reserve a,b,m,x,y,i1,i2,i3,i for Integer,
  k,p,q,n for Nat,
  c,c1,c2 for Element of NAT,
  z for set;
reserve fp,fp1 for FinSequence of NAT,

  b,c,d, n for Element of NAT,
  a for Nat;
reserve i,m,m1,m2,m3,r,s,a,b,c,c1,c2,x,y for Integer;

theorem
  m1 <> 0 & m2 <> 0 & m3 <> 0 & (not (m1 gcd m2) divides (a - b) or not
(m1 gcd m3) divides (a - c) or not (m2 gcd m3) divides (b - c)) implies not ex
  x st (x-a) mod m1 = 0 & (x-b) mod m2 = 0 & (x-c) mod m3 = 0 by Th41;
