Computing high utility motifs is a fundamental data mining method for discovering useful itemsets yielding high utility values. Minimal and maximal high utility itemsets are two examples of compact representations used to reduce the output size due to the large and incomprehensible number of patterns. In this paper, we present a novel method for mining minimal and maximal high utility itemsets using propositional satisfiability. First, we show that minimal and maximal high utility patterns are X-minimal models of a CNF formula. Then, to improve the scalability issue of our method, we harness a decomposition paradigm that splits the transaction database into smaller and independent transaction sub-bases, allowing an efficient enumeration of minimal and maximal high utility itemsets. Finally, through extensive evaluation studies on various real-world datasets, we demonstrate that our approach is very competitive w.r.t. to the state-of-the-art specialized solutions.