Halting problem = undecidability of all program properties?

[i]UNDERGRAD QUALITY[/i] incoming: An old thread on /math/ got me thinking about this. We know the typical proof uses
func G(x): if Halts(x, x) then loop forever
else false
and G(G) as a counterexample. Would this
func P(x): if ReturnsOdd(x, x) then 2
else 1
mean you can't prove a program always returns odd numbers because of P(P)? What about any other simple property like ``returns alphanumeric character'' or ``returns a valid s-expression''? You can always construct a function that ends in a contradiction by just returning the opposite thing.

>>30
That's like saying it's impossible to have strong materials because there will always be a nigger who tries to break it in half.

Holy shit, just restrict the problem to the space of programs that don't moronically contradict themselves and lie to the halting function, end of the goddamned fucking problem.