The present preprint specifies and defines all Terms, Properties, Relationships and Axioms of TestTDO (software Testing Top-Domain Ontology) v1.3, which is a slightly updated version of its predecessor, TestTDO v1.2. TestTDO is a top-domain ontology built in the context of a four-layered ontological architecture named FCD-OntoArch (Foundational, Core, and Domain Ontological Architecture for Sciences). This is a four-layered ontological architecture, which considers Foundational, Core, Domain and Instance levels. In turn, the domain level is split down in two sub-levels, namely: Top-domain and Low-domain ontological levels. Ontologies at the same level can be related to each other, except for the foundational level where only the ThingFO ontology is found. In addition, ontologies' terms and relationships at lower levels can be semantically enriched by ontologies' terms properties and relationships from the higher levels. Some TestTDO's terms and are extended primarily from SituationCO (Situation Core Ontology), and ProcessCO (Process Core Ontology) concepts. Stereotypes are the mechanism used for enriching TestTDO terms. Note that annotations of updates from the previous version (v1.2) to the current one (v1.3) can be found in Appendix A.