Jesaminecollins
Just leave and stop prolonging the agony for her.
...just leave now and stop messing her about.
Jack I really hope you're not paying any attention to this^
Does your wife know that you know that she's cheated?
If she does, then go ahead and tell her, and as others have said, try and be concise, and not get into any emotional, pleading discussions. From you posts, it sounds like you are already emotionally detached, and your feelings for her are completely dead. So she will know pretty quickly that she's not going to change your mind.
If she doesn't, well that's a whole other ball game, and sticking to the script might be near on impossible, because she will likely enter a phase of denial and saying and doing anything to win you back.
Still, try and stick to the script, present her with evidence if you can, and tell her nothing she can say or do will change your mind, repeat.
DO you have children?