% Mizar problem: t74_mcart_1,mcart_1,1388,28 
fof(t74_mcart_1,conjecture,(
    ! [A,B,C,D] : 
      ( ! [E] : 
          ( r2_hidden(E,A)
        <=> ? [F,G,H] : 
              ( r2_hidden(F,B)
              & r2_hidden(G,C)
              & r2_hidden(H,D)
              & E = k3_mcart_1(F,G,H) ) )
     => A = k3_zfmisc_1(B,C,D) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d2_zfmisc_1,d3_mcart_1,d3_zfmisc_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k3_mcart_1,dt_k3_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t2_subset,t2_tarski,t6_boole,t7_boole,t8_boole]),
    [file(mcart_1,t74_mcart_1)]).

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

fof(d2_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    []).

fof(d3_mcart_1,axiom,(
    ! [A,B,C] : k3_mcart_1(A,B,C) = k4_tarski(k4_tarski(A,B),C) ),
    file(mcart_1,d3_mcart_1),
    []).

fof(d3_zfmisc_1,axiom,(
    ! [A,B,C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) ),
    file(zfmisc_1,d3_zfmisc_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

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

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(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

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(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(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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),
    []).