If your spouse cheats on you (even if he/she admits it to you and you have evidence) in order for the ground to be recognized by the court you must have a third party witness willing to testify under oath they saw your spouse and OM/OW having sexual intercourse. Not kissing, not touching but full blown sex.
So, when one files for divorce using the grounds of adultery, the cheating spouse will always contest the grounds as they are nearly impossible to prove in court and they will get away with it.
I've been wondering about this. Can you have them asked in court, under oath, whether they've had sex with someone else? Sure, they can lie, but they would be risking contempt of court. Judges don't much like being lied to.