Hi I'm trying to prove if this set is linearly independent

$s=1-x^4,1+x+x^3+x^4,1+x-x^3+x^4,1-x^2$

I need to prove

$c1(1-x^4)+c2(1+x+x^3+x^4)+c3(1+x-x^3+x^4)+c4(1-x^2)=0$

So I've rearranged the equation as

$x^4(-c1+c2+c3)+x^3(c2-c3)+x^2(-c4)+x(c2+c3)+(c1+c2+c3+c4)=0$

Then:

$-c1+c2+c3=0$

$c2-c3=0$

$-c4=0$

$c2+c3=0$

$c1+c2+c3+c4=0$

After this step how can I prove c1=c2=c3=c4=0 since my system is overdetermined