TLAPS-Bench: Formally Proving Correctness of Real-World System Specifications with TLA+ Proof System

TLAPS-Bench is a benchmark and execution harness for constructing machine-checked proofs for real-world system specifications in TLA+ with agentic AI. Proving correctness of complex system specifications requires discovering inductive invariants, reasoning about intricate state transitions, and decomposing proofs into tractable obligations. TLAPS-Bench provides a proof harness that supports iterative proof development atop the TLA+ Proof System (TLAPS), where agents are equipped with proof tools and libraries, with safeguards against reward hacking. Using the harness, we have employed AI agents to prove desired properties for important system specifications that were not proved before, spanning cache coherence, Byzantine consensus, and write-ahead logs. TLAPS-Bench contains 265 proof targets (each encodes a property to prove) from 95 TLA+ specifications of real-world systems. We evaluated frontier AI agents, represented by Codex with GPT models, on a subset of 70 proof targets across 12 specifications. The highest-scoring model, GPT-6.1 Sol (max), proved 31 (44.3%) proof targets. The results show challenges and opportunities in end-to-end proof development.