LLM-Assisted Formal Verification of Bit-vector Invertibility Conditions in Rocq

11 pages•Published: October 23, 2026

Ha Truong, Jordin Palmeri, Liam Secrist, Jacob Schuckman, Arjun Viswanathan and Yoni Zohar

Abstract

Invertibility conditions are properties used by the cvc5 Satisfiability Modulo Theories (SMT) solver to reason about quantified bit-vector formulas. Previous work has proven 122 of 160 invertibility conditions for arbitrary bit-width. We prove the remaining 38 properties in the Rocq interactive theorem prover (ITP) with the help of Google Gemini and Claude Code. This paper presents our efforts in completing this set of proof goals and a case study for using AI assistants in proof projects.

Keyphrases: claude code, google gemini, large language models, rocq, smt

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 80-90.

Links:	https://easychair.org/publications/paper/MjQR
	https://doi.org/10.29007/xtl7

BibTeX entry

@inproceedings{LPAR-26:LLM_Assisted_Formal_Verification,
  author    = {Ha Truong and Jordin Palmeri and Liam Secrist and Jacob Schuckman and Arjun Viswanathan and Yoni Zohar},
  title     = {LLM-Assisted Formal Verification of Bit-vector Invertibility Conditions in Rocq},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/MjQR},
  doi       = {10.29007/xtl7},
  pages     = {80-90},
  year      = {2026}}

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