% Mizar problem: t33_grfunc_1,grfunc_1,297,66 
fof(t33_grfunc_1,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( A = k2_xboole_0(B,C)
               => ( k1_relat_1(A) = k2_xboole_0(k1_relat_1(B),k1_relat_1(C))
                  & k2_relat_1(A) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,rc1_funct_1,t13_relat_1,t26_relat_1]),
    [file(grfunc_1,t33_grfunc_1)]).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(t13_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) ),
    file(relat_1,t13_relat_1),
    []).

fof(t26_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(relat_1,t26_relat_1),
    []).