Inductive Theorem Proving by Consistency for First-Order Clauses
Harald Ganzinger, Jürgen Stuber · Teubner-Texte zur Informatik · 1992
We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of first-order clauses with equality. Technically proofs by consistency will be similar to proofs by case analysis over the term structure. As our method also allows to prove sufficient-completeness of function definitions in parallel with proving an inductive theorem we need not distinguish between constructors and defined functions. Our method is linear and refutationally complete with respect to the perfect model, it supports lemmas in a natural way, and it provides for powerful simplification and elimination techniques.