An example of a very non-movable effective divisor

We give a negative answer to a question of Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa, and Testa on effective divisors of positive self-intersection on smooth projective surfaces. The main result of this paper is obtained by generative AI, particularly Chatgpt 5.5 pro and the Rethlas system.