Since we expect P != NP, finding proofs is an exponential search problem.
P != NP does not imply that one can’t do better than an exponential search for finding proofs. For instance an O(n^log(n)) algorithm for finding proofs would not contradict P != NP.
P != NP does not imply that one can’t do better than an exponential search for finding proofs. For instance an O(n^log(n)) algorithm for finding proofs would not contradict P != NP.