Despite the strategic problem in this example, the proof may appear to work, only because of an error in the application of a basic rule late in the proof. Remember, the basic or non-hypothetical rules are just &E, &I, vI, DN, MP, and MT. Which rule is used incorrectly (it doesn't correspond to the rule diagram), in a way that makes the proof appear superficially complete. In other words, which rule is used incorrectly to make it look like the proof is complete on the surface, but when we investigate more closely how the rule was used, we see that the proof is not successful. Q, (P R), (Q -R) |- -(-P -Q) 1 (1) Q A Aim: -(-P -Q) -Q 2 (2) (P R) A 3 (3) (Q -R) A 4 (4) P A/CP |- -Q 2,4 (5) R 2,4 MP 1,3 (6) -R 1,3 MP 1,2,3,4 (7) 5,6 I 1,2,3,4 (8) -Q 1-7 IP 2,3,4 (9) (P -Q) 4-8 CP 2,3 (10) -(-P -Q) 9 DN