= Solution
A <term-generated model> is a structure in which every element is the value of a <closed term> of the original language. Equivalently its <substructure> generated by the empty set, including interpretations of named constants, is the entire structure. This is the relevant meaning of “term model” for a model of an arbitrary <complete theory>, rather than a claim about one particular syntactic construction.
Each <closed term> $t$ gives the parameter-free defining formula $x=t$. Thus
$$
\boxed{\text{term-generated}\ \Longrightarrow\ \text{pointwise definable}.}
$$
The next parts show that pointwise definability implies atomicity, and <countable> atomicity is equivalent to primeness. Therefore property (i) implies all three other properties.
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