MU Puzzle in Automated Theorem Provers

Wed, 21 May 2025 08:20:28 -0700

I recently began re-reading Gödel, Escher, Bach and was intrigued by the MU puzzle, which is Hofstadter’s introduction to formal systems. The puzzle is this: the MIU language consists of the “axiom” MI as well as all strings constructed according to the following four rules.

If you have the string xI, then you can construct the string xIU (where x is any string of any length).
If you have Mx, then you can construct Mxx.
If III appears anywhere in a string, you can replace it with U.
If UU appears anywhere in a string, you can remove it.

Can you ever construct the string MI?

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MU Puzzle in Automated Theorem Provers