Puzzletober 2025: Rivals

After hearing some faint voices across the hall, the newcomer enters the lounge. It is occupied by three people, two of whom are thoroughly engaged in a civil debate. The third walks up to him and says, "Those two have been arguing for the past few minutes about whether a hot dog is a sandwich. It got quite heated earlier, though I know it's all in good fun. They've been rivals for as long as I can recall, always trying to one-up each other. It must be fate that they got to play each other in the tournament. Before their game, he wanted to wager his room key, the one to room four, but she convinced him not to. It's a relief he listened, however hesitantly, since he lost to her... You look like you want to say something?" "Yes. There's a block of ice in one of the sinks down here." "Uh-huh... I think I have something for that in my room. Wait there for me."

Rules: Shade exactly half of the cells in this grid. All shaded masses of cells must have greater area than all unshaded masses of cells. The pre-placed symbols represent rotational centers of symmetry for any shaded or unshaded masses that overlap them. One cell has already been shaded for you.

Logic Pad link (has answer check)