A closed λ-term M is easy if, for any
other closed term N, the lambda theory generated by
M = N is consistent. Recently, it has been introduced
a general technique to prove the easiness of λ-terms through the
semantical notion of simple easiness. Simple easiness implies easiness and allows to prove
consistency results via construction of suitable filter models of
λ-calculus living in the category of complete partial orderings: given
a simple easy term M and an arbitrary closed term N, it
is possible to build (in a canonical way) a non-trivial filter model which equates the
interpretation of M and N. The question whether easiness
implies simple easiness constitutes Problem 19 in the TLCA list of open problems. In this
paper we negatively answer the question providing a non-empty co-r.e. (complement of a
recursively enumerable) set of easy, but not simple easy, λ-terms.