MINNEAPOLIS -- After a series of stinging rebukes from federal judges, the NFL has a significant, favorable ruling in hand from a higher court.

The lockout remains in place, and the same panel that sided with the league to keep it will hear arguments next month on the legality of the NFL's first work stoppage in nearly 14 years.

So as owners and players and their legal counsel return to court-ordered mediation on Tuesday morning, the likelihood of the league giving ground in talks has clearly decreased.

Commissioner Roger Goodell arrived Tuesday morning with other league leaders, and other owners entered the courthouse in separate small groups. Linebacker Mike Vrabel showed up shortly before attorneys for the players.

With restlessness and uncertainty surrounding the NFL with the start of training camps a little more than two months away, the players could be in a tricky place.

DeMaurice Smith, the head of the NFL Players Association, sounded defiant outside the courthouse in Minneapolis on Monday despite the 2-1 decision from the three-judge panel of the 8th U.S. Circuit Court of Appeals.

"Right now our guys are working out for free, because they dig the game," Smith said.

The hearing is scheduled for June 3.

"We'd like to make progress, but it'll be hard to do. We have to wait to see what happens June 3," Pittsburgh Steelers president Art Rooney II said earlier on his way into the federal courthouse for Monday's mediation.

"We look forward to the argument. Look: This is something that the players are prepared for," Smith said. "It's a disappointment obviously, but as far as we can tell this is the first sports league in history who sued to not play its game. Congratulations."

Both sides stuck to their message.

The owners want to stay out of court, blaming the players for preferring litigation. The players claim they're only interested in playing and that the owners are preventing them and fans from enjoying the game.

"We have an opportunity to resolve this matter and get the game back on the field, and that really should be our exclusive focus," NFL lead negotiator Jeff Pash said.