We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node properties, and edges encode supporting or attacking relations. Unlike existing automated essay scoring systems, IntelliProof emphasizes the user experience: each relation is initially classified and scored by an LLM, then visualized for enhanced understanding. The system provides justifications for classifications and produces quantitative measures for essay coherence. It enables rapid exploration of argumentative quality while retaining human oversight. In addition, IntelliProof provides a set of tools for a better understanding of an argumentative essay and its corresponding graph in natural language, bridging the gap between the structural semantics of argumentative essays and the user's understanding of a given text.