The phrase "satisfied without" is correct and usable in written English
It can be used when expressing contentment or fulfillment in the absence of something.
Example: "She felt satisfied without the need for external validation."
Alternatives: "content without" or "fulfilled without"
This formula means, there is no path in which the state "!Apoptosis & Proliferate & Angiogenesis" (state S2) is satisfied without satisfying "CyclinD > 1 ∨ P53 < 1 ∨ HIF1 > 1" (state S1) first.
Additionally, patients were asked to rate their satisfaction with the procedure on a scale (not a visual analogue) of 0 (not satisfied) to 10 (completely satisfied without reservation) and to state whether they would have the operation again under similar circumstances.
"You know your father's never satisfied without them," she protested.
The prevailing wisdom is that the court cannot be satisfied without spending more money.
You'll feel satisfied without having to undo a notch on your belt.
McGregor never defended the belt, which means Aldo reclaims the title – but Aldo said he wouldn't be satisfied without a rematch.
The lobster spring rolls are long, skinny things, wrapped in phyllo with two hot sauces, the kind of tidbits that satisfy without distracting you from the stage.
An omelette can set you up for the day, fill a hole at lunch or satisfy, without over-facing, at 8pm.
Here it's roasted over wood and stuffed with root vegetables and house-baked beans, and it's the rare vegetarian dish that satisfies without seeming like a token.
The municipalities are now looking for private help as the Environmental Protection Agency imposes standards on water quality that municipalities cannot satisfy without outside financing and expertise.The French multinationals have again been especially successful here.
The needs and expectations of this diverse population of users can be hard to satisfy without their active cooperation and collaboration.
