P filed suit against D alleging infringement of a patent. D counterclaimed, seeking a declaratory judgment of non-infringement, invalidity, and unenforceability, and alleging antitrust violations on the part of P, his company, and his attorneys. P filed a motion to dismiss the antitrust counterclaim. D voluntarily dismissed the antitrust counterclaim, but then filed an amended counterclaim alleging many of the same antitrust violations against P alone. D again dismissed its antitrust counterclaim, prompting P to move for sanctions on the ground that D's attorneys 'multiplied the proceedings ... unreasonably and vexatiously.' The district court denied the motion for sanctions. P conceded that he could not prove his infringement case against D. P asked the district court to enter judgment of non-infringement in favor of D and to dismiss D's invalidity and unenforceability counterclaim without prejudice. D moved for summary judgment of non-infringement and summary judgment of invalidity of claims. The district court entered judgment of non-infringement of all claims and deferred its rulings on the outstanding motion for summary judgment of invalidity of claims. The district court granted D's motion for summary judgment of invalidity of claims. P appealed the claim construction rulings, the grant of summary judgment of non-infringement based thereon, the grant of summary judgment of invalidity of claims, and the district court's denial of sanctions.