We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free \(\lambda \)-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between \(\lambda \)-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition.

我们最近设计了两个演算作为实现完整高阶逻辑叠加的垫脚石：无布尔\(\lambda \) - 叠加和一阶逻辑与解释布尔值的叠加。踩着这些石头，我们终于得出了一个可靠的、可反驳的完整演算，用于具有多态性、外延性、希尔伯特选择和亨金语义的高阶逻辑。除了结合微积分的两个前身的复杂性之外，新的挑战还来自\(\lambda\) -项和布尔值之间的相互作用。我们在 Zipperposition 中的实现优于所有其他高阶定理证明器，并且与 Zipperposition 中布尔的早期实用原型相当。