Examples for "An algorithm for evaluating the validity of a singly-quantified monadic predicate logic argument"

1. 19 or 24 Categorical Syllogisms
Table Name
1 bArbArA
2 cElArEnt
3 dArII
4 fErIO
5 cEsArE
6 cAmEstrEs
7 bArOcO
8 fEstInO
9* dArAptI
10 dAtIsI
11 dIsAmIs
12* fElAptOn
13 bOcArdO
14 fErIsOn
15* brAmAntIp
16 dImArIs
17 cAmEnEs
18* fEsApO
19 frEsIsOn
20* (from 1)
21* (from 2)
22* (from 5)
23* (from 6)
24 (from 17)
*requires existential import (EI) for validity

2. ∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => R P => Q P => R P Q R Q ^ ~R Q => P P ^ ~R
1 1 1 1 1 TRUE TRUE TRUE 13 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 FALSE TRUE FALSE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 TRUE FALSE TRUE 3 1 0 1 FALSE TRUE FALSE
4 1 0 0 TRUE FALSE FALSE 4 1 0 0 FALSE TRUE TRUE
5 0 1 1 TRUE TRUE TRUE 5 0 1 1 FALSE FALSE FALSE
6 0 1 0 FALSE TRUE TRUE 6 0 1 0 TRUE FALSE FALSE
7 0 0 1 TRUE TRUE TRUE 7 0 0 1 FALSE TRUE FALSE
8 0 0 0 TRUE TRUE TRUE 8 0 0 0 FALSE TRUE FALSE
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => ~Q P => R P => ~Q P Q R Q => ~R Q^P P ^ ~R
2 1 1 1 1 FALSE TRUE FALSE 14 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 TRUE FALSE FALSE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 TRUE TRUE TRUE 3 1 0 1 TRUE FALSE FALSE
4 1 0 0 TRUE FALSE TRUE 4 1 0 0 TRUE FALSE TRUE
5 0 1 1 FALSE TRUE TRUE 5 0 1 1 FALSE FALSE FALSE
6 0 1 0 TRUE TRUE TRUE 6 0 1 0 TRUE FALSE FALSE
7 0 0 1 TRUE TRUE TRUE 7 0 0 1 TRUE FALSE FALSE
8 0 0 0 TRUE TRUE TRUE 8 0 0 0 TRUE FALSE FALSE
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R P^Q P^R P Q R R => Q Q => P P^R
3 1 1 1 1 TRUE TRUE TRUE 15 1 1 1 1 TRUE TRUE TRUE
2 1 1 0 FALSE TRUE FALSE 2 1 1 0 TRUE TRUE FALSE
3 1 0 1 TRUE FALSE TRUE 3 1 0 1 FALSE TRUE TRUE
4 1 0 0 TRUE FALSE FALSE 4 1 0 0 TRUE TRUE FALSE
5 0 1 1 TRUE FALSE FALSE 5 0 1 1 TRUE FALSE FALSE
6 0 1 0 FALSE FALSE FALSE 6 0 1 0 TRUE FALSE FALSE
7 0 0 1 TRUE FALSE FALSE 7 0 0 1 FALSE TRUE FALSE
8 0 0 0 TRUE FALSE FALSE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => ~R P^Q P ^ ~R P Q R R^Q Q => P P^R
4 1 1 1 1 FALSE TRUE FALSE 16 1 1 1 1 TRUE TRUE TRUE
2 1 1 0 TRUE TRUE TRUE 2 1 1 0 FALSE TRUE FALSE
3 1 0 1 TRUE FALSE FALSE 3 1 0 1 FALSE TRUE TRUE
4 1 0 0 TRUE FALSE TRUE 4 1 0 0 FALSE TRUE FALSE
5 0 1 1 FALSE FALSE FALSE 5 0 1 1 TRUE FALSE FALSE
6 0 1 0 TRUE FALSE FALSE 6 0 1 0 FALSE FALSE FALSE
7 0 0 1 TRUE FALSE FALSE 7 0 0 1 FALSE TRUE FALSE
8 0 0 0 TRUE FALSE FALSE 8 0 0 0 FALSE TRUE FALSE
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∀
P Q R R => ~Q P => Q P => ~R P Q R R => Q Q => ~P P => ~R
5 1 1 1 1 FALSE TRUE FALSE 17 1 1 1 1 TRUE FALSE FALSE
2 1 1 0 TRUE TRUE TRUE 2 1 1 0 TRUE FALSE TRUE
3 1 0 1 TRUE FALSE FALSE 3 1 0 1 FALSE TRUE FALSE
4 1 0 0 TRUE FALSE TRUE 4 1 0 0 TRUE TRUE TRUE
5 0 1 1 FALSE TRUE TRUE 5 0 1 1 TRUE TRUE TRUE
6 0 1 0 TRUE TRUE TRUE 6 0 1 0 TRUE TRUE TRUE
7 0 0 1 TRUE TRUE TRUE 7 0 0 1 FALSE TRUE TRUE
8 0 0 0 TRUE TRUE TRUE 8 0 0 0 TRUE TRUE TRUE
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => Q P => ~Q P => ~R P Q R R => ~Q Q => P P ^ ~R
6 1 1 1 1 TRUE FALSE FALSE 18 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 TRUE FALSE TRUE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 FALSE TRUE FALSE 3 1 0 1 TRUE TRUE FALSE
4 1 0 0 TRUE TRUE TRUE 4 1 0 0 TRUE TRUE TRUE
5 0 1 1 TRUE TRUE TRUE 5 0 1 1 FALSE FALSE FALSE
6 0 1 0 TRUE TRUE TRUE 6 0 1 0 TRUE FALSE FALSE
7 0 0 1 FALSE TRUE TRUE 7 0 0 1 TRUE TRUE FALSE
8 0 0 0 TRUE TRUE TRUE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => Q P ^ ~Q P ^ ~R P Q R R => ~Q Q^P P ^ ~R
7 1 1 1 1 TRUE FALSE FALSE 19 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 TRUE FALSE TRUE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 FALSE TRUE FALSE 3 1 0 1 TRUE FALSE FALSE
4 1 0 0 TRUE TRUE TRUE 4 1 0 0 TRUE FALSE TRUE
5 0 1 1 TRUE FALSE FALSE 5 0 1 1 FALSE FALSE FALSE
6 0 1 0 TRUE FALSE FALSE 6 0 1 0 TRUE FALSE FALSE
7 0 0 1 FALSE FALSE FALSE 7 0 0 1 TRUE FALSE FALSE
8 0 0 0 TRUE FALSE FALSE 8 0 0 0 TRUE FALSE FALSE

3. ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => ~Q P^Q P ^ ~R P Q R Q => R P => Q P^R
8 1 1 1 1 FALSE TRUE FALSE 20 1 1 1 1 TRUE TRUE TRUE
2 1 1 0 TRUE TRUE TRUE 2 1 1 0 FALSE TRUE FALSE
3 1 0 1 TRUE FALSE FALSE 3 1 0 1 TRUE FALSE TRUE
4 1 0 0 TRUE FALSE TRUE 4 1 0 0 TRUE FALSE FALSE
5 0 1 1 FALSE FALSE FALSE 5 0 1 1 TRUE TRUE FALSE
6 0 1 0 TRUE FALSE FALSE 6 0 1 0 FALSE TRUE FALSE
7 0 0 1 TRUE FALSE FALSE 7 0 0 1 TRUE TRUE FALSE
8 0 0 0 TRUE FALSE FALSE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q => P P^R P Q R Q => ~R P => Q P ^ ~R
9 1 1 1 1 TRUE TRUE TRUE 21 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 FALSE TRUE FALSE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 TRUE TRUE TRUE 3 1 0 1 TRUE FALSE FALSE
4 1 0 0 TRUE TRUE FALSE 4 1 0 0 TRUE FALSE TRUE
5 0 1 1 TRUE FALSE FALSE 5 0 1 1 FALSE TRUE FALSE
6 0 1 0 FALSE FALSE FALSE 6 0 1 0 TRUE TRUE FALSE
7 0 0 1 TRUE TRUE FALSE 7 0 0 1 TRUE TRUE FALSE
8 0 0 0 TRUE TRUE FALSE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q^P P^R P Q R R => Q P => ~Q P ^ ~R
10 1 1 1 1 TRUE TRUE TRUE 22 1 1 1 1 TRUE FALSE FALSE
2 1 1 0 FALSE TRUE FALSE 2 1 1 0 TRUE FALSE TRUE
3 1 0 1 TRUE FALSE TRUE 3 1 0 1 FALSE TRUE FALSE
4 1 0 0 TRUE FALSE FALSE 4 1 0 0 TRUE TRUE TRUE
5 0 1 1 TRUE FALSE FALSE 5 0 1 1 TRUE TRUE FALSE
6 0 1 0 FALSE FALSE FALSE 6 0 1 0 TRUE TRUE FALSE
7 0 0 1 TRUE FALSE FALSE 7 0 0 1 FALSE TRUE FALSE
8 0 0 0 TRUE FALSE FALSE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q^R Q => P P^R P Q R R => ~Q P => Q P ^ ~R
11 1 1 1 1 TRUE TRUE TRUE 23 1 1 1 1 FALSE TRUE FALSE
2 1 1 0 FALSE TRUE FALSE 2 1 1 0 TRUE TRUE TRUE
3 1 0 1 FALSE TRUE TRUE 3 1 0 1 TRUE FALSE FALSE
4 1 0 0 FALSE TRUE FALSE 4 1 0 0 TRUE FALSE TRUE
5 0 1 1 TRUE FALSE FALSE 5 0 1 1 FALSE TRUE FALSE
6 0 1 0 FALSE FALSE FALSE 6 0 1 0 TRUE TRUE FALSE
7 0 0 1 FALSE TRUE FALSE 7 0 0 1 TRUE TRUE FALSE
8 0 0 0 FALSE TRUE FALSE 8 0 0 0 TRUE TRUE FALSE
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => ~R Q => P P ^ ~R P Q R R => Q Q => ~P P => ~R
12 1 1 1 1 FALSE TRUE FALSE 24 1 1 1 1 TRUE FALSE FALSE
2 1 1 0 TRUE TRUE TRUE 2 1 1 0 TRUE FALSE TRUE
3 1 0 1 TRUE TRUE FALSE 3 1 0 1 FALSE TRUE FALSE
4 1 0 0 TRUE TRUE TRUE 4 1 0 0 TRUE TRUE TRUE
5 0 1 1 FALSE FALSE FALSE 5 0 1 1 TRUE TRUE TRUE
6 0 1 0 TRUE FALSE FALSE 6 0 1 0 TRUE TRUE TRUE
7 0 0 1 TRUE TRUE FALSE 7 0 0 1 FALSE TRUE TRUE
8 0 0 0 TRUE TRUE FALSE 8 0 0 0 TRUE TRUE TRUE

4. ∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => R P => Q P => R P Q R Q ^ ~R Q => P P ^ ~R
1 1 1 1 1 1 1 1 13 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 1 0 1 3 1 0 1 0 1 0
4 1 0 0 1 0 0 4 1 0 0 0 1 1
5 0 1 1 1 1 1 5 0 1 1 0 0 0
6 0 1 0 0 1 1 6 0 1 0 1 0 0
7 0 0 1 1 1 1 7 0 0 1 0 1 0
8 0 0 0 1 1 1 8 0 0 0 0 1 0
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => ~Q P => R P => ~Q P Q R Q => ~R Q^P P ^ ~R
2 1 1 1 1 0 1 0 14 1 1 1 1 0 1 0
2 1 1 0 1 0 0 2 1 1 0 1 1 1
3 1 0 1 1 1 1 3 1 0 1 1 0 0
4 1 0 0 1 0 1 4 1 0 0 1 0 1
5 0 1 1 0 1 1 5 0 1 1 0 0 0
6 0 1 0 1 1 1 6 0 1 0 1 0 0
7 0 0 1 1 1 1 7 0 0 1 1 0 0
8 0 0 0 1 1 1 8 0 0 0 1 0 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R P^Q P^R P Q R R => Q Q => P P^R
3 1 1 1 1 1 1 1 15 1 1 1 1 1 1 1
2 1 1 0 0 1 0 2 1 1 0 1 1 0
3 1 0 1 1 0 1 3 1 0 1 0 1 1
4 1 0 0 1 0 0 4 1 0 0 1 1 0
5 0 1 1 1 0 0 5 0 1 1 1 0 0
6 0 1 0 0 0 0 6 0 1 0 1 0 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => ~R P^Q P ^ ~R P Q R R^Q Q => P P^R
4 1 1 1 1 0 1 0 16 1 1 1 1 1 1 1
2 1 1 0 1 1 1 2 1 1 0 0 1 0
3 1 0 1 1 0 0 3 1 0 1 0 1 1
4 1 0 0 1 0 1 4 1 0 0 0 1 0
5 0 1 1 0 0 0 5 0 1 1 1 0 0
6 0 1 0 1 0 0 6 0 1 0 0 0 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 0 1 0
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∀
P Q R R => ~Q P => Q P => ~R P Q R R => Q Q => ~P P => ~R
5 1 1 1 1 0 1 0 17 1 1 1 1 1 0 0
2 1 1 0 1 1 1 2 1 1 0 1 0 1
3 1 0 1 1 0 0 3 1 0 1 0 1 0
4 1 0 0 1 0 1 4 1 0 0 1 1 1
5 0 1 1 0 1 1 5 0 1 1 1 1 1
6 0 1 0 1 1 1 6 0 1 0 1 1 1
7 0 0 1 1 1 1 7 0 0 1 0 1 1
8 0 0 0 1 1 1 8 0 0 0 1 1 1
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => Q P => ~Q P => ~R P Q R R => ~Q Q => P P ^ ~R
6 1 1 1 1 1 0 0 18 1 1 1 1 0 1 0
2 1 1 0 1 0 1 2 1 1 0 1 1 1
3 1 0 1 0 1 0 3 1 0 1 1 1 0
4 1 0 0 1 1 1 4 1 0 0 1 1 1
5 0 1 1 1 1 1 5 0 1 1 0 0 0
6 0 1 0 1 1 1 6 0 1 0 1 0 0
7 0 0 1 0 1 1 7 0 0 1 1 1 0
8 0 0 0 1 1 1 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => Q P ^ ~Q P ^ ~R P Q R R => ~Q Q^P P ^ ~R
7 1 1 1 1 1 0 0 19 1 1 1 1 0 1 0
2 1 1 0 1 0 1 2 1 1 0 1 1 1
3 1 0 1 0 1 0 3 1 0 1 1 0 0
4 1 0 0 1 1 1 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 0 0
6 0 1 0 1 0 0 6 0 1 0 1 0 0
7 0 0 1 0 0 0 7 0 0 1 1 0 0
8 0 0 0 1 0 0 8 0 0 0 1 0 0

5. ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => ~Q P^Q P ^ ~R P Q R Q => R P => Q P^R
8 1 1 1 1 0 1 0 20 1 1 1 1 1 1 1
2 1 1 0 1 1 1 2 1 1 0 0 1 0
3 1 0 1 1 0 0 3 1 0 1 1 0 1
4 1 0 0 1 0 1 4 1 0 0 1 0 0
5 0 1 1 0 0 0 5 0 1 1 1 1 0
6 0 1 0 1 0 0 6 0 1 0 0 1 0
7 0 0 1 1 0 0 7 0 0 1 1 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q => P P^R P Q R Q => ~R P => Q P ^ ~R
9 1 1 1 1 1 1 1 21 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 1 1 1 3 1 0 1 1 0 0
4 1 0 0 1 1 0 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 1 1 0 7 0 0 1 1 1 0
8 0 0 0 1 1 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q^P P^R P Q R R => Q P => ~Q P ^ ~R
10 1 1 1 1 1 1 1 22 1 1 1 1 1 0 0
2 1 1 0 0 1 0 2 1 1 0 1 0 1
3 1 0 1 1 0 1 3 1 0 1 0 1 0
4 1 0 0 1 0 0 4 1 0 0 1 1 1
5 0 1 1 1 0 0 5 0 1 1 1 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q^R Q => P P^R P Q R R => ~Q P => Q P ^ ~R
11 1 1 1 1 1 1 1 23 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 0 1 1 3 1 0 1 1 0 0
4 1 0 0 0 1 0 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 0 1 0 7 0 0 1 1 1 0
8 0 0 0 0 1 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => ~R Q => P P ^ ~R P Q R R => Q Q => ~P P => ~R
12 1 1 1 1 0 1 0 24 1 1 1 1 1 0 0
2 1 1 0 1 1 1 2 1 1 0 1 0 1
3 1 0 1 1 1 0 3 1 0 1 0 1 0
4 1 0 0 1 1 1 4 1 0 0 1 1 1
5 0 1 1 0 0 0 5 0 1 1 1 1 1
6 0 1 0 1 0 0 6 0 1 0 1 1 1
7 0 0 1 1 1 0 7 0 0 1 0 1 1
8 0 0 0 1 1 0 8 0 0 0 1 1 1

6. ∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => R P => Q P => R P Q R Q ^ ~R Q => P P ^ ~R
1 1 1 1 1 1 1 1 13 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 1 0 1 3 1 0 1 0 1 0
4 1 0 0 1 0 0 4 1 0 0 0 1 1
5 0 1 1 1 1 1 5 0 1 1 0 0 0
6 0 1 0 0 1 1 6 0 1 0 1 0 0
7 0 0 1 1 1 1 7 0 0 1 0 1 0
8 0 0 0 1 1 1 8 0 0 0 0 1 0
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => ~Q P => R P => ~Q P Q R Q => ~R Q^P P ^ ~R
2 1 1 1 1 0 1 0 14 1 1 1 1 0 1 0
2 1 1 0 1 0 0 2 1 1 0 1 1 1
3 1 0 1 1 1 1 3 1 0 1 1 0 0
4 1 0 0 1 0 1 4 1 0 0 1 0 1
5 0 1 1 0 1 1 5 0 1 1 0 0 0
6 0 1 0 1 1 1 6 0 1 0 1 0 0
7 0 0 1 1 1 1 7 0 0 1 1 0 0
8 0 0 0 1 1 1 8 0 0 0 1 0 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R P^Q P^R P Q R R => Q Q => P P^R
3 1 1 1 1 1 1 1 15 1 1 1 1 1 1 1
2 1 1 0 0 1 0 2 1 1 0 1 1 0
3 1 0 1 1 0 1 3 1 0 1 0 1 1
4 1 0 0 1 0 0 4 1 0 0 1 1 0
5 0 1 1 1 0 0 5 0 1 1 1 0 0
6 0 1 0 0 0 0 6 0 1 0 1 0 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∃ ∀ ∃
P Q R Q => ~R P^Q P ^ ~R P Q R R^Q Q => P P^R
4 1 1 1 1 0 1 0 16 1 1 1 1 1 1 1
2 1 1 0 1 1 1 2 1 1 0 0 1 0
3 1 0 1 1 0 0 3 1 0 1 0 1 1
4 1 0 0 1 0 1 4 1 0 0 0 1 0
5 0 1 1 0 0 0 5 0 1 1 1 0 0
6 0 1 0 1 0 0 6 0 1 0 0 0 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 0 1 0
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∀
P Q R R => ~Q P => Q P => ~R P Q R R => Q Q => ~P P => ~R
5 1 1 1 1 0 1 0 17 1 1 1 1 1 0 0
2 1 1 0 1 1 1 2 1 1 0 1 0 1
3 1 0 1 1 0 0 3 1 0 1 0 1 0
4 1 0 0 1 0 1 4 1 0 0 1 1 1
5 0 1 1 0 1 1 5 0 1 1 1 1 1
6 0 1 0 1 1 1 6 0 1 0 1 1 1
7 0 0 1 1 1 1 7 0 0 1 0 1 1
8 0 0 0 1 1 1 8 0 0 0 1 1 1
∃ ∃ ∃ ∀ ∀ ∀ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => Q P => ~Q P => ~R P Q R R => ~Q Q => P P ^ ~R
6 1 1 1 1 1 0 0 18 1 1 1 1 0 1 0
2 1 1 0 1 0 1 2 1 1 0 1 1 1
3 1 0 1 0 1 0 3 1 0 1 1 1 0
4 1 0 0 1 1 1 4 1 0 0 1 1 1
5 0 1 1 1 1 1 5 0 1 1 0 0 0
6 0 1 0 1 1 1 6 0 1 0 1 0 0
7 0 0 1 0 1 1 7 0 0 1 1 1 0
8 0 0 0 1 1 1 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∃ ∃
P Q R R => Q P ^ ~Q P ^ ~R P Q R R => ~Q Q^P P ^ ~R
7 1 1 1 1 1 0 0 19 1 1 1 1 0 1 0
2 1 1 0 1 0 1 2 1 1 0 1 1 1
3 1 0 1 0 1 0 3 1 0 1 1 0 0
4 1 0 0 1 1 1 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 0 0
6 0 1 0 1 0 0 6 0 1 0 1 0 0
7 0 0 1 0 0 0 7 0 0 1 1 0 0
8 0 0 0 1 0 0 8 0 0 0 1 0 0

7. ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R R => ~Q P^Q P ^ ~R P Q R Q => R P => Q P^R
8 1 1 1 1 0 1 0 20 1 1 1 1 1 1 1
2 1 1 0 1 1 1 2 1 1 0 0 1 0
3 1 0 1 1 0 0 3 1 0 1 1 0 1
4 1 0 0 1 0 1 4 1 0 0 1 0 0
5 0 1 1 0 0 0 5 0 1 1 1 1 0
6 0 1 0 1 0 0 6 0 1 0 0 1 0
7 0 0 1 1 0 0 7 0 0 1 1 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q => P P^R P Q R Q => ~R P => Q P ^ ~R
9 1 1 1 1 1 1 1 21 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 1 1 1 3 1 0 1 1 0 0
4 1 0 0 1 1 0 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 1 1 0 7 0 0 1 1 1 0
8 0 0 0 1 1 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => R Q^P P^R P Q R R => Q P => ~Q P ^ ~R
10 1 1 1 1 1 1 1 22 1 1 1 1 1 0 0
2 1 1 0 0 1 0 2 1 1 0 1 0 1
3 1 0 1 1 0 1 3 1 0 1 0 1 0
4 1 0 0 1 0 0 4 1 0 0 1 1 1
5 0 1 1 1 0 0 5 0 1 1 1 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 1 0 0 7 0 0 1 0 1 0
8 0 0 0 1 0 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∃ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q^R Q => P P^R P Q R R => ~Q P => Q P ^ ~R
11 1 1 1 1 1 1 1 23 1 1 1 1 0 1 0
2 1 1 0 0 1 0 2 1 1 0 1 1 1
3 1 0 1 0 1 1 3 1 0 1 1 0 0
4 1 0 0 0 1 0 4 1 0 0 1 0 1
5 0 1 1 1 0 0 5 0 1 1 0 1 0
6 0 1 0 0 0 0 6 0 1 0 1 1 0
7 0 0 1 0 1 0 7 0 0 1 1 1 0
8 0 0 0 0 1 0 8 0 0 0 1 1 0
∃ ∃ ∃ ∀ ∀ ∃ ∃ ∃ ∃ ∀ ∀ ∃
P Q R Q => ~R Q => P P ^ ~R P Q R R => Q Q => ~P P => ~R
12 1 1 1 1 0 1 0 24 1 1 1 1 1 0 0
2 1 1 0 1 1 1 2 1 1 0 1 0 1
3 1 0 1 1 1 0 3 1 0 1 0 1 0
4 1 0 0 1 1 1 4 1 0 0 1 1 1
5 0 1 1 0 0 0 5 0 1 1 1 1 1
6 0 1 0 1 0 0 6 0 1 0 1 1 1
7 0 0 1 1 1 0 7 0 0 1 0 1 1
8 0 0 0 1 1 0 8 0 0 0 1 1 1