A federal appeals court Friday stamped “The End” on a lawsuit by two Harvard twins who claim that Mark Zuckerberg stole their idea for a social networking site, ruling the duo have to stick with the deal they struck with Facebook since they were smart enough not to be duped.

Facebook settled the claims of intellectual property theft leveled at the Facebook founder by the Winkelvoss twins. The duo sued in 2004, alleging that Zuckerberg agreed to help the twins with their social network project, only to slowroll them and launch his own project instead. After mediation, the parties agreed to trade $20 million cash and more than a million Facebook shares for the Winkelvoss twins company ConnectU.

The litigation, which played a central role in the hit 2010 film The Social Network, continued when the twins alleged that Facebook had deceived them about the value of the shares and that they were entitled to four times as many shares. A district court ruled in 2008 that the settlement should stand.

The U.S. 9th Circuit of Appeals agreed Monday (.pdf) that the Harvard grad twins weren’t dumb or badly represented, and that the whole sideshow ought to end.

“The Winklevosses are sophisticated parties who were locked in a contentious struggle over ownership rights in one of the world’s fastest-growing companies,” Chief Judge Alex Kozinski wrote. “They engaged in discovery, which gave them access to a good deal of information about their opponents. They brought half-a-dozen lawyers to the mediation. Howard Winklevoss — father of Cameron and Tyler, former accounting professor at Wharton School of Business and an expert in valuation — also participated. A party seeking to rescind a settlement agreement [...] under these circumstances faces a steep uphill battle.

“With the help of a team of lawyers and a financial advisory, they made a deal that appears quite favorable in light of recent market activity,” Kozinski wrote, noting that the value of the shares the twins own has continued to grow in value as investors are putting money into Facebook at a $50 billion valuation. “For whatever reason, they now want to back out. Like the district court, we see no basis for allowing them to do so. At some point, litigation must come to an end. That point has now been reached.”

Twisting the knife a bit, the court also noted that the Winkelvosses were “not the first parties bested by a competitor who then seek to gain through litigation what they were unable to achieve in the marketplace,” and adding, as if to taunt the former Olympian rowers, “And the courts might have obliged, had the Winklevosses not settled their dispute and signed a release of all claims against Facebook.”

The twins, who reportedly settled for in excess of $60 million in stock and cash, could appeal the decision to a full panel of appeals court justices or to the U.S. Supreme Court. Or they could just be happy with having become millionaires themselves at a young age without ever having built a successful company.

Given this lawsuit, one expects the former, not the latter, from the Winkelvii.

Update: The twins’ lawyer plans to ask the for a rehearing by a full set of appeals court justices, according to a statement being Tweeted by Tyler Winklevoss using the hashtag #FightForJusticeWillGoOn:

Statement from our appellate attorney Jerome Falk: “The Ninth Circuit has affirmed the District Court’s enforcement of the settlement over my clients’ objection on the ground that the settlement was obtained in violation of the federal securities laws. I appreciate the Ninth Circuit’s thorough discussion of the issues. However, I respectfully disagree with the Ninth Circuit’s conclusions. In my judgment, the opinion raises extremely significant questions of federal law that merit review by the entire Ninth Circuit Court of Appeals. For that reason, my colleagues and I will file a Petition For Rehearing En Banc within the next fifteen days.

Photo: USA’s Cameron Winklevoss, left, and twin brother Tyler take the start of their Men’s pair repechage at the Beijing 2008 Olympics in Beijing, Monday, Aug. 11, 2008. Gregory Bull/AP