% Mizar problem: t12_mcart_2,mcart_2,509,38 
fof(t12_mcart_2,conjecture,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k4_zfmisc_1(k2_zfmisc_1(A,B),C,D,E) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_2,d3_zfmisc_1,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k3_zfmisc_1,dt_k4_zfmisc_1,t54_mcart_1,t9_mcart_2]),
    [file(mcart_2,t12_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(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_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(t54_mcart_1,axiom,(
    ! [A,B,C,D] : k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D) ),
    file(mcart_1,t54_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),
    []).