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arXiv · 2605.21200

Tao's Equational Proof Challenge Accepted (Technical Report)

Lydia Kondylidou·Jasmin Blanchette·Marijn J. H. Heule
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Abstract

In the context of the Equational Theories Project, Terence Tao posed the challenge of finding alternatives to a complicated 62-step proof found by the Vampire superposition prover. We introduce a proof minimization tool called Krympa. Using a combination of brute force and heuristics, and exploiting both Vampire and the Twee equational prover, the tool reduces the 62-step proof to 20 steps, each corresponding to a rewrite. In an empirical evaluation, it also performs well on 1431 equational problems originating from the same project, reducing in particular a 151-step proof to only 10 steps.

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Lydia Kondylidou, Jasmin Blanchette, Marijn J. H. Heule. 2026-05-20. Tao's Equational Proof Challenge Accepted (Technical Report). https://arxiv.org/abs/2605.21200

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