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ex7d-proof-general.txt
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ex7d-proof-general.txt
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> TELL P1
> TELL Q1 ^ R1
> TELL (P1 ^ R1) => S1
> PROOF P1 ^ S1
Proof:
1. P1 [Premise]
2. R1 [Premise]
3. ~P1 v ~R1 v S1 [Premise]
4. ~P1 v ~S1 [Negated Goal]
5. ~P1 v ~R1 [Resolution on S1: 3, 4]
6. ~P1 [Resolution on R1: 2, 5]
7. () [Resolution on P1: 1, 6]
> TELL P2 => ~(Q2 v R2)
> TELL (~Q2 ^ ~R2) => S2
> PROOF P2 => S2
Proof:
1. ~P2 v ~Q2 [Premise]
2. ~P2 v ~R2 [Premise]
3. Q2 v R2 v S2 [Premise]
4. P2 [Negated Goal]
5. ~S2 [Negated Goal]
6. ~Q2 [Resolution on P2: 1, 4]
7. ~R2 [Resolution on P2: 2, 4]
8. Q2 v R2 [Resolution on S2: 3, 5]
9. Q2 [Resolution on R2: 7, 8]
10. () [Resolution on Q2: 6, 9]
> TELL P3 => (S3 ^ ~U3)
> TELL U3
> PROOF ~P3
Proof:
1. ~P3 v ~U3 [Premise]
2. U3 [Premise]
3. P3 [Negated Goal]
4. ~U3 [Resolution on P3: 1, 3]
5. () [Resolution on U3: 2, 4]
> TELL (~P4 v Q4) => R4
> TELL S4 v ~Q4
> TELL ~U4
> TELL P4 => U4
> TELL (~P4 ^ R4) => ~S4
> PROOF ~Q4
Proof:
1. P4 v R4 [Premise]
2. ~Q4 v S4 [Premise]
3. ~U4 [Premise]
4. ~P4 v U4 [Premise]
5. P4 v ~R4 v ~S4 [Premise]
6. Q4 [Negated Goal]
7. P4 v ~S4 [Resolution on R4: 1, 5]
8. S4 [Resolution on Q4: 2, 6]
9. ~P4 [Resolution on U4: 3, 4]
10. ~S4 [Resolution on P4: 7, 9]
11. () [Resolution on S4: 8, 10]