The novelty surrounding all things OntoClean described here, is that we made a tutorial out of a scientific paper and used an example that is different from the (in?)famous manual example to clean up a ‘dirty’ taxonomy.
I’m assuming you have at least heard of OntoClean, which is an ontology-inspired method to examine the taxonomy of an ontology, which may be useful especially when the classes (/universals/concepts/..) have no or only a few properties or attributes declared. Based on that ontological information provided by the modeller, it will highlight violations of ontological principles in the taxonomy so that the ontologist may fix it. Its most recent overview is described in Guarino & Welty’s book chapter  and there are handouts and slides that show some of the intermediate steps; a 1.5-page summary is included as section 5.2.2 in my textbook .
Besides that paper-based description , there have been two attempts to get the reasoning with the meta-properties going in a way that can exploit existing technologies, which are OntOWLClean  and OntOWL2Clean . As the names suggest, those existing and widely-used mechanisms are OWL and the DL-based reasoners for OWL, and the latter uses OWL2-specific language features (such as role chains) whereas the former does not. As it happened, some of my former students of the OE course wanted to try the OntoOWLClean approach by Welty, and, as they were with three students in the mini-project team, they also had to make their own example taxonomy, and compare the two approaches. It is their—Todii Mashoko, Siseko Neti, and Banele Matsebula’s—report and materials we—Zola Mahlaza and I—have brushed up and rearranged into a tutorial on OntoClean with OWL and a DL reasoner with accompanying OWL files for the main stages in the process.
There are the two input ontologies in OWL (the domain ontology to clean and the ‘ontoclean ontology’ that codes the rules in the TBox), an ontology for the stage after punning the taxonomy into the ABox, and one after having assigned the meta-properties, so that students can check they did the steps correctly with respect to the tutorial example and instructions. The first screenshot below shows a section of the ontology after pushing the taxonomy into the ABox and having assigned the meta-properties. The second screenshot illustrates a state after having selected, started, and run the reasoner and clicked on “explain” to obtain some justifications why the ontology is inconsistent.
Those explanations, like shown in the second screenshot, indicate which OntoClean rule has been violated. Among others, there’s the OntoClean rule that (1) classes that are dependent may have as subclasses only those classes that are also dependent. The ontology, however, has: i) Father is dependent, ii) Male is non-dependent, and iii) Father has as subclass Male. This subsumption violates rule (1). Indeed, not all males are fathers, so it would be, at least, the other way around (fathers are males), but it also could be remodelled in the ontology such that father is a role that a male can play.
Let us look at the second generated explanation, which is about violating another OntoClean rule: (2) sortal classes have only as subclasses classes that are also sortals. Now, the ontology has: i) Ball is a sortal, ii) Sphere is a non-sortal, and iii) Ball has as subclass Sphere. This violates rule (2). So, the hierarchy has to be updated such that Sphere is not subsumed by Ball anymore. (e.g., Ball has as shape some Sphere, though note that not all balls are spherical [notably, rugby balls are not]). More explanations of the rule violations are described in the tutorial.
Seeing that there are several possible options to change the taxonomy, there is no solution ontology. We considered creating one, but there are at least two ‘levels’ that will influence what a solution may look like: one could be based on a (minimum or not) number of changes with respect to the assigned meta-properties and another on re-examining the assigned meta-properties (and then restructuring the hierarchy). In fact, and unlike the original OntoClean example, there is at least one case where there is a meta-property assignment that would generally be considered to be wrong, even though it does show the application of the OntoClean rule correctly. How best to assign a meta-property, i.e., which one it should be, is not always easy, and the student is also encouraged to consider that aspect of the method. Some guidance on how to best modify the taxonomy—like Father is-a Male vs. Father inheres-in some Male—may be found in other sections and chapters of the textbook, among other resources.
p.s.: this tutorial is the result of one of the activities to improve on the OE open textbook, which are funded by the DOT4D project, as was the tool to render the axioms in DL in Protégé. A few more things are in the pipeline (TBC).
 Guarino, N. and Welty, C. A. (2009). An overview of OntoClean. In Staab, S. and Studer, R., editors, Handbook on Ontologies, International Handbooks on Information Systems, pages 201-220. Springer.
 Keet, C. M. (2018). An introduction to ontology engineering. College Publications, vol 20. 344p.
 Welty, C. A. (2006). OntOWLClean: Cleaning OWL ontologies with OWL. In Bennett, B. and Fellbaum, C., editors, Proceedings of the Fourth International Conference on Formal Ontology in Information Systems (FOIS 2006), Baltimore, Maryland, USA, November 9-11, 2006, volume 150 of Frontiers in Artificial Intelligence and Applications, pages 347-359. IOS Press.
 Glimm, B., Rudolph, S., Volker, J. (2010). Integrated metamodeling and diagnosis in OWL 2. In Peter F. Patel-Schneider, Yue Pan, Pascal Hitzler, Peter Mika, Lei Zhang, Je_ Z. Pan, Ian Horrocks, and Birte Glimm, editors, Proceedings of the 9th International Semantic Web Conference, LNCS vol 6496, pages 257-272. Springer.