% Mizar problem: t43_relat_2,relat_2,660,64 
fof(t43_relat_2,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( ( v8_relat_2(A)
              & v8_relat_2(B) )
           => v8_relat_2(k3_xboole_0(A,B)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relat_1,commutativity_k3_xboole_0,d16_relat_2,d3_xboole_0,d8_relat_2,dt_k3_relat_1,dt_k3_xboole_0,dt_k4_tarski,dt_m1_subset_1,existence_m1_subset_1,fc1_relat_1,fc1_zfmisc_1,idempotence_k3_xboole_0,rc1_relat_1,rc1_xboole_0,rc2_relat_1,rc2_xboole_0,t1_subset,t2_subset,t30_relat_1]),
    [file(relat_2,t43_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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d16_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d8_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    []).

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

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

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

fof(t30_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_1),
    []).