SAT solvers settle combinatorial problems beyond the reach of interactive theorem provers and produce LRAT certificates for independent verification. We present LRAT-Catcher, a standalone, general-purpose tool that imports a DIMACS formula together with an LRAT certificate into Lean 4 as a theorem. LRAT-Catcher runs the formally verified LRAT checker from Lean core as compiled native code via reflection. This scales to instances where Mathlib's explicit proof-term import exhausts memory. LRAT-Catcher also composes cube-and-conquer solving runs entirely inside Lean. Per-cube refutations are combined with a cover-completeness certificate, itself an LRAT proof, into a single unsatisfiability theorem. Verified encodings connect CNF-level results to the original combinatorial problems. We evaluate the tool against Mathlib's proof-term import and the external checker cake_lpr on establishing the Schur number S(4) = 44 and the Ramsey number R(4,4) = 18 as Lean theorems.
String constraint solvers are crucial for reasoning about string-manipulating programs. However, many practical string constraints are undecidable, and real-world applications often present complex constraints that challenge current solvers. The rise of multi-core architectures offers an opportunity for parallel solving. A key parallel solving method is \emph{cube-and-conquer}, in which the quality of splitting heuristics is critical to effectively dividing the search space. Unfortunately, manually designing the heuristics is labor-intensive, and handcrafted heuristics are often sub-optimal. This paper introduces a data-driven approach to automatically generating splitting heuristics. We frame the problem of selecting a splitting atom as a learning task, using features from input formulas and dynamic data from solver execution. We implement this approach in two popular string solvers, Z3seq and Z3str4, demonstrating that the learned heuristics outperform manually designed ones in the number of solved formulas and the average solving time.