Just my own opinion based on my experiences with predators. A fox would go through a 10x6 door easily. They will as a rule just grab a bird and run, maybe come back once or twice that night but not usually. Generally will show up another night to repeat the offense. A racoon, or especially a pair or family will happily kill everything they can get ahold of but eating a dozen chickens is impossible for me to believe. They would have eaten parts of them and left a mess, maybe hauling off one or two. I also think they would have gone through the chicken door, though a big male might not fit. Coyotes maybe. I don't know how common they are near you nor how much hunting pressure they get. Around here, they might grab one or two but they wouldn't hang around long enough to kill the whole flock, and very few folks around here will bother them. I vote dogs! They are unafraid of people, and they will haul them quite a ways. They also will get so excited with the killing that they will clean the whole flock out. I've had them just keep coming back to pick up the bodies and carry them away. Whoever owns them knows they did it because the dogs would carry at least one home to chew on. However, they will never admit that they know.
Jim
