Discovering disjointness axioms is a very important task in ontology learning and knowledge base enrichment. To help overcome the knowledge-acquisition bottleneck, we propose a grammar-based genetic programming method for mining OWL class disjointness axioms from the Web of data. The effectiveness of the method is evaluated by sampling a large RDF dataset for training and testing the discovered axioms on the full dataset. First, we applied Grammatical Evolution to discover axioms based on a random sample of DBpedia, a large open knowledge graph consisting of billions of elementary assertions (RDF triples). Then, the discovered axioms are tested for accuracy on the whole DBpedia. We carried out experiments with different parameter settings and analyze output results as well as suggest extensions.