There might have been a flaw in my suggestion.
I shall be more logical:
Predicate: Cats can sometimes catch spiders.
Predicate: These are big spiders.
Conclusion: You need big cats.
So the OP needs to buy a couple of tigers. Or lions.
yes that is more like it, i would suggest a scottish wildcat and a snow leopard just to be safe and you can pet the big snow furry ones tail as you doze off