Theorem Proving with Ordering and Equality Constrained Clauses

An Implementation Kernel for Theorem Proving with Equality Clauses

keywords: Automated theorem proving, rst-order clauses with equality. Abstract We provide a standard abstract architecture around which high-performance theorem provers for full clausal logic with equality can be built. A WAM-like heap structure for storing terms (as DAG's, with structure sharing) and several substitution trees Gra95b] are central in the architecture. These two data structures ...

Theorem Proving with Constrained

Deduction methods for rst-order constrained clauses with equality are described within an abstract framework: constraint strategies, consisting of an inference system, a constraint inheritance strategy and redundancy criteria for clauses and inferences. We give simple conditions for such a constraint strategy to be complete (refutationally and in the sense of Knuth-Bendix-like completion). This...

Paramodulation and Theorem-proving in First-Order Theories with Equality

Proving correctness of imperative programs by linearizing constrained Horn clauses

We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form {φ} prog {ψ}, where the assertions φ and ψ are predicates defined by a set Spec of possibly recursive Horn clauses with linear arithmetic (LA) constraints in their premis...

Inductive Theorem Proving by Consistency for First-Order Clauses

We show how the method of proof by consistency can be extended to proving properties of the perfect model of a set of rst-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 suucient-completeness of function deenitions in parallel with proving an in-ductive theorem we need not disti...