% Mizar ND problem: t4_borsuk_2,borsuk_2,232,64 
fof(dh_c1_8__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c1_8__borsuk_2)
        & v2_pre_topc(c1_8__borsuk_2)
        & l1_pre_topc(c1_8__borsuk_2) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_8__borsuk_2))
         => ? [B] : 
              ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
              & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
              & v5_pre_topc(B,k5_topmetr,c1_8__borsuk_2)
              & k1_funct_1(B,0) = A
              & k1_funct_1(B,1) = A ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v2_pre_topc(C)
          & l1_pre_topc(C) )
       => ! [D] : 
            ( m1_subset_1(D,u1_struct_0(C))
           => ? [E] : 
                ( v1_funct_1(E)
                & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(C))
                & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(C))
                & v5_pre_topc(E,k5_topmetr,C)
                & k1_funct_1(E,0) = D
                & k1_funct_1(E,1) = D ) ) ) ),
    introduced(definition,[new_symbol(c1_8__borsuk_2),file(borsuk_2,c1_8__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_8__borsuk_2)]).

fof(dh_c2_8__borsuk_2,definition,
    ( ( m1_subset_1(c2_8__borsuk_2,u1_struct_0(c1_8__borsuk_2))
     => ? [A] : 
          ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
          & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
          & v5_pre_topc(A,k5_topmetr,c1_8__borsuk_2)
          & k1_funct_1(A,0) = c2_8__borsuk_2
          & k1_funct_1(A,1) = c2_8__borsuk_2 ) )
   => ! [B] : 
        ( m1_subset_1(B,u1_struct_0(c1_8__borsuk_2))
       => ? [C] : 
            ( v1_funct_1(C)
            & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
            & m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
            & v5_pre_topc(C,k5_topmetr,c1_8__borsuk_2)
            & k1_funct_1(C,0) = B
            & k1_funct_1(C,1) = B ) ) ),
    introduced(definition,[new_symbol(c2_8__borsuk_2),file(borsuk_2,c2_8__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_8__borsuk_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(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

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

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

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

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

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

fof(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_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(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_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

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(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(rc1_borsuk_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v5_pre_topc(B,A,A)
          & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(borsuk_2,rc1_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,rc1_borsuk_2)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(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_borsuk_1,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v5_pre_topc(C,A,B)
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ),
    file(borsuk_1,rc2_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,rc2_borsuk_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(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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k22_borsuk_1,axiom,(
    l1_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,k22_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k22_borsuk_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k3_topmetr,axiom,
    ( v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr)
    & l1_pre_topc(k3_topmetr) ),
    file(topmetr,k3_topmetr),
    [interesting(0.9),axiom,file(topmetr,k3_topmetr)]).

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_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(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(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_borsuk_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k5_topmetr))
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(borsuk_2,cc1_borsuk_2),
    [interesting(0.9),axiom,file(borsuk_2,cc1_borsuk_2)]).

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_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v2_pre_topc(B) ) ) ),
    file(pre_topc,cc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,cc1_pre_topc)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(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(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

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

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

fof(fc1_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(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(fc2_topmetr,theorem,
    ( ~ v3_struct_0(k3_topmetr)
    & v1_pre_topc(k3_topmetr)
    & v2_pre_topc(k3_topmetr) ),
    file(topmetr,fc2_topmetr),
    [interesting(0.9),axiom,file(topmetr,fc2_topmetr)]).

fof(fc3_topmetr,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(topmetr,fc3_topmetr)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(fc5_borsuk_1,theorem,
    ( ~ v3_struct_0(k22_borsuk_1)
    & v1_pre_topc(k22_borsuk_1)
    & v2_pre_topc(k22_borsuk_1) ),
    file(borsuk_1,fc5_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,fc5_borsuk_1)]).

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_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

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_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_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_pre_topc,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc3_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc3_pre_topc)]).

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(rc4_pre_topc,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & ~ v3_struct_0(B)
          & v1_pre_topc(B) ) ) ),
    file(pre_topc,rc4_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc4_pre_topc)]).

fof(rc5_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_pre_topc(B,A)
          & v1_pre_topc(B)
          & v2_pre_topc(B) ) ) ),
    file(pre_topc,rc5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc5_pre_topc)]).

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(redefinition_k5_topmetr,definition,(
    k5_topmetr = k22_borsuk_1 ),
    file(topmetr,k5_topmetr),
    [interesting(0.9),axiom,file(topmetr,k5_topmetr)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k5_topmetr,axiom,
    ( v1_pre_topc(k5_topmetr)
    & m1_pre_topc(k5_topmetr,k3_topmetr) ),
    file(topmetr,k5_topmetr),
    [interesting(0.9),axiom,file(topmetr,k5_topmetr)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

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

fof(dt_c1_8__borsuk_2,assumption,
    ( ~ v3_struct_0(c1_8__borsuk_2)
    & v2_pre_topc(c1_8__borsuk_2)
    & l1_pre_topc(c1_8__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c1_8__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_8__borsuk_2)]).

fof(dt_c2_8__borsuk_2,assumption,(
    m1_subset_1(c2_8__borsuk_2,u1_struct_0(c1_8__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,c2_8__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_8__borsuk_2)]).

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

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

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

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

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

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

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

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

fof(existence_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_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

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

fof(fc1_borsuk_1,theorem,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & v2_pre_topc(B)
        & l1_pre_topc(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( ~ v1_xboole_0(k3_borsuk_1(A,B,C))
        & v1_relat_1(k3_borsuk_1(A,B,C))
        & v1_funct_1(k3_borsuk_1(A,B,C))
        & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
        & v5_pre_topc(k3_borsuk_1(A,B,C),A,B)
        & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ),
    file(borsuk_1,fc1_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,fc1_borsuk_1)]).

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(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k3_borsuk_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v1_funct_1(k3_borsuk_1(A,B,C))
        & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
        & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ),
    file(borsuk_1,k3_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k3_borsuk_1)]).

fof(de_c3_8__borsuk_2,definition,(
    c3_8__borsuk_2 = k3_borsuk_1(k5_topmetr,c1_8__borsuk_2,c2_8__borsuk_2) ),
    introduced(definition,[new_symbol(c3_8__borsuk_2),file(borsuk_2,c3_8__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c3_8__borsuk_2)]).

fof(dt_c3_8__borsuk_2,plain,
    ( v1_funct_1(c3_8__borsuk_2)
    & v1_funct_2(c3_8__borsuk_2,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
    & m2_relset_1(c3_8__borsuk_2,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[cc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_borsuk_2,rc1_membered,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,free_g1_pre_topc,reflexivity_r1_tarski,dt_g1_pre_topc,dt_u1_pre_topc,cc15_membered,cc1_funct_1,cc1_funct_2,cc2_funct_1,cc2_xreal_0,cc5_funct_2,cc6_funct_2,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc1_xreal_0,rc2_borsuk_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k2_zfmisc_1,dt_k3_topmetr,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,cc1_borsuk_2,cc1_pre_topc,cc1_relset_1,fc1_borsuk_1,fc1_struct_0,fc1_subset_1,fc2_topmetr,fc5_borsuk_1,rc1_pre_topc,rc2_pre_topc,rc3_pre_topc,rc3_struct_0,rc4_pre_topc,rc5_pre_topc,t3_subset,existence_m2_relset_1,redefinition_k5_topmetr,redefinition_m2_relset_1,dt_k3_borsuk_1,dt_k5_topmetr,dt_m2_relset_1,dt_u1_struct_0,dt_c1_8__borsuk_2,dt_c2_8__borsuk_2,de_c3_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,c3_8__borsuk_2),[file(borsuk_2,c3_8__borsuk_2)]]).

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(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

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

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(e1_8__borsuk_2,plain,(
    v5_pre_topc(c3_8__borsuk_2,k5_topmetr,c1_8__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[cc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc6_membered,rc1_borsuk_2,rc1_membered,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,cc1_funct_2,cc2_funct_1,cc2_xreal_0,cc5_funct_2,cc6_funct_2,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc1_xreal_0,rc2_borsuk_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,free_g1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_g1_pre_topc,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_u1_pre_topc,cc1_borsuk_2,cc1_relset_1,fc1_borsuk_1,fc1_struct_0,fc1_subset_1,rc3_struct_0,t3_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_m1_pre_topc,existence_m2_relset_1,redefinition_m2_relset_1,dt_k22_borsuk_1,dt_k3_borsuk_1,dt_k3_topmetr,dt_l1_pre_topc,dt_m1_pre_topc,dt_m2_relset_1,dt_u1_struct_0,dt_c2_8__borsuk_2,cc1_pre_topc,fc2_topmetr,fc5_borsuk_1,rc1_pre_topc,rc2_pre_topc,rc3_pre_topc,rc4_pre_topc,rc5_pre_topc,redefinition_k5_topmetr,dt_k5_topmetr,dt_c1_8__borsuk_2,dt_c3_8__borsuk_2,de_c3_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e1_8__borsuk_2),[file(borsuk_2,e1_8__borsuk_2)]]).

fof(rc1_yellow_6,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v5_seqm_3(A) ) ),
    file(yellow_6,rc1_yellow_6),
    [interesting(0.9),axiom,file(yellow_6,rc1_yellow_6)]).

fof(rc2_yellow_6,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v5_seqm_3(A)
      & v2_pralg_1(A) ) ),
    file(yellow_6,rc2_yellow_6),
    [interesting(0.9),axiom,file(yellow_6,rc2_yellow_6)]).

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(fc3_yellow_6,theorem,(
    ! [A,B] : 
      ( l1_struct_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v5_seqm_3(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B)) ) ) ),
    file(yellow_6,fc3_yellow_6),
    [interesting(0.9),axiom,file(yellow_6,fc3_yellow_6)]).

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

fof(redefinition_k1_borsuk_1,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) ),
    file(borsuk_1,k1_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k1_borsuk_1)]).

fof(dt_k1_borsuk_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_borsuk_1(A,B,C))
        & v1_funct_2(k1_borsuk_1(A,B,C),B,A)
        & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) ),
    file(borsuk_1,k1_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k1_borsuk_1)]).

fof(dt_k23_borsuk_1,axiom,(
    m1_subset_1(k23_borsuk_1,u1_struct_0(k22_borsuk_1)) ),
    file(borsuk_1,k23_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k23_borsuk_1)]).

fof(dt_k24_borsuk_1,axiom,(
    m1_subset_1(k24_borsuk_1,u1_struct_0(k22_borsuk_1)) ),
    file(borsuk_1,k24_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,k24_borsuk_1)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

fof(d3_borsuk_1,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_borsuk_1(A,B,C) = k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) ) ) ) ),
    file(borsuk_1,d3_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,d3_borsuk_1)]).

fof(e2_8__borsuk_2,plain,(
    c3_8__borsuk_2 = k1_borsuk_1(u1_struct_0(c1_8__borsuk_2),u1_struct_0(k5_topmetr),c2_8__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[reflexivity_r1_tarski,cc1_xreal_0,rc1_borsuk_2,rc3_funct_1,free_g1_pre_topc,antisymmetry_r2_hidden,existence_m1_relset_1,dt_g1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_xreal_0,cc8_xreal_0,fc1_subset_1,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc1_yellow_6,rc2_borsuk_1,rc2_funct_1,rc2_subset_1,rc2_xreal_0,rc2_yellow_6,rc3_xreal_0,rc4_xreal_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_m1_pre_topc,existence_m2_relset_1,redefinition_m2_relset_1,dt_k22_borsuk_1,dt_k2_funcop_1,dt_k3_topmetr,dt_l1_pre_topc,dt_m1_pre_topc,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc1_pre_topc,cc2_xreal_0,cc7_xreal_0,fc1_borsuk_1,fc2_topmetr,fc3_yellow_6,fc5_borsuk_1,rc1_pre_topc,rc1_xreal_0,rc2_pre_topc,rc3_pre_topc,rc4_pre_topc,rc5_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,redefinition_k1_borsuk_1,redefinition_k5_topmetr,dt_k1_borsuk_1,dt_k3_borsuk_1,dt_k5_topmetr,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_8__borsuk_2,dt_c2_8__borsuk_2,dt_c3_8__borsuk_2,de_c3_8__borsuk_2,cc1_borsuk_2,fc1_struct_0,rc3_struct_0,d3_borsuk_1]),
    [interesting(0.8),file(borsuk_2,e2_8__borsuk_2),[file(borsuk_2,e2_8__borsuk_2)]]).

fof(d17_borsuk_1,definition,(
    k23_borsuk_1 = 0 ),
    file(borsuk_1,d17_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,d17_borsuk_1)]).

fof(d18_borsuk_1,definition,(
    k24_borsuk_1 = 1 ),
    file(borsuk_1,d18_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,d18_borsuk_1)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t13_funcop_1)]).

fof(e3_8__borsuk_2,plain,
    ( k1_funct_1(c3_8__borsuk_2,0) = c2_8__borsuk_2
    & k1_funct_1(c3_8__borsuk_2,1) = c2_8__borsuk_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[reflexivity_r1_tarski,cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,existence_m1_relset_1,dt_g1_pre_topc,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_subset_1,fc3_topmetr,fc4_subset_1,fc5_membered,fc6_membered,rc1_borsuk_2,rc1_funct_2,rc1_membered,rc1_subset_1,rc1_xreal_0,rc1_yellow_6,rc2_borsuk_1,rc2_subset_1,rc2_yellow_6,rc3_funct_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,abstractness_v1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k22_borsuk_1,dt_k3_borsuk_1,dt_k3_topmetr,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc1_borsuk_2,cc1_funct_1,cc1_pre_topc,cc2_funct_1,fc1_borsuk_1,fc1_struct_0,fc2_membered,fc2_topmetr,fc3_yellow_6,fc5_borsuk_1,rc1_funct_1,rc1_pre_topc,rc2_funct_1,rc2_pre_topc,rc3_pre_topc,rc3_struct_0,rc4_pre_topc,rc5_pre_topc,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k1_borsuk_1,redefinition_k5_topmetr,dt_k1_borsuk_1,dt_k1_funct_1,dt_k23_borsuk_1,dt_k24_borsuk_1,dt_k2_funcop_1,dt_k5_topmetr,dt_u1_struct_0,dt_c1_8__borsuk_2,dt_c2_8__borsuk_2,dt_c3_8__borsuk_2,de_c3_8__borsuk_2,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e2_8__borsuk_2,d17_borsuk_1,d18_borsuk_1,t13_funcop_1]),
    [interesting(0.8),file(borsuk_2,e3_8__borsuk_2),[file(borsuk_2,e3_8__borsuk_2)]]).

fof(i5_8__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i5_8__borsuk_2)]),
    [interesting(0.8),trivial,file(borsuk_2,i5_8__borsuk_2)]).

fof(i4_8__borsuk_2,plain,
    ( k1_funct_1(c3_8__borsuk_2,0) = c2_8__borsuk_2
    & k1_funct_1(c3_8__borsuk_2,1) = c2_8__borsuk_2 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[e3_8__borsuk_2,i5_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i4_8__borsuk_2),[file(borsuk_2,i4_8__borsuk_2)]]).

fof(i3_8__borsuk_2,plain,
    ( v5_pre_topc(c3_8__borsuk_2,k5_topmetr,c1_8__borsuk_2)
    & k1_funct_1(c3_8__borsuk_2,0) = c2_8__borsuk_2
    & k1_funct_1(c3_8__borsuk_2,1) = c2_8__borsuk_2 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[e1_8__borsuk_2,i4_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i3_8__borsuk_2),[file(borsuk_2,i3_8__borsuk_2)]]).

fof(i2_8__borsuk_2,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
      & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
      & v5_pre_topc(A,k5_topmetr,c1_8__borsuk_2)
      & k1_funct_1(A,0) = c2_8__borsuk_2
      & k1_funct_1(A,1) = c2_8__borsuk_2 ) ),
    inference(take,[status(thm),assumptions([dt_c1_8__borsuk_2,dt_c2_8__borsuk_2])],[cc1_xreal_0,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,free_g1_pre_topc,dt_g1_pre_topc,dt_k5_ordinal2,dt_u1_pre_topc,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc5_membered,rc1_borsuk_2,rc1_membered,rc1_xreal_0,rc2_borsuk_1,rc3_funct_1,abstractness_v1_pre_topc,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k22_borsuk_1,dt_k2_zfmisc_1,dt_k3_topmetr,dt_k5_numbers,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_borsuk_2,cc1_funct_1,cc1_pre_topc,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,fc1_struct_0,fc1_subset_1,fc2_membered,fc2_topmetr,fc3_topmetr,fc4_subset_1,fc5_borsuk_1,rc1_funct_1,rc1_funct_2,rc1_pre_topc,rc1_subset_1,rc2_funct_1,rc2_pre_topc,rc2_subset_1,rc3_pre_topc,rc3_struct_0,rc4_pre_topc,rc5_pre_topc,rc5_struct_0,redefinition_k5_topmetr,redefinition_m2_relset_1,dt_k1_funct_1,dt_k5_topmetr,dt_m2_relset_1,dt_u1_struct_0,dt_c1_8__borsuk_2,dt_c2_8__borsuk_2,dt_c3_8__borsuk_2,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,i3_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i2_8__borsuk_2),[file(borsuk_2,i2_8__borsuk_2)]]).

fof(i2_8_tmp__borsuk_2,plain,
    ( m1_subset_1(c2_8__borsuk_2,u1_struct_0(c1_8__borsuk_2))
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
        & m2_relset_1(A,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
        & v5_pre_topc(A,k5_topmetr,c1_8__borsuk_2)
        & k1_funct_1(A,0) = c2_8__borsuk_2
        & k1_funct_1(A,1) = c2_8__borsuk_2 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__borsuk_2]),discharge_asm(discharge,[dt_c2_8__borsuk_2])],[dt_c2_8__borsuk_2,i2_8__borsuk_2]),
    [interesting(0.8),i1_8__borsuk_2]).

fof(i1_8__borsuk_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_8__borsuk_2))
     => ? [B] : 
          ( v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
          & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
          & v5_pre_topc(B,k5_topmetr,c1_8__borsuk_2)
          & k1_funct_1(B,0) = A
          & k1_funct_1(B,1) = A ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__borsuk_2])],[i2_8_tmp__borsuk_2,dh_c2_8__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i1_8__borsuk_2),[file(borsuk_2,i1_8__borsuk_2)]]).

fof(i1_8_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c1_8__borsuk_2)
      & v2_pre_topc(c1_8__borsuk_2)
      & l1_pre_topc(c1_8__borsuk_2) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_8__borsuk_2))
       => ? [B] : 
            ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
            & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(c1_8__borsuk_2))
            & v5_pre_topc(B,k5_topmetr,c1_8__borsuk_2)
            & k1_funct_1(B,0) = A
            & k1_funct_1(B,1) = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__borsuk_2])],[dt_c1_8__borsuk_2,i1_8__borsuk_2]),
    [interesting(1),t4_borsuk_2]).

fof(t4_borsuk_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ? [C] : 
              ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A))
              & m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(A))
              & v5_pre_topc(C,k5_topmetr,A)
              & k1_funct_1(C,0) = B
              & k1_funct_1(C,1) = B ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__borsuk_2,dh_c1_8__borsuk_2]),
    [interesting(1),file(borsuk_2,t4_borsuk_2),[file(borsuk_2,t4_borsuk_2)]]).