An Interval Graph

Six professors had been to the library on the day when the rare tractate was stolen. Each had entered once, stayed for some time and then left. If two were in the library at the same time, then at least one of them saw the other. Detectives questioned the professors and gathered the following testimony:


A said he saw B and E
B reported he saw A and I
C claimed he saw D and I
D said he saw A and I
E testified to seeing B and C
I said that she saw C and E

One of the professors lied. Who was it?