% Mizar problem: t43_zfmisc_1,zfmisc_1,692,60 
fof(t43_zfmisc_1,conjecture,(
    ! [A,B,C] : ~ ( k1_tarski(A) = k2_xboole_0(B,C)
      & ~ ( B = k1_tarski(A)
          & C = k1_tarski(A) )
      & ~ ( B = k1_xboole_0
          & C = k1_tarski(A) )
      & ~ ( B = k1_tarski(A)
          & C = k1_xboole_0 ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,fc1_xboole_0,fc2_xboole_0,fc3_xboole_0,idempotence_k2_xboole_0,l1_zfmisc_1,l4_zfmisc_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,t7_xboole_1]),
    [file(zfmisc_1,t43_zfmisc_1)]).

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

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

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

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

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

fof(l1_zfmisc_1,axiom,(
    ! [A] : k1_tarski(A) != k1_xboole_0 ),
    file(zfmisc_1,l1_zfmisc_1),
    []).

fof(l4_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,l4_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(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).