There have been many examples of innovations that solved contradictions in the history of science and technology and business. Altshuller and his colleagues inductively analyzed the invention patents and established common patterns in problem solving as TRIZ. Despite TRIZ’s unique view of invention patents in contradiction solving, TRIZ has a trial-and-error to solve problems like Brainstorming. The development of theory leads to the process of proving theories deductively for generalization at the stage of collecting and classifying data and constructing theories inductively. Ancient Egypt and China empirically knew that the length of the three sides of the triangle was three, four, and five in the right triangle, about a thousand years earlier than Pythagoras. However, they did not prove a2+b2=c2 based on symbols and logics. In this paper, we define terms and symbols used in contradiction solving methodology, and prove problem solving objectives and correct problem solving strategies by truth table for each contradiction problem type. This study analyzed the process of contradiction solving based on the type of contradiction problem with creative innovative cases. While many studies on idea generation and creative problem solving use inductive reasoning, this paper firstly showed the general principle as deductive proof using symbolic logic. Existing research on brainstorming, creative problem solving, and new product development suggests that we make good various ideas by divergent thinking, followed by choosing a good idea by using convergent thinking among these ideas. The contradiction solving methodology of this paper approaches contrary to existing studies on brainstorming, creative problem solving, and new product development. First, we identify the types of contradiction problems through logical convergent thinking, and determine correct problem solving strategies for each problem type. As the problem space is narrowed, eliminating arbitrary alternatives makes it possible to solve problems efficiently in a short period of time. By formalizing the contradiction solving methodology, innovation can be achieved systematically, not by chance.