premise: The black and white dog is running with a red pail in its mouth.
hypothesis: A dog is running with something in its mouth.
explanation_1: The colors of the dogs fur notwithstanding, the dog is already running with the red pail, with is a thing of some kind, facilitating the second statement, where the dog is still running and not it's something instead of the red pail.
premise_logic: exists e1 s1 s2 s3 x1 x2 x3.(n_mouth(x3) & of(x3,x1) & n_thing(x1) & n_dog(x1) & a_white(s2) & Theme(s2,x1) & a_black(s1) & Theme(s1,x1) & in(e1,x3) & with(e1,x2) & n_pail(x2) & a_red(s3) & Theme(s3,x2) & Actor(e1,x1) & v_run(e1))
hypothesis_logic: exists e1 x1 x2 x3.(with(e1,x2) & in(x2,x3) & n_mouth(x3) & of(x3,x1) & n_thing(x1) & n_thing(x2) & Actor(e1,x1) & v_run(e1) & n_dog(x1))
premise_sim: exists e1 s1 s2 s3 x1 x2 x3.(with(e1,x2) & v_run(e1) & of(x3,x1) & n_thing(x1) & n_pail(x2) & n_mouth(x3) & n_dog(x1) & in(e1,x3) & a_white(s2) & a_red(s3) & a_black(s1) & Theme(s3,x2) & Theme(s2,x1) & Theme(s1,x1) & Actor(e1,x1))
hypothesis_sim: exists e1 x1 x2 x3.(with(e1,x2) & v_run(e1) & of(x3,x1) & n_thing(x2) & n_thing(x1) & n_mouth(x3) & n_dog(x1) & in(x2,x3) & Actor(e1,x1))