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The phrase "disprove this statement" is correct and can be used in written English.
It can be used when someone is presenting a statement or claim, and is challenging someone else to provide evidence or arguments that prove the statement to be false. Example: "The author claims that vaccines are dangerous, but scientific research has consistently shown their effectiveness and safety. Can you disprove this statement?".
Exact(1)
However, there is no literature available to support or disprove this statement.
Similar(59)
We disproved this statement, and by investigating four different cases, we showed that the effectiveness of the random user selection approach strongly depends on the type of output function.
I think the large number of very successful genetic screens with results published in the top journals disproves this statement.
In 1943 Byers and Lord (1943) disproved this statement in a follow-up study of 20 children with documented Pb poisoning.
Additional research has turned up no documentation that would prove or disprove the statement.
The evidence seems to disprove this.
He then proceeded to disprove this.
Can anyone disprove this train of logic?
Labor has produced nothing to disprove this.
Upwardly trending corn yields disprove this theory.
Does your research prove or disprove this belief?
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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