Constraint Manipulation in SGGS

SGGS (Semantically-Guided Goal-Sensitive theorem proving) is a clausal theorem-proving method, with a seemingly rare combination of properties: it is first order, DPLL-style model based, semantically guided, goal sensitive, and proof confluent. SGGS works with constrained clauses, and uses a sequence of constrained clauses to represent a tentative model of the given set of clauses. A basic building block in SGGS inferences is splitting, which partitions a clause into clauses that have the same set of ground instances. Splitting introduces constraints and their manipulation, which is the subject of this paper. Specifically, splitting a clause with respect to another clause requires to compute their difference, which captures the ground instances of one that are not ground instances of the other. We give a set of inference rules to compute clause difference, and reduce SGGS constraints to standard form, and we prove that it is guaranteed to terminate, provided the standardization rules are applied within the clause difference computation.