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"provably false" is correct and usable in written English
You can use it when you want to emphasize that something is definitely false and that this fact can be proven. For example: "The statement that the Earth is flat is provably false."
Exact(26)
He said the assertion that the weapons were not covered by the law was "provably false".
Everything she says about me is not only completely false but provably false".
"These accusations are provably false," Herbalife's chief financial officer, John G. DeSimone, told The New York Times in 2014.
In 1988, he and Pete Dawkins, a former West Point football star and Vietnam War hero, slugged it out with blunt and sometimes provably false campaign television advertisements.
His assertions are provably false, replies Richard Brooks, a tax inspector, who was so ashamed of working for a Revenue that cut sweetheart deals for multinationals he resigned to become Private Eye's star reporter.
Here McCain bears responsibility, having attacked Obama with a string of provably false claims — for example, that the Democrat wouldn't visit wounded troops unless he could bring cameras — and McCarthyite tactics of guilt by association.
Similar(32)
Certainly, people here are, because these things are provably untrue.
Almost none of that is provably untrue.
Fortunately, the charges against me are not only totally made up but are provably untrue.
Trump's willingness to say things that are provably untrue, of course, is not something that began with his campaign.
But then our assumption (i.e., that k is known) is false, and provably so.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com