You are locked in a room that has three doors. Two doors have bombs that trigger when the doorknob turns. One door leads out of the room. One man stands at each door. One of the men lies about what he says, and two of the men tell the truth. Man 1 stands at door 1, man 2 stands at door 2, and man 3 stands at door 3.
Here is what each man says:
Man 1: Man 2 is a liar
Man 2: Door 2 leads out of the room
Man 3: Door 1 does not lead out of the room
Which door lead out of the room?