% Mizar problem: t24_mcart_3,mcart_3,1067,11 
fof(t24_mcart_3,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L] : 
      ( ~ r1_xboole_0(k2_mcart_3(A,B,C,D,E,F),k2_mcart_3(G,H,I,J,K,L))
     => ( ~ r1_xboole_0(A,G)
        & ~ r1_xboole_0(B,H)
        & ~ r1_xboole_0(C,I)
        & ~ r1_xboole_0(D,J)
        & ~ r1_xboole_0(E,K)
        & ~ r1_xboole_0(F,L) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_3,dt_k2_mcart_2,dt_k2_mcart_3,dt_k2_zfmisc_1,symmetry_r1_xboole_0,t10_mcart_3,t127_zfmisc_1]),
    [file(mcart_3,t24_mcart_3)]).

fof(d2_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_zfmisc_1(k2_mcart_2(A,B,C,D,E),F) ),
    file(mcart_3,d2_mcart_3),
    []).

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

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

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(t10_mcart_3,axiom,(
    ! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E),F) ),
    file(mcart_3,t10_mcart_3),
    []).

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),
    []).