Catalyzes the cyclization of 5-formylamidoimidazole-4-carboxamide ribonucleotide to IMP. H2O + IMP = 5-formamido-1-(5-phospho-D-ribosyl)imidazole-4-carboxamide Optimum pH is 6-8.5. Fully active at 80 degrees Celsius. Gradually loses some activity from 90 to 100 degrees Celsius. 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.