% Mizar problem: t174_orders_1,orders_1,1583,58 
fof(t174_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : ~ ( r2_orders_1(A,B)
          & k3_relat_1(A) = B
          & r5_orders_1(A,B)
          & ! [C] : ~ r7_orders_1(A,C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,d6_relat_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,dt_k4_relat_1,idempotence_k2_xboole_0,involutiveness_k4_relat_1,t137_orders_1,t151_orders_1,t163_orders_1,t173_orders_1,t38_relat_1]),
    [file(orders_1,t174_orders_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(d6_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    []).

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(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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(t137_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_orders_1(A,B)
         => r2_orders_1(k4_relat_1(A),B) ) ) ),
    file(orders_1,t137_orders_1),
    []).

fof(t151_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_orders_1(A,B)
        <=> r5_orders_1(k4_relat_1(A),B) ) ) ),
    file(orders_1,t151_orders_1),
    []).

fof(t163_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r7_orders_1(A,B)
        <=> r6_orders_1(k4_relat_1(A),B) ) ) ),
    file(orders_1,t163_orders_1),
    []).

fof(t173_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : ~ ( r2_orders_1(A,B)
          & k3_relat_1(A) = B
          & r4_orders_1(A,B)
          & ! [C] : ~ r6_orders_1(A,C) ) ) ),
    file(orders_1,t173_orders_1),
    []).

fof(t38_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k3_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,t38_relat_1),
    []).