Preface to First order theorem proving

First-order theorem proving modulo equations

We present refutationally complete calculi for first-order clauses with equality. General paramodulation calculi cannot efficiently deal with equations such as associativity and commutativity axioms. Therefore we will separate a set of equations (called E-equations) from a specification and give them a special treatment, avoiding paramodulations with E-equations but using E-unification for the ...

First-Order Theorem Proving and Vampire

In this paper we give a short introduction in first-order theorem proving and the use of the theorem prover VAMPIRE. We discuss the superposition calculus and explain the key concepts of saturation and redundancy elimination, present saturation algorithms and preprocessing, and demonstrate how these concepts are implemented in VAMPIRE. Further, we also cover more recent topics and features of V...

An Improved Propositional Approach to First-Order Theorem Proving

Ordered semantic hyper-linking (OSHL) is a theorem prover for first-order logic that generates models and uses them to instantiate first-order clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHL-U extends OSHL with rules for unit clauses and with heuristics. The unit rules in OHSL-U are designed to minimize the use of blind instantiation to generate groun...

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

Comparing Unification Algorithms in First-Order Theorem Proving

Unification is one of the key procedures in first-order theorem provers. Most first-order theorem provers use the Robinson unification algorithm. Although its complexity is in the worst case exponential, the algorithm is easy to implement and examples where it may show exponential behaviour are believed to be atypical. More sophisticated algorithms, such as the Martelli and Montanari algorithm,...