Researches in Mathematics Education about proof by contradiction revealed some difficulties of the students but also that this kind of argumentation comes spontaneously in certain situations. In this paper we shall show some processes that might lead the student to produce a proof by contradiction. In particular, we shall point out a deep link between a certain kind of examples (which we call non-examples) generated during the stage of conjecture production, and the structure of the argumentation with which the conjecture is justified. (Contains 2 figures.) [For complete proceedings, see ED500859.]