NAD(+) hydrolase (NADase) that catalyzes cleavage of NAD(+) into ADP-D-ribose (ADPR) and nicotinamide. H2O + NAD(+) = ADP-D-ribose + H(+) + nicotinamide The TIR domain mediates NAD(+) hydrolase (NADase) activity. Self-association of TIR domains is required for NADase activity.