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We combine constrained literals for model representation with key conceptsfrom first-order superposition and propositional conflict-driven clauselearning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL)deciding the Bernays-Sch\"onfinkel fragment. Our calculus uses first-orderliterals constrained by disequations between tuples of terms for compact modelrepresentation. From superposition, NRCL inherits the abstract redundancycriterion and the monotone model operator. CDCL adds the dynamic,conflict-driven search for an atom ordering inducing a model. As a result, inNRCL a false clause can be found effectively modulo the current modelcandidate. It guides the derivation of a first-order ordered resolvent that isnever redundant. Similar to 1UIP-learning in CDCL, the learned resolventinduces backtracking and, by blocking the previous conflict state viapropagation, it enforces progress towards finding a model or a refutation. Thenon-redundancy result also implies that only finitely many clauses can begenerated by NRCL on the Bernays-Sch\"onfinkel fragment, which serves as anargument for termination.

NRCL - A Model Building Approach to the Bernays-Sch\"onfinkel Fragment (Full Paper)