Custom compare class not working as I expect for pointers to a user defined class in a std::set container

I can't figure out why in this code example the std::set container is not ordering the Entities as I expect on the basis of the compare class I defined. Anyone can help me please? Thanks

 #include <iostream>
 #include <set>

 class Entity {
 public:
 int num;
 Entity(int num):num(num){}
     bool operator< (const Entity& _entity) const { return (this->num < _entity.num); }
 };

 struct my_cmp {
     bool operator() (const Entity* lhs, const Entity* rhs) const { return (lhs < rhs); }
 };

 class EntityManager {
     private:
        std::set<Entity*, my_cmp> entities;
   public:
        void AddEntity(int num) { entities.insert(new Entity(num)); }
        void ListAllEntities() const {
              unsigned int i = 0; 
              for (auto& entity: entities) {
                  std::cout << "Entity[" << i << "]: num:" << entity->num << std::endl;
                  i++;
              }
         }
};

int main(void) {
    EntityManager manager;
    manager.AddEntity(2);
    manager.AddEntity(1);
    manager.AddEntity(4);
    manager.AddEntity(3);
    manager.ListAllEntities();
    return 0;
}

Output:

Entity[0]: num:2

Entity[1]: num:1

Entity[2]: num:4

Entity[3]: num:3

I would expect the following output instead:

Entity[1]: num:1

Entity[0]: num:2

Entity[3]: num:3

Entity[2]: num:4