A negation of statment that is always true statement is never true?

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A negation of statment that is always true statement is never true?

Example: Let x be an integer, the following statement is always true:

"either x is even or x is odd".

However, the negation of the above statement is possibly never true:

"Neither x is odd and x is even".

We might possibly generate a snippet of if else statement that never be entered into.