2. Existential Out The Existential Out rule is DANGEROUS.

3. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Ba&Ma Anne is a married bunny. INVALID!

4. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny. BARELY OK Provided that n is a brand new name.

5. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny. BARELY OK n is like a new social security number.

6. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny. BARELY OK n is like a new social security number.

7. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny. WATCH OUT! There are extra deductions for violating the restriction on the EO rule.

8. Existential Out The Existential Out rule is DANGEROUS. #x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny. WATCH OUT! There are extra deductions for violating the restriction on the EO rule. The EO Restriction: The letter chosen for the instance must be new to the proof.

9. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A -$x(Bx>Vx) GOAL

10. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA ?&-??,? &I -$x(Bx>Vx) 3-? -I

11. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O ?&-??,? &I -$x(Bx>Vx) 3-? -I

12. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O ?&-??,? &I -$x(Bx>Vx) 3-? -I

13. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O ?&-??,? &I -$x(Bx>Vx) 3-? -I

14. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O 7) Ba4 &O 8) Ma4 &O ?&-??,? &I -$x(Bx>Vx) 3-? -I

15. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O 7) Ba4 &O 8) Ma4 &O 9) Va6,7 >O ?&-??,? &I -$x(Bx>Vx) 3-? -I

16. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O 7) Ba4 &O 8) Ma4 &O 9) Va6,7 >O 10) -Va5,8 >O ?&-??,? &I -$x(Bx>Vx) 3-? -I

17. Sample Proof 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O 7) Ba4 &O 8) Ma4 &O 9) Va6,7 >O 10) -Va5,8 >O 11) Va&-Va9,10 &I -$x(Bx>Vx) 3-11 -I

18. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA ?&-??,? &I -$x(Bx>Vx) 3-? -I

19. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba>Va3 $O 5) Ma>-Va2 $O ?&-??,? &I -$x(Bx>Vx) 3-? -I

20. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba>Va3 $O 5) Ma>-Va2 $O 6) Ba&Ma1 #O ?&-??,? &I -$x(Bx>Vx) 3-? -I

21. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba>Va3 $O 5) Ma>-Va2 $O 6) Ba&Ma1 #O ?&-??,? &I -$x(Bx>Vx) 3-? -I #O Restriction VIOLATED!

22. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba>Va3 $O 5) Ma>-Va2 $O 6) Ba&Ma1 #O ?&-??,? &I -$x(Bx>Vx) 3-? -I #O Restriction VIOLATED! ADVICE: DO #O FIRST!

23. EO Strategy 1) #x(Bx&Mx)A 2) $x(Mx>-Vx)A 3) $x(Bx>Vx)PA 4) Ba&Ma1 #O 5) Ma>-Va2 $O 6) Ba>Va3 $O ?&-??,? &I -$x(Bx>Vx) 3-? -I #O Restriction VIOLATED! ADVICE: DO #O FIRST! For more click here