prove to be false (She refuted the theory that the earth was flat.)
allege to be false, try to refute (*She refuted the theory that the earth was round.)
Refute is a factive or success verb, like know and remember, which presupposes the objective truth or falsity of the proposition. Many writers, including a slim majority of the Usage Panel, accept the non-factive "try to refute" sense, but the distinction is worth respecting.
Steven Pinker, The Sense of Style, s. 279