# A Survey on Theorem Provers in Formal Methods

arXiv: https://arxiv.org/abs/1912.03028 · HTML: https://mlsanity.com/paper/1912.03028/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 8 of 8)

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- [Efficient PRM Training Data Synthesis via Formal Verification](https://mlsanity.com/paper/2505.15960/) (2025)
- [StepProof: Step-by-step verification of natural language mathematical proofs](https://mlsanity.com/paper/2506.10558/) (2025)
- [Towards Large Language Model Aided Program Refinement](https://mlsanity.com/paper/2406.18616/) (2024)
- [Improving Autoformalization Using Direct Dependency Retrieval](https://mlsanity.com/paper/2511.11990/) (2025)
- [Learning to Prove Trigonometric Identities](https://mlsanity.com/paper/2207.06679/) (2022)
- [Towards Generalizable and Faithful Logic Reasoning over Natural Language via Resolution Refutation](https://mlsanity.com/paper/2404.01677/) (2024)

## Abstract (arXiv)

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians to prove theorems by computer programs. However, these tools evolved with time and now play vital role in the modeling and reasoning about complex and large-scale systems, especially safety-critical systems. Technically, mathematical formalisms and automated reasoning based-approaches are employed to perform inferences and to generate proofs in theorem provers. In literature, there is a shortage of comprehensive documents that can provide proper guidance about the preferences of theorem provers with respect to their designs, performances, logical frameworks, strengths, differences and their application areas. In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these tools. Theorem provers are investigated based on various parameters, which includes: implementation architecture, logic and calculus used, library support, level of automation, programming paradigm, programming language, differences and application areas.