How to move a unique_ptr from one set to another? (C++)

The code below is giving the error: Call to deleted constructor of 'std::unique_ptr<int>' 'unique_ptr' has been explicitly marked deleted here passing argument to parameter 'item' here.

Could someone please explain why this is? I would have thought everything would be fine because I'm using std::move in the call to foo.add.

#include <iostream>
#include <memory>
#include <set>

class Foo {
 public:
  void add(std::unique_ptr<int> item) {
    set.emplace(std::move(item));
  }
 private:
  std::set<std::unique_ptr<int>> set;
};

int main() {
  Foo foo;

  std::set<std::unique_ptr<int>> set;
  set.emplace(std::make_unique<int>(1));
  set.emplace(std::make_unique<int>(2));
  set.emplace(std::make_unique<int>(3));

  for (auto &item : set) {
    foo.add(std::move(item)); // error on this line
  }

  return 0;
}