% Mizar problem: t64_mcart_1,mcart_1,1285,53 
fof(t64_mcart_1,conjecture,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ~ r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H))
     => ( ~ r1_xboole_0(A,E)
        & ~ r1_xboole_0(B,F)
        & ~ r1_xboole_0(C,G)
        & ~ r1_xboole_0(D,H) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_zfmisc_1,dt_k4_zfmisc_1,symmetry_r1_xboole_0,t127_zfmisc_1,t53_mcart_1]),
    [file(mcart_1,t64_mcart_1)]).

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

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_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),
    []).

fof(t53_mcart_1,axiom,(
    ! [A,B,C,D] : k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) ),
    file(mcart_1,t53_mcart_1),
    []).