What is the best way to keep clean a forum ?

You can trick them sometimes.

Back in 2013, I had an "Are you a spambot?" question which had a HTML element named tos aka terms of service. I don't know if that'll still work, probably because it's an obscure method, but there are plenty of ways to sneak past them, as-long as the baddies don't focus squarely on you.
 
I could imagine it would be hard to stop all of the bot spammers by yourself. As others have mentioned it would be best to hire moderators to help you with the spam control and other aspects of the forum.

And moderators who actually care about your forum, I have some moderators in another forum I run who I am considering letting go because of this.

Moderators are overrated in many cases. I mean, don't get me wrong, I appreciate them, but the first line of defense is having effective spambot protection - at registration.
 
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