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"shown to be wrong" is correct and commonly used in written English.
It is typically used to indicate that something has been proven or demonstrated to be incorrect or false. Example: Despite his confident claims, his arguments were eventually shown to be wrong by the overwhelming evidence.
Exact(53)
They were shown to be wrong.
The doubters were shown to be wrong.
That idea doesn't seem to die just because it's repeatedly shown to be wrong.
He gave some clear, very clear evidence yesterday which has shown to be wrong.
He continues to restate facts after they have been shown to be wrong.
Scientists not only can be wrong but can be shown to be wrong very publicly.
Similar(7)
In particular, it is very disappointing that the law explicitly links homosexuality with child sex abuse, which countless studies have shown to be conclusively wrong.
The decision was instantly shown to be the wrong one as Katherine Brunt and Shrubsole removed openers Kycia Knight and Stefanie Taylor in the first two overs.
That claim can be evaluated and shown to be untrue or simply wrong.
If they can then, just possibly, the old quip will be shown to be wrong and the future of fusion might actually arrive.
Montana's history with corporate influence on elections has shown that to be wrong.
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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