WASHINGTON (AP) — On Wednesday, the Supreme Court grappled with the complexities of determining when convicted murderers should be deemed intellectually disabled, a status that would exempt them from capital punishment.

The justices engaged in a two-hour session, hearing arguments in a case brought from Alabama. The state is seeking to execute a man whom lower federal courts have identified as intellectually disabled, but the outcome of these deliberations remained uncertain.

The case revolves around Joseph Clifton Smith, a 55-year-old who has spent nearly half of his life on death row following his conviction for a 1997 murder where he brutally beat a man to death.

In 2002, the Supreme Court set a precedent by barring the execution of individuals with intellectual disabilities. Further rulings in 2014 and 2017 emphasized the need for states to consider additional evidence in marginal cases due to potential inaccuracies in IQ testing.

Smith’s case presents a dilemma: his IQ test results hover just above the standard disability threshold of 70, with scores between 72 and 78. His attorneys point out that he was placed in special education classes and quit school after the seventh grade. At the time of the crime, his academic abilities were significantly below average, performing math at a kindergarten level, spelling at a third-grade level, and reading at a fourth-grade level.

Seth Waxman, representing Smith, told the justices his client received a “diagnosis of mental retardation” — then the commonly accepted term for mental disability — in the seventh grade.

Alabama, 20 other states and the Trump administration all are asking the high court, which is more conservative than it was a decade ago, to cut back on those earlier decisions.

Chief Justice John Roberts and Justices Samuel Alito and Clarence Thomas dissented in both cases, and Alito and Thomas sounded as if they would side with Alabama.

A ruling for Smith would lead to messy court fights for other death row inmates “where everything is up for grabs in every case,” Alito said.

Alabama lawyer Robert M. Overing said Smith’s case should be an easy win for the state because Smith never scored below 70 on any IQ test.

“There is no way that he can prove an IQ below 70,” Overing said.

Alabama appealed to the Supreme Court after lower courts ruled that Smith is intellectually disabled, looking beyond the test scores. The justices had previously sent his case back to the federal appeals court in Atlanta, where the judges affirmed that they had taken a “holistic” approach to Smith’s case, seemingly in line with high court decisions.

But the justices said in June they would take a new look at the case.

Waxman urged the justices to affirm the lower courts rather than issue a decision that would effectively rely exclusively on test scores and rule out additional evidence in cases with borderline IQ scores.

Justice Elena Kagan said courts have to consider the additional evidence, but “that’s not to say you have to accept it.”

Rights groups focused on disabilities wrote in a brief supporting Smith that “intellectual disability diagnoses based solely on IQ test scores are faulty and invalid.”

Smith was convicted and sentenced to death for the beating death of Durk Van Dam in Mobile County. Van Dam was found dead in his pickup truck. Prosecutors said he had been beaten to death with a hammer and robbed of $150, his boots and tools.

A federal judge in 2021 vacated Smith’s death sentence, though she acknowledged “this is a close case.”

Alabama law defines intellectual disability as an IQ of 70 or below, along with significant or substantial deficits in adaptive behavior and the onset of those issues before the age of 18.

A decision in Hamm v. Smith, 24-872, is expected by early summer.

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Chandler reported from Montgomery, Ala.