The utilization of social media material in journalistic workflows is increasing, demanding automated methods for the identification of mis- and disinformation. Since textual contradiction across social media posts can be a signal of rumorousness, we seek to model how claims in Twitter posts are being textually contradicted. We identify two different contexts in which contradiction emerges: its broader form can be observed across independently posted tweets and its more specific form in threaded conversations. We define how the two scenarios differ in terms of central elements of argumentation: claims and conversation structure. We design and evaluate models for the two scenarios uniformly as 3-way Recognizing Textual Entailment tasks in order to represent claims and conversation structure implicitly in a generic inference model, while previous studies used explicit or no representation of these properties. To address noisy text, our classifiers use simple similarity features derived from the string and part-of-speech level. Corpus statistics reveal distribution differences for these features in contradictory as opposed to non-contradictory tweet relations, and the classifiers yield state of the art performance.