VAMPIRE
Vampire 8.0, [RV02,Vor05] is an automatic theorem prover for first-order classical logic. It consists of a shell and a kernel. The 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, and a lightweight basicness. The CASC version uses the Knuth-Bendix ordering. The lexicographic path ordering has been implemented recently but will not be used for this CASC. 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 some costly operations, e.g., checks of ordering constraints. Although the kernel of the system works only with clausal normal forms, the shell 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 proved, the system produces a verifiable proof, which validates both the clausification phase and the refutation of the CNF.
Keywords for this software
References in zbMATH (referenced in 147 articles , 1 standard article )
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- Bonacina, Maria Paola; Plaisted, David A.: Semantically-guided goal-sensitive reasoning: model representation (2016)
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- Benzmüller, Christoph; Sultana, Nik; Paulson, Lawrence C.; Theiß, Frank: The higher-order prover Leo-II (2015)
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- Kaliszyk, Cezary; Schulz, Stephan; Urban, Josef; Vyskočil, Jiří: System description: E.T. 0.1 (2015)
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- Kotelnikov, Evgenii; Kovács, Laura; Voronkov, Andrei: A first class Boolean sort in first-order theorem proving and TPTP (2015)
- Kühlwein, Daniel; Urban, Josef: MaLeS: a framework for automatic tuning of automated theorem provers (2015)
- Reger, Giles; Suda, Martin; Voronkov, Andrei: Playing with AVATAR (2015)
- Reger, Giles; Tishkovsky, Dmitry; Voronkov, Andrei: Cooperating proof attempts (2015)
- Stojanović {\Dj}urđević, Sana; Narboux, Julien; Janičić, Predrag: Automated generation of machine verifiable and readable proofs: a case study of Tarski’s geometry (2015)
- Alama, Jesse; Heskes, Tom; Kühlwein, Daniel; Tsivtsivadze, Evgeni; Urban, Josef: Premise selection for mathematics by corpus analysis and kernel methods (2014)
- Kaliszyk, Cezary; Urban, Josef: Learning-assisted automated reasoning with $\mathsfFlyspeck$ (2014)
- Blanchette, Jasmin Christian; Böhme, Sascha; Paulson, Lawrence C.: Extending Sledgehammer with SMT solvers (2013)