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Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consistent subsets using minimal inconsistent sets and a resolution method, to improve the run-time performance of the reasoning processing. A minimal inconsistent set contains a minimal explanation for the inconsistency of a given ontology. Thus, it can replace the consistency checking operation, which is executed frequently in existing approaches. When selecting subsets of the inconsistent ontology, formulas which can be directly or indirectly resolved with the negation of the query formula are selected because only those formulas affect the consequences of the reasoner. Therefore, the complexity of the reasoning processing is significantly reduced. Tests show that the run-time performance of the inconsistency reasoner is significantly improved.