If we post a program and try to construct a Turing machine to solve it but are not successful, does this prove that no Turing machine exists? If not, why would prove this?

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The Answer of If we post a program and try to construct a Turing machine to solve it but are not successful, does this prove that no Turing machine exists? If not, why would prove this?

If We Post a Program and Try to Construct a Turing