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Given a web service W, a stub is a simple service S intended to impersonate W and simulate some of its input-output patterns. When W's behavior is represented by a logic formula φ, S can use a satisfiability solver to drive the simulation and generate valid messages compliant with φ. A satisfiability solver for a variant of first-order temporal logic, called LTL-FO+, is described. Using a chain of existing, off-the-shelf tools, a stub can be generated from a set of LTL-FO+ formulæ expressing a wide range of constraints, including message sequences, parameter values, and interdependencies between both. This, in turn, produces a faithful simulation of the original service that can be used for development and testing.