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(Adapted from Barwise+Etchemendy:1993 .) Given the following, can you prove that the unicorn is mythical? How about magical? Horned?

Note: If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned.