Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Equational problems anddisunification
Journal of Symbolic Computation
Induction = I-axiomatization + first-order consistency
Information and Computation - Special issue on RTA-98
Inductive Theorem Proving by Consistency for First-Order Clauses
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Resolution decision procedures
Handbook of automated reasoning
Combining superposition, sorts and splitting
Handbook of automated reasoning
Superposition for Fixed Domains
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Disunification for ultimately periodic interpretations
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and 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
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Saturation-based calculi such as superposition can be successfully instantiated to decision procedures for many decidable fragments of first-order logic. In case of termination without generating an empty clause, a saturated clause set implicitly represents a minimal model for all clauses, based on the underlying term ordering of the superposition calculus. In general, it is not decidable whether a ground atom, a clause or even a formula holds in this minimal model of a satisfiable saturated clause set. We extend our superposition calculus for fixed domains with syntactic disequality constraints in a non-equational setting. Based on this calculus, we present several new decidability results for validity in the minimal model of a satisfiable finitely saturated clause set that in particular extend the decidability results known for ARM (Atomic Representations of term Models) and DIG (Disjunctions of Implicit Generalizations) model representations.