I'm a postdoctoral researcher. My professor recently asked me to co-supervise one of her doctoral students, whom she also employed full-time as a research scientist. Since I had no prior experience advising at the doctoral level, I gladly accepted. Unfortunately, the guy turned out to be a phenomenally poor researcher. He was habitually late for work, took absences without leave, lacked subject-matter knowledge that we expect even of undergraduate students, and had extremely poor oral and written communication skills. I worked my best to help him, and we even managed to get a paper published (though I had to completely rewrite his draft, many parts of which were completely nonsensical or even plagiarised). However, his bad work habits continued, and despite my tutelage he remained unwilling or unable to fill the gaps in his knowledge. After about six months of my co-supervision, my professor decided to dismiss him from the doctoral programme and from employment.
I'm currently seeking employment, including tenure-track positions. My question is whether and how I should list this failed student on my CV. On the one hand, I think it would be helpful to show that I have at least some experience advising at the doctoral level. But I don't want it to reflect poorly on me that the only such experience I had was ultimately a failure. Should I list him or not? And if so, what explanation, if any, should I include in the CV as to why the supervision didn't continue past six months?