Vampire is an automatic theorem prover for first-order classical logic developed in the Computer Science Department of the University of Manchester by Prof. Andrei Voronkov together with Kryštof Hoder and previously with Dr. Alexandre Riazanov. So far it has won the "world cup for theorem provers" (the CADE ATP System Competition) in the most prestigious CNF (MIX) division eleven times (1999, 2001–2010).
Its kernel implements the calculi of ordered binary resolution and superposition for handling equality. The splitting rule and negative equality splitting can be simulated by the introduction of new predicate definitions and dynamic folding of such definitions. A DPLL-style splitting is also supported. A number of standard redundancy criteria and simplification techniques are used for pruning the search space:tautology deletion, subsumption resolution, rewriting by ordered unit equalities, basicness restrictions and irreducibility of substitution terms. The reduction ordering used is the standard Knuth-Bendix ordering.
A number of efficient indexing techniques are used to implement all major operations on sets of terms and clauses. Run-time algorithm specialisation is used to accelerate forward matching.
Although the kernel of the system works only with clausal normal forms, the preprocessor component accepts a problem in the full first-order logic syntax, clausifies it and performs a number of useful transformations before passing the result to the kernel. When a theorem is proven, the system produces a verifiable proof, which validates both the clausification phase and the refutation of the CNF.
Along with proving theorems, Vampire has other related functionalities such as generating interpolants.
Executables can be obtained from the system web vprover.org. A somewhat outdated version is available under LGPL here, as part of Sigma KEE.