As said upthread: you throw him out.
It's the only way.
What's going on here is a game of chicken. You KNOW he's cheated: he KNOWS you know - fucking hell, how could it be more obvious?!?!
But by God he's not going to admit it. He isn't sure if it's going to work, but he's going to give it all he's got: the strategy is: deny, deny, deny, just keep denying - she will HAVE to run out of steam and give in eventually, yeah? What can she actually say if I keep denying? She WILL, eventually, just mutter something and leave it - pray God she'll do that!
So, you turn that on its head. Cut the crap. You don't get bogged down in the 'have you cheated?' - because you know he's cheated. He's out. There is no denial to be made.
Out. We're over.
He wants to try again/give it another go?
Then he starts talking, he tells you everything, and it better bloody be everything. Because you don't want to be in a relationship with a liar. Oh, and by the way did I MENTION that I already KNOW you've cheated, fuckwit? So leave the denials behind, and start telling me a few truths.
That's where you go from here. Nuclear is now the only option... unless of course you do want to shut up, and put up.