% Mizar problem: t16_mcart_2,mcart_2,551,43 
fof(t16_mcart_2,conjecture,(
    ! [A,B] : 
      ( k2_mcart_2(A,A,A,A,A) = k2_mcart_2(B,B,B,B,B)
     => A = B ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d2_mcart_2,dt_k1_xboole_0,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k4_zfmisc_1,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,t14_mcart_2,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(mcart_2,t16_mcart_2)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(t14_mcart_2,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( k2_mcart_2(A,B,C,D,E) = k2_mcart_2(F,G,H,I,J)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | C = k1_xboole_0
        | D = k1_xboole_0
        | E = k1_xboole_0
        | ( A = F
          & B = G
          & C = H
          & D = I
          & E = J ) ) ) ),
    file(mcart_2,t14_mcart_2),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).