In the medical field, there are many clinical texts such as electronic medical records, and research on Japanese natural language processing using these texts has been conducted. One such research involves Recognizing Textual Entailment (RTE) in clinical texts using a semantic analysis and logical inference system, ccg2lambda. However, it is difficult for existing inference systems to correctly determine the entailment relations , if the input sentence contains medical domain specific paraphrases such as disease names. In this study, we propose a method to supplement the equivalence relations of disease names as axioms by identifying candidates for paraphrases that lack in theorem proving. Candidates of paraphrases are identified by using a model for the NER task for disease names and a disease name dictionary. We also construct an inference test set that requires knowledge injection of disease names and evaluate our inference system. Experiments showed that our inference system was able to correctly infer for 106 out of 149 inference test sets.