Assuming it's in federal court? Probably a 12(b)(6) motion to dismiss for failure to state a claim — essentially the defendant would say "your honor, even if everything my opponent claims is true, there's no valid legal claim here." Not a lot of Latin terms involved. (If it's in California state court — because, f/x, they're both residents of California — it's called a "demurrer," which is antiquated, though not Latin. I think a few other states still have demurrers.) It might also get tossed out under Rule 12(b)(1) for lack of subject-matter jurisdiction. Whatever attorney they suckered into bringing it could also be subject to sanctions, which would go up significantly if you followed it with a frivolous appeal.
What if whoever filed it tried to argue that losing the Atlasia election caused them emotional distress or something and thus sued for damages?
Also did any attorneys get sanctioned in the past for filing say, Birther lawsuits or those joke lawsuits against God?