Maybe we can use the brute force of a "math superoptimizer" to "compress" it to something far more reasonable. If we teach said opimizer what structures are well understood by humans we might actually understand at last parts.

I don't know why people keep thinking there's something special about the way we humans do calculations vs what could be achieved with a complex enough computer

Math is not about proofing something, or creating a as big as possible collection of lemmas. Math is about creating structures that can use as tools to solve problems. And problem solving is a task done by humans, so math is only useful if humans understand it and have a intuition.

These are not mere calculations. See, an understandable proof has more structure than plain first order logic alone. This allows such proofs to be extended and worked upon as well as real life implications to be discovered.

I have a couple of experiences of doing similar big projects where we counted the number of some objects (I haven't checked how big they are.. I have run SAT solvers for a couple of weeks, I didn't try to record some "proof size", I imagine it would be as big if not bigger than 200 terabytes).

Once I could tell a mathematician the count, in both cases someone they proved the result in an alternative way fairly soon afterwards :)