MainProving theorems showcases the mastery of logical reasoning and the ability to search through an infinitely large space of actions towards a target, signifying a remarkable problem-solving skill. Since the 1950s (refs. 6,7), the pursuit of better theorem-proving capabilities has been a constant focus of artificial intelligence (AI) research8. Mathematical olympiads are the most reputed theorem-proving competitions in the world, with a similarly long history dating back to 1959, playing an in...