After four years of relentless legal effort, the state of Georgia has finally achieved its aim: it has executed an intellectually disabled prisoner in an apparent flagrant violation of the US constitution.

Warren Hill, who was aged 54 but who had the cognitive ability of a young boy, was pronounced dead at 7.55pm on Tuesday, having been administered a lethal injection. It was the culmination of an aggressive push by state authorities to kill him that has seen him served four death warrants in the past four years.

Hill had a lifelong recognised condition of intellectual disability, with his first recording of an abnormally low IQ made at the age of seven. All seven medical experts who saw him – including three appointed by the state itself – concluded that he was mentally impaired by a “preponderance of the evidence”.

Georgia, however, was not satisfied by that unanimous body of opinion, and required Hill to prove he was disabled “beyond a reasonable doubt” – a standard no other state in the union requires and which experts say is almost impossible to match.

Hill was put on death row for the murder of a fellow prison inmate, Joseph Handspike. He was originally sentenced to life for murdering his girlfriend Myra Wright in 1985.

Hill’s execution appears to be a clear breach of the US constitution. In 2002, the US supreme court ruled that it was unlawful to judicially kill an intellectually disabled person, under the Eighth Amendment prohibition of cruel and unusual punishment.

Then last year, in Hall v Florida, the high court made clear that death penalty states could not arbitrarily impose their own definitions of what constituted intellectual disability.

Yet earlier on Tuesday, the same supreme court refused to stay Hill’s execution. It did not explain its decision, with only the justices Sonia Sotomayor and Stephen Breyer dissenting.

Hill’s lawyer, Brian Kammer, who fought doggedly over many years to save his life, called the execution “a grostesque miscarriage of justice” and an “abomination”.

He said:“Georgia has been allowed to execute an unquestionably intellectually disabled man, in direct contravention of the supreme court’s clear precedent prohibiting such cruelty.”

He added: “The memory of Mr Hill’s illegal execution will live on as a moral stain on the people of this state and on the courts that allowed this to happen.”