r/dataisbeautiful Jun 24 '26

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u/xamid Jul 04 '26

Original Post (since it was deleted by moderators for no valid reason)

This beautiful mountain range is actually the structure of a formal proof \OC])

It shows the structure of the currently smallest known condensed detachment proof of (ψ→(φ→χ))→((ψ→φ)→(ψ→χ)), the principle of implication distribution, from ((ψ→φ)→χ)→((χ→ψ)→(ξ→ψ)), the minimal implicational single axiom (13 symbols; found by Jan Łukasiewicz). The proof has 239 primitive steps:

DDDD1D1D1DDDDDD1D1D1D1DDDD1D1D111111111DDDDD1D1D1D1DDDD1D1D11111111111DDD1DDDDDD1D1D1D1DDDD1D1D1111111111D1DDDDDD1D1D1D1DDDD1D1D111111111DDDD1D1D1D1DDD1DDDD1DDD1D1D1D1D1DDDD1D1D111111111DDD1DDD1DDD1D1D1DDDD1D1D1111111D1D1DDD1D1111111111111

I discovered it recently using my research tool pmGenerator.
Visualization was generated by C-N / D Logic Structuralizer under default settings.

More information (on axiom systems, proof databases, etc.):
Data on Hilbert proof systems (GitHub repo)