% Mizar problem: t7_mcart_2,mcart_2,433,54 
fof(t7_mcart_2,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( k1_mcart_2(A,B,C,D,E) = k1_mcart_2(F,G,H,I,J)
     => ( A = F
        & B = G
        & C = H
        & D = I
        & E = J ) ) ),
    inference(mizar_bg_added,[status(thm)],[d1_mcart_2,dt_k1_mcart_2,dt_k4_mcart_1,dt_k4_tarski,t33_mcart_1,t33_zfmisc_1]),
    [file(mcart_2,t7_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(dt_k1_mcart_2,axiom,(
    $true ),
    file(mcart_2,k1_mcart_2),
    []).

fof(dt_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

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

fof(t33_mcart_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( k4_mcart_1(A,B,C,D) = k4_mcart_1(E,F,G,H)
     => ( A = E
        & B = F
        & C = G
        & D = H ) ) ),
    file(mcart_1,t33_mcart_1),
    []).

fof(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).