arXiv:2610.31481v1 Announce Type: new Abstract: We studied 153 students in an undergraduate proof-based mathematics course with staggered-access to an AI support system. Students were randomly assigned to receive an AI chatbot and a homework-feedback interface earlier or later in the course. During the period when only the early-access group had access, their homework scores were 2.56 points higher, but exam performance did not differ significantly between groups, suggesting that improved AI-supported homework performance did not translate into detectable gains on a subsequent exam. After all students received access, every additional 100 messages sent to the AI chatbot was associated with a 3.02-point lower score on the subsequent exam. A mediation analysis showed a significant indirect association linking lower baseline self-efficacy to greater chatbot use and, in turn, lower exam scores: a one-point decrease in self-efficacy corresponded to 0.62 fewer exam points through chatbot use. These findings raise concerns that students may use the chatbot to offload their cognitive reasoning. Use of the homework-feedback interface, which required students to submit their proof attempts before receiving feedback, was not negatively associated with exam performance. We recommend against using a chatbot for AI tutoring and suggest exploring a tutor embedded in the course activities.