Pascal Fontaine

Geoff Sutcliffe, Alexander Steen, Pascal Fontaine et al.

This paper describes the TPTP format for representing interpretations. It provides a background survey that helped ensure that the representation format is adequate for different types of interpretations: Tarskian, Herbrand, and Kripke interpretations. The needs of applications that use models are considered. The syntax and semantics of the format are expounded in detail, with multiple examples. Verification of models is discussed. Some tools that support processing the format are noted. The properties of interpretations represented in the format are discussed.

Mikoláš Janota, Haniel Barbosa, Pascal Fontaine et al.

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.