% Mizar ND problem: t3_seq_1,seq_1,39,76 
fof(dh_c1_2__seq_1,definition,
    ( ( ( v1_relat_1(c1_2__seq_1)
        & v1_funct_1(c1_2__seq_1) )
     => ( ( v1_funct_1(c1_2__seq_1)
          & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
          & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) )
      <=> ( k1_relat_1(c1_2__seq_1) = k5_numbers
          & ! [A] : 
              ( r2_hidden(A,k5_numbers)
             => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,k1_numbers)
            & m2_relset_1(B,k5_numbers,k1_numbers) )
        <=> ( k1_relat_1(B) = k5_numbers
            & ! [C] : 
                ( r2_hidden(C,k5_numbers)
               => v1_xreal_0(k1_funct_1(B,C)) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__seq_1),file(seq_1,c1_2__seq_1)]),
    [interesting(0.8),axiom,file(seq_1,c1_2__seq_1)]).

fof(e1_2_1__seq_1,assumption,
    ( v1_funct_1(c1_2__seq_1)
    & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
    & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) ),
    introduced(assumption,[file(seq_1,e1_2_1__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,e1_2_1__seq_1)]).

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(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(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(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(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(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(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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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(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(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(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_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

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(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(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_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(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(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(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(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_k4_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

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(dt_c1_2__seq_1,assumption,
    ( v1_relat_1(c1_2__seq_1)
    & v1_funct_1(c1_2__seq_1) ),
    introduced(assumption,[file(seq_1,c1_2__seq_1)]),
    [interesting(0.8),axiom,file(seq_1,c1_2__seq_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_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(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(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(e2_2_1__seq_1,plain,(
    k1_relat_1(c1_2__seq_1) = k5_numbers ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__seq_1,e1_2_1__seq_1])],[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,antisymmetry_r2_hidden,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_membered,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_2__seq_1,fc2_membered,fc6_membered,t6_boole,e1_2_1__seq_1,d1_funct_2]),
    [interesting(0.65),file(seq_1,e2_2_1__seq_1),[file(seq_1,e2_2_1__seq_1)]]).

fof(dh_c1_2_1__seq_1,definition,
    ( ( r2_hidden(c1_2_1__seq_1,k5_numbers)
     => v1_xreal_0(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1)) )
   => ! [A] : 
        ( r2_hidden(A,k5_numbers)
       => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ),
    introduced(definition,[new_symbol(c1_2_1__seq_1),file(seq_1,c1_2_1__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,c1_2_1__seq_1)]).

fof(e4_2_1__seq_1,assumption,(
    r2_hidden(c1_2_1__seq_1,k5_numbers) ),
    introduced(assumption,[file(seq_1,e4_2_1__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,e4_2_1__seq_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_c1_2_1__seq_1,assumption,(
    $true ),
    introduced(assumption,[file(seq_1,c1_2_1__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,c1_2_1__seq_1)]).

fof(d1_xreal_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,d1_xreal_0)]).

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

fof(e5_2_1__seq_1,plain,(
    r2_hidden(c1_2_1__seq_1,k1_relat_1(c1_2__seq_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_1__seq_1,e4_2_1__seq_1,e1_2_1__seq_1])],[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,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_membered,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_2__seq_1,dt_c1_2_1__seq_1,fc2_membered,fc6_membered,t1_subset,t6_boole,t7_boole,e4_2_1__seq_1,e1_2_1__seq_1,d1_funct_2]),
    [interesting(0.65),file(seq_1,e5_2_1__seq_1),[file(seq_1,e5_2_1__seq_1)]]).

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(e6_2_1__seq_1,plain,(
    r2_hidden(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1),k2_relat_1(c1_2__seq_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_1__seq_1,e4_2_1__seq_1,e1_2_1__seq_1])],[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_2__seq_1,dt_c1_2_1__seq_1,t1_subset,t7_boole,e5_2_1__seq_1,d5_funct_1]),
    [interesting(0.65),file(seq_1,e6_2_1__seq_1),[file(seq_1,e6_2_1__seq_1)]]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.9),axiom,file(relset_1,t12_relset_1)]).

fof(e3_2_1__seq_1,plain,(
    r1_tarski(k2_relat_1(c1_2__seq_1),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__seq_1,e1_2_1__seq_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc6_membered,rc1_membered,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_relat_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_2__seq_1,fc2_membered,t3_subset,e1_2_1__seq_1,t12_relset_1]),
    [interesting(0.65),file(seq_1,e3_2_1__seq_1),[file(seq_1,e3_2_1__seq_1)]]).

fof(e7_2_1__seq_1,plain,(
    r2_hidden(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__seq_1,e4_2_1__seq_1,dt_c1_2__seq_1,e1_2_1__seq_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc6_membered,rc1_membered,rc1_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_numbers,dt_k2_relat_1,dt_c1_2__seq_1,dt_c1_2_1__seq_1,fc2_membered,t1_subset,t3_subset,t7_boole,e6_2_1__seq_1,e3_2_1__seq_1]),
    [interesting(0.65),file(seq_1,e7_2_1__seq_1),[file(seq_1,e7_2_1__seq_1)]]).

fof(i5_2_1__seq_1,theorem,(
    $true ),
    introduced(tautology,[file(seq_1,i5_2_1__seq_1)]),
    [interesting(0.65),trivial,file(seq_1,i5_2_1__seq_1)]).

fof(i4_2_1__seq_1,plain,(
    v1_xreal_0(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2_1__seq_1,e4_2_1__seq_1,dt_c1_2__seq_1,e1_2_1__seq_1])],[cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc15_membered,cc4_membered,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_numbers,dt_c1_2__seq_1,dt_c1_2_1__seq_1,cc2_xreal_0,fc2_membered,d1_xreal_0,e7_2_1__seq_1,i5_2_1__seq_1]),
    [interesting(0.65),file(seq_1,i4_2_1__seq_1),[file(seq_1,i4_2_1__seq_1)]]).

fof(i3_2_1__seq_1,plain,
    ( r2_hidden(c1_2_1__seq_1,k5_numbers)
   => v1_xreal_0(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__seq_1,dt_c1_2__seq_1,e1_2_1__seq_1]),discharge_asm(discharge,[e4_2_1__seq_1])],[e4_2_1__seq_1,i4_2_1__seq_1]),
    [interesting(0.65),file(seq_1,i3_2_1__seq_1),[file(seq_1,i3_2_1__seq_1)]]).

fof(i3_2_1_tmp__seq_1,plain,
    ( r2_hidden(c1_2_1__seq_1,k5_numbers)
   => v1_xreal_0(k1_funct_1(c1_2__seq_1,c1_2_1__seq_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__seq_1,e1_2_1__seq_1]),discharge_asm(discharge,[dt_c1_2_1__seq_1])],[dt_c1_2_1__seq_1,i3_2_1__seq_1]),
    [interesting(0.65),i2_2_1__seq_1]).

fof(i2_2_1__seq_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k5_numbers)
     => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__seq_1,e1_2_1__seq_1])],[i3_2_1_tmp__seq_1,dh_c1_2_1__seq_1]),
    [interesting(0.65),file(seq_1,i2_2_1__seq_1),[file(seq_1,i2_2_1__seq_1)]]).

fof(i1_2_1__seq_1,plain,
    ( k1_relat_1(c1_2__seq_1) = k5_numbers
    & ! [A] : 
        ( r2_hidden(A,k5_numbers)
       => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__seq_1,e1_2_1__seq_1])],[e2_2_1__seq_1,i2_2_1__seq_1]),
    [interesting(0.65),file(seq_1,i1_2_1__seq_1),[file(seq_1,i1_2_1__seq_1)]]).

fof(e1_2__seq_1,plain,
    ( ( v1_funct_1(c1_2__seq_1)
      & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
      & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) )
   => ( k1_relat_1(c1_2__seq_1) = k5_numbers
      & ! [A] : 
          ( r2_hidden(A,k5_numbers)
         => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__seq_1]),discharge_asm(discharge,[e1_2_1__seq_1])],[e1_2_1__seq_1,i1_2_1__seq_1]),
    [interesting(0.8),file(seq_1,e1_2__seq_1),[file(seq_1,e1_2__seq_1)]]).

fof(e2_2__seq_1,assumption,(
    k1_relat_1(c1_2__seq_1) = k5_numbers ),
    introduced(assumption,[file(seq_1,e2_2__seq_1)]),
    [interesting(0.8),axiom,file(seq_1,e2_2__seq_1)]).

fof(e3_2__seq_1,assumption,(
    ! [A] : 
      ( r2_hidden(A,k5_numbers)
     => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ),
    introduced(assumption,[file(seq_1,e3_2__seq_1)]),
    [interesting(0.8),axiom,file(seq_1,e3_2__seq_1)]).

fof(dh_c1_2_2__seq_1,definition,
    ( ( r2_hidden(c1_2_2__seq_1,k2_relat_1(c1_2__seq_1))
     => r2_hidden(c1_2_2__seq_1,k1_numbers) )
   => ! [A] : 
        ( r2_hidden(A,k2_relat_1(c1_2__seq_1))
       => r2_hidden(A,k1_numbers) ) ),
    introduced(definition,[new_symbol(c1_2_2__seq_1),file(seq_1,c1_2_2__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,c1_2_2__seq_1)]).

fof(e1_2_2__seq_1,assumption,(
    r2_hidden(c1_2_2__seq_1,k2_relat_1(c1_2__seq_1)) ),
    introduced(assumption,[file(seq_1,e1_2_2__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,e1_2_2__seq_1)]).

fof(dt_c1_2_2__seq_1,assumption,(
    $true ),
    introduced(assumption,[file(seq_1,c1_2_2__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,c1_2_2__seq_1)]).

fof(dh_c2_2_2__seq_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_2__seq_1))
        & c1_2_2__seq_1 = k1_funct_1(c1_2__seq_1,A) )
   => ( r2_hidden(c2_2_2__seq_1,k1_relat_1(c1_2__seq_1))
      & c1_2_2__seq_1 = k1_funct_1(c1_2__seq_1,c2_2_2__seq_1) ) ),
    introduced(definition,[new_symbol(c2_2_2__seq_1),file(seq_1,c2_2_2__seq_1)]),
    [interesting(0.65),axiom,file(seq_1,c2_2_2__seq_1)]).

fof(e2_2_2__seq_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_2__seq_1))
      & c1_2_2__seq_1 = k1_funct_1(c1_2__seq_1,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[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_2__seq_1,dt_c1_2_2__seq_1,t1_subset,t7_boole,e1_2_2__seq_1,d5_funct_1]),
    [interesting(0.65),file(seq_1,e2_2_2__seq_1),[file(seq_1,e2_2_2__seq_1)]]).

fof(dt_c2_2_2__seq_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[dh_c2_2_2__seq_1,e2_2_2__seq_1]),
    [interesting(0.65),file(seq_1,c2_2_2__seq_1),[file(seq_1,c2_2_2__seq_1)]]).

fof(e3_2_2__seq_1,plain,(
    r2_hidden(c2_2_2__seq_1,k1_relat_1(c1_2__seq_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[dh_c2_2_2__seq_1,e2_2_2__seq_1]),
    [interesting(0.65),file(seq_1,e3_2_2__seq_1),[file(seq_1,e3_2_2__seq_1)]]).

fof(e5_2_2__seq_1,plain,(
    v1_xreal_0(k1_funct_1(c1_2__seq_1,c2_2_2__seq_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[cc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,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,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc15_membered,cc6_membered,cc7_xreal_0,cc9_membered,fc1_ordinal2,fc2_membered,fc5_membered,rc1_xreal_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_numbers,dt_k1_funct_1,dt_k1_relat_1,dt_k5_numbers,dt_c1_2__seq_1,dt_c2_2_2__seq_1,cc2_xreal_0,t1_subset,t7_boole,e2_2__seq_1,e3_2__seq_1,e3_2_2__seq_1]),
    [interesting(0.65),file(seq_1,e5_2_2__seq_1),[file(seq_1,e5_2_2__seq_1)]]).

fof(e4_2_2__seq_1,plain,(
    c1_2_2__seq_1 = k1_funct_1(c1_2__seq_1,c2_2_2__seq_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[dh_c2_2_2__seq_1,e2_2_2__seq_1]),
    [interesting(0.65),file(seq_1,e4_2_2__seq_1),[file(seq_1,e4_2_2__seq_1)]]).

fof(e6_2_2__seq_1,plain,(
    r2_hidden(c1_2_2__seq_1,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[cc1_xreal_0,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc4_membered,cc7_xreal_0,rc1_xreal_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_numbers,dt_c1_2__seq_1,dt_c1_2_2__seq_1,dt_c2_2_2__seq_1,cc2_xreal_0,fc2_membered,t1_subset,t7_boole,e5_2_2__seq_1,e4_2_2__seq_1,d1_xreal_0]),
    [interesting(0.65),file(seq_1,e6_2_2__seq_1),[file(seq_1,e6_2_2__seq_1)]]).

fof(i3_2_2__seq_1,theorem,(
    $true ),
    introduced(tautology,[file(seq_1,i3_2_2__seq_1)]),
    [interesting(0.65),trivial,file(seq_1,i3_2_2__seq_1)]).

fof(i2_2_2__seq_1,plain,(
    r2_hidden(c1_2_2__seq_1,k1_numbers) ),
    inference(conclusion,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1,dt_c1_2_2__seq_1,e1_2_2__seq_1])],[e6_2_2__seq_1,i3_2_2__seq_1]),
    [interesting(0.65),file(seq_1,i2_2_2__seq_1),[file(seq_1,i2_2_2__seq_1)]]).

fof(i1_2_2__seq_1,plain,
    ( r2_hidden(c1_2_2__seq_1,k2_relat_1(c1_2__seq_1))
   => r2_hidden(c1_2_2__seq_1,k1_numbers) ),
    inference(discharge_asm,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1,dt_c1_2_2__seq_1]),discharge_asm(discharge,[e1_2_2__seq_1])],[e1_2_2__seq_1,i2_2_2__seq_1]),
    [interesting(0.65),file(seq_1,i1_2_2__seq_1),[file(seq_1,i1_2_2__seq_1)]]).

fof(i1_2_2_tmp__seq_1,plain,
    ( r2_hidden(c1_2_2__seq_1,k2_relat_1(c1_2__seq_1))
   => r2_hidden(c1_2_2__seq_1,k1_numbers) ),
    inference(discharge_asm,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1]),discharge_asm(discharge,[dt_c1_2_2__seq_1])],[dt_c1_2_2__seq_1,i1_2_2__seq_1]),
    [interesting(0.8),e4_2__seq_1]).

fof(e4_2__seq_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_relat_1(c1_2__seq_1))
     => r2_hidden(A,k1_numbers) ) ),
    inference(let,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1])],[i1_2_2_tmp__seq_1,dh_c1_2_2__seq_1]),
    [interesting(0.8),file(seq_1,e4_2__seq_1),[file(seq_1,e4_2__seq_1)]]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(e5_2__seq_1,plain,(
    r1_tarski(k2_relat_1(c1_2__seq_1),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e2_2__seq_1,e3_2__seq_1,dt_c1_2__seq_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc6_membered,rc1_membered,rc1_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc4_membered,cc6_membered,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k2_relat_1,dt_c1_2__seq_1,fc2_membered,t1_subset,t3_subset,t7_boole,e4_2__seq_1,d3_tarski]),
    [interesting(0.8),file(seq_1,e5_2__seq_1),[file(seq_1,e5_2__seq_1)]]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.9),axiom,file(relset_1,t11_relset_1)]).

fof(e6_2__seq_1,plain,
    ( v1_funct_1(c1_2__seq_1)
    & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
    & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e3_2__seq_1,dt_c1_2__seq_1,e2_2__seq_1])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,antisymmetry_r2_hidden,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_ordinal2,fc5_membered,rc1_membered,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k4_relset_1,dt_k5_numbers,dt_m2_relset_1,dt_c1_2__seq_1,fc2_membered,fc6_membered,t3_subset,t6_boole,e5_2__seq_1,e2_2__seq_1,d1_funct_2,t11_relset_1]),
    [interesting(0.8),file(seq_1,e6_2__seq_1),[file(seq_1,e6_2__seq_1)]]).

fof(i4_2__seq_1,theorem,(
    $true ),
    introduced(tautology,[file(seq_1,i4_2__seq_1)]),
    [interesting(0.8),trivial,file(seq_1,i4_2__seq_1)]).

fof(i3_2__seq_1,plain,
    ( v1_funct_1(c1_2__seq_1)
    & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
    & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) ),
    inference(conclusion,[status(thm),assumptions([e3_2__seq_1,dt_c1_2__seq_1,e2_2__seq_1])],[e6_2__seq_1,i4_2__seq_1]),
    [interesting(0.8),file(seq_1,i3_2__seq_1),[file(seq_1,i3_2__seq_1)]]).

fof(i2_2__seq_1,plain,
    ( ( k1_relat_1(c1_2__seq_1) = k5_numbers
      & ! [A] : 
          ( r2_hidden(A,k5_numbers)
         => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) )
   => ( v1_funct_1(c1_2__seq_1)
      & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
      & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__seq_1]),discharge_asm(discharge,[e2_2__seq_1,e3_2__seq_1])],[e2_2__seq_1,e3_2__seq_1,i3_2__seq_1]),
    [interesting(0.8),file(seq_1,i2_2__seq_1),[file(seq_1,i2_2__seq_1)]]).

fof(i1_2__seq_1,plain,
    ( ( v1_funct_1(c1_2__seq_1)
      & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
      & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) )
  <=> ( k1_relat_1(c1_2__seq_1) = k5_numbers
      & ! [A] : 
          ( r2_hidden(A,k5_numbers)
         => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_2__seq_1])],[e1_2__seq_1,i2_2__seq_1]),
    [interesting(0.8),file(seq_1,i1_2__seq_1),[file(seq_1,i1_2__seq_1)]]).

fof(i1_2_tmp__seq_1,plain,
    ( ( v1_relat_1(c1_2__seq_1)
      & v1_funct_1(c1_2__seq_1) )
   => ( ( v1_funct_1(c1_2__seq_1)
        & v1_funct_2(c1_2__seq_1,k5_numbers,k1_numbers)
        & m2_relset_1(c1_2__seq_1,k5_numbers,k1_numbers) )
    <=> ( k1_relat_1(c1_2__seq_1) = k5_numbers
        & ! [A] : 
            ( r2_hidden(A,k5_numbers)
           => v1_xreal_0(k1_funct_1(c1_2__seq_1,A)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__seq_1])],[dt_c1_2__seq_1,i1_2__seq_1]),
    [interesting(1),t3_seq_1]).

fof(t3_seq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ( v1_funct_1(A)
          & v1_funct_2(A,k5_numbers,k1_numbers)
          & m2_relset_1(A,k5_numbers,k1_numbers) )
      <=> ( k1_relat_1(A) = k5_numbers
          & ! [B] : 
              ( r2_hidden(B,k5_numbers)
             => v1_xreal_0(k1_funct_1(A,B)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__seq_1,dh_c1_2__seq_1]),
    [interesting(1),file(seq_1,t3_seq_1),[file(seq_1,t3_seq_1)]]).