To show that something is not what it has been claimed to be; refute.
Example:
A week before the election he was still struggling to disprove his opponent's lies about his connections to organized crime.
Disprove, which includes the negative prefix dis-, is clearly the opposite of prove. One may have to disprove something for which the evidence has already been accepted, so the disprover often encounters violent objections to the new evidence that weakens the old. Galileo was forced to deny the new findings with which he and Copernicus had disproved the old conception of the earth's being at the center of the planetary system.