In this article we describe VAMPIRE: a high‐performance theorem prover for first‐order
logic. As our description is mostly targeted to the developers of such systems and specialists …

Implementations of theorem provers that use generative procedures like resolution
(Robinson, 1965b; Chang and Lee, 1973) or Knuth-Bendix completion (Knuth and Bendix …

We present a concept for an automated theorem prover that employs a search control based
on ideas from several areas of artificial intelligence (AI). The combination of case-based …

A crucial operation of saturation theorem provers is deletion of subsumed formulas.
Designers of proof calculi, however, usually discuss this only informally, and the rare formal …

In this abstract we describe version 1.1 of the theorem prover Vampire. We give a general
description and comment on Vampire's original features and differences with the previously …

Deciding the satisfiability of a Quantified Boolean Formula (QBF) is an important research
issue in Artificial Intelligence. Many reasoning tasks involving planning [1], abduction …

We designed a superposition calculus for a clausal fragment of extensional polymorphic
higher-order logic that includes anonymous functions but excludes Booleans. The inference …

Decades of work have gone into developing efficient proof calculi, data structures,
algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag …

We introduce refutationally complete superposition calculi for intentional and extensional
clausal λ-free higher-order logic, two formalisms that allow partial application and applied …

For most applications of first-order theorem provers a proof should be found within a fixed
time limit. When the time limit is set, systems can perform much better by using algorithms …