these are four students, one is writing.
A student is writing something.
Saying "a student" would imply it is one of the four students, and only one of them is writing.
exists p1 x1.(n_thing(x1) & exists e1 x2 x3 x4.((x1 = x2) & Theme(e1,x4) & Actor(e1,x3) & v_write(e1) & (x2 = x4) & n_thing(x3) & card_eq_1(x3) & n_student(x2) & card_eq_4(x2)))
exists e1 x1 x2.(Theme(e1,x2) & Actor(e1,x1) & v_write(e1) & n_thing(x2) & n_student(x1))