The other part of the contract....

What is the name of your state (only U.S. law)? Alaska

I had a gym membership. In the contract it allows for a move out claus. It a nutshell if I move more than 40 miles and provide written notice of move with a short list of "such as" examples of written notice. Nothing is defined as what is a move or how long it must be or does it define anything as unacceptable proof of move
However when I tryed to exercise this clause my first attempt was ignored. They responded to my second attempt after they continued to autobill me with an "oh sorry but if you want to use that claus you have to follow the rules on this form" and sent me a new list of do's and dont's for moving. When I argued this was not disclosed when I signed the membership they said to bad and sent me to collections.
When I brought this up with the collector and pointed out in the signed contract I was in the right they to insist that this new previously undisclosed and un signed list is valid and binding. The collector is still following through with the collection
Can they do that?

You follow the established procedure for disputing a debt that you do not believe is valid. It is well documented online how to do this. The collector isn't going to care about anything you tell them over the phone.

I did..

When I was first notified of the debt I did respond in writing outlining the dispute, included a copy of the contract and and my copies of the written notice of cancelatio. They responded in writing sighting the same contract I gave them pluss the extra new document. Pointing to this new (un signed) document provided as proof that its a valid debt and continued with the give us money speech

Now what do I do?

You can tell them in writing that you won't pay it and to stop contacting you. Their recourse would be to sue you. Whether or not they will is anybody's guess. You should also get a free copy of your credit report (which you should be doing anyway). If it's on your credit report, follow the procedure for disputing that.