% Mizar problem: t24_relat_2,relat_2,219,33 
fof(t24_relat_2,conjecture,(
    ! [A] : 
      ( v4_relat_2(k6_relat_1(A))
      & v1_relat_2(k6_relat_1(A)) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,d10_relat_1,d12_relat_2,d4_relat_2,dt_k3_relat_1,dt_k4_tarski,dt_k6_relat_1,dt_m1_subset_1,existence_m1_subset_1,fc1_zfmisc_1,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,t1_subset,t22_relat_2,t23_relat_2,t2_subset]),
    [file(relat_2,t24_relat_2)]).

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

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(d10_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) ),
    file(relat_1,d10_relat_1),
    []).

fof(d12_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
      <=> r4_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d12_relat_2),
    []).

fof(d4_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,C),A) )
             => C = D ) ) ) ),
    file(relat_2,d4_relat_2),
    []).

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

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

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_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_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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(t22_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( v3_relat_2(A)
          & v8_relat_2(A) )
       => v1_relat_2(A) ) ) ),
    file(relat_2,t22_relat_2),
    []).

fof(t23_relat_2,axiom,(
    ! [A] : 
      ( v3_relat_2(k6_relat_1(A))
      & v8_relat_2(k6_relat_1(A)) ) ),
    file(relat_2,t23_relat_2),
    []).

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