How do I optimize my code to solve SAT with a Rubik's cube in O(n²)?

In short, I created an algorithm that solves SAT by modeling it with a generalized Rubik's cube, and it doesn't matter if it's not the most optimal Rubik's cube solution — so I wrote the paper.

Paper in IPFS: https://dweb.link/ipfs/bafybeiagsscemkz7zcfaube6r4iybjepegun5monxkvgc3ddevyvdsxe5y

Paper and Code Zenodo DOI: https://doi.org/10.5281/zenodo.18975934

Then I tried to implement it in code and it worked perfectly! Because it's O(n²).

Code Demo in IPFS: https://dweb.link/ipfs/bafkreibfkkp4plhf2tgex5wn22pyyjm7qvvgoyjzqdqihupn7cc62vurgi

But when I tried feeding it any .cnf or SAT instance, it became EXTREMELY SLOW. Then I tried implementing it in C++ on Colab for better speed

Code IPYNB in IPFS: https://dweb.link/ipfs/bafkreiaatmyqgoxqqic2gxvs77h7p6xkzfsbezprqiphek4kxypaeyydlu

, and I fed it a .cnf file with these specs:

I ran it on Colab on a v5e1 — it's already been 8 minutes and it's still trying to solve it.

So the question is: What do you recommend to optimize the code as much as possible, without using heuristics?