The reordering is: 4. If an animal is in the yard, then it is mine. 1. If an animal belongs to me, then I trust it. 5. If I trust an animal, then I admit it into my study. 3. If I admit an animal into my study, then it will beg when told to do so. 6. If an animal begs when told to do so, then that animal is a dog. 2. If an animal is a dog, then that animal gnaws bones. ∴ If an animal is in the yard, then that animal gnaws bones.
Work Step by Step
Universal transitivity: ∀x,P(x)→Q(x). ∀x,Q(x)→R(x). ∴∀x,P(x)→R(x).