Often the term intransitive is used to refer to the stronger property of antitransitivity.

stronger property

the adjective strong or the adverb strongly may be added to a mathematical notion to indicate a related stronger notion; for example, a strong antichain is an antichain satisfying certain additional conditions, and likewise a strongly regular graph is a regular graph meeting stronger conditions. When used in this way, the stronger notion (such as "strong antichain") is a technical term with a precisely defined meaning; the nature of the extra conditions cannot be derived from the definition of the weaker notion (such as "antichain")