This volume contains selected papers from the workshops on Disproving and the Second International Workshop on Pragmatics of Decision Procedures (PDPAR), which both were held at the Second International Joint Conference on Automated Reasoning (IJCAR) 2004 in Cork, Ireland. Clearly, the topics of the two workshops are closely related. Both are based on the recognition that an automated reasoning system needs to show a good behaviour also in the case where a conjecture is not valid. In theory, the Disproving workshop focuses on what can be done in case no proof exists and on providing output that helps the user forward (like a model, a counter example, or a repaired theorem). The PDPAR workshop focuses on the situation where the validity prob...