The presented approach aims at identifying false conjectures about free data types. Given a specification and a conjecture, the method performs a search for a model of an according counter specification. The model search is tailor-made for the semantical setting of free data types, where the fixed domain allows to describe models just in terms of interpretations. For sake of interpretation construction, a theory specific calculus is provided. The concrete rules are ‘executed’ by a procedure known as model generation. As most free data types have infinite domains, the ability of automatically solving the non-consequence problem is necessarily limited. That problem is addressed by limiting the instantiation of the axioms. This approximation leads to a restricted notion of model correctness, which is discussed. At the same time, it enables model completeness for free data types, unlike approaches based on limiting the domain size.