% Mizar ND problem: t2_brouwer,brouwer,119,20 
fof(dh_c1_4__brouwer,definition,
    ( ( m2_subset_1(c1_4__brouwer,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_4__brouwer)))
         => k2_topreal9(c1_4__brouwer,A,0) = k1_struct_0(k15_euclid(c1_4__brouwer),A) ) )
   => ! [B] : 
        ( m2_subset_1(B,k1_numbers,k5_numbers)
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
           => k2_topreal9(B,C,0) = k1_struct_0(k15_euclid(B),C) ) ) ),
    introduced(definition,[new_symbol(c1_4__brouwer),file(brouwer,c1_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c1_4__brouwer)]).

fof(dh_c2_4__brouwer,definition,
    ( ( m1_subset_1(c2_4__brouwer,u1_struct_0(k15_euclid(c1_4__brouwer)))
     => k2_topreal9(c1_4__brouwer,c2_4__brouwer,0) = k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_4__brouwer)))
       => k2_topreal9(c1_4__brouwer,A,0) = k1_struct_0(k15_euclid(c1_4__brouwer),A) ) ),
    introduced(definition,[new_symbol(c2_4__brouwer),file(brouwer,c2_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c2_4__brouwer)]).

fof(cc2_tex_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc2_tex_1),
    [interesting(0.9),axiom,file(tex_1,cc2_tex_1)]).

fof(cc3_tex_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc3_tex_1),
    [interesting(0.9),axiom,file(tex_1,cc3_tex_1)]).

fof(cc4_tex_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A) ) ) ) ),
    file(tex_1,cc4_tex_1),
    [interesting(0.9),axiom,file(tex_1,cc4_tex_1)]).

fof(cc5_tex_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v3_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & ~ v2_tdlat_3(A) ) ) ) ),
    file(tex_1,cc5_tex_1),
    [interesting(0.9),axiom,file(tex_1,cc5_tex_1)]).

fof(rc10_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & ~ v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A) ) ),
    file(tex_1,rc10_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc10_tex_1)]).

fof(rc11_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & ~ v2_tdlat_3(A)
      & ~ v3_tdlat_3(A) ) ),
    file(tex_1,rc11_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc11_tex_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc4_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A) ) ) ),
    file(tops_1,rc4_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc4_tops_1)]).

fof(rc5_tops_1,theorem,(
    ! [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)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B)
          & v2_tops_1(B,A)
          & v3_tops_1(B,A) ) ) ),
    file(tops_1,rc5_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc5_tops_1)]).

fof(rc7_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & v1_tdlat_3(A)
      & ~ v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A) ) ),
    file(tex_1,rc7_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc7_tex_1)]).

fof(rc8_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & v2_tdlat_3(A)
      & v3_tdlat_3(A)
      & v4_tdlat_3(A)
      & v5_tdlat_3(A) ) ),
    file(tex_1,rc8_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc8_tex_1)]).

fof(rc9_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A)
      & ~ v1_tdlat_3(A)
      & ~ v2_tdlat_3(A) ) ),
    file(tex_1,rc9_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc9_tex_1)]).

fof(free_g1_pre_topc,definition,(
    ! [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),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

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),
    [interesting(0.9),axiom,file(pre_topc,g1_pre_topc)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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),
    [interesting(0.9),axiom,file(pre_topc,u1_pre_topc)]).

fof(cc10_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    file(tex_2,cc10_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc10_tex_2)]).

fof(cc11_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc11_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc11_tex_2)]).

fof(cc1_tex_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A) ) ) ) ),
    file(tex_1,cc1_tex_1),
    [interesting(0.9),axiom,file(tex_1,cc1_tex_1)]).

fof(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc3_borsuk_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_borsuk_2(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_connsp_1(A) ) ) ) ),
    file(borsuk_2,cc3_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc3_borsuk_2)]).

fof(cc3_nat_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(cc3_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]).

fof(cc4_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc4_tex_2)]).

fof(cc4_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_tops_1(B,A)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc4_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc4_tops_1)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]).

fof(cc5_tops_1,theorem,(
    ! [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)
              & v2_tops_1(B,A) )
           => ( v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc5_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc5_tops_1)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc6_tex_2)]).

fof(cc6_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v3_tops_1(B,A) )
           => ( v1_xboole_0(B)
              & v3_pre_topc(B,A)
              & v4_pre_topc(B,A)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v2_tops_1(B,A)
              & v3_tops_1(B,A) ) ) ) ) ),
    file(tops_1,cc6_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc6_tops_1)]).

fof(cc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc7_tex_2)]).

fof(cc8_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    file(tex_2,cc8_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc8_tex_2)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(cc9_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc9_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc9_tex_2)]).

fof(fc1_revrot_1,theorem,(
    ! [A] : 
      ( ( ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ( ~ v1_xboole_0(u1_struct_0(A))
        & ~ v1_realset1(u1_struct_0(A)) ) ) ),
    file(revrot_1,fc1_revrot_1),
    [interesting(0.9),axiom,file(revrot_1,fc1_revrot_1)]).

fof(fc2_pscomp_1,theorem,
    ( ~ v1_xboole_0(k5_ordinal2)
    & v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2)
    & ~ v1_setfam_1(k5_ordinal2) ),
    file(pscomp_1,fc2_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,fc2_pscomp_1)]).

fof(fc3_topreal9,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & v3_xreal_0(C) )
     => v1_xboole_0(k2_topreal9(A,B,C)) ) ),
    file(topreal9,fc3_topreal9),
    [interesting(0.9),axiom,file(topreal9,fc3_topreal9)]).

fof(fc4_topreal9,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C)
        & ~ v3_xreal_0(C) )
     => ~ v1_xboole_0(k2_topreal9(A,B,C)) ) ),
    file(topreal9,fc4_topreal9),
    [interesting(0.9),axiom,file(topreal9,fc4_topreal9)]).

fof(rc10_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc10_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc10_tex_2)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]).

fof(rc1_pscomp_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc1_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,rc1_pscomp_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_tex_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc1_tex_2)]).

fof(rc1_topalg_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
          & ~ v1_xboole_0(B)
          & v1_jordan1(B,A) ) ) ),
    file(topalg_2,rc1_topalg_2),
    [interesting(0.9),axiom,file(topalg_2,rc1_topalg_2)]).

fof(rc1_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) ),
    file(tops_1,rc1_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc1_tops_1)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]).

fof(rc2_pscomp_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc2_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,rc2_pscomp_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc2_tops_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc2_tops_1)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_borsuk_2,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v1_borsuk_2(A) ) ),
    file(borsuk_2,rc3_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,rc3_borsuk_2)]).

fof(rc3_nat_1,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]).

fof(rc3_pscomp_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v1_setfam_1(A) ) ),
    file(pscomp_1,rc3_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,rc3_pscomp_1)]).

fof(rc3_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_pre_topc(A) ) ),
    file(tex_1,rc3_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc3_tex_1)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc3_tops_1,theorem,(
    ! [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)
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc3_tops_1),
    [interesting(0.9),axiom,file(tops_1,rc3_tops_1)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_pscomp_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & ~ v1_setfam_1(A) ) ),
    file(pscomp_1,rc4_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,rc4_pscomp_1)]).

fof(rc4_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A) ) ),
    file(tex_1,rc4_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc4_tex_1)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(rc5_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(tex_1,rc5_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc5_tex_1)]).

fof(rc5_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]).

fof(rc6_pre_topc,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(pre_topc,rc6_pre_topc)]).

fof(rc6_tex_1,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(tex_1,rc6_tex_1),
    [interesting(0.9),axiom,file(tex_1,rc6_tex_1)]).

fof(rc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]).

fof(rc7_pre_topc,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(pre_topc,rc7_pre_topc)]).

fof(rc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc7_tex_2)]).

fof(rc8_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc8_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc8_tex_2)]).

fof(rc9_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_2,rc9_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc9_tex_2)]).

fof(abstractness_v1_pre_topc,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(pre_topc,v1_pre_topc)]).

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

fof(redefinition_m2_subset_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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

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

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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

fof(dt_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),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_nat_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

fof(cc1_real_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(real_1,cc1_real_1),
    [interesting(0.9),axiom,file(real_1,cc1_real_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc1_tops_1,theorem,(
    ! [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)
           => ( v3_pre_topc(B,A)
              & v4_pre_topc(B,A) ) ) ) ) ),
    file(tops_1,cc1_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc1_tops_1)]).

fof(cc2_nat_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

fof(cc2_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

fof(cc2_tops_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_xboole_0(B)
           => v2_tops_1(B,A) ) ) ) ),
    file(tops_1,cc2_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc2_tops_1)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc3_tops_1,theorem,(
    ! [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)
           => v3_tops_1(B,A) ) ) ) ),
    file(tops_1,cc3_tops_1),
    [interesting(0.9),axiom,file(tops_1,cc3_tops_1)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_borsuk_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v3_struct_0(A)
       => v2_t_0topsp(A) ) ) ),
    file(borsuk_2,cc4_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc4_borsuk_2)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(fc1_jordan5a,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & v3_compts_1(k15_euclid(A))
        & v1_borsuk_2(k15_euclid(A)) ) ) ),
    file(jordan5a,fc1_jordan5a),
    [interesting(0.9),axiom,file(jordan5a,fc1_jordan5a)]).

fof(fc1_pscomp_1,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers)
    & ~ v1_setfam_1(k1_numbers) ),
    file(pscomp_1,fc1_pscomp_1),
    [interesting(0.9),axiom,file(pscomp_1,fc1_pscomp_1)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(tex_2,fc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,fc1_tex_2)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_revrot_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers) )
     => ( ~ v3_struct_0(k15_euclid(A))
        & v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & ~ v3_realset2(k15_euclid(A)) ) ) ),
    file(revrot_1,fc3_revrot_1),
    [interesting(0.9),axiom,file(revrot_1,fc3_revrot_1)]).

fof(fc6_topreal9,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k2_topreal9(A,B,C),A) ) ) ),
    file(topreal9,fc6_topreal9),
    [interesting(0.9),axiom,file(topreal9,fc6_topreal9)]).

fof(fc9_topreal9,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A))
        & v1_jordan2c(k2_topreal9(A,B,C),A)
        & v1_jordan1(k2_topreal9(A,B,C),A) ) ) ),
    file(topreal9,fc9_topreal9),
    [interesting(0.9),axiom,file(topreal9,fc9_topreal9)]).

fof(rc1_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc1_pre_topc)]).

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

fof(rc2_pre_topc,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc2_pre_topc)]).

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

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(rc5_struct_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(redefinition_k1_struct_0,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    [interesting(0.9),axiom,file(struct_0,k1_struct_0)]).

fof(dt_k15_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_pre_topc(k15_euclid(A))
        & v2_pre_topc(k15_euclid(A))
        & l1_pre_topc(k15_euclid(A)) ) ) ),
    file(euclid,k15_euclid),
    [interesting(0.9),axiom,file(euclid,k15_euclid)]).

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    [interesting(0.9),axiom,file(struct_0,k1_struct_0)]).

fof(dt_k2_topreal9,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & v1_xreal_0(C) )
     => m1_subset_1(k2_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ),
    file(topreal9,k2_topreal9),
    [interesting(0.9),axiom,file(topreal9,k2_topreal9)]).

fof(dt_c1_4__brouwer,assumption,(
    m2_subset_1(c1_4__brouwer,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(brouwer,c1_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c1_4__brouwer)]).

fof(dt_c2_4__brouwer,assumption,(
    m1_subset_1(c2_4__brouwer,u1_struct_0(k15_euclid(c1_4__brouwer))) ),
    introduced(assumption,[file(brouwer,c2_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c2_4__brouwer)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_c1_4_1__brouwer,assumption,(
    $true ),
    introduced(assumption,[file(brouwer,c1_4_1__brouwer)]),
    [interesting(0.65),axiom,file(brouwer,c1_4_1__brouwer)]).

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

fof(dh_c1_4_1__brouwer,definition,
    ( ~ ( r2_hidden(c1_4_1__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0))
        & ~ r2_hidden(c1_4_1__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0))
          & ~ r2_hidden(A,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ) ),
    introduced(definition,[new_symbol(c1_4_1__brouwer),file(brouwer,c1_4_1__brouwer)]),
    [interesting(0.65),axiom,file(brouwer,c1_4_1__brouwer)]).

fof(e1_4_1__brouwer,assumption,(
    r2_hidden(c1_4_1__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ),
    introduced(assumption,[file(brouwer,e1_4_1__brouwer)]),
    [interesting(0.65),axiom,file(brouwer,e1_4_1__brouwer)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

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

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(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),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

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

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

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

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(de_c2_4_1__brouwer,definition,(
    c2_4_1__brouwer = c1_4_1__brouwer ),
    introduced(definition,[new_symbol(c2_4_1__brouwer),file(brouwer,c2_4_1__brouwer)]),
    [interesting(0.65),axiom,file(brouwer,c2_4_1__brouwer)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(e2_4_1__brouwer,plain,(
    m1_subset_1(c1_4_1__brouwer,u1_struct_0(k15_euclid(c1_4__brouwer))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc4_tops_1,rc5_tex_2,rc5_tops_1,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_k1_xboole_0,dt_k5_ordinal2,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc3_borsuk_2,cc3_nat_1,cc4_borsuk_2,cc4_tops_1,cc4_xreal_0,cc5_tops_1,cc5_xreal_0,cc6_tops_1,cc8_tex_2,cc8_xreal_0,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc1_struct_0,fc2_pscomp_1,fc3_topreal9,fc4_relat_1,fc4_topreal9,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_topalg_2,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc4_xreal_0,rc5_struct_0,rc5_tex_1,rc6_pre_topc,rc6_tex_1,rc7_pre_topc,t8_boole,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m2_subset_1,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_tops_1,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc1_subset_1,fc3_revrot_1,fc6_topreal9,fc9_topreal9,rc1_pre_topc,rc1_subset_1,rc2_subset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k15_euclid,dt_k2_topreal9,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,t1_subset,t7_boole,spc0_numerals,spc0_boole,e1_4_1__brouwer]),
    [interesting(0.65),file(brouwer,e2_4_1__brouwer),[file(brouwer,e2_4_1__brouwer)]]).

fof(dt_c2_4_1__brouwer,plain,(
    m1_subset_1(c2_4_1__brouwer,u1_struct_0(k15_euclid(c1_4__brouwer))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc3_xreal_0,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc6_xreal_0,cc8_tex_2,cc8_xreal_0,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc2_xreal_0,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc4_xreal_0,rc5_tex_1,rc5_tops_1,rc6_pre_topc,rc6_tex_1,rc7_pre_topc,t1_subset,t4_subset,t5_subset,free_g1_pre_topc,dt_g1_pre_topc,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_u1_pre_topc,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,rc1_nat_1,rc1_pscomp_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc4_pscomp_1,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m2_subset_1,cc1_nat_1,cc1_real_1,cc2_nat_1,fc1_jordan5a,fc1_pscomp_1,rc1_pre_topc,existence_m1_subset_1,dt_k15_euclid,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c1_4_1__brouwer,de_c2_4_1__brouwer,e2_4_1__brouwer]),
    [interesting(0.65),file(brouwer,c2_4_1__brouwer),[file(brouwer,c2_4_1__brouwer)]]).

fof(dt_k20_euclid,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A)))
        & m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k20_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ),
    file(euclid,k20_euclid),
    [interesting(0.9),axiom,file(euclid,k20_euclid)]).

fof(dt_k5_toprns_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,u1_struct_0(k15_euclid(A))) )
     => m1_subset_1(k5_toprns_1(A,B),k1_numbers) ) ),
    file(toprns_1,k5_toprns_1),
    [interesting(0.9),axiom,file(toprns_1,k5_toprns_1)]).

fof(t1_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t2_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(t4_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(real,t8_real)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(t8_topreal9,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
                 => ( r2_hidden(C,k2_topreal9(A,D,B))
                  <=> r1_xreal_0(k5_toprns_1(A,k20_euclid(A,C,D)),B) ) ) ) ) ) ),
    file(topreal9,t8_topreal9),
    [interesting(0.9),axiom,file(topreal9,t8_topreal9)]).

fof(e3_4_1__brouwer,plain,(
    r1_xreal_0(k5_toprns_1(c1_4__brouwer,k20_euclid(c1_4__brouwer,c2_4_1__brouwer,c2_4__brouwer)),0) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc5_tex_1,rc5_tops_1,rc6_tex_1,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_l1_struct_0,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,fc3_topreal9,fc4_topreal9,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_topalg_2,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k1_numbers,dt_k20_euclid,dt_k2_topreal9,dt_k5_numbers,dt_k5_toprns_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,dt_c2_4_1__brouwer,de_c2_4_1__brouwer,cc1_nat_1,cc1_real_1,cc2_nat_1,cc2_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc6_topreal9,fc9_topreal9,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,t1_subset,t7_boole,spc0_numerals,spc0_boole,e1_4_1__brouwer,t8_topreal9]),
    [interesting(0.65),file(brouwer,e3_4_1__brouwer),[file(brouwer,e3_4_1__brouwer)]]).

fof(t26_toprns_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => r1_xreal_0(0,k5_toprns_1(A,B)) ) ) ),
    file(toprns_1,t26_toprns_1),
    [interesting(0.9),axiom,file(toprns_1,t26_toprns_1)]).

fof(e4_4_1__brouwer,plain,(
    k5_toprns_1(c1_4__brouwer,k20_euclid(c1_4__brouwer,c2_4_1__brouwer,c2_4__brouwer)) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc5_tex_1,rc5_tops_1,rc6_pre_topc,rc6_tex_1,rc7_pre_topc,t1_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_l1_struct_0,dt_c1_4_1__brouwer,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k1_numbers,dt_k20_euclid,dt_k5_numbers,dt_k5_toprns_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c2_4_1__brouwer,de_c2_4_1__brouwer,cc1_nat_1,cc1_real_1,cc2_nat_1,fc1_jordan5a,fc1_pscomp_1,rqLessOrEqual__r1_xreal_0__r0_r0,t1_numerals,spc0_numerals,spc0_boole,e3_4_1__brouwer,t26_toprns_1]),
    [interesting(0.65),file(brouwer,e4_4_1__brouwer),[file(brouwer,e4_4_1__brouwer)]]).

fof(t29_toprns_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
             => ( k5_toprns_1(A,k20_euclid(A,B,C)) = 0
              <=> B = C ) ) ) ) ),
    file(toprns_1,t29_toprns_1),
    [interesting(0.9),axiom,file(toprns_1,t29_toprns_1)]).

fof(e5_4_1__brouwer,plain,(
    c2_4_1__brouwer = c2_4__brouwer ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc5_tex_1,rc5_tops_1,rc6_pre_topc,rc6_tex_1,rc7_pre_topc,t1_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_l1_struct_0,dt_c1_4_1__brouwer,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k1_numbers,dt_k20_euclid,dt_k5_numbers,dt_k5_toprns_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c2_4_1__brouwer,de_c2_4_1__brouwer,cc1_nat_1,cc1_real_1,cc2_nat_1,fc1_jordan5a,fc1_pscomp_1,t1_numerals,spc0_numerals,spc0_boole,e4_4_1__brouwer,t29_toprns_1]),
    [interesting(0.65),file(brouwer,e5_4_1__brouwer),[file(brouwer,e5_4_1__brouwer)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e6_4_1__brouwer,plain,(
    r2_hidden(c1_4_1__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[cc2_tex_1,cc3_tex_1,cc3_xreal_0,cc4_tex_1,cc5_tex_1,cc6_xreal_0,cc8_xreal_0,rc10_tex_1,rc11_tex_1,rc2_xreal_0,rc3_funct_1,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_tops_1,rc4_xreal_0,rc5_tops_1,rc7_tex_1,rc8_tex_1,rc9_tex_1,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_k1_xboole_0,dt_k5_ordinal2,dt_u1_pre_topc,cc10_tex_2,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tex_2,cc4_tops_1,cc4_xreal_0,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tops_1,cc7_tex_2,cc7_xreal_0,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc2_pscomp_1,fc4_relat_1,rc10_tex_2,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc5_tex_1,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_2,rc8_tex_2,rc9_tex_2,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc3_tops_1,cc4_borsuk_2,cc4_tex_2,cc6_tex_2,fc1_jordan5a,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc3_revrot_1,rc1_pre_topc,rc1_subset_1,rc1_tex_2,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc5_tex_2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k1_struct_0,dt_k15_euclid,dt_k1_struct_0,dt_k1_tarski,dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,dt_c2_4_1__brouwer,de_c2_4_1__brouwer,fc1_tex_2,fc2_subset_1,t1_subset,t7_boole,e5_4_1__brouwer,d1_tarski]),
    [interesting(0.65),file(brouwer,e6_4_1__brouwer),[file(brouwer,e6_4_1__brouwer)]]).

fof(i3_4_1__brouwer,theorem,(
    $true ),
    introduced(tautology,[file(brouwer,i3_4_1__brouwer)]),
    [interesting(0.65),trivial,file(brouwer,i3_4_1__brouwer)]).

fof(i2_4_1__brouwer,plain,(
    r2_hidden(c1_4_1__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer,e1_4_1__brouwer])],[e6_4_1__brouwer,i3_4_1__brouwer]),
    [interesting(0.65),file(brouwer,i2_4_1__brouwer),[file(brouwer,i2_4_1__brouwer)]]).

fof(i1_4_1__brouwer,plain,(
    ~ ( r2_hidden(c1_4_1__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0))
      & ~ r2_hidden(c1_4_1__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__brouwer,dt_c1_4_1__brouwer,dt_c2_4__brouwer]),discharge_asm(discharge,[e1_4_1__brouwer])],[e1_4_1__brouwer,i2_4_1__brouwer]),
    [interesting(0.65),file(brouwer,i1_4_1__brouwer),[file(brouwer,i1_4_1__brouwer)]]).

fof(i1_4_1_tmp__brouwer,plain,(
    ~ ( r2_hidden(c1_4_1__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0))
      & ~ r2_hidden(c1_4_1__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer]),discharge_asm(discharge,[dt_c1_4_1__brouwer])],[dt_c1_4_1__brouwer,i1_4_1__brouwer]),
    [interesting(0.8),e1_4__brouwer]).

fof(e1_4__brouwer,plain,(
    r1_tarski(k2_topreal9(c1_4__brouwer,c2_4__brouwer,0),k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ),
    inference(let,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer])],[i1_4_1_tmp__brouwer,cc2_tex_1,cc3_tex_1,cc4_tex_1,cc5_tex_1,rc10_tex_1,rc11_tex_1,rc3_funct_1,rc4_tops_1,rc5_tops_1,rc7_tex_1,rc8_tex_1,rc9_tex_1,free_g1_pre_topc,dt_g1_pre_topc,dt_k5_ordinal2,dt_u1_pre_topc,cc10_tex_2,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc3_borsuk_2,cc3_nat_1,cc3_tex_2,cc4_tex_2,cc4_tops_1,cc4_xreal_0,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tex_2,cc6_tops_1,cc7_tex_2,cc8_tex_2,cc8_xreal_0,cc9_tex_2,fc1_revrot_1,fc2_pscomp_1,fc3_topreal9,fc4_topreal9,rc10_tex_2,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_tex_2,rc1_topalg_2,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc4_xreal_0,rc5_tex_1,rc5_tex_2,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_2,rc8_tex_2,rc9_tex_2,abstractness_v1_pre_topc,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc6_xreal_0,cc7_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc1_tex_2,fc2_subset_1,fc3_revrot_1,fc6_topreal9,fc9_topreal9,rc1_pre_topc,rc1_subset_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k1_struct_0,dt_k15_euclid,dt_k1_struct_0,dt_k2_topreal9,dt_c1_4__brouwer,dt_c2_4__brouwer,spc0_numerals,spc0_boole,d3_tarski,dh_c1_4_1__brouwer]),
    [interesting(0.8),file(brouwer,e1_4__brouwer),[file(brouwer,e1_4__brouwer)]]).

fof(dt_c3_4__brouwer,assumption,(
    $true ),
    introduced(assumption,[file(brouwer,c3_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c3_4__brouwer)]).

fof(dh_c3_4__brouwer,definition,
    ( ~ ( r2_hidden(c3_4__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer))
        & ~ r2_hidden(c3_4__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer))
          & ~ r2_hidden(A,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ) ),
    introduced(definition,[new_symbol(c3_4__brouwer),file(brouwer,c3_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,c3_4__brouwer)]).

fof(e2_4__brouwer,assumption,(
    r2_hidden(c3_4__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer)) ),
    introduced(assumption,[file(brouwer,e2_4__brouwer)]),
    [interesting(0.8),axiom,file(brouwer,e2_4__brouwer)]).

fof(e4_4__brouwer,plain,(
    k5_toprns_1(c1_4__brouwer,k20_euclid(c1_4__brouwer,c2_4__brouwer,c2_4__brouwer)) = 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc5_tex_1,rc5_tops_1,rc6_pre_topc,rc6_tex_1,rc7_pre_topc,t1_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_l1_struct_0,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k1_numbers,dt_k20_euclid,dt_k5_numbers,dt_k5_toprns_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c2_4__brouwer,cc1_nat_1,cc1_real_1,cc2_nat_1,fc1_jordan5a,fc1_pscomp_1,t1_numerals,spc0_numerals,spc0_boole,t29_toprns_1]),
    [interesting(0.8),file(brouwer,e4_4__brouwer),[file(brouwer,e4_4__brouwer)]]).

fof(e3_4__brouwer,plain,(
    c3_4__brouwer = c2_4__brouwer ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer,e2_4__brouwer])],[cc2_tex_1,cc3_tex_1,cc3_xreal_0,cc4_tex_1,cc5_tex_1,cc6_xreal_0,cc8_xreal_0,rc10_tex_1,rc11_tex_1,rc2_xreal_0,rc3_funct_1,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_tops_1,rc4_xreal_0,rc5_tops_1,rc7_tex_1,rc8_tex_1,rc9_tex_1,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_k1_xboole_0,dt_k5_ordinal2,dt_u1_pre_topc,cc10_tex_2,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc3_borsuk_2,cc3_nat_1,cc3_tex_2,cc4_tops_1,cc4_xreal_0,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tops_1,cc7_tex_2,cc7_xreal_0,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc2_pscomp_1,fc4_relat_1,rc10_tex_2,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc5_tex_1,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_2,rc8_tex_2,rc9_tex_2,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc3_tops_1,cc4_borsuk_2,cc4_tex_2,cc6_tex_2,fc1_jordan5a,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc3_revrot_1,rc1_pre_topc,rc1_subset_1,rc1_tex_2,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc5_tex_2,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k1_struct_0,dt_k15_euclid,dt_k1_struct_0,dt_k1_tarski,dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer,fc1_tex_2,fc2_subset_1,t1_subset,t7_boole,e2_4__brouwer,d1_tarski]),
    [interesting(0.8),file(brouwer,e3_4__brouwer),[file(brouwer,e3_4__brouwer)]]).

fof(e5_4__brouwer,plain,(
    r2_hidden(c3_4__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer,e2_4__brouwer])],[cc10_tex_2,cc2_tex_1,cc3_tex_1,cc3_tex_2,cc4_tex_1,cc4_tex_2,cc5_tex_1,cc5_tex_2,cc6_tex_2,cc7_tex_2,rc10_tex_1,rc10_tex_2,rc11_tex_1,rc1_tex_2,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc5_tex_2,rc6_tex_2,rc7_tex_1,rc7_tex_2,rc8_tex_1,rc8_tex_2,rc9_tex_1,rc9_tex_2,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_k1_xboole_0,dt_u1_pre_topc,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc2_funct_1,cc4_tops_1,cc5_tops_1,cc6_tops_1,cc8_tex_2,cc9_tex_2,fc12_relat_1,fc1_revrot_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tops_1,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc4_tex_1,rc4_tex_2,rc4_tops_1,rc5_tex_1,rc5_tops_1,rc6_tex_1,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_l1_pre_topc,dt_l1_struct_0,cc1_funct_1,cc1_relat_1,cc1_tops_1,cc1_xreal_0,cc2_tex_2,cc2_tops_1,cc3_borsuk_2,cc3_nat_1,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_struct_0,fc1_subset_1,fc2_pscomp_1,fc3_revrot_1,fc3_topreal9,fc4_topreal9,rc1_nat_1,rc1_pre_topc,rc1_pscomp_1,rc1_subset_1,rc1_topalg_2,rc1_xreal_0,rc2_nat_1,rc2_pre_topc,rc2_pscomp_1,rc2_subset_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_struct_0,rc3_xreal_0,rc4_pscomp_1,rc4_xreal_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k15_euclid,dt_k1_numbers,dt_k20_euclid,dt_k2_topreal9,dt_k5_numbers,dt_k5_toprns_1,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer,cc1_nat_1,cc1_real_1,cc2_nat_1,cc2_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc6_topreal9,fc9_topreal9,t1_numerals,t1_subset,t7_boole,spc0_numerals,spc0_boole,e4_4__brouwer,e3_4__brouwer,t8_topreal9,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.8),file(brouwer,e5_4__brouwer),[file(brouwer,e5_4__brouwer)]]).

fof(i6_4__brouwer,theorem,(
    $true ),
    introduced(tautology,[file(brouwer,i6_4__brouwer)]),
    [interesting(0.8),trivial,file(brouwer,i6_4__brouwer)]).

fof(i5_4__brouwer,plain,(
    r2_hidden(c3_4__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer,e2_4__brouwer])],[e5_4__brouwer,i6_4__brouwer]),
    [interesting(0.8),file(brouwer,i5_4__brouwer),[file(brouwer,i5_4__brouwer)]]).

fof(i4_4__brouwer,plain,(
    ~ ( r2_hidden(c3_4__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer))
      & ~ r2_hidden(c3_4__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer,dt_c3_4__brouwer]),discharge_asm(discharge,[e2_4__brouwer])],[e2_4__brouwer,i5_4__brouwer]),
    [interesting(0.8),file(brouwer,i4_4__brouwer),[file(brouwer,i4_4__brouwer)]]).

fof(i4_4_tmp__brouwer,plain,(
    ~ ( r2_hidden(c3_4__brouwer,k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer))
      & ~ r2_hidden(c3_4__brouwer,k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer]),discharge_asm(discharge,[dt_c3_4__brouwer])],[dt_c3_4__brouwer,i4_4__brouwer]),
    [interesting(0.8),i3_4__brouwer]).

fof(i3_4__brouwer,plain,(
    r1_tarski(k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer),k2_topreal9(c1_4__brouwer,c2_4__brouwer,0)) ),
    inference(let,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer])],[i4_4_tmp__brouwer,cc2_tex_1,cc3_tex_1,cc4_tex_1,cc5_tex_1,rc10_tex_1,rc11_tex_1,rc3_funct_1,rc4_tops_1,rc5_tops_1,rc7_tex_1,rc8_tex_1,rc9_tex_1,free_g1_pre_topc,dt_g1_pre_topc,dt_k5_ordinal2,dt_u1_pre_topc,cc10_tex_2,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc3_borsuk_2,cc3_nat_1,cc3_tex_2,cc4_tex_2,cc4_tops_1,cc4_xreal_0,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tex_2,cc6_tops_1,cc7_tex_2,cc8_tex_2,cc8_xreal_0,cc9_tex_2,fc1_revrot_1,fc2_pscomp_1,fc3_topreal9,fc4_topreal9,rc10_tex_2,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_tex_2,rc1_topalg_2,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc4_xreal_0,rc5_tex_1,rc5_tex_2,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_2,rc8_tex_2,rc9_tex_2,abstractness_v1_pre_topc,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc6_xreal_0,cc7_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc1_tex_2,fc2_subset_1,fc3_revrot_1,fc6_topreal9,fc9_topreal9,rc1_pre_topc,rc1_subset_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k1_struct_0,dt_k15_euclid,dt_k1_struct_0,dt_k2_topreal9,dt_c1_4__brouwer,dt_c2_4__brouwer,spc0_numerals,spc0_boole,d3_tarski,dh_c3_4__brouwer]),
    [interesting(0.8),file(brouwer,i3_4__brouwer),[file(brouwer,i3_4__brouwer)]]).

fof(i2_4__brouwer,plain,(
    k2_topreal9(c1_4__brouwer,c2_4__brouwer,0) = k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_4__brouwer,dt_c2_4__brouwer])],[cc2_tex_1,cc3_tex_1,cc4_tex_1,cc5_tex_1,rc10_tex_1,rc11_tex_1,rc3_funct_1,rc4_tops_1,rc5_tops_1,rc7_tex_1,rc8_tex_1,rc9_tex_1,free_g1_pre_topc,dt_g1_pre_topc,dt_k5_ordinal2,dt_u1_pre_topc,cc10_tex_2,cc11_tex_2,cc1_tex_1,cc1_tex_2,cc1_xreal_0,cc2_funct_1,cc3_borsuk_2,cc3_nat_1,cc3_tex_2,cc4_tex_2,cc4_tops_1,cc4_xreal_0,cc5_tex_2,cc5_tops_1,cc5_xreal_0,cc6_tex_2,cc6_tops_1,cc7_tex_2,cc8_tex_2,cc8_xreal_0,cc9_tex_2,fc1_revrot_1,fc2_pscomp_1,fc3_topreal9,fc4_topreal9,rc10_tex_2,rc1_funct_1,rc1_nat_1,rc1_pscomp_1,rc1_relat_1,rc1_tex_2,rc1_topalg_2,rc1_tops_1,rc1_xreal_0,rc2_funct_1,rc2_nat_1,rc2_pscomp_1,rc2_relat_1,rc2_tex_2,rc2_tops_1,rc2_xreal_0,rc3_borsuk_2,rc3_nat_1,rc3_pscomp_1,rc3_tex_1,rc3_tex_2,rc3_tops_1,rc3_xreal_0,rc4_pscomp_1,rc4_tex_1,rc4_tex_2,rc4_xreal_0,rc5_tex_1,rc5_tex_2,rc6_pre_topc,rc6_tex_1,rc6_tex_2,rc7_pre_topc,rc7_tex_2,rc8_tex_2,rc9_tex_2,abstractness_v1_pre_topc,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc1_funct_1,cc1_nat_1,cc1_real_1,cc1_relat_1,cc1_tops_1,cc2_nat_1,cc2_tex_2,cc2_tops_1,cc2_xreal_0,cc3_tops_1,cc3_xreal_0,cc4_borsuk_2,cc6_xreal_0,cc7_xreal_0,fc1_jordan5a,fc1_pscomp_1,fc1_struct_0,fc1_subset_1,fc1_tex_2,fc2_subset_1,fc3_revrot_1,fc6_topreal9,fc9_topreal9,rc1_pre_topc,rc1_subset_1,rc2_pre_topc,rc2_subset_1,rc3_struct_0,rc5_struct_0,reflexivity_r1_tarski,redefinition_k1_struct_0,dt_k15_euclid,dt_k1_struct_0,dt_k2_topreal9,dt_c1_4__brouwer,dt_c2_4__brouwer,spc0_numerals,spc0_boole,d10_xboole_0,e1_4__brouwer,i3_4__brouwer]),
    [interesting(0.8),file(brouwer,i2_4__brouwer),[file(brouwer,i2_4__brouwer)]]).

fof(i2_4_tmp__brouwer,plain,
    ( m1_subset_1(c2_4__brouwer,u1_struct_0(k15_euclid(c1_4__brouwer)))
   => k2_topreal9(c1_4__brouwer,c2_4__brouwer,0) = k1_struct_0(k15_euclid(c1_4__brouwer),c2_4__brouwer) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_4__brouwer]),discharge_asm(discharge,[dt_c2_4__brouwer])],[dt_c2_4__brouwer,i2_4__brouwer]),
    [interesting(0.8),i1_4__brouwer]).

fof(i1_4__brouwer,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_4__brouwer)))
     => k2_topreal9(c1_4__brouwer,A,0) = k1_struct_0(k15_euclid(c1_4__brouwer),A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_4__brouwer])],[i2_4_tmp__brouwer,dh_c2_4__brouwer]),
    [interesting(0.8),file(brouwer,i1_4__brouwer),[file(brouwer,i1_4__brouwer)]]).

fof(i1_4_tmp__brouwer,plain,
    ( m2_subset_1(c1_4__brouwer,k1_numbers,k5_numbers)
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k15_euclid(c1_4__brouwer)))
       => k2_topreal9(c1_4__brouwer,A,0) = k1_struct_0(k15_euclid(c1_4__brouwer),A) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__brouwer])],[dt_c1_4__brouwer,i1_4__brouwer]),
    [interesting(1),t2_brouwer]).

fof(t2_brouwer,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
         => k2_topreal9(A,B,0) = k1_struct_0(k15_euclid(A),B) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_4_tmp__brouwer,dh_c1_4__brouwer]),
    [interesting(1),file(brouwer,t2_brouwer),[file(brouwer,t2_brouwer)]]).