The U.S. Supreme Court appeared to find no easy way to resolve an international child custody battle between a U.S. Army soldier and a Scottish woman in a battle with important ramifications for the power of federal courts.

The justices heard arguments in Chafin v. Chafin, in which Sgt. Jeffrey Lee Chafin argues his appeal of a federal district court order returning his daughter to Scotland is not moot just because the child has left the country — an issue that has created a split in the federal appellate courts.