I believe nature dictates that predators don't eat other predators, they only kill them, unless they are starving.
There are plenty of natural predators that eat other predators if opportunity arises... Even your common K-9 will eat other predators (even their own kind) if it's meal time and that is what is available...
One also has to be careful of what they define as predator and prey... A chicken might very well be prey to many things, but it's also a predator to smaller prey like mice, and insects...
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