% Mizar ND problem: t4_hahnban,hahnban,55,37 
fof(dh_c1_2__hahnban,definition,
    ( ! [A,B] : 
        ( ( ~ v1_xboole_0(B)
          & m1_subset_1(B,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,A))) )
       => ( ~ v1_xboole_0(B)
          & v1_fraenkel(B) ) )
   => ! [C,D,E] : 
        ( ( ~ v1_xboole_0(E)
          & m1_subset_1(E,k1_zfmisc_1(k4_rfunct_3(C,D))) )
       => ( ~ v1_xboole_0(E)
          & v1_fraenkel(E) ) ) ),
    introduced(definition,[new_symbol(c1_2__hahnban),file(hahnban,c1_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c1_2__hahnban)]).

fof(dh_c2_2__hahnban,definition,
    ( ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
       => ( ~ v1_xboole_0(A)
          & v1_fraenkel(A) ) )
   => ! [B,C] : 
        ( ( ~ v1_xboole_0(C)
          & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,B))) )
       => ( ~ v1_xboole_0(C)
          & v1_fraenkel(C) ) ) ),
    introduced(definition,[new_symbol(c2_2__hahnban),file(hahnban,c2_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c2_2__hahnban)]).

fof(dh_c3_2__hahnban,definition,
    ( ( ( ~ v1_xboole_0(c3_2__hahnban)
        & m1_subset_1(c3_2__hahnban,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
     => ( ~ v1_xboole_0(c3_2__hahnban)
        & v1_fraenkel(c3_2__hahnban) ) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
       => ( ~ v1_xboole_0(A)
          & v1_fraenkel(A) ) ) ),
    introduced(definition,[new_symbol(c3_2__hahnban),file(hahnban,c3_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c3_2__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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(existence_m1_rfunct_3,axiom,(
    ! [A,B] : 
    ? [C] : m1_rfunct_3(C,A,B) ),
    file(rfunct_3,m1_rfunct_3),
    [interesting(0.9),axiom,file(rfunct_3,m1_rfunct_3)]).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    [interesting(0.9),axiom,file(partfun1,k4_partfun1)]).

fof(dt_m1_rfunct_3,axiom,(
    $true ),
    file(rfunct_3,m1_rfunct_3),
    [interesting(0.9),axiom,file(rfunct_3,m1_rfunct_3)]).

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(fc1_partfun1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,fc1_partfun1)]).

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(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(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(redefinition_k4_rfunct_3,definition,(
    ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ),
    file(rfunct_3,k4_rfunct_3),
    [interesting(0.9),axiom,file(rfunct_3,k4_rfunct_3)]).

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

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k4_rfunct_3,axiom,(
    ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ),
    file(rfunct_3,k4_rfunct_3),
    [interesting(0.9),axiom,file(rfunct_3,k4_rfunct_3)]).

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

fof(dt_c1_2__hahnban,assumption,(
    $true ),
    introduced(assumption,[file(hahnban,c1_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c1_2__hahnban)]).

fof(dt_c2_2__hahnban,assumption,(
    $true ),
    introduced(assumption,[file(hahnban,c2_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c2_2__hahnban)]).

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(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_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(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_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(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

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(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

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(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(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

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(dt_c3_2__hahnban,assumption,
    ( ~ v1_xboole_0(c3_2__hahnban)
    & m1_subset_1(c3_2__hahnban,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) ),
    introduced(assumption,[file(hahnban,c3_2__hahnban)]),
    [interesting(0.8),axiom,file(hahnban,c3_2__hahnban)]).

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

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(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(dt_c1_2_1__hahnban,assumption,(
    $true ),
    introduced(assumption,[file(hahnban,c1_2_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_2_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(dh_c1_2_1__hahnban,definition,
    ( ~ ( r2_hidden(c1_2_1__hahnban,c3_2__hahnban)
        & ~ ( v1_relat_1(c1_2_1__hahnban)
            & v1_funct_1(c1_2_1__hahnban) ) )
   => ! [A] : 
        ~ ( r2_hidden(A,c3_2__hahnban)
          & ~ ( v1_relat_1(A)
              & v1_funct_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_2_1__hahnban),file(hahnban,c1_2_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,c1_2_1__hahnban)]).

fof(e1_2_1__hahnban,assumption,(
    r2_hidden(c1_2_1__hahnban,c3_2__hahnban) ),
    introduced(assumption,[file(hahnban,e1_2_1__hahnban)]),
    [interesting(0.65),axiom,file(hahnban,e1_2_1__hahnban)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(t120_partfun1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,k4_partfun1(A,B))
     => ( v1_funct_1(C)
        & m2_relset_1(C,A,B) ) ) ),
    file(partfun1,t120_partfun1),
    [interesting(0.9),axiom,file(partfun1,t120_partfun1)]).

fof(e2_2_1__hahnban,plain,
    ( v1_relat_1(c1_2_1__hahnban)
    & v1_funct_1(c1_2_1__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c1_2_1__hahnban,dt_c3_2__hahnban,e1_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,reflexivity_r1_tarski,existence_m1_rfunct_3,dt_k1_xboole_0,dt_m1_rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t8_boole,existence_m1_relset_1,existence_m1_subset_1,redefinition_k4_rfunct_3,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_rfunct_3,dt_m1_relset_1,dt_m1_subset_1,dt_c1_2__hahnban,dt_c2_2__hahnban,cc15_membered,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k4_partfun1,dt_m2_relset_1,dt_c1_2_1__hahnban,dt_c3_2__hahnban,fc1_partfun1,t1_subset,t7_boole,e1_2_1__hahnban,t120_partfun1]),
    [interesting(0.65),file(hahnban,e2_2_1__hahnban),[file(hahnban,e2_2_1__hahnban)]]).

fof(i3_2_1__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i3_2_1__hahnban)]),
    [interesting(0.65),trivial,file(hahnban,i3_2_1__hahnban)]).

fof(i2_2_1__hahnban,plain,
    ( v1_relat_1(c1_2_1__hahnban)
    & v1_funct_1(c1_2_1__hahnban) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c1_2_1__hahnban,dt_c3_2__hahnban,e1_2_1__hahnban])],[e2_2_1__hahnban,i3_2_1__hahnban]),
    [interesting(0.65),file(hahnban,i2_2_1__hahnban),[file(hahnban,i2_2_1__hahnban)]]).

fof(i1_2_1__hahnban,plain,(
    ~ ( r2_hidden(c1_2_1__hahnban,c3_2__hahnban)
      & ~ ( v1_relat_1(c1_2_1__hahnban)
          & v1_funct_1(c1_2_1__hahnban) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c1_2_1__hahnban,dt_c3_2__hahnban]),discharge_asm(discharge,[e1_2_1__hahnban])],[e1_2_1__hahnban,i2_2_1__hahnban]),
    [interesting(0.65),file(hahnban,i1_2_1__hahnban),[file(hahnban,i1_2_1__hahnban)]]).

fof(i1_2_1_tmp__hahnban,plain,(
    ~ ( r2_hidden(c1_2_1__hahnban,c3_2__hahnban)
      & ~ ( v1_relat_1(c1_2_1__hahnban)
          & v1_funct_1(c1_2_1__hahnban) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c3_2__hahnban]),discharge_asm(discharge,[dt_c1_2_1__hahnban])],[dt_c1_2_1__hahnban,i1_2_1__hahnban]),
    [interesting(0.8),e1_2__hahnban]).

fof(e1_2__hahnban,plain,(
    v1_fraenkel(c3_2__hahnban) ),
    inference(let,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c3_2__hahnban])],[i1_2_1_tmp__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_k4_partfun1,dt_m1_rfunct_3,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_partfun1,rc1_membered,redefinition_k4_rfunct_3,dt_k1_zfmisc_1,dt_k4_rfunct_3,dt_m1_subset_1,dt_c1_2__hahnban,dt_c2_2__hahnban,cc15_membered,cc1_fraenkel,fc1_subset_1,rc1_fraenkel,rc1_subset_1,rc2_subset_1,antisymmetry_r2_hidden,dt_c3_2__hahnban,d1_fraenkel,dh_c1_2_1__hahnban]),
    [interesting(0.8),file(hahnban,e1_2__hahnban),[file(hahnban,e1_2__hahnban)]]).

fof(e2_2__hahnban,plain,
    ( ~ v1_xboole_0(c3_2__hahnban)
    & v1_fraenkel(c3_2__hahnban) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c3_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,reflexivity_r1_tarski,existence_m1_rfunct_3,dt_k4_partfun1,dt_m1_rfunct_3,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc1_partfun1,rc1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_rfunct_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_rfunct_3,dt_m1_subset_1,dt_c1_2__hahnban,dt_c2_2__hahnban,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_fraenkel,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc1_subset_1,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,dt_c3_2__hahnban,cc15_membered,rc1_fraenkel,t6_boole,t7_boole,e1_2__hahnban]),
    [interesting(0.8),file(hahnban,e2_2__hahnban),[file(hahnban,e2_2__hahnban)]]).

fof(i3_2__hahnban,theorem,(
    $true ),
    introduced(tautology,[file(hahnban,i3_2__hahnban)]),
    [interesting(0.8),trivial,file(hahnban,i3_2__hahnban)]).

fof(i2_2__hahnban,plain,
    ( ~ v1_xboole_0(c3_2__hahnban)
    & v1_fraenkel(c3_2__hahnban) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban,dt_c3_2__hahnban])],[e2_2__hahnban,i3_2__hahnban]),
    [interesting(0.8),file(hahnban,i2_2__hahnban),[file(hahnban,i2_2__hahnban)]]).

fof(i2_2_tmp__hahnban,plain,
    ( ( ~ v1_xboole_0(c3_2__hahnban)
      & m1_subset_1(c3_2__hahnban,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
   => ( ~ v1_xboole_0(c3_2__hahnban)
      & v1_fraenkel(c3_2__hahnban) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban]),discharge_asm(discharge,[dt_c3_2__hahnban])],[dt_c3_2__hahnban,i2_2__hahnban]),
    [interesting(0.8),i1_2__hahnban]).

fof(i1_2__hahnban,plain,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
     => ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__hahnban,dt_c2_2__hahnban])],[i2_2_tmp__hahnban,dh_c3_2__hahnban]),
    [interesting(0.8),file(hahnban,i1_2__hahnban),[file(hahnban,i1_2__hahnban)]]).

fof(i1_2_tmp__hahnban,plain,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k4_rfunct_3(c1_2__hahnban,c2_2__hahnban))) )
     => ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__hahnban,dt_c2_2__hahnban])],[dt_c1_2__hahnban,dt_c2_2__hahnban,i1_2__hahnban]),
    [interesting(1),t4_hahnban]).

fof(t4_hahnban,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) )
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__hahnban,dh_c1_2__hahnban,dh_c2_2__hahnban]),
    [interesting(1),file(hahnban,t4_hahnban),[file(hahnban,t4_hahnban)]]).