conflict with (something)
To interfere or clash with something. Wait, no, I can't meet with you at 3:00—that conflicts with a conference call I have. I cannot support you in this action, sir, as it conflicts with my religious beliefs.
conflict with something
to clash with something. (Does not refer to fighting.) This date conflicts with my doctor's appointment. As far as I can tell, the date you suggest does not conflict with anything.