Experiments on Automating Boolos' Curious Inference

10 pages•Published: October 23, 2026

Abstract

Boolos’ Curious Inference (BCI) is a well-known example of a class of first-order reasoning problems that require infeasibly many proof steps in a first-order proof calculus but exhibit short and elegant proofs in second-order (or higher-order) logic. Consequently, BCI remains intractable for contemporary first-order automated theorem provers. Although the original problem formulation is also beyond the capabilities of current higher-order provers, previous work by Benzmüller et al. demonstrates that augmenting the problem statement with suitable higher-order formulas allows these provers to succeed. Building on this work, we introduce a procedure for identifying and generating such candidate augmentations. This procedure is implemented in the new ciao tool. Using ciao as a pre-processing tool makes BCI fully automatically solvable for the very first time.

Keyphrases: boolos curious inference, cut introduction, higher order logic, proof length

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 525-534.

Links:	https://easychair.org/publications/paper/Njnd
	https://doi.org/10.29007/rbsg