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The phrase "firmly rule out" is correct and usable in written English.
It means to decisively eliminate or reject something as a possibility or option. You can use it in any situation where you want to emphasize that something has been completely excluded or eliminated. Example: After conducting numerous tests, the doctors firmly ruled out any serious health conditions and concluded that the patient's symptoms were due to stress and anxiety.
Exact(5)
May refuses to firmly rule out extending article 50.
Our constraints on the orbit of β Pic b firmly rule out the possibility of a transit of the planet at 10-σ significance.However, we confirm that the Hill sphere ofβPic b will transit, giving us a rare chance to probe the circumplanetary environment of a young, evolving exoplanet.
This forced silence has become more problematic for the candidates as the primary has grown closer, particularly given the speculation about Mr. Giuliani, which he has seemed to encourage in recent days by declining to firmly rule out staying in office.
In suggesting a "multilateral dialogue" on the Kashmir issue and offering to mediate between India and Pakistan, Erdoğan irked Indian officials, who "firmly rule out third party mediation on Kashmir".
Thus, to more firmly rule out the non-replicated associations herein, replication efforts in much larger cohorts would be needed.
Similar(55)
But American and British officials have firmly ruled out co-operation with Assad.
It was a gamble that John Major so firmly ruled out electoral and constitutional change.
The possibility that it will be Mr Bayrou rather than Mr Sarkozy or Ms Royal cannot be firmly ruled out.
But she firmly ruled out reducing arms sales, which she described as an obligation under the Taiwan Relations Act.
Two of the most-rumored candidates, Hillary Rodham Clinton, the secretary of state, and Mr. Geithner himself, have been firmly ruled out, the sources said.
With stretched public finances, it is hard to see how university finances can be stable in the long run without tuition fees; yet they are firmly ruled out.
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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