% Mizar problem: t32_zfmisc_1,zfmisc_1,541,26 
fof(t32_zfmisc_1,conjecture,(
    ! [A,B] : k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_tarski,commutativity_k2_xboole_0,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,dt_k3_tarski,idempotence_k2_xboole_0,l52_zfmisc_1,t41_enumset1]),
    [file(zfmisc_1,t32_zfmisc_1)]).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

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

fof(l52_zfmisc_1,axiom,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) ),
    file(zfmisc_1,l52_zfmisc_1),
    []).

fof(t41_enumset1,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    []).