But that's exactly what I meant. So the brute force program proposed in the post I replied to doesn't exist, right?

Let's say, you have proposition A. You write a program to brute force proofs for A. If it finds a proof, it will halt and output Yes, if it finds a disproof it will halt and output No, otherwise it will check the next proof.

So if you say that your brute force program can proof/disproof proposition A (and A1, A2, A3, ... for that matter), you will have to proof that your program will halt for sure after a finite number of steps. Now that's proposition B.

If you find a clever proof for proposition B, then you can claim that you wrote a program that can proof or disproof proposition A - maybe in a zillion years, but it can.

If you can't find such a proof for proposition B, you can always try to write a brute force program to proof/disproof proposition B... then C, D, E, etc. :)

And here comes the halting problem: you may be able to proof that a specific program will halt on a specific input, but it can be very hard to proof. But you can't proof that a specific program will halt on every input. This is directly related to Godel's incompleteness of formal systems.