You might find my orbit-diagrams repo interesting: https://github.com/jasonincanada/orbit-diagrams

It's a way to render function application/composition in 3D. In particular you'd probably like the proof of B = S (K S) K:

https://raw.githubusercontent.com/jasonincanada/orbit-diagra...

I have no experience with SKI calculus so I may be misinterpreting how to apply these functions. But it seems to me that the definition of F doesn't work quite right. After trying my own hand at it for several minutes and getting stuck, I looked at the Wikipedia page and found a different definition for S.

I don't know of these two systems with the same name are computationally equivalent or if the author simply made a crucial mistake in the definitions.

Oops the author has indeed made a crucial late-at-night-stare-at-the-screen-too-much typo, thanks for pointing it out! Fixed.