% Mizar problem: t39_mcart_3,mcart_3,1318,61 
fof(t39_mcart_3,conjecture,(
    ! [A,B,C,D,E,F,G] : 
      ( m1_subset_1(G,k1_zfmisc_1(A))
     => ! [H] : 
          ( m1_subset_1(H,k1_zfmisc_1(B))
         => ! [I] : 
              ( m1_subset_1(I,k1_zfmisc_1(C))
             => ! [J] : 
                  ( m1_subset_1(J,k1_zfmisc_1(D))
                 => ! [K] : 
                      ( m1_subset_1(K,k1_zfmisc_1(E))
                     => ! [L] : 
                          ( m1_subset_1(L,k1_zfmisc_1(F))
                         => m1_subset_1(k2_mcart_3(G,H,I,J,K,L),k1_zfmisc_1(k2_mcart_3(A,B,C,D,E,F))) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_k2_mcart_2,dt_k2_zfmisc_1,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_mcart_3,dt_m1_subset_1,t3_subset,d2_mcart_3,t38_mcart_3]),
    [file(mcart_3,t39_mcart_3)]).

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(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_3,axiom,(
    $true ),
    file(mcart_3,k2_mcart_3),
    []).

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_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(t38_mcart_3,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_tarski(E,F)
        & r1_tarski(G,H)
        & r1_tarski(I,J)
        & r1_tarski(K,L) )
     => r1_tarski(k2_mcart_3(A,C,E,G,I,K),k2_mcart_3(B,D,F,H,J,L)) ) ),
    file(mcart_3,t38_mcart_3),
    []).