arXiv:2605.06882v1 Announce Type: new Abstract: Large Language Models (LLMs) have achieved great improvements in recent years. Nevertheless, it still remains unclear how good LLMs are for reasoning tasks, especially for long-chain ones. In this paper, we evaluate LLMs' performance on the simplest yet long-chain reasoning task, namely the Equivalence Class Problem (ECP), i.e., determining whether two variables are equal given a set of randomly generated equivalence relations. We consider both reasoning and non-reasoning representative LLMs over a large variety of problem instances, ranging over different numbers of variables, connectivity probabilities, prompts, and other factors. The experimental results show that non-reasoning LLMs fail ECP, while reasoning models are significantly better but still struggle to completely solve this problem. Interestingly, considering various connectivity probabilities with a fixed number of variables, we observe that, for non-reasoning models, the hardest problem instances coincide with the phase transition point of ln n/(n-1), suggesting the chaos of the problem; in contrast, for reasoning models, the hardest ones coincide with the biggest diameter, suggesting the reasoning difficulty of the problem.