Structuring of Computer-Generated Proofs by Cut Introduction

As modern Automated Deduction systems rely heavily on the use of a machine-oriented representation of a given problem, together with sophisticated redundancy-avoiding techniques, a major task in convincing human users of the correctness of automatically generated proofs is the intelligible representation of these proofs. In this paper, we propose the use of the cut-rule in the human-oriented presentation of computer-generated proofs. The intelligent application of cuts enables the integration of essential lemmata and therefore shortens and structures proof presentation. We show that many translation techniques in Automated Deduction, such as antiprenexing and some forms of normal form translations, can be described as cuts and are indeed part of the deductive solution of a problem. Furthermore, we demonstrate the connection between symmetric simplification, quantorial extension principles and the application of the cut-rule.

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