You shouldn't have "True" in NDSolve anywhere. I would say cleaning up your equation and re-post?
(it means that P, x, or t are defined so that they Evaluated to True - and as a multiple against p^{1,0} this is not a function, that is, True * f[x] is not acceptable anywhere in the PDE)
I can guarantee (you you can just see in examples in mm's help), that derivatives of P are allowed in IC or BC (allowed, not necessarily giving solutions in all cases, but would not be an error)
(in other words: Clear[P,s,x,t] or reset Quit[] kernel and remember if you give P x s t values they are no longer variables. also: x>1 cannot be multiplied times a function, see Help as to how "Solve" conditions can be used properly with PDE)