I would argue that there are a few ways this phrase can be inverted:
No rights reserved
Implies that the author waives all rights to his/her work (i.e. ultimately places it in the public domain)
All rights included
I've seen this one in the context of royalty-free music being used in the commercial sense, where if you pay for the license, you can use that song anytime anywhere, with all rights to the song. This seems to be the opposite of "All rights reserved" which we should know by now what it means
Copyleft
While not really a phrase, it is the opposite of copyright itself. Used primarily in software but maybe some other media can also be considered copyleft. As far as I'm aware, it has some ties with copyright itself (that you cannot remove attribution from the author, and, in case of software, must distribute it as is, without putting any restrictions yourself)
There are probably more means other than what I've listed, and I would love to hear your thoughts and suggestions!
I like All rights refused
Refused by whom? Refused to the owner?
If "All rights reserved" means "I, the rights holder, reserve the usage of all copy rights for myself only. You have no such rights." then "All rights refused" must mean "I, the rights holder, refuse all copy rights to this work. You can do whatever."
I guess I like it because it's catchy and aggressively anti-copyright.
But if you're actually going to release something where copyright might become an issue it's of course better to use a real license like CC.