Flight Instructor reported an NMAC event during landing pattern training which resulted in the student executing a go-around to avoid a collision. The conflict Pilot stated no radio calls were heard.

Narrative

While a student was on a first solo in the traffic pattern Aircraft Y reported 3 miles south of the field inbound to land Runway XX. While my student made the call to turn left downwind I noticed that Aircraft Y was directly above my student on the left downwind as well. I told Aircraft Y to not descend because of my student below him; but he did not respond; instead; he continued his left downwind for Runway XX; only extending his downwind after I told him to over the radio. My student then executed a go-around for Runway XX while Aircraft Y landed. As my student lined up for short final on XX again; Aircraft Y began rolling out to the runway getting ready to takeoff. I promptly told him to stop moving; as my student was about to land. I then spoke to the pilot of Aircraft Y and asked him why he was flying recklessly. He then stated that he did not see my student on ADS-B and that my student was not making radio calls; both are false statements. He then denied that what he did was reckless; and then promptly took off and headed southeast of ZZZ.