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I want a 3D-plot with mesh lines as written in the code below:

(*Test plots in 3D*)
Clear[x, y, f, g];
$Assumptions = True;
$Assumptions = {x, y} \[Element] Reals;
f[x_, y_] := (1 + x^2*y^2)/((1 + x^2)*(1 + y^2))
p1 = Plot3D[f[x, y], {x, -4, 4}, {y, -4, 4}, 
BoxRatios -> {1, 1, 1.05}, MeshFunctions -> {#1 &, #2 &, #3 &}, 
Mesh -> {1, 1, 4}, 
MeshStyle -> {Directive[Thick, Cyan], Directive[Thick, Green], 
Directive[Thick, Black]}, ColorFunction -> "RoseColors", 
PlotRange -> {-0.1, 1.1}, 
PlotLabel -> 
Style["\!\(\*SubscriptBox[\(R\), \(N\)]\)" , 20, Black], 
PlotLegends -> BarLegend["RoseColors"], 
AxesLabel -> {Style["x[\!\(\*SubscriptBox[\(x\), \(0\)]\)]", 18, 
 Black], Style["y[\!\(\*SubscriptBox[\(y\), \(0\)]\)]" , 18, 
 Black], Style["z[\!\(\*SubscriptBox[\(z\), \(0\)]\)]" , 20, 
 Black]}, AxesStyle -> Directive[Black, 16]]
 Export["exportP1.pdf", p1]

This code gives me the correct output in the notebook, but the exported "pdf" image file contains broken mesh lines. The exported file looks as below: enter image description here As one can notice, the green lines are broken and others too. Could someone help me in getting the right "pdf" image?

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