% Mizar problem: t18_urysohn3,urysohn3,1228,16 
fof(t18_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_urysohn3(D,A,B,C)
                     => ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_urysohn1)
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( ~ r1_xreal_0(E,k9_urysohn3(A,k8_urysohn3(A,B,C,D),F))
                               => r2_hidden(F,k5_urysohn3(k5_urysohn1,A,k4_urysohn3(A,B,C,D),E)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,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_k2_xboole_0,commutativity_k4_subset_1,connectedness_r1_supinf_1,connectedness_r1_xreal_0,d16_supinf_1,d1_supinf_2,d1_urysohn1,d1_xboole_0,d2_xboole_0,d4_urysohn1,d4_urysohn3,d5_urysohn1,d5_urysohn3,d6_urysohn3,d9_supinf_1,dt_g1_pre_topc,dt_k1_funct_1,dt_k1_numbers,dt_k1_pcomps_1,dt_k1_seqfunc,dt_k1_supinf_2,dt_k1_urysohn1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_urysohn1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_supinf_1,dt_k3_topmetr,dt_k3_urysohn1,dt_k4_subset_1,dt_k4_urysohn1,dt_k4_urysohn3,dt_k5_numbers,dt_k5_ordinal2,dt_k5_urysohn1,dt_k5_urysohn3,dt_k6_measure5,dt_k6_supinf_1,dt_k6_urysohn3,dt_k7_urysohn3,dt_k8_urysohn3,dt_k9_supinf_1,dt_k9_urysohn3,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_seqfunc,dt_m1_subset_1,dt_m1_supinf_1,dt_m2_relset_1,dt_m2_subset_1,dt_m2_urysohn3,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_seqfunc,existence_m1_subset_1,existence_m1_supinf_1,existence_m2_relset_1,existence_m2_subset_1,existence_m2_urysohn3,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_supinf_1,fc1_urysohn1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_membered,fc2_topmetr,fc2_urysohn1,fc3_topmetr,fc3_urysohn1,fc4_subset_1,fc5_membered,fc6_membered,free_g1_pre_topc,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_membered,rc1_nat_1,rc1_pre_topc,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_partfun1,rc2_pre_topc,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_pcomps_1,redefinition_k1_seqfunc,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_urysohn3,redefinition_k6_measure5,redefinition_k6_supinf_1,redefinition_k7_urysohn3,redefinition_k9_urysohn3,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_supinf_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_xboole_0,t10_supinf_1,t120_supinf_1,t1_boole,t1_numerals,t1_real,t1_subset,t29_supinf_1,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t5_urysohn1,t6_boole,t6_real,t76_supinf_1,t7_boole,t7_real,t8_boole,t8_real]),
    [file(urysohn3,t18_urysohn3)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    []).

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(d16_supinf_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( B = k9_supinf_1(A)
          <=> ( m1_supinf_1(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,k3_supinf_1)
                 => ( m1_supinf_1(C,A)
                   => r1_supinf_1(B,C) ) ) ) ) ) ) ),
    file(supinf_1,d16_supinf_1),
    []).

fof(d1_supinf_2,axiom,(
    k1_supinf_2 = 0 ),
    file(supinf_2,d1_supinf_2),
    []).

fof(d1_urysohn1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( A = k1_urysohn1
      <=> ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ( r2_hidden(B,A)
            <=> ~ r1_xreal_0(0,B) ) ) ) ) ),
    file(urysohn1,d1_urysohn1),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d4_urysohn1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( A = k4_urysohn1
      <=> ! [B] : 
            ( m1_subset_1(B,k1_numbers)
           => ( r2_hidden(B,A)
            <=> ? [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                  & r2_hidden(B,k3_urysohn1(C)) ) ) ) ) ) ),
    file(urysohn1,d4_urysohn1),
    []).

fof(d4_urysohn3,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)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v5_compts_1(A)
                  & v4_pre_topc(B,A)
                  & v4_pre_topc(C,A)
                  & r1_xboole_0(B,C) )
               => ( B = k6_measure5
                  | ! [D] : 
                      ( m2_urysohn3(D,A,B,C)
                     => ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,k5_urysohn1,k1_pcomps_1(u1_struct_0(A)))
                            & m2_relset_1(E,k5_urysohn1,k1_pcomps_1(u1_struct_0(A))) )
                         => ( E = k4_urysohn3(A,B,C,D)
                          <=> ! [F] : 
                                ( m1_subset_1(F,k1_numbers)
                               => ( r2_hidden(F,k5_urysohn1)
                                 => ( ( r2_hidden(F,k1_urysohn1)
                                     => k1_funct_1(E,F) = k6_measure5 )
                                    & ( r2_hidden(F,k2_urysohn1)
                                     => k1_funct_1(E,F) = u1_struct_0(A) )
                                    & ( r2_hidden(F,k4_urysohn1)
                                     => ! [G] : 
                                          ( m2_subset_1(G,k1_numbers,k5_numbers)
                                         => ( r2_hidden(F,k3_urysohn1(G))
                                           => k1_funct_1(E,F) = k1_funct_1(k1_seqfunc(k4_urysohn1,k1_pcomps_1(u1_struct_0(A)),D,G),F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(urysohn3,d4_urysohn3),
    []).

fof(d5_urysohn1,axiom,(
    k5_urysohn1 = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k1_urysohn1,k4_urysohn1),k2_urysohn1) ),
    file(urysohn1,d5_urysohn1),
    []).

fof(d5_urysohn3,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)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m2_urysohn3(D,A,B,C)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(k3_supinf_1))
                         => ( F = k6_urysohn3(A,B,C,D,E)
                          <=> ! [G] : 
                                ( r2_hidden(G,F)
                              <=> ( r2_hidden(G,k4_urysohn1)
                                  & ! [H] : 
                                      ( m1_subset_1(H,k1_numbers)
                                     => ~ ( H = G
                                          & r2_hidden(E,k1_funct_1(k4_urysohn3(A,B,C,D),H)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(urysohn3,d5_urysohn3),
    []).

fof(d6_urysohn3,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)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m2_urysohn3(D,A,B,C)
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k3_topmetr))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
                     => ( E = k8_urysohn3(A,B,C,D)
                      <=> ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( k6_urysohn3(A,B,C,D,F) = k6_measure5
                               => k7_urysohn3(A,k3_topmetr,E,F) = 0 )
                              & ! [G] : 
                                  ( ( ~ v1_xboole_0(G)
                                    & m1_subset_1(G,k1_zfmisc_1(k3_supinf_1)) )
                                 => ( G = k6_urysohn3(A,B,C,D,F)
                                   => k7_urysohn3(A,k3_topmetr,E,F) = k9_supinf_1(G) ) ) ) ) ) ) ) ) ) ) ),
    file(urysohn3,d6_urysohn3),
    []).

fof(d9_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( m1_supinf_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k3_supinf_1)
               => ( r2_hidden(C,A)
                 => r1_supinf_1(C,B) ) ) ) ) ) ),
    file(supinf_1,d9_supinf_1),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

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_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_seqfunc,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_seqfunc(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_funct_1(k1_seqfunc(A,B,C,D))
        & m2_relset_1(k1_seqfunc(A,B,C,D),A,B) ) ) ),
    file(seqfunc,k1_seqfunc),
    []).

fof(dt_k1_supinf_2,axiom,(
    m1_subset_1(k1_supinf_2,k3_supinf_1) ),
    file(supinf_2,k1_supinf_2),
    []).

fof(dt_k1_urysohn1,axiom,(
    m1_subset_1(k1_urysohn1,k1_zfmisc_1(k1_numbers)) ),
    file(urysohn1,k1_urysohn1),
    []).

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_urysohn1,axiom,(
    m1_subset_1(k2_urysohn1,k1_zfmisc_1(k1_numbers)) ),
    file(urysohn1,k2_urysohn1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_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_topmetr,axiom,
    ( v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & l1_pre_topc(k3_topmetr) ),
    file(topmetr,k3_topmetr),
    []).

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_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_urysohn1,axiom,(
    m1_subset_1(k4_urysohn1,k1_zfmisc_1(k1_numbers)) ),
    file(urysohn1,k4_urysohn1),
    []).

fof(dt_k4_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m2_urysohn3(D,A,B,C) )
     => ( v1_funct_1(k4_urysohn3(A,B,C,D))
        & v1_funct_2(k4_urysohn3(A,B,C,D),k5_urysohn1,k1_pcomps_1(u1_struct_0(A)))
        & m2_relset_1(k4_urysohn3(A,B,C,D),k5_urysohn1,k1_pcomps_1(u1_struct_0(A))) ) ) ),
    file(urysohn3,k4_urysohn3),
    []).

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_k5_urysohn1,axiom,(
    m1_subset_1(k5_urysohn1,k1_zfmisc_1(k1_numbers)) ),
    file(urysohn1,k5_urysohn1),
    []).

fof(dt_k5_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k1_pcomps_1(u1_struct_0(B)))
        & m1_relset_1(C,A,k1_pcomps_1(u1_struct_0(B)))
        & m1_subset_1(D,A) )
     => m1_subset_1(k5_urysohn3(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(urysohn3,k5_urysohn3),
    []).

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_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_urysohn3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m2_urysohn3(D,A,B,C)
        & m1_subset_1(E,u1_struct_0(A)) )
     => m1_subset_1(k6_urysohn3(A,B,C,D,E),k1_zfmisc_1(k3_supinf_1)) ) ),
    file(urysohn3,k6_urysohn3),
    []).

fof(dt_k7_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k7_urysohn3(A,B,C,D),u1_struct_0(B)) ) ),
    file(urysohn3,k7_urysohn3),
    []).

fof(dt_k8_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
        & m2_urysohn3(D,A,B,C) )
     => ( v1_funct_1(k8_urysohn3(A,B,C,D))
        & v1_funct_2(k8_urysohn3(A,B,C,D),u1_struct_0(A),u1_struct_0(k3_topmetr))
        & m2_relset_1(k8_urysohn3(A,B,C,D),u1_struct_0(A),u1_struct_0(k3_topmetr)) ) ) ),
    file(urysohn3,k8_urysohn3),
    []).

fof(dt_k9_supinf_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => m1_subset_1(k9_supinf_1(A),k3_supinf_1) ) ),
    file(supinf_1,k9_supinf_1),
    []).

fof(dt_k9_urysohn3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k9_urysohn3(A,B,C),k1_numbers) ) ),
    file(urysohn3,k9_urysohn3),
    []).

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_seqfunc,axiom,(
    ! [A,B,C] : 
      ( m1_seqfunc(C,A,B)
     => ( v1_relat_1(C)
        & v1_funct_1(C) ) ) ),
    file(seqfunc,m1_seqfunc),
    []).

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

fof(dt_m1_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ! [B] : 
          ( m1_supinf_1(B,A)
         => m1_subset_1(B,k3_supinf_1) ) ) ),
    file(supinf_1,m1_supinf_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_m2_urysohn3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ! [D] : 
          ( m2_urysohn3(D,A,B,C)
         => m1_seqfunc(D,k4_urysohn1,k1_pcomps_1(u1_struct_0(A))) ) ) ),
    file(urysohn3,m2_urysohn3),
    []).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

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_seqfunc,axiom,(
    ! [A,B] : 
    ? [C] : m1_seqfunc(C,A,B) ),
    file(seqfunc,m1_seqfunc),
    []).

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

fof(existence_m1_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k3_supinf_1))
     => ? [B] : m1_supinf_1(B,A) ) ),
    file(supinf_1,m1_supinf_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(existence_m2_urysohn3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ? [D] : m2_urysohn3(D,A,B,C) ) ),
    file(urysohn3,m2_urysohn3),
    []).

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(fc22_membered,axiom,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    []).

fof(fc23_membered,axiom,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    []).

fof(fc24_membered,axiom,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    []).

fof(fc25_membered,axiom,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    []).

fof(fc26_membered,axiom,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    []).

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

fof(fc2_topmetr,axiom,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr) ),
    file(topmetr,fc2_topmetr),
    []).

fof(fc2_urysohn1,axiom,
    ( ~ v1_xboole_0(k4_urysohn1)
    & v1_membered(k4_urysohn1)
    & v2_membered(k4_urysohn1) ),
    file(urysohn1,fc2_urysohn1),
    []).

fof(fc3_topmetr,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(B)
        & m1_relset_1(B,A,u1_struct_0(k3_topmetr)) )
     => ( v1_xcmplx_0(k1_funct_1(B,C))
        & v1_xreal_0(k1_funct_1(B,C)) ) ) ),
    file(topmetr,fc3_topmetr),
    []).

fof(fc3_urysohn1,axiom,
    ( ~ v1_xboole_0(k5_urysohn1)
    & v1_membered(k5_urysohn1)
    & v2_membered(k5_urysohn1) ),
    file(urysohn1,fc3_urysohn1),
    []).

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(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(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

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_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    []).

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_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    []).

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_pcomps_1,axiom,(
    ! [A] : k1_pcomps_1(A) = k1_zfmisc_1(A) ),
    file(pcomps_1,k1_pcomps_1),
    []).

fof(redefinition_k1_seqfunc,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_seqfunc(C,A,B)
        & v4_ordinal2(D) )
     => k1_seqfunc(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seqfunc,k1_seqfunc),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

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

fof(redefinition_k5_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k1_pcomps_1(u1_struct_0(B)))
        & m1_relset_1(C,A,k1_pcomps_1(u1_struct_0(B)))
        & m1_subset_1(D,A) )
     => k5_urysohn3(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(urysohn3,k5_urysohn3),
    []).

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_k7_urysohn3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(A)) )
     => k7_urysohn3(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(urysohn3,k7_urysohn3),
    []).

fof(redefinition_k9_urysohn3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_funct_1(B)
        & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
        & m1_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k9_urysohn3(A,B,C) = k1_funct_1(B,C) ) ),
    file(urysohn3,k9_urysohn3),
    []).

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_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_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(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(t10_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(A,k3_supinf_1) ) ),
    file(supinf_1,t10_supinf_1),
    []).

fof(t120_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( A = C
                      & B = D )
                   => ( r1_xreal_0(C,D)
                    <=> r1_supinf_1(A,B) ) ) ) ) ) ) ),
    file(supinf_1,t120_supinf_1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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(t29_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(A,B)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(A,C) ) ) ) ) ),
    file(supinf_1,t29_supinf_1),
    []).

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(t5_urysohn1,axiom,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( r2_hidden(B,k3_urysohn1(A))
           => ( r1_xreal_0(0,B)
              & r1_xreal_0(B,1) ) ) ) ) ),
    file(urysohn1,t5_urysohn1),
    []).

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(t76_supinf_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_supinf_1)) )
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( r2_hidden(B,A)
           => r1_supinf_1(B,k9_supinf_1(A)) ) ) ) ),
    file(supinf_1,t76_supinf_1),
    []).

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),
    []).