Use conjective symbols and the nine valid inference rules MP, MT, SIMP, CONJ, ABS, ADD, DS, HS

Either animals are mere mechanisms (M) or they feel pain (P). If either animals feel pain or they have souls (S), then they have a right not to be subjected to needless pain (R) and humans have a duty not to inflict needless pain on them (D). It is not the case that animals are mere mechanisms. Thereofore, animals have a right not to be subjected to needless pain.