Existence of a SAT-only proof for R(4,5) ≤ 25

Determine whether there exists a proof of the upper bound R(4,5) ≤ 25 that relies exclusively on SAT solver calls to a propositional encoding of the blue 4-clique and red 5-clique constraints (i.e., establishing the unsatisfiability of R(4,5,25) purely via SAT solving), without invoking additional high-level arguments or preprocessing beyond the SAT formulation.

Background

The paper presents a formal proof of R(4,5)=25 in HOL4 that combines high-level mathematical arguments with computational steps verified via a SAT solver interface. While SAT encodings dramatically reduce the search space, the authors note that a proof relying only on SAT calls—without additional high-level splitting or preprocessing—has not been achieved to date.

Clarifying whether a purely SAT-based approach suffices would delineate the boundary between algorithmic encoding power and the necessity of higher-level combinatorial reasoning in formal proofs of Ramsey bounds.