(A) That the exploration and subsequent mapping of the underwater cave system’s Byzantine interior requires extensive experience and caution has been proven both by the near-death experiences of amateur cave divers and by the massive costs of the rescue operations to save those amateur cave divers.
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Incorrect. Subject verb agreement error - for statement format "..exploration and subsequent mapping.. requires.." - 'require' should be used instead of 'requires'
(B) That the exploration and subsequent mapping of the underwater cave system’s Byzantine interior require extensive experience and caution has been proven just as much by the near-death experiences of amateur cave divers as by the massive costs of the rescue operations to save those amateur cave divers.
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Correct. - Though this sentence changes the meaning of the original sentence slightly by indicating the equal magnitude of proof is provided by 'near-death experience' and 'massive costs of rescue operation', this sentence does not have any grammatical error.
(C) Proven just as much by the near-death experiences of amateur cave divers as well as by the massive costs of the rescue operations to save those amateur cave divers, the exploration and subsequent mapping of the underwater cave system’s interior requires extensive experience and caution.
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Incorrect. Subject verb agreement error - 'exploration and subsequent mapping.. requires..'
(D) The exploration and subsequent mapping of the underwater cave system’s interior requires extensive experience and caution, as has been proven not only by the near-death experiences of amateur cave divers but also by the massive costs of the rescue operations to save them.
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Incorrect. Subject verb agreement error - 'exploration and subsequent mapping.. require..' should be used instead of 'exploration and subsequent mapping.. requires..'
(E) The process of exploring and mapping the underwater cave system’s interior require extensive experience and caution, proven both by the near-death experiences of amateur cave divers as much as by the massive costs of the rescue operations to save them.
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Incorrect. - sentence format '..proven both by X as much as by Y..' is incorrect, instead it should be 'proven both by X & by Y'.