TW-TST 2002 Problem 3

Suppose $x,y,,a,b,c,d,e,f$ are real numbers satifying i) $\max{(a,0)}+\max{(b,0)}<x+ay+bz<1+\min{(a,0)}+\min{(b,0)}$ , and ii) $\max{(c,0)}+\max{(d,0)}<cx+y+dz<1+\min{(c,0)}+\min{(d,0)}$ , and iii) $\max{(e,0)}+\max{(f,0)}<ex+fy+z<1+\min{(e,0)}+\min{(f,0)}$ . Prove that $0<x,y,z<1$ .