% Mizar problem: t70_zfmisc_1,zfmisc_1,860,50 
fof(t70_zfmisc_1,conjecture,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_tarski,dt_k4_xboole_0,l39_zfmisc_1]),
    [file(zfmisc_1,t70_zfmisc_1)]).

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

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

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

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

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(l39_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A)
    <=> ( ~ r2_hidden(A,C)
        & ( r2_hidden(B,C)
          | A = B ) ) ) ),
    file(zfmisc_1,l39_zfmisc_1),
    []).