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The phrase "a system that does not exist" is correct and usable in written English.
You can use it when discussing theoretical concepts, hypothetical scenarios, or critiquing ideas that lack practical application.
Example: "The proposal outlines a system that does not exist, making it difficult to implement in real-world situations."
Alternatives: "an imaginary system" or "a non-existent system".
Exact(1)
"I do not like the term 'former East' because 'former East' is relevant to a system that does not exist anymore," she said.
Similar(59)
To create an operating system that does not exist — because it would be too dangerous.
But all our structures are modelled on a two-party system that doesn't exist anymore," he said.
"We're talking about a supplementary transport system – not replacing rail, lorries, bikes, adding another system that doesn't exist but that does make sense".
The question is the rest of the system that doesn't exist.
Synthetic biology is an engineering discipline that seeks to construct living systems that do not exist in nature.
Synthetic biologists try to engineer useful biological systems that do not exist in nature.
It's a thing that doesn't exist that now does exist that needs an identity in a system.
Today, that doesn't exist anymore.
Today that doesn't exist.
In civilian life, that doesn't exist".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com