% Mizar problem: t120_limfunc1,limfunc1,2547,36 
fof(t120_limfunc1,conjecture,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
       => ( v3_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A))
          & k5_limfunc1(k21_seq_1(k1_numbers,k1_numbers,A)) = k18_complex1(k5_limfunc1(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc1_seq_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_membered,cc2_xreal_0,cc3_arytm_3,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,connectedness_r1_xreal_0,d10_seq_1,d12_limfunc1,d6_limfunc1,dt_k15_seq_1,dt_k16_complex1,dt_k16_seq_1,dt_k17_seq_1,dt_k18_complex1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_rfunct_2,dt_k1_seq_1,dt_k1_seq_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_seq_1,dt_k21_seq_1,dt_k22_seq_1,dt_k2_relat_1,dt_k2_rfunct_2,dt_k2_seq_2,dt_k2_zfmisc_1,dt_k4_relset_1,dt_k5_limfunc1,dt_k5_numbers,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_ordinal2,fc1_seq_1,fc2_membered,fc5_membered,fc6_membered,fc7_seq_1,fc8_seq_1,projectivity_k16_complex1,projectivity_k18_complex1,rc1_arytm_3,rc1_membered,rc1_seq_1,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_k16_seq_1,redefinition_k17_seq_1,redefinition_k18_complex1,redefinition_k1_rfunct_2,redefinition_k1_seq_1,redefinition_k21_seq_1,redefinition_k22_seq_1,redefinition_k2_seq_2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,t1_real,t1_subset,t25_rfunct_2,t26_seq_4,t27_seq_4,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(limfunc1,t120_limfunc1)]).

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

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

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

fof(cc12_membered,axiom,(
    ! [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),
    []).

fof(cc13_membered,axiom,(
    ! [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),
    []).

fof(cc14_membered,axiom,(
    ! [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),
    []).

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

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

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

fof(cc18_membered,axiom,(
    ! [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),
    []).

fof(cc19_membered,axiom,(
    ! [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),
    []).

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

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

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

fof(cc1_seq_1,axiom,(
    ! [A,B] : 
      ( v2_membered(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( v1_funct_1(C)
           => ( v1_funct_1(C)
              & v1_seq_1(C) ) ) ) ) ),
    file(seq_1,cc1_seq_1),
    []).

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

fof(cc20_membered,axiom,(
    ! [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),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

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

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

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

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

fof(cc3_xreal_0,axiom,(
    ! [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),
    []).

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

fof(cc4_xreal_0,axiom,(
    ! [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),
    []).

fof(cc5_xreal_0,axiom,(
    ! [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),
    []).

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

fof(cc6_xreal_0,axiom,(
    ! [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),
    []).

fof(cc7_xreal_0,axiom,(
    ! [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),
    []).

fof(cc8_xreal_0,axiom,(
    ! [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),
    []).

fof(cc9_membered,axiom,(
    ! [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),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d10_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k20_seq_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => k1_funct_1(B,C) = k18_complex1(k1_seq_1(A,C)) ) ) ) ) ) ),
    file(seq_1,d10_seq_1),
    []).

fof(d12_limfunc1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
       => ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ( B = k5_limfunc1(A)
            <=> ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( v1_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) ),
    file(limfunc1,d12_limfunc1),
    []).

fof(d6_limfunc1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( v3_limfunc1(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,k1_numbers)
             => ? [C] : 
                  ( m1_subset_1(C,k1_numbers)
                  & ~ r1_xreal_0(C,B)
                  & r2_hidden(C,k4_relset_1(k1_numbers,k1_numbers,A)) ) )
          & ? [B] : 
              ( m1_subset_1(B,k1_numbers)
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,k5_numbers,k1_numbers)
                    & m2_relset_1(C,k5_numbers,k1_numbers) )
                 => ( ( v1_limfunc1(C)
                      & r1_tarski(k1_rfunct_2(C),k4_relset_1(k1_numbers,k1_numbers,A)) )
                   => ( v4_seq_2(k2_rfunct_2(A,C))
                      & k2_seq_2(k2_rfunct_2(A,C)) = B ) ) ) ) ) ) ) ),
    file(limfunc1,d6_limfunc1),
    []).

fof(dt_k15_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k15_seq_1(A))
        & v1_funct_1(k15_seq_1(A)) ) ) ),
    file(seq_1,k15_seq_1),
    []).

fof(dt_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k16_complex1(A)) ) ),
    file(complex1,k16_complex1),
    []).

fof(dt_k16_seq_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k16_seq_1(A,B,C))
        & m2_relset_1(k16_seq_1(A,B,C),A,k1_numbers) ) ) ),
    file(seq_1,k16_seq_1),
    []).

fof(dt_k17_seq_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k17_seq_1(A))
        & v1_funct_2(k17_seq_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k17_seq_1(A),k5_numbers,k1_numbers) ) ) ),
    file(seq_1,k17_seq_1),
    []).

fof(dt_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => m1_subset_1(k18_complex1(A),k1_numbers) ) ),
    file(complex1,k18_complex1),
    []).

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

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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

fof(dt_k1_rfunct_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k1_rfunct_2(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(rfunct_2,k1_rfunct_2),
    []).

fof(dt_k1_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => m1_subset_1(k1_seq_1(A,B),k1_numbers) ) ),
    file(seq_1,k1_seq_1),
    []).

fof(dt_k1_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => v1_xreal_0(k1_seq_2(A)) ) ),
    file(seq_2,k1_seq_2),
    []).

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

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

fof(dt_k20_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k20_seq_1(A))
        & v1_funct_1(k20_seq_1(A)) ) ) ),
    file(seq_1,k20_seq_1),
    []).

fof(dt_k21_seq_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k21_seq_1(A,B,C))
        & m2_relset_1(k21_seq_1(A,B,C),A,k1_numbers) ) ) ),
    file(seq_1,k21_seq_1),
    []).

fof(dt_k22_seq_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k22_seq_1(A))
        & v1_funct_2(k22_seq_1(A),k5_numbers,k1_numbers)
        & m2_relset_1(k22_seq_1(A),k5_numbers,k1_numbers) ) ) ),
    file(seq_1,k22_seq_1),
    []).

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

fof(dt_k2_rfunct_2,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers)
        & v1_funct_1(B)
        & v1_funct_2(B,k5_numbers,k1_numbers)
        & m1_relset_1(B,k5_numbers,k1_numbers) )
     => ( v1_funct_1(k2_rfunct_2(A,B))
        & v1_funct_2(k2_rfunct_2(A,B),k5_numbers,k1_numbers)
        & m2_relset_1(k2_rfunct_2(A,B),k5_numbers,k1_numbers) ) ) ),
    file(rfunct_2,k2_rfunct_2),
    []).

fof(dt_k2_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => m1_subset_1(k2_seq_2(A),k1_numbers) ) ),
    file(seq_2,k2_seq_2),
    []).

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

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),
    []).

fof(dt_k5_limfunc1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & m1_relset_1(A,k1_numbers,k1_numbers) )
     => m1_subset_1(k5_limfunc1(A),k1_numbers) ) ),
    file(limfunc1,k5_limfunc1),
    []).

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

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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),
    []).

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

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

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

fof(fc1_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_xcmplx_0(k1_funct_1(A,B))
        & v1_xreal_0(k1_funct_1(A,B)) ) ) ),
    file(seq_1,fc1_seq_1),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( 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),
    []).

fof(fc7_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k15_seq_1(A))
        & v1_funct_1(k15_seq_1(A))
        & v1_seq_1(k15_seq_1(A)) ) ) ),
    file(seq_1,fc7_seq_1),
    []).

fof(fc8_seq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => ( v1_relat_1(k20_seq_1(A))
        & v1_funct_1(k20_seq_1(A))
        & v1_seq_1(k20_seq_1(A)) ) ) ),
    file(seq_1,fc8_seq_1),
    []).

fof(projectivity_k16_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k16_complex1(k16_complex1(A)) = k16_complex1(A) ) ),
    file(complex1,k16_complex1),
    []).

fof(projectivity_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(k18_complex1(A)) = k18_complex1(A) ) ),
    file(complex1,k18_complex1),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

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

fof(rc1_seq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_seq_1(A) ) ),
    file(seq_1,rc1_seq_1),
    []).

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

fof(rc2_xreal_0,axiom,(
    ? [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),
    []).

fof(rc3_xreal_0,axiom,(
    ? [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),
    []).

fof(rc4_xreal_0,axiom,(
    ? [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),
    []).

fof(redefinition_k16_seq_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k16_seq_1(A,B,C) = k15_seq_1(C) ) ),
    file(seq_1,k16_seq_1),
    []).

fof(redefinition_k17_seq_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k17_seq_1(A) = k15_seq_1(A) ) ),
    file(seq_1,k17_seq_1),
    []).

fof(redefinition_k18_complex1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k18_complex1(A) = k16_complex1(A) ) ),
    file(complex1,k18_complex1),
    []).

fof(redefinition_k1_rfunct_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k1_rfunct_2(A) = k2_relat_1(A) ) ),
    file(rfunct_2,k1_rfunct_2),
    []).

fof(redefinition_k1_seq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A) )
     => k1_seq_1(A,B) = k1_funct_1(A,B) ) ),
    file(seq_1,k1_seq_1),
    []).

fof(redefinition_k21_seq_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k21_seq_1(A,B,C) = k20_seq_1(C) ) ),
    file(seq_1,k21_seq_1),
    []).

fof(redefinition_k22_seq_1,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k22_seq_1(A) = k20_seq_1(A) ) ),
    file(seq_1,k22_seq_1),
    []).

fof(redefinition_k2_seq_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m1_relset_1(A,k5_numbers,k1_numbers) )
     => k2_seq_2(A) = k1_seq_2(A) ) ),
    file(seq_2,k2_seq_2),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [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),
    []).

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

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

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

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

fof(t25_rfunct_2,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k1_numbers,k1_numbers) )
         => ( r1_tarski(k1_rfunct_2(A),k4_relset_1(k1_numbers,k1_numbers,B))
           => ( k22_seq_1(k2_rfunct_2(B,A)) = k2_rfunct_2(k21_seq_1(k1_numbers,k1_numbers,B),A)
              & k17_seq_1(k2_rfunct_2(B,A)) = k2_rfunct_2(k16_seq_1(k1_numbers,k1_numbers,B),A) ) ) ) ) ),
    file(rfunct_2,t25_rfunct_2),
    []).

fof(t26_seq_4,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seq_2(A)
       => v4_seq_2(k22_seq_1(A)) ) ) ),
    file(seq_4,t26_seq_4),
    []).

fof(t27_seq_4,axiom,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k5_numbers,k1_numbers)
        & m2_relset_1(A,k5_numbers,k1_numbers) )
     => ( v4_seq_2(A)
       => k2_seq_2(k22_seq_1(A)) = k18_complex1(k2_seq_2(A)) ) ) ),
    file(seq_4,t27_seq_4),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

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

fof(t3_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

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

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

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

fof(t5_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

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

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

fof(t6_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

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

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

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

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).