For implementing the CYK algorithm for parsing, we need to have a grammar in CNF (Chomsky Normal Form) defined for a language.
Is there any such CNF grammar readily available which covers all (or most of) the English language?
You may want to check out some of the materials provided for the assignment "A3: CKY algorithm" by Prof. Dr. A. Koller who has converted the ATIS grammar for the purpose:
CL16 page: https://coli-saar.github.io/cl16
Also relevant: http://users.sussex.ac.uk/~johnca/cfg-resources
'Hope this helps.