Stockfish 6 solved the position shown in post #5 when I gave it 20 seconds of time to think. Powered by i7-4770. You guys may have to specify what you mean by "can't" ;) I didn't bother studying and testing the other positions yet but I'm confident that SF will succeed at them.
Modern computers are not powerful enough to allow chess programs to look through every single possible combination up to the next 5+ moves (takes insane amount of time). That is why they have to cut both depth and lines out of their search. The less time engine is given, the more it has to cut. The more it has to cut, the more likely it will make mistakes. Same with human players: you might see GM missing a mate in 1 in bullet.
The position in #5 is tricky for the computer because it requires it to see the fifty-move-rule up ahead. Human can just stare at the pattern and realize that it will be a draw without thinking through the exact 50 moves of how it's going to happen. Engines do utilize positional analysis but apparently they lack the solution for that type of case so they really have to crank up the search/evaluation time in order to spot the draw by raw calculation.
Modern computers are not powerful enough to allow chess programs to look through every single possible combination up to the next 5+ moves (takes insane amount of time). That is why they have to cut both depth and lines out of their search. The less time engine is given, the more it has to cut. The more it has to cut, the more likely it will make mistakes. Same with human players: you might see GM missing a mate in 1 in bullet.
The position in #5 is tricky for the computer because it requires it to see the fifty-move-rule up ahead. Human can just stare at the pattern and realize that it will be a draw without thinking through the exact 50 moves of how it's going to happen. Engines do utilize positional analysis but apparently they lack the solution for that type of case so they really have to crank up the search/evaluation time in order to spot the draw by raw calculation.