Non-Boolean SAT

Question

I was wondering about the complexity of SAT tests with variables $x_i = 0 \lor 1 \lor 2 \dots \lor n$, with clauses being of the form $x_i = a \implies x_j \neq b$. When $n=2$, we have 2SAT, which has linear time algorithms. Meanwhile, if $n > 2$, then if we can almost convert it to 2SAT by having Boolean variables $x_{i,a}$ corresponding to the statement $x_i = a$, however this allows for $x_{i,1}=x_{i,2}= \dots = x_{i,n}=0$, which would leave $x_i$ unassigned.