A theorem is a sentence that is postulated to logically follow from the axioms of an ontology. Theorems help documenting the (intended or unintended) consequences of an ontology. Theorems can be proved with a theorem prover.
A DOL file may associate an ontology with one ore more theorems. The theorems that are associated with a given ontology can be found as follows: In a given repository select an ontology. (If it is a heterogenous ontology, you may need to select a child ontology). The theorems are displayed in the "Theorem" subtab under the "Content" tab. Here is an example .