If a creditor formally objects to the discharge of a particular debt you should be prepared to defend yourself against the objection in the appropriate form and within the time given to you by the court.

Who has to prove non-dischargeability?

The creditor has to show facts which prove that your debt is non-dischargeable if it is a debt that will be discharged unless the creditor objects. However the fact that the creditor has the burden of proof does not been that you can sit and wait. You should be ready to provide your own evidence to answer the creditors allegations in the complaint.