% Mizar problem: t33_zfmisc_1,zfmisc_1,552,42 
fof(t33_zfmisc_1,conjecture,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_tarski,d5_tarski,dt_k1_tarski,dt_k2_tarski,dt_k4_tarski,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,t10_zfmisc_1,t69_enumset1,t6_zfmisc_1,t8_zfmisc_1,t9_zfmisc_1]),
    [file(zfmisc_1,t33_zfmisc_1)]).

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

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

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

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

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

fof(t10_zfmisc_1,axiom,(
    ! [A,B,C,D] : ~ ( k2_tarski(A,B) = k2_tarski(C,D)
      & A != C
      & A != D ) ),
    file(zfmisc_1,t10_zfmisc_1),
    []).

fof(t69_enumset1,axiom,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    []).

fof(t6_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    file(zfmisc_1,t6_zfmisc_1),
    []).

fof(t8_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => A = B ) ),
    file(zfmisc_1,t8_zfmisc_1),
    []).

fof(t9_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) ),
    file(zfmisc_1,t9_zfmisc_1),
    []).