reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r for Real;
reserve p,p1,p2 for Prime;

theorem
  93 satisfies_Sierpinski_problem_89
  proof
    set n = 93;
    thus n is_a_product_of_two_different_primes
    proof
      take P3,P31;
      thus thesis;
    end;
    thus n+1 is_a_product_of_two_different_primes
    proof
      take P2,P47;
      thus thesis;
    end;
    thus n+2 is_a_product_of_two_different_primes
    proof
      take P5,P19;
      thus thesis;
    end;
  end;
