Check if two “select”s are equivalent

Question

Is there a way to check if two (non-trivial) select are equivalent?

Initially I was hoping for a formally equivalence between two selects, but the answers in proving

Answer 1

Run both of them and compare the results. Use the EXCEPT operation to subtract the set returned by the first query from the set returned by the second query. If the result is an empty set then they are equivalent.

The problem with this method is that it does not prove that two queries are equivalent for ANY database. It depends on the content of your database. For example, if your DB is empty, then any two select statements are equivalent according to this method.

Proving equivalence by just analyzing the queries is an unsolved problem AFAIK (but I'm not exactly a database theory guru, so dont trust me on that ;)) Also, you can have a look at this question: Proving SQL query equivalency