Looking for an old Mario game



I'm looking for this really old Mario game I used to play when I was little.
I don't remember much from it, but I think it had four levels, and the last one was inside a cave with lava, and I think it was impossible to finish...

I know it's not a lot of information, but it's pretty much the only things I remember, and I would love to play it again.
Super Mario World?
No, it was a really short game, might have been a demo version (...)
By levels I mean 1-1, 1-2, 1-3 and 1-4.

Sorry, It's too long ago since I played it...
No such game. Nintendo didn't release demos back then. However, there's a really old DOS fan game that fits that profile, called something stupid like "Mario."
Thank you thank you so much!
Perry Mason, you rock.
This is it; http://www.dosgamesarchive.com/download/mario/
No problem. I think there's also an updated version called "Mario & Luigi" with a title screen and Luigi added but nothing more. I could be off. To be honest I'm not sure Nintendo was particularly happy with the guy making that fan game (I'm probably wrong about that but it was before fan games were popular.)