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In the contemporary era of information explosion, we are often faced with the mixture of massive \emph{truth} (true information) and \emph{rumor} (false information) flooded over social networks. Under such circumstances, it is very essential to infer whether each claim (e.g., news, messages) is a truth or a rumor, and identify their \emph{sources}, i.e., the users who initially spread those claims. While most prior arts have been dedicated to the two tasks respectively, this paper aims to offer the joint inference on truth/rumor and their sources. Our insight is that a joint inference can enhance the mutual performance on both sides. To this end, we propose a framework named SourceCR, which alternates between two modules, i.e., \emph{credibility-reliability training} for truth/rumor inference and \emph{division-querying} for source detection, in an iterative manner. To elaborate, the former module performs a simultaneous estimation of claim credibility and user reliability by virtue of an Expectation Maximization algorithm, which takes the source reliability outputted from the latter module as the initial input. Meanwhile, the latter module divides the network into two different subnetworks labeled via the claim credibility, and in each subnetwork launches source detection by applying querying of theoretical budget guarantee to the users selected via the estimated reliability from the former module. The proposed SourceCR is provably convergent, and algorithmic implementable with reasonable computational complexity. We empirically validate the effectiveness of the proposed framework in both synthetic and real datasets, where the joint inference leads to an up to 35\% accuracy of credibility gain and 29\% source detection rate gain compared with the separate counterparts.