Refute employs a SAT solver to find a finite model of the negated conjecture. The translation from HOL to propositional logic is parameterized by the cardinalities of the atomic types occurring in the conjecture. Refute enumerates the possible cardinalities for each atomic type. If a formula has a finite counterexample, the tool eventually finds it, unless it runs out of resources.
Refute, like most of Isabelle/HOL, is written in Standard ML. Unlike Isabelle itself, which adheres to the LCF small-kernel discipline, Refute does not certify its results and must be trusted.
Refute is available as part of Isabelle/HOL for all major platforms under a BSD-style license from
http://www.cl.cam.ac.uk/research/hvg/Isabelle
We expect Refute to beat Satallax but also to be beaten by Nitpick.