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
Testing for the ground (co-)reducibility property in term-rewriting systems
CAAP '90 Selected papers of the conference on Fifteenth colloquium on trees in algebra and programming
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
Extending Decision Procedures with Induction Schemes
CADE-17 Proceedings of the 17th International Conference on 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
Ground Reducibility is EXPTIME-complete
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Automata-driven automated induction
LICS '97 Proceedings of the 12th 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
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Deciding the inductive validity of ∀∃* queries
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Inductive decidability using implicit induction
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Tree automata with equality constraints modulo equational theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Predicate completion for non-Horn clause sets
CADE'11 Proceedings of the 23rd international conference on Automated deduction
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Superposition modulo non-linear arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Completeness and decidability results for first-order clauses with indices
CADE'13 Proceedings of the 24th international conference on Automated Deduction
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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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 minimal term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the minimal 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 refutationally complete in the limit for a first-order fixed domain semantics. For saturated Horn theories and classes of positive formulas, we can even employ the calculus to prove properties of the minimal model itself, going beyond the scope of known superposition-based approaches.