Natural Language Inference (NLI) determines whether a premise entails, contradicts, or is neutral with respect to a hypothesis. The task is often framed as emulating human inference, in which commonsense knowledge plays a major role. This study examines whether Large Language Models (LLMs) can reliably generate factual commonsense axioms for NLI, and evaluates their utility on the SNLI and ANLI benchmarks using Llama-3.1-70B and gpt-oss-120b. Because commonsense axioms lack explicit textual references, standard factuality metrics are ill-suited to their evaluation. We therefore introduce a reference-free method using an LLM-as-Judge framework. The evaluation reveals a substantial gap between models: gpt-oss-120b generates predominantly accurate axioms, whereas Llama produces more incorrect than correct ones. We further evaluate three prompting pipelines: direct inference, inference augmented with generated commonsense axioms, and a hybrid approach that selectively incorporates highly factual axioms based on judged factuality. The hybrid approach yields consistent accuracy gains of 3.87%-8.5% across tested configurations. Targeted commonsense knowledge also helps models overcome a bias toward the Neutral class by providing essential real-world context.

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