Large Language Models (LLMs) demonstrate remarkable performance in machine translation. Recent studies indicate that for high-resource languages, LLM surpasses encoder-decoder neural machine translation (NMT) models. However, evaluation datasets used in many LLM-based translation studies are often compromised by data leakage and lack demanding datasets that accurately gauge the potential and limitations of LLMs in human-like translation. This paper introduces a manually constructed Korean-English discourse-level corpus comprising 600 text instances featuring six linguistic phenomena: lexical ambiguity, zero anaphora, slang, idiom, figurative language, and implicature. Utilizing this challenge test set, we investigated LLM’s Korean-to-English translation capability, particularly in cases requiring inter-sentential context based semantic inference. The findings reveal that state-of-the-art LLM, such as GPT-4o, still struggle with specific linguistic phenomena that can be challenging for machine translation. Additionally, step-by-step prompting, such as Chain-of-Thought (CoT) prompting, significantly enhance the translation performance of LLMs compared to zero-shot prompting.