Show NP != co-NP implies P != NP
Analyze the show np != co-np implies p != np.
Examples
Input: "proof_case_1"
Output: true
Input: "proof_case_2"
Output: true
Hints
Recall the definitions of P, NP, co-NP, and the relationship between NP and co-NP.
Consider the contrapositive of the statement "If NP = co-NP, then P = NP" and its implications on the P vs NP problem.
Explore the consequences of NP ≠ co-NP on the existence of NP-complete problems and the structure of the polynomial hierarchy.
Show NP != co-NP implies P != NP
Analyze the show np != co-np implies p != np.