# Do LLMs Game Formalization? Evaluating Faithfulness in Logical Reasoning

arXiv: https://arxiv.org/abs/2604.19459 · HTML: https://mlsanity.com/paper/2604.19459/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 4 of 4)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [Demonstrating specification gaming in reasoning models](https://mlsanity.com/paper/2502.13295/) (2025)
- [Strategies for Improving NL-to-FOL Translation with LLMs: Data Generation, Incremental Fine-Tuning, and Verification](https://mlsanity.com/paper/2409.16461/) (2024)

## Built on by (most cited first, 4 of 4)

- [Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory](https://mlsanity.com/paper/2606.20642/) (2026)
- [Analyzing the Narration Gap in LLM-Solver Loops](https://mlsanity.com/paper/2606.19588/) (2026)
- [Agentic Proof and Property-Based Testing via Property-Templates in Data-Intensive Computing](https://mlsanity.com/paper/2607.09072/) (2026)
- [ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization](https://mlsanity.com/paper/2609.34960/) (2026)

## Abstract (arXiv)

Formal verification guarantees proof validity but not formalization faithfulness. For natural-language logical reasoning, where models construct axiom systems from scratch without library constraints, this gap between valid proofs and faithful translations is especially acute. We investigate whether frontier models exploit this gap when generating Lean 4 proofs, a behavior we term formalization gaming. We evaluate GPT-5 and DeepSeek-R1 on 303 first-order logic problems (203 from FOLIO, 100 from Multi-LogiEval), comparing unified generation against a two-stage pipeline that separates formalization from proving. Despite compilation rates of 87-99%, we find no evidence of systematic gaming in unified generation: models prefer reporting failure over forcing proofs, even under prompting designed to encourage it. However, unfaithfulness that evades our detection signals may still occur. The two-stage pipeline reveals two distinct modes of unfaithfulness: GPT-5 fabricates axioms during proof generation, a reactive fallback detectable via cross-stage comparison, while DeepSeek-R1 mistranslates premises during formalization, producing internally consistent outputs that evade detection entirely. These findings show that high compilation rates or accuracies should not be equated with faithful reasoning. Code and data are available at https://github.com/koreankiwi99/formalization-gaming.