Is there water on the floor, or are you sure it's going into the stool?
Do you hear water trickling after the refill valve shuts off?
Do you have the correct flapper, does it seat properly and is the chain adjusted to have a small amount of slack when the flapper is closed? Is there too much slack in the chain, permitting it to get between the flapper and its seat?
What is the water level in the tank when the refill valve shuts off? It should be a couple of inches below the top of the overflow tube.

Did you replace the gasket and flapper, but not the entire flush valve? It sounds like the seat on the flush valve is nicked or something, so you should have replaced with a new kit at that point. There is also the chance that you used an incorrect flapper for your toilet if you bought it separately. You could try switching to another flapper. What's the brand of your toilet? (Mention it when you buy the new one.)

Thanks folks. After your input, I went back and did some more checking on the toilet. There is NO water on the floor. I do not hear water trickle after shut off; we replaced the overflow and flapper (one unit); we did not replace the input part with the float. I did observe that the chain was tight, but after giving it some slack, it still does the same thing. I put coloring in the tank, but did not observe a color change in the bowl until the tank refilled. The water level drops at least 1/2 inch. and the water level stops at about 1.5 inches below the overflow when fuill. I do not know the brand -- new construction--house is 9 yrs old. Time for a new toilet?? Hate spending money, but water bill is too high. Might pay for a new one.

Maybe the fill valve is messed up, and after a while it's filling to the top of the overflow tube (which leads to the bowl). I'd observe with the lid off for that 40 minutes, and if that is the case, replace it.

homebound, I did just that, and the water line actually receeds. I saw NO color from the tank coming into the bowl.
I'm completely confused on this one. BTW, it's only taking 15 to 20 min. for the water line to drop enough to trigger the float to open.

There is a rubber tube leading from the fill valve to the overflow pipe. If this tube is inserted into the overflow pipe deeper than the water level of the tank it can cause a siphon to form drawing water from the tank.

Good point. That tube is clipped onto the edge of the overflow tube and aimed into it. It is not supposed to be inserted down into the tube.

Yea!!! Y E S!!! You got it wood cutter! Thanks man. That
was driving me crazy, and such a simple fix. MUCH appreciated

Why is it I can fix someone else's problem from a thousand miles away, but I can't do anything in my own house in less than 4 tries?

I hear you weed cutter. I think that sometimes we're just too close to the problem. But you sure fixed mine and I thank you for it.