Laelaps
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In Greek mythology, Laelaps was a legendary dog who never failed to catch what he was hunting. He was a gift from Zeus to Europa.
The hound was passed down to King Minos. Minos fell ill and called Prokris of Athens to his aid. When she cured him he gave her Laelaps and a javelin that never missed its target. Prokris's husband decided to use the hound to hunt the Teumessian fox, a fox that could never be caught. This was a paradox, a dog who always caught his prey and a fox that could never be caught. The chase went on for quite a while until Zeus turned both to stone, perplexed by their contradictary fates.