% Mizar problem: t13_mcart_3,mcart_3,674,42 
fof(t13_mcart_3,conjecture,(
    ! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k4_zfmisc_1(k3_zfmisc_1(A,B,C),D,E,F) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_3,d3_zfmisc_1,dt_k2_mcart_2,dt_k2_mcart_3,dt_k2_zfmisc_1,dt_k3_zfmisc_1,dt_k4_zfmisc_1,t10_mcart_3,t53_mcart_1]),
    [file(mcart_3,t13_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(d3_zfmisc_1,axiom,(
    ! [A,B,C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) ),
    file(zfmisc_1,d3_zfmisc_1),
    []).

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(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_1),
    []).

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(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),
    []).