Consider the following statements
${\mathrm{S}}_1:$ The number of real roots of

$\cos \left(e^x\right)=(2007{)}^x+(2007{)}^{-x}$ is zero.

${\mathrm{S}}_2:$ The number of real roots of

$(x+1{)}^{2006}+(x+2{)}^{2006}+(x+3{)}^{2006}+\dots \dots +$
$(x+2007{)}^{2006}=0$ is zero.

${\mathrm{S}}_3:$ The number of real roots of $x^4+x^2+1=0$ is zero.

Then the true statement(s) is/are