#include <bits/stdc++.h>
using namespace std;

struct node{
    int l, r;
    bool operator < (node t) const& {
        return r - l < t.r - t.l;
    }
};

int main(){
    set <node> st;
    st.insert({1, 2});
    st.insert({3, 5});
    st.insert({6, 7});
    cout << st.size() << "\n";
    return 0;
}   

The output is 2 instead of 3 because {1, 2} and {6, 7} have the same (r-l) value. Since sets only store unique values, when we are to insert {6, 7}, the compiler thinks that the value already exists so just does nothing on this line.

What should we do if we want to store all values in the set then? Just change the operator overloading to

bool operator < (node t) const& {
    if(r - l == t.r - t.l) return l < t.l;
    return r - l < t.r - t.l;
}

That is, we would want to make sure that no two "different" elements have the same value in the < operator overloading.

#include <bits/stdc++.h>
using namespace std;

struct node{
    int l, r;
    bool operator < (node t) const& {
 return r - l < t.r - t.l;
    }
};

int main(){
    multiset <node> st;
    st.insert({6, 7});
    st.insert({3, 5});
    st.insert({1, 2});
    cout << st.size() << " ";
    st.erase({1, 2});
    cout << st.size() << "\n";
    
    return 0;
}   

The output is 3 1. The reason is actually similar to the previous one. When we call st.erase({1, 2}), all elements with r-l = 2-1 = 1 are erased, thus leaving only {3, 5} in the multiset. Actually, the parameter in st.erase() does not even have to be in the multiset (meaning that st.erase({5, 6}) does the same thing as st.erase({1, 2})).

Also, another note is that since we have changed the meaning of <, we would expect {6, 7} to come before {1, 2} in the multiset.

#include <bits/stdc++.h>
using namespace std;

struct node{
    int l, r;
    bool operator < (node t) const& {
	return r - l < t.r - t.l;
    }
};

int main(){
    multiset <node> st;
    st.insert({1, 2});
    st.insert({2, 3});
    st.insert({3, 4});
    cout << st.size() << "\n";
    st.extract({4, 5});
    cout << st.size() << "\n";
    return 0;
}   

The output is 3 2. When we call st.extract({4, 5}), it turns out that {1, 2} is extracted from the multiset.