An Ehrenfeucht-Fraïssé Game

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Symbolization Key:
UD:the natural numbers: 0, 1, 2, 3, ... (all whole numbers from 0 on up)
Lxy:x is less than y
Exy:x is equal to y
n:0, the number zero
o:1, the number one
t:2, the number two

Sentence:

∃x.∀y (E(x,t) & L(x,y))

Game play:

Defender is defending the sentence's truth, Challenger is trying to make it false.

First, Defender chooses value of x:

Then, Challenger chooses value of y:

Results:

Winner is: