% Mizar problem: t130_zfmisc_1,zfmisc_1,1630,52 
fof(t130_zfmisc_1,conjecture,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => ( k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0
        & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0 ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_tarski,d1_xboole_0,d5_tarski,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_tarski,fc1_xboole_0,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,t128_zfmisc_1,t129_zfmisc_1]),
    [file(zfmisc_1,t130_zfmisc_1)]).

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

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

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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

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

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(t128_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D))
    <=> ( A = C
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t128_zfmisc_1),
    []).

fof(t129_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D)))
    <=> ( r2_hidden(A,C)
        & B = D ) ) ),
    file(zfmisc_1,t129_zfmisc_1),
    []).