Representing first order sentences as conceptual graphs

Solution 1:

I don't really know about the technical details of Conceptual Graphs, but I do know that it is based off Existential Graphs, and here are the respective representations in Existential Graphs:

$\forall x \ part(x,x)$:

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$\forall x \forall y \ ((part(x,y) \land part(y,x)) \to x = y)$: enter image description here

$\forall x \forall y \forall z \ ((part(x,y) \land part(y,z)) \to part(x,z))$:

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The last two certainly look like what you have!