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This paper concerns Boolean satisfiability (SAT) solvers based on OrderedBinary Decision Diagrams (BDDs), especially those that can generate proofs ofunsatisfiability. Mengel (arXiv:2306.00886) has presented a theoreticalanalysis that a BDD-based SAT solver can generate a proof of unsatisfiabilityfor the pigeonhole problem (PHP$_n$) in polynomial time, even when the problemis encoded in the standard ``direct'' form. His approach is based on bucketelimination, using different orderings for the variables in the BDDs than inthe buckets. We show experimentally that these proofs scale as $O(n^5)$. Wealso confirm the exponential scaling that occurs when the same variableordering is used for the BDDs as for the buckets.

Notes on "Bounds on BDD-Based Bucket Elimination''