Catalyzes the conversion of (8S)-3',8-cyclo-7,8-dihydroguanosine 5'-triphosphate to cyclic pyranopterin monophosphate (cPMP). (8S)-3',8-cyclo-7,8-dihydroguanosine 5'-triphosphate = cyclic pyranopterin phosphate + diphosphate kcat is 0.17 min(-1). Cofactor biosynthesis; molybdopterin biosynthesis. Homohexamer; trimer of dimers. Belongs to the MoaC family.