"which requires an inexhaustible supply. "

But this is how you can stress the theorem. I know it will take a long time, so consider a universe where only 1000 bits of matter actually exist, then try to use the theorem and you won't have enough ink to even hold the theorem, and sets in memory. It's the same for our universe, just with more bits.

"you could simply add those sentences to your list of proof rules " Thanks, for responding. Do you mean axioms? I don't understand why that would be a solution. I'll have to read Godel again.