user21827: I have been working on a checkmate-in-3 problem for a long time. So long that I am becoming convinced it is not solvable. 
Is there a way to prove it is not solvable?
I want to avoid putting the problem in an engine, in case it will show me a solution. For the same reason I do not want to share the problem.

user19877: The only way to prove it with 100% accuracy is to use a special engine. Since you do not want to see the solution yourself, then you could ask someone you trust to use it for you. Having a friend sit there and attempt to solve it will not really prove anything since he is human, and may not be strong enough to guarantee a correct answer.
You are almost asking an impossible question in that you want to know the answer, but not willing to let anyone see it or to use a computer to solve it yourself. You cannot have it all.
There are special engines that are designed to prove or disprove mate-in-x problems. The ChessBase program Fritz has always had this function. I am not sure if others do though.
Here is a screenshot of the help file.


user12629: Three moves is probably in the realm where you could manually brute-force it, although it may take some effort. 
Pick a move, a reply, a second move, and a second reply. Then start looking at whether White has a checkmate from that position. If not, then White's second move was incorrect, so change it. If you eliminate all possible White second moves this way, then go back to White's first move, and change it. If you eliminate all White first moves too, then you have proven that a mate in 3 does not exist.
If you do find a White checkmate from one of these positions, then change Black's previous move. If the solution is valid, White will have a checkmate for all possible Black replies.

21827: <p>I have been working on a checkmate-in-3 problem for a long time. So long that I am becoming convinced it is not solvable. </p>

<p>Is there a way to prove it is not solvable?</p>

<p>I want to avoid putting the problem in an engine, in case it will show me a solution. For the same reason I do not want to share the problem.</p>
 19877: <p>The only way to prove it with 100% accuracy is to use a special engine. Since you do not want to see the solution yourself, then you could ask someone you trust to use it for you. Having a friend sit there and attempt to solve it will not really prove anything since he is human, and may not be strong enough to guarantee a correct answer.</p>

<p>You are almost asking an impossible question in that you want to know the answer, but not willing to let anyone see it or to use a computer to solve it yourself. You cannot have it all.</p>

<p>There are special engines that are designed to prove or disprove mate-in-x problems. The ChessBase program Fritz has always had this function. I am not sure if others do though.</p>

<p>Here is a screenshot of the help file.</p>

<p><a href="https://i.stack.imgur.com/WGMKs.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/WGMKs.png" alt="enter image description here"></a></p>
 12629: <p>Three moves is probably in the realm where you could manually brute-force it, although it may take some effort. </p>

<p>Pick a move, a reply, a second move, and a second reply. Then start looking at whether White has a checkmate from that position. If not, then White's second move was incorrect, so change it. If you eliminate all possible White second moves this way, then go back to White's first move, and change it. If you eliminate all White first moves too, then you have proven that a mate in 3 does not exist.</p>

<p>If you do find a White checkmate from one of these positions, then change Black's previous move. If the solution is valid, White will have a checkmate for <em>all</em> possible Black replies.</p>
