% Mizar problem: t135_orders_1,orders_1,709,38 
fof(t135_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_orders_1(A,B)
         => v3_orders_1(k2_wellord1(A,B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,d5_orders_1,d6_wellord1,d8_orders_1,dt_k2_wellord1,dt_k2_zfmisc_1,dt_k3_xboole_0,idempotence_k3_xboole_0,l142_orders_1,l143_orders_1,l144_orders_1,l145_orders_1]),
    [file(orders_1,t135_orders_1)]).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

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(d6_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    []).

fof(d8_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r3_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B) ) ) ) ),
    file(orders_1,d8_orders_1),
    []).

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(l142_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
         => v1_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l142_orders_1),
    []).

fof(l143_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
         => v8_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l143_orders_1),
    []).

fof(l144_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_relat_2(A,B)
         => v4_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l144_orders_1),
    []).

fof(l145_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r6_relat_2(A,B)
         => v6_relat_2(k2_wellord1(A,B)) ) ) ),
    file(orders_1,l145_orders_1),
    []).