Extending SMT Solving with Non-Ground Clause Learning

21 pages•Published: October 23, 2026

Abstract

Quantifier instantiation is currently the main approach to non-ground SMT solving: solvers generate ground instances and solve the resulting ground SMT problems with CDCL(T)-style reasoning. When a conflict is found, conflict analysis learns only a ground clause, even though the conflict comes from instances of non-ground clauses. Yet non-ground reasoning can give exponentially shorter proofs than purely ground reasoning. We propose a calculus that consists of ground instantiations, CDCL(T)-style rules, and non-ground conflict analysis. The solver reasons on ground instances, but the resolution steps of conflict analysis are performed on their original non-ground clauses. This produces learned clauses that are typically more general than the ground conflict. With a suitable strategy, the learned clauses are even non-redundant. We also show how chronological backtracking can be included in SMT solving. Our calculus gives a common setting for CDCL(T)-style SMT solving, a range of instantiation-based procedures, and non-ground clause learning, and we prove that it simulates CDCL, SCL(FOL), SCL(T), and even Resolution.

Keyphrases: cdcl, scl, smt

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 309-329.

Links:	https://easychair.org/publications/paper/vXQW
	https://doi.org/10.29007/x89r

BibTeX entry

@inproceedings{LPAR-26:Extending_SMT_Solving_with,
  author    = {Yasmine Briefs and Christoph Weidenbach},
  title     = {Extending SMT Solving with Non-Ground Clause Learning},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/vXQW},
  doi       = {10.29007/x89r},
  pages     = {309-329},
  year      = {2026}}

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