Given the constantly growing proliferation of false claims online in recent years, there has been also a growing research interest in automatically distinguishing false rumors from factually true claims. Here, we propose a general-purpose framework for fully-automatic fact checking using external sources, tapping the potential of the entire Web as a knowledge source to confirm or reject a claim. Our framework uses a deep neural network with LSTM text encoding to combine semantic kernels with task-specific embeddings that encode a claim together with pieces of potentially relevant text fragments from the Web, taking the source reliability into account. The evaluation results show good performance on two different tasks and datasets: (i) rumor detection and (ii) fact checking of the answers to a question in community question answering forums.