% Mizar problem: t1_urysohn3,urysohn3,106,47 
fof(t1_urysohn3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v5_compts_1(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( r1_xboole_0(B,C)
               => ( B = k6_measure5
                  | ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ? [E] : 
                          ( v1_funct_1(E)
                          & v1_funct_2(E,k3_urysohn1(D),k1_pcomps_1(u1_struct_0(A)))
                          & m2_relset_1(E,k3_urysohn1(D),k1_pcomps_1(u1_struct_0(A)))
                          & r1_tarski(B,k1_funct_1(E,0))
                          & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(E,1))
                          & ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k3_urysohn1(D))
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k3_urysohn1(D))
                                 => ( ~ r1_xreal_0(G,F)
                                   => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(D),E,F),A)
                                      & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(D),E,G),A)
                                      & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(D),E,F)),k6_urysohn1(A,k3_urysohn1(D),E,G)) ) ) ) ) ) ) ) ) ) ) ) ),
    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_membered,cc1_nat_1,cc1_relset_1,cc1_supinf_1,cc1_urysohn3,cc1_xreal_0,cc20_membered,cc2_membered,cc2_nat_1,cc2_supinf_1,cc2_xreal_0,cc3_membered,cc3_nat_1,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d3_pre_topc,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_pcomps_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_supinf_1,dt_k3_urysohn1,dt_k4_xboole_0,dt_k5_numbers,dt_k5_ordinal2,dt_k6_measure5,dt_k6_pre_topc,dt_k6_supinf_1,dt_k6_urysohn1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc1_nat_1,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_supinf_1,fc1_urysohn1,fc2_membered,fc2_pre_topc,fc37_membered,fc38_membered,fc39_membered,fc3_nat_1,fc3_xreal_0,fc40_membered,fc41_membered,fc4_nat_1,fc4_subset_1,fc5_membered,fc5_pre_topc,fc6_membered,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,l1_urysohn3,rc1_membered,rc1_nat_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_partfun1,rc2_subset_1,rc2_xreal_0,rc3_nat_1,rc3_struct_0,rc3_supinf_1,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,redefinition_k1_nat_1,redefinition_k1_pcomps_1,redefinition_k5_numbers,redefinition_k6_measure5,redefinition_k6_supinf_1,redefinition_k6_urysohn1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e4_3__urysohn3,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t1_arithm,t1_numerals,t1_real,t1_subset,t2_real,t2_subset,t32_urysohn1,t3_boole,t3_real,t3_subset,t4_boole,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(urysohn3,t1_urysohn3)]).

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

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

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_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) ),
    file(supinf_1,cc1_supinf_1),
    []).

fof(cc1_urysohn3,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_supinf_1)) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(urysohn3,cc1_urysohn3),
    []).

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

fof(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc2_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) ),
    file(supinf_1,cc2_supinf_1),
    []).

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

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

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

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(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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(d3_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,d3_pre_topc),
    []).

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

fof(dt_k1_pcomps_1,axiom,(
    ! [A] : m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ),
    file(pcomps_1,k1_pcomps_1),
    []).

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_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

fof(dt_k3_urysohn1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k3_urysohn1(A),k1_zfmisc_1(k1_numbers)) ) ),
    file(urysohn1,k3_urysohn1),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

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_k6_measure5,axiom,
    ( v1_xboole_0(k6_measure5)
    & v5_measure5(k6_measure5)
    & m1_subset_1(k6_measure5,k1_zfmisc_1(k6_supinf_1)) ),
    file(measure5,k6_measure5),
    []).

fof(dt_k6_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k6_pre_topc),
    []).

fof(dt_k6_supinf_1,axiom,
    ( ~ v1_xboole_0(k6_supinf_1)
    & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ),
    file(supinf_1,k6_supinf_1),
    []).

fof(dt_k6_urysohn1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(C)
        & v1_funct_2(C,B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(C,B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,B) )
     => m1_subset_1(k6_urysohn1(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(urysohn1,k6_urysohn1),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

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(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

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(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc10_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & v2_xreal_0(k2_xcmplx_0(B,A))
        & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc10_xreal_0),
    []).

fof(fc11_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B))
        & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc11_xreal_0),
    []).

fof(fc12_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A))
        & ~ v2_xreal_0(k2_xcmplx_0(B,A))
        & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(xreal_0,fc12_xreal_0),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_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_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) ),
    file(supinf_1,fc1_supinf_1),
    []).

fof(fc1_urysohn1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k3_urysohn1(A))
        & v1_membered(k3_urysohn1(A))
        & v2_membered(k3_urysohn1(A)) ) ) ),
    file(urysohn1,fc1_urysohn1),
    []).

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

fof(fc2_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) ),
    file(pre_topc,fc2_pre_topc),
    []).

fof(fc37_membered,axiom,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    []).

fof(fc38_membered,axiom,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    []).

fof(fc39_membered,axiom,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc39_membered),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc3_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc3_xreal_0),
    []).

fof(fc40_membered,axiom,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc40_membered),
    []).

fof(fc41_membered,axiom,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B))
        & v5_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc41_membered),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_1),
    []).

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

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(fc5_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k2_pre_topc(A),A) ) ),
    file(pre_topc,fc5_pre_topc),
    []).

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_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc7_xreal_0),
    []).

fof(fc8_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v2_xreal_0(B) )
     => ( v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc8_xreal_0),
    []).

fof(fc9_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A)
        & v1_xreal_0(B)
        & ~ v3_xreal_0(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B))
        & v2_xreal_0(k2_xcmplx_0(A,B))
        & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc9_xreal_0),
    []).

fof(l1_urysohn3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v5_compts_1(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v4_pre_topc(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( ( v4_pre_topc(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ~ ( B != k6_measure5
                  & r1_xboole_0(B,C)
                  & ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k3_urysohn1(0),k1_pcomps_1(u1_struct_0(A)))
                        & m2_relset_1(D,k3_urysohn1(0),k1_pcomps_1(u1_struct_0(A))) )
                     => ~ ( r1_tarski(B,k1_funct_1(D,0))
                          & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(D,1))
                          & ! [E] : 
                              ( m2_subset_1(E,k1_numbers,k3_urysohn1(0))
                             => ! [F] : 
                                  ( m2_subset_1(F,k1_numbers,k3_urysohn1(0))
                                 => ( ~ r1_xreal_0(F,E)
                                   => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(0),D,E),A)
                                      & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(0),D,F),A)
                                      & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(0),D,E)),k6_urysohn1(A,k3_urysohn1(0),D,F)) ) ) ) ) ) ) ) ) ) ) ),
    file(urysohn3,l1_urysohn3),
    []).

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_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

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

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

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

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

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

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_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc3_supinf_1,axiom,(
    ? [A] : v3_supinf_1(A) ),
    file(supinf_1,rc3_supinf_1),
    []).

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(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    []).

fof(rc7_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(redefinition_k1_pcomps_1,axiom,(
    ! [A] : k1_pcomps_1(A) = k1_zfmisc_1(A) ),
    file(pcomps_1,k1_pcomps_1),
    []).

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

fof(redefinition_k6_measure5,axiom,(
    k6_measure5 = k1_xboole_0 ),
    file(measure5,k6_measure5),
    []).

fof(redefinition_k6_supinf_1,axiom,(
    k6_supinf_1 = k1_numbers ),
    file(supinf_1,k6_supinf_1),
    []).

fof(redefinition_k6_urysohn1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_numbers))
        & v1_funct_1(C)
        & v1_funct_2(C,B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_relset_1(C,B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(D,B) )
     => k6_urysohn1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(urysohn1,k6_urysohn1),
    []).

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(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_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(s1_nat_1__e4_3__urysohn3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & v5_compts_1(A)
        & l1_pre_topc(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & v4_pre_topc(C,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ( ? [D] : 
              ( v1_funct_1(D)
              & v1_funct_2(D,k3_urysohn1(0),k1_pcomps_1(u1_struct_0(A)))
              & m2_relset_1(D,k3_urysohn1(0),k1_pcomps_1(u1_struct_0(A)))
              & r1_tarski(B,k1_funct_1(D,0))
              & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(D,1))
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k3_urysohn1(0))
                 => ! [F] : 
                      ( m2_subset_1(F,k1_numbers,k3_urysohn1(0))
                     => ( ~ r1_xreal_0(F,E)
                       => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(0),D,E),A)
                          & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(0),D,F),A)
                          & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(0),D,E)),k6_urysohn1(A,k3_urysohn1(0),D,F)) ) ) ) ) )
          & ! [G] : 
              ( m2_subset_1(G,k1_numbers,k5_numbers)
             => ( ? [H] : 
                    ( v1_funct_1(H)
                    & v1_funct_2(H,k3_urysohn1(G),k1_pcomps_1(u1_struct_0(A)))
                    & m2_relset_1(H,k3_urysohn1(G),k1_pcomps_1(u1_struct_0(A)))
                    & r1_tarski(B,k1_funct_1(H,0))
                    & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(H,1))
                    & ! [I] : 
                        ( m2_subset_1(I,k1_numbers,k3_urysohn1(G))
                       => ! [J] : 
                            ( m2_subset_1(J,k1_numbers,k3_urysohn1(G))
                           => ( ~ r1_xreal_0(J,I)
                             => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(G),H,I),A)
                                & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(G),H,J),A)
                                & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(G),H,I)),k6_urysohn1(A,k3_urysohn1(G),H,J)) ) ) ) ) )
               => ? [K] : 
                    ( v1_funct_1(K)
                    & v1_funct_2(K,k3_urysohn1(k1_nat_1(G,1)),k1_pcomps_1(u1_struct_0(A)))
                    & m2_relset_1(K,k3_urysohn1(k1_nat_1(G,1)),k1_pcomps_1(u1_struct_0(A)))
                    & r1_tarski(B,k1_funct_1(K,0))
                    & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(K,1))
                    & ! [L] : 
                        ( m2_subset_1(L,k1_numbers,k3_urysohn1(k1_nat_1(G,1)))
                       => ! [M] : 
                            ( m2_subset_1(M,k1_numbers,k3_urysohn1(k1_nat_1(G,1)))
                           => ( ~ r1_xreal_0(M,L)
                             => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(k1_nat_1(G,1)),K,L),A)
                                & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(k1_nat_1(G,1)),K,M),A)
                                & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(k1_nat_1(G,1)),K,L)),k6_urysohn1(A,k3_urysohn1(k1_nat_1(G,1)),K,M)) ) ) ) ) ) ) ) )
       => ! [G] : 
            ( m2_subset_1(G,k1_numbers,k5_numbers)
           => ? [N] : 
                ( v1_funct_1(N)
                & v1_funct_2(N,k3_urysohn1(G),k1_pcomps_1(u1_struct_0(A)))
                & m2_relset_1(N,k3_urysohn1(G),k1_pcomps_1(u1_struct_0(A)))
                & r1_tarski(B,k1_funct_1(N,0))
                & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(N,1))
                & ! [O] : 
                    ( m2_subset_1(O,k1_numbers,k3_urysohn1(G))
                   => ! [P] : 
                        ( m2_subset_1(P,k1_numbers,k3_urysohn1(G))
                       => ( ~ r1_xreal_0(P,O)
                         => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(G),N,O),A)
                            & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(G),N,P),A)
                            & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(G),N,O)),k6_urysohn1(A,k3_urysohn1(G),N,P)) ) ) ) ) ) ) ) ) ),
    file(urysohn3,s1_nat_1__e4_3__urysohn3),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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(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(t32_urysohn1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v5_compts_1(A)
       => ! [B] : 
            ( ( v4_pre_topc(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ! [C] : 
                ( ( v4_pre_topc(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r1_xboole_0(B,C)
                 => ( B = k1_xboole_0
                    | ! [D] : 
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ! [E] : 
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,k3_urysohn1(D),k1_zfmisc_1(u1_struct_0(A)))
                              & m2_relset_1(E,k3_urysohn1(D),k1_zfmisc_1(u1_struct_0(A))) )
                           => ~ ( r1_tarski(B,k1_funct_1(E,0))
                                & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(E,1))
                                & ! [F] : 
                                    ( m2_subset_1(F,k1_numbers,k3_urysohn1(D))
                                   => ! [G] : 
                                        ( m2_subset_1(G,k1_numbers,k3_urysohn1(D))
                                       => ( ~ r1_xreal_0(G,F)
                                         => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(D),E,F),A)
                                            & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(D),E,G),A)
                                            & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(D),E,F)),k6_urysohn1(A,k3_urysohn1(D),E,G)) ) ) ) )
                                & ! [F] : 
                                    ( ( v1_funct_1(F)
                                      & v1_funct_2(F,k3_urysohn1(k1_nat_1(D,1)),k1_zfmisc_1(u1_struct_0(A)))
                                      & m2_relset_1(F,k3_urysohn1(k1_nat_1(D,1)),k1_zfmisc_1(u1_struct_0(A))) )
                                   => ~ ( r1_tarski(B,k1_funct_1(F,0))
                                        & C = k4_xboole_0(k2_pre_topc(A),k1_funct_1(F,1))
                                        & ! [G] : 
                                            ( m2_subset_1(G,k1_numbers,k3_urysohn1(k1_nat_1(D,1)))
                                           => ! [H] : 
                                                ( m2_subset_1(H,k1_numbers,k3_urysohn1(k1_nat_1(D,1)))
                                               => ! [I] : 
                                                    ( m2_subset_1(I,k1_numbers,k3_urysohn1(k1_nat_1(D,1)))
                                                   => ( ~ r1_xreal_0(H,G)
                                                     => ( v3_pre_topc(k6_urysohn1(A,k3_urysohn1(k1_nat_1(D,1)),F,G),A)
                                                        & v3_pre_topc(k6_urysohn1(A,k3_urysohn1(k1_nat_1(D,1)),F,H),A)
                                                        & r1_tarski(k6_pre_topc(A,k6_urysohn1(A,k3_urysohn1(k1_nat_1(D,1)),F,G)),k6_urysohn1(A,k3_urysohn1(k1_nat_1(D,1)),F,H))
                                                        & ( r2_hidden(I,k3_urysohn1(D))
                                                         => k6_urysohn1(A,k3_urysohn1(k1_nat_1(D,1)),F,I) = k1_funct_1(E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(urysohn1,t32_urysohn1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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),
    []).