% Mizar problem: t45_mcart_5,mcart_5,1952,73 
fof(t45_mcart_5,conjecture,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( m1_subset_1(I,k1_zfmisc_1(A))
     => ! [J] : 
          ( m1_subset_1(J,k1_zfmisc_1(B))
         => ! [K] : 
              ( m1_subset_1(K,k1_zfmisc_1(C))
             => ! [L] : 
                  ( m1_subset_1(L,k1_zfmisc_1(D))
                 => ! [M] : 
                      ( m1_subset_1(M,k1_zfmisc_1(E))
                     => ! [N] : 
                          ( m1_subset_1(N,k1_zfmisc_1(F))
                         => ! [O] : 
                              ( m1_subset_1(O,k1_zfmisc_1(G))
                             => ! [P] : 
                                  ( m1_subset_1(P,k1_zfmisc_1(H))
                                 => m1_subset_1(k2_mcart_5(I,J,K,L,M,N,O,P),k1_zfmisc_1(k2_mcart_5(A,B,C,D,E,F,G,H))) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_mcart_4,dt_k2_zfmisc_1,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_mcart_5,dt_m1_subset_1,t3_subset,d2_mcart_5,t44_mcart_5]),
    [file(mcart_5,t45_mcart_5)]).

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

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(t44_mcart_5,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] : 
      ( ( r1_tarski(A,I)
        & r1_tarski(B,J)
        & r1_tarski(C,K)
        & r1_tarski(D,L)
        & r1_tarski(E,M)
        & r1_tarski(F,N)
        & r1_tarski(G,O)
        & r1_tarski(H,P) )
     => r1_tarski(k2_mcart_5(A,B,C,D,E,F,G,H),k2_mcart_5(I,J,K,L,M,N,O,P)) ) ),
    file(mcart_5,t44_mcart_5),
    []).