With nearly $315 million in damages at stake, the U.S. Supreme Court on Wednesday appeared divided over whether injured sailors and families of the 2000 USS Cole bombing gave proper notice of their lawsuit to the Republic of Sudan eight years ago.

The justices heard hourlong arguments in Republic of Sudan v. Harrison, stemming from a default judgment won by the Cole plaintiffs who claimed Sudan provided material support to al-Qaida and Osama bin Laden. The terrorist attack in Yemen killed 17 sailors and injured 39 others.

But during arguments, the justices struggled with an arcane issue that could force the Cole families—if they lose—to restart their long and difficult litigation under the Foreign Sovereign Immunities Act, or FSIA. Did they comply with the act by mailing notice of their complaint to Sudan's embassy in the United States? Or were they required by the act and international law to send it to the foreign affairs minister's address in Sudan?