It will be impressive, if Claude was trained on scientific literature about SAT solvers and tutorials about programming language in question, without access to any real SAT solver code. But it is not the case.
Why do you need LLM-generated code when you can take original, which was consumed by LLM?
Or, I could ask another question: Could Claude give you SAT solver which will be 1% more effective than state-of-art in the area? We don't need another mediocre SAT solver.