Is two months' notice before contract expiry enough to terminate an employee?

Dear Lawyer,

I am a part of the HR Team of a company on the mainland. In our company, in order to terminate a contract, a notice of 3 months has to be served.

We need to terminate the contract of an employee and only two months remain for the completion of the contract. We have mentioned the below statement in our contract:

"In case the company is the party who desires the termination, the company shall notify the employee in writing, three months prior to the termination date or for the remaining period of the contract, whichever is shorter. However, if the company fails to serve the above-mentioned notice, the college shall compensate the employee with three months aggregate salary or the remaining period of the contract, whichever is shorter."

So please confirm if two months' notice is enough and this employee has no standing to challenge us in the court.