When we get the new Tory leader, we'll know pretty quickly. If they're serious they'll activate article 50. If they're not, they'll delay it "while they get the negotiating team in order and make serious decisions about their goals" in order to allow the Jul-Sep GDP figures to come out. These will show a 1-2% drop in GDP, and employment figures will also show a slide, along with other bad economic indications. They'll then use this as an excuse to "re-consider" activating article 50 "in the light of new evidence" (also know as the blinkin' obvious and widely predicted actually happening) and hold a commons vote on article 50.
I think it's pretty unlikely, personally, the EU is too unpopular among Tory voters and members for them to be willing to put the country's interest ahead of party interests.