Let $C$ be the clause $¬p(x) ∨ q(f(x))$. Provide two Herbrand structures $H_1$ and $H_2$ such that $[C]_{H_1}$ is true and $[C]_{H_2}$ is false.
The domain of the Herbrand's structure is $D = \{x, f(x)\}$. It's not clear to me if $x$ should be included in the domain since we want only ground terms, which means the terms that are not variables, but I'm very confused because I have seen examples that they do include even constant terms. Anyway, I'm stuck here and I need some help on how to continue from here. Thanks!