How can you prove a conjecture false?
The word "conjecture" can be taken a number of ways.
If the "conjecture" involves an inference based on false or
defective information, you need only show convincing or conclusive
evidence that the information is false or faulty.
If the "conjecture" is the result of surmise or guessing, then
it is nothing more than a guess itself, and, therefore, has no
basis in fact or logic.
If the "conjecture" is an unproven mathematical hypothesis, you
will need to disprove its validity from its basis. Start with the
basic crux of the problem and work step by step until you disprove
(or prove) the hypothesis to be untrue (or true). Make sure you
have good arguments and sound mathematics.