We report on an exploration of variants of Boolos' curious inference using higher-order automated theorem provers (ATPs). Surprisingly, only a single shorthand notation still had to be provided by hand. All higher-order lemmas required for obtaining short proof are automatically discovered by the computer. Given the observations and suggestions in this paper, full proof automation of Boolos' example on the speedup of proof lengths, and related examples, now seems to be within reach for higher-order ATPs.
翻译:令人惊讶的是,只有一张短手标记仍必须由手来提供。 获得短证据所需的所有高单 Lemmas都是由计算机自动发现的。 鉴于本文中的意见和建议,Boolos关于加快证据长度的例子的完整证明自动化和相关的例子,现在似乎可以在更高单的ATP中找到。