Originally Posted by

**Ackbeet** I think your parentheses might mess things up a bit. How about this:

$\displaystyle \forall u\,\forall w\,\forall x\,\forall y\,\forall z\,

\big((G(w,u)\land G(x,u)\land G(y,u)\land G(z,u))\to$

$\displaystyle ((w=x)\vee(w=y)\vee(w=z)\vee(x=y)\vee(x=z)\vee(y=z ))\big).$

This expression is not fully parenthesized, I understand. If your teacher is picky about that, then just go with your original statement, which is correct as far as I can see. My version takes advantage of the associativity of AND and OR.

I don't think there are any FOL translations of the sentence that are much clearer than this.