Equational problems anddisunification
Journal of Symbolic Computation
Automating inductionless induction using test sets
Journal of Symbolic Computation
A method for simultaneous search for refutations and models by equational constraint solving
Journal of Symbolic Computation
Automated theorem proving by test set induction
Journal of Symbolic Computation
Induction = I-axiomatization + first-order consistency
Information and Computation - Special issue on RTA-98
Unification in Extension of Shallow Equational Theories
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Superposition with Simplification as a Desision Procedure for the Monadic Class with Equality
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Towards an Automatic Analysis of Security Protocols in First-Order Logic
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Inductive Theorem Proving by Consistency for First-Order Clauses
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Combining superposition, sorts and splitting
Handbook of automated reasoning
Basic Paramodulation and Decidable Theories
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Model building with ordered resolution: extracting models from saturated clause sets
Journal of Symbolic Computation - Special issue: First order theorem proving
Tree automata with equality constraints modulo equational theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Decidability Results for Saturation-Based Model Building
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a perfect term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the perfect model's term-generated domain, as new Skolem functions are introduced. For many applications, this is not desired. Therefore, we propose the first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain. This calculus is sound and complete for a first-order fixed domain semantics. For some classes of formulas and theories, we can even employ the calculus to prove properties of the perfect model itself, going beyond the scope of known superposition based approaches.