% Mizar ND problem: t5_hahnban,hahnban,68,68 
fof(dh_c1_3__hahnban,definition,
    ( ( ( ~ v1_xboole_0(c1_3__hahnban)
        & v1_fraenkel(c1_3__hahnban) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( A = k3_tarski(c1_3__hahnban)
           => ( k1_relat_1(A) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
              & k2_relat_1(A) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) ) )
   => ! [B] : 
        ( ( ~ v1_xboole_0(B)
          & v1_fraenkel(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( C = k3_tarski(B)
             => ( k1_relat_1(C) = k3_tarski(a_1_0_hahnban(B))
                & k2_relat_1(C) = k3_tarski(a_1_1_hahnban(B)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__hahnban),file(hahnban,c1_3__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c1_3__hahnban)]).

fof(dh_c2_3__hahnban,definition,
    ( ( ( v1_relat_1(c2_3__hahnban)
        & v1_funct_1(c2_3__hahnban) )
     => ( c2_3__hahnban = k3_tarski(c1_3__hahnban)
       => ( k1_relat_1(c2_3__hahnban) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
          & k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( A = k3_tarski(c1_3__hahnban)
         => ( k1_relat_1(A) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
            & k2_relat_1(A) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__hahnban),file(hahnban,c2_3__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c2_3__hahnban)]).

fof(e1_3__hahnban,assumption,(
    c2_3__hahnban = k3_tarski(c1_3__hahnban) ),
    introduced(assumption,[file(hahnban,e1_3__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,e1_3__hahnban)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(dt_c1_3__hahnban,assumption,
    ( ~ v1_xboole_0(c1_3__hahnban)
    & v1_fraenkel(c1_3__hahnban) ),
    introduced(assumption,[file(hahnban,c1_3__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c1_3__hahnban)]).

fof(dt_c2_3__hahnban,assumption,
    ( v1_relat_1(c2_3__hahnban)
    & v1_funct_1(c2_3__hahnban) ),
    introduced(assumption,[file(hahnban,c2_3__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c2_3__hahnban)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_1_0_hahnban,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_1_0_hahnban(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k1_relat_1(C) ) ) ) ),
    file(hahnban,a_1_0_hahnban),
    [interesting(0.9),axiom,file(hahnban,a_1_0_hahnban)]).

fof(dh_c1_3_1__hahnban,definition,
    ( ( ~ ( r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban))
          & ! [A] : 
              ~ ( r2_hidden(c1_3_1__hahnban,A)
                & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) )
      & ( ? [A] : 
            ( r2_hidden(c1_3_1__hahnban,A)
            & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) )
       => r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ) )
   => ! [B] : 
        ( ~ ( r2_hidden(B,k1_relat_1(c2_3__hahnban))
            & ! [C] : 
                ~ ( r2_hidden(B,C)
                  & r2_hidden(C,a_1_0_hahnban(c1_3__hahnban)) ) )
        & ( ? [C] : 
              ( r2_hidden(B,C)
              & r2_hidden(C,a_1_0_hahnban(c1_3__hahnban)) )
         => r2_hidden(B,k1_relat_1(c2_3__hahnban)) ) ) ),
    introduced(definition,[new_symbol(c1_3_1__hahnban),file(hahnban,c1_3_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_3_1__hahnban)]).

fof(e1_3_1_1__hahnban,assumption,(
    r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ),
    introduced(assumption,[file(hahnban,e1_3_1_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,e1_3_1_1__hahnban)]).

fof(dt_c1_3_1__hahnban,assumption,(
    $true ),
    introduced(assumption,[file(hahnban,c1_3_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_3_1__hahnban)]).

fof(dh_c1_3_1_1__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c2_3__hahnban,c1_3_1__hahnban)),A)
        & r2_hidden(A,c1_3__hahnban) )
   => ( r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c2_3__hahnban,c1_3_1__hahnban)),c1_3_1_1__hahnban)
      & r2_hidden(c1_3_1_1__hahnban,c1_3__hahnban) ) ),
    introduced(definition,[new_symbol(c1_3_1_1__hahnban),file(hahnban,c1_3_1_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c1_3_1_1__hahnban)]).

fof(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(t8_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    [interesting(0.9),axiom,file(funct_1,t8_funct_1)]).

fof(e2_3_1_1__hahnban,plain,(
    r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c2_3__hahnban,c1_3_1__hahnban)),c2_3__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3_1__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,d5_tarski,e1_3_1_1__hahnban,t8_funct_1]),
    [interesting(0.5),file(hahnban,e2_3_1_1__hahnban),[file(hahnban,e2_3_1_1__hahnban)]]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e3_3_1_1__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c2_3__hahnban,c1_3_1__hahnban)),A)
      & r2_hidden(A,c1_3__hahnban) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_tarski,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,d5_tarski,e2_3_1_1__hahnban,e1_3__hahnban,d4_tarski]),
    [interesting(0.5),file(hahnban,e3_3_1_1__hahnban),[file(hahnban,e3_3_1_1__hahnban)]]).

fof(dt_c1_3_1_1__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[dh_c1_3_1_1__hahnban,e3_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,c1_3_1_1__hahnban),[file(hahnban,c1_3_1_1__hahnban)]]).

fof(de_c2_3_1_1__hahnban,definition,(
    c2_3_1_1__hahnban = c1_3_1_1__hahnban ),
    introduced(definition,[new_symbol(c2_3_1_1__hahnban),file(hahnban,c2_3_1_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c2_3_1_1__hahnban)]).

fof(e4_3_1_1__hahnban,plain,
    ( r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c2_3__hahnban,c1_3_1__hahnban)),c1_3_1_1__hahnban)
    & r2_hidden(c1_3_1_1__hahnban,c1_3__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[dh_c1_3_1_1__hahnban,e3_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,e4_3_1_1__hahnban),[file(hahnban,e4_3_1_1__hahnban)]]).

fof(d1_fraenkel,definition,(
    ! [A] : 
      ( v1_fraenkel(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,d1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,d1_fraenkel)]).

fof(e5_3_1_1__hahnban,plain,
    ( v1_relat_1(c1_3_1_1__hahnban)
    & v1_funct_1(c1_3_1_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c1_3_1_1__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,d5_tarski,e4_3_1_1__hahnban,d1_fraenkel]),
    [interesting(0.5),file(hahnban,e5_3_1_1__hahnban),[file(hahnban,e5_3_1_1__hahnban)]]).

fof(dt_c2_3_1_1__hahnban,plain,
    ( v1_relat_1(c2_3_1_1__hahnban)
    & v1_funct_1(c2_3_1_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[dt_c1_3_1_1__hahnban,de_c2_3_1_1__hahnban,e5_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,c2_3_1_1__hahnban),[file(hahnban,c2_3_1_1__hahnban)]]).

fof(de_c3_3_1_1__hahnban,definition,(
    c3_3_1_1__hahnban = k1_relat_1(c2_3_1_1__hahnban) ),
    introduced(definition,[new_symbol(c3_3_1_1__hahnban),file(hahnban,c3_3_1_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c3_3_1_1__hahnban)]).

fof(dt_c3_3_1_1__hahnban,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[dt_c1_3_1_1__hahnban,dt_k1_relat_1,dt_c2_3_1_1__hahnban,de_c2_3_1_1__hahnban,de_c3_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,c3_3_1_1__hahnban),[file(hahnban,c3_3_1_1__hahnban)]]).

fof(e6_3_1_1__hahnban,plain,
    ( r2_hidden(c1_3_1__hahnban,c3_3_1_1__hahnban)
    & r2_hidden(c3_3_1_1__hahnban,a_1_0_hahnban(c1_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_c2_3_1_1__hahnban,de_c2_3_1_1__hahnban,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c1_3_1_1__hahnban,dt_c2_3__hahnban,dt_c3_3_1_1__hahnban,de_c3_3_1_1__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_hahnban,d5_tarski,e4_3_1_1__hahnban,t8_funct_1]),
    [interesting(0.5),file(hahnban,e6_3_1_1__hahnban),[file(hahnban,e6_3_1_1__hahnban)]]).

fof(i3_3_1_1__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i3_3_1_1__hahnban)]),
    [interesting(0.5),trivial,file(hahnban,i3_3_1_1__hahnban)]).

fof(i2_3_1_1__hahnban,plain,
    ( r2_hidden(c1_3_1__hahnban,c3_3_1_1__hahnban)
    & r2_hidden(c3_3_1_1__hahnban,a_1_0_hahnban(c1_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[e6_3_1_1__hahnban,i3_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,i2_3_1_1__hahnban),[file(hahnban,i2_3_1_1__hahnban)]]).

fof(i1_3_1_1__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(c1_3_1__hahnban,A)
      & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) ),
    inference(take,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3_1_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,dt_k1_relat_1,dt_m1_subset_1,cc15_membered,cc1_fraenkel,rc1_fraenkel,antisymmetry_r2_hidden,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c3_3_1_1__hahnban,t2_tarski,fraenkel_a_1_0_hahnban,i2_3_1_1__hahnban]),
    [interesting(0.5),file(hahnban,i1_3_1_1__hahnban),[file(hahnban,i1_3_1_1__hahnban)]]).

fof(e1_3_1__hahnban,plain,(
    ~ ( r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban))
      & ! [A] : 
          ~ ( r2_hidden(c1_3_1__hahnban,A)
            & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,e1_3__hahnban]),discharge_asm(discharge,[e1_3_1_1__hahnban])],[e1_3_1_1__hahnban,i1_3_1_1__hahnban]),
    [interesting(0.65),file(hahnban,e1_3_1__hahnban),[file(hahnban,e1_3_1__hahnban)]]).

fof(e2_3_1__hahnban,assumption,(
    ? [A] : 
      ( r2_hidden(c1_3_1__hahnban,A)
      & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) ),
    introduced(assumption,[file(hahnban,e2_3_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,e2_3_1__hahnban)]).

fof(dh_c3_3_1__hahnban,definition,
    ( ? [A] : 
        ( m1_subset_1(A,c1_3__hahnban)
        & c2_3_1__hahnban = k1_relat_1(A) )
   => ( m1_subset_1(c3_3_1__hahnban,c1_3__hahnban)
      & c2_3_1__hahnban = k1_relat_1(c3_3_1__hahnban) ) ),
    introduced(definition,[new_symbol(c3_3_1__hahnban),file(hahnban,c3_3_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c3_3_1__hahnban)]).

fof(dh_c2_3_1__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(c1_3_1__hahnban,A)
        & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) )
   => ( r2_hidden(c1_3_1__hahnban,c2_3_1__hahnban)
      & r2_hidden(c2_3_1__hahnban,a_1_0_hahnban(c1_3__hahnban)) ) ),
    introduced(definition,[new_symbol(c2_3_1__hahnban),file(hahnban,c2_3_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c2_3_1__hahnban)]).

fof(dt_c2_3_1__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e2_3_1__hahnban])],[dh_c2_3_1__hahnban,e2_3_1__hahnban]),
    [interesting(0.65),file(hahnban,c2_3_1__hahnban),[file(hahnban,c2_3_1__hahnban)]]).

fof(e3_3_1__hahnban,plain,
    ( r2_hidden(c1_3_1__hahnban,c2_3_1__hahnban)
    & r2_hidden(c2_3_1__hahnban,a_1_0_hahnban(c1_3__hahnban)) ),
    inference(consider,[status(thm),assumptions([e2_3_1__hahnban])],[dh_c2_3_1__hahnban,e2_3_1__hahnban]),
    [interesting(0.65),file(hahnban,e3_3_1__hahnban),[file(hahnban,e3_3_1__hahnban)]]).

fof(e4_3_1__hahnban,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_3__hahnban)
      & c2_3_1__hahnban = k1_relat_1(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,cc15_membered,cc1_fraenkel,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_relat_1,dt_m1_subset_1,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3_1__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_hahnban,e3_3_1__hahnban]),
    [interesting(0.65),file(hahnban,e4_3_1__hahnban),[file(hahnban,e4_3_1__hahnban)]]).

fof(dt_c3_3_1__hahnban,plain,(
    m1_subset_1(c3_3_1__hahnban,c1_3__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban])],[dh_c3_3_1__hahnban,e4_3_1__hahnban]),
    [interesting(0.65),file(hahnban,c3_3_1__hahnban),[file(hahnban,c3_3_1__hahnban)]]).

fof(e5_3_1__hahnban,plain,(
    c2_3_1__hahnban = k1_relat_1(c3_3_1__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban])],[dh_c3_3_1__hahnban,e4_3_1__hahnban]),
    [interesting(0.65),file(hahnban,e5_3_1__hahnban),[file(hahnban,e5_3_1__hahnban)]]).

fof(e6_3_1__hahnban,plain,(
    r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c3_3_1__hahnban,c1_3_1__hahnban)),c3_3_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3_1__hahnban,dt_c3_3_1__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_hahnban,d5_tarski,e3_3_1__hahnban,e5_3_1__hahnban,t8_funct_1]),
    [interesting(0.65),file(hahnban,e6_3_1__hahnban),[file(hahnban,e6_3_1__hahnban)]]).

fof(e7_3_1__hahnban,plain,(
    r2_hidden(k4_tarski(c1_3_1__hahnban,k1_funct_1(c3_3_1__hahnban,c1_3_1__hahnban)),c2_3__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_tarski,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_1__hahnban,dt_c2_3__hahnban,dt_c3_3_1__hahnban,t1_subset,t7_boole,d5_tarski,e6_3_1__hahnban,e1_3__hahnban,d4_tarski]),
    [interesting(0.65),file(hahnban,e7_3_1__hahnban),[file(hahnban,e7_3_1__hahnban)]]).

fof(e8_3_1__hahnban,plain,(
    r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_fraenkel,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_fraenkel,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_c1_3__hahnban,cc15_membered,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3_1__hahnban,dt_c2_3__hahnban,dt_c3_3_1__hahnban,t1_subset,t7_boole,d5_tarski,e7_3_1__hahnban,t8_funct_1]),
    [interesting(0.65),file(hahnban,e8_3_1__hahnban),[file(hahnban,e8_3_1__hahnban)]]).

fof(i4_3_1__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i4_3_1__hahnban)]),
    [interesting(0.65),trivial,file(hahnban,i4_3_1__hahnban)]).

fof(i3_3_1__hahnban,plain,(
    r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_1__hahnban,e2_3_1__hahnban,e1_3__hahnban])],[e8_3_1__hahnban,i4_3_1__hahnban]),
    [interesting(0.65),file(hahnban,i3_3_1__hahnban),[file(hahnban,i3_3_1__hahnban)]]).

fof(i2_3_1__hahnban,plain,
    ( ? [A] : 
        ( r2_hidden(c1_3_1__hahnban,A)
        & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) )
   => r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_1__hahnban,e1_3__hahnban]),discharge_asm(discharge,[e2_3_1__hahnban])],[e2_3_1__hahnban,i3_3_1__hahnban]),
    [interesting(0.65),file(hahnban,i2_3_1__hahnban),[file(hahnban,i2_3_1__hahnban)]]).

fof(i1_3_1__hahnban,plain,
    ( ~ ( r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban))
        & ! [A] : 
            ~ ( r2_hidden(c1_3_1__hahnban,A)
              & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) )
    & ( ? [A] : 
          ( r2_hidden(c1_3_1__hahnban,A)
          & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) )
     => r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_1__hahnban,e1_3__hahnban])],[e1_3_1__hahnban,i2_3_1__hahnban]),
    [interesting(0.65),file(hahnban,i1_3_1__hahnban),[file(hahnban,i1_3_1__hahnban)]]).

fof(i1_3_1_tmp__hahnban,plain,
    ( ~ ( r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban))
        & ! [A] : 
            ~ ( r2_hidden(c1_3_1__hahnban,A)
              & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) ) )
    & ( ? [A] : 
          ( r2_hidden(c1_3_1__hahnban,A)
          & r2_hidden(A,a_1_0_hahnban(c1_3__hahnban)) )
     => r2_hidden(c1_3_1__hahnban,k1_relat_1(c2_3__hahnban)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban]),discharge_asm(discharge,[dt_c1_3_1__hahnban])],[dt_c1_3_1__hahnban,i1_3_1__hahnban]),
    [interesting(0.8),e2_3__hahnban]).

fof(e2_3__hahnban,plain,(
    ! [A] : 
      ( ~ ( r2_hidden(A,k1_relat_1(c2_3__hahnban))
          & ! [B] : 
              ~ ( r2_hidden(A,B)
                & r2_hidden(B,a_1_0_hahnban(c1_3__hahnban)) ) )
      & ( ? [B] : 
            ( r2_hidden(A,B)
            & r2_hidden(B,a_1_0_hahnban(c1_3__hahnban)) )
       => r2_hidden(A,k1_relat_1(c2_3__hahnban)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[i1_3_1_tmp__hahnban,dh_c1_3_1__hahnban]),
    [interesting(0.8),file(hahnban,e2_3__hahnban),[file(hahnban,e2_3__hahnban)]]).

fof(e3_3__hahnban,plain,(
    k1_relat_1(c2_3__hahnban) = k3_tarski(a_1_0_hahnban(c1_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_fraenkel,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k3_tarski,dt_c1_3__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_hahnban,e2_3__hahnban,d4_tarski]),
    [interesting(0.8),file(hahnban,e3_3__hahnban),[file(hahnban,e3_3__hahnban)]]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(fraenkel_a_1_1_hahnban,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_1_1_hahnban(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k2_relat_1(C) ) ) ) ),
    file(hahnban,a_1_1_hahnban),
    [interesting(0.9),axiom,file(hahnban,a_1_1_hahnban)]).

fof(dh_c1_3_2__hahnban,definition,
    ( ( ~ ( r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban))
          & ! [A] : 
              ~ ( r2_hidden(c1_3_2__hahnban,A)
                & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) )
      & ( ? [A] : 
            ( r2_hidden(c1_3_2__hahnban,A)
            & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) )
       => r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ) )
   => ! [B] : 
        ( ~ ( r2_hidden(B,k2_relat_1(c2_3__hahnban))
            & ! [C] : 
                ~ ( r2_hidden(B,C)
                  & r2_hidden(C,a_1_1_hahnban(c1_3__hahnban)) ) )
        & ( ? [C] : 
              ( r2_hidden(B,C)
              & r2_hidden(C,a_1_1_hahnban(c1_3__hahnban)) )
         => r2_hidden(B,k2_relat_1(c2_3__hahnban)) ) ) ),
    introduced(definition,[new_symbol(c1_3_2__hahnban),file(hahnban,c1_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_3_2__hahnban)]).

fof(e1_3_2_1__hahnban,assumption,(
    r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ),
    introduced(assumption,[file(hahnban,e1_3_2_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,e1_3_2_1__hahnban)]).

fof(dt_c1_3_2__hahnban,assumption,(
    $true ),
    introduced(assumption,[file(hahnban,c1_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_3_2__hahnban)]).

fof(dh_c2_3_2_1__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(k4_tarski(c1_3_2_1__hahnban,c1_3_2__hahnban),A)
        & r2_hidden(A,c1_3__hahnban) )
   => ( r2_hidden(k4_tarski(c1_3_2_1__hahnban,c1_3_2__hahnban),c2_3_2_1__hahnban)
      & r2_hidden(c2_3_2_1__hahnban,c1_3__hahnban) ) ),
    introduced(definition,[new_symbol(c2_3_2_1__hahnban),file(hahnban,c2_3_2_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c2_3_2_1__hahnban)]).

fof(dh_c1_3_2_1__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_3__hahnban))
        & c1_3_2__hahnban = k1_funct_1(c2_3__hahnban,A) )
   => ( r2_hidden(c1_3_2_1__hahnban,k1_relat_1(c2_3__hahnban))
      & c1_3_2__hahnban = k1_funct_1(c2_3__hahnban,c1_3_2_1__hahnban) ) ),
    introduced(definition,[new_symbol(c1_3_2_1__hahnban),file(hahnban,c1_3_2_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c1_3_2_1__hahnban)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e2_3_2_1__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c2_3__hahnban))
      & c1_3_2__hahnban = k1_funct_1(c2_3__hahnban,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3_2__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,e1_3_2_1__hahnban,d5_funct_1]),
    [interesting(0.5),file(hahnban,e2_3_2_1__hahnban),[file(hahnban,e2_3_2_1__hahnban)]]).

fof(dt_c1_3_2_1__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban])],[dh_c1_3_2_1__hahnban,e2_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,c1_3_2_1__hahnban),[file(hahnban,c1_3_2_1__hahnban)]]).

fof(e3_3_2_1__hahnban,plain,
    ( r2_hidden(c1_3_2_1__hahnban,k1_relat_1(c2_3__hahnban))
    & c1_3_2__hahnban = k1_funct_1(c2_3__hahnban,c1_3_2_1__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban])],[dh_c1_3_2_1__hahnban,e2_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,e3_3_2_1__hahnban),[file(hahnban,e3_3_2_1__hahnban)]]).

fof(e4_3_2_1__hahnban,plain,(
    r2_hidden(k4_tarski(c1_3_2_1__hahnban,c1_3_2__hahnban),c2_3__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3_2__hahnban,dt_c1_3_2_1__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,d5_tarski,e3_3_2_1__hahnban,t8_funct_1]),
    [interesting(0.5),file(hahnban,e4_3_2_1__hahnban),[file(hahnban,e4_3_2_1__hahnban)]]).

fof(e5_3_2_1__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(k4_tarski(c1_3_2_1__hahnban,c1_3_2__hahnban),A)
      & r2_hidden(A,c1_3__hahnban) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c1_3_2_1__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,d5_tarski,e4_3_2_1__hahnban,e1_3__hahnban,d4_tarski]),
    [interesting(0.5),file(hahnban,e5_3_2_1__hahnban),[file(hahnban,e5_3_2_1__hahnban)]]).

fof(dt_c2_3_2_1__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[dh_c2_3_2_1__hahnban,e5_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,c2_3_2_1__hahnban),[file(hahnban,c2_3_2_1__hahnban)]]).

fof(de_c3_3_2_1__hahnban,definition,(
    c3_3_2_1__hahnban = c2_3_2_1__hahnban ),
    introduced(definition,[new_symbol(c3_3_2_1__hahnban),file(hahnban,c3_3_2_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c3_3_2_1__hahnban)]).

fof(e6_3_2_1__hahnban,plain,
    ( r2_hidden(k4_tarski(c1_3_2_1__hahnban,c1_3_2__hahnban),c2_3_2_1__hahnban)
    & r2_hidden(c2_3_2_1__hahnban,c1_3__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[dh_c2_3_2_1__hahnban,e5_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,e6_3_2_1__hahnban),[file(hahnban,e6_3_2_1__hahnban)]]).

fof(e7_3_2_1__hahnban,plain,
    ( v1_relat_1(c2_3_2_1__hahnban)
    & v1_funct_1(c2_3_2_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c1_3_2_1__hahnban,dt_c2_3_2_1__hahnban,t1_subset,t7_boole,d5_tarski,e6_3_2_1__hahnban,d1_fraenkel]),
    [interesting(0.5),file(hahnban,e7_3_2_1__hahnban),[file(hahnban,e7_3_2_1__hahnban)]]).

fof(dt_c3_3_2_1__hahnban,plain,
    ( v1_relat_1(c3_3_2_1__hahnban)
    & v1_funct_1(c3_3_2_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[dt_c2_3_2_1__hahnban,de_c3_3_2_1__hahnban,e7_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,c3_3_2_1__hahnban),[file(hahnban,c3_3_2_1__hahnban)]]).

fof(de_c4_3_2_1__hahnban,definition,(
    c4_3_2_1__hahnban = k2_relat_1(c3_3_2_1__hahnban) ),
    introduced(definition,[new_symbol(c4_3_2_1__hahnban),file(hahnban,c4_3_2_1__hahnban)]),
    [interesting(0.5),axiom,file(hahnban,c4_3_2_1__hahnban)]).

fof(dt_c4_3_2_1__hahnban,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[dt_c2_3_2_1__hahnban,dt_k2_relat_1,dt_c3_3_2_1__hahnban,de_c3_3_2_1__hahnban,de_c4_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,c4_3_2_1__hahnban),[file(hahnban,c4_3_2_1__hahnban)]]).

fof(e8_3_2_1__hahnban,plain,
    ( r2_hidden(c1_3_2_1__hahnban,k1_relat_1(c3_3_2_1__hahnban))
    & c1_3_2__hahnban = k1_funct_1(c3_3_2_1__hahnban,c1_3_2_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c1_3_2_1__hahnban,dt_c2_3_2_1__hahnban,dt_c3_3_2_1__hahnban,de_c3_3_2_1__hahnban,t1_subset,t7_boole,d5_tarski,e6_3_2_1__hahnban,t8_funct_1]),
    [interesting(0.5),file(hahnban,e8_3_2_1__hahnban),[file(hahnban,e8_3_2_1__hahnban)]]).

fof(e9_3_2_1__hahnban,plain,
    ( r2_hidden(c1_3_2__hahnban,c4_3_2_1__hahnban)
    & r2_hidden(c4_3_2_1__hahnban,a_1_1_hahnban(c1_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c1_3_2_1__hahnban,dt_c2_3_2_1__hahnban,dt_c3_3_2_1__hahnban,dt_c4_3_2_1__hahnban,de_c3_3_2_1__hahnban,de_c4_3_2_1__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_hahnban,d5_tarski,e8_3_2_1__hahnban,e6_3_2_1__hahnban,d5_funct_1]),
    [interesting(0.5),file(hahnban,e9_3_2_1__hahnban),[file(hahnban,e9_3_2_1__hahnban)]]).

fof(i3_3_2_1__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i3_3_2_1__hahnban)]),
    [interesting(0.5),trivial,file(hahnban,i3_3_2_1__hahnban)]).

fof(i2_3_2_1__hahnban,plain,
    ( r2_hidden(c1_3_2__hahnban,c4_3_2_1__hahnban)
    & r2_hidden(c4_3_2_1__hahnban,a_1_1_hahnban(c1_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[e9_3_2_1__hahnban,i3_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,i2_3_2_1__hahnban),[file(hahnban,i2_3_2_1__hahnban)]]).

fof(i1_3_2_1__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(c1_3_2__hahnban,A)
      & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) ),
    inference(take,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3_2_1__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,dt_k2_relat_1,dt_m1_subset_1,cc15_membered,cc1_fraenkel,rc1_fraenkel,antisymmetry_r2_hidden,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c4_3_2_1__hahnban,t2_tarski,fraenkel_a_1_1_hahnban,i2_3_2_1__hahnban]),
    [interesting(0.5),file(hahnban,i1_3_2_1__hahnban),[file(hahnban,i1_3_2_1__hahnban)]]).

fof(e1_3_2__hahnban,plain,(
    ~ ( r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban))
      & ! [A] : 
          ~ ( r2_hidden(c1_3_2__hahnban,A)
            & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,e1_3__hahnban]),discharge_asm(discharge,[e1_3_2_1__hahnban])],[e1_3_2_1__hahnban,i1_3_2_1__hahnban]),
    [interesting(0.65),file(hahnban,e1_3_2__hahnban),[file(hahnban,e1_3_2__hahnban)]]).

fof(e2_3_2__hahnban,assumption,(
    ? [A] : 
      ( r2_hidden(c1_3_2__hahnban,A)
      & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) ),
    introduced(assumption,[file(hahnban,e2_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,e2_3_2__hahnban)]).

fof(dh_c4_3_2__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c3_3_2__hahnban))
        & c1_3_2__hahnban = k1_funct_1(c3_3_2__hahnban,A) )
   => ( r2_hidden(c4_3_2__hahnban,k1_relat_1(c3_3_2__hahnban))
      & c1_3_2__hahnban = k1_funct_1(c3_3_2__hahnban,c4_3_2__hahnban) ) ),
    introduced(definition,[new_symbol(c4_3_2__hahnban),file(hahnban,c4_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c4_3_2__hahnban)]).

fof(dh_c2_3_2__hahnban,definition,
    ( ? [A] : 
        ( r2_hidden(c1_3_2__hahnban,A)
        & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) )
   => ( r2_hidden(c1_3_2__hahnban,c2_3_2__hahnban)
      & r2_hidden(c2_3_2__hahnban,a_1_1_hahnban(c1_3__hahnban)) ) ),
    introduced(definition,[new_symbol(c2_3_2__hahnban),file(hahnban,c2_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c2_3_2__hahnban)]).

fof(dt_c2_3_2__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e2_3_2__hahnban])],[dh_c2_3_2__hahnban,e2_3_2__hahnban]),
    [interesting(0.65),file(hahnban,c2_3_2__hahnban),[file(hahnban,c2_3_2__hahnban)]]).

fof(dh_c3_3_2__hahnban,definition,
    ( ? [A] : 
        ( m1_subset_1(A,c1_3__hahnban)
        & c2_3_2__hahnban = k2_relat_1(A) )
   => ( m1_subset_1(c3_3_2__hahnban,c1_3__hahnban)
      & c2_3_2__hahnban = k2_relat_1(c3_3_2__hahnban) ) ),
    introduced(definition,[new_symbol(c3_3_2__hahnban),file(hahnban,c3_3_2__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c3_3_2__hahnban)]).

fof(e3_3_2__hahnban,plain,
    ( r2_hidden(c1_3_2__hahnban,c2_3_2__hahnban)
    & r2_hidden(c2_3_2__hahnban,a_1_1_hahnban(c1_3__hahnban)) ),
    inference(consider,[status(thm),assumptions([e2_3_2__hahnban])],[dh_c2_3_2__hahnban,e2_3_2__hahnban]),
    [interesting(0.65),file(hahnban,e3_3_2__hahnban),[file(hahnban,e3_3_2__hahnban)]]).

fof(e4_3_2__hahnban,plain,(
    ? [A] : 
      ( m1_subset_1(A,c1_3__hahnban)
      & c2_3_2__hahnban = k2_relat_1(A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,cc15_membered,cc1_fraenkel,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3_2__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_hahnban,e3_3_2__hahnban]),
    [interesting(0.65),file(hahnban,e4_3_2__hahnban),[file(hahnban,e4_3_2__hahnban)]]).

fof(dt_c3_3_2__hahnban,plain,(
    m1_subset_1(c3_3_2__hahnban,c1_3__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[dh_c3_3_2__hahnban,e4_3_2__hahnban]),
    [interesting(0.65),file(hahnban,c3_3_2__hahnban),[file(hahnban,c3_3_2__hahnban)]]).

fof(e5_3_2__hahnban,plain,(
    c2_3_2__hahnban = k2_relat_1(c3_3_2__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[dh_c3_3_2__hahnban,e4_3_2__hahnban]),
    [interesting(0.65),file(hahnban,e5_3_2__hahnban),[file(hahnban,e5_3_2__hahnban)]]).

fof(e6_3_2__hahnban,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c3_3_2__hahnban))
      & c1_3_2__hahnban = k1_funct_1(c3_3_2__hahnban,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_fraenkel,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3_2__hahnban,dt_c3_3_2__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_hahnban,e3_3_2__hahnban,e5_3_2__hahnban,d5_funct_1]),
    [interesting(0.65),file(hahnban,e6_3_2__hahnban),[file(hahnban,e6_3_2__hahnban)]]).

fof(dt_c4_3_2__hahnban,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[dh_c4_3_2__hahnban,e6_3_2__hahnban]),
    [interesting(0.65),file(hahnban,c4_3_2__hahnban),[file(hahnban,c4_3_2__hahnban)]]).

fof(e7_3_2__hahnban,plain,
    ( r2_hidden(c4_3_2__hahnban,k1_relat_1(c3_3_2__hahnban))
    & c1_3_2__hahnban = k1_funct_1(c3_3_2__hahnban,c4_3_2__hahnban) ),
    inference(consider,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[dh_c4_3_2__hahnban,e6_3_2__hahnban]),
    [interesting(0.65),file(hahnban,e7_3_2__hahnban),[file(hahnban,e7_3_2__hahnban)]]).

fof(e8_3_2__hahnban,plain,(
    r2_hidden(k4_tarski(c4_3_2__hahnban,c1_3_2__hahnban),c3_3_2__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_fraenkel,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_fraenkel,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,dt_c1_3__hahnban,cc15_membered,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_tarski,dt_c1_3_2__hahnban,dt_c3_3_2__hahnban,dt_c4_3_2__hahnban,t1_subset,t7_boole,d5_tarski,e7_3_2__hahnban,t8_funct_1]),
    [interesting(0.65),file(hahnban,e8_3_2__hahnban),[file(hahnban,e8_3_2__hahnban)]]).

fof(e9_3_2__hahnban,plain,(
    r2_hidden(k4_tarski(c4_3_2__hahnban,c1_3_2__hahnban),c2_3__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_fraenkel,fc2_subset_1,fc3_subset_1,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_3__hahnban,dt_c1_3_2__hahnban,dt_c2_3__hahnban,dt_c3_3_2__hahnban,dt_c4_3_2__hahnban,t1_subset,t7_boole,d5_tarski,e8_3_2__hahnban,e1_3__hahnban,d4_tarski]),
    [interesting(0.65),file(hahnban,e9_3_2__hahnban),[file(hahnban,e9_3_2__hahnban)]]).

fof(t20_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k2_relat_1(C)) ) ) ) ),
    file(relat_1,t20_relat_1),
    [interesting(0.9),axiom,file(relat_1,t20_relat_1)]).

fof(e10_3_2__hahnban,plain,(
    r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k4_tarski,dt_c1_3_2__hahnban,dt_c2_3__hahnban,dt_c4_3_2__hahnban,t1_subset,t7_boole,d5_tarski,e9_3_2__hahnban,t20_relat_1]),
    [interesting(0.65),file(hahnban,e10_3_2__hahnban),[file(hahnban,e10_3_2__hahnban)]]).

fof(i4_3_2__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i4_3_2__hahnban)]),
    [interesting(0.65),trivial,file(hahnban,i4_3_2__hahnban)]).

fof(i3_3_2__hahnban,plain,(
    r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_2__hahnban,e2_3_2__hahnban,e1_3__hahnban])],[e10_3_2__hahnban,i4_3_2__hahnban]),
    [interesting(0.65),file(hahnban,i3_3_2__hahnban),[file(hahnban,i3_3_2__hahnban)]]).

fof(i2_3_2__hahnban,plain,
    ( ? [A] : 
        ( r2_hidden(c1_3_2__hahnban,A)
        & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) )
   => r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_2__hahnban,e1_3__hahnban]),discharge_asm(discharge,[e2_3_2__hahnban])],[e2_3_2__hahnban,i3_3_2__hahnban]),
    [interesting(0.65),file(hahnban,i2_3_2__hahnban),[file(hahnban,i2_3_2__hahnban)]]).

fof(i1_3_2__hahnban,plain,
    ( ~ ( r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban))
        & ! [A] : 
            ~ ( r2_hidden(c1_3_2__hahnban,A)
              & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) )
    & ( ? [A] : 
          ( r2_hidden(c1_3_2__hahnban,A)
          & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) )
     => r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,dt_c1_3_2__hahnban,e1_3__hahnban])],[e1_3_2__hahnban,i2_3_2__hahnban]),
    [interesting(0.65),file(hahnban,i1_3_2__hahnban),[file(hahnban,i1_3_2__hahnban)]]).

fof(i1_3_2_tmp__hahnban,plain,
    ( ~ ( r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban))
        & ! [A] : 
            ~ ( r2_hidden(c1_3_2__hahnban,A)
              & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) ) )
    & ( ? [A] : 
          ( r2_hidden(c1_3_2__hahnban,A)
          & r2_hidden(A,a_1_1_hahnban(c1_3__hahnban)) )
     => r2_hidden(c1_3_2__hahnban,k2_relat_1(c2_3__hahnban)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban]),discharge_asm(discharge,[dt_c1_3_2__hahnban])],[dt_c1_3_2__hahnban,i1_3_2__hahnban]),
    [interesting(0.8),e4_3__hahnban]).

fof(e4_3__hahnban,plain,(
    ! [A] : 
      ( ~ ( r2_hidden(A,k2_relat_1(c2_3__hahnban))
          & ! [B] : 
              ~ ( r2_hidden(A,B)
                & r2_hidden(B,a_1_1_hahnban(c1_3__hahnban)) ) )
      & ( ? [B] : 
            ( r2_hidden(A,B)
            & r2_hidden(B,a_1_1_hahnban(c1_3__hahnban)) )
       => r2_hidden(A,k2_relat_1(c2_3__hahnban)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[i1_3_2_tmp__hahnban,dh_c1_3_2__hahnban]),
    [interesting(0.8),file(hahnban,e4_3__hahnban),[file(hahnban,e4_3__hahnban)]]).

fof(e5_3__hahnban,plain,(
    k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_fraenkel,rc1_fraenkel,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k3_tarski,dt_c1_3__hahnban,dt_c2_3__hahnban,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_hahnban,e4_3__hahnban,d4_tarski]),
    [interesting(0.8),file(hahnban,e5_3__hahnban),[file(hahnban,e5_3__hahnban)]]).

fof(i5_3__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i5_3__hahnban)]),
    [interesting(0.8),trivial,file(hahnban,i5_3__hahnban)]).

fof(i4_3__hahnban,plain,(
    k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[e5_3__hahnban,i5_3__hahnban]),
    [interesting(0.8),file(hahnban,i4_3__hahnban),[file(hahnban,i4_3__hahnban)]]).

fof(i3_3__hahnban,plain,
    ( k1_relat_1(c2_3__hahnban) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
    & k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban,e1_3__hahnban])],[e3_3__hahnban,i4_3__hahnban]),
    [interesting(0.8),file(hahnban,i3_3__hahnban),[file(hahnban,i3_3__hahnban)]]).

fof(i2_3__hahnban,plain,
    ( c2_3__hahnban = k3_tarski(c1_3__hahnban)
   => ( k1_relat_1(c2_3__hahnban) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
      & k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__hahnban,dt_c1_3__hahnban]),discharge_asm(discharge,[e1_3__hahnban])],[e1_3__hahnban,i3_3__hahnban]),
    [interesting(0.8),file(hahnban,i2_3__hahnban),[file(hahnban,i2_3__hahnban)]]).

fof(i2_3_tmp__hahnban,plain,
    ( ( v1_relat_1(c2_3__hahnban)
      & v1_funct_1(c2_3__hahnban) )
   => ( c2_3__hahnban = k3_tarski(c1_3__hahnban)
     => ( k1_relat_1(c2_3__hahnban) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
        & k2_relat_1(c2_3__hahnban) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__hahnban]),discharge_asm(discharge,[dt_c2_3__hahnban])],[dt_c2_3__hahnban,i2_3__hahnban]),
    [interesting(0.8),i1_3__hahnban]).

fof(i1_3__hahnban,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( A = k3_tarski(c1_3__hahnban)
       => ( k1_relat_1(A) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
          & k2_relat_1(A) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__hahnban])],[i2_3_tmp__hahnban,dh_c2_3__hahnban]),
    [interesting(0.8),file(hahnban,i1_3__hahnban),[file(hahnban,i1_3__hahnban)]]).

fof(i1_3_tmp__hahnban,plain,
    ( ( ~ v1_xboole_0(c1_3__hahnban)
      & v1_fraenkel(c1_3__hahnban) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( A = k3_tarski(c1_3__hahnban)
         => ( k1_relat_1(A) = k3_tarski(a_1_0_hahnban(c1_3__hahnban))
            & k2_relat_1(A) = k3_tarski(a_1_1_hahnban(c1_3__hahnban)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__hahnban])],[dt_c1_3__hahnban,i1_3__hahnban]),
    [interesting(1),t5_hahnban]).

fof(t5_hahnban,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_tarski(A)
           => ( k1_relat_1(B) = k3_tarski(a_1_0_hahnban(A))
              & k2_relat_1(B) = k3_tarski(a_1_1_hahnban(A)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__hahnban,dh_c1_3__hahnban]),
    [interesting(1),file(hahnban,t5_hahnban),[file(hahnban,t5_hahnban)]]).