A software company can define a software process line (SPrL) to deal with projects with different characteristics. This entails defining a base process and its variation points; the SPrL is then tailored to each project. This approach avoids the co-evolution problems but is expensive to set up. In companies that register project events, this information could be used to discover the SPrL. However, traditional discovery algorithms focus on extracting a single process, which can be overly complex and would not be useful for managing future projects. Filtering out less frequent behavior leads to the discovery of simpler models, but these may not include relevant behavior. To address these issues, we propose the v-algorithm, which discovers a SPrL from process logs. Two thresholds split the log into three clusters based on relation frequency. The first one is used to generate the base process, the second one is used to identify variable elements, and the last one is discarded. We used the v-algorithm to discover the SPrL of Mobius, a small Chilean software company. We also discuss how the values of the thresholds affect the process discovery quality dimensions, extending existing metrics to the SPrL case.