% Mizar problem: t55_funct_1,funct_1,978,59 
fof(t55_funct_1,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d9_funct_1,dt_k1_relat_1,dt_k2_funct_1,dt_k2_relat_1,dt_k4_relat_1,fc3_funct_1,involutiveness_k4_relat_1,rc1_funct_1,rc3_funct_1,t37_relat_1]),
    [file(funct_1,t55_funct_1)]).

fof(d9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => k2_funct_1(A) = k4_relat_1(A) ) ) ),
    file(funct_1,d9_funct_1),
    []).

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

fof(dt_k2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_1(A))
        & v1_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,k2_funct_1),
    []).

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

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(fc3_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) )
     => ( v1_relat_1(k4_relat_1(A))
        & v1_funct_1(k4_relat_1(A)) ) ) ),
    file(funct_1,fc3_funct_1),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

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

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(t37_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k2_relat_1(A) = k1_relat_1(k4_relat_1(A))
        & k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) ) ) ),
    file(relat_1,t37_relat_1),
    []).