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The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure-only involving clauses over the alphabet of either one, but not both, of the theorieswhen refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signaturesdoi:10.1016/j.ic.2005.10.002 fatcat:nbdf4na2ibbppabvatomqr7aja