% Mizar problem: t13_zfmisc_1,zfmisc_1,243,31 
fof(t13_zfmisc_1,conjecture,(
    ! [A,B] : 
      ( k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A)
     => A = B ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_xboole_0,d1_tarski,dt_k1_tarski,dt_k2_xboole_0,idempotence_k2_xboole_0,l21_zfmisc_1,reflexivity_r1_tarski]),
    [file(zfmisc_1,t13_zfmisc_1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

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

fof(dt_k2_xboole_0,axiom,(
    $true ),
    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(l21_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B)
     => r2_hidden(A,B) ) ),
    file(zfmisc_1,l21_zfmisc_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).