We propose SETI (Systematicity Evaluation of Textual Inference), a novel and comprehensive benchmark designed for evaluating pre-trained language models (PLMs) for their systematicity capabilities in the domain of textual inference. Specifically, SETI offers three different NLI tasks and corresponding datasets to evaluate various types of systematicity in reasoning processes. In order to solve these tasks, models are required to perform compositional inference based on known primitive constituents. We conduct experiments of SETI on six widely used PLMs. Results show that various PLMs are able to solve unseen compositional inferences when having encountered the knowledge of how to combine primitives, with good performance. However, they are considerably limited when this knowledge is unknown to the model (40-100 \% points decrease). Furthermore, we find that PLMs are able to improve dramatically once exposed to crucial compositional knowledge in minimalistic shots. These findings position SETI as the first benchmark for measuring the future progress of PLMs in achieving systematicity generalization in the textual inference.