% Mizar ND problem: t3_borsuk_2,borsuk_2,205,13 
fof(dh_c1_6__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c1_6__borsuk_2)
        & v2_pre_topc(c1_6__borsuk_2)
        & l1_pre_topc(c1_6__borsuk_2) )
     => ! [A] : 
          ( ( ~ v3_struct_0(A)
            & v2_pre_topc(A)
            & l1_pre_topc(A) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(c1_6__borsuk_2),u1_struct_0(A))
                & m2_relset_1(B,u1_struct_0(c1_6__borsuk_2),u1_struct_0(A)) )
             => ( v3_tops_2(B,c1_6__borsuk_2,A)
               => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,A,B),A,c1_6__borsuk_2) ) ) ) )
   => ! [C] : 
        ( ( ~ v3_struct_0(C)
          & v2_pre_topc(C)
          & l1_pre_topc(C) )
       => ! [D] : 
            ( ( ~ v3_struct_0(D)
              & v2_pre_topc(D)
              & l1_pre_topc(D) )
           => ! [E] : 
                ( ( v1_funct_1(E)
                  & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
                  & m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
               => ( v3_tops_2(E,C,D)
                 => v1_t_0topsp(k2_tops_2(C,D,E),D,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__borsuk_2),file(borsuk_2,c1_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_6__borsuk_2)]).

fof(dh_c2_6__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c2_6__borsuk_2)
        & v2_pre_topc(c2_6__borsuk_2)
        & l1_pre_topc(c2_6__borsuk_2) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
            & m2_relset_1(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
         => ( v3_tops_2(A,c1_6__borsuk_2,c2_6__borsuk_2)
           => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,A),c2_6__borsuk_2,c1_6__borsuk_2) ) ) )
   => ! [B] : 
        ( ( ~ v3_struct_0(B)
          & v2_pre_topc(B)
          & l1_pre_topc(B) )
       => ! [C] : 
            ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(c1_6__borsuk_2),u1_struct_0(B))
              & m2_relset_1(C,u1_struct_0(c1_6__borsuk_2),u1_struct_0(B)) )
           => ( v3_tops_2(C,c1_6__borsuk_2,B)
             => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,B,C),B,c1_6__borsuk_2) ) ) ) ),
    introduced(definition,[new_symbol(c2_6__borsuk_2),file(borsuk_2,c2_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_6__borsuk_2)]).

fof(dh_c3_6__borsuk_2,definition,
    ( ( ( v1_funct_1(c3_6__borsuk_2)
        & v1_funct_2(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
        & m2_relset_1(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
     => ( v3_tops_2(c3_6__borsuk_2,c1_6__borsuk_2,c2_6__borsuk_2)
       => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c2_6__borsuk_2,c1_6__borsuk_2) ) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
          & m2_relset_1(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
       => ( v3_tops_2(A,c1_6__borsuk_2,c2_6__borsuk_2)
         => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,A),c2_6__borsuk_2,c1_6__borsuk_2) ) ) ),
    introduced(definition,[new_symbol(c3_6__borsuk_2),file(borsuk_2,c3_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c3_6__borsuk_2)]).

fof(e1_6__borsuk_2,assumption,(
    v3_tops_2(c3_6__borsuk_2,c1_6__borsuk_2,c2_6__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e1_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e1_6__borsuk_2)]).

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

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

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

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

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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_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_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(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(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(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(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_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(redefinition_k4_pre_topc,definition,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(pre_topc,k4_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k4_pre_topc)]).

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_tops_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => ( v1_funct_1(k2_tops_2(A,B,C))
        & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A))
        & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(tops_2,k2_tops_2),
    [interesting(0.9),axiom,file(tops_2,k2_tops_2)]).

fof(dt_k4_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ),
    file(pre_topc,k4_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k4_pre_topc)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [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_6__borsuk_2,assumption,
    ( ~ v3_struct_0(c1_6__borsuk_2)
    & v2_pre_topc(c1_6__borsuk_2)
    & l1_pre_topc(c1_6__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c1_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_6__borsuk_2)]).

fof(dt_c2_6__borsuk_2,assumption,
    ( ~ v3_struct_0(c2_6__borsuk_2)
    & v2_pre_topc(c2_6__borsuk_2)
    & l1_pre_topc(c2_6__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c2_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_6__borsuk_2)]).

fof(dt_c3_6__borsuk_2,assumption,
    ( v1_funct_1(c3_6__borsuk_2)
    & v1_funct_2(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
    & m2_relset_1(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,c3_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c3_6__borsuk_2)]).

fof(dt_c4_6__borsuk_2,assumption,(
    m1_subset_1(c4_6__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_6__borsuk_2))) ),
    introduced(assumption,[file(borsuk_2,c4_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c4_6__borsuk_2)]).

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(d2_t_0topsp,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_t_0topsp(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v3_pre_topc(D,A)
                     => v3_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ),
    file(t_0topsp,d2_t_0topsp),
    [interesting(0.9),axiom,file(t_0topsp,d2_t_0topsp)]).

fof(dh_c4_6__borsuk_2,definition,
    ( ( m1_subset_1(c4_6__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_6__borsuk_2)))
     => ~ ( v3_pre_topc(c4_6__borsuk_2,c2_6__borsuk_2)
          & ~ v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2),c1_6__borsuk_2) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_6__borsuk_2)))
       => ~ ( v3_pre_topc(A,c2_6__borsuk_2)
            & ~ v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),A),c1_6__borsuk_2) ) ) ),
    introduced(definition,[new_symbol(c4_6__borsuk_2),file(borsuk_2,c4_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c4_6__borsuk_2)]).

fof(e3_6__borsuk_2,assumption,(
    v3_pre_topc(c4_6__borsuk_2,c2_6__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e3_6__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e3_6__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(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(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(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(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(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(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_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(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

fof(fc2_pre_topc,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) ),
    file(pre_topc,fc2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,fc2_pre_topc)]).

fof(fc5_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k2_pre_topc(A),A) ) ),
    file(pre_topc,fc5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,fc5_pre_topc)]).

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_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_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(redefinition_k5_pre_topc,definition,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k5_pre_topc(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(pre_topc,k5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k5_pre_topc)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k2_pre_topc)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k5_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k5_pre_topc)]).

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(d3_pre_topc,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,d3_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,d3_pre_topc)]).

fof(d5_tops_2,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( l1_pre_topc(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_tops_2(C,A,B)
              <=> ( k1_relat_1(C) = k2_pre_topc(A)
                  & k2_relat_1(C) = k2_pre_topc(B)
                  & v2_funct_1(C)
                  & v5_pre_topc(C,A,B)
                  & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ),
    file(tops_2,d5_tops_2),
    [interesting(0.9),axiom,file(tops_2,d5_tops_2)]).

fof(e2_6__borsuk_2,plain,
    ( k1_relat_1(c3_6__borsuk_2) = k2_pre_topc(c1_6__borsuk_2)
    & k2_relat_1(c3_6__borsuk_2) = k2_pre_topc(c2_6__borsuk_2)
    & v2_funct_1(c3_6__borsuk_2)
    & v5_pre_topc(c3_6__borsuk_2,c1_6__borsuk_2,c2_6__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_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_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_borsuk_2,rc1_membered,rc2_borsuk_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc3_funct_1,rc3_struct_0,t3_subset,existence_l1_pre_topc,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tops_2,dt_l1_pre_topc,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,d3_pre_topc,e1_6__borsuk_2,d5_tops_2]),
    [interesting(0.8),file(borsuk_2,e2_6__borsuk_2),[file(borsuk_2,e2_6__borsuk_2)]]).

fof(t68_tops_2,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l1_struct_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( ( k2_relat_1(C) = k2_pre_topc(B)
                      & v2_funct_1(C) )
                   => k5_pre_topc(A,B,C,D) = k4_pre_topc(B,A,k2_tops_2(A,B,C),D) ) ) ) ) ) ),
    file(tops_2,t68_tops_2),
    [interesting(0.9),axiom,file(tops_2,t68_tops_2)]).

fof(e4_6__borsuk_2,plain,(
    k5_pre_topc(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2,c4_6__borsuk_2) = k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_6__borsuk_2,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_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_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_borsuk_2,rc1_membered,rc2_borsuk_1,rc6_pre_topc,rc7_pre_topc,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_m1_relset_1,dt_k10_relat_1,dt_k2_zfmisc_1,dt_k9_relat_1,dt_l1_pre_topc,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_pre_topc,fc4_subset_1,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_funct_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_pre_topc,redefinition_k5_pre_topc,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tops_2,dt_k4_pre_topc,dt_k5_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,dt_c4_6__borsuk_2,fc1_subset_1,t3_subset,d3_pre_topc,e2_6__borsuk_2,t68_tops_2]),
    [interesting(0.8),file(borsuk_2,e4_6__borsuk_2),[file(borsuk_2,e4_6__borsuk_2)]]).

fof(t55_tops_2,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( v3_pre_topc(D,B)
                     => v3_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ),
    file(tops_2,t55_tops_2),
    [interesting(0.9),axiom,file(tops_2,t55_tops_2)]).

fof(e5_6__borsuk_2,plain,(
    v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2),c1_6__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_6__borsuk_2,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2,e3_6__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_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_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_borsuk_2,rc1_membered,rc2_borsuk_1,rc6_pre_topc,rc7_pre_topc,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_relset_1,dt_k10_relat_1,dt_k2_zfmisc_1,dt_k9_relat_1,dt_l1_struct_0,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_pre_topc,fc4_subset_1,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_funct_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_subset_1,existence_m2_relset_1,redefinition_k4_pre_topc,redefinition_k5_pre_topc,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k2_relat_1,dt_k2_tops_2,dt_k4_pre_topc,dt_k5_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,dt_c4_6__borsuk_2,fc1_subset_1,t3_subset,d3_pre_topc,e4_6__borsuk_2,e2_6__borsuk_2,e3_6__borsuk_2,t55_tops_2]),
    [interesting(0.8),file(borsuk_2,e5_6__borsuk_2),[file(borsuk_2,e5_6__borsuk_2)]]).

fof(i6_6__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i6_6__borsuk_2)]),
    [interesting(0.8),trivial,file(borsuk_2,i6_6__borsuk_2)]).

fof(i5_6__borsuk_2,plain,(
    v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2),c1_6__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c4_6__borsuk_2,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2,e3_6__borsuk_2])],[e5_6__borsuk_2,i6_6__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i5_6__borsuk_2),[file(borsuk_2,i5_6__borsuk_2)]]).

fof(i4_6__borsuk_2,plain,(
    ~ ( v3_pre_topc(c4_6__borsuk_2,c2_6__borsuk_2)
      & ~ v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2),c1_6__borsuk_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_6__borsuk_2,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2]),discharge_asm(discharge,[e3_6__borsuk_2])],[e3_6__borsuk_2,i5_6__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i4_6__borsuk_2),[file(borsuk_2,i4_6__borsuk_2)]]).

fof(i4_6_tmp__borsuk_2,plain,
    ( m1_subset_1(c4_6__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_6__borsuk_2)))
   => ~ ( v3_pre_topc(c4_6__borsuk_2,c2_6__borsuk_2)
        & ~ v3_pre_topc(k4_pre_topc(c2_6__borsuk_2,c1_6__borsuk_2,k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c4_6__borsuk_2),c1_6__borsuk_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2]),discharge_asm(discharge,[dt_c4_6__borsuk_2])],[dt_c4_6__borsuk_2,i4_6__borsuk_2]),
    [interesting(0.8),i3_6__borsuk_2]).

fof(i3_6__borsuk_2,plain,(
    v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c2_6__borsuk_2,c1_6__borsuk_2) ),
    inference(let,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,e1_6__borsuk_2])],[i4_6_tmp__borsuk_2,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,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_funct_1,cc2_membered,cc3_membered,cc4_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,dt_k2_zfmisc_1,dt_k9_relat_1,dt_l1_struct_0,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,redefinition_k4_pre_topc,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_tops_2,dt_k4_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2,fc1_subset_1,d2_t_0topsp,dh_c4_6__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i3_6__borsuk_2),[file(borsuk_2,i3_6__borsuk_2)]]).

fof(i2_6__borsuk_2,plain,
    ( v3_tops_2(c3_6__borsuk_2,c1_6__borsuk_2,c2_6__borsuk_2)
   => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c2_6__borsuk_2,c1_6__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,dt_c3_6__borsuk_2]),discharge_asm(discharge,[e1_6__borsuk_2])],[e1_6__borsuk_2,i3_6__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i2_6__borsuk_2),[file(borsuk_2,i2_6__borsuk_2)]]).

fof(i2_6_tmp__borsuk_2,plain,
    ( ( v1_funct_1(c3_6__borsuk_2)
      & v1_funct_2(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
      & m2_relset_1(c3_6__borsuk_2,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
   => ( v3_tops_2(c3_6__borsuk_2,c1_6__borsuk_2,c2_6__borsuk_2)
     => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,c3_6__borsuk_2),c2_6__borsuk_2,c1_6__borsuk_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2]),discharge_asm(discharge,[dt_c3_6__borsuk_2])],[dt_c3_6__borsuk_2,i2_6__borsuk_2]),
    [interesting(0.8),i1_6__borsuk_2]).

fof(i1_6__borsuk_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
        & m2_relset_1(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
     => ( v3_tops_2(A,c1_6__borsuk_2,c2_6__borsuk_2)
       => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,A),c2_6__borsuk_2,c1_6__borsuk_2) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__borsuk_2,dt_c2_6__borsuk_2])],[i2_6_tmp__borsuk_2,dh_c3_6__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i1_6__borsuk_2),[file(borsuk_2,i1_6__borsuk_2)]]).

fof(i1_6_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c1_6__borsuk_2)
      & v2_pre_topc(c1_6__borsuk_2)
      & l1_pre_topc(c1_6__borsuk_2)
      & ~ v3_struct_0(c2_6__borsuk_2)
      & v2_pre_topc(c2_6__borsuk_2)
      & l1_pre_topc(c2_6__borsuk_2) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2))
          & m2_relset_1(A,u1_struct_0(c1_6__borsuk_2),u1_struct_0(c2_6__borsuk_2)) )
       => ( v3_tops_2(A,c1_6__borsuk_2,c2_6__borsuk_2)
         => v1_t_0topsp(k2_tops_2(c1_6__borsuk_2,c2_6__borsuk_2,A),c2_6__borsuk_2,c1_6__borsuk_2) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__borsuk_2,dt_c2_6__borsuk_2])],[dt_c1_6__borsuk_2,dt_c2_6__borsuk_2,i1_6__borsuk_2]),
    [interesting(1),t3_borsuk_2]).

fof(t3_borsuk_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_pre_topc(B)
            & l1_pre_topc(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_tops_2(C,A,B)
               => v1_t_0topsp(k2_tops_2(A,B,C),B,A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__borsuk_2,dh_c1_6__borsuk_2,dh_c2_6__borsuk_2]),
    [interesting(1),file(borsuk_2,t3_borsuk_2),[file(borsuk_2,t3_borsuk_2)]]).