A theft occurred in a treasury, and the public security organ investigated and determined that this is a typical case of internal theft, and it can be concluded that at least one of the treasury managers A, B, C, and D is the perpetrator. The investigators questioned four people, and their answers were as follows: a: if B is not a thief, I am not a thief. B: I am not a thief, C is a thief C: An or B is a thief. D: B or C is a thief. It turned out that only one of the four of them told the truth.
According to the above statement, which of the following options must be false?
B is not a thief