Yes, this is non-free, and it probably wouldn't work as you intend to anyway.
See section 12 on https://people.debian.org/~bap/dfsg-faq.html, especially items h and m.
So, let's address some of the comments.
The data that is output by a program is not part of the program itself, except in rather rare cases where the program outputs its own source code.
A text written using Libreoffice is not part of Libreoffice, and doesn't fall under the copyright of the Libreoffice authors.
A program compiled using GCC is not part of GCC, and doesn't fall under the copyright of the GCC authors.
Statistics gathered by a web crawler are not part of the web crawler itself, and do not fall under the copyright of the web crawler's authors.
This distinction is very important. Copyright law works by granting the author some exclusive rights over their work. Other people are not allowed to exercise these rights unless they have the author's permission. However, as surprising as this may be, use of a software program is not one of those exclusive rights. A user does not need the author's permission to use a program.
This is also called "fair use". The exact details of what is considered "fair use" and what is not vary from country to country, but this is not important for this discussion. I am pretty sure that running a program and publishing the output is considered fair use everywhere.
This is what Barak's FAQ is referring to when it says:
There are certain rights granted to anyone who is in lawful possession of copy of a work, even when that work is under copyright.
(Under US copyright law it's not clear that it is even possible to restrict use, once someone has a legal copy.) We can only consider restrictions on distribution.
The GPL FAQ also tries to clarify this:
[...] the copyright on the editors and tools does not cover the code you write. Using them does not place any restrictions, legally, on the license you use for your code.
And even more explicitly here:
“Fair use” is use that is allowed without any special permission. Since you don't need the developers' permission for such use, you can do it regardless of what the developers said about it—in the license or elsewhere, whether that license be the GNU GPL or any other free software license.
Please note that just because this is from a DFSG FAQ and the GPL, that does not mean it only applies to the Debian project and the GPL. This is how copyright law itself works, so it applies universally.
The OSI FAQ says:
Can I restrict how people use an Open Source licensed program? No.
So, if copyright law doesn't give you the right to decide how other people use the data generated by your program, how can you still restrict that use?
With a F/OSS license, you can not. F/OSS licenses only grant the user some additional rights which they do not have by default, and then they usually place some restrictions on these additional rights. But they do not ask the user to give up a right which they have by default. This is also why you never need to make sure that the user agrees to an F/OSS license (clickwrap). The user is free to refuse the license, in which case they just fall back to their fair use rights, which the F/OSS license doesn't try to take away, so there is no problem.
You could try to use an EULA to get the user to agree to give up their right of publishing the data without the disclaimer. However, there are problems with this:
At least in some jurisdictions, such clauses are only effective if the user actively indicates that they accept them, so you need a clickwrap, and then you obviously also need a clause in your license prohibiting removal of the clickwrap.
AFAICT, it only binds the person installing the software. If someone happens to find themselves in front of a legally obtained installation of the software, presses "run" and then publishes the data without including your "mandatory" disclaimer, I don't see how you could do anything about that at all. Well, maybe you could "clickwrap" the "run" button.
I am sure that such a license wouldn't be considered F/OSS-compliant. Neither by Debian, nor the FSF, nor the OSI. In their FAQs, they all write explicitly that compliant licenses can only restrict distribution, not use.
Another note: Please do not add additional clauses to well-known F/OSS-Licenses. It only causes confusion. There is a reason why Debian, the FSF and the OSI all publish catalogs of "known good" licenses, and not a single one of these licenses includes any restriction whatsoever on use.
The best course of action really is to just include a standard disclaimer for the software itself and stop worrying about what other people do with their data.
To quote the OSI FAQ again:
Note that nearly all Open Source licenses also state that there is no warranty: you can't sue if it blows up your computer or destroys your data, even if it was the program's fault.
But the AGPL also does this!
The relevant part of the AGPL reads:
Notwithstanding any other provision of this License, if you modify the Program, your modified version must prominently offer all users interacting with it remotely through a computer network (if your version supports such interaction) an opportunity to receive the Corresponding Source of your version by providing access to the Corresponding Source from a network server at no charge, through some standard or customary means of facilitating copying of software.
Note that this only applies if someone modifies and distributes the program, not if they merely use it. The user of an AGPLed web-based text editor is not required to include a link to the editor's source in the texts they write.