Official Rules of Basic WFF 'N PROOF

Strategies of Adventurous WFF 'N PROOF
© Layman E. Allen 2002
Professor of Law & Senior Research Scientist, University of Michigan

This is a 24-example learning program for becoming aware of some of the most powerful strategies for playing Adventurous WFF 'N PROOF. If you work your way carefully through this exercise and understand each of the responses that are suggested as the appropriate answers, you will be well on your way to becoming a player of Adventurous WFF 'N PROOF to be reckoned with.

Summary of Strategic Principles and Definitions

**Adventurous WFF 'N PROOF: Strategic Principles**
Strategic Principle #1: BAF	Strategic Principle #2: SSU
Setting a tautology as the Goal is a Bold A-Flub, IF AND ONLY IF, there is an R in the remaining Resources and the Mover who set the Goal challenges the next move as a CA-Flub. A Mover makes a Bold A-Flub when that Mover makes an A-Flub move and then challenges the next Mover for making a CA-Flub.	A Mover makes a Sneaky Snuggle-Up move, IF AND ONLY IF, the next Mover can make an A-Flub move.

**Tautology: Definition**
A tautology is a theorm, that is, the WFF that is the final conclusion of a Proof that does not have any premisses. Return to Summary.

Summary of Strategies

**Examples of Bold A-Flub (BAF)and Sneaky Snuggle-Up (SSU) Strategies**
B1	B2	B3	B4	B5	B6
B7	B8	S9	S10	S11	S12
S13	S14	S15	S16	S17	S18
S19	S20	S21	S22	S23	S24

BAF B1

**Bold A-Flub B1**
Resources AAKKKNRRR ppqr	What Goal from the Resources in the column to the left would be a Bold A-Flub? For the appropriate answer, click here: B1 BAF

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**STRONG ADVICE FOR LEARNING THIS STUFF**
Write out your answers in full on a sheet of paper to each of the questions asked in order as they are asked before clicking on the highlighted answers.

BAF B2

**Bold A-Flub B2**
Resources CCCCNRRR pppqrs	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B2 BAF

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BAF B3

**Bold A-Flub B3**
Resources CCCKRRR pppq	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B3 BAF

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BAF B4

**Bold A-Flub B4**
Resources ACCCCR ppq	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B4 BAF

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**STRONG ADVICE FOR LEARNING THIS STUFF**
Write out your answers in full on a sheet of paper to each of the questions asked in order as they are asked before clicking on the highlighted answers.

BAF B5

**Bold A-Flub B5**
Resources EEEENRR pppqrs	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B5 BAF

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BAF B6

**Bold A-Flub B6**
Resources KNNRRR ppppqqrs	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B6 BAF

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BAF B7

**Bold A-Flub B7**
Resources EEENNNR pppqqrs	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B7 BAF

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**STRONG ADVICE FOR LEARNING THIS STUFF**
Write out your answers in full on a sheet of paper to each of the questions asked in order as they are asked before clicking on the highlighted answers.

BAF B8

**Bold A-Flub B8**
Resources CKNRRR ppppq	What Goal from the Resources in the column to the left would be a Bold A-Flub? See B8 BAF

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SSU S9

**Sneaky Snuggle-Up S9**
Resources NRRR ppqqrrsss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S9 SSU

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SSU S10

**Sneaky Snuggle-Up S10**
Resources NNNRRR ppqqqrrss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S10 SSU

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SSU S11

**Sneaky Snuggle-Up S11**
Resources ARRR ppqqrrrrs	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S11 SSU

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SSU S12

**Sneaky Snuggle-Up S12**
Resources AKRRR pprrssss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S12 SSU

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SSU S13

**Sneaky Snuggle-Up S13**
Resources ACRRR ppqrrsss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S13 SSU

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SSU S14

**Sneaky Snuggle-Up S14**
Resources AERRR ppppqs	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S14 SSU

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SSU S15

**Sneaky Snuggle-Up S15**
Resources AARRR ppqrrrsss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S15 SSU

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SSU S16

**Sneaky Snuggle-Up S16**
Resources AAARRR ppqrssss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S16 SSU

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**Sneaky Snuggle-Up S17**
Resources CRRR ppqrrsss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S17 SSU

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SSU S18

**Sneaky Snuggle-Up S18**
Resources CNRRR ppqrrrss	What Goal from the in the column to the left Resources would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S18 SSU

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SSU S19

**Sneaky Snuggle-Up S19**
Resources CKRRR ppqrrrsss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S19 SSU

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SSU S20

**Sneaky Snuggle-Up S20**
Resources CKKRRR ppqrssss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S20 SSU

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SSU S21

**Sneaky Snuggle-Up S21**
Resources KNNRRR ppqqrrss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S21 SSU

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SSU S22

**Sneaky Snuggle-Up S22**
Resources EKNNRRR ppqrrrss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S22 SSU

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SSU S23

**Sneaky Snuggle-Up S23**
Resources KKNNRRR ppqrrrss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S23 SSU

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SSU S24

**Sneaky Snuggle-Up S24**
Resources CKNNRRR pprssss	What Goal from the Resources in the column to the left would allow the next Mover to make an A-Flub? In other words, what Goal would be a Sneaky Snuggle-Up. See S24 SSU

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This is the last example in this 24-example learning program for becoming aware of some of the most powerful strategies for playing Adventurous WFF 'N PROOF. If you work your way carefully through this exercise and understand each of the responses that are suggested as the appropriate answers, you will be well on your way to becoming a player of Adventurous WFF 'N PROOF to be reckoned with.

S24 SSU

**Appropriate Answer for the Goal to the S24 Sneaky Snuggle-Up Problem**
Resources CKNNRRR pprssss Remaining Resources RRR rsss	Goal CKNNpps If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of CKNNpps creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S24 Flub-Resource-Solution-Proof

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S23 SSU

**Appropriate Answer for the Goal to the S23 Sneaky Snuggle-Up Problem**
Resources KKNNRRR ppqrrrss Remaining Resources RRR qrrss	Goal KNKNppr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of KNKNppr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S23 Flub-Resource-Solution-Proof

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S22 SSU

**Appropriate Answer for the Goal to the S22 Sneaky Snuggle-Up Problem**
Resources EKNNRRR ppqrrrss Remaining Resources RRR qrrss	Goal KENNppr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of KENNppr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S22 Flub-Resource-Solution-Proof

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S21 SSU

**Appropriate Answer for the Goal to the S21 Sneaky Snuggle-Up Problem**
Resources KNNRRR ppqqrrss Remaining Resources RRR pqrrss	Goal NKNpq If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of NKNpq creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S21 Flub-Resource-Solution-Proof

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S20 SSU

**Appropriate Answer for the Goal to the S20 Sneaky Snuggle-Up Problem**
Resources CKKRRR ppqrssss Remaining Resources RRR rsss	Goal CKKppqs If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of CKKppqs creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S20 Flub-Resource-Solution-Proof

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S19 SSU

**Appropriate Answer for the Goal to the S19 Sneaky Snuggle-Up Problem**
Resources CKRRR ppqrrrsss Remaining Resources RRR qrrsss	Goal CKppr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of CKppr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S19 Flub-Resource-Solution-Proof

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S18 SSU

**Appropriate Answer for the Goal to the S18 Sneaky Snuggle-Up Problem**
Resources CNRRR ppqrrrss Remaining Resources RRR pqrrss	Goal CNpr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of CNpr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S18 Flub-Resource-Solution-Proof

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S17 SSU

**Appropriate Answer for the A-Flub S17 Sneaky Snuggle-Up Problem**
Resources CRRR ppqrrsss Remaining Resources RRR pqrsss	Goal Cpr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of Cpr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S17 Flub-Resource-Solution-Proof

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S16 SSU

**Appropriate Answer for the Goal to the S16 Sneaky Snuggle-Up Problem**
Resources AAARRR ppqrssss Remaining Resources RRR rsss	Goal AAAppqs If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of AAAppqs creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S16 Flub-Resource-Solution-Proof

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S15 SSU

**Appropriate Answer for the Goal to the S15 Sneaky Snuggle-Up Problem**
Resources AARRR ppqrrrsss Remaining Resources RRR qrrsss	Goal AAppr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of AAppr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S15 Flub-Resource-Solution-Proof

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S14 SSU

**Appropriate Answer for the Goal to the S14 Sneaky Snuggle-Up Problem**
Resources AERRR ppppqs Remaining Resources RRR pps	Goal AEpqp * * AEppp is alphabetically prior to AEpqp, but it is a tautology.	Setting the Goal of AEpqp creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S14 Flub-Resource-Solution-Proof

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S13 SSU

**Appropriate Answer for the Goal to the S13 Sneaky Snuggle-Up Problem**
Resources ACRRR ppqrrsss Remaining Resources RRR prsss	Goal ACpqr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of ACprs creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S13 Flub-Resource-Solution-Proof

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S12 SSU

**Appropriate Answer for the Goal to the S12 Sneaky Snuggle-Up Problem**
Resources AKRRR pprrssss Remaining Resources RRR rssss	Goal AKppr If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of AKppr creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S12 Flub-Resource-Solution-Proof

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S11 SSU

**Appropriate Answer for the Goal to the S11 Sneaky Snuggle-Up Problem**
Resources ARRR ppqqrrrrs Remaining Resources RRR pqrrrrs	Goal Apq If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of Apq creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S11 Flub-Resource-Solution-Proof

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S10 SSU

**Appropriate Answer for the Goal to the S10 Sneaky Snuggle-Up Problem**
Resources NNNRRR ppqqqrrss Remaining Resources NRRR pqqqrrss	Goal NNp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of NNp creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S10 Flub Resource-Solution-Proof

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S9 SSUN

**Appropriate Answer for the Goal to the S9 Sneaky Snuggle-Up Problem**
Resources NRRR ppqqrrsss Remaining Resources NRRR pqqrrsss	Goal p If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Setting the Goal of p creates a situation where the next mover can make an A-Flub. Which one of the Remaining Resources moved where would be an A-Flub? After that A-Flub, which of the then remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See S9 Flub-Resource-Solution-Proof

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B8 BAF

**Appropriate Answer for the Goal to the B8 Bold A-Flub Problem**
Resources CKNRRR ppppq Remaining Resources RRR pq	Goal CKNppp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B8 Resource-Solution-Proof

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B7 BAF

**Appropriate Answer for the Goal to the B7 Bold A-Flub Problem**
Resources EEENNNR pppqqrs Remaining Resources NR prs	Goal EENpqENpq If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B7 Resource-Solution-Proof

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B6 BAF

**Appropriate Answer for the Goal to the B6 Bold A-Flub Problem**
Resources KNNRRR ppppqqrs Remaining Resources RRR ppqqrs	Goal NKNpp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B6 Resource-Solution-Proof

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B5 BAF

**Appropriate Answer for the Goal to the B5 Bold A-Flub Problem**
Resources EEEENRR pppqrs Remaining Resources EEENRR pqrs	Goal Epp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B5 Resource-Solution-Proof

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B4 BAF

**Appropriate Answer for the Goal to the B4 Bold A-Flub Problem**
Resources ACCCCR ppq Remaining Resources CCCR	Goal ACppq If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B4 Resource-Solution-Proof

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B3 BAF

**Appropriate Answer for the Goal to the B3 Bold A-Flub Problem**
Resources CCCKRRR pppq Remaining Resources CRRR	Goal CKCpqpp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B3 Resource-Solution-Proof

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B2 BAF

**Appropriate Answer for the Goal to the B2 Bold A-Flub Problem**
Resources CCCCNRRR pppqrs Remaining Resources RRR s	Goal CpCCCNpqrp If your Goal differs from the suggested one, check to see which is alphabetically-prior.	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? See B2 Resource-Solution-Proof

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B1 BAF

**Appropriate Answer for the Goal to the B1 Bold A-Flub Problem**
Resources AAKKKNRRR ppqr Remaining Resources KKRRR	Goal AANppKqr *	Which one of the Remaining Resources would enable the construction of a Solution and Proof of that Solution? What is the Solution? What is the Proof? For suggested answers to these questions, see B1 Resource-Solution-Proof

* Note
For purposes of each of the 24 exercises in this learning program, assume that the Goals to be set can use up to 11 Resources. Given that extension of the usual 7-Resource Goal limitation in WFF 'N PROOF, each of AANppKrq, AANppq, AANppr, AApNpKqr, AApNpKrq, AApNpq, AApNpr, AKqrANpp, AKqrApNp, AKrqANpp, AKrqANpp, ANpp, AqANpp, AqApNp, ArANpp, ArApNp, and ApNp are also tautologies that could work as Bold A-Flubs in this first exercise when set as the Goal from the Resources available. Throughout this learning program about strategies for playing Adventurous WFF 'N PROOF, the alphabetically-prior equivalent alternative tautology will be the one presented as the appropriate answer. The 17 alternative A-Flub tautologies presented above are in their alphabetically-prior order. The AANppKqr is given as the appropriate answer here because it is alphabetically-prior to the 17 other alternatives. It is alphabetically-prior to them because its first seven characters, AANppKq, are alphabetically-prior to the first seven letters of all of the alternatives. For example, AANppKqr is alphabetically-prior to AANppKrq, because its Kqr is alphabetically-prior to the Krq in AANppKrq.

The chances are considerably less than 1 in 18 that you selected the tautology for the Goal that matches the one that was specified as the appropriate answer in Example B1. However, now that you know what is expected, you should be able to do better in selecting the Goal and, furthermore, to continue to improve as you go along.

**Urgent Request**
It will be little short of miraculous if everywhere throughout this program there is not some alphabetically-prior expression overlooked as the appropriate answer. If you believe that your Bold A-Flub expression is alphabetically-prior to the one given, PLEASE communicate your expression to me at laymanal@umich.edu so that it can replace the one given if it is, indeed, alphabetically-prior. Those who furnish successful replacements will be explicitly recognized by name in the program for doing so. Any other suggestions for improvement of the program, including typographical errors, are also welcome. ... Layman E. Allen

See B1 Resource-Solution-Proof Back to Main Menu

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S24 Flub-Resource-Solution-Proof


A-Flub Move s to Premisses or Essential, or R to Rules or Essential	Resource s or R whichever one was not used to make the A-Flub	Solution s/R(PRS24) Goal CKNNpps	Proof `PRS24\| s --** CKNNpps` `-----+----------------` `1\|_s s` `2\|a\|_KNNpp s` `\|b\| s 1R` `3\| CKNNprs 2,Ci` You are all done!

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S23 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS23) Goal KNKNppr	Proof `PRS23\| r --** KNKNppr` `-----+----------------` `1\|_r s` `2\|a\|_KNpp s` `\|b\| p 1R` `\|c\| Np a,Ko` `3\| NKNpp 2,Ni` `4\| KNKNppr 3,1,Ki` `Go to SSU S24`

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S22 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS22) Goal KENNppr	Proof `PRS22\| r --** KENNppr` `-----+----------------` `1\|_r s` `2\|a\|_Npp s` `\|b\| p a,NNo` `3\| CNNpp 2,Ci` `4\|a\|_p s` `\|b\| NNp a,NNi` `5\| CpNNp 4,Ci` `6\| ENpp 3,5,Ei` `7\| KENNppr 6,1,Ki` `Go to SSU S23`

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S21 Flub-Resource-Solution-Proof


A-Flub Move p to Premisses or Essential, or R to Rules or Essential	Resource p or R whichever one was not used to make the A-Flub	Solution p/R(PRS21) Goal NKNpq	Proof `PRS21\| p --** NKNpq` `-----+-------------` `1\|_p s` `2\|a\|_KNpq s` `\|b\| p 1R` `\|c\| Np a,Ko` `3\| NKNpq 2,Ni` `Go to SSU S22`

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S20 Flub-Resource-Solution-Proof


A-Flub Move s to Premisses or Essential, or R to Rules or Essential	Resource s or R whichever one was not used to make the A-Flub	Solution s/R(PRS20) Goal CKKppqs	Proof `PRS20\| s --** CKKppqs` `-----+---------------` `1\|_s s` `2\|a\|_KKppq s` `\|b\| s 1R` `3\| CKKppqs 2,Ci` `Go to SSU S21`

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S19 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS19) Goal CKppr	Proof `PRS19\| r --** CKppr` `-----+-------------` `1\|_r s` `2\|a\|_Kpp s` `\|b\| r 1R` `3\| CKppr 2,Ci` `Go to SSU S20`

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S18 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS18) Goal CNpr	Proof `PRS18\| r --** CNpr` `-----+------------` `1\|_r s` `2\|a\|_Np s` `\|b\| r 1R` `3\| CNpr 2,Ci` `Go to SSU S19`

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S17 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS17) Goal Cpr	Proof `PRS17\| r --** Cpr` `-----+-----------` `1\|_r s` `2\|a\|_p s` `\|b\| r 1R` `3\| Cpr 2,Ci` `Go to SSU S18`

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S16 Flub-Resource-Solution-Proof


A-Flub Move s to Premisses or Essential, or R to Rules or Essential	Resource s or R whichever one was not used to make the A-Flub	Solution s/R(PRS16) Goal AAAppqs	Proof `PRS16\| s --** AAAppqs` `-----+---------------` `1\|_s s` `2\| AAAppqs 1,Ai` `Go to SSU S17`

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S15 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS15) Goal `AAppr`	Proof `PRS15\| r --** AAppr` `-----+-------------` `1\|_r s` `2\| AAppr 1,Ai` `Go to SSU S16`

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S14 Flub-Resource-Solution-Proof


A-Flub Move p to Premisses or Essential, or R to Rules or Essential	Resource p or R whichever one was not used to make the A-Flub	Solution p/R(PRS14) Goal `AEpqp`	Proof `PRS14\| p --** AEpqp` `-----+-------------` `1\|_p s` `2\| AEpqp 1,Ai` `Go to SSU S15`

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S13 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS13) Goal ACpqr	Proof `PRS13\| r --** ACpqr` `-----+-------------` `1\|_r s` `2\| ACpqr 1,Ai` `Go to SSU S14`

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S12 Flub-Resource-Solution-Proof


A-Flub Move r to Premisses or Essential, or R to Rules or Essential	Resource r or R whichever one was not used to make the A-Flub	Solution r/R(PRS12) Goal AKppr	Proof `PRS12\| r --** AKppr` `-----+-------------` `1\|_r s` `2\| AKppr 1,Ai` `Go to SSU S13`

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S11 Flub-Resource-Solution-Proof


A-Flub Move p to Premisses or Essential, or R to Rules or Essential	Resource p or R whichever one was not used to make the A-Flub	Solution p/R(PRS11) Goal Apq	Proof `PRS11\| p --**` Apq `-----+-----------` `1\|_p s` `2\| Apq 1,Ai` `Go to SSU S12`

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S10 Flub-Resource-Solution-Proof


A-Flub Move p to Premisses or Essential, or R to Rules or Essential	Resource p or R whichever one was not used to make the A-Flub	Solution p/R(PRS10) Goal NNp	Proof `PRS10\| p --** NNp` `-----+------------` `1\|_p s` `2\| NNp 1,NNi` `Go to SSU S11`

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S9 Flub-Resource-Solution-Proof


A-Flub Move p to Premisses or Essential, or R to Rules or Essential	Resource p or R whichever one was not used to make the A-Flub	Solution p/R(PRS9) Goal p	Proof `PRS9\| p --** p` `----+---------` `1\|_p s` `2\| p 1,Rp` `Go to SSU S10`

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B8 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B8 Problem**
Remaining Resources RRR pq Solution Resource R	Solution /R(PRB8) Goal `CKNppp`	Proof `PRB8\| --** CKNppp` `----+---------------` `1\|a\|_KNpp s` `\|b\|1\|_Np s` `\| \|2\| p aR,Ko` `\| \|3\| Np aR,Ko` `\|e\| p d,No` `2\| CKNppp 1,Ci` Go to SSU S9

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B7 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B7 Problem**
Remaining Resources NR prs Solution Resource R	Solution /R(PRB7) Goal EENpqENpq	Proof of Proof-Rule B7 `PRB7\| --** EENpqENpq` `----+-------------------` `1\|a\|_ENpq s` `\|b\| ENpq a,Rp` `2\| ENpq 1,Ci` `3\| ENpq 1,Ci` `4\| EENpqENpq 2,3,Ei` Go to BAF B8

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B6 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B6 Problem**
Remaining Resources RRR ppqrs Solution Resource R	Solution /R(PRB6) Goal NKNpp	Proof of Proof-Rule B6 `PRB6\| --** NKNpp` `----+--------------` `1\|a\|_KNpp s` `\|b\| p a,Ko` `\|c\| Np a,Ko` `2\| NKNpp 1,Ni` Go to BAF B7

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B5 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B5 Problem**
Remaining Resources EEENRR pqrs Solution Resource R	Solution /R(PRB5) Goal Epp	Proof of Proof-Rule B5 `PRB5\| --** Epp` `----+-------------` `1\|a\|_p s` `\|b\| p a,Rp` `2\| Cpp 1,Ci` `3\| Cpp 2,Rp` `4\| Epp 2,3,Ei` Go to BAF B6

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B4 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B4 Problem**
Remaining Resources CCCR Solution Resource R	Solution /R(PRB4) Goal ACppq	Proof `PRB4\| --** ACppq` `----+------------` `1\|a\|_p s` `\|b\| p a,Rp` `2\| Cpp 1,Ci` `3\| ACppq` Go to BAF B5

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B3 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B3 Problem**
Remaining Resources CRRR Solution Resource R	Solution /R(PRB3) Goal CKCpqpp	Proof `PRB3\| --** CKCpqpp` `----+--------------` `1\|a\|_KCpqp s` `\|b\| p a,Ko` `2\| CKCpqpp 1,Ci` Go to BAF B4

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B2 Resource-Solution-Proof

**Appropriate Answers for the Resource, Solution, and Proof to the B2 Problem**
Remaining Resources RRR s Solution Resource R	Solution /R(PRB2) Goal CpCCCNpqrp	Proof `PRB2\| --** CpCCCNpqrp` `----+-----------------` `1\|a\|_p s` `\|b\|1\|_CCNpqr s` `\| \|2\| p aR` `\|c\| CCCNpqrp b,Ci` `2\| CpCCCNpqrp 1,Ci` Go to BAF B3

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B1 Resource-Solution-Proof

**Tabular Summary of a Sample Proof**
Tabular Summary of Sample Proof `Name \|` `of \|Statement of Rule or Theorm` `Proof\| tobe Proved` `PRB# \| --** ANpp` `-----+----------------` `1\|a\|_NANpp s` `\|b\| KpNp a,NAKi` `\|c\| p b,Ko` `\|d\| Np b,Ko` `2\| ANpp 1,No`	Justification of Proof `s` `a,NAoKi` `b,Ko` `b,Ko` `1,No`	Itemization of Proof `1 a` `b` `c` `d` `2`	The Proof `(With its subproof (1) and its WFFs (1a, 1b, 1c, 1d, and 2))` `\| \|_NANpp` `\| \| KpNp` `\| \| p` `\| \| Np` `\| ANpp`

**Appropriate Answers for the Resource, Solution, and Proof to the B1 Problem**
Remaining Resources KKRRR Solution Resource R	Solution /R(PRB1) Goal AANppKqr	Proof of Proof-Rule B1 (PRB1)* `PRB1\| --** AANppKqr` `----+---------------------` `1\|a\|_NAANppKqr s` `\|b\| KNANppNKqr a,NAoKi` `\|c\| NANpp b,Ko` `\|d\| KpNp c,NAKi` `\|e\| p d,Ko` `\|f\| Np d,Ko` `2\| AANppKqr 1,No` Go to BAF B2

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