<human>: My girlfriend and I broke up after a long talk about our relationship. We have been having troubles, and on top of that I am moving to another city. We just concluded that we should cut our ties here. Still be friends and such, but at least have the summer to forget about one another. 

The thing is, I know that this happened, but I don't think I have really processed it. It just doesn't feel real to me. Yeah, I've cried, but I don't think I'm as sad as I should be. It feels like just another day where we are together, but we're not. I can't get that through my head though. I don't know how to. I still feel attached - and I'd feel guilty for talking to other girls. Just like how I'd feel broken if she was seeing another guy. 

I have been going no contact for 4 days. But, honestly it feels like another day where we are together. Is this normal?

Can you summarize the given text in a few sentences?
<bot>: Broke up amicably with girlfriend. Can't get it through my head that we are actually broken up. Feels like we are still together, even though I've gone no contact.