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Several formal systems proving the valid forms of Aristotelian syllogism has been built. However, the previous research has not answered the two questions: (1) how to infer the primary forms of syllogism by which the other valid forms of syllogism can be deducted; and (2) whether formal system of Aristotelian syllogism can be run automatically; if yes, by which language and grammar it can be done. The paper solves the two questions. For the question (1), the paper sets up a rule system to product all the valid forms of syllogism including that primary ones for deducting the other valid forms of syllogism. For the question (2), the paper proposes the sufficient conditions for a formal system being an automata, to which the formal system FA created by the paper is conformable. So the paper asserts FA can prove all the valid forms of Aristotelian syllogism automatically in computers nowadays.