Extrinsic apoptosis is a programmed cell death triggered by external ligands, such as the TNF-related apoptosis inducing ligand (TRAIL). Depending on the cell line, the specific molecular mechanisms leading to cell death may significantly differ. Precise characterization of these differences is crucial for understanding and exploiting extrinsic apoptosis. Cells show distinct behaviors on several aspects of apoptosis, including (i) the relative order of caspases activation, (ii) the necessity of mitochondria outer membrane permeabilization (MOMP) for effector caspase activation, and (iii) the survival of cell lines overexpressing Bcl2. These differences are attributed to the activation of one of two pathways, leading to classification of cell lines into two groups: type I and type II. In this work we challenge this type I/type II cell line classification. We encode the three aforementioned distinguishing behaviors in a formal language, called signal temporal logic (STL), and use it to extensively test the validity of a previously-proposed model of TRAIL-induced apoptosis with respect to experimental observations made on different cell lines. After having solved a few inconsistencies using STL-guided parameter search, we show that these three criteria do not define consistent cell line classifications in type I or type II, and suggest mutants that are predicted to exhibit ambivalent behaviors. In particular, this finding sheds light on the role of a feedback loop between caspases, and reconciliates two apparently-conflicting views regarding the importance of either upstream or downstream processes for cell-type determination. More generally, our work suggests that these three distinguishing behaviors should be merely considered as type I/II features rather than cell-type defining criteria. On the methodological side, this work illustrates the biological relevance of STL-diagrams, STL population data, and STL-guided parameter search implemented in the tool Breach. Such tools are well-adapted to the ever-increasing availability of heterogeneous knowledge on complex signal transduction pathways.