None of that is required. SR doesn't come with a proper mathematical proof so that it can be disproved by the method of contradiction. To bring down the glass house of relativity it is enough to show that the speed of light is not a constant. Then Einstein point is moot that the alleged space and time changes.I have yet to see anyone use Lorentz transformations to examine the system described a few posts up to illustrate their claim special relativity has a contradiction. I have yet to see anyone demonstrate special relativity has a contradiction at all.
In short show a c+v is possible.