Given an incompatibility that's satisfied by _solution,
        The `conflict resolution`_ constructs a new incompatibility that encapsulates the root
        cause of the conflict and backtracks _solution until the new
        incompatibility will allow _propagate() to deduce new assignments.

        Adds the new incompatibility to _incompatibilities and returns it.

        .. _conflict resolution: https://github.com/dart-lang/pub/tree/master/doc/solver.md#conflict-resolution

def _resolve_conflict(
        self, incompatibility
    ):  # type: (Incompatibility) -> Incompatibility
        """
        Given an incompatibility that's satisfied by _solution,
        The `conflict resolution`_ constructs a new incompatibility that encapsulates the root
        cause of the conflict and backtracks _solution until the new
        incompatibility will allow _propagate() to deduce new assignments.

        Adds the new incompatibility to _incompatibilities and returns it.

        .. _conflict resolution: https://github.com/dart-lang/pub/tree/master/doc/solver.md#conflict-resolution
        """
        self._log("conflict: {}".format(incompatibility))

        new_incompatibility = False
        while not incompatibility.is_failure():
            # The term in incompatibility.terms that was most recently satisfied by
            # _solution.
            most_recent_term = None

            # The earliest assignment in _solution such that incompatibility is
            # satisfied by _solution up to and including this assignment.
            most_recent_satisfier = None

            # The difference between most_recent_satisfier and most_recent_term;
            # that is, the versions that are allowed by most_recent_satisfier and not
            # by most_recent_term. This is None if most_recent_satisfier totally
            # satisfies most_recent_term.
            difference = None

            # The decision level of the earliest assignment in _solution *before*
            # most_recent_satisfier such that incompatibility is satisfied by
            # _solution up to and including this assignment plus
            # most_recent_satisfier.
            #
            # Decision level 1 is the level where the root package was selected. It's
            # safe to go back to decision level 0, but stopping at 1 tends to produce
            # better error messages, because references to the root package end up
            # closer to the final conclusion that no solution exists.
            previous_satisfier_level = 1

            for term in incompatibility.terms:
                satisfier = self._solution.satisfier(term)

                if most_recent_satisfier is None:
                    most_recent_term = term
                    most_recent_satisfier = satisfier
                elif most_recent_satisfier.index < satisfier.index:
                    previous_satisfier_level = max(
                        previous_satisfier_level, most_recent_satisfier.decision_level
                    )
                    most_recent_term = term
                    most_recent_satisfier = satisfier
                    difference = None
                else:
                    previous_satisfier_level = max(
                        previous_satisfier_level, satisfier.decision_level
                    )

                if most_recent_term == term:
                    # If most_recent_satisfier doesn't satisfy most_recent_term on its
                    # own, then the next-most-recent satisfier may be the one that
                    # satisfies the remainder.
                    difference = most_recent_satisfier.difference(most_recent_term)
                    if difference is not None:
                        previous_satisfier_level = max(
                            previous_satisfier_level,
                            self._solution.satisfier(difference.inverse).decision_level,
                        )

            # If most_recent_identifier is the only satisfier left at its decision
            # level, or if it has no cause (indicating that it's a decision rather
            # than a derivation), then incompatibility is the root cause. We then
            # backjump to previous_satisfier_level, where incompatibility is
            # guaranteed to allow _propagate to produce more assignments.
            if (
                previous_satisfier_level < most_recent_satisfier.decision_level
                or most_recent_satisfier.cause is None
            ):
                self._solution.backtrack(previous_satisfier_level)
                if new_incompatibility:
                    self._add_incompatibility(incompatibility)

                return incompatibility

            # Create a new incompatibility by combining incompatibility with the
            # incompatibility that caused most_recent_satisfier to be assigned. Doing
            # this iteratively constructs an incompatibility that's guaranteed to be
            # true (that is, we know for sure no solution will satisfy the
            # incompatibility) while also approximating the intuitive notion of the
            # "root cause" of the conflict.
            new_terms = []
            for term in incompatibility.terms:
                if term != most_recent_term:
                    new_terms.append(term)

            for term in most_recent_satisfier.cause.terms:
                if term.dependency != most_recent_satisfier.dependency:
                    new_terms.append(term)

            # The most_recent_satisfier may not satisfy most_recent_term on its own
            # if there are a collection of constraints on most_recent_term that
            # only satisfy it together. For example, if most_recent_term is
            # `foo ^1.0.0` and _solution contains `[foo >=1.0.0,
            # foo <2.0.0]`, then most_recent_satisfier will be `foo <2.0.0` even
            # though it doesn't totally satisfy `foo ^1.0.0`.
            #
            # In this case, we add `not (most_recent_satisfier \ most_recent_term)` to
            # the incompatibility as well, See the `algorithm documentation`_ for
            # details.
            #
            # .. _algorithm documentation: https://github.com/dart-lang/pub/tree/master/doc/solver.md#conflict-resolution
            if difference is not None:
                new_terms.append(difference.inverse)

            incompatibility = Incompatibility(
                new_terms, ConflictCause(incompatibility, most_recent_satisfier.cause)
            )
            new_incompatibility = True

            partially = "" if difference is None else " partially"
            bang = "!"
            self._log(
                "{} {} is{} satisfied by {}".format(
                    bang, most_recent_term, partially, most_recent_satisfier
                )
            )
            self._log(
                '{} which is caused by "{}"'.format(bang, most_recent_satisfier.cause)
            )
            self._log("{} thus: {}".format(bang, incompatibility))

        raise SolveFailure(incompatibility)