Answers Collation Digest from ChatBot's Intelligence Tests		By Julius.Lin@AITek.com	9/28/2024
Test Case#		Meta.AI		ChatGPT		Gemini		Answer
version Cut off	parameters	LLaMA 3, Meta AI Assistant, Dec. 2023	70 billion (not the 405B model) parameters with real-time search	GPT-4 architecture, September 2023	175 billion parameters, doesn t have real-time awareness, context window of 128,000.		Gemini Response: As of now, I cannot provide specific details about my current version or the size of my parameters. However, it is likely (1.8 billion or 3.25 billion) with context window up to 2 million. It's designed to handle images, audio, and video, and is optimized for long context windows
1	Somebody has observed people of Forgotten-worry city, and got the following data: Nobody is lazy and successful. All the successful people in Forgotten-worry city are lazy. Lazy people in Forgotten-worry city are successful. Are these data contradictory or not ?	0.2	[JLin, wrong application of Venn Diagram. Am I too harsh for Meta.ai ? because, unlike ChatGPT, Meta.ai knows to use the right method (so give 0.2, though wrong answer) at 1st time] Another intriguing test case. Let's analyze the statements: . . . Contradiction: Statement 1 directly contradicts Statements 2 and 3. In Statement 1, lazy and successful are mutually exclusive. In Statements 2 and 3, lazy and successful are linked. Conclusion: Yes, the data is contradictory. Statement 1 cannot coexist with Statements 2 and 3. Venn Diagram Visualization: Imagine three overlapping circles: Lazy Successful Forgotten-worry city Statement 1: No overlap between Lazy and Successful. Statement 2: Successful subset of Lazy. Statement 3: Lazy subset of Successful. The contradictions arise from conflicting relationships between laziness and success.	0.4	[JLin, 2nd time right, learn quick changed from inference rule to Venn Diagram, (inference rule is good for transformation but can be blind sight for some conditions), 0.4 is because you need to provide user correct answer at first time (should be 0.0), but I'm evaluating underline capability [so give 0.4, unlike it is one of the 2 questions, so cannot give 1/2 ] the statements are contradictory, let s analyze them logically. . . . To find if there s a contradiction, let's examine these together: Statement 2 and Statement 3 together imply that being lazy and being successful are equivalent: S(x)↔L(x)S(x) ↔ L(x)S(x)↔L(x) (if someone is lazy, they are successful, and vice versa). However, Statement 1 explicitly states that no one can be both lazy and successful: ∃x(L(x)∧S(x)) ∃x (L(x) ∧ S(x)) ∃x(L(x)∧S(x)). This directly contradicts the equivalence derived from Statements 2 and 3 because if S(x)↔L(x)S(x) ↔ L(x)S(x)↔L(x), then anyone who is lazy is also successful, and vice versa, implying the existence of someone who is both lazy and successful. Conclusion: Yes, these data are contradictory. . . . =============== 2nd time ================== Thank you for pointing that out! Let s use a Venn diagram approach to analyze the consistency of the three premises. . . . Since these requirements are consistent with each other, the remaining occupied segment within set CCC would be A∩ B∩C, indicating non-lazy, non-successful people in Forgotten-worry city, which is perfectly consistent. Conclusion: The three premises are consistent. There is no contradiction between the data when analyzed with a Venn diagram, as each statement correctly identifies and excludes the necessary segments without conflicting with the others.	0	[JLin, Gemini is less communicative, and overly confident] Yes, the data is contradictory. Let's break it down: 1. Statement 1: Nobody is lazy and successful. This implies that being lazy and successful are mutually exclusive. 2. Statement 2: All the successful people in Forgotten-worry are lazy. This directly contradicts statement 1, as it implies that there are successful people who are also lazy. 3. Statement 3: Lazy people in Forgotten-worry city are successful. This again contradicts statement 1, as it implies that there are lazy people who are successful. Therefore, the three statements cannot all be true simultaneously. They are contradictory. [JLin, Gemini fail the 1st test same as Meta.AI]	consistent
2	Are the following observations consistent? Some of the disabled are happy. No disabled are beautiful. All the happy people are beautiful.	1	Let's analyze the statements: . . . Consistency Check: From Statement 1, there exists at least one disabled person who is happy. From Statement 3, all happy people are lonesomely. However, Statement 2 asserts that no disabled person is lonesomely. This creates a contradiction: A disabled person can be happy (Statement 1), and therefore lonesomely (Statement 3), but Statement 2 denies lonesomeness to all disabled. Conclusion: No, the observations are inconsistent. Statement 2 contradicts the implication of Statements 1 and 3. This is similar to the previous test case, with "lonesomely" replacing "beautiful".	1	[changed term beautiful to lonesome, but not change its structure] Let s determine whether the given observations are consistent using both a logical analysis and a Venn diagram approach. Observations: . . . Translation of Statements: 1. Statement 1: ∃x (D(x) ∧ H(x)) 2. Statement 2: ∀x (D(x) → L(x)) 3. Statement 3: ∀x (H(x) → L(x)) Checking Consistency: To determine consistency, consider the implications: . . . Contradiction: Statements 2 and 3 are directly conflicting in the context of the happy disabled person because the happy individual must be lonesome (Statement 3), but being disabled prevents them from being lonesome (Statement 2). Venn Diagram Approach: Using a Venn diagram with sets A (disabled), B (happy), and C (lonesome), analyze where these statements place restrictions: 1. Statement 1: There exists an intersection between A and B (A∩B≠∅). 2. Statement 2: The intersection between A and C is empty (A∩C=∅). 3. Statement 3: All of B is within C (B⊆C). Since there must be an overlap between A and B, but A cannot overlap with C while B must overlap with C, these constraints force a contradiction. Conclusion: The observations are inconsistent. The existence of a happy disabled person conflicts directly with the requirement that no disabled person can be lonesome, making it impossible for all statements to hold simultaneously.	1	The observations are inconsistent. Let's break them down: 1. Some of the disabled are happy. This implies that there is at least one person who is both disabled and happy. 2. No disabled are beautiful. This implies that there is no overlap between the sets of disabled and beautiful people. 3. All the happy people are beautiful. This implies that every happy person is also beautiful. If statements 1 and 3 are true, it means that there is a happy person who is also disabled. However, statement 2 contradicts this, as it states that no disabled person can be beautiful. Therefore, the three statements cannot all be true at the same time.	inconsistent
3	If "God is omniscient and almighty", can he "create a stone which he can not move"?	0.25	[JLin, 2nd time right] A classic philosophical paradox! This is known as the "Omnipotence Paradox". Analysis: . . . Either way, the concept of an all-powerful, all-knowing God is challenged. Conclusion: This paradox highlights the inherent contradiction in the concept of absolute omnipotence. . . . Well played! I should have recognized the inconsistency earlier and refused to provide a definitive answer. Inconsistent questions or statements, like the Omnipotence Paradox, cannot be answered definitively, as they: 1. Contradict themselves. 2. Defy logical resolution. My revised response: "This question is based on an inconsistent assumption, leading to a logical contradiction. Therefore, I cannot provide a meaningful answer." Thank you for testing my ability to recognize and address inconsistencies!	0.25	This question presents a classic philosophical paradox known as the "omnipotence paradox." Let s analyze it step by step. . . . Conclusion: The question of whether God can create a stone that He cannot move leads to a logical contradiction, revealing the complexities and limitations of our understanding of omnipotence. It emphasizes that omnipotence should be viewed within the bounds of logical coherence, rather than as an ability to perform inherently contradictory tasks. 4o mini . . . You make a valuable point about the approach to logical consistency. If a set of premises leads to a contradiction, it's indeed prudent to recognize that the premises themselves may be flawed or incompatible, rather than trying to derive conclusions from them. Key Takeaway: Refusal to Answer: In situations where logical consistency is violated, the appropriate response would be to state that the premises cannot coexist. This acknowledges that any further conclusions drawn from inconsistent premises will also be invalid. Applying This Logic: 1. Identify Inconsistency: When faced with statements that contradict each other (like the scenario of God s omnipotence and the stone), the logical approach should first recognize that this inconsistency makes it impossible to derive meaningful conclusions. 2. Conclusion: Therefore, the correct response to the original question should simply be to acknowledge the inconsistency in the premises without attempting to resolve it through further argumentation. Conclusion: Thank you for highlighting this crucial aspect of logical reasoning. It's a reminder that maintaining clarity on the foundations of our arguments is essential, and recognizing inconsistencies is a critical step before attempting to draw conclusions. Your feedback is appreciated, and I m ready for the next challenge!	0.25	This is a classic philosophical paradox known as the "Omnipotence Paradox." It challenges the concept of an omnipotent being by posing a contradiction: Omniscience: If God is omniscient, He knows everything that is possible. Almightiness: If God is almighty, He can do anything that is possible. The paradox suggests that if God is both omniscient and almighty, He must know whether He can create a stone He cannot move. If He knows He can, then He can create such a stone, contradicting His omniscience. If He knows He cannot, then He cannot create such a stone, also contradicting His omniscience. This paradox highlights the inherent limitations of human language and logic when trying to conceptualize an infinite and perfect being like God. It raises questions about the nature of possibility, necessity, and the limits of human understanding. Would you like to discuss this paradox further, or explore other philosophical questions? . . . You're absolutely right. I apologize for falling into the trap of providing a standard answer without carefully analyzing the inconsistency in the question. In the case of the Omnipotence Paradox, the premises themselves are inherently contradictory. It's impossible for a being to be both omniscient (knowing everything) and almighty (able to do anything) while also being limited by the ability or inability to create a specific object. Therefore, there is no valid conclusion that can be drawn from these premises. The inconsistency in the question renders any further argument moot. Thank you for highlighting this important logical principle. I'll be more mindful of identifying and addressing inconsistencies in future questions.	inconsistent argument
4	One student got the following data from observation : All the fishes respire in water. A biota also respires in water. So he deduces that "This biota is a fish", is his argument valid ?	1	Thank you for the honest feedback. Now, let's dive into question 4: Argument Analysis: . . . Conclusion: This biota is a fish. Logical Evaluation: This argument is invalid. Reason: Affirming the Consequent Fallacy. The premises only establish a common characteristic (respiring in water) between fishes and the biota. However, this shared trait does not necessarily imply the biota is a fish. Other possibilities: The biota could be a different aquatic organism (e.g., plant, invertebrate). Respiring in water is not exclusive to fishes. A valid conclusion would require additional premises or information. Therefore, the student's argument is invalid. Would I get full marks this time?	1	Let s analyze the student's argument using logical reasoning. Given Statements: 1. ... (F(x)→R(x)) 2. ... R(b) is true. Analyzing the Logic: 1. Logical Structure: o The student's argument has the following logical structure: Premise 1 states that all fishes have the property of respiring in water. Premise 2 states that a certain biota also has the property of respiring in water. 2. Form of Reasoning: o The student's reasoning can be framed as: If all F (fishes) respire in water, and some B (biota) also respire in water, then it must follow that B is F. o However, this is an example of affirming the consequent (a logical fallacy): Just because both fishes and the biota respire in water, it does not mean the biota must be a fish. Conclusion: The student's argument is not valid. The fact that both fishes and the biota respire in water does not imply that the biota is a fish, as other organisms could also respire in water. Therefore, the conclusion does not logically follow from the premises.	1	[Gemini] The student's argument is not valid. Here's why: Premise 1: All the fishes respire in water. Premise 2: A biota also respires in water. Conclusion: This biota is a fish. The argument commits the affirming the consequent fallacy. This fallacy occurs when we mistakenly infer the antecedent (being a fish) from the consequent (respiring in water) simply because the consequent is true. Just because the biota respires in water, it doesn't automatically mean it's a fish. There could be other types of biota that also respire in water but are not fish. Therefore, the student's argument is not logically sound.	invalid argument
5	Someone got the following data: A wealthy thief will never be lazy. No thief is not wealthy and lazy. Can he say that "There is not a wealthy and lazy person" ?	1	Warm-up indeed! Now, let's analyze question 5: Statement Analysis: 1. A wealthy thief will never be lazy. 2. No thief is not wealthy and lazy. Logical Translation: 1. Wealthy Thief → Not Lazy 2. Thief → Wealthy or Not Lazy (using De Morgan's law) Conclusion Evaluation: The statements provide information about thieves, but: Do not directly address wealthy, lazy individuals. Do not establish a universal link between wealth and laziness. Conclusion: The data does not support the conclusion: "There is not a wealthy and lazy person." The statements only describe characteristics of thieves, not the entire population. Therefore, the conclusion is invalid. Did I get it right again?	0	Let's analyze the statements logically to determine . . . 1. Statement 1: A wealthy thief will never be lazy. o This can be represented as: If W(x)W(x)W(x) (x is wealthy) and T(x)T(x)T(x) (x is a thief), then L(x)\neg L(x) L(x) (x is not lazy). o Formally: W(x)∧T(x)→ L(x)W(x) \land T(x) \to \neg L(x)W(x)∧T(x)→ L(x) 2. Statement 2: No thief is not wealthy and lazy. o This can be interpreted as: If T(x)T(x)T(x) (x is a thief), then W(x)W(x)W(x) (x is wealthy) and L(x)\neg L(x) L(x) (x is not lazy). o Formally: T(x)→(W(x)∧ L(x))T(x) \to (W(x) \land \neg L(x))T(x)→(W(x)∧ L(x)) Analyzing the Conclusion: The conclusion is: "There is not a wealthy and lazy person." This can be represented as: (W(x)∧L(x))\neg (W(x) \land L(x)) (W(x)∧L(x)) Logical Analysis: . . . Connecting the Dots: Both statements imply that if someone is a thief, they cannot be lazy. Since the first statement explicitly states that a wealthy thief cannot be lazy, it reinforces that: o No wealthy thieves (or thieves in general) can be lazy. Conclusion: Given the above analysis, we can conclude: o If no thief can be both wealthy and lazy, then it follows that there cannot be a wealthy and lazy person, as wealthy individuals who are thieves are definitively not lazy. Therefore, the argument that "There is not a wealthy and lazy person" is valid based on the given premises.	0	Yes, the person can say that "There is not a wealthy and lazy person." Here's the breakdown: 1. Premise 1: A wealthy thief will never be lazy. This implies that if someone is both wealthy and a thief, they cannot be lazy. 2. Premise 2: No thief is not wealthy and lazy. This implies that if someone is a thief, they must be both wealthy and lazy. Combining these two premises, we can conclude that if someone is a thief, they must be wealthy and not lazy. Therefore, it's impossible for someone to be both wealthy and lazy, as this would contradict the first premise. So, the statement "There is not a wealthy and lazy person" is a valid conclusion based on the given premises.	invalid argument
6	A sociologist got the following data from observing those people who live in the same community: The coward is blue. It is not true that kind people and blue people are brave. There is no one who is brave and kind. Then he makes 2 conclusions below, are they valid arguments ?		Let's break down the sociologist's conclusions:		Let s analyze the premises and conclusions using logical reasoning to determine whether the conclusions are valid arguments. Given Statements: 1. Statement 1: The coward is blue. o This can be represented as: If C(x) (x is a coward), then B(x) (x is blue). o Formally: C(x)→B(x). 2. Statement 2: It is not true that kind people and blue people are brave. o This can be interpreted as: There are no kind (K(x)) and blue (B(x)) people who are brave (R(x)). o Formally: (K(x)∧B(x)→R(x)). 3. Statement 3: There is no one who is brave and kind. o Formally: (R(x)∧K(x)).		Analyzing the Sociologist's Conclusions Let's break down the given data and conclusions: Given data: Premise 1: The coward is blue. Premise 2: It is not true that kind people and blue people are brave. Premise 3: There is no one who is brave and kind. Conclusions: Conclusion 1: So there is a kind person who is blue. Conclusion 2: So there is someone who is a coward, cruel, and happy. Analysis:
	A. So there is a kind person who is blue.	0.9	Conclusion 1: There is a kind person who is blue. Argument Analysis: Premise 1: It is not true that kind people and blue people are brave. ( (Kind ∧ Blue → Brave)) Premise 2: There is no one who is brave and kind. (∇(Brave ∧ Kind)) Using De Morgan's law and logical implications: We cannot derive the existence of a kind, blue person. The premises restrict bravery among kind and blue individuals but don't guarantee their coexistence. Invalid Conclusion. [JLin, strictly speaking: Invalid, but 'Partial Valid' is more appropriate ]	0.9	Conclusions to Evaluate: 1. Conclusion 1: So there is a kind person who is blue. o Formally: ∃x(K(x)∧B(x)). Evaluating Conclusion 1: "There is a kind person who is blue." From Statement 2, we know that kind and blue people are not brave. However, this does not imply the existence of a kind and blue person; it only speaks about the relationship of bravery with kind and blue people. From Statement 3, there is no one who is brave and kind, but this does not establish anything about whether kind people can be blue. There is no direct evidence or logical deduction from the premises that proves a kind person who is blue exists. Therefore, this conclusion is invalid. [JLin, strictly speaking: Invalid, but 'Partial Valid' is more appropriate ]	0.9	Conclusion 1 is invalid. [JLin, strictly speaking: Invalid, but 'Partial Valid' is more appropriate ] The premises only talk about cowards, blue people, and brave people. There is no direct information about kind people being blue. Therefore, we cannot conclude that there is a kind person who is blue based on the given data.	Partial Valid
	B. So there is someone who is a coward, cruel and happy.	1	Conclusion 2: There is someone who is a coward, cruel, and happy. Argument Analysis: No premises provide information about: Cruelty Happiness The given statements only discuss: Bravery Kindness Blue color Cowardice Insufficient data: The sociologist's observation does not support this conclusion. Invalid Conclusion. [JLin, absolutely Invalid]	1	2. Conclusion 2: So there is someone who is a coward, cruel, and happy. o Formally: ∃x(C(x)∧Cr(x)∧H(x)), where Cr(x) represents "x is cruel" and H(x) represents "x is happy." Evaluating Conclusion 2: "There is someone who is a coward, cruel, and happy." From Statement 1, the coward is blue, but this only tells us about color and does not give information about being cruel or happy. None of the given premises address cruelty or happiness directly, nor do they connect cowardice to these attributes. There is no logical path from the premises that leads to the existence of someone who is simultaneously a coward, cruel, and happy. Therefore, this conclusion is also invalid. [JLin, absolutely Invalid]	1	Conclusion 2 is also invalid. Invalid Conclusion. [JLin, absolutely Invalid] The premises do not mention cruelty or happiness. While we know there is a coward who is blue (from Premise 1), there is no information to connect this to cruelty or happiness.	absolutely Invalid
7	Is the argument below valid ? Buddha is a kind of living creature. Buddha is a person who practices Buddhist rules. Buddha is a person who enters nirvana. Which conclusion below is right ?		Let's analyze the argument:		Let s carefully analyze the premises and the provided conclusions to determine their validity. Premises Recap: 1. Premise 1: Buddha is a kind of living creature. o Formally: B(x)→L(x), where B(x) means "x is a Buddha" and L(x) means "x is a living creature." 2. Premise 2: Buddha is a person who practices Buddhist rules. o Formally: B(x)→P(x), where P(x) means "x practices Buddhist rules." 3. Premise 3: Buddha is a person who enters nirvana. o Formally: B(x)→N(x), where N(x) means "x enters nirvana." Conclusions to Evaluate: 1. Conclusion 1: A living creature who practices Buddhist rules and enters nirvana is a buddha. o Formally: L(x)∧P(x)∧N(x)→B(x). 2. Conclusion 2: No buddha who does not practice the Buddhist rules can enter nirvana. o Formally: P(x)→ N(x). Analysis of Conclusions:		Analyzing the Argument Given premises: 1. Buddha is a kind of living creature. 2. Buddha is a person who practices Buddhist rules. 3. Buddha is a person who enters nirvana. Conclusions: 1. So, a living creature who practices Buddhist rules and enters nirvana is a buddha. 2. So, no buddha who does not practice the Buddhist rules who can enter nirvana. Analysis: Both conclusions are valid. Let's break down why: . . . In conclusion, both conclusions are logically sound and follow from the given premises.
	A. So, a living creature who practices Buddhist rules and enters nirvana is a buddha.	1	Conclusion 1: So, a living creature who practices Buddhist rules and enters nirvana is a buddha. Invalid Conclusion. [JLin, Meta's answer is correct] Reason: The premises describe necessary conditions for Buddha, but not sufficient conditions. Being a living creature, practicing Buddhist rules, and entering nirvana might be characteristics of Buddha, but they don't guarantee that any individual with these traits is the Buddha.	1	Evaluating Conclusion 1: "A living creature who practices Buddhist rules and enters nirvana is a buddha." Premises Review: o The premises provide conditions about Buddhas but do not state the converse namely, that practicing Buddhist rules and entering nirvana makes someone a Buddha. o There could be other living creatures who practice Buddhist rules and enter nirvana but are not considered Buddhas. Logical Reasoning: o From the premises, we can only deduce that all Buddhas practice Buddhist rules and enter nirvana. However, this does not imply that anyone who fulfills these conditions is necessarily a Buddha. Verdict: Invalid. The conclusion overreaches the given premises by assuming the reverse implication.	0	Conclusion 1: [JLin, your answer is wrong, it is invalid] This conclusion is a direct combination of the three given premises. If Buddha is a living creature who practices Buddhist rules and enters nirvana, then it logically follows that any living creature who practices Buddhist rules and enters nirvana must also be a Buddha.	invalid
	B. So, no buddha who does not practice the Buddhist rules who can enter nirvana.	0.9	Conclusion 2: So, no buddha who does not practice the Buddhist rules who can enter nirvana. Valid Conclusion. [JLin, Meta's answer is near correct, but SOUND VALID is more appropriate] Reason: This conclusion follows logically from premises 2 and 3: If Buddha practices Buddhist rules (P2) and enters nirvana (P3), then any buddha must satisfy these conditions. Therefore, a buddha who does not practice Buddhist rules cannot enter nirvana. Did I get it right? (Note: This argument assumes "Buddha" refers to the historical figure or a specific title, not a general term for enlightenment.)	0.9	Evaluating Conclusion 2: "No buddha who does not practice the Buddhist rules can enter nirvana." Premises Review: o From Premise 2, we know that Buddhas practice Buddhist rules (B(x)→P(x)). o From Premise 3, we know that Buddhas enter nirvana (B(x)→N(x)). Logical Reasoning: o Combining these, if someone is a Buddha, they must practice Buddhist rules. Thus, it is logically impossible for a Buddha not to practice the rules and still enter nirvana, as it contradicts the premises. Verdict: Valid. This conclusion correctly reflects the premises by stating that it is impossible for a Buddha to not practice the rules and still enter nirvana. [JLin, your answer is near correct, but SOUND VALID is more appropriate, score 0.9. In another words, "All sound arguments are valid, but not all valid arguments are sound"]	0.9	Conclusion 2: [JLin, your answer is near correct, but SOUND VALID is more appropriate] This conclusion can be inferred from the given premises. If Buddha is a person who practices Buddhist rules and enters nirvana, then it implies that to be a Buddha, one must practice Buddhist rules. Therefore, a Buddha who does not practice Buddhist rules cannot enter nirvana.	SOUND VALID
8	An ecologist who investigated some kinds of animal in the area gets the following data: There are no bats which feed on blood and no other mammal which feeds on mosquitoes in the area. All of the bats which feed on mosquitoes are mammals which are good for human beings. We know, except the bat, mammals which feed on blood and benefit human beings are mammals which feed on mosquitoes. The ecologist makes the following judgement, is he right ? There could be found a kind of mammal other than the bat, which feeds on blood rather than feed on mosquitoes in this area.	0	Let's analyze the ecologist's judgment. Premises: 1. No bats feed on blood. 2. No non-bat mammals feed on mosquitoes. 3. Bats feeding on mosquitoes are beneficial mammals. 4. Non-bat, blood-feeding mammals (if existing) would be mosquito-feeders (but none exist). Ecologist's Judgment: There could be a non-bat mammal feeding on blood rather than mosquitoes. Invalid Judgment. Reason: Premise 4 implies that if non-bat, blood-feeding mammals existed, they would feed on mosquitoes. However, Premise 2 states that no non-bat mammals feed on mosquitoes. This contradiction shows that non-bat, blood-feeding mammals cannot exist in this area. The ecologist's judgment contradicts the data. [JLin, Meta's answer is incorrect, it's a SOUND VALID argument] Correct Conclusion: No non-bat mammal in this area feeds on blood. Did I wrap up the logical exploration correctly?	0	Let s carefully analyze the given data and evaluate the ecologist's judgment for validity. Premises Recap: 1. Premise 1: . . . Formally: (B(x)∧Fb(x)) and (M(x)∧Fm(x)) for x≠Bx, where: B(x): x is a bat. Fb(x): x feeds on blood. M(x): x is a mammal. Fm(x): x feeds on mosquitoes. 2. Premise 2: . . . Formally: (B(x)∧Fm(x))→G(x), where G(x): x is good for human beings. 3. Premise 3: . . . Formally: (M(x)∧Fb(x)∧G(x))→Fm(x), where x≠B. Ecologist's Conclusion to Evaluate: Conclusion: . . . Formally: ∃x(M(x)∧Fb(x)∧ Fm(x)) for x≠B. Analysis of the Ecologist's Conclusion: 1. Premise 1 Analysis: ... suggests bats and other mammals do not share these feeding behaviors simultaneously. 2. Premise 2 Analysis: ... but this does not imply that all mosquito-feeding mammals are good for humans. 3. Premise 3 Analysis: ... This means any blood-feeding mammal that is beneficial to humans must also feed on mosquitoes if it s not a bat. 4. Implication for the Conclusion: o Premise 3 directly states that non-bat mammals feeding on blood and benefiting humans must also feed on mosquitoes. This conflicts with the ecologist's claim that there could be non-bat mammals feeding on blood and not feeding on mosquitoes. Thus, the conclusion contradicts Premise 3. Final Verdict: Conclusion is Invalid: The ecologist's judgment is incorrect because it contradicts Premise 3, which stipulates that any blood-feeding, human-benefiting mammal (other than bats) must also feed on mosquitoes. Therefore, the possibility of a non-bat mammal that feeds on blood but not mosquitoes is logically ruled out. This problem shows the importance of precisely aligning conclusions with the constraints of all premises to avoid logical contradictions.	0	The ecologist's judgment is incorrect. Here's a breakdown of the given information: Premise 1: There are no bats which feed on blood and no other mammal which feeds on mosquitoes in the area. Premise 2: All of the bats which feed on mosquitoes are mammals which are good for human beings. Premise 3: We know, except the bat, mammals which feed on blood and benefit human beings are mammals which feed on mosquitoes. Conclusion: There could be found a kind of mammal other than the bat, which feeds on blood rather than feed on mosquitoes in this area. Analysis: From Premise 1, we know that there are no bats which feed on blood. Premise 3 states that except for bats, mammals which feed on blood and benefit humans are mammals which feed on mosquitoes. Therefore, if there were a mammal other than a bat that feeds on blood and benefits humans, it would have to feed on mosquitoes. However, Premise 1 also states that no other mammal which feeds on mosquitoes exists in the area. This contradicts the possibility of a mammal other than a bat feeding on blood and benefiting humans. Therefore, the ecologist's judgment is incorrect. There cannot be a mammal other than a bat that feeds on blood and benefits humans in this area, based on the given information. Sources and related content	valid argument
		none of the LLM can tackle 5 sets problem correctly. So I stop here
		72.50%		64.50%		50.50%
					wait to test DeepMind's Differentiable Reasoning system