Your denial is very strong. I've been there. You WANT for him to be loyal to you so badly that you will take any crumb that it might be possible in the farthest reaches of your imagination.
What you want, and what the truth is, do not agree. I know the pain. Have a good cry, and accept what is the truth.
But wait! You are not helpless, this isn't the end, you will not live in misery forever, although it most definitely seems like it right now.
Let's look at what has happened. Ok, you played sleuth, you found out what you suspected or feared, and it is true.
Now what would Sherlock Holmes do? Imagine yourself sitting there with the pipe in your mouth, pondering the results of your taping the conversation, and the gaslighting and denial your xabf tried to pass on as the truth.
Sherlock wouldn't deny the truth. He would accept it, and so will you.
What does it mean concerning the exabf?
1) he likes to have his cake and eat it too. So...take away his cake.
2) He knows you want to believe him, and want him back...so he focuses on how to lie his way out of this one. So what would Sherlock do? deny yourself to him unless he came forward with some huge confession of the truth, sought atonement, begged, pleaded, and would accept some long-term therapy without any sexual favors granted during that period...the long haul approach to reconcilation...what are the chances of this relalistically? Slim to none...and you know it.
3) He is hedging his bets. Not sure which of you will suit him better--the ex or you, so he plays both of you. She wants him back badly enough she is even willing to share him sexually with you during this period because she knows you want an honest guy, she just wants a bad boy.
So...Sherlock would deny him yourself, again, same as number two. If he ends up with the exgf, which he probably will (why would he want to experience a single painful thought about his own actions--she provides the necessary distraction from that pain) then You are better off because you are out of the cycle of lying and cheating...and he will cheat on her too, just give it time.
I know this is so painful. But you can make the logical decisions that Holmes would...and reject him.
Now what?
Onto the next case...solve the case of you. What are your needs? Your loves? The things that make you happy in life? Hobbies? friends? Family? A job well done at work? Your cat? and onward....
continue being Holmes but focus on YOU instead of him...you are a detective, you can solve the mystery of Yourself...what makes you happy to be alive, what simple joys in life that are awaiting your focus and attention, not the loser xabf.
Now I see you as the female version of Holmes...solving the mystery of yourself, and enjoying all the things you discover about YOU!
That's what you haven't done yet. Solved the mystery of yourself. There's where the joy in discovery comes in, instead of the heartache. There are wonderful things about yourself that you haven't sleuthed around to find...time to have some fun enjoyable and enlightening detective work.
Alanon is kind of like that too...another venue to use to discover you.Self-help books another. Therapy if you like--another. Making a list of the things you truly enjoy, or would like to try in life, discovery of you.
Onto the next case Holmes--you're a smart cookie--time to solve this one--YOU.