The U.S. Supreme Court appeared likely Monday to say in a Florida case that states can’t rely on intelligence test scores alone in borderline cases to determine that a death row inmate is mentally able and thus eligible to be executed.

The justices heard arguments on a snowy morning in a challenge from an inmate who claims there is ample evidence to show that he is mentally disabled and protected from being put to death, even though most of his IQ scores have topped 70.