The phrase "already disputed" is correct and usable in written English.
It can be used to indicate that something has been challenged or questioned prior to the current discussion or context.
Example: "The validity of the research findings was already disputed by several experts in the field."
Alternatives: "previously contested" or "already challenged".
Fred Wilpon, the chief operating officer of the Mets, has already disputed one of the stories in the book.
Some scientists have already disputed the report's suggestion that the Antarctic will be unaffected by the rise in global temperatures.
If Vice President Al Gore is to win the presidency, the winning votes must now come in stacks of already disputed ballots in two counties.
In what will be one of the more talked-about passages in this book — already disputed in the news — Mr. Suskind contends that Mr. Obama did decide in early 2009 that a plan should be pulled together "to restructure many of the large, troubled banks starting with Citigroup," but that he discovered nearly a month later that this directive "had been ignored by the Treasury".
This and other problematic cases were already disputed in antiquity, and more recently have sparked a host of complex formalized reconstructions of Aristotle's modal syllogistic.
For what it's worth, the website Blue Lives Matter has already disputed how the shooting is being portrayed by activists and the media.
Chris Colinsworth on NBC is already disputing the first call from the replacements, saying it was a push in the back rather than a clip.
Other companies are already disputing Cellectis's claim.
A "yes" vote would be likely to deepen divisions in the Church over the issue as some of its members already dispute the authority of women priests.
On one level, some of the election experts said, there was justification for the filing of a federal case because there are already disputes in several areas of the state.
But there are already disputes about who owns the data.
