They conducted a trial. It is called an impeachment. They failed to obtain a conviction, but it is highly inaccurate to say they refused to conduct a trial.
Impeachment already occurred by the action of the House.
Removal could only come through a conviction by the Senate.
A real trial was not allowed by the Senate, and everyone knows it. The “trial” that occurred was not conducted like a real trial. Evidence and witnesses were banned from being heard. And the GOP did that.