Shrume addressed this at length, but I'll add one point...
1 Cor 14:14 (NASB) says, "For if I pray in a tongue, my spirit prays, but my mind is unfruitful."
It doesn't say the prayer is unfruitful, and you are interpreting "unfruitful" to mean "useless". I suggest you consider an alternate meaning which I believe fits the context better: "disengaged". Other translations say, "unproductive".
If only my spirit prays, my mind is disengaged. (Paul goes on...) So I will pray with my spirit and I will pray with the mind (thereby engaging it) .