% Mizar problem: t44_mcart_5,mcart_5,1941,68 
fof(t44_mcart_5,conjecture,(
    ! [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)) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_5,dt_k1_zfmisc_1,dt_k2_mcart_4,dt_k2_mcart_5,dt_k2_zfmisc_1,dt_m1_subset_1,existence_m1_subset_1,reflexivity_r1_tarski,t119_zfmisc_1,t3_subset,t41_mcart_4]),
    [file(mcart_5,t44_mcart_5)]).

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

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

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

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

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

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

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

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    []).

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

fof(t41_mcart_4,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] : 
      ( ( r1_tarski(A,H)
        & r1_tarski(B,I)
        & r1_tarski(C,J)
        & r1_tarski(D,K)
        & r1_tarski(E,L)
        & r1_tarski(F,M)
        & r1_tarski(G,N) )
     => r1_tarski(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N)) ) ),
    file(mcart_4,t41_mcart_4),
    []).