% Mizar problem: t50_card_4,card_4,616,64 
fof(t50_card_4,conjecture,(
    ! [A,B] : 
      ( ( v1_card_4(A)
        & v1_card_4(B) )
     => v1_card_4(k5_xboole_0(A,B)) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,commutativity_k5_xboole_0,d6_xboole_0,dt_k2_xboole_0,dt_k4_xboole_0,dt_k5_xboole_0,idempotence_k2_xboole_0,t47_card_4,t49_card_4]),
    [file(card_4,t50_card_4)]).

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(commutativity_k5_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k5_xboole_0(B,A) ),
    file(xboole_0,k5_xboole_0),
    []).

fof(d6_xboole_0,axiom,(
    ! [A,B] : k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) ),
    file(xboole_0,d6_xboole_0),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_xboole_0,axiom,(
    $true ),
    file(xboole_0,k5_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(t47_card_4,axiom,(
    ! [A,B] : 
      ( ( v1_card_4(A)
        & v1_card_4(B) )
     => v1_card_4(k2_xboole_0(A,B)) ) ),
    file(card_4,t47_card_4),
    []).

fof(t49_card_4,axiom,(
    ! [A,B] : 
      ( v1_card_4(A)
     => v1_card_4(k4_xboole_0(A,B)) ) ),
    file(card_4,t49_card_4),
    []).