Ethics of Care - Proof that p. (This might be funny for philosophers, I guess, who enjoyed some of the other proofs that P. It somewhat resembles Goodman's proof, I know.)
If a woman is in a mutually caring relationship with another woman they would both intuitively realize that p.
The fact that many men have thought up counterexamples to p is inconsequential, as counterexamples are just typical examples of the antoganistic nature of male oriented thinking. Women would never attempt to think up counterexamples. Rather we would attempt to reconcile our position with the opressed voice of not p, while shrugging off and transcending the hostile nature of masculine thinking.