C++ inheritance

#include "vertex.h"
#include "graph.h"
#include "set.h"

using namespace std;


class base
{
public:
   base()
   {
      index = i++;
   }

   ~base() = default;

   virtual string print() const
   {
      return "Base " + to_string(index);
   }

   friend std::ostream &operator<<(std::ostream &out, const base &rhs);

   bool operator==(const base &rhs) const
   {
      return index == rhs.index;
   }

   bool operator<(const base &rhs) const
   {
      return index < rhs.index;
   }

protected:
   static int i;
   int index;
};

int base::i = 0;

class derived : public base
{
public:
   derived() : base()
   {
   }

   string print() const override
   {
      return "Derived " + to_string(index);
   }

};

void printClass(const custom::set<base> &s1)
{
   for (auto it = s1.begin(); it != s1.end(); it++)
   {
      std::cout << *it << " " << endl;
   }
}

inline std::ostream &operator<<(std::ostream &out, const base &rhs)
{
   out << rhs.print();
   return out;
}


int main()
{

   custom::set<base> s1;
   derived d;
   base b;

   //s1.insert(b);
   s1.insert(d);

   printClass(s1);
   //Base 0
   //Base 1


   return 0;
}