Beyond Theorem Proving: Formulation, Framework and Benchmark for Formal Problem-Solving

FPS, a deterministic Markov decision process, solves problems using FTP environments, offering process-verified solutions. D-FPS decouples solving and answer verification for better human alignment. Proven expressiveness, soundness, and completeness, FPS showcases through benchmarks. RPE verifies symbolic correctness. Four FTP models and two prompting methods serve as baselines, achieving limited success on benchmarks. AI innovations in formal math, automated theorem proving, and large language models are showcased. Systems like Minif2f, Internlm2.5-stepprover, and Lean-star use machine learning and expert iteration to tackle complex problems. Research focuses on deep learning models and their applications in theorem proving, mathematical reasoning, and physics.