% Mizar problem: t139_zfmisc_1,zfmisc_1,1847,11 
fof(t139_zfmisc_1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] : 
          ( ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
            | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) )
         => r1_tarski(B,D) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k1_xboole_0,dt_k2_zfmisc_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,t113_zfmisc_1,t138_zfmisc_1,t2_xboole_1]),
    [file(zfmisc_1,t139_zfmisc_1)]).

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

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

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

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(t113_zfmisc_1,axiom,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    []).

fof(t138_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
     => ( k2_zfmisc_1(A,B) = k1_xboole_0
        | ( r1_tarski(A,C)
          & r1_tarski(B,D) ) ) ) ),
    file(zfmisc_1,t138_zfmisc_1),
    []).

fof(t2_xboole_1,axiom,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    []).