We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi . In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation. We define a proof system combining resolution and the OBDD proof system.
"An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams." J. Symbolic Logic 73 (1) 227 - 237, March 2008. https://doi.org/10.2178/jsl/1208358751