is there any set membership of which is not decidable in polynomial time but semidecidable in P?

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As there are c.e. set and computable set, is there any set membership of which is not decidable in polynomial time but semidecidable in P? Any reference?

Under the c.e. level that is all set are computable, is there any setsmembership of which is not decidable in NP time but semidecidable in NP? and are the similar problem in other computational complexity?

Thanks in advance.