End-to-end verification of grouped-window CNF translation

Establish a formal proof that the grouped-window decomposition and CNF-to-CTF translation preserve satisfiability, thereby extending the verified correctness guarantees from the clause-by-clause sliding-window pipeline to grouped-window, dense sliding-window, overlapping-group, and general 3-CNF inputs.

Background

The verified Rocq formalisation covers a clause-by-clause translation in which each clause becomes a separate tier. The VFR prototype, however, uses a grouped-window decomposition that merges clauses sharing the same variable triple.

The paper shows that the grouped representation is sound in one direction but does not generally preserve the converse implication because its weak predicate does not enforce consistency across overlapping windows. The authors explicitly identify closing this verification gap as the principal obstacle to an end-to-end verified solver.