Explicit Reversible Resolution proofs for Sink-or-Clash CNF

Construct explicit efficient proofs in the Reversible Resolution proof system for the unsatisfiable CNF encoding the Sink-or-Clash total search problem (and related UEOPL^dt-complete problems such as Cube-OPDC), thereby providing concrete SOPL^dt proofs consistent with known class containments.

Background

The authors give an explicit efficient resolution proof (characterizing PLS^dt) for the CNF corresponding to Sink-or-Clash. Since Sink-or-Clash lies in UEOPL^dt ⊂ SOPL^dt, efficient proofs in weaker systems (e.g., Reversible Resolution, which characterizes SOPL^dt) are known to exist in principle.

However, no explicit Reversible Resolution proofs are currently known for the Sink-or-Clash CNF, motivating the construction of such concrete proofs to better understand proof-system characterizations of UEOPL^dt and SOPL^dt.