NASHVILLE (AP) — With an execution scheduled for next week, 32 death row inmates in Tennessee are asking the state's high court to declare Tennessee's lethal injection method unconstitutional.

In arguments before the court on Wednesday, inmates' attorney Kelley Henry said that "unassailable science" shows Tennessee's latest three-drug cocktail will cause excruciating pain.

Referencing the constitutional ban on cruel and unusual punishment, she told the court, "If the 8th Amendment means anything, you will rule for the plaintiffs."

But U.S. Supreme Court precedent requires the inmates to show there is a more humane alternative available. Associate Solicitor General Jennifer Smith argued the inmates were unable to meet that requirement.

In court filings, the inmates say the barbiturate pentobarbital is better than the 3-drug cocktail, which they say causes extreme suffering but renders the inmate unable to cry out.

Smith said that if pentobarbital were available, the state certainly would have used it when it executed Billy Ray Irick in August.

"If they had identified a single supplier, we would have gone to that supplier," Smith said. "I'm pretty certain we would have used it because it was found to be constitutional by the court."

Pentobarbital became widely unavailable for executions after an uproar over its use in that context several years ago.

Henry said notes from the Correction Department's drug procurer show pentobarbital is available. But Smith disputed the meaning of those notes, saying they show the state attempted to procure pentobarbital unsuccessfully.

Because of state law that makes the identity of those involved with executions secret, the inmates' attorneys were not allowed to question the procurer.

Justice Sharon Lee asked Smith how it was fair to ask inmates to "prove what they can't possibly prove because they can't get the records."

Smith said there was nothing preventing their attorneys from contacting pharmacists themselves about the drug's availability.

"It gets complicated in this case because the alternative they identified is a form of execution we do use," she said. But that is just happenstance. If the inmates had identified a different alternative drug they would not expect to find out from the state whether it was available.

The court did not say when it expects to rule. Edmund Zagorski is scheduled to be executed on Oct. 11. He was sentenced in 1984 in the slayings of two men during a drug deal.