How to prove that $\vdash \neg(\square F\land p)$ in $KD$? The allowed rules are natural deduction rules and the axiom $\square p\to\diamond p$ where $\diamond p=\neg\square\neg p$.
I actually don't have any ideas except that I have to assume $\square F\land p$ and deduce $F$ by using any propositional tautology, any known inference rule, or the Necessitation Rule, or the Distribution Axiom (https://en.wikipedia.org/wiki/Modal_logic#Axiomatic_systems). The Necessitation rule looks totally irrelevant here. So the only "modal" tool is the distribution axiom, but I can't see how it can be applied.