From a fallibilist perspective, mathematics gradually develops with problems, conjectures, proofs, and refutations. To attain such authentic mathematical learning, it is important to intentionally treat refutation in mathematics classrooms, such as facing or proposing counterexamples and coping with them. In particular, analysing students' behaviour in response to counterexamples can lead to a design of teaching materials and instruction based on students' existing knowledge and strategies. In this paper, we construct a framework for capturing students' actions of inventing a new statement that holds for counterexamples to an original statement. We then illustrate a specific aspect of this framework with an episode that took place in an eighth grade classroom, and discuss two approaches to deductively generating a new statement. [For the complete proceedings, see ED597799.]