% Mizar problem: t42_zfmisc_1,zfmisc_1,684,65 
fof(t42_zfmisc_1,conjecture,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[rc1_xboole_0,rc2_xboole_0,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,fc1_xboole_0,l46_zfmisc_1]),
    [file(zfmisc_1,t42_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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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

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

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(l46_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,k2_tarski(B,C))
    <=> ~ ( A != k1_xboole_0
          & A != k1_tarski(B)
          & A != k1_tarski(C)
          & A != k2_tarski(B,C) ) ) ),
    file(zfmisc_1,l46_zfmisc_1),
    []).