Proof by contradiction, three-step template

The prompt

If a+|a|=0, try to prove that a<0.

Step 1: List the conditions and questions in the original proposition.

Step 2: Merge the conditions listed in Step 1 into one. Define it as wj.

Step 3: Let us think it step by step. Please consider all possibilities. If the intersection between wj (defined in Step 2) and the negation of the question is not empty at least in one possibility, the original proposition is false. Otherwise, the original proposition is true.

Answer:

Expected result

A step-by-step proof-by-contradiction that correctly derives a<0, following the three-step template rather than jumping straight to an answer.

Why it works

A zero-shot template for indirect reasoning: instead of asking the model to prove something directly, it lists conditions, merges them, then checks whether negating the claim is consistent with those conditions. Research measured this improving accuracy on factual and mathematical reasoning versus direct prompting — swap in your own proposition and reuse the same three-step scaffold.