse(inverse(X_21))),identity) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity))) )],[refute_0_159,refute_0_160]) ).

cnf(refute_0_162,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = double_divide(double_divide(identity,inverse(inverse(X_21))),identity),
    inference(resolve,[$cnf( $equal(multiply(identity,identity),identity) )],[refute_0_158,refute_0_161]) ).

cnf(refute_0_163,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) != double_divide(double_divide(identity,inverse(inverse(X_21))),identity)
    | double_divide(double_divide(identity,inverse(inverse(X_21))),identity) != multiply(inverse(inverse(X_21)),identity)
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = multiply(inverse(inverse(X_21)),identity) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)))),bind(Y,$fot(double_divide(double_divide(identity,inverse(inverse(X_21))),identity))),bind(Z,$fot(multiply(inverse(inverse(X_21)),identity)))]]) ).

cnf(refute_0_164,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),identity) != multiply(inverse(inverse(X_21)),identity)
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = multiply(inverse(inverse(X_21)),identity) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),double_divide(double_divide(identity,inverse(inverse(X_21))),identity)) )],[refute_0_162,refute_0_163]) ).

cnf(refute_0_165,plain,
    double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) = multiply(inverse(inverse(X_21)),identity),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),identity),multiply(inverse(inverse(X_21)),identity)) )],[refute_0_147,refute_0_164]) ).

cnf(refute_0_166,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) != X_21
    | double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) != multiply(inverse(inverse(X_21)),identity)
    | multiply(inverse(inverse(X_21)),identity) = X_21 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),X_21) ),[0],$fot(multiply(inverse(inverse(X_21)),identity))]]) ).

cnf(refute_0_167,plain,
    ( double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)) != X_21
    | multiply(inverse(inverse(X_21)),identity) = X_21 ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),multiply(inverse(inverse(X_21)),identity)) )],[refute_0_165,refute_0_166]) ).

cnf(refute_0_168,plain,
    multiply(inverse(inverse(X_21)),identity) = X_21,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,inverse(inverse(X_21))),multiply(identity,identity)),X_21) )],[refute_0_142,refute_0_167]) ).

cnf(refute_0_169,plain,
    multiply(inverse(inverse(X_22)),identity) = X_22,
    inference(subst,[],[refute_0_168:[bind(X_21,$fot(X_22))]]) ).

cnf(refute_0_170,plain,
    ( multiply(inverse(inverse(X_22)),identity) != X_22
    | double_divide(identity,multiply(inverse(inverse(X_22)),identity)) != inverse(X_22)
    | double_divide(identity,X_22) = inverse(X_22) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,multiply(inverse(inverse(X_22)),identity)),inverse(X_22)) ),[0,1],$fot(X_22)]]) ).

cnf(refute_0_171,plain,
    ( double_divide(identity,multiply(inverse(inverse(X_22)),identity)) != inverse(X_22)
    | double_divide(identity,X_22) = inverse(X_22) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),identity),X_22) )],[refute_0_169,refute_0_170]) ).

cnf(refute_0_172,plain,
    double_divide(identity,X_22) = inverse(X_22),
    inference(resolve,[$cnf( $equal(double_divide(identity,multiply(inverse(inverse(X_22)),identity)),inverse(X_22)) )],[refute_0_135,refute_0_171]) ).

cnf(refute_0_173,plain,
    double_divide(identity,A) = inverse(A),
    inference(subst,[],[refute_0_172:[bind(X_22,$fot(A))]]) ).

cnf(refute_0_174,plain,
    ( multiply(A,identity) != inverse(double_divide(identity,A))
    | double_divide(identity,A) != inverse(A)
    | multiply(A,identity) = inverse(inverse(A)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(A,identity),inverse(double_divide(identity,A))) ),[1,0],$fot(inverse(A))]]) ).

cnf(refute_0_175,plain,
    ( multiply(A,identity) != inverse(double_divide(identity,A))
    | multiply(A,identity) = inverse(inverse(A)) ),
    inference(resolve,[$cnf( $equal(double_divide(identity,A),inverse(A)) )],[refute_0_173,refute_0_174]) ).

cnf(refute_0_176,plain,
    multiply(A,identity) = inverse(inverse(A)),
    inference(resolve,[$cnf( $equal(multiply(A,identity),inverse(double_divide(identity,A))) )],[refute_0_127,refute_0_175]) ).

cnf(refute_0_177,plain,
    multiply(double_divide(X_21,inverse(inverse(X_17))),identity) = inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))),
    inference(subst,[],[refute_0_176:[bind(A,$fot(double_divide(X_21,inverse(inverse(X_17)))))]]) ).

cnf(refute_0_178,plain,
    ( multiply(double_divide(X_21,inverse(inverse(X_17))),identity) != inverse(inverse(double_divide(X_21,inverse(inverse(X_17)))))
    | inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) != inverse(multiply(inverse(inverse(X_17)),X_21))
    | multiply(double_divide(X_21,inverse(inverse(X_17))),identity) = inverse(multiply(inverse(inverse(X_17)),X_21)) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(multiply(double_divide(X_21,inverse(inverse(X_17))),identity))),bind(Y,$fot(inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))))),bind(Z,$fot(inverse(multiply(inverse(inverse(X_17)),X_21))))]]) ).

cnf(refute_0_179,plain,
    ( inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))) != inverse(multiply(inverse(inverse(X_17)),X_21))
    | multiply(double_divide(X_21,inverse(inverse(X_17))),identity) = inverse(multiply(inverse(inverse(X_17)),X_21)) ),
    inference(resolve,[$cnf( $equal(multiply(double_divide(X_21,inverse(inverse(X_17))),identity),inverse(inverse(double_divide(X_21,inverse(inverse(X_17)))))) )],[refute_0_177,refute_0_178]) ).

cnf(refute_0_180,plain,
    multiply(double_divide(X_21,inverse(inverse(X_17))),identity) = inverse(multiply(inverse(inverse(X_17)),X_21)),
    inference(resolve,[$cnf( $equal(inverse(inverse(double_divide(X_21,inverse(inverse(X_17))))),inverse(multiply(inverse(inverse(X_17)),X_21))) )],[refute_0_126,refute_0_179]) ).

cnf(refute_0_181,plain,
    double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),
    introduced(tautology,[refl,[$fot(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)))]]) ).

cnf(refute_0_182,plain,
    ( multiply(double_divide(X_21,inverse(inverse(X_17))),identity) != inverse(multiply(inverse(inverse(X_17)),X_21))
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity))
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity))) ),[1,1],$fot(inverse(multiply(inverse(inverse(X_17)),X_21)))]]) ).

cnf(refute_0_183,plain,
    ( multiply(double_divide(X_21,inverse(inverse(X_17))),identity) != inverse(multiply(inverse(inverse(X_17)),X_21))
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))) ),
    inference(resolve,[$cnf( $equal(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity))) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) = double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))),
    inference(resolve,[$cnf( $equal(multiply(double_divide(X_21,inverse(inverse(X_17))),identity),inverse(multiply(inverse(inverse(X_17)),X_21))) )],[refute_0_180,refute_0_183]) ).

cnf(refute_0_185,plain,
    ( double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != X_21
    | double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21)))
    | double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))) = X_21 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),X_21) ),[0],$fot(double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))))]]) ).

cnf(refute_0_186,plain,
    ( double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)) != X_21
    | double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))) = X_21 ),
    inference(resolve,[$cnf( $equal(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21)))) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    double_divide(X_17,inverse(multiply(inverse(inverse(X_17)),X_21))) = X_21,
    inference(resolve,[$cnf( $equal(double_divide(X_17,multiply(double_divide(X_21,inverse(inverse(X_17))),identity)),X_21) )],[refute_0_121,refute_0_186]) ).

cnf(refute_0_188,plain,
    double_divide(inverse(X_39),inverse(multiply(inverse(inverse(inverse(X_39))),X_39))) = X_39,
    inference(subst,[],[refute_0_187:[bind(X_17,$fot(inverse(X_39))),bind(X_21,$fot(X_39))]]) ).

cnf(refute_0_189,plain,
    multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) = inverse(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25))),
    inference(subst,[],[refute_0_8:[bind(A,$fot(multiply(inverse(X_26),X_25))),bind(B,$fot(inverse(inverse(inverse(X_25)))))]]) ).

cnf(refute_0_190,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) = X_12,
    inference(subst,[],[refute_0_55:[bind(A,$fot(identity)),bind(B,$fot(X_11)),bind(C,$fot(X_12))]]) ).

cnf(refute_0_191,plain,
    inverse(X_12) = double_divide(X_12,identity),
    inference(subst,[],[inverse:[bind(A,$fot(X_12))]]) ).

cnf(refute_0_192,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_193,plain,
    double_divide(X_12,identity) = inverse(X_12),
    inference(resolve,[$cnf( $equal(inverse(X_12),double_divide(X_12,identity)) )],[refute_0_191,refute_0_192]) ).

cnf(refute_0_194,plain,
    ( double_divide(X_12,identity) != inverse(X_12)
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) != X_12
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)),X_12) ),[0,1,0],$fot(inverse(X_12))]]) ).

cnf(refute_0_195,plain,
    ( double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)) != X_12
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
    inference(resolve,[$cnf( $equal(double_divide(X_12,identity),inverse(X_12)) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(double_divide(X_12,identity),X_11)),X_12) )],[refute_0_190,refute_0_195]) ).

cnf(refute_0_197,plain,
    inverse(double_divide(identity,inverse(X_11))) = multiply(inverse(X_11),identity),
    inference(subst,[],[refute_0_47:[bind(A,$fot(inverse(X_11))),bind(B,$fot(identity))]]) ).

cnf(refute_0_198,plain,
    double_divide(identity,double_divide(identity,inverse(X_11))) = inverse(double_divide(identity,inverse(X_11))),
    inference(subst,[],[refute_0_172:[bind(X_22,$fot(double_divide(identity,inverse(X_11))))]]) ).

cnf(refute_0_199,plain,
    ( double_divide(identity,double_divide(identity,inverse(X_11))) != inverse(double_divide(identity,inverse(X_11)))
    | inverse(double_divide(identity,inverse(X_11))) != multiply(inverse(X_11),identity)
    | double_divide(identity,double_divide(identity,inverse(X_11))) = multiply(inverse(X_11),identity) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(identity,double_divide(identity,inverse(X_11))))),bind(Y,$fot(inverse(double_divide(identity,inverse(X_11))))),bind(Z,$fot(multiply(inverse(X_11),identity)))]]) ).

cnf(refute_0_200,plain,
    ( inverse(double_divide(identity,inverse(X_11))) != multiply(inverse(X_11),identity)
    | double_divide(identity,double_divide(identity,inverse(X_11))) = multiply(inverse(X_11),identity) ),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_11))),inverse(double_divide(identity,inverse(X_11)))) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    double_divide(identity,double_divide(identity,inverse(X_11))) = multiply(inverse(X_11),identity),
    inference(resolve,[$cnf( $equal(inverse(double_divide(identity,inverse(X_11))),multiply(inverse(X_11),identity)) )],[refute_0_197,refute_0_200]) ).

cnf(refute_0_202,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),
    introduced(tautology,[refl,[$fot(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)))]]) ).

cnf(refute_0_203,plain,
    ( double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) != double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11))
    | double_divide(identity,double_divide(identity,inverse(X_11))) != multiply(inverse(X_11),identity)
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11))) ),[1,0],$fot(multiply(inverse(X_11),identity))]]) ).

cnf(refute_0_204,plain,
    ( double_divide(identity,double_divide(identity,inverse(X_11))) != multiply(inverse(X_11),identity)
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) = double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),
    inference(resolve,[$cnf( $equal(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_11),identity)) )],[refute_0_201,refute_0_204]) ).

cnf(refute_0_206,plain,
    ( double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) != X_12
    | double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) != double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11))
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),X_12) ),[0],$fot(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)))]]) ).

cnf(refute_0_207,plain,
    ( double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)) != X_12
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = X_12 ),
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11))) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = X_12,
    inference(resolve,[$cnf( $equal(double_divide(double_divide(identity,double_divide(identity,inverse(X_11))),multiply(inverse(X_12),X_11)),X_12) )],[refute_0_196,refute_0_207]) ).

cnf(refute_0_209,plain,
    multiply(inverse(X_11),identity) = inverse(inverse(inverse(X_11))),
    inference(subst,[],[refute_0_176:[bind(A,$fot(inverse(X_11)))]]) ).

cnf(refute_0_210,plain,
    double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),
    introduced(tautology,[refl,[$fot(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)))]]) ).

cnf(refute_0_211,plain,
    ( multiply(inverse(X_11),identity) != inverse(inverse(inverse(X_11)))
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) != double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11))
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11))) ),[1,0],$fot(inverse(inverse(inverse(X_11))))]]) ).

cnf(refute_0_212,plain,
    ( multiply(inverse(X_11),identity) != inverse(inverse(inverse(X_11)))
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)) ),
    inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11))) )],[refute_0_210,refute_0_211]) ).

cnf(refute_0_213,plain,
    double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) = double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_11),identity),inverse(inverse(inverse(X_11)))) )],[refute_0_209,refute_0_212]) ).

cnf(refute_0_214,plain,
    ( double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) != X_12
    | double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) != double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11))
    | double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),X_12) ),[0],$fot(double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)))]]) ).

cnf(refute_0_215,plain,
    ( double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)) != X_12
    | double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12 ),
    inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11))) )],[refute_0_213,refute_0_214]) ).

cnf(refute_0_216,plain,
    double_divide(inverse(inverse(inverse(X_11))),multiply(inverse(X_12),X_11)) = X_12,
    inference(resolve,[$cnf( $equal(double_divide(multiply(inverse(X_11),identity),multiply(inverse(X_12),X_11)),X_12) )],[refute_0_208,refute_0_215]) ).

cnf(refute_0_217,plain,
    double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)) = X_26,
    inference(subst,[],[refute_0_216:[bind(X_11,$fot(X_25)),bind(X_12,$fot(X_26))]]) ).

cnf(refute_0_218,plain,
    ( multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) != inverse(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)))
    | double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)) != X_26
    | multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) = inverse(X_26) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))),inverse(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)))) ),[1,0],$fot(X_26)]]) ).

cnf(refute_0_219,plain,
    ( multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) != inverse(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)))
    | multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) = inverse(X_26) ),
    inference(resolve,[$cnf( $equal(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)),X_26) )],[refute_0_217,refute_0_218]) ).

cnf(refute_0_220,plain,
    multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))) = inverse(X_26),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_26),X_25),inverse(inverse(inverse(X_25)))),inverse(double_divide(inverse(inverse(inverse(X_25))),multiply(inverse(X_26),X_25)))) )],[refute_0_189,refute_0_219]) ).

cnf(refute_0_221,plain,
    multiply(multiply(inverse(identity),X_33),inverse(inverse(inverse(X_33)))) = inverse(identity),
    inference(subst,[],[refute_0_220:[bind(X_25,$fot(X_33)),bind(X_26,$fot(identity))]]) ).

cnf(refute_0_222,plain,
    ( multiply(multiply(inverse(identity),X_33),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | inverse(identity) != identity
    | multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(identity),X_33),inverse(inverse(inverse(X_33)))),inverse(identity)) ),[0,0,0],$fot(identity)]]) ).

cnf(refute_0_223,plain,
    ( multiply(multiply(inverse(identity),X_33),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_222]) ).

cnf(refute_0_224,plain,
    multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = inverse(identity),
    inference(resolve,[$cnf( $equal(multiply(multiply(inverse(identity),X_33),inverse(inverse(inverse(X_33)))),inverse(identity)) )],[refute_0_221,refute_0_223]) ).

cnf(refute_0_225,plain,
    multiply(identity,X_33) = inverse(inverse(X_33)),
    inference(subst,[],[refute_0_15:[bind(X_3,$fot(X_33))]]) ).

cnf(refute_0_226,plain,
    multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),
    introduced(tautology,[refl,[$fot(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))))]]) ).

cnf(refute_0_227,plain,
    ( multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) != multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33))))
    | multiply(identity,X_33) != inverse(inverse(X_33))
    | multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33))))) ),[1,0],$fot(inverse(inverse(X_33)))]]) ).

cnf(refute_0_228,plain,
    ( multiply(identity,X_33) != inverse(inverse(X_33))
    | multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33))))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) = multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))),
    inference(resolve,[$cnf( $equal(multiply(identity,X_33),inverse(inverse(X_33))) )],[refute_0_225,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) != multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33))))
    | multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = inverse(identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),inverse(identity)) ),[0],$fot(multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))))]]) ).

cnf(refute_0_231,plain,
    ( multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = inverse(identity) ),
    inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33))))) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    ( multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | inverse(identity) != identity
    | multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = identity ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))),identity) ),[0],$fot(inverse(identity))]]) ).

cnf(refute_0_233,plain,
    ( multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = identity ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_232]) ).

cnf(refute_0_234,plain,
    ( multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))) != inverse(identity)
    | multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = identity ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))),inverse(identity)) )],[refute_0_231,refute_0_233]) ).

cnf(refute_0_235,plain,
    multiply(inverse(inverse(X_33)),inverse(inverse(inverse(X_33)))) = identity,
    inference(resolve,[$cnf( $equal(multiply(multiply(identity,X_33),inverse(inverse(inverse(X_33)))),inverse(identity)) )],[refute_0_224,refute_0_234]) ).

cnf(refute_0_236,plain,
    multiply(inverse(inverse(inverse(X_17))),inverse(inverse(inverse(inverse(X_17))))) = identity,
    inference(subst,[],[refute_0_235:[bind(X_33,$fot(inverse(X_17)))]]) ).

cnf(refute_0_237,plain,
    double_divide(identity,inverse(inverse(inverse(X_17)))) = inverse(inverse(inverse(inverse(X_17)))),
    inference(subst,[],[refute_0_172:[bind(X_22,$fot(inverse(inverse(inverse(X_17)))))]]) ).

cnf(refute_0_238,plain,
    ( double_divide(identity,inverse(inverse(inverse(X_17)))) != X_17
    | double_divide(identity,inverse(inverse(inverse(X_17)))) != inverse(inverse(inverse(inverse(X_17))))
    | inverse(inverse(inverse(inverse(X_17)))) = X_17 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_17)))),X_17) ),[0],$fot(inverse(inverse(inverse(inverse(X_17)))))]]) ).

cnf(refute_0_239,plain,
    ( double_divide(identity,inverse(inverse(inverse(X_17)))) != X_17
    | inverse(inverse(inverse(inverse(X_17)))) = X_17 ),
    inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_17)))),inverse(inverse(inverse(inverse(X_17))))) )],[refute_0_237,refute_0_238]) ).

cnf(refute_0_240,plain,
    inverse(inverse(inverse(inverse(X_17)))) = X_17,
    inference(resolve,[$cnf( $equal(double_divide(identity,inverse(inverse(inverse(X_17)))),X_17) )],[refute_0_118,refute_0_239]) ).

cnf(refute_0_241,plain,
    ( multiply(inverse(inverse(inverse(X_17))),inverse(inverse(inverse(inverse(X_17))))) != identity
    | inverse(inverse(inverse(inverse(X_17)))) != X_17
    | multiply(inverse(inverse(inverse(X_17))),X_17) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(inverse(X_17))),inverse(inverse(inverse(inverse(X_17))))),identity) ),[0,1],$fot(X_17)]]) ).

cnf(refute_0_242,plain,
    ( multiply(inverse(inverse(inverse(X_17))),inverse(inverse(inverse(inverse(X_17))))) != identity
    | multiply(inverse(inverse(inverse(X_17))),X_17) = identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(inverse(inverse(X_17)))),X_17) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    multiply(inverse(inverse(inverse(X_17))),X_17) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(inverse(X_17))),inverse(inverse(inverse(inverse(X_17))))),identity) )],[refute_0_236,refute_0_242]) ).

cnf(refute_0_244,plain,
    multiply(inverse(inverse(inverse(X_39))),X_39) = identity,
    inference(subst,[],[refute_0_243:[bind(X_17,$fot(X_39))]]) ).

cnf(refute_0_245,plain,
    ( multiply(inverse(inverse(inverse(X_39))),X_39) != identity
    | double_divide(inverse(X_39),inverse(multiply(inverse(inverse(inverse(X_39))),X_39))) != X_39
    | double_divide(inverse(X_39),inverse(identity)) = X_39 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_39),inverse(multiply(inverse(inverse(inverse(X_39))),X_39))),X_39) ),[0,1,0],$fot(identity)]]) ).

cnf(refute_0_246,plain,
    ( double_divide(inverse(X_39),inverse(multiply(inverse(inverse(inverse(X_39))),X_39))) != X_39
    | double_divide(inverse(X_39),inverse(identity)) = X_39 ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(inverse(X_39))),X_39),identity) )],[refute_0_244,refute_0_245]) ).

cnf(refute_0_247,plain,
    double_divide(inverse(X_39),inverse(identity)) = X_39,
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),inverse(multiply(inverse(inverse(inverse(X_39))),X_39))),X_39) )],[refute_0_188,refute_0_246]) ).

cnf(refute_0_248,plain,
    double_divide(inverse(X_39),identity) = inverse(inverse(X_39)),
    inference(subst,[],[refute_0_4:[bind(A,$fot(inverse(X_39)))]]) ).

cnf(refute_0_249,plain,
    double_divide(inverse(X_39),inverse(identity)) = double_divide(inverse(X_39),inverse(identity)),
    introduced(tautology,[refl,[$fot(double_divide(inverse(X_39),inverse(identity)))]]) ).

cnf(refute_0_250,plain,
    ( double_divide(inverse(X_39),inverse(identity)) != double_divide(inverse(X_39),inverse(identity))
    | inverse(identity) != identity
    | double_divide(inverse(X_39),inverse(identity)) = double_divide(inverse(X_39),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),double_divide(inverse(X_39),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_251,plain,
    ( inverse(identity) != identity
    | double_divide(inverse(X_39),inverse(identity)) = double_divide(inverse(X_39),identity) ),
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),double_divide(inverse(X_39),inverse(identity))) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    double_divide(inverse(X_39),inverse(identity)) = double_divide(inverse(X_39),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_70,refute_0_251]) ).

cnf(refute_0_253,plain,
    ( double_divide(inverse(X_39),identity) != inverse(inverse(X_39))
    | double_divide(inverse(X_39),inverse(identity)) != double_divide(inverse(X_39),identity)
    | double_divide(inverse(X_39),inverse(identity)) = inverse(inverse(X_39)) ),
    inference(subst,[],[refute_0_39:[bind(X,$fot(double_divide(inverse(X_39),inverse(identity)))),bind(Y,$fot(double_divide(inverse(X_39),identity))),bind(Z,$fot(inverse(inverse(X_39))))]]) ).

cnf(refute_0_254,plain,
    ( double_divide(inverse(X_39),identity) != inverse(inverse(X_39))
    | double_divide(inverse(X_39),inverse(identity)) = inverse(inverse(X_39)) ),
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),double_divide(inverse(X_39),identity)) )],[refute_0_252,refute_0_253]) ).

cnf(refute_0_255,plain,
    double_divide(inverse(X_39),inverse(identity)) = inverse(inverse(X_39)),
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),identity),inverse(inverse(X_39))) )],[refute_0_248,refute_0_254]) ).

cnf(refute_0_256,plain,
    ( double_divide(inverse(X_39),inverse(identity)) != X_39
    | double_divide(inverse(X_39),inverse(identity)) != inverse(inverse(X_39))
    | inverse(inverse(X_39)) = X_39 ),
    introduced(tautology,[equality,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),X_39) ),[0],$fot(inverse(inverse(X_39)))]]) ).

cnf(refute_0_257,plain,
    ( double_divide(inverse(X_39),inverse(identity)) != X_39
    | inverse(inverse(X_39)) = X_39 ),
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),inverse(inverse(X_39))) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    inverse(inverse(X_39)) = X_39,
    inference(resolve,[$cnf( $equal(double_divide(inverse(X_39),inverse(identity)),X_39) )],[refute_0_247,refute_0_257]) ).

cnf(refute_0_259,plain,
    inverse(inverse(a2)) = a2,
    inference(subst,[],[refute_0_258:[bind(X_39,$fot(a2))]]) ).

cnf(refute_0_260,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_261,plain,
    ( a2 != a2
    | inverse(inverse(a2)) = a2 ),
    inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    a2 != a2,
    inference(resolve,[$cnf( $equal(inverse(inverse(a2)),a2) )],[refute_0_261,refute_0_19]) ).

cnf(refute_0_263,plain,
    a2 = a2,
    introduced(tautology,[refl,[$fot(a2)]]) ).

cnf(refute_0_264,plain,
    $false,
    inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_263,refute_0_262]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n010.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 07:58:09 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.40  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40  
% 0.14/0.40  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.46  
%------------------------------------------------------------------------------