> Where is the proof based system able to invent every possible thought paradigm of humans a priori?

Beyond the realm of feasibility, I'd imagine. The gulf between what is theoretically possible and what is realistically doable is gargantuan.

> I assumed that, because the resource limits of a very rich human (meaning for whom money is never the limit)

The resources of a very rich human are extremely limited, in the grand scheme of things. They can only mobilize so much of the global economy, and even the entire global economy is only capable of doing so much. That's what I'm getting at: Just because there's some theoretical configuration of matter that would constitute a superintelligence, does not guarantee that humanity, collectively, is capable of producing it. Some things are just beyond us.