In my homework I was asked to prove that a deduction system for modal logic with $\rightarrow$, $\neg$ and $\square$, with 4 axioms and 2 inference rules (MP and a $\square$-generalization rule), is weakened and turned incomplete once you take away the generalization rule.
Now, since I don't want you to solve my homework for me, I just want a hint about the possible approaches to prove that a deduction system is incomplete (not necessarily a modal logic system even).
So far I tried taking a counterexample and showing the resulting formal proof sequence will be infinite, but the my proof was just growing exponentially complex (rather than rely on induction).