Viacom CEO Philippe Dauman and board member George Abrams have asked a Massachusetts court to hold a trial “no later than four months from now” on their plea to overturn Sumner Redstone’s effort to oust them from his family trust and the National Amusements board.

They added, in a just-disclosed filing made yesterday, that they’d like the discovery process to “commence immediately and conclude within three months.”

They want the court to rule that Redstone, who turns 93 tomorrow, was not competent to make the decision on Friday to remove them from the trust and theater chain’s board. They’ve alleged that his daughter, Shari — who’s President of National Amusements and Vice Chair of Viacom and CBS — manipulated him to win control of her father’s media empire.

Redstone’s seven-member trust will control his 80% ownership stake in National Amusements when he’s deemed incapable of governing his own affairs, or passes. The theater chain owns 80% stakes in Viacom and in CBS.

Shari Redstone responded that she’s “looking forward to an expedited dismissal of this meritless suit.”

Dauman and Abrams’ motion at the Massachusetts Probate and Family Court says that “Expedited proceedings are warranted in order to ensure timely resolution of this dispute, which involves billions of dollars in assets and will require medical examination(s) and other proceedings to ascertain the mental state” of Redstone.

It adds that Redstone’s “health and mental condition are…severely and rapidly declining.”

The discovery process likely will include “one medical examination of Mr. Redstone, as well as deposition and document discovery of Ms. Redstone and other relevant persons into the degree of undue influence exercised in recent months by Ms. Redstone over Mr. Redstone’s affairs,” according to the filing.

The fate of the companies “hangs in the balance,” it adds.

Lawyers representing Sumner Redstone asked the Los Angeles County Superior Court on Monday to confirm the “the validity of his actions” against Dauman and Abrams.