% Mizar problem: t188_orders_1,orders_1,2223,44 
fof(t188_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
       => v6_relat_2(k4_relat_1(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[involutiveness_k4_relat_1,dt_k4_relat_1,l113_orders_1]),
    [file(orders_1,t188_orders_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(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(l113_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
       => v6_relat_2(k4_relat_1(A)) ) ) ),
    file(orders_1,l113_orders_1),
    []).