I don't understand how you want to prove that the random number generator is not random...? If you want to show that the numbers are generated mathematically (and thus not random) then you can simply check your documentation, we know they are not random.
If you want to prove it without exploiting the fact that you already know them not to be random, you would probably have to try to reproduce the algorithm just from a list of generated pseudo-random numbers. I don't see how you're going to do that by the method you explained.

The only real random numbers can be generated by using some physical random occurrence (such as radioactive decay) but that is simply unpractical for most purposes as a pseudo-random number generator will do just fine.