Examining logical inconsistencies among multiple statements (such as collections of sentences or question-answer pairs) is a crucial challenge in machine learning, particularly for ensuring the safety and reliability of models. Traditional methods that rely on 1:1 pairwise comparisons often fail to capture inconsistencies that only emerge when more than two statements are evaluated collectively. To address this gap, we introduce the task of set-consistency verification, an extension of natural language inference (NLI) that assesses the logical coherence of entire sets rather than isolated pairs. Building on this task, we present the Set-Consistency Energy Network (SC-Energy), a novel model that employs a margin-based loss to learn the compatibility among a collection of statements. Our approach not only efficiently verifies inconsistencies and pinpoints the specific statements responsible for logical contradictions, but also significantly outperforms existing methods, including prompting-based LLM models. Furthermore, we release two new datasets: Set-LConVQA and Set-SNLI for set-consistency verification task.