The First Order Truth behind Undecidability of Regular Path Queries Determinacy

In our paper [G{\l}uch, Marcinkowski, Ostropolski-Nalewaja, LICS ACM, 2018] we have solved an old problem stated in [Calvanese, De Giacomo, Lenzerini, Vardi, SPDS ACM, 2000] showing that query determinacy is undecidable for Regular Path Queries. Here a strong generalisation of this result is shown, and -- we think -- a very unexpected one. We prove that no regularity is needed: determinacy remains undecidable even for finite unions of conjunctive path queries.