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Large Language Models (LLMs) have been widely found to struggle with logical reasoning, where even fine-tuned models fail dramatically on out-of-distribution problems. However, existing work has focused on relatively complex “many-hop” reasoning problems. In this paper, we analyse the performance of fine-tuned LLMs on simple reasoning problems, all of which can be solved in at most three inference steps. Due to the simplicity of these problems, the model cannot encounter test problems that are fundamentally different from those it has seen during training. Unfortunately, however, we find that the models remain highly brittle, being susceptible to seemingly innocent perturbations, such as the addition of duplicates to the set of premises and shuffling the order in which the premises are presented.