Catalyzes thiolytic cleavage of beta-ketoadipyl-CoA to succinyl-CoA and acetyl-CoA. acetyl-CoA + succinyl-CoA = 3-oxoadipyl-CoA + CoA Aromatic compound metabolism; beta-ketoadipate pathway; acetyl-CoA and succinyl-CoA from 3-oxoadipate: step 2/2. Belongs to the thiolase-like superfamily. Thiolase family.