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MELBOURNE, Australia – When the draw for the Australian Open was made, it wasn’t Roger Federer of Switzerland who was being widely touted as the prime contender to claim an 18th major title.

All that hype surrounded American Serena Williams, but she was knocked out in the fourth round Saturday.

Federer is three match victories away from a title, but after his 6-3, 7-5, 6-4 demolition of 10th-seeded Jo-Wilfried Tsonga of France in the fourth round on Monday, he seemed up for the challenge.

Progressing in the men’s bracket along with Federer were top-ranked Rafael Nadal, a Spaniard who had a 7-6 (7-3), 7-5, 7-6 (7-3) victory over No. 16 Kei Nishikori of Japan — though he was broken twice and got a time violation in the third set — and Wimbledon champion Andy Murray of Britain.

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Murray, seeded fourth, overcame a racket-smashing, frustrating finish to the third set to beat Stephane Robert of France 6-1, 6-2, 6-7 (6-8), 6-2.

Murray cracked the frame of his racket after wasting four match points at the end of the third set.

“I don’t feel like I killed it, but it won’t be getting used again,” Murray said of the damage he did to the racket. “Sometimes it’s necessary.”

In a quarterfinal match, seventh-seeded Tomas Berdych of the Czech Republic defeated No. 3 David Ferrer of Spain 6-1, 6-4, 2-6, 6-4.

Federer is back in the quarterfinals of a Grand Slam event for the first time since last year’s French Open — equaling American Jimmy Connors’ Open-era record with his 41st trip to the last eight in a major tournament.

He next plays Murray, a three-time Australian Open finalist. A victory could set up a semifinal against Nadal, who next plays first-time major quarterfinalist Grigor Dimitrov of Bulgaria.

Since winning his last Australian title in 2010, Federer has lost in the semifinals each year at Melbourne Park — including last year’s loss to Murray, who has an 11-9 edge in their head-to-head meetings.

“It’s good to see he took care of his draw, and here we are again,” the sixth-seeded Federer said. “I’m looking forward to the match, I must say. We had an interesting year last year with some ups and downs. It’s a good start to the season for both of us already.”

Murray had minor back surgery in September and is trying to keep his expectations in check in his second tournament since the operation.

“I said at the start of the tournament, I can’t honestly say my expectations are as high as if I’d been playing for the last four months,” Murray said.

“But I’m not far away from winning the event. Anyone’s that’s in the quarters is close.”

Murray wasn’t the only frustrated player.

Tsonga, aggravated at not being able to seriously threaten Federer, screamed and smacked a ball into the crowd after losing an exchange of close volleys.

In the women’s bracket, two-time finalist Li Na of China stayed in contention for another title match by beating No. 28 Flavia Pennetta of Italy 6-2, 6-2 to advance to the semifinals.

The fourth-seeded Li lost her serve once — while leading 5-0 in the opening set — and finished off the 67-minute match with an easy forehand to the open court that Pennetta watched flat-footed from a distance.

Li’s semifinal opponent will be No. 30 Eugenie Bouchard of Canada.

Bouchard, 19, playing in her first Australian Open, beat No. 14 Ana Ivanovic of Serbia 7-5, 5-7, 6-2.

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