% Mizar problem: t106_orders_1,orders_1,423,30 
fof(t106_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
       => v3_orders_1(k4_relat_1(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d5_orders_1,dt_k4_relat_1,involutiveness_k4_relat_1,l113_orders_1,t27_relat_2,t40_relat_2,t42_relat_2]),
    [file(orders_1,t106_orders_1)]).

fof(d5_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A) ) ) ) ),
    file(orders_1,d5_orders_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(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(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),
    []).

fof(t27_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
       => v1_relat_2(k4_relat_1(A)) ) ) ),
    file(relat_2,t27_relat_2),
    []).

fof(t40_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
       => v4_relat_2(k4_relat_1(A)) ) ) ),
    file(relat_2,t40_relat_2),
    []).

fof(t42_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
       => v8_relat_2(k4_relat_1(A)) ) ) ),
    file(relat_2,t42_relat_2),
    []).