Process mining discovers and analyzes a process model from historical event logs. The prior art methods use the attributes of case-id, activity, and timestamp hidden in an event log as clues to discover a process model. However, a user needs to manually specify them, and this can be an exhaustive task. In this paper, we propose a two-stage key attribute identification method to avoid such a manual investigation, and thus this is toward fully automated process discovery. One of the challenging tasks is how to avoid exhaustive computation due to combinatorial explosion. For this, we narrow down candidates for each key attribute by using supervised machine learning in the first stage and identify the best combination of the in the second stage. Our computational complexity can be reduced from $\mathcal{O}(N^3)$ to $\mathcal{O}(k^3)$ where $N$ and $k$ are the numbers of columns and candidates we keep in the first stage, and usually $k$ is much smaller than $N$. We evaluated our method with 14 open datasets and showed that our method could identify the key attributes even with $k = 2$ for about 20 seconds for many datasets.