Labelled Splitting

Saturation-based theorem provers are typically based on a calculus consisting of inference and reduction rules that operate on sets of clauses. While inference rules produce new clauses, reduction rules allow the removal or simplification of redundant clauses and are an essential ingredient for efficient implementations. The power of reduction rules can be further amplified by the use of the splitting rule, which is based on explicit case analysis on variable- disjoint components of a clause. In this thesis, I give a formalization of splitting and backtracking for first-order logic using a labelling scheme that annotates clauses and clause sets with additional information, and I present soundness and completeness results for the corresponding calculus. The backtracking process as formalized here generalizes optimizations that are currently being used, and I present the results of integrating the improved backtracking into SPASS