Building on the principles of case-based reasoning, we investigate the extraction of arguments from legal case databases. An argument is modeled as a set of factors that frequently support one party (plaintiff or defendant) over the other. The relevance of an argument is assessed by the number of cases that confirm it versus those that contradict it. Following established practices in data mining, we introduce a condensed representation of arguments called closed arguments, which capture the strongest form of support given the factors they contain. We develop propositional SAT-based encodings to enable the extraction of both arguments and closed arguments using SAT solvers. Additionally, we define a more compact condensed representation called maximal arguments, which eliminates redundancy by retaining only the most informative arguments with respect to given thresholds. We propose a level-wise algorithm that builds on our SAT-based approach for argument extraction. Preliminary experiments demonstrate the feasibility of our SAT-based mining methods.