% Mizar problem: t22_mcart_2,mcart_2,805,67 
fof(t22_mcart_2,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ~ r1_xboole_0(k2_mcart_2(A,B,C,D,E),k2_mcart_2(F,G,H,I,J))
     => ( ~ r1_xboole_0(A,F)
        & ~ r1_xboole_0(B,G)
        & ~ r1_xboole_0(C,H)
        & ~ r1_xboole_0(D,I)
        & ~ r1_xboole_0(E,J) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_2,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k4_zfmisc_1,symmetry_r1_xboole_0,t127_zfmisc_1,t9_mcart_2]),
    [file(mcart_2,t22_mcart_2)]).

fof(d2_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k4_zfmisc_1(A,B,C,D),E) ),
    file(mcart_2,d2_mcart_2),
    []).

fof(dt_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

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(t9_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E) ),
    file(mcart_2,t9_mcart_2),
    []).