Catalyzes the reduction of oxygen to water. Subunits I, II and III form the functional core of the enzyme complex. Electrons originating in caldariella quinol are transferred to the binuclear center formed by heme A3 and Cu(B). Subunit I binds heme a and the bimetallic center. 2 a quinol + O2 = 2 a quinone + 2 H2O Belongs to the heme-copper respiratory oxidase family.