% Mizar problem: t72_zfmisc_1,zfmisc_1,865,45 
fof(t72_zfmisc_1,conjecture,(
    ! [A,B,C] : 
      ( k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B)
    <=> ( ~ r2_hidden(A,C)
        & ~ r2_hidden(B,C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,commutativity_k2_tarski,dt_k2_tarski,dt_k4_xboole_0,symmetry_r1_xboole_0,t55_zfmisc_1,t57_zfmisc_1,t83_xboole_1]),
    [file(zfmisc_1,t72_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(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t55_zfmisc_1,axiom,(
    ! [A,B,C] : ~ ( r1_xboole_0(k2_tarski(A,B),C)
      & r2_hidden(A,C) ) ),
    file(zfmisc_1,t55_zfmisc_1),
    []).

fof(t57_zfmisc_1,axiom,(
    ! [A,B,C] : ~ ( ~ r2_hidden(A,B)
      & ~ r2_hidden(C,B)
      & ~ r1_xboole_0(k2_tarski(A,C),B) ) ),
    file(zfmisc_1,t57_zfmisc_1),
    []).

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).