Because of some "inherent" limitations, such as specifications of initial state or structures of domain actions, some goals can't be arrived together, which we call a planning task with goal conflicts. This planning task can hardly be resolved until goal conflicts are eliminated. And in such cases, people often need to know which goal conflicts a planning task contains and choose a new set of goals. In this paper, we present a technique for automatically detecting conflicts among goals by construction of a causal-link graph that captures the interactions between actions relevant to a given goal. By statically analyzing "competitive" preconditions of actions in a causal-link graph, we may inference which goals can't be reached together, without trying all best to resolve such an irresolvable planning task. Our method is sound and scaleable, but not complete; however, it may provide important information when people think about how to reconstruct an appropriate goal set.