  We demonstrate a family of propositional formulas in conjunctive normal form
so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to
refute using the tree-like OBDD refutation system of Atserias, Kolaitis and
Vardi with respect to all variable orderings. All known symbolic quantifier
elimination algorithms for satisfiability generate tree-like proofs when run on
unsatisfiable CNFs, so this lower bound applies to the run-times of these
algorithms. Furthermore, the lower bound generalizes earlier results on
OBDD-based proofs of unsatisfiability in that it applies for all variable
orderings, it applies when the clauses are processed according to an arbitrary
schedule, and it applies when variables are eliminated via quantification.
