Problem with overlay in sp package

Dear colleges,

        I need a help for selecting a grid inside the area with the
overlay() function, the idea is create a regular grid for all the area
and before select only the grid inside the sub area, my script for this
are:

require(splancs)
require(sp)
#Create random points
x <- runif(n=500,min=0, max=20)
y <- runif(n=500,min=0, max=20)
xy<-cbind(x,y)
plot(x=x,y=y,axes=F, xlab="", ylab="",
     xlim=c(-1,20),ylim=c(0,21))
pt0 <- c(0.5,0.5)##First point of grid
##Create sub area
limx<-c(2.5,2.5,18,18,2.5)
limy<-c(2.5,18,18,2.5,2.5)
lim=cbind(limx,limy)
lim<-as.matrix(lim)
##Convert in spatial objects of sp package
#Random points
pontos <- SpatialPoints(cbind(x,y))
pontos<- SpatialPoints(list(x,y))
pontos<- SpatialPoints(data.frame(x,y))
#Create the grid
grid0= GridTopology(c(0.5,0.5), c(1,1), c(20,20))
grid<-SpatialGrid(grid = grid0)
##Sub area
limite=SpatialPolygons(list(Polygons(list(Polygon(lim)),"lim")))
##For view
plot(limite)#Sub area
points(pontos)#Random points
points(grid,col='red')#Grid
clip<-overlay(grid,limite)##Select the grid inside the sub area
sel.grid <-grid[!is.na(clip),]##Removing Na's that represents the grid
outside the sub area

But in this point I have a problem, there are any solution or other
approach for my problem,
Thanks,