Wrong guy?

So my SO and I have been fighting about him being on Facebook all the time. When he's with me, in the bedroom, in the bathroom, if we go out to eat. So we got into another fight about it and he said he was going to delete it, while I'm on the phone with him he told me twice he was just going to delete it then a couple seconds later he says well I just logged out... However, I would keep track of when he got on because he wouldn't text me back he'd get on Facebook then message me back and it took 30-60 minutes... So I started calling him out on it when I seen he was online and he kept denying it... And now that he is logged out I haven't seen him get back on. I hate to think about the fact that he lied to me.... How do I go about this?