Theory
If :ancestorOf a owl:TransitiveProperty, then:
:Splinter :ancestorOf :Yoshi .
:Yoshi :ancestorOf :Mira .
entails :Splinter :ancestorOf :Mira . — and any longer chain collapses too.
Three hops, one entailment per pair, all materialised by the reasoner:
asserted: :A :ancestorOf :B . :B :ancestorOf :C . :C :ancestorOf :D .
inferred: :A :ancestorOf :C , :A :ancestorOf :D , :B :ancestorOf :D .
This is why transitivity is so powerful for hierarchies (ancestry, part-of, supervises, depends-on) — you assert only the direct links and the reasoner answers any reachability question for free.