Surviving shows we are smart.
That's not true, though. Cockroaches would most likely survive too, doesn't mean they are smart (which they aren't).
Bacteria would survive, too.
If something survives a disaster such as an impact by a huge asteroid, that doesn't imply that that something is smart/intelligent. If something is intelligent enough, though, that
does imply that that something is (
very likely) going to survive.