Huntsville - A Texas inmate was executed on Wednesday for setting a fire that killed his 18-month-old daughter and her two young half-sisters at an East Texas home 15 years ago.Raphael Holiday, 36, became the 13th convicted killer put to death this year in Texas, which carries out capital punishment more than any other state. It has accounted for half of all executions in the US so far this year.The lethal injection was carried out after the US Supreme Court rejected an appeal seeking to halt Holiday's punishment so new attorneys could be appointed to pursue additional unspecified appeals in his case.Earlier on Wednesday, the judge in Holiday's trial court stopped the execution after Holiday's trial attorney filed an appeal saying the conviction and some trial testimony were both improper. The judge agreed the issues should be reviewed and withdrew his execution warrant. The Texas attorney general's office appealed, the judge's order voided and the warrant reinstated, clearing the way for the lethal injection to move forward.At the Supreme Court, Austin-based lawyer Gretchen Sween argued that Holiday's court-appointed attorneys abandoned him after the justices in June refused to review his case. Those lawyers advised Holiday his legal issues were exhausted and new appeals and a clemency petition would be fruitless.'I'm not afraid of dying'Holiday protested, wrote a federal judge to order them off his case and asked that Sween be allowed to represent him."I'm not afraid of dying," Holiday told The Associated Press recently from a visiting cage outside death row. "I know at some point we all die. It's just the way of dying."If I have to die, I want at least a fair chance of fighting."Holiday insisted he didn't know how the log cabin he once shared with his common-law wife and the children in the Madison County woods about 100 miles north of Houston caught fire in September 2000."I loved my kids," Holiday said. "I never would do harm to any of them."Evidence and testimony showed Holiday was irate over a protective order his estranged wife obtained after his arrest for sexually assaulting one of the children. Holiday, from prison, contended he knew nothing about the assault.Electrical problemAccording to court records, he showed up at the home and forced the girls' grandmother at gunpoint to douse the interior with gasoline.After it ignited, he sped away in the grandmother's car, hit a police car that arrived outside the cabin and then led officers on a chase that ended two counties away when he wrecked.Defence attorneys at his trial suggested an electrical problem or a pilot light started the blaze in the early hours of September 6 2000, killing Holiday's daughter, Justice, and her half-sisters, Tierra Lynch, 7, and Jasmine DuPaul, 5.The girls' grandmother told a jury she watched Holiday bend down and then the flames erupted, court records show. Jurors convicted him of capital murder and decided he should be put to death.Texas carried out 10 executions in 2014.