LLM2SMT: Building an SMT Solver with Zero Human-Written Code

2026-03-06

AI Summary

This work investigates whether large language models can autonomously construct software systems with formal reasoning capabilities, specifically by generating from scratch a complete DPLL(T)-style SMT solver. The resulting solver supports quantifier-free uninterpreted functions (QF_UF), incorporates preprocessing and the Nieuwenhuis–Oliveras congruence closure algorithm, and automatically produces formal proofs in Lean for unsatisfiable instances. To the best of our knowledge, this is the first SMT solver fully generated by a large language model without any human-written code that is capable of emitting machine-checkable proofs. Experimental evaluation on standard SMT-LIB benchmarks demonstrates competitive performance, substantially advancing the frontier of AI-driven autonomous construction of sophisticated formal reasoning tools.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Whether LLMs can reason or write software is widely debated, but whether they can write software that itself reasons is largely unexplored. We present a case study in which an LLM coding agent builds a complete DPLL(T)-style SMT solver for QF_UF with zero human-written code. The solver implements the Nieuwenhuis-Oliveras congruence closure algorithm, includes preprocessing, and emits Lean proofs for unsatisfiable instances. We describe the development process and key challenges, and show that the resulting solver is competitive on SMT-LIB benchmarks.

Problem

• LLM
• SMT solver
• automated reasoning
• code generation
• QF_UF

Innovation

• LLM
• SMT solver
• DPLL(T)
• congruence closure
• automated reasoning