Sesquiterpene cyclase that first catalyzes the cyclization of farnesyl diphosphate (FPP) to the bicyclic sesquiterpene (+)-beta-caryophyllene intermediate, and then its conversion to (+)-caryolan-1-ol via a second cyclization and the addition of a water molecule. (2E,6E)-farnesyl diphosphate = (+)-(E)-beta-caryophyllene + diphosphate (+)-(E)-beta-caryophyllene + H2O = (+)-caryolan-1-ol Binds 3 Mg(2+) ions per subunit. To a lesser extent, can also use Mn(2+) instead of Mg(2+). Cannot use Fe(2+), Co(2+), Zn(2+), Ni(2+), or Cu(2+). kcat is 0.025 sec(-1) for (+)-caryolan-1-ol formation (at pH 7.5 and 30 degrees Celsius). Optimum pH is 7.5 for (+)-caryolan-1-ol synthesis. Optimum temperature is 30 degrees Celsius for (+)-caryolan-1-ol synthesis. Secondary metabolite biosynthesis; terpenoid biosynthesis. Expressed under the control of A-factor (2-isocapryloyl-3R-hydroxymethyl-gamma-butyrolactone), in an AdpA-dependent manner. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Cells lacking this gene do not produce (+)-caryolan-1-ol. A study of the reaction mechanism indicates that (+)-caryolan-1-ol is synthesized by a proton attack on the C-8/C-9 double bond of (+)-beta-caryophyllene. Belongs to the terpene synthase family.