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We investigate the extent to which the language processing of LLMs resembles human cognitive processes, focusing on a human cognitive bias called the $\textit{neglect-zero effect}$. This effect refers to the human tendency to ignore $\textit{zero-models}$, which are configurations that render a proposition vacuously true by virtue of an empty set. We focus on two types of inferences driven by the neglect-zero effect, and examine how LLMs process these inferences by comparing their behavior with that in an inference that does not involve the neglect-zero effect. For this purpose, we employ a paradigm based on $\textit{structural priming}$, where recent exposure to a preceding sentence (the $\textit{prime}$) facilitates the processing of a subsequent sentence (the $\textit{target}$) due to their structural similarity. We prepare primes to force LLMs to consider the zero-model, and analyze whether they also consider it in the target. The results suggest that the neglect-zero effect may not occur in the LLMs analyzed in this study. Our code is available at this https URL