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A program is described which can provide a computer with quick logical facility for syllogisms and moderately more complicated sentences. The program realizes a method for proving that a sentence of quantification theory is logically true. The program, furthermore, provides a decision procedure over a subclass of the sentences of quantification theory. The subclass of sentences for which the program provides a decision procedure includes all syllogisms. Full justification of the method is given. A program for the IBM 704 Data Processing Machine is outlined which realizes the method. Production runs of the program indicate that for a class of moderately complicated sentences the program can produce proofs in intervals ranging up to two minutes.