The SMT-LIB benchmark collection is a large set of problems for SMT solvers. It has been continuously maintained and expanded since its creation in the early 2000s by the SMT-LIB initiative. It has been used since 2005 by the annual SMT solver competition to compare the performance of SMT solvers, and by researchers to study novel solving techniques. Effective use of the collection often requires access to benchmark metadata (e.g., date, source, satisfiability status, theory symbol count, and so on). Furthermore, this metadata and the past competition results contain a wealth of historical information about the development of SMT solving. In this paper, we report on our efforts to collect and curate all metadata from the SMT-LIB benchmarks together with the results of all past SMT-COMP competitions in a single SQLite database. We also present tools to explore this database and extract relevant insights. Since APIs for SQLite databases are available for all major programming languages, the database makes it easy to add features using SMT benchmark metadata to SMT development tools. To illustrate the structure of the collected data we perform multiple case studies. In particular, we present a comparison of SMT solvers that is independent of the changing hardware and benchmarks used by the competition. The database is released annually on Zenodo, and serves as an archive of the state of SMT-LIB and, by extension, of the state of the art in SMT.

Abstract First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference logic is a quite popular fragment of linear arithmetic which is less expressive than Presburger arithmetic. Difference logic on integers with uninterpreted unary predicates is known to be decidable, even in the presence of quantifiers. We here show that (quantified) difference logic on real numbers with a single uninterpreted unary predicate is undecidable, quite surprisingly. Moreover, we prove that difference logic on integers, together with order on reals, combined with uninterpreted unary predicates, remains decidable.

This paper describes a new format for representing Tarskian-style interpretations for formulae in typed first-order logic, using the TPTP TF0 language. It further describes a technique and an implemented tool for verifying models using this representation, and a tool for visualizing interpretations. The research contributes to the advancement of au- tomated reasoning technology for model finding, which has several applications, including verification.

SMT solvers generally tackle quantifiers by instantiating their variables with tuples of terms from the ground part of the formula. Recent enumerative approaches for quantifier instantiation consider tuples of terms in some heuristic order. This paper studies different strategies to order such tuples and their impact on performance. We decouple the ordering problem into two parts. First is the order of the sequence of terms to consider for each quantified variable, and second is the order of the instantiation tuples themselves. While the most and least preferred tuples, i.e. those with all variables assigned to the most or least preferred terms, are clear, the combinations in between allow flexibility in an implementation. We look at principled strategies of complete enumeration, where some strategies are more fair, meaning they treat all the variables the same but some strategies may be more adventurous, meaning that they may venture further down the preference list. We further describe new techniques for discarding irrelevant instantiations which are crucial for the performance of these strategies in practice. These strategies are implemented in the SMT solver cvc5, where they contribute to the diversification of the solver's configuration space, as shown by our experimental results.

Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic datatypes, which is currently supported by several mainstream SMT solvers. In this paper, we study this particular theory of datatypes and prove that it is strongly polite, showing also how it can be combined with other arbitrary disjoint theories using polite combination. Our results cover both inductive and finite datatypes, as well as their union. The combination method uses a new, simple, and natural notion of additivity, that enables deducing strong politeness from (weak) politeness.

The efficiency of satisfiability modulo theories (SMT) solvers is dependent on the capability of theory reasoners to provide small conflict sets, i.e. small unsatisfiable subsets from unsatisfiable sets of literals. Decision procedures for uninterpreted symbols (i.e. congruence closure algorithms) date back from the very early days of SMT. Nevertheless, to the best of our knowledge, the complexity of generating smallest conflict sets for sets of literals with uninterpreted symbols and equalities had not yet been determined, although the corresponding decision problem was believed to be NP-complete. We provide here an NP-completeness proof, using a simple reduction from SAT.