Session 1. Invited Talk: Colin Stirling -- Games, Automata and Matching -- Session 2. Higher-Order Logic -- Formalization of Continuous Probability Distributions -- Compilation as Rewriting in Higher Order Logic -- Barendregt’s Variable Convention in Rule Inductions -- Automating Elementary Number-Theoretic Proofs Using Gröbner Bases -- Session 3. Description Logic -- Optimized Reasoning in Description Logics Using Hypertableaux -- Conservative Extensions in the Lightweight Description Logic -- An Incremental Technique for Automata-Based Decision Procedures -- Session 4. Intuitionistic Logic -- Bidirectional Decision Procedures for the Intuitionistic Propositional Modal Logic IS4 -- A Labelled System for IPL with Variable Splitting -- Session 5. Invited Talk: Ashish Tiwari -- Logical Interpretation: Static Program Analysis Using Theorem Proving -- Session 6. Satisfiability Modulo Theories -- Solving Quantified Verification Conditions Using Satisfiability Modulo Theories -- Efficient E-Matching for SMT Solvers -- -Decision by Decomposition -- Towards Efficient Satisfiability Checking for Boolean Algebra with Presburger Arithmetic -- Session 7. Induction, Rewriting, and Polymorphism -- Improvements in Formula Generalization -- On the Normalization and Unique Normalization Properties of Term Rewrite Systems -- Handling Polymorphism in Automated Deduction -- Session 8. First-Order Logic -- Automated Reasoning in Kleene Algebra -- SRASS - A Semantic Relevance Axiom Selection System -- Labelled Clauses -- Automatic Decidability and Combinability Revisited -- Session 9. Invited Talk: K. Rustan M. Leino -- Designing Verification Conditions for Software -- Session 10. Model Checking and Verification -- Encodings of Bounded LTL Model Checking in Effectively Propositional Logic -- Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems -- The KeY system 1.0 (Deduction Component) -- KeY-C: A Tool for Verification of C Programs -- The Bedwyr System for Model Checking over Syntactic Expressions -- System for Automated Deduction (SAD): A Tool for Proof Verification -- Session 11. Invited Talk: Peter Baumgartner -- Logical Engineering with Instance-Based Methods -- Session 12. Termination -- Predictive Labeling with Dependency Pairs Using SAT -- Dependency Pairs for Rewriting with Non-free Constructors -- Proving Termination by Bounded Increase -- Certified Size-Change Termination -- Session 13. Tableaux and First-Order Systems -- Encoding First Order Proofs in SAT -- Hyper Tableaux with Equality -- System Description: E- KRHyper -- System Description: Spass Version 3.0.

This book constitutes the refereed proceedings of the 21st International Conference on Automated Deduction, CADE-21, held in Bremen, Germany, in July 2007. The 28 revised full papers and 6 system descriptions presented were carefully reviewed and selected from 64 submissions. All current aspects of automated deduction are addressed, ranging from theoretical and methodological issues to presentation and evaluation of theorem provers and logical reasoning systems. The papers are organized in topical sections on higher-order logic, description logic, intuitionistic logic, satisfiability modulo theories, induction, rewriting, and polymorphism, first-order logic, model checking and verification, termination, as well as tableaux and first-order systems.