Serena Williams of the United States celebrates a point during...

Serena Williams of the United States celebrates a point during her women's singles fourth round match against Sloane Stephens of the United States on Day Seven of the 2013 US Open at USTA Billie Jean King National Tennis Center. (Sept. 1, 2013) Credit: Getty

The future will have to wait for Sloane Stephens at the U.S. Open. That's because the weight of history, in the form of the indomitable Serena Williams, is just too difficult to handle.

Williams again proved that Arthur Ashe Stadium is her house and no one is going to casually move in. The four-time Open champion was at full throttle Sunday, her serve booming, her forehand firing, her underrated defense on red alert. Her 6-4, 6-1 victory over Stephens was a master class, her dominance complete.

It's the 31-year-old Williams, after all, who has 16 career Grand Slam titles and 54 total victories. It's the 20-year-old Stephens who is looking for her first victory, even her first final.

Stephens has the basic tools with which to build a stellar career. On Sunday, she faced the weapons arsenal of one of the sport's greatest players.

"There were times I played some really good tennis," Stephens said. "Second set got away from me a little bit, but overall I thought I played great. She's No. 1 in the world for a reason . . . All in all, I thought she played great."

Williams' serve, the best ever, was wickedly effective. She won 26 of 31 first-serve points and 11 of 19 on the second serve. She pumped one up to 125 mph, and Stephens broke her serve only when Williams made consecutive double faults at the end of the seventh game of the first set.

Williams was credited with 22 winners against 13 unforced errors. Stephens had 15 winners, most off her dangerous flick forehand, but she had 29 unforced errors. And Williams ran down every ball, returning with pace and angle.

"I think my defense was good," she said. "I generally have been playing better defense this year, moving better and trying to be faster."

It would be a stretch to call this a rivalry. Williams and Stephens have played only three times, with Stephens earning her one victory over an ailing Williams at the Australian Open at the start of the season.

Stephens initiated a bit of a contretemps this past spring when she was quoted in a magazine article saying that Williams never talked with her afterward and unfollowed her on Twitter. Williams took the high road when asked to comment, saying she respects Stephens and expects her to become a great player. Stephens backed off, though there does not seem to be apparent warmth between the two. Stephens did give Williams a big smile in the postmatch handshake. "I told her, 'Good job,' " Williams said.

As Williams storms forward toward a fifth Open title -- she will face Carla Suarez Navarro next -- Stephens will go in search of a top-10 world ranking by the end of the season. She's currently No. 17, needs maybe 200 points to get to No. 10 and will play at least four tournaments this fall. "I think I have a pretty good shot," Stephens said. "If I don't make it, shame on me."

As the 15th seed here, Stephens could have hoped for a slightly kinder draw than facing Williams in the fourth round. But she knows that if she is to be counted among the best, she has to beat the best when the chance arises.

"Things happen in their time," Stephens said. "It's an honor to be able to play on the court with one of the greatest tennis players of all time."

As for being an heir apparent to Williams, Stephens is entirely practical about her situation. "I think it's tough because there's a lot of us," she said. "I think just because I'm in the top 20 now, next year there could be three other American girls in the top 20. Right now I'm carrying a little torch. But I'm OK with it. I embrace it for now."

Asked what Stephens needs to do to get to the next level, Williams said: "I don't think she has to work on anything. I think she is at the next level."

Just not Serena Williams' level.

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