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$\vdash \lnot (p \supset q) \supset (p \land \lnot q)$

I need to prove the above proposition via intuitionistic logic rules and/or natural logic rules. I guess it is not possible to prove with intuitionistic logic becuase we cannot use PBC rule.

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    Your guess that it is not intuitionistically valid is right -- proving $\vdash \neg\neg p \supset p$ from it is an easy exercise. What exactly do you mean by "natural logic" -- the same as [natural deduction](http://en.wikipedia.org/wiki/Natural_deduction)? If so, an answer will depend on your precise axioms: there are various equivalent ways to introduce classical reasoning in ND, and without knowing which one you're using it is hard to give a relevant hint.2011-11-15
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    There don't seem to be any predicates here.2013-02-16

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