"The reason for that is simple - GPT lacks logical reasoning capabilities. It can 'fake' them on the surface level, it might even fake them really well for extremely common problems, but as soon as you prod deeper or tack on an extra requirement or two, it starts spinning in circles indefinitely."

Those unqualified statements are false. GPT4 may not have been able to pass your particularly complex reasoning task, but that does not mean that it can't reason.

My tone is really out of extreme frustration because misjudgement like you are displaying literally puts the fate of the human race at risk.