% Mizar problem: t52_mcart_1,mcart_1,1004,39 
fof(t52_mcart_1,conjecture,(
    ! [A,B,C,D,E,F] : 
      ( ~ r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F))
     => ( ~ r1_xboole_0(A,D)
        & ~ r1_xboole_0(B,E)
        & ~ r1_xboole_0(C,F) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d3_zfmisc_1,dt_k2_zfmisc_1,dt_k3_zfmisc_1,symmetry_r1_xboole_0,t127_zfmisc_1]),
    [file(mcart_1,t52_mcart_1)]).

fof(d3_zfmisc_1,axiom,(
    ! [A,B,C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) ),
    file(zfmisc_1,d3_zfmisc_1),
    []).

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

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

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(t127_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_xboole_0(A,B)
        | r1_xboole_0(C,D) )
     => r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t127_zfmisc_1),
    []).