The short version, without references or argumentation:

Science can't prove that there aren't any supernatural requirements for a sentient mind.

However, Science has proven that most of our intuitions about our own cognition are wrong.

Since intuition is the only evidence we have that subjectivity and qualia can arise from mysterious nonphysical processes but not computational, physical processes, Occam's Razor demands that we accept the explanation which accords with proven laws of physics.