Abstract
This chapter describes the soundness of the IRP-calculus. It presents a proof of soundness theorem for the ERP-calculus. This is shown in the same way as the soundness theorem for the one-sorted RP-calculus. The chapter presents a proof with the soundness lemma that each EE-model of E-clause set satisfies each clause deduced from this set by E-factorization, E-resolution, or E-paramodulation. The soundness proof is obtained from the soundness lemma as an immediate consequence. For the proof of the soundness lemma presented in the chapter, a technical lemma, which exploits a trivial but essential circumstance regarding soundness, is used. The crucial point in the proof is the existence of the ti. This is guaranteed only because it is demanded that for each sort symbol s, which is minimal, there must exist a constant symbol. The approach to the soundness theorem is the same as for the RP-calculus.
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