
model
$\displaystyle \forall x_1\forall x_2\dots\forall x_{n1},\exists x_{n}{{\neg{x_{n}=x_1}}\land\neg{x_n=x_2}\land\dot s,\land{\neg{x_n=x_{n1}}\$
i would like to know how to show form the above sentence that every model of phi_n must have at least n elements in the underlying set

If $\displaystyle \phi_n$ is $\displaystyle \forall x_1,\dots,x_{n1}.\,x_n\ne x_1\land\dots\land x_n\ne x_{n1}$, then $\displaystyle \phi_n$ is not a sentence since $\displaystyle x_n$ is a free variable.
A remark concerning notation. Subscripts consisting of more than one symbol must be enclosed in parentheses or braces. Otherwise, it is not clear whether X_n1 means $\displaystyle X_n1$ or $\displaystyle X_{n1}$. You can use /\, \/ and ~ to denote conjunction, disjunction and negation, respectively, in ASCII. It is also not too hard to write LaTeX code for these formulas. The formula above is produced by [tex]\forall x_1,\dots,x_{n1}.x_n\ne x_1\land\dots\land x_n\ne x_{n1}[/tex]. Also, \lor produces $\displaystyle \lor$, \neg produces $\displaystyle \neg$ and \exists gives $\displaystyle \exists$.