Equivalent formulae with different CNF

Question

I was not able to find or come up with two formulae which are equivalent but have different CNF. All my ideas reduce to the same formula after applying transformations. The requirements are the following:

Give an example which shows that proving equivalence of two formulas by bringing them into conjunctive normal form is incomplete. By incompleteness, we mean that there are examples of formulas which are equivalent but their conjunctive normal form is not the same.