“Ziggy is a lion who is not a carnivore. Therefore not all lions are carnivores.”
I translated it as:
$L(z) \land \lnot C(z)\vdash \lnot\forall x~[ L(x) \to C(x)]$
However, I have no idea how to prove it with natural deduction. Maybe someone could give me hints?
Hint: $\neg \forall x = \exists x \neg$.