Final answer:
Competition is the conflict resolution style that is ideal for the given conditions.
Step-by-step explanation:
The conflict resolution style that is ideal for the given conditions is Competition.
Competition is a conflict resolution style where parties pursue their own goals and interests, often disregarding the needs and goals of others. It involves a win-lose mentality, where one party seeks to dominate and achieve their objectives at the expense of others.
In the given scenario, where mutually exclusive goals are involved, equally powerful parties are present, consensus cannot be reached, and integrating or dominating styles have not been successful, competition is the most appropriate style. It allows for temporary solutions to be developed, although they may not be ideal or sustainable in the long run.