The fact that he used his AS as an excuse to cheat on you just tells me that he's a total loser and has a lot of growing up to do. If you need closure, perhaps you should sit down with him one last time and just tell him all the things that are bugging you. I think that letting him know how you feel will expel any pent up anger/frustration you have with him. I realize that you might not want to see or talk to him again but I really think that venting to him will help.
Four years is a long time to be hung up with someone. If exploring new relationships doesn't sound like something you want to do, try maybe exploring a new hobby instead to get your mind off of him and instead, set on moving forward with your life. I hope you find a way to move forward from this and to find happiness.