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Such an algorithm takes $1^{(k)}$ and outputs a tautology $\\tau_k$ of size at least $k$ such that $P$ is not p-bounded on the set of all $\\tau_k$'s.\n  We consider two more general search problems involving finding a hard formula, {\\bf Cert} and {\\bf Find}, motivated by two hypothetical situations: that one can prove that $\\np \\neq co\\np$ and that no optimal proof system exists. 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