The idea that verbs are "1- /2- etc. place" predicates derives from predicate logic. It says that such predicates are functions (in the mathematical sense) that take a defined number of arguments in order to deliver a value, in this case the value (the outcome) is a logical proposition which may then be true or false.
The idea that verbs can be taken to be logical predicates of this kind is a scientific theory, a theoretical model. The idea is strictly speaking true of the theoretical model, not directly of the verb. Verbs in natural language are fairly flexible, their meaning can appear in different nuances, and the number of grammatical arguments may vary accordingly. The logical calculus does not provide for anything like this, so this is a point where linguists start tinkering with the theory. So you can be relaxed about a verb being a 1-place predicate or not, they will usually be flexible and therefore correspond to different logical predicates.
The type of argument that a verb takes is a different matter. In linguistics, different sorts of entities are distinguished, and single "individuals" or "groups" are two different examples of entities. So a one-place verb may take an individual or a group as its argument, but it remains 1-place because in the logical model, only one step is needed to convert the predicate into a sentence. (This is the case in your example with "leave").
An example of flexibility is that some verbs alternate between 1 and 2 places, for example: "[The car] collided with [the tractor]" or "[The car and the tractor] collided." The second example is technically a 1-place predicate, but has a group as its subject. In the first example, the members of this group are distributed over 2 argument positions. The logical predicates here are of different type, the natural language meaning is not so much different (it's just that in the 2-place version, the object may be more passive).
