Catalyzes the conversion of geranylfarnesyl diphosphate (GFPP) and hexaprenyl diphosphate (HexPP) into beta-geranylfarnesene and beta-hexaprene, respectively (PubMed:23554321, PubMed:25882275). Also produces beta-heptaprene from heptaprenyl diphosphate (HepPP) as a minor product (PubMed:25882275). (2E,6E,10E,14E)-geranylfarnesyl diphosphate = beta-geranylfarnesene + diphosphate all-trans-hexaprenyl diphosphate = beta-hexaprene + diphosphate all-trans-heptaprenyl diphosphate = beta-heptaprene + diphosphate Belongs to the large terpene synthase family.