Legal judgment prediction(LJP) is an essential task for legal AI. While prior methods studied on this topic in a pseudo setting by employing the judge-summarized case narrative as the input to predict the judgment, neglecting critical case life-cycle information in real court setting could threaten the case logic representation quality and prediction correctness. In this paper, we introduce a novel challenging dataset from real courtrooms to predict the legal judgment in a reasonably encyclopedic manner by leveraging the genuine input of the case -- plaintiffs claims and court debate data, from which the cases facts are automatically recognized by comprehensively understanding the multi-role dialogues of the court debate, and then learnt to discriminate the claims so as to reach the final judgment through multi-task learning. An extensive set of experiments with a large civil trial data set shows that the proposed model can more accurately characterize the interactions among claims, fact and debate for legal judgment prediction, achieving significant improvements over strong state-of-the-art baselines. Moreover, the user study conducted with real judges and law school students shows the neural predictions can also be interpretable and easily observed, and thus enhancing the trial efficiency and judgment quality.