Is there any second-order logic finite satisfiability checker? I know that there are implementations of first-order (finite) satisfiability checking that, given a finite set of axioms, searches for a finite model that satisfies them all.
I would like to ask whether there is a second-order logic (finite) satisfiability checker. Although, we can always write a (naive) algorithm that enumerates all possible finite interpretations and check whether they are a model or not, I would like to know if there is some implementation/research doing something more intelligent (instead of a blind search).
There are Nitpick and Nunchaku that are model finders for higher-order logic.
Nunchaku is more recent and can build models for axioms containing higher-order quantification. But, as the problem is generally undecidable, it may not find a (finite) model even if one exists.