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Paris Saint-Germain left no doubt it was Europe's top club with a historic victory in the Champions League.

Now, PSG is intent on conquering the world.

Les Rouge-et-Bleu turned in a dominating performance at the Club World Cup on Sunday, brushing aside Lionel Messi and Inter Miami with a first-half blitz that resulted in a 4-0 victory in Atlanta.

While the European powerhouses complained mightily about having to play in the newly expanded tournament at the end of a grueling season, PSG is taking the 32-team competition seriously.

Outside of a 1-0 loss to Brazilian club Botafogo in group play, PSG has won three games by a cumulative 10-0 since arriving in the United States.

"It's clear that this is a historic season for us. We intend to continue making history with this competition," PSG coach Luis Enrique said. "We're fighting to claim silverware. This season is very long for all the teams. But we're excited to be here."

PSG advanced to the quarterfinals, where it will face Bayern Munich this Saturday in Atlanta. The German club defeated Brazilian club Flamengo 4-2.

Enrique said defeating Messi and Inter Miami on Sunday was trickier than it seemed.

Joao Neves' early strike sent PSG ahead, and then it scored three more in a flurry before halftime to take an unassailable lead.

Former PSG and Barcelona star Messi impressed in the second half, as Miami battled hard, but could not find a way through.

"It is difficult to play against players of this caliber." Enrique told reporters.

"It was difficult, but, I think, as a team, we did an excellent job.

"There's a visible difference between the first and second halves. Their quality is evident, and I think we deserved the victory.

"It was harder than it may seem, after the first half."

The Spanish coach said his PSG team, which won the Champions League, Ligue 1 and the French Cup to claim its first ever treble, is in spectacular form and is hoping to triumph in the United States.

"Clearly, we are experiencing a historic season for our club, we aim to go far in this competition," continued Enrique.

"We are in the quarterfinals, with only eight teams remaining. Our goal is to progress as far as possible and to compete for the trophy. But, for that, we need to overcome two more knockout rounds.

"The season is very long, as it is for all teams, but the motivation to be competitive is there."

PSG winger Ousmane Dembele said he was "glad to see" Messi and his former Barcelona teammates Luis Suarez, Jordi Alba, Sergio Busquets and Javier Mascherano.

"Leo is a unique person, to share a game with him was magnificent. I was a kid watching his magic on the television, so it's unique," said PSG defender Lucas Beraldo.

Messi barely touched the ball in the first half, as the Herons struggled mightily just to get across the halfway line.

The pink-clad fans in the 65,574-strong crowd at Mercedes-Benz Stadium tried to stir the underdogs with occasional chants of "Messi! Messi! Messi!" But to no avail.

PSG was simply too good.

'Reality' hits

"With their youthful players and high caliber — and an amazing coach — they didn't let us relax for one second," Inter Miami coach Mascherano said.

"I feel like this is a team that will be remembered."

Mascherano added that he was pleased with his team's performance at the tournament.

"We achieved the goal we had set for ourselves, we were very aware that we could compete (only) up to a certain level, and today reality has shown that," Mascherano told reporters.

"I am very proud of my players, of the work they did in the competition. We tried to show in each match what we could do.

"The gap is what it is, but I am very proud of them."

Mascherano said his Argentine compatriot Messi was able to show his quality, despite the defeat.

"I think Leo played a great game, within the options we had. In the second half, we found him much more. In the first half, we couldn't, due to Paris' pressure," said the coach.

"They slowed their tempo in the second half, and we were able to show what we usually do in Major League Soccer."

Despite PSG being arguably the best team in the world at the moment, the Mercedes-Benz Stadium in Atlanta was filled with Inter Miami shirts, mostly with eight-time Ballon d'Or winner Messi's number 10 on the back.

"PSG is in great form, champions of everything, but people still pay for a ticket to see Leo Messi, even at 38 years old," added Mascherano.

In another encouraging sign for PSG, French star Dembele got his first action of the tournament after sustaining a left quad injury while on duty with the French national team.

He came on a substitute for Neves in the 62nd minute.

"It is very important for us to have injured players come back into the fold," Enrique said. "We have to focus on our goals and get our players back."

Especially when there's another trophy within reach.