I think Zhuge Liang's real rival was Zhou Yu. First off they were competing against each other while allied against Cao Cao. Zhou Yu tried to have Zhuge Liang killed a couple of times, but Zhuge Liang was too clever. The faliure of his 3 ploys against Zhuge Liang pretty much lead to Zhou Yu's downfall. Zhuge Liang and Sima Yi meanwhile were merely commanders of opposing armies that clashed a number of times. I don't even recall them conversing once.
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That's not a bad thing. That's a good thing. I like me, you like me, and I'm going to help you like you.