How does std:set check if there is an equivalent element in set during the insertion?

Question

Let's use the following code as an example.

auto cmp = [](ll a, ll b) {
    return gcd(12, a) < gcd(12, b);
};
set<ll, decltype(cmp)> s(cmp);
for(ll i = 0; i < 2; i++){
    ll x;
    cin >> x;
    s.insert(x);
    cout << "Success! \n";
}

I defined new comparator that compares numbers by their greatest common divisor with 12.

First I successfully inserted 5. And then I tried to insert 7, but it was not successful.

I know that gcd(12, 5) = gcd(12, 7) = 1.

But I am failing to understand how does std::set check if 5 is equivalent to 7.

It can find out that gcd(12, 7) is not less than gcd(12, 5) using comparator comp I gave it, but how does it figure out that gcd(12, 7) is equal to gcd(12, 5)?

Answer 1

It calls the comparator twice, with different order of arguments.

If cmp(x, y) and cmp(y, x) are both false, then x and y are considered to be equivalent.