Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Term rewriting and all that
System Description: Spass Version 3.0
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Separation logic + superposition calculus = heap theorem prover
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Model Evolution with equality - Revised and implemented
Journal of Symbolic Computation
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We present a new calculus for first-order theorem proving with equality, ${\mathcal ME}$+Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of both--rather complementary--calculi in a single framework. For instance, Model Evolution, as a lifted version of the propositional DPLL procedure, contributes a non-ground splitting rule that effectively permits to split a clause into non variable disjoint subclauses. In the paper we present the calculus in detail. Our main result is its completeness under semantically justified redundancy criteria and simplification rules.