Catalyzes the cyclization of 5-formylamidoimidazole-4-carboxamide ribonucleotide to IMP. H2O + IMP = 5-formamido-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide Purine metabolism; IMP biosynthesis via de novo pathway; IMP from 5-formamido-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide: step 1/1. Belongs to the archaeal IMP cyclohydrolase family.