Internet routing depends on economic relationships between ASes (Autonomous Systems). Despite extensive prior research of these relationships, their characterization remains imprecise. In this paper, we focus on provider-free ASes that reach the entire Internet without paying anyone for the traffic delivery. While the ground truth about PFS (set of the provider-free ASes) lies outside the public domain, we use trustworthy non-verifiable sources as a baseline for result validation. Straightforward extraction of PFS from public datasets of inter-AS economic relationships yields poor results. Then, we develop a more sophisticated Temporal Cone (TC) algorithm that relies on topological statistics (customer cones of ASes) and exploits the temporal diversity of the datasets. Our evaluation shows that the TC algorithm infers PFS from the same public datasets with a significantly higher accuracy. We also assess the sensitivity of the TC algorithm to its parameters.