Bounded-depth Frege complexity of Tseitin formulas for all graphs

We prove that there is a constant K such that Tseitin formulas for a connected graph G requires proofs of size 2tw(G)javax.xml.bind.JAXBElement@531a834b in depth-d Frege systems for [Formula presented], where tw(G) is the treewidth of G. This extends Håstad's recent lower bound from grid graphs to any graph. Furthermore, we prove tightness of our bound up to a multiplicative constant in the top exponent. Namely, we show that if a Tseitin formula for a graph G has size s, then for all large enough d, it has a depth-d Frege proof of size 2tw(G)javax.xml.bind.JAXBElement@25a4b51fpoly(s). Through this result we settle the question posed by M. Alekhnovich and A. Razborov of showing that the class of Tseitin formulas is quasi-automatizable for resolution.