# Correct Chains, Wrong Answers: Dissociating Reasoning from Output in LLM Logic

arXiv: https://arxiv.org/abs/2604.13065 · HTML: https://mlsanity.com/paper/2604.13065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 13 of its 16 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 13 of 13)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Thinking Fast and Slow in Large Language Models](https://mlsanity.com/paper/2212.05206/) (2022)
- [A Peek into Token Bias: Large Language Models Are Not Yet Genuine Reasoners](https://mlsanity.com/paper/2406.11050/) (2024)
- [LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2404.15522/) (2024)
- [IDEA: Enhancing the Rule Learning Ability of Large Language Model Agent through Induction, Deduction, and Abduction](https://mlsanity.com/paper/2408.10455/) (2024)

## Abstract (arXiv)

LLMs can execute every step of chain-of-thought reasoning correctly and still produce wrong final answers. We introduce the Novel Operator Test, a benchmark that separates operator logic from operator name, enabling rigorous distinction between genuine reasoning and pattern retrieval. By evaluating Boolean operators under unfamiliar names across depths 1-10 on five models (up to 8,100 problems each), we demonstrate a reasoning-output dissociation that existing benchmarks cannot detect. At Claude Sonnet 4's depth 7, all 31 errors have verifiably correct reasoning yet wrong declared answers; 17/19 errors in mixed-operator chains exhibit the same pattern. The benchmark reveals two failure types: strategy failures at depth 2, where models attempt terse retrieval (+62pp from scaffolding), and content failures at depth 7, where models reason fully but err systematically (+8-30pp, 0/300 errors post-intervention). A Trojan operator (XOR's truth table under a novel name) confirms name alone does not gate reasoning (p >= 0.49), while Llama's novelty gap widens to 28pp at depth 8-9 with the Trojan at 92-100%, isolating genuine difficulty with novel logic from name unfamiliarity.