Loop-Detection in Hyper-Tableaux by Powerful Model Generation

Automated reasoning systems often su er from redundancy: similar parts of derivations are repeated again and again. This leads us to the problem of loopdetection, which clearly is undecidable in general. Nevertheless, we tackle this problem by extending the hyper-tableau calculus as proposed in [Baumgartner, 1998] by generalized terms with exponents, that can be computed by means of computer algebra systems. Although the proposed loop-detection rule is incomplete, the overall calculus remains complete, because loop-detection is only used as an additional, optional mechanism. In summary, this work combines approaches from tableau-based theorem proving, model generation, and integrates computer algebra systems in the theorem proving process.