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This paper shows how bounded model checking can be applied to parameter synthesis for parametric timed automata with continuous time. While it is known that the general problem is undecidable even for reachability, we show how to synthesize a part of the set of all the parameter valuations under which the given property holds in a model. The results form a full theory which can be easily applied to parametric verification of a wide range of temporal formulae --- we present such an implementation for the existential part of CTL−X.