In the first two years of the project, we made progress on all three objectives.
The first objective is concerned with improving higher-order SMT and lambda-superposition.
First, for higher-order SMT, we designed a new quantifier instantiation strategy, MBQI-Enum, based on a combination of models and grammars, which is now the best strategy on a vast benchmark suite, thereby improving on the state of the art. This work was published at the highly competitive TACAS 2025 conference. In ongoing follow-up work that is submitted for review, we extended the strategy to come up with Hilbert choice instantiations, further increasing the success rate.
Second, for lambda-superposition, we continued work started in 2021 as part of my ERC starting grant project Matryoshka and currently have an almost finished 120 page draft of the design and correctness proof of a new “optimistic” version of the lambda-superposition calculus, which addresses the three weaknesses of old, “pessimistic” lambda-superposition head on: imprecise term order, explosive function extensionality, and explosive higher-order unification. We expect this work to be submitted for publication by the end of 2025.
Third, for both higher-order SMT and lambda-superposition, we designed a technique called iterative monomorphization that transforms problems expressed in an expressive, so-called polymorphic logical language to problems in a less expressive, so-called monomorphic language.
Objective 2 is about integration in interactive verification platforms. We have developed a new built-in lambda-superposition prover, called slam, for the Isabelle/HOL proof assistant, increasing both the success rate of proof automation and its trustworthiness. This work is under review. We have started work on integrating external proofs by induction, as developed by other teams. We have developed a technique to extract lemma instantiations from superposition proofs (published at CADE 2025). And we have developed a new architecture for “hammer” tools that does not rely on automated theorem provers (published at ITP 2025).
Objective 3 is about case studies. This part will become more important later in the project. For the moment, we can point to a smaller (but nonetheless sizable) case study: the formal verification of the superposition calculus (published at ITP 2024).
