A closed λ-term M is easy if, for anyother closed term N, the lambda theory generated byM = N is consistent. Recently, it has been introduceda general technique to prove the easiness of λ-terms through thesemantical notion of simple easiness. Simple easiness implies easiness and allows to proveconsistency results via construction of suitable filter models ofλ-calculus living in the category of complete partial orderings: givena simple easy term M and an arbitrary closed term N, itis possible to build (in a canonical way) a non-trivial filter model which equates theinterpretation of M and N. The question whether easinessimplies simple easiness constitutes Problem 19 in the TLCA list of open problems. In thispaper we negatively answer the question providing a non-empty co-r.e. (complement of arecursively enumerable) set of easy, but not simple easy, λ-terms.
