If things are not all equal, then we can slice off a section of the axiom, and start dissecting it, via science. The axiom only applies if things are exactly equal.

E.g. Gravity wave detectors have found oddities, just above the noise floor. These are likely equipment artifacts. They are also consistent with us being in a simulation, and us touching close to the resolution limit. If true (quite unlikely) then it would prove the axiom false.