Tautologists all agree 
Consider the sentence, "Tautologists all agree."*

Especially uttered in context, we can readily understand that tautologists are folks who announce tautologies. Tautologies are necessarily true, so people who know tautologies have matching beliefs. So tautologists all agree. QED

One might argue against this proof on any of several grounds.

One might object: Neologisms can't just be uttered in ways that give them precise meanings. The entirety of neologizing English literature, from William Shakespeare to Joss Whedon, stands as evidence against this. Neologisms can (at least sometimes) have meanings that are as precise as paleologisms.

One might instead object: Tautologists might announce different tautologies. For example, Timmy says "If p, then p" but Tammy says "All bachelors are unmarried". They don't disagree, but they don't explicitly agree either.

Here's another possible objection: Tautologists might disagree on matters besides the tautologies they utter. So they would disagree as speakers if not strictly qua tautologists.

Let's suppose that the objections can be answered and that the proof given above goes through. That would mean that "Tautologists all agree" is itself a tautology.

Yet "tautologist" is a neologism. Before the first time the sentence was uttered, the word was not explicitly part of anyone's vocabulary. Was the sentence already a tautology before that first utterance?

We might answer no to this question by distinguishing the language pre-utterance from the language post-utterance. The word is not part of English-before, and so the sentence is not a tautology in English-before. The word is a part of English-after, and the sentence is a tautology in that so-slightly different language. This would also allow us to avoid saying that introducing the neologism creates a new tautology. Instead, coining a word shifts from English-before to English-after, and the sentence had (in some logical sense) always been a tautology of the latter language.

We are still left with some staggering consequences, though. Not only is it the case that there is a countable infinity of tautologies you might utter using familiar vocabulary. You might introduce a neologism at any time, and so there are at least as many word-coining tautologies which you could bust out with at any moment.

* Credit for this goes to Cristyn, who said it in response to some tautology which I uttered. She was being snarky, though, because I had uttered the tautology for purposes of non-trivial conversational implicature. As one does.

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