is there a short, unambiguous way to write that a statement isnt always true?

What I mean specifically is that for example if you have a statement P, then its negation ¬P is the statement that P never holds. Ie, if P is false, then ¬P is true, and vice versa. I was wondering if there is a word/symbol/sentence for the weaker statement that a given statement P isn't necessarily true (aka P is not a tautology).

I know using quantifiers I could write this as ∃x, ¬P(x), but I was wondering if there was a shorter, perhaps more naturalistic way of writing P isn't true. I'm mostly interested because of situations where I want to write that one thing doesn't imply another, which is not quite the same as nonimplication, and I want to avoid confusing the two.

Solution 1:

Using modal logic you can write $\neg \square P$

Using meta-logic you can write $\not \vDash P$