ATLANTA (AP) — A judge has denied a Georgia death row inmate's latest challenge to a state requirement that defendants must prove intellectual disability beyond a reasonable doubt in order to be spared from execution.

Towaliga Circuit Judge Thomas Wilson wrote in an order dated Monday that he's procedurally barred from considering the challenge because a lawyer for Warren Lee Hill did not cite any new law or evidence to support his petition. Hill's lawyer had argued that a U.S. Supreme Court ruling in May bolsters his arguments against Georgia's "beyond a reasonable doubt" standard, the toughest in the nation.

The high court in 2002 barred execution of the intellectually disabled, but left the states to determine who is intellectually disabled.

The U.S. Supreme Court in May knocked down a Florida law that said any inmate who tests above 70 on an IQ test is not intellectually disabled and may be executed. The opinion said IQ tests have a margin of error and inmates whose scores fall within the margin must be allowed to present other evidence of intellectual disability.

In a court filing in August, Brian Kammer, a lawyer for Hill, said the high court's ruling also "highlights the error of the Georgia standard." Hill's lawyers have long argued Georgia's high standard for proving intellectual disability is problematic because psychiatric diagnoses are subject to a degree of uncertainty that is virtually impossible to overcome.

Hill's lawyers have long argued that Hill is intellectually disabled, but the state has consistently argued that Hill's defense has failed to prove it beyond a reasonable doubt. Georgia's standard has repeatedly been upheld by state and federal courts.

Though Wilson decided he couldn't consider Hill's challenge, he also wrote in his order that he hopes the Georgia Supreme Court will weigh whether the U.S. Supreme Court ruling in the Florida case is applicable to Hill's case.

Kammer said Wednesday he plans to appeal Wilson's order.

Hill was sentenced to death in Lee County for the 1990 beating death of fellow inmate Joseph Handspike. At the time Hill was already serving a life sentence for murder in the 1986 slaying of his girlfriend.

Hill has come within hours of execution three times, most recently in July 2013. Each time, a court has granted a last-minute delay based on challenges raised by his lawyers. Only one of those challenges was related to his intellectual abilities, and it was later dismissed. No execution date is currently scheduled for Hill.