The film tells the story of Jackie Robinson and, under the guidance of team executive Branch Rickey, Robinson's signing with the Brooklyn Dodgers to become the first African-American player to break the baseball color barrier. The story focuses mostly on the 1947 Brooklyn Dodgers season and somewhat on Robinson's 1946 season with the Montreal Royals, which emphasize his battles with racism.
In 1945, after sportswriter Wendell Smith suggests that Rickey consider Robinson as the black ballplayer Rickey is looking for, Robinson and his team, the Kansas City Monarchs, stop by a gas station. When the attendant refuses Robinson entry to the washroom, Robinson says they will find another station at which to fill up the team bus, and the attendant relents. As Robinson steps out, a scout for the Dodgers sent by Rickey approaches him and invites him to Brooklyn. He is offered a $600 per month contract and a $3,500 signing bonus, which Robinson accepts after being warned by Rickey that he must control his temper if he wants to play. Robinson proposes to his girlfriend, Rachel, by phone and she accepts.
During spring training, Robinson makes it to the franchise farm team in Montreal. After a great season there and spring training in Panama, he advances to the Dodgers. Most of the team soon signs a petition, stating they refuse to play with Robinson, but manager Leo Durocher insists Robinson will play with the main team. When Durocher is suspended for actions in his personal life, leaving the Dodgers without a manager to start the regular season, Burt Shotton agrees to manage the team.
In a game against the Philadelphia Phillies, manager Ben Chapman taunts Robinson, causing him to go back to the dugout and smash his bat out of frustration. With encouragement from Rickey, Robinson then returns to the field and hits a single, steals second base and advances to third on a throwing error, and scores the winning run. When Chapman's behavior toward Robinson generates bad press for the team, the Phillies' owner requires him to pose with Robinson for newspapers and magazine photos.
Later, Robinson's teammate, Pee Wee Reese, comes to understand what kind of pressure Robinson is facing, and makes a public show of solidarity, standing with his arm around Robinson's shoulders before a hostile crowd in Cincinnati, silencing them.
In a game against the St. Louis Cardinals, Enos Slaughter "accidentally" spikes Robinson on the back of the leg with his cleats while running the bases.
Robinson's home run against Pittsburgh Pirates pitcher Fritz Ostermueller, who had earlier hit him in the head, helps clinch the National League pennant for the Dodgers, sending them to the World Series, which they would lose to the New York Yankees. A concluding postscript describes how Rickey, Robinson, and many of his teammates went on to have distinguished careers, including inductions into the Baseball Hall of Fame, besides Chapman, who was fired and forbidden to join an MLB team forever due to his racism. The notes also describe the entrance of other African Americans into the Major Leagues, beginning with the season after Robinson's debut.

Question: What did the petition state that most of the Dodgers' players signed?
Answer: That they refused to play with Robinson
Alternative answer: that they refused to play with Robinson