I'm going to look through my girlfriends phone after she lied to me about talking to her ex all day
What do you expect to find on your girlfriends phone?
I don't know, but maybe I'll find out if she's cheating on me.
Feeling like your girlfriend is cheating on you can be rough. But, it doesn't give you the right to violate her privacy by looking through her phone. You should ask her why she lied to you and if there is something going on with her ex or not.
It's stupid, I would never trust my girlfriend anyways.
If you can't trust your girlfriend, then maybe this relationship isn't for you. Trust is important in any healthy relationship, and without it you're only going to have conflict. Think about ending the relationship and starting over with someone you can have faith in.