If their approach is reproducible and correct, they have successfully disproved the conjecture. If errors are found, corrections will be made. They had started

If their approach is reproducible and correct, they have successfully disproved the conjecture. If errors are found, corrections will be made. They had started attempting to prove the conjecture. This result could be considered a failure of that proof. Showing they’re capable of performing the research makes them good mathematicians. I believe the answer to your last question is “lots.”