We make conjectures about objects: these can be graphs, matrices, natural numbers, game positions, etc. These objects have invariants associated with them: real numbers that measure various features of the objects. They also have properties associated with them.
Our programs only know the objects, invariants and properties that we have told them. We plan to keep updated lists of the special objects we have coded as counterexamples to conjectures, as well as the various invariants and properties we have used to date (and their code) on Github: https://github.com/math1um/objects-invariants-properties