If the statements above are true, which of the following statements must also be true about primary-school rooms in the city? A. Some third-floor rooms in primary schools do not have fireproof doors. B. No second-floor classrooms in primary schools have fireproof doors. C. In primary schools, rooms above the second floor that are not classrooms do not have fireproof doors. D. Any fourth-floor classrooms in primary schools have fireproof doors. E. Primary schools with classrooms on the first floor only do not have any fireproof doors.