Is proof finding known to be NP-complete or easier?
It's harder. It's also not generally possible. By Gödel's incompleteness theorem, there are theorems that can neither be proven nor disproven. In addition, any computable axiom schema will still result in some such theorems. If you had an algorithm to prove or disprove any provable or disprovable theorem, and tell if it can't be done, you could make a computable axiom schema to make the system complete.
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?