C++ stable_sort not stable?

Question

I am using C++ stable_sort to sort a vector of my class objects in ascending order using a comparator function, but the sort is not stable. A work around that worked was to reverse iterate and reversing the logic in the comparator. But cant understand why it shouldnt work normally. Code:

using namespace std;
class Pair{
    string str;
    int num;
public:
    Pair(string s, int n):str(s), num(n)
    {}
    Pair(const Pair &a)
    {
        str = a.str;
        num = a.num;
    }
    int Num()
    {
        return num;
    }
    string Str() const{
        return str;
    }
    void set(string s, int n)
    {
        str = s;
        num=n;
    }
    void print() const{
        cout<<"\n"<<num<<" "<<str;
    }
};

bool comparator( Pair a,  Pair b)
{
    return a.Num()<=b.Num();
}

int main() {
    int n;
    cin >> n;
    vector<Pair> arr;
    for(int a0 = 0; a0 < n; a0++){
        int x;
        string s;
        cin >> x >> s;
        if((a0+1)<=n/2)
            s="-";
        Pair p(s, x);
        arr.push_back(p);
    }
    cout<<"\n Before sort";
    for(auto i:arr)
        i.print();

    stable_sort(arr.begin(), arr.end(), comparator);
    cout<<"\n\n After sort";
    for(auto i:arr)
        i.print();

    return 0;
}

Result: Before sort 0 - 6 - 0 - 6 - 4 - 0 - 6 - 0 - 6 - 0 - 4 that 3 be 0 to 1 be 5 question 1 or 2 not 4 is 2 to 4 the

After sort 0 to 0 - 0 - 0 - 0 - 0 - 1 or 1 be 2 to 2 not 3 be 4 the 4 is 4 that 4 - 5 question 6 - 6 - 6 - 6 -

Answer 1

comp - comparison function object (i.e. an object that satisfies the requirements of Compare) which returns ​true if the first argument is less than (i.e. is ordered before) the second.

from stable_sort. The comparator must implement a strict weak ordering. See also here for a table of the exact requirements.

Your comparator is wrong, it also returns true for equal elements.