'Descente Infinie' Induction-Based Saturation Procedures

In [11], we have shown that implicit induction and saturation proof techniques share the same logic, witnessed by an inference system implementing the Fermat's 'Descente Infinie' induction principle. As a case study, a simple paramodulation-based inference system has been proved as an instance of it. In this paper, we detail the instantiation method to treat general saturation-based systems and apply it to analyse a non-trivial resolution-based system. We also propose a methodology to build variants of existing systems, which preserve crucial properties like soundness and refutational completeness.