An extension of semantic resolution is proposed. It is also an extension of the set of support as it can be considered as a particular case of semantic resolution. It is proved sound and refutationally complete. The extension is based on our former method for model building. The approach uses constrained clauses (or c-clauses), i.e. couples [clause : constraint]. Two important new features are introduced with respect to semantic resolution. Firstly, the method builds its own (finite or

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... models to guide the search or to stop it if the initial set of clauses is satisfiable. Secondly, instead of evaluating a clause in an interpretation it imposes conditions (coded in its rules) to force a c-clause not to be evaluated to true in the interpretation it builds. The extension is limited in this paper to binary resolution but generalizing it to nary-resolution should be straightforward. The prover implementing our method is an extension of OT-TER and compares advantageously with it (if binary resolution is used in OTTER), both in the search space and in the proof lenght of a relevant non trivial example. Last but not least, model building is incremental. This feature is specially useful when dealing with large set of clauses.