Q = ZZ/2[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10] /  ideal(x1^2-x1,x2^2-x2,x3^2-x3,x4^2-x4,x5^2-x5,x6^2-x6,x7^2-x7,x8^2-x8,x9^2-x9,x10^2-x10); 

Ge = 0_Q;
Le = 0_Q;
Lem = 1_Q;

RingElement | RingElement :=(x,y)->x+y+x*y;
RingElement & RingElement :=(x,y)->x*y;

f1 = x4 & (1+x5) & (1+x6);
f2 = x1;
f3 = x1;
f4 = 1+Ge;
f5 = (1+x7) & (1+x8);
f6 = ((1+x7) & (1+x8)) | x5;
f7 = x3 & x9;
f8 = x9 | x10;
f9 = x2 & (1+Ge) & Le;
f10 = (1+Ge) & ((x2 & Lem) | Le);

(f1, f2, f3, f4, f5, f6, f7, f8, f9, f10)

I = ideal(f1+x1, f2+x2, f3+x3, f4+x4, f5+x5, f6+x6, f7+x7, f8+x8, f9+x9, f10+x10);

G = gens gb I