I'm trying to understand the problem of HORNSAT: given a set of Horn clauses, is there a satisfying assignment. A Horn clause has the form $(x_1 \wedge x_2 \wedge \cdots x_k) \rightarrow v $ where all variables appear positively. What I don't understand is why we can't just set all variables to true, since we never have $\dots \rightarrow \neg v$.
Perhaps the easiest way for me to understand this would be to see an unsatisfiable instance of HORNSAT.