Using the sample characters from character examples, here are a few examples of conflict resolution.
Jennifer Hall and Burly Jim are in a saloon, and have a disagreement over the bill. Jim tries to look imposing, drawing himself up to his full height, which just annoys Jennifer further. She takes the first swing, kicking him in the stomach. Jim feels it, but that's not going to stop him. He responds with a solid uppercut. Since they're evenly matched in Brawn, Jim and Jennifer can continue to trade blows without a clear winner. Their descriptors don't suggest a clear advantage at fisticuffs, either. If they go on long enough, Resilience will become a factor - Jim will get tired first, and Jennifer will gain the upper hand.
After a while, Jim pauses to blink the sweat out of his eyes. Jennifer takes advantage and bounces his head off the table. Jim backs off, and, seeing stars, turns to the room. He calls out “Hey lads! Give us a hand here! This skirt's not playing fair!”
While Jennifer's edge in Resilience paid off with a solid hit on Jim, Jim has changed the focus of the conflict again. He's invoked Influence, trying to get the crowd of onlookers to pitch in. Jim has Jennifer seriously out-gunned in Influence, so Jennifer finds that she's suddenly facing an angry crowd.
As the crowd moves in, Jennifer decides to get out of saloon before this gets serious. She back-flips over the nearest drunk and grabs a billiard ball. She flings it at Jim before running for the door. Jim gets smacked right between the eyes, knocking him off his feet briefly. Neither Jim not anyone else in the room come even close to Jennifer in Warfare.