gmail imap issue

I have my email harvested into my gmail account. However, it only does this once every 40 minutes or so. I want my email faster then that, so I setup my phone through imap to the original email account, so now I get it instantly.

The problem I have is that I get the email twice: once when it is sent to my phone through my original email through imap, and once 40 or so minutes later when gmail harvests it. I tried to setup a filter to mark the mail as read once it comes into my inbox at the gmail account, however, even when it is marked as read it still sends it to my phone.

I understand that I could sent to archive, but I like to leave the emails in my inbox so that later I can deal with ones that I dont deal with on my phone.

Anyway to fix this so that I still get my email instantly through my phone from the email account, and then when gmail harvests the same mail 40 or some minutes later it stays in my inbox but does not send to my phone?