This disproof attempts to show a contradiction between some relational operator, ≻, and some operands S, L, P, R. However, the grader has circled some S as incorrect, indicating that there isn't any contradiction here. The subgraph R≻S≻P might clue you in that these relations are from the game Rock, Paper, Scissors: rock crushes scissors, and scissors cuts paper.

The next leap of logic to make is that the L and circled S are from the five-weapon expansion, Rock, Paper, Scissors, Lizard, Spock. Indeed, the first occurrence of Spock in the puzzle is P≻S, or paper disproves Spock. This means that there isn't a contradiction at all, just a poor choice of operand name! The solution is the name of the circled S, SPOCK.

This puzzle was unsolved during the hunt, although a team said they were about to submit the answer but ran out of time. This is an "intuitive leap" puzzle where the entire puzzle revolves around making one logical connection with very little context - hopefully next time I can make something that's a little less obtuse!