Assumption is not an assertive act. Assumption is a directive act and that is why it is performed using an imperative sentence, "Assume/ suppose/ let ...!". "Discharging assumption" is a separate act of returning to the assertive mode.

John Corcoran

I would hardly call your suppositional rules ordinary reasoning. Those are the contrivances of a formal deductive system. But in any case, the ideas of assumption discharge and subdeduction are peculiar to certain ways of setting up or displaying your proof procedures and can in principle be dispensed with.

In a sequent-style system every sequent can stand on its own; no sequent has a peculiar compromised status that segregates it from other sequents. One can still talk the talk (in the metalanguage) of "undischarged assumptions" or "propositions within a subdeduction" with regard to proof strategies, but they need not be structured as such on the page. Or, to put it in Berislav Žarnić 's terms, directive and assertive modes need not be represented differently in the notation of the object language.

I agree with Karl Pfeifer 's comment; there is ordinary reasoning and there are rules we codify we (sometimes) intend to represent ordinary reasoning (assuming we've a grip on what "ordinary" reasoning is).

That said, even assuming you're asking about, say, mental processes in ordinary reasoning, your question is unclear. What does it mean to "simply close a subderivation" as opposed to "discharge assumptions"? I'll try to answer your question anyway.

My current thinking is in ordinary reasoning we suppose (always voluntarily) content (always) for some purpose we reason towards, then we 'tale back' our supposition in one of four cases (this is not exhaustive; put aside errors, frustration, tiredness, etc.): (i) When met with a contradiction; (ii) When we reach our goal; (iii) When we reach a separate - but satisfying - goal; (iv) When we recognize our goal requires too much effort to uncover with this supposition. This suffices to maybe provide an answer to your question.

Specifically, I'm inclined to say (i) is involuntarily, and (ii), (iii), and (iv), voluntarily. if a mental process is voluntary then it's an act; If involuntary it's not obviously an act. I could be talked into (i) not being an act because involuntary. The answer to your question then - if you agree with the preceding - is discharging an assumption is sometimes an act and sometimes not.

I say "maybe provide and answer" because it's unclear how you're counting acts. If you've something else in mind, do share.