The white and black cat pawed at the piece of fabric.
A cat played with a piece of cloth.
A cat may pawed at a piece of fabric or cloth because he was irritated with it, wanted to destroy it, etc, so we cannot infer he played with it.
exists e1 s1 s2 x1 x2 x3 x4.(n_piece(x3) & n_cat(x1) & a_black(s2) & Theme(s2,x1) & a_white(s1) & Theme(s1,x1) & a_topic(x1) & at(e1,x3) & of(x3,x4) & n_fabric(x4) & Theme(e1,x2) & v_paw(e1) & (x1 = x2))
exists e1 x1 x2 x3.(with(e1,x2) & of(x2,x3) & n_cloth(x3) & n_piece(x2) & Theme(e1,x1) & v_play(e1) & n_cat(x1))