Is there a way to conclusively prove that any time spent further considering an idea is a waste, and if so, should that idea be tossed out? Failing that, if yo

Is there a way to conclusively prove that any time spent further considering an idea is a waste, and if so, should that idea be tossed out? Failing that, if you can show that an idea is almost certainly wrong, is it appropriate to almost never condescend to discuss it? It's important to have a good answer for this stuff. Time is an important resource. If we spend 1000 years answering questions that should have been solved in 50, we have failed at science.