RV-12 pilot reported a being overflown by another aircraft after touchdown at a non-towered airport on a training flight. The other aircraft was not communicating in the traffic pattern during the event; performed a go around; then returned for a landing.

Narrative

On the morning of Day 0; at approximately XA:00-XA:15; my instructor and I were conducting pattern work in an RV-12 at ZZZ; a non-towered airport. Weather was VMC; with multiple aircraft operating in the pattern. The CTAF in use was XXX.XXX MHz; and at the time there were approximately 4-5 aircraft actively flying consistent and coordinated pattern operations using correct radio procedures.We were on final approach for landing and had made the appropriate calls throughout the pattern. During the ground roll phase after touchdown; an unexpected and extremely hazardous event occurred. A Beechcraft Musketeer flew directly overhead; passing approximately 25-30 feet above our aircraft; aligned on the same runway heading. This aircraft had not made any position calls prior to the near collision and was not heard on frequency at any point during the event.It became immediately apparent that the Beechcraft had either made a straight-in approach or entered the pattern incorrectly and without any situational awareness of other traffic. The aircraft also cut off multiple other aircraft (estimated 3-4) that were already established in the pattern; creating a significant hazard to all involved.Following the near miss; the Beechcraft continued flying and eventually made a go-around. It then began making radio calls approximately 3-4 minutes later when established on base to final. Upon landing; my instructor and I approached the pilot of Aircraft Y to debrief the incident. The pilot admitted that they had been using the wrong frequency during their initial arrival and pattern entry; and only switched to the correct CTAF after the event occurred. In addition to that information; the pilot also admitted to not having flown for 7-8 years; and that he took the aircraft up for an annual. Posing a whole separate issue. They did not specify which frequency they had initially been on. Additionally; the pilot acknowledged not making any calls prior to or during the near collision.