GO:0004641:   phosphoribosylformylglycinamidine cyclo-ligase activity
Catalysis of the reaction: 2-(formamido)-N(1)-(5-phospho-D-ribosyl)acetamidine + ATP = 5-amino-1-(5-phospho-D-ribosyl)imidazole + ADP + 2 H(+) + phosphate.