Assuming that our proof calculus for predicate logic is sound, show that the validity of the following

sequents cannot be proved by finding for each sequent a model such that all formulas to the left of $$

evaluate to T and the sole formula to the right of $$ evaluates to F

a$.$x$$yS$($x$,$y$)$y$$xS$($x$,$y$)$

b$.$xP$($x$),$yQ$($y$)$z$($P$($z$)$Q$($z$))$

c$.$x$($P$($x$)$Q$($x$))$x$($P$($x$)->$Q$($x$)$

efg$)$