What brands of nail polish are oil-based? How can one tell?

I got this nail art stamping kit at the mall. The woman who sold it to me suggested using oil-based nail polish because it was be easier and the results would be more desirable. When I went to the store, none of the bottles said oil-based.What brands of nail polish are oil-based? How can one tell?
No nail polishes are oil based that I know of. The woman who sold this product to you likely is just trying to meet her sales quota, and may not know what she is talking about.