We evaluate the ability of contemporary large language models (LLMs) to perform argumentative reasoning. We frame our experiments in terms of the argument mining (AM) and argument pair extraction (APE) tasks, and evaluate their ability to perform reasoning at increasing levels of abstraction in the input and output representations (e.g., arbitrary label sets, semantic graphs). We find that, although LLMs are able to match or surpass the state-of-the-art in AM and APE, their argumentative reasoning performance is very dependent on the input and output representation. We also find an "exemplar effect", where too many exemplars increasingly become detrimental for task performance, and about 4-5 being the optimal amount. Neither result extends to chain-of-thought (CoT) prompting: we find the exemplar effect to be nullified, and our results suggest that CoT allows for better performance under ill-conditioned problems. We hope that the work reported contributes to the improvement of argumentative reasoning in LLMs.