We present various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses. Refutation completeness is established via the use of well-founded orderings on clauses for defining a Herbrand model for a consistent set of clauses. We also formulate an abstract notion of redundancy and show that the deletion of redundant c...

We present an algorithm for finding a smallest Resolution refutation of any 2CNF in polynomial time.

The ⁄-calculus possesses a strong notion of extensionality, called “the Ê-rule”, which has been the subject of many investigations. It is a longstanding open problem whether the equivalence obtained by closing the theory of Böhm trees under the Ê-rule is strictly included in Morris’s original observational theory, as conjectured by Sallé in the seventies. In a recent work, Breuvart et al. have ...