Verified satisfiability-preserving variable permutation search

Prove that variable permutations preserve satisfiability for arbitrary 3-CNF formulas and develop a verified greedy search algorithm for finding a variable ordering that transforms a formula into sliding-window form, with the goal of avoiding the factorial complexity of exhaustive permutation enumeration.

Background

The verified Rocq development includes an exhaustive search over all variable permutations and proves that it finds a sliding-window ordering whenever one exists. Because this search has factorial complexity, the implementation relies on an unverified heuristic for larger instances.

The paper identifies both a satisfiability-preservation proof for variable permutation and a verified greedy search as missing components needed to extend formal guarantees beyond small formulas.