% Mizar problem: t59_enumset1,enumset1,369,63 
fof(t59_enumset1,conjecture,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_enumset1,dt_k2_enumset1,dt_k2_xboole_0,dt_k5_enumset1,l66_enumset1]),
    [file(enumset1,t59_enumset1)]).

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

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

fof(dt_k2_enumset1,axiom,(
    $true ),
    file(enumset1,k2_enumset1),
    []).

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

fof(dt_k5_enumset1,axiom,(
    $true ),
    file(enumset1,k5_enumset1),
    []).

fof(l66_enumset1,axiom,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) ),
    file(enumset1,l66_enumset1),
    []).