Abstract Lifting Boolean-reasoning techniques to the SMT level most often requires producing theory lemmas that rule out theory-inconsistent truth assignments. With standard SMT solving, it is common to “lazily” generate such lemmas on demand during the search; with some harder SMT-level tasks —such as unsat-core extraction, MaxSMT, $$\mathcal {T}$$ T -OBDD or $$\mathcal {T}$$ T -SDD compilation— it may be beneficial or even necessary to “eagerly” pre-compute all the needed theory lemmas upfront. Whereas in principle “classic” eager SMT encodings could do the job, they are specific for very few and easy theories, they do not comply with theory combination, and may produce lots of unnecessary lemma In this paper, we present theory-agnostic methods for enumerating complete sets of theory lemmas tailored to a given formula. Starting from AllSMT as a baseline approach, we propose improved lemma-enumeration techniques, including divide&conquer, projected enumeration, and theory-driven partitioning, which are highly parallelizable and which may drastically improve scalability. An experimental evaluation demonstrates that these techniques significantly enhance efficiency and enable the method to scale to substantially more complex instances.

In Knowledge Compilation (KC) a propositional knowledge base is compiled off-line into some target form, typically into deterministic decomposable negation normal form (d-DNNF) or one of its subcases, which is then used on-line to answer a large number of queries in polytime, such as clausal entailment, model counting, and others. The general idea is to push as much of the computational effort into the off-line compilation phase, which is amortized over all on-line polytime queries. In this paper, we present for the first time a novel and general technique to leverage d-DNNF compilation and querying to SMT level. Intuitively, before d-DNNF compilation, the input SMT formula is combined with a list of pre-computed ad-hoc theory lemmas, so that the queries at SMT level reduce to those at propositional level. This approach has several features: (i) it works for every theory, or theory combination thereof; (ii) it works for all forms of d-DNNF; (iii) it is easy to implement on top of any d-DNNF compiler and any theory-lemma enumerator, which are used as black boxes; (iv) most importantly, these compiled SMT d-DNNFs can be queried in polytime by means of a standard propositional d-DNNF reasoner. As proof of concept, we have implemented a tool on top of state-of-the-art d-DNNF packages and of the MathSAT SMT solver. Some preliminary empirical evaluation supports the feasibility and effectiveness of the approach.