The phrase "and will not acknowledge" is correct and usable in written English.
It can be used to indicate that someone refuses to recognize or accept something, often in a formal or serious context.
Example: "Despite the overwhelming evidence presented, he remains silent and will not acknowledge the truth."
Alternatives: "and refuses to recognize" or "and does not accept".
She keeps sending messages when I called her out and will not acknowledge her wrong sounds, keeps telling lies and has put those lies in her notes.
Israel says it refuses to accept responsibility and will not acknowledge the right of return but will show "empathy" for the refugees, said a special adviser to Mr. Barak, Yossi Alpher.
Somebody that has a problem and will not acknowledge it, will not work on it and therefore, is not going to change it – that makes your situation very clear," Dr. Phil explains.
Tourists and most resident Germans and Czechs will not acknowledge the horrible secret to which only a few scholars today attest.
And you -- you will not acknowledge that even though the Supreme Court said there was no precedent, even though the district court judgment and a three-judge panel judgment cannot be considered precedent binding the en banc panel of the court, you still insist that somehow there was precedent there that you were bound by.
It is shocking to us that in this day and age, the president will not acknowledge — much less condemn — the rise in anti-Semitic rhetoric and actions.
Above all, don't tempt the universe by shaking a fist at fear and saying that you will not acknowledge its existence.
The United States fails to see that the international treaties it won't sign, the criminal court it will not acknowledge and the United Nations system it does not adequately support are all efforts, however compromised, at developing a new global contract to contain the chaos.
Because the presence of armed Americans on their soil raises sensitivities about sovereignty, some countries that have sought the assistance of the United States will not acknowledge it, and the D.E.A. is reluctant to disclose the details of the commando teams' deployments.
Beneath debates about science and economics he found arguments about morality and the proper relations between humans and nature though those involved often do not, or will not acknowledge this.
Without a federal law, Mr. Specter said, hospitals will not acknowledge their errors, and he cited his state's experience to prove his point.
