% Mizar problem: t23_mcart_2,mcart_2,820,51 
fof(t23_mcart_2,conjecture,(
    ! [A,B,C,D,E] : k2_mcart_2(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E)) = k1_tarski(k1_mcart_2(A,B,C,D,E)) ),
    inference(mizar_bg_added,[status(thm)],[d1_mcart_2,d2_mcart_2,dt_k1_mcart_2,dt_k1_tarski,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k4_mcart_1,dt_k4_tarski,dt_k4_zfmisc_1,t12_mcart_2,t35_zfmisc_1,t65_mcart_1,t6_mcart_2]),
    [file(mcart_2,t23_mcart_2)]).

fof(d1_mcart_2,axiom,(
    ! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_tarski(k4_mcart_1(A,B,C,D),E) ),
    file(mcart_2,d1_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(dt_k1_mcart_2,axiom,(
    $true ),
    file(mcart_2,k1_mcart_2),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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

fof(t12_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k4_zfmisc_1(k2_zfmisc_1(A,B),C,D,E) ),
    file(mcart_2,t12_mcart_2),
    []).

fof(t35_zfmisc_1,axiom,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    []).

fof(t65_mcart_1,axiom,(
    ! [A,B,C,D] : k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D)) ),
    file(mcart_1,t65_mcart_1),
    []).

fof(t6_mcart_2,axiom,(
    ! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_mcart_1(k4_tarski(A,B),C,D,E) ),
    file(mcart_2,t6_mcart_2),
    []).