Vampire theorem prover
Vampire is an automatic theorem prover for first-order classical logic developed in the Computer Science Department of the University of Manchester. Its kernel implements the calculi of ordered binary resolution and superposition for handling equality. The splitting rule and negative equality splitting are simulated by the introduction of new predicate definitions and dynamic folding of such definitions. A number of standard redundancy criteria and simplification techniques are used for pruning the search space: subsumption, tautology deletion (optionally modulo commutativity), subsumption resolution, rewriting by ordered unit equalities, basicness restrictions and irreducibility of substitution terms.
The reduction orderings used are the standard Knuth-Bendix ordering and a special non-recursive version of the Knuth-Bendix ordering. A number of efficient indexing techniques is used to implement all major operations on sets of terms and clauses. Run-time algorithm specialisation is used to accelerate some costly operations, e.g., checks of ordering constraints. 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.
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