A verb to combine “to prove” and “to disprove”

Suppose there is proposition p, and the sentence is:

[1] That [whatever it is] neither proves nor disproves p. [In a sense, it is irrelevant.]

Can I state it in one verb, like:

That does not [verb] p.

Some possible candidates (but not what I am looking for as it contains the word “truthfulness”):

[2] That does not affect the truthfulness of p.

[3] That does not verify the truthfulness of p.

Or, is it the case that:

[4] That does not disprove p.

implicitly contains [1]?

The adjective inconclusive comes immediately to mind.

ADJECTIVE

Not leading to a firm conclusion or result; not ending doubt or dispute:

Inconclusive is different than irrelevant (and many of its synonyms). While something irrelevant is disqualified from impacting a conclusion, something inconclusive may impact the conclusion, but is insufficient to form the conclusion in itself.

"The circumstantial evidence was inconclusive in the murder investigation, but the price of eggs in China was irrelevant."

It seems the positive action of proving is not "verbally" comparable to the inconclusive status of the argument. The verb conclude "combines" prove and disprove by defining an action at the intersection of prove and disprove. In any frame of reference, proving p as true simultaneously disproves p as false. One could coin antonyms of conclude, like contraclude to mean "not closing (the investigation)", but we are simply stating that the argument has not yet "combined" prove and disprove in a conclusion.

This is a very interesting convergence of philosophy and language. You can imagine yourself in a plane looking down on two Interstate highways. From the perspective of your question, they seem to "intersect", but from every other perspective, they clearly pass over one another without touching.

Since p and the truthfulness of p are separate entities,

The simplest way to express the concept you are considering is:

"That leaves p (or the truthfulness of p) open for investigation (or discussion)."

A single word that provides the sense you want could be one of resolve, determine, decide, or settle. They are all approximate synonyms in this context.

The definition of resolve is:

: to find an answer or solution to (something) : to settle or solve (something)
: to make a definite and serious decision to do something
: to make a formal decision about something usually by a vote
_{(Source: Merriam-Webster)}

So, in your sentence:

That line of reasoning, while interesting, does nothing to resolve the proposition p, and is therefore tangential to our discussion.