Update app.py

app.py

@@ -998,24 +998,40 @@ def check_and_resolve_discrepancy(initial_response, sympy_output):
     
     try:
         resolution_prompt = f"""Here is a mathematics question with two answers.
-        The first, called Original solution, is a complete solution.
-        The second, called SymPy Verification, will only provide the final answer.
-        
-        If the SymPy Verification answer is consistent with the final answer Original solution,
-        then please write "SYMPY_CORRECT: True" on its own line and say that the answers are consistent and briefly explain why. 
-        
-        Before you assert that the SymPy and Original solution evaluate to the same number, CAREFULLY calculate the value of each. 
-        If the expressions are not obviously identical, double check: CALCULATE each solution CORRECTLY out to 10 decimal places and compare the results.
-        
-        If the two answers are inconsistent with each other then please:
-        1. Identify which solution is correct
-        2. Explain the error in the incorrect solution
-        3. Write "Here is the revised complete solution:" and then write out the ENTIRE solution from beginning 
-           to end, including all parts that were correct and the corrections for any incorrect parts. 
-           Do not refer to the original solution or say things like "the rest remains the same" - write 
-           out everything in full. 
-        4. Start with "SYMPY_CORRECT: False" on its own line.
-
+1. First, write out both answers:
+   - Original solution: [write the final answer]
+   - SymPy solution: [write the SymPy answer]
+
+2. To prove equivalence, you MUST do at least ONE of the following:
+   a) Algebraically transform one expression into the other through valid steps
+   b) Show that they evaluate to the sane number. 
+       NOTE: Before you assert that the SymPy and Original solution evaluate to the same number, CAREFULLY calculate the value of each. If the expressions are not obviously identical, double check: CALCULATE each solution CORRECTLY out to 10 decimal places and compare the results.
+
+3. For special functions (like hypergeometric functions):
+   - Do not assume equivalence without verification
+   - Use series expansions or numerical evaluation at test points if needed
+   - Explicitly state if you cannot verify equivalence
+
+4. After your analysis, conclude ONE of the following:
+
+   If equivalence is PROVEN:
+   - Write "SYMPY_CORRECT: True" on its own line
+   - Explain exactly how you proved equivalence
+   - Show all steps of the verification
+
+   If equivalence CANNOT be proven:
+   - Write "SYMPY_CORRECT: False" on its own line
+   - Explain why equivalence cannot be established
+   - Write "Here is the revised complete solution:" and provide a new solution that validates against SymPy
+
+   If verification is INCONCLUSIVE:
+   - Write "SYMPY_CORRECT: Inconclusive" on its own line
+   - Explain why equivalence cannot be determined
+   - Request a new SymPy verification with additional checks
+
+Never claim solutions match without showing explicit mathematical proof of equivalence.
+Please maintain the same LaTeX formatting as the original solution.
+   
 Original solution:
 {initial_response}