What fox was destined never to be caught, creating a paradox with Laelaps?

The fox destined never to be caught, creating a paradox with Laelaps, was the Teumessian fox.

The Teumessian fox was a gigantic supernatural animal associated with Teumessos in Boeotia. In the myth, the beast was sent to prey on the children of Thebes, possibly as divine punishment for a national crime. Creon, ruler of Thebes, charged Amphitryon with the impossible task of destroying it.

Amphitryon’s proposed solution was Laelaps, the magical hound that was fated to catch everything it pursued. The plan exposed a contradiction in the animals’ destinies: the dog could not fail to catch its quarry, while the fox could not be caught. Greek myth leaves no natural winner to this contest.

Zeus ultimately transformed both creatures into stone. Later astronomical tradition associated Laelaps with Canis Major and the fox with Canis Minor, although the ancient literary traditions and the animals’ exact constellation identities are not completely uniform. The fox is also called the Teumessian vixen or Cadmean vixen.