"resolution with" is correct and usable in written English.
You can use it to mean a determination to resolve something. For example, "He had a strong resolution with himself to succeed."
Both South Korea and Japan welcomed the resolution, with Japanese Prime Minister Shinzo Abe calling it a "resolute action".
What's next - a Cyprus resolution with Turkey?
Still, officials at the agency viewed this resolution with chagrin.
Lord knows we didn't get resolution with Donald Trump.
Approaching maximum theoretical resolution with help from an unlikely source.
It has 240x320 resolution with 16-bit color.
Semantically-Driven Coreference Resolution with Embodied Construction Grammar.
The company said it would discuss a resolution with the government.
Obama says what's needed next is an enforceable resolution with consequences to destroy the weapons.
His aides say he still hopes to negotiate a resolution with Mr. Hevesi.
Ms. Baker of Navigenics said a resolution with New York did not seem imminent.
