% Mizar problem: t16_mcart_5,mcart_5,1165,24 
fof(t16_mcart_5,conjecture,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_2(k4_zfmisc_1(A,B,C,D),E,F,G,H) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_5,dt_k2_mcart_2,dt_k2_mcart_4,dt_k2_mcart_5,dt_k2_zfmisc_1,dt_k4_zfmisc_1,t12_mcart_5,t53_mcart_1,t9_mcart_2]),
    [file(mcart_5,t16_mcart_5)]).

fof(d2_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H) ),
    file(mcart_5,d2_mcart_5),
    []).

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

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

fof(dt_k2_mcart_5,axiom,(
    $true ),
    file(mcart_5,k2_mcart_5),
    []).

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(t12_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_zfmisc_1(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),H) ),
    file(mcart_5,t12_mcart_5),
    []).

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),
    []).

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),
    []).