Catalyzes the oxidation of 5,10-methylenetetrahydrofolate to 5,10-methenyltetrahydrofolate and then the hydrolysis of 5,10-methenyltetrahydrofolate to 10-formyltetrahydrofolate. (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + NADP(+) = 5,10-methenyltetrahydrofolate + NADPH 5,10-methenyltetrahydrofolate + H2O = (6S)-10-formyltetrahydrofolate + H(+) The NAD(+)-dependent dehydrogenase is activated by inorganic phosphate. One-carbon metabolism; tetrahydrofolate interconversion. Homodimer. Belongs to the tetrahydrofolate dehydrogenase/cyclohydrolase family.