% Mizar problem: t26_mcart_4,mcart_4,1339,25 
fof(t26_mcart_4,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] : 
      ( ~ r1_xboole_0(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
     => ( ~ r1_xboole_0(A,H)
        & ~ r1_xboole_0(B,I)
        & ~ r1_xboole_0(C,J)
        & ~ r1_xboole_0(D,K)
        & ~ r1_xboole_0(E,L)
        & ~ r1_xboole_0(F,M)
        & ~ r1_xboole_0(G,N) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_4,dt_k2_mcart_3,dt_k2_mcart_4,dt_k2_zfmisc_1,symmetry_r1_xboole_0,t11_mcart_4,t127_zfmisc_1]),
    [file(mcart_4,t26_mcart_4)]).

fof(d2_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G) ),
    file(mcart_4,d2_mcart_4),
    []).

fof(dt_k2_mcart_3,axiom,(
    $true ),
    file(mcart_3,k2_mcart_3),
    []).

fof(dt_k2_mcart_4,axiom,(
    $true ),
    file(mcart_4,k2_mcart_4),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_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(t11_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E),F),G) ),
    file(mcart_4,t11_mcart_4),
    []).

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),
    []).