premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
15
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stringlengths 684
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⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not humble or curious is kind or generous. If someone is both not generous and quiet then someone is strong and vice versa. Everyone who is happy is quiet or creative and vice versa. If alice is either tall or brave then someone is not creative or wise. Everyone who is both not curious and happy is strong or not funny. Everyone who is creative is generous and vice versa. If lucy is either not rich or creative then someone is calm and vice versa. Everyone who is old or not patient is generous. If someone is either not rich or wise then someone is not happy and vice versa. If alice is both not old and rich then someone is not humble. Everyone who is either not tall or not generous is either creative or not rich and vice versa. Everyone who is not strong or not quiet is both brave and not humble and vice versa. Everyone who is strong or not creative is creative or not calm. Everyone who is either not curious or not old is either happy or not generous and vice versa. If someone is not patient or not brave then someone is not curious and vice versa. Everyone who is either strong or humble is both not strong and not kind. Someone is either not wise or not generous. Someone is not happy. Someone is not strong. Someone is either not kind or old. John is not patient. Someone is both quiet and not generous. Someone is both not happy and tall. | Alice is not creative. | neutral | (![X]:((~humble(X)|curious(X))=>(kind(X)|generous(X))))&
((?[X]:((~generous(X)&quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:(happy(X)<=>(quiet(X)|creative(X))))&
(((tall(alice)<~>brave(alice)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~curious(X)&happy(X))=>(strong(X)|~funny(X))))&
(![X]:(creative(X)<=>generous(X)))&
(((~rich(lucy)<~>creative(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((old(X)|~patient(X))=>generous(X)))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:(~happy(X))))&
(((~old(alice)&rich(alice)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(brave(X)&~humble(X))))&
(![X]:((strong(X)|~creative(X))=>(creative(X)|~calm(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(happy(X)<~>~generous(X))))&
((?[X]:((~patient(X)|~brave(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)<~>humble(X))=>(~strong(X)&~kind(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is not happy or not curious is both patient and old and vice versa.
Everyone who is not generous or not quiet is not brave or happy and vice versa.
Everyone who is both not wise and not quiet is brave or kind.
Everyone who is either funny or not quiet is not funny and vice versa.
Everyone who is creative is either not brave or not creative and vice versa.
Everyone who is not calm is either curious or not quiet.
Everyone who is both calm and funny is both not strong and creative and vice versa.
If lucy is old then someone is funny and vice versa.
Everyone who is both not old and old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
John is either not rich or not tall.
Lucy is not tall.
Someone is either humble or creative.
Someone is either not generous or calm.
Someone is humble or not brave.
Someone is not generous or not brave.
John is not calm.
Lucy is kind. | Paul is wise. | entailment | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~wise(X)&~quiet(X))=>(brave(X)|kind(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>~funny(X)))&
(![X]:(creative(X)<=>(~brave(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(~strong(X)&creative(X))))&
((old(lucy))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
((~rich(john)<~>~tall(john)))&
(~tall(lucy))&
(?[X]:((humble(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(~calm(john))&
(kind(lucy)) | wise(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5728081776384580345382053
% SZS output start Proof for 5728081776384580345382053
9. ! [X0] : ((old(X0) & ~old(X0)) <=> ~wise(X0)) [input p8]
25. ~wise(paul) [input hypothesis]
47. ! [X0] : (((old(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | (~old(X0) | old(X0)))) [nnf transformation 9]
48. ! [X0] : (((old(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | ~old(X0) | old(X0))) [flattening 47]
102. ~old(X0) | wise(X0) [cnf transformation 48]
103. old(X0) | wise(X0) [cnf transformation 48]
138. ~wise(paul) [cnf transformation 25]
159. wise(X0) [subsumption resolution 102,103]
254. $false [subsumption resolution 138,159]
% SZS output end Proof for 5728081776384580345382053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and wise is both patient and kind. Everyone who is both not wise and not happy is wise and vice versa. Everyone who is old or not tall is either quiet or patient. Everyone who is not rich or not happy is curious and vice versa. Everyone who is not strong is not tall or strong. Everyone who is not curious or happy is not humble or old. Everyone who is not tall is both not rich and kind and vice versa. Everyone who is not strong is either wise or strong. If someone is either quiet or old then someone is not kind or not curious. If mary is either wise or not kind then someone is tall and vice versa. If paul is not humble then lucy is not wise. Everyone who is rich or not tall is both not strong and not rich and vice versa. Everyone who is either not happy or wise is not curious or not patient and vice versa. Everyone who is not calm is not quiet or generous. Everyone who is either generous or not quiet is either not old or patient and vice versa. If someone is either humble or not creative then someone is either kind or rich and vice versa. Someone is not humble or not old. Someone is not quiet. Mary is tall or not humble. Someone is quiet. Someone is not creative or not rich. | Lucy is not calm. | neutral | (![X]:((old(X)&wise(X))=>(patient(X)&kind(X))))&
(![X]:((~wise(X)&~happy(X))<=>wise(X)))&
(![X]:((old(X)|~tall(X))=>(quiet(X)<~>patient(X))))&
(![X]:((~rich(X)|~happy(X))<=>curious(X)))&
(![X]:(~strong(X)=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)|happy(X))=>(~humble(X)|old(X))))&
(![X]:(~tall(X)<=>(~rich(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>strong(X))))&
((?[X]:((quiet(X)<~>old(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(((wise(mary)<~>~kind(mary)))<=>(?[X]:(tall(X))))&
((~humble(paul))=>(~wise(lucy)))&
(![X]:((rich(X)|~tall(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(~curious(X)|~patient(X))))&
(![X]:(~calm(X)=>(~quiet(X)|generous(X))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~old(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((kind(X)<~>rich(X)))))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:(~quiet(X)))&
((tall(mary)|~humble(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)|~rich(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not funny is not patient or not creative and vice versa.
Everyone who is not brave or not kind is strong.
If fred is not happy then someone is either creative or not old.
Everyone who is either funny or wise is both not funny and happy.
Everyone who is either old or funny is either generous or not brave.
Everyone who is calm is kind or happy and vice versa.
Everyone who is both not brave and creative is not creative and vice versa.
Everyone who is both not old and quiet is both not humble and old.
If mary is both old and not wise then someone is not generous and vice versa.
Everyone who is not humble or not creative is creative or kind.
If john is both not kind and not strong then someone is both not quiet and not funny.
If someone is wise then fred is brave or wise and vice versa.
If mary is not rich then alice is both not humble and rich.
If someone is either not tall or not kind then someone is patient.
Everyone who is patient is rich or not creative.
Alice is either creative or rich.
Alice is generous.
Mary is not happy or kind.
Someone is curious or tall.
Paul is creative or curious.
Paul is not old.
Mary is funny or not wise. | Alice is not tall. | neutral | (![X]:(~funny(X)<=>(~patient(X)|~creative(X))))&
(![X]:((~brave(X)|~kind(X))=>strong(X)))&
((~happy(fred))=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:((funny(X)<~>wise(X))=>(~funny(X)&happy(X))))&
(![X]:((old(X)<~>funny(X))=>(generous(X)<~>~brave(X))))&
(![X]:(calm(X)<=>(kind(X)|happy(X))))&
(![X]:((~brave(X)&creative(X))<=>~creative(X)))&
(![X]:((~old(X)&quiet(X))=>(~humble(X)&old(X))))&
(((old(mary)&~wise(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~humble(X)|~creative(X))=>(creative(X)|kind(X))))&
(((~kind(john)&~strong(john)))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:(wise(X)))<=>((brave(fred)|wise(fred))))&
((~rich(mary))=>((~humble(alice)&rich(alice))))&
((?[X]:((~tall(X)<~>~kind(X))))=>(?[X]:(patient(X))))&
(![X]:(patient(X)=>(rich(X)|~creative(X))))&
((creative(alice)<~>rich(alice)))&
(generous(alice))&
((~happy(mary)|kind(mary)))&
(?[X]:((curious(X)|tall(X))))&
((creative(paul)|curious(paul)))&
(~old(paul))&
((funny(mary)|~wise(mary))) | ~tall(alice) | [] | null | 0 |
If mary is either not patient or humble then someone is either not humble or rich and vice versa.
Everyone who is not kind or quiet is either not kind or tall.
Everyone who is not calm is quiet.
Everyone who is kind is not old.
Everyone who is not funny is not rich or not tall.
Everyone who is not rich or not happy is not calm or brave.
Everyone who is creative is funny or kind.
Everyone who is both not funny and tall is quiet or brave and vice versa.
Everyone who is both patient and kind is either not happy or not quiet.
Everyone who is creative or rich is not rich.
Everyone who is generous is both calm and not creative.
If someone is either not funny or not humble then susan is not patient.
Everyone who is either not funny or not old is calm or not kind.
If someone is not creative then john is both strong and not tall and vice versa.
Everyone who is patient or not calm is both not wise and old.
If john is funny or curious then lucy is either generous or tall.
Someone is either humble or curious.
John is calm.
Fred is wise or rich.
Someone is not tall or not quiet.
Susan is both curious and not rich. | Susan is tall. | entailment | (((~patient(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|~kind(X))))&
((?[X]:(~creative(X)))<=>((strong(john)&~tall(john))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>curious(X))))&
(calm(john))&
((wise(fred)|rich(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
((curious(susan)&~rich(susan))) | tall(susan) | [
"p2",
"p5",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7253105108131259492712077
% SZS output start Proof for 7253105108131259492712077
3. ! [X0] : (~calm(X0) => quiet(X0)) [input p2]
6. ! [X0] : ((~happy(X0) | ~rich(X0)) => (brave(X0) | ~calm(X0))) [input p5]
8. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (brave(X0) | quiet(X0))) [input p7]
10. ! [X0] : ((rich(X0) | creative(X0)) => ~rich(X0)) [input p9]
22. ~tall(susan) [input hypothesis]
24. ! [X0] : (quiet(X0) | calm(X0)) [ennf transformation 3]
28. ! [X0] : ((brave(X0) | ~calm(X0)) | (happy(X0) & rich(X0))) [ennf transformation 6]
29. ! [X0] : (brave(X0) | ~calm(X0) | (happy(X0) & rich(X0))) [flattening 28]
34. ! [X0] : (~rich(X0) | (~rich(X0) & ~creative(X0))) [ennf transformation 10]
46. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & ((brave(X0) | quiet(X0)) | (~tall(X0) | funny(X0)))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & (brave(X0) | quiet(X0) | ~tall(X0) | funny(X0))) [flattening 46]
74. calm(X0) | quiet(X0) [cnf transformation 24]
77. ~calm(X0) | brave(X0) | rich(X0) [cnf transformation 29]
83. ~quiet(X0) | tall(X0) [cnf transformation 47]
84. ~brave(X0) | tall(X0) [cnf transformation 47]
88. ~rich(X0) | ~rich(X0) [cnf transformation 34]
113. ~tall(susan) [cnf transformation 22]
114. ~rich(X0) [duplicate literal removal 88]
213. brave(X0) | rich(X0) | quiet(X0) [resolution 77,74]
216. brave(X0) | quiet(X0) [subsumption resolution 213,114]
270. quiet(X0) | tall(X0) [resolution 216,84]
272. tall(X0) [subsumption resolution 270,83]
274. $false [resolution 272,113]
% SZS output end Proof for 7253105108131259492712077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not humble is kind and vice versa. Everyone who is either not strong or not generous is both humble and kind. Everyone who is patient or rich is not generous. Everyone who is either not calm or funny is tall or not rich. If someone is not happy or not patient then someone is old and vice versa. If john is happy or calm then someone is either not creative or not strong and vice versa. Everyone who is patient is not quiet. If someone is not humble or not curious then alice is both rich and not creative. Everyone who is both not generous and funny is either curious or not brave and vice versa. Everyone who is either generous or quiet is not happy and vice versa. Everyone who is brave is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. Everyone who is quiet is not quiet or not humble and vice versa. Everyone who is brave or patient is not tall and vice versa. If someone is both not old and not strong then susan is tall and vice versa. Alice is creative or quiet. Someone is either not tall or strong. Alice is both not creative and not strong. Susan is either not generous or not curious. | Alice is not kind. | contradiction | (![X]:((wise(X)<~>~humble(X))<=>kind(X)))&
(![X]:((~strong(X)<~>~generous(X))=>(humble(X)&kind(X))))&
(![X]:((patient(X)|rich(X))=>~generous(X)))&
(![X]:((~calm(X)<~>funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:(old(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))=>((rich(alice)&~creative(alice))))&
(![X]:((~generous(X)&funny(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|patient(X))<=>~tall(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
((creative(alice)|quiet(alice)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~creative(alice)&~strong(alice)))&
((~generous(susan)<~>~curious(susan))) | ~kind(alice) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7604202065397026651273384
% SZS output start Proof for 7604202065397026651273384
1. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> kind(X0)) [input p0]
4. ! [X0] : ((~calm(X0) <~> funny(X0)) => (~rich(X0) | tall(X0))) [input p3]
7. ! [X0] : (patient(X0) => ~quiet(X0)) [input p6]
8. ? [X0] : (~curious(X0) | ~humble(X0)) => (~creative(alice) & rich(alice)) [input p7]
9. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p8]
11. ! [X0] : (brave(X0) <=> (wise(X0) | ~curious(X0))) [input p10]
13. (~rich(alice) | patient(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~humble(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((patient(X0) | brave(X0)) <=> ~tall(X0)) [input p14]
21. ~kind(alice) [input hypothesis]
25. ! [X0] : ((~rich(X0) | tall(X0)) | (~calm(X0) <=> funny(X0))) [ennf transformation 4]
26. ! [X0] : (~rich(X0) | tall(X0) | (~calm(X0) <=> funny(X0))) [flattening 25]
27. ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 7]
28. (~creative(alice) & rich(alice)) | ! [X0] : (curious(X0) & humble(X0)) [ennf transformation 8]
30. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ~kind(X0)) & (kind(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 1]
32. ! [X0] : (~rich(X0) | tall(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [nnf transformation 26]
43. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~funny(X0) | generous(X0)))) [nnf transformation 9]
44. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~funny(X0) | generous(X0))) [flattening 43]
46. ! [X0] : ((brave(X0) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | ~brave(X0))) [nnf transformation 11]
47. ! [X0] : ((brave(X0) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | ~brave(X0))) [flattening 46]
48. ((~rich(alice) | patient(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [nnf transformation 13]
49. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [flattening 48]
50. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | (rich(alice) & ~patient(alice))) [rectify 49]
51. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK3) | ~curious(sK3)) [choice axiom]
52. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK3) | ~curious(sK3)) | (rich(alice) & ~patient(alice))) [skolemisation 50,51]
53. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 14]
54. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 53]
55. ! [X0] : (((patient(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [nnf transformation 15]
56. ! [X0] : ((patient(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [flattening 55]
66. kind(X0) | wise(X0) | humble(X0) [cnf transformation 30]
76. ~funny(X0) | tall(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 32]
86. ~quiet(X0) | ~patient(X0) [cnf transformation 27]
87. rich(alice) | humble(X0) [cnf transformation 28]
95. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
103. ~wise(X0) | brave(X0) [cnf transformation 47]
108. ~rich(alice) | patient(alice) | curious(X0) [cnf transformation 52]
109. ~rich(alice) | patient(alice) | calm(X0) [cnf transformation 52]
110. ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
111. quiet(X0) | quiet(X0) [cnf transformation 54]
113. ~brave(X0) | ~tall(X0) [cnf transformation 56]
126. ~kind(alice) [cnf transformation 21]
127. ~humble(X0) | ~quiet(X0) [duplicate literal removal 110]
128. quiet(X0) [duplicate literal removal 111]
182. 13 <=> ! [X0] : curious(X0) [avatar definition]
183. curious(X0) <- (13) [avatar component clause 182]
190. 15 <=> ! [X0] : humble(X0) [avatar definition]
191. humble(X0) <- (15) [avatar component clause 190]
194. 16 <=> rich(alice) [avatar definition]
196. rich(alice) <- (16) [avatar component clause 194]
198. 15 | 16 [avatar split clause 87,194,190]
200. 17 <=> ! [X0] : calm(X0) [avatar definition]
201. calm(X0) <- (17) [avatar component clause 200]
203. 18 <=> patient(alice) [avatar definition]
205. patient(alice) <- (18) [avatar component clause 203]
206. 17 | 18 | ~16 [avatar split clause 109,194,203,200]
207. 13 | 18 | ~16 [avatar split clause 108,194,203,182]
218. ~humble(X0) [subsumption resolution 127,128]
258. $false <- (15) [subsumption resolution 191,218]
259. ~15 [avatar contradiction clause 258]
266. ~patient(X0) [resolution 86,128]
267. $false <- (18) [resolution 266,205]
268. ~18 [avatar contradiction clause 267]
279. wise(alice) | humble(alice) [resolution 66,126]
280. wise(alice) [subsumption resolution 279,218]
281. brave(alice) [resolution 280,103]
284. ~tall(alice) [resolution 281,113]
290. funny(alice) | ~curious(alice) [resolution 95,281]
291. funny(alice) <- (13) [subsumption resolution 290,183]
326. tall(alice) | ~calm(alice) | ~rich(alice) <- (13) [resolution 76,291]
327. ~calm(alice) | ~rich(alice) <- (13) [subsumption resolution 326,284]
328. ~rich(alice) <- (13, 17) [subsumption resolution 327,201]
329. $false <- (13, 16, 17) [subsumption resolution 328,196]
330. ~13 | ~16 | ~17 [avatar contradiction clause 329]
331. $false [avatar sat refutation 198,206,207,259,268,330]
% SZS output end Proof for 7604202065397026651273384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not creative is either not calm or not rich.
If someone is either tall or not old then paul is both not quiet and funny.
Everyone who is either curious or old is both not kind and brave and vice versa.
If mary is either funny or strong then someone is both humble and not wise.
If someone is not rich then fred is either not creative or tall and vice versa.
If someone is either quiet or not quiet then someone is not wise or creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
Someone is not old or not quiet.
Someone is not rich or wise.
Lucy is either happy or not strong.
Someone is either not patient or old.
Someone is not happy or not tall. | Fred is not happy. | contradiction | (![X]:((humble(X)|~creative(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((tall(X)<~>~old(X))))=>((~quiet(paul)&funny(paul))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~rich(X)|wise(X))))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((~happy(X)|~tall(X)))) | ~happy(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 708320394325059175481547
% SZS output start Proof for 708320394325059175481547
13. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p12]
22. ~happy(fred) [input hypothesis]
62. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 13]
63. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 62]
125. happy(X0) | ~old(X0) [cnf transformation 63]
126. happy(X0) | old(X0) [cnf transformation 63]
142. ~happy(fred) [cnf transformation 22]
252. happy(X0) [subsumption resolution 125,126]
286. $false [subsumption resolution 142,252]
% SZS output end Proof for 708320394325059175481547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then paul is rich or creative and vice versa. If someone is both not tall and not old then mary is both wise and funny. If someone is either not quiet or creative then someone is not old or not tall and vice versa. Everyone who is either quiet or not generous is not quiet. Everyone who is creative is either brave or not old and vice versa. Everyone who is either not tall or rich is either not quiet or not generous and vice versa. If mary is either creative or kind then someone is both old and creative. Everyone who is not rich is either calm or not quiet and vice versa. Everyone who is both not old and not rich is either calm or rich and vice versa. If someone is either not brave or humble then someone is kind and vice versa. If someone is old then susan is either old or not wise and vice versa. Everyone who is wise or humble is either not calm or not quiet and vice versa. Everyone who is generous is not kind and vice versa. If someone is not kind or creative then lucy is both happy and rich. Everyone who is not quiet or not patient is either patient or humble. Paul is both not calm and not kind. Someone is both funny and calm. Alice is both not creative and humble. Someone is both not humble and not wise. Someone is both not quiet and not creative. Someone is curious. Someone is both wise and not tall. John is either brave or patient. | Alice is quiet. | contradiction | ((~patient(susan))<=>((rich(paul)|creative(paul))))&
((?[X]:((~tall(X)&~old(X))))=>((wise(mary)&funny(mary))))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((quiet(X)<~>~generous(X))=>~quiet(X)))&
(![X]:(creative(X)<=>(brave(X)<~>~old(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(~quiet(X)<~>~generous(X))))&
(((creative(mary)<~>kind(mary)))=>(?[X]:((old(X)&creative(X)))))&
(![X]:(~rich(X)<=>(calm(X)<~>~quiet(X))))&
(![X]:((~old(X)&~rich(X))<=>(calm(X)<~>rich(X))))&
((?[X]:((~brave(X)<~>humble(X))))<=>(?[X]:(kind(X))))&
((?[X]:(old(X)))<=>((old(susan)<~>~wise(susan))))&
(![X]:((wise(X)|humble(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>~kind(X)))&
((?[X]:((~kind(X)|creative(X))))=>((happy(lucy)&rich(lucy))))&
(![X]:((~quiet(X)|~patient(X))=>(patient(X)<~>humble(X))))&
((~calm(paul)&~kind(paul)))&
(?[X]:((funny(X)&calm(X))))&
((~creative(alice)&humble(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:(curious(X)))&
(?[X]:((wise(X)&~tall(X))))&
((brave(john)<~>patient(john))) | quiet(alice) | [
"p7",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 217259147851715614561645
% SZS output start Proof for 217259147851715614561645
8. ! [X0] : (~rich(X0) <=> (calm(X0) <~> ~quiet(X0))) [input p7]
9. ! [X0] : ((~rich(X0) & ~old(X0)) <=> (calm(X0) <~> rich(X0))) [input p8]
12. ! [X0] : ((humble(X0) | wise(X0)) <=> (~calm(X0) <~> ~quiet(X0))) [input p11]
18. humble(alice) & ~creative(alice) [input p17]
24. quiet(alice) [input hypothesis]
49. ! [X0] : ((~rich(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0)))) & (((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | rich(X0))) [nnf transformation 8]
50. ! [X0] : (((~rich(X0) & ~old(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (rich(X0) | old(X0)))) [nnf transformation 9]
51. ! [X0] : (((~rich(X0) & ~old(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | rich(X0) | old(X0))) [flattening 50]
61. ! [X0] : (((humble(X0) | wise(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~humble(X0) & ~wise(X0)))) [nnf transformation 12]
62. ! [X0] : ((humble(X0) | wise(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~humble(X0) & ~wise(X0)))) [flattening 61]
102. ~quiet(X0) | calm(X0) | rich(X0) [cnf transformation 49]
111. ~rich(X0) | calm(X0) | ~rich(X0) [cnf transformation 51]
121. ~humble(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 62]
138. humble(alice) [cnf transformation 18]
147. quiet(alice) [cnf transformation 24]
150. ~rich(X0) | calm(X0) [duplicate literal removal 111]
351. calm(alice) | rich(alice) [resolution 102,147]
352. calm(alice) [subsumption resolution 351,150]
390. ~calm(alice) | ~quiet(alice) [resolution 121,138]
392. ~quiet(alice) [subsumption resolution 390,352]
393. $false [subsumption resolution 392,147]
% SZS output end Proof for 217259147851715614561645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not generous is not brave and vice versa. If someone is not happy then someone is both not creative and rich and vice versa. Everyone who is rich is both funny and not curious and vice versa. If susan is either humble or not curious then lucy is not rich or old and vice versa. If someone is not brave or not humble then someone is not creative or rich and vice versa. Everyone who is either not patient or humble is either old or curious and vice versa. If john is both not brave and not funny then alice is either funny or patient and vice versa. If someone is calm or wise then someone is not strong or calm. Everyone who is both not happy and creative is wise or brave and vice versa. Everyone who is either brave or not patient is either brave or wise. Everyone who is either funny or not kind is kind and vice versa. Everyone who is not generous or quiet is both strong and not tall. Everyone who is not rich or not tall is quiet or patient and vice versa. If john is not generous then paul is both quiet and old and vice versa. Someone is funny. Alice is generous or not quiet. Someone is calm or humble. John is either humble or not calm. Fred is wise or not wise. | Susan is tall. | contradiction | (![X]:((brave(X)|~generous(X))<=>~brave(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)&rich(X)))))&
(![X]:(rich(X)<=>(funny(X)&~curious(X))))&
(((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
(?[X]:(funny(X)))&
((generous(alice)|~quiet(alice)))&
(?[X]:((calm(X)|humble(X))))&
((humble(john)<~>~calm(john)))&
((wise(fred)|~wise(fred))) | tall(susan) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1648877779917364313389622
% SZS output start Proof for 1648877779917364313389622
1. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~brave(X0)) [input p0]
12. ! [X0] : ((quiet(X0) | ~generous(X0)) => (~tall(X0) & strong(X0))) [input p11]
20. tall(susan) [input hypothesis]
26. ! [X0] : ((~tall(X0) & strong(X0)) | (~quiet(X0) & generous(X0))) [ennf transformation 12]
27. ! [X0] : (((~generous(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 1]
28. ! [X0] : ((~generous(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & ~brave(X0)))) [flattening 27]
62. ~brave(X0) | ~brave(X0) [cnf transformation 28]
64. ~generous(X0) | brave(X0) | brave(X0) [cnf transformation 28]
112. ~tall(X0) | generous(X0) [cnf transformation 26]
127. tall(susan) [cnf transformation 20]
132. ~brave(X0) [duplicate literal removal 62]
133. ~generous(X0) | brave(X0) [duplicate literal removal 64]
279. generous(susan) [resolution 112,127]
282. brave(susan) [resolution 133,279]
285. $false [subsumption resolution 282,132]
% SZS output end Proof for 1648877779917364313389622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then alice is either tall or humble and vice versa.
Everyone who is kind is not quiet and vice versa.
Everyone who is humble is both not old and not calm and vice versa.
Everyone who is either not strong or not old is not happy and vice versa.
If someone is either generous or not funny then someone is both not generous and not brave and vice versa.
If someone is not quiet or not wise then someone is not wise.
Everyone who is not curious or old is not old.
If someone is not calm then lucy is not creative or not quiet and vice versa.
Everyone who is either not humble or not wise is both not curious and old and vice versa.
Everyone who is not generous is both not humble and creative and vice versa.
If someone is both not calm and patient then john is not strong and vice versa.
Everyone who is both not happy and not old is either not curious or not happy.
Everyone who is humble is not strong or not kind.
Everyone who is strong or kind is not creative or not old and vice versa.
If someone is both not patient and not funny then someone is not tall or not curious.
Everyone who is both not strong and calm is either not calm or not curious and vice versa.
Alice is both not creative and kind.
Someone is not wise.
Someone is not quiet.
Someone is both patient and not calm.
John is not humble.
Someone is either not calm or funny.
Lucy is not curious or creative.
John is both calm and not tall. | John is not quiet. | entailment | ((?[X]:(strong(X)))<=>((tall(alice)<~>humble(alice))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:(humble(X)<=>(~old(X)&~calm(X))))&
(![X]:((~strong(X)<~>~old(X))<=>~happy(X)))&
((?[X]:((generous(X)<~>~funny(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
((?[X]:((~quiet(X)|~wise(X))))=>(?[X]:(~wise(X))))&
(![X]:((~curious(X)|old(X))=>~old(X)))&
((?[X]:(~calm(X)))<=>((~creative(lucy)|~quiet(lucy))))&
(![X]:((~humble(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
(![X]:(~generous(X)<=>(~humble(X)&creative(X))))&
((?[X]:((~calm(X)&patient(X))))<=>(~strong(john)))&
(![X]:((~happy(X)&~old(X))=>(~curious(X)<~>~happy(X))))&
(![X]:(humble(X)=>(~strong(X)|~kind(X))))&
(![X]:((strong(X)|kind(X))<=>(~creative(X)|~old(X))))&
((?[X]:((~patient(X)&~funny(X))))=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~strong(X)&calm(X))<=>(~calm(X)<~>~curious(X))))&
((~creative(alice)&kind(alice)))&
(?[X]:(~wise(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)&~calm(X))))&
(~humble(john))&
(?[X]:((~calm(X)<~>funny(X))))&
((~curious(lucy)|creative(lucy)))&
((calm(john)&~tall(john))) | ~quiet(john) | [
"p1",
"p6",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6661597170040016776967860
% SZS output start Proof for 6661597170040016776967860
2. ! [X0] : (kind(X0) <=> ~quiet(X0)) [input p1]
7. ! [X0] : ((old(X0) | ~curious(X0)) => ~old(X0)) [input p6]
11. ? [X0] : (patient(X0) & ~calm(X0)) <=> ~strong(john) [input p10]
14. ! [X0] : ((kind(X0) | strong(X0)) <=> (~old(X0) | ~creative(X0))) [input p13]
20. ? [X0] : (~calm(X0) & patient(X0)) [input p19]
25. quiet(john) [input hypothesis]
30. ! [X0] : (~old(X0) | (~old(X0) & curious(X0))) [ennf transformation 7]
40. ! [X0] : ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))) [nnf transformation 2]
61. (? [X0] : (patient(X0) & ~calm(X0)) | strong(john)) & (~strong(john) | ! [X0] : (~patient(X0) | calm(X0))) [nnf transformation 11]
62. (? [X0] : (patient(X0) & ~calm(X0)) | strong(john)) & (~strong(john) | ! [X1] : (~patient(X1) | calm(X1))) [rectify 61]
63. ? [X0] : (patient(X0) & ~calm(X0)) => (patient(sK5) & ~calm(sK5)) [choice axiom]
64. ((patient(sK5) & ~calm(sK5)) | strong(john)) & (~strong(john) | ! [X1] : (~patient(X1) | calm(X1))) [skolemisation 62,63]
66. ! [X0] : (((kind(X0) | strong(X0)) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | (~kind(X0) & ~strong(X0)))) [nnf transformation 14]
67. ! [X0] : ((kind(X0) | strong(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | (~kind(X0) & ~strong(X0)))) [flattening 66]
77. ? [X0] : (~calm(X0) & patient(X0)) => (~calm(sK9) & patient(sK9)) [choice axiom]
78. ~calm(sK9) & patient(sK9) [skolemisation 20,77]
86. ~quiet(X0) | ~kind(X0) [cnf transformation 40]
104. ~old(X0) | ~old(X0) [cnf transformation 30]
117. ~strong(john) | ~patient(X1) | calm(X1) [cnf transformation 64]
126. kind(X0) | strong(X0) | old(X0) [cnf transformation 67]
138. patient(sK9) [cnf transformation 78]
139. ~calm(sK9) [cnf transformation 78]
146. quiet(john) [cnf transformation 25]
150. ~old(X0) [duplicate literal removal 104]
234. 19 <=> strong(john) [avatar definition]
248. 22 <=> ! [X1] : (~patient(X1) | calm(X1)) [avatar definition]
249. ~patient(X1) | calm(X1) <- (22) [avatar component clause 248]
250. 22 | ~19 [avatar split clause 117,234,248]
252. kind(X0) | strong(X0) [subsumption resolution 126,150]
281. ~kind(john) [resolution 86,146]
289. strong(john) [resolution 252,281]
292. 19 [avatar split clause 289,234]
293. calm(sK9) <- (22) [resolution 249,138]
295. $false <- (22) [subsumption resolution 293,139]
296. ~22 [avatar contradiction clause 295]
299. $false [avatar sat refutation 250,292,296]
% SZS output end Proof for 6661597170040016776967860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and generous is kind or old.
Everyone who is both happy and not kind is not generous or not calm.
Everyone who is either kind or rich is tall or not strong and vice versa.
If someone is not happy or not curious then john is not humble.
If someone is not rich then someone is either tall or not wise.
Everyone who is either happy or curious is creative and vice versa.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
Everyone who is not strong is not quiet or not rich and vice versa.
If paul is creative then someone is both rich and curious.
Everyone who is both not generous and old is patient or funny and vice versa.
If mary is either brave or not funny then someone is kind or not funny and vice versa.
Everyone who is humble or not curious is both calm and generous.
Someone is tall or not happy.
Someone is either not kind or not calm.
Alice is rich or not calm.
Someone is calm.
Mary is old or not strong. | John is happy. | neutral | (![X]:((~kind(X)&generous(X))=>(kind(X)|old(X))))&
(![X]:((happy(X)&~kind(X))=>(~generous(X)|~calm(X))))&
(![X]:((kind(X)<~>rich(X))<=>(tall(X)|~strong(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~rich(X))))&
((creative(paul))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~generous(X)&old(X))<=>(patient(X)|funny(X))))&
(((brave(mary)<~>~funny(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((humble(X)|~curious(X))=>(calm(X)&generous(X))))&
(?[X]:((tall(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~calm(X))))&
((rich(alice)|~calm(alice)))&
(?[X]:(calm(X)))&
((old(mary)|~strong(mary))) | happy(john) | [] | null | 0 |
Everyone who is either not curious or not kind is not happy or not strong.
Everyone who is not kind or not strong is either not humble or rich.
Everyone who is either kind or not kind is kind or not funny and vice versa.
Everyone who is not curious or quiet is not humble.
If someone is not kind then someone is not generous or not strong and vice versa.
If alice is either humble or brave then fred is not tall or not quiet.
If someone is both not curious and rich then john is generous.
If someone is not humble then someone is not brave.
If fred is both strong and not old then alice is both happy and not brave and vice versa.
Everyone who is not wise or calm is both kind and not wise.
Everyone who is not creative or quiet is either not wise or wise and vice versa.
If someone is either not humble or generous then mary is both not humble and quiet.
Everyone who is not patient is both not brave and not funny.
If someone is not old or kind then paul is patient or curious and vice versa.
Everyone who is either not happy or not funny is either patient or not patient and vice versa.
Everyone who is not quiet or humble is not humble or not quiet and vice versa.
Someone is either not strong or not rich.
Alice is both not generous and happy.
Someone is either rich or humble.
Alice is either quiet or not brave.
Fred is either not happy or not calm.
Someone is not quiet.
Someone is not humble or strong.
Someone is either not kind or not patient. | Alice is not brave. | entailment | (![X]:((~curious(X)<~>~kind(X))=>(~happy(X)|~strong(X))))&
(![X]:((~kind(X)|~strong(X))=>(~humble(X)<~>rich(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(kind(X)|~funny(X))))&
(![X]:((~curious(X)|quiet(X))=>~humble(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~generous(X)|~strong(X)))))&
(((humble(alice)<~>brave(alice)))=>((~tall(fred)|~quiet(fred))))&
((?[X]:((~curious(X)&rich(X))))=>(generous(john)))&
((?[X]:(~humble(X)))=>(?[X]:(~brave(X))))&
(((strong(fred)&~old(fred)))<=>((happy(alice)&~brave(alice))))&
(![X]:((~wise(X)|calm(X))=>(kind(X)&~wise(X))))&
(![X]:((~creative(X)|quiet(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~humble(X)<~>generous(X))))=>((~humble(mary)&quiet(mary))))&
(![X]:(~patient(X)=>(~brave(X)&~funny(X))))&
((?[X]:((~old(X)|kind(X))))<=>((patient(paul)|curious(paul))))&
(![X]:((~happy(X)<~>~funny(X))<=>(patient(X)<~>~patient(X))))&
(![X]:((~quiet(X)|humble(X))<=>(~humble(X)|~quiet(X))))&
(?[X]:((~strong(X)<~>~rich(X))))&
((~generous(alice)&happy(alice)))&
(?[X]:((rich(X)<~>humble(X))))&
((quiet(alice)<~>~brave(alice)))&
((~happy(fred)<~>~calm(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:((~humble(X)|strong(X))))&
(?[X]:((~kind(X)<~>~patient(X)))) | ~brave(alice) | [
"p3",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 89389604456357650135632
% SZS output start Proof for 89389604456357650135632
4. ! [X0] : ((quiet(X0) | ~curious(X0)) => ~humble(X0)) [input p3]
16. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p15]
20. quiet(alice) <~> ~brave(alice) [input p19]
25. brave(alice) [input hypothesis]
32. ! [X0] : (~humble(X0) | (~quiet(X0) & curious(X0))) [ennf transformation 4]
61. ! [X0] : (((humble(X0) | ~quiet(X0)) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | (~humble(X0) & quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((humble(X0) | ~quiet(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | (~humble(X0) & quiet(X0)))) [flattening 61]
69. (brave(alice) | ~quiet(alice)) & (~brave(alice) | quiet(alice)) [nnf transformation 20]
91. ~humble(X0) | ~quiet(X0) [cnf transformation 32]
131. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 62]
139. ~brave(alice) | quiet(alice) [cnf transformation 69]
147. brave(alice) [cnf transformation 25]
149. humble(X0) | ~quiet(X0) [duplicate literal removal 131]
205. 12 <=> brave(alice) [avatar definition]
268. ~quiet(X0) [subsumption resolution 149,91]
290. ~brave(alice) [subsumption resolution 139,268]
291. ~12 [avatar split clause 290,205]
321. 12 [avatar split clause 147,205]
322. $false [avatar sat refutation 291,321]
% SZS output end Proof for 89389604456357650135632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not tall or old.
If someone is both old and not tall then someone is both calm and curious and vice versa.
If john is not wise then lucy is both not happy and calm.
Everyone who is either not wise or brave is patient.
If someone is not funny or not quiet then john is wise or not creative and vice versa.
Everyone who is both calm and not patient is not funny and vice versa.
Everyone who is not rich is not old and vice versa.
Everyone who is quiet or brave is either strong or wise and vice versa.
If alice is either rich or not tall then alice is both strong and quiet.
If lucy is either not tall or quiet then someone is not tall or generous and vice versa.
If fred is both old and quiet then alice is not kind or not humble and vice versa.
If susan is tall then someone is not creative.
Everyone who is not happy is both brave and quiet and vice versa.
If someone is happy or tall then alice is both not kind and not brave.
Everyone who is not wise is both wise and rich.
If alice is either not patient or brave then someone is either not creative or brave.
John is not tall or quiet.
Lucy is not quiet.
Paul is both not tall and not brave.
Someone is not generous.
Someone is kind.
Someone is not strong.
Lucy is either not wise or not rich.
Someone is both tall and old. | Fred is not rich. | contradiction | (![X]:(old(X)=>(~tall(X)|old(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:((calm(X)&curious(X)))))&
((~wise(john))=>((~happy(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>brave(X))=>patient(X)))&
((?[X]:((~funny(X)|~quiet(X))))<=>((wise(john)|~creative(john))))&
(![X]:((calm(X)&~patient(X))<=>~funny(X)))&
(![X]:(~rich(X)<=>~old(X)))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)<~>wise(X))))&
(((rich(alice)<~>~tall(alice)))=>((strong(alice)&quiet(alice))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((old(fred)&quiet(fred)))<=>((~kind(alice)|~humble(alice))))&
((tall(susan))=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)<=>(brave(X)&quiet(X))))&
((?[X]:((happy(X)|tall(X))))=>((~kind(alice)&~brave(alice))))&
(![X]:(~wise(X)=>(wise(X)&rich(X))))&
(((~patient(alice)<~>brave(alice)))=>(?[X]:((~creative(X)<~>brave(X)))))&
((~tall(john)|quiet(john)))&
(~quiet(lucy))&
((~tall(paul)&~brave(paul)))&
(?[X]:(~generous(X)))&
(?[X]:(kind(X)))&
(?[X]:(~strong(X)))&
((~wise(lucy)<~>~rich(lucy)))&
(?[X]:((tall(X)&old(X)))) | ~rich(fred) | [
"p6",
"p10",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7392877151381981570263615
% SZS output start Proof for 7392877151381981570263615
7. ! [X0] : (~rich(X0) <=> ~old(X0)) [input p6]
11. (quiet(fred) & old(fred)) <=> (~humble(alice) | ~kind(alice)) [input p10]
14. ? [X0] : (tall(X0) | happy(X0)) => (~brave(alice) & ~kind(alice)) [input p13]
24. ? [X0] : (old(X0) & tall(X0)) [input p23]
25. ~rich(fred) [input hypothesis]
35. (~brave(alice) & ~kind(alice)) | ! [X0] : (~tall(X0) & ~happy(X0)) [ennf transformation 14]
51. ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))) [nnf transformation 7]
59. ((quiet(fred) & old(fred)) | (humble(alice) & kind(alice))) & ((~humble(alice) | ~kind(alice)) | (~quiet(fred) | ~old(fred))) [nnf transformation 11]
60. ((quiet(fred) & old(fred)) | (humble(alice) & kind(alice))) & (~humble(alice) | ~kind(alice) | ~quiet(fred) | ~old(fred)) [flattening 59]
73. ? [X0] : (old(X0) & tall(X0)) => (old(sK9) & tall(sK9)) [choice axiom]
74. old(sK9) & tall(sK9) [skolemisation 24,73]
91. ~old(X0) | rich(X0) [cnf transformation 51]
110. old(fred) | kind(alice) [cnf transformation 60]
118. ~kind(alice) | ~tall(X0) [cnf transformation 35]
136. tall(sK9) [cnf transformation 74]
138. ~rich(fred) [cnf transformation 25]
260. 27 <=> kind(alice) [avatar definition]
265. 28 <=> old(fred) [avatar definition]
267. old(fred) <- (28) [avatar component clause 265]
269. 27 | 28 [avatar split clause 110,265,260]
281. 31 <=> ! [X0] : ~tall(X0) [avatar definition]
282. ~tall(X0) <- (31) [avatar component clause 281]
292. 31 | ~27 [avatar split clause 118,260,281]
323. rich(fred) <- (28) [resolution 91,267]
324. $false <- (28) [subsumption resolution 323,138]
325. ~28 [avatar contradiction clause 324]
326. $false <- (31) [resolution 282,136]
329. ~31 [avatar contradiction clause 326]
330. $false [avatar sat refutation 269,292,325,329]
% SZS output end Proof for 7392877151381981570263615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and humble then someone is funny or quiet.
If someone is tall then alice is quiet or brave and vice versa.
If someone is not creative or rich then fred is both generous and rich.
If john is either not generous or not rich then alice is kind and vice versa.
Everyone who is not wise or rich is humble or not calm.
If someone is either humble or quiet then someone is both curious and not curious and vice versa.
Everyone who is not calm is not happy and vice versa.
Everyone who is both generous and not creative is both humble and not kind.
If susan is both not creative and not patient then someone is calm.
If lucy is strong then fred is either brave or funny.
If john is either not tall or not funny then someone is patient or strong.
If someone is not old or not curious then someone is both tall and rich.
Everyone who is not wise or brave is not creative and vice versa.
Everyone who is rich or not humble is either patient or not creative.
If alice is both rich and not funny then someone is either curious or not happy.
If fred is both curious and strong then someone is old and vice versa.
Paul is either rich or not curious.
Susan is both humble and not happy.
Someone is both brave and not curious.
Someone is both not happy and not humble.
Susan is not quiet or kind.
John is rich or curious. | John is old. | neutral | ((?[X]:((~patient(X)&humble(X))))=>(?[X]:((funny(X)|quiet(X)))))&
((?[X]:(tall(X)))<=>((quiet(alice)|brave(alice))))&
((?[X]:((~creative(X)|rich(X))))=>((generous(fred)&rich(fred))))&
(((~generous(john)<~>~rich(john)))<=>(kind(alice)))&
(![X]:((~wise(X)|rich(X))=>(humble(X)|~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:(~calm(X)<=>~happy(X)))&
(![X]:((generous(X)&~creative(X))=>(humble(X)&~kind(X))))&
(((~creative(susan)&~patient(susan)))=>(?[X]:(calm(X))))&
((strong(lucy))=>((brave(fred)<~>funny(fred))))&
(((~tall(john)<~>~funny(john)))=>(?[X]:((patient(X)|strong(X)))))&
((?[X]:((~old(X)|~curious(X))))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((~wise(X)|brave(X))<=>~creative(X)))&
(![X]:((rich(X)|~humble(X))=>(patient(X)<~>~creative(X))))&
(((rich(alice)&~funny(alice)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(((curious(fred)&strong(fred)))<=>(?[X]:(old(X))))&
((rich(paul)<~>~curious(paul)))&
((humble(susan)&~happy(susan)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~happy(X)&~humble(X))))&
((~quiet(susan)|kind(susan)))&
((rich(john)|curious(john))) | old(john) | [] | null | 0 |
Everyone who is either kind or not old is rich and vice versa.
If paul is both not generous and wise then susan is either not curious or not kind.
If paul is patient then someone is both tall and not kind.
Everyone who is both happy and not wise is wise.
Everyone who is both not calm and generous is not calm.
If someone is not strong or not wise then john is not old.
Everyone who is both not funny and patient is not rich and vice versa.
If someone is both happy and not generous then lucy is both strong and not kind and vice versa.
If fred is not wise then fred is funny and vice versa.
If someone is not quiet or not calm then mary is both not patient and not funny and vice versa.
Everyone who is both creative and not calm is either patient or not kind.
Everyone who is old or rich is not rich.
If mary is not humble or not brave then someone is not patient or not creative.
If paul is quiet then someone is not happy or not wise and vice versa.
If mary is wise or not brave then lucy is either not creative or humble.
If john is either not humble or not rich then someone is old or happy.
Someone is kind.
Someone is not tall or not quiet.
Paul is not wise.
Someone is not curious or wise.
Someone is humble.
Someone is both kind and not old. | Lucy is quiet. | entailment | (![X]:((kind(X)<~>~old(X))<=>rich(X)))&
(((~generous(paul)&wise(paul)))=>((~curious(susan)<~>~kind(susan))))&
((patient(paul))=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((happy(X)&~wise(X))=>wise(X)))&
(![X]:((~calm(X)&generous(X))=>~calm(X)))&
((?[X]:((~strong(X)|~wise(X))))=>(~old(john)))&
(![X]:((~funny(X)&patient(X))<=>~rich(X)))&
((?[X]:((happy(X)&~generous(X))))<=>((strong(lucy)&~kind(lucy))))&
((~wise(fred))<=>(funny(fred)))&
((?[X]:((~quiet(X)|~calm(X))))<=>((~patient(mary)&~funny(mary))))&
(![X]:((creative(X)&~calm(X))=>(patient(X)<~>~kind(X))))&
(![X]:((old(X)|rich(X))=>~rich(X)))&
(((~humble(mary)|~brave(mary)))=>(?[X]:((~patient(X)|~creative(X)))))&
((quiet(paul))<=>(?[X]:((~happy(X)|~wise(X)))))&
(((wise(mary)|~brave(mary)))=>((~creative(lucy)<~>humble(lucy))))&
(((~humble(john)<~>~rich(john)))=>(?[X]:((old(X)|happy(X)))))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)|~quiet(X))))&
(~wise(paul))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:(humble(X)))&
(?[X]:((kind(X)&~old(X)))) | quiet(lucy) | [
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 305525295775062902916670
% SZS output start Proof for 305525295775062902916670
7. ! [X0] : ((patient(X0) & ~funny(X0)) <=> ~rich(X0)) [input p6]
10. ? [X0] : (~calm(X0) | ~quiet(X0)) <=> (~funny(mary) & ~patient(mary)) [input p9]
12. ! [X0] : ((rich(X0) | old(X0)) => ~rich(X0)) [input p11]
23. ~quiet(lucy) [input hypothesis]
36. ! [X0] : (~rich(X0) | (~rich(X0) & ~old(X0))) [ennf transformation 12]
44. ! [X0] : (((patient(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((patient(X0) & ~funny(X0)) | rich(X0)) & (~rich(X0) | ~patient(X0) | funny(X0))) [flattening 44]
52. (? [X0] : (~calm(X0) | ~quiet(X0)) | (funny(mary) | patient(mary))) & ((~funny(mary) & ~patient(mary)) | ! [X0] : (calm(X0) & quiet(X0))) [nnf transformation 10]
53. (? [X0] : (~calm(X0) | ~quiet(X0)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X0] : (calm(X0) & quiet(X0))) [flattening 52]
54. (? [X0] : (~calm(X0) | ~quiet(X0)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : (calm(X1) & quiet(X1))) [rectify 53]
55. ? [X0] : (~calm(X0) | ~quiet(X0)) => (~calm(sK2) | ~quiet(sK2)) [choice axiom]
56. ((~calm(sK2) | ~quiet(sK2)) | funny(mary) | patient(mary)) & ((~funny(mary) & ~patient(mary)) | ! [X1] : (calm(X1) & quiet(X1))) [skolemisation 54,55]
92. patient(X0) | rich(X0) [cnf transformation 45]
99. ~patient(mary) | quiet(X1) [cnf transformation 56]
107. ~rich(X0) | ~rich(X0) [cnf transformation 36]
123. ~quiet(lucy) [cnf transformation 23]
124. ~rich(X0) [duplicate literal removal 107]
204. 18 <=> patient(mary) [avatar definition]
205. ~patient(mary) <- (~18) [avatar component clause 204]
225. 23 <=> ! [X1] : quiet(X1) [avatar definition]
226. quiet(X1) <- (23) [avatar component clause 225]
229. 23 | ~18 [avatar split clause 99,204,225]
309. rich(mary) <- (~18) [resolution 92,205]
312. $false <- (~18) [subsumption resolution 309,124]
313. 18 [avatar contradiction clause 312]
316. $false <- (23) [resolution 226,123]
319. ~23 [avatar contradiction clause 316]
320. $false [avatar sat refutation 229,313,319]
% SZS output end Proof for 305525295775062902916670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or strong then paul is not funny and vice versa.
Everyone who is not calm is not old or happy.
If fred is either curious or strong then someone is both not funny and not quiet.
Everyone who is not strong or generous is both calm and funny and vice versa.
Everyone who is not curious is both happy and brave.
If someone is not strong or not kind then someone is both funny and rich and vice versa.
Everyone who is not rich or not curious is not strong or not old and vice versa.
If someone is generous then alice is either quiet or rich and vice versa.
If mary is both happy and kind then susan is generous.
Everyone who is not old is tall.
Everyone who is either not brave or not quiet is not curious.
Everyone who is calm is kind and vice versa.
Everyone who is not patient or not creative is both wise and tall.
If susan is either not curious or not funny then john is both calm and not rich and vice versa.
Everyone who is happy is either not curious or curious and vice versa.
Everyone who is either not kind or not quiet is humble or not old and vice versa.
Alice is either not tall or not wise.
Someone is either not tall or tall.
Susan is rich or quiet.
Someone is both not wise and tall.
Someone is not funny.
Paul is not kind or not humble.
Someone is happy or generous.
Someone is brave. | Paul is generous. | contradiction | ((?[X]:((~happy(X)<~>strong(X))))<=>(~funny(paul)))&
(![X]:(~calm(X)=>(~old(X)|happy(X))))&
(((curious(fred)<~>strong(fred)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)&funny(X))))&
(![X]:(~curious(X)=>(happy(X)&brave(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~strong(X)|~old(X))))&
((?[X]:(generous(X)))<=>((quiet(alice)<~>rich(alice))))&
(((happy(mary)&kind(mary)))=>(generous(susan)))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((~brave(X)<~>~quiet(X))=>~curious(X)))&
(![X]:(calm(X)<=>kind(X)))&
(![X]:((~patient(X)|~creative(X))=>(wise(X)&tall(X))))&
(((~curious(susan)<~>~funny(susan)))<=>((calm(john)&~rich(john))))&
(![X]:(happy(X)<=>(~curious(X)<~>curious(X))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(humble(X)|~old(X))))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((~tall(X)<~>tall(X))))&
((rich(susan)|quiet(susan)))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:(~funny(X)))&
((~kind(paul)|~humble(paul)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:(brave(X))) | generous(paul) | [
"p0",
"p3",
"p4",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2442997332840597279687821
% SZS output start Proof for 2442997332840597279687821
1. ? [X0] : (~happy(X0) <~> strong(X0)) <=> ~funny(paul) [input p0]
4. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (funny(X0) & calm(X0))) [input p3]
5. ! [X0] : (~curious(X0) => (brave(X0) & happy(X0))) [input p4]
15. ! [X0] : (happy(X0) <=> (~curious(X0) <~> curious(X0))) [input p14]
21. ? [X0] : ~funny(X0) [input p20]
25. generous(paul) [input hypothesis]
32. ! [X0] : ((brave(X0) & happy(X0)) | curious(X0)) [ennf transformation 5]
37. (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | funny(paul)) & (~funny(paul) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) [nnf transformation 1]
38. (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | funny(paul)) & (~funny(paul) | ! [X1] : ((~happy(X1) | ~strong(X1)) & (strong(X1) | happy(X1)))) [rectify 37]
39. ? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) => ((~strong(sK0) | happy(sK0)) & (strong(sK0) | ~happy(sK0))) [choice axiom]
40. (((~strong(sK0) | happy(sK0)) & (strong(sK0) | ~happy(sK0))) | funny(paul)) & (~funny(paul) | ! [X1] : ((~happy(X1) | ~strong(X1)) & (strong(X1) | happy(X1)))) [skolemisation 38,39]
44. ! [X0] : (((generous(X0) | ~strong(X0)) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | (~generous(X0) & strong(X0)))) [nnf transformation 4]
45. ! [X0] : ((generous(X0) | ~strong(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | (~generous(X0) & strong(X0)))) [flattening 44]
61. ! [X0] : ((happy(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 15]
70. ? [X0] : ~funny(X0) => ~funny(sK7) [choice axiom]
71. ~funny(sK7) [skolemisation 21,70]
77. ~funny(paul) | ~happy(X1) | ~strong(X1) [cnf transformation 40]
87. funny(X0) | strong(X0) [cnf transformation 45]
88. ~generous(X0) | funny(X0) [cnf transformation 45]
90. curious(X0) | happy(X0) [cnf transformation 32]
120. happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 61]
134. ~funny(sK7) [cnf transformation 71]
138. generous(paul) [cnf transformation 25]
140. happy(X0) | ~curious(X0) [duplicate literal removal 120]
142. 1 <=> funny(paul) [avatar definition]
156. 4 <=> ! [X1] : (~happy(X1) | ~strong(X1)) [avatar definition]
157. ~happy(X1) | ~strong(X1) <- (4) [avatar component clause 156]
158. 4 | ~1 [avatar split clause 77,142,156]
268. happy(X0) [subsumption resolution 140,90]
312. strong(sK7) [resolution 87,134]
315. funny(paul) [resolution 88,138]
319. 1 [avatar split clause 315,142]
320. ~strong(X1) <- (4) [subsumption resolution 157,268]
327. $false <- (4) [resolution 312,320]
328. ~4 [avatar contradiction clause 327]
329. $false [avatar sat refutation 158,319,328]
% SZS output end Proof for 2442997332840597279687821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or rich is not calm or not wise and vice versa.
Everyone who is both not tall and not curious is calm or generous and vice versa.
Everyone who is both calm and funny is not curious.
Everyone who is brave or not funny is either not funny or not wise and vice versa.
Everyone who is either not kind or not creative is not strong or not wise.
If alice is either strong or not funny then susan is both funny and not patient and vice versa.
Everyone who is both not rich and not wise is curious.
Everyone who is either old or humble is patient or wise.
Everyone who is funny or not tall is either rich or wise and vice versa.
Everyone who is either not old or tall is either not generous or calm and vice versa.
If alice is not calm or not curious then someone is either creative or not generous.
Everyone who is not brave or not humble is either kind or creative and vice versa.
Everyone who is not happy or not old is not curious or not strong and vice versa.
If susan is both rich and funny then susan is quiet.
If john is either not funny or curious then someone is strong or not generous.
Everyone who is generous or brave is not kind or not tall and vice versa.
Mary is not curious or not wise.
Someone is not curious.
John is wise or kind.
Fred is either not brave or kind.
John is patient.
Someone is both not strong and not happy.
Someone is both happy and not quiet.
Alice is both not tall and generous. | Susan is not funny. | neutral | (![X]:((~brave(X)|rich(X))<=>(~calm(X)|~wise(X))))&
(![X]:((~tall(X)&~curious(X))<=>(calm(X)|generous(X))))&
(![X]:((calm(X)&funny(X))=>~curious(X)))&
(![X]:((brave(X)|~funny(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(~strong(X)|~wise(X))))&
(((strong(alice)<~>~funny(alice)))<=>((funny(susan)&~patient(susan))))&
(![X]:((~rich(X)&~wise(X))=>curious(X)))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|wise(X))))&
(![X]:((funny(X)|~tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>calm(X))))&
(((~calm(alice)|~curious(alice)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)|~strong(X))))&
(((rich(susan)&funny(susan)))=>(quiet(susan)))&
(((~funny(john)<~>curious(john)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((generous(X)|brave(X))<=>(~kind(X)|~tall(X))))&
((~curious(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((wise(john)|kind(john)))&
((~brave(fred)<~>kind(fred)))&
(patient(john))&
(?[X]:((~strong(X)&~happy(X))))&
(?[X]:((happy(X)&~quiet(X))))&
((~tall(alice)&generous(alice))) | ~funny(susan) | [] | null | 0 |
If alice is not curious then mary is funny.
If someone is not kind or wise then someone is both not strong and generous.
If someone is either not rich or strong then paul is either not tall or funny.
Everyone who is tall or not old is both not wise and not old.
If paul is either not rich or not quiet then someone is both not brave and not curious.
If someone is both old and not happy then lucy is not old or generous.
Everyone who is not old or not brave is not calm.
Everyone who is brave is either brave or not wise.
Everyone who is not tall or quiet is both rich and not curious and vice versa.
If lucy is either not patient or not generous then someone is not rich and vice versa.
Everyone who is not wise is both not wise and brave and vice versa.
If someone is not calm then paul is both not humble and creative.
Everyone who is either tall or funny is either patient or not calm and vice versa.
Everyone who is both not humble and patient is not calm or generous.
If paul is either not old or quiet then someone is kind or not creative.
Someone is rich or not brave.
Someone is either funny or not strong.
Someone is happy or not creative.
Someone is quiet or not old.
Someone is not funny.
Someone is not funny or not happy. | Alice is old. | entailment | ((~curious(alice))=>(funny(mary)))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>((~tall(paul)<~>funny(paul))))&
(![X]:((tall(X)|~old(X))=>(~wise(X)&~old(X))))&
(((~rich(paul)<~>~quiet(paul)))=>(?[X]:((~brave(X)&~curious(X)))))&
((?[X]:((old(X)&~happy(X))))=>((~old(lucy)|generous(lucy))))&
(![X]:((~old(X)|~brave(X))=>~calm(X)))&
(![X]:(brave(X)=>(brave(X)<~>~wise(X))))&
(![X]:((~tall(X)|quiet(X))<=>(rich(X)&~curious(X))))&
(((~patient(lucy)<~>~generous(lucy)))<=>(?[X]:(~rich(X))))&
(![X]:(~wise(X)<=>(~wise(X)&brave(X))))&
((?[X]:(~calm(X)))=>((~humble(paul)&creative(paul))))&
(![X]:((tall(X)<~>funny(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((~humble(X)&patient(X))=>(~calm(X)|generous(X))))&
(((~old(paul)<~>quiet(paul)))=>(?[X]:((kind(X)|~creative(X)))))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|~happy(X)))) | old(alice) | [
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6541711226758015040225114
% SZS output start Proof for 6541711226758015040225114
4. ! [X0] : ((~old(X0) | tall(X0)) => (~old(X0) & ~wise(X0))) [input p3]
8. ! [X0] : (brave(X0) => (brave(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : (~wise(X0) <=> (brave(X0) & ~wise(X0))) [input p10]
22. ~old(alice) [input hypothesis]
29. ! [X0] : ((~old(X0) & ~wise(X0)) | (old(X0) & ~tall(X0))) [ennf transformation 4]
34. ! [X0] : ((brave(X0) <~> ~wise(X0)) | ~brave(X0)) [ennf transformation 8]
45. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ~brave(X0)) [nnf transformation 34]
52. ! [X0] : ((~wise(X0) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((~wise(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | wise(X0))) [flattening 52]
76. ~wise(X0) | old(X0) [cnf transformation 29]
87. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 45]
98. brave(X0) | wise(X0) [cnf transformation 53]
118. ~old(alice) [cnf transformation 22]
119. wise(X0) | ~brave(X0) [duplicate literal removal 87]
207. wise(X0) [subsumption resolution 98,119]
269. old(X0) [resolution 76,207]
270. $false [resolution 269,118]
% SZS output end Proof for 6541711226758015040225114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not humble is not generous and vice versa.
Everyone who is not quiet is kind or tall and vice versa.
Everyone who is either not generous or not creative is either patient or strong and vice versa.
If someone is either not humble or humble then susan is both wise and not old and vice versa.
If someone is either not generous or not happy then lucy is either not strong or not creative.
If john is both strong and not patient then lucy is either curious or not old.
If someone is not brave then fred is not tall or not calm and vice versa.
If someone is both not wise and patient then someone is both not humble and not brave and vice versa.
Everyone who is either not wise or not happy is either humble or kind and vice versa.
Everyone who is funny or humble is both curious and not old.
Everyone who is both not generous and not calm is not kind.
Everyone who is not curious is not tall or calm and vice versa.
If paul is curious or funny then someone is either wise or not tall.
If someone is both humble and calm then lucy is both rich and not old.
Everyone who is either not calm or patient is not strong or kind.
If someone is old then alice is not quiet and vice versa.
Alice is not humble.
Someone is both not tall and brave.
Lucy is brave.
Someone is either not creative or strong.
Someone is both curious and wise.
John is funny.
Someone is either not funny or not patient.
Someone is humble. | Susan is wise. | entailment | (![X]:((strong(X)<~>~humble(X))<=>~generous(X)))&
(![X]:(~quiet(X)<=>(kind(X)|tall(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((~humble(X)<~>humble(X))))<=>((wise(susan)&~old(susan))))&
((?[X]:((~generous(X)<~>~happy(X))))=>((~strong(lucy)<~>~creative(lucy))))&
(((strong(john)&~patient(john)))=>((curious(lucy)<~>~old(lucy))))&
((?[X]:(~brave(X)))<=>((~tall(fred)|~calm(fred))))&
((?[X]:((~wise(X)&patient(X))))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)<~>kind(X))))&
(![X]:((funny(X)|humble(X))=>(curious(X)&~old(X))))&
(![X]:((~generous(X)&~calm(X))=>~kind(X)))&
(![X]:(~curious(X)<=>(~tall(X)|calm(X))))&
(((curious(paul)|funny(paul)))=>(?[X]:((wise(X)<~>~tall(X)))))&
((?[X]:((humble(X)&calm(X))))=>((rich(lucy)&~old(lucy))))&
(![X]:((~calm(X)<~>patient(X))=>(~strong(X)|kind(X))))&
((?[X]:(old(X)))<=>(~quiet(alice)))&
(~humble(alice))&
(?[X]:((~tall(X)&brave(X))))&
(brave(lucy))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((curious(X)&wise(X))))&
(funny(john))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:(humble(X))) | wise(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7759668893722511742537655
% SZS output start Proof for 7759668893722511742537655
4. ? [X0] : (~humble(X0) <~> humble(X0)) <=> (~old(susan) & wise(susan)) [input p3]
25. ~wise(susan) [input hypothesis]
42. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (old(susan) | ~wise(susan))) & ((~old(susan) & wise(susan)) | ! [X0] : ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 4]
43. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X0] : ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [flattening 42]
44. (? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X1] : ((~humble(X1) | ~humble(X1)) & (humble(X1) | humble(X1)))) [rectify 43]
45. ? [X0] : ((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) => ((~humble(sK0) | humble(sK0)) & (humble(sK0) | ~humble(sK0))) [choice axiom]
46. (((~humble(sK0) | humble(sK0)) & (humble(sK0) | ~humble(sK0))) | old(susan) | ~wise(susan)) & ((~old(susan) & wise(susan)) | ! [X1] : ((~humble(X1) | ~humble(X1)) & (humble(X1) | humble(X1)))) [skolemisation 44,45]
97. wise(susan) | humble(X1) | humble(X1) [cnf transformation 46]
98. wise(susan) | ~humble(X1) | ~humble(X1) [cnf transformation 46]
153. ~wise(susan) [cnf transformation 25]
154. wise(susan) | humble(X1) [duplicate literal removal 97]
155. wise(susan) | ~humble(X1) [duplicate literal removal 98]
159. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
160. ~humble(X1) <- (1) [avatar component clause 159]
167. 3 <=> ! [X1] : humble(X1) [avatar definition]
168. humble(X1) <- (3) [avatar component clause 167]
171. 4 <=> wise(susan) [avatar definition]
174. 1 | 4 [avatar split clause 155,171,159]
175. 3 | 4 [avatar split clause 154,171,167]
313. ~4 [avatar split clause 153,171]
314. $false <- (1, 3) [subsumption resolution 160,168]
315. ~1 | ~3 [avatar contradiction clause 314]
316. $false [avatar sat refutation 174,175,313,315]
% SZS output end Proof for 7759668893722511742537655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or happy is old. Everyone who is both kind and not kind is not brave or curious. Everyone who is quiet is not wise and vice versa. Everyone who is not generous or not old is not quiet and vice versa. If lucy is not curious then someone is not rich or not patient and vice versa. If someone is either funny or not quiet then someone is both not rich and not creative and vice versa. Everyone who is both curious and not brave is both patient and strong. Everyone who is quiet is either not rich or funny. Everyone who is either humble or not curious is either not happy or not quiet. Everyone who is either not creative or not patient is both happy and generous. Everyone who is not happy or patient is either not calm or not humble and vice versa. Everyone who is either not quiet or not strong is not humble. Everyone who is both not kind and not old is either not generous or not quiet and vice versa. If lucy is either not curious or not rich then mary is either not quiet or curious. If someone is brave then someone is both not brave and tall. If someone is wise then lucy is creative or not tall and vice versa. Someone is curious or not old. Fred is not wise. Someone is old or not rich. Someone is both not kind and not brave. John is not kind. Mary is not humble or humble. Fred is either curious or not creative. Someone is patient or not wise. | Fred is creative. | neutral | (![X]:((~humble(X)|happy(X))=>old(X)))&
(![X]:((kind(X)&~kind(X))=>(~brave(X)|curious(X))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((~generous(X)|~old(X))<=>~quiet(X)))&
((~curious(lucy))<=>(?[X]:((~rich(X)|~patient(X)))))&
((?[X]:((funny(X)<~>~quiet(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((curious(X)&~brave(X))=>(patient(X)&strong(X))))&
(![X]:(quiet(X)=>(~rich(X)<~>funny(X))))&
(![X]:((humble(X)<~>~curious(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>~patient(X))=>(happy(X)&generous(X))))&
(![X]:((~happy(X)|patient(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>~humble(X)))&
(![X]:((~kind(X)&~old(X))<=>(~generous(X)<~>~quiet(X))))&
(((~curious(lucy)<~>~rich(lucy)))=>((~quiet(mary)<~>curious(mary))))&
((?[X]:(brave(X)))=>(?[X]:((~brave(X)&tall(X)))))&
((?[X]:(wise(X)))<=>((creative(lucy)|~tall(lucy))))&
(?[X]:((curious(X)|~old(X))))&
(~wise(fred))&
(?[X]:((old(X)|~rich(X))))&
(?[X]:((~kind(X)&~brave(X))))&
(~kind(john))&
((~humble(mary)|humble(mary)))&
((curious(fred)<~>~creative(fred)))&
(?[X]:((patient(X)|~wise(X)))) | creative(fred) | [] | null | 0 |
If someone is not funny then someone is curious or not tall.
If someone is curious or not calm then mary is not tall and vice versa.
Everyone who is both creative and not rich is patient or brave.
Everyone who is both not creative and strong is either not calm or not happy.
If mary is both happy and strong then someone is either not tall or not creative.
Everyone who is either not wise or not brave is both old and generous and vice versa.
Everyone who is tall is not tall or not kind.
Everyone who is curious or brave is both not tall and not humble and vice versa.
If lucy is not strong or funny then someone is not funny or not creative and vice versa.
If someone is generous then susan is not calm or not curious.
Everyone who is strong is calm or not happy.
Everyone who is either curious or not tall is both humble and old.
Everyone who is both creative and not humble is not wise.
Everyone who is old is both not tall and kind.
If someone is both strong and not happy then lucy is both tall and curious and vice versa.
Everyone who is generous or not strong is brave.
Someone is not creative.
Lucy is both strong and old.
Alice is either not funny or not wise.
Someone is either not funny or not brave.
Alice is either not funny or not strong.
Fred is both not strong and not funny.
Someone is both funny and calm.
Paul is both curious and old. | Alice is not wise. | entailment | ((?[X]:(~funny(X)))=>(?[X]:((curious(X)|~tall(X)))))&
((?[X]:((curious(X)|~calm(X))))<=>(~tall(mary)))&
(![X]:((creative(X)&~rich(X))=>(patient(X)|brave(X))))&
(![X]:((~creative(X)&strong(X))=>(~calm(X)<~>~happy(X))))&
(((happy(mary)&strong(mary)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(![X]:((~wise(X)<~>~brave(X))<=>(old(X)&generous(X))))&
(![X]:(tall(X)=>(~tall(X)|~kind(X))))&
(![X]:((curious(X)|brave(X))<=>(~tall(X)&~humble(X))))&
(((~strong(lucy)|funny(lucy)))<=>(?[X]:((~funny(X)|~creative(X)))))&
((?[X]:(generous(X)))=>((~calm(susan)|~curious(susan))))&
(![X]:(strong(X)=>(calm(X)|~happy(X))))&
(![X]:((curious(X)<~>~tall(X))=>(humble(X)&old(X))))&
(![X]:((creative(X)&~humble(X))=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)&kind(X))))&
((?[X]:((strong(X)&~happy(X))))<=>((tall(lucy)&curious(lucy))))&
(![X]:((generous(X)|~strong(X))=>brave(X)))&
(?[X]:(~creative(X)))&
((strong(lucy)&old(lucy)))&
((~funny(alice)<~>~wise(alice)))&
(?[X]:((~funny(X)<~>~brave(X))))&
((~funny(alice)<~>~strong(alice)))&
((~strong(fred)&~funny(fred)))&
(?[X]:((funny(X)&calm(X))))&
((curious(paul)&old(paul))) | ~wise(alice) | [
"p3",
"p5",
"p7",
"p10",
"p12",
"p13",
"p14",
"p15",
"p17",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4551699644868743873412787
% SZS output start Proof for 4551699644868743873412787
4. ! [X0] : ((strong(X0) & ~creative(X0)) => (~calm(X0) <~> ~happy(X0))) [input p3]
6. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (generous(X0) & old(X0))) [input p5]
8. ! [X0] : ((brave(X0) | curious(X0)) <=> (~humble(X0) & ~tall(X0))) [input p7]
11. ! [X0] : (strong(X0) => (~happy(X0) | calm(X0))) [input p10]
13. ! [X0] : ((~humble(X0) & creative(X0)) => ~wise(X0)) [input p12]
14. ! [X0] : (old(X0) => (kind(X0) & ~tall(X0))) [input p13]
15. ? [X0] : (~happy(X0) & strong(X0)) <=> (curious(lucy) & tall(lucy)) [input p14]
16. ! [X0] : ((~strong(X0) | generous(X0)) => brave(X0)) [input p15]
18. old(lucy) & strong(lucy) [input p17]
19. ~funny(alice) <~> ~wise(alice) [input p18]
21. ~funny(alice) <~> ~strong(alice) [input p20]
25. wise(alice) [input hypothesis]
29. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 4]
30. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | ~strong(X0) | creative(X0)) [flattening 29]
37. ! [X0] : ((~happy(X0) | calm(X0)) | ~strong(X0)) [ennf transformation 11]
38. ! [X0] : (~happy(X0) | calm(X0) | ~strong(X0)) [flattening 37]
40. ! [X0] : (~wise(X0) | (humble(X0) | ~creative(X0))) [ennf transformation 13]
41. ! [X0] : (~wise(X0) | humble(X0) | ~creative(X0)) [flattening 40]
42. ! [X0] : ((kind(X0) & ~tall(X0)) | ~old(X0)) [ennf transformation 14]
43. ! [X0] : (brave(X0) | (strong(X0) & ~generous(X0))) [ennf transformation 16]
51. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ~strong(X0) | creative(X0)) [nnf transformation 30]
55. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~generous(X0) | ~old(X0))) & ((generous(X0) & old(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 6]
56. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | ~generous(X0) | ~old(X0)) & ((generous(X0) & old(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [flattening 55]
57. ! [X0] : (((brave(X0) | curious(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 8]
58. ! [X0] : ((brave(X0) | curious(X0) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 57]
65. (? [X0] : (~happy(X0) & strong(X0)) | (~curious(lucy) | ~tall(lucy))) & ((curious(lucy) & tall(lucy)) | ! [X0] : (happy(X0) | ~strong(X0))) [nnf transformation 15]
66. (? [X0] : (~happy(X0) & strong(X0)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X0] : (happy(X0) | ~strong(X0))) [flattening 65]
67. (? [X0] : (~happy(X0) & strong(X0)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X1] : (happy(X1) | ~strong(X1))) [rectify 66]
68. ? [X0] : (~happy(X0) & strong(X0)) => (~happy(sK4) & strong(sK4)) [choice axiom]
69. ((~happy(sK4) & strong(sK4)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X1] : (happy(X1) | ~strong(X1))) [skolemisation 67,68]
72. (wise(alice) | funny(alice)) & (~wise(alice) | ~funny(alice)) [nnf transformation 19]
76. (strong(alice) | funny(alice)) & (~strong(alice) | ~funny(alice)) [nnf transformation 21]
83. ~happy(X0) | ~calm(X0) | ~strong(X0) | creative(X0) [cnf transformation 51]
90. ~wise(X0) | generous(X0) | brave(X0) [cnf transformation 56]
97. ~humble(X0) | ~brave(X0) [cnf transformation 58]
104. ~happy(X0) | calm(X0) | ~strong(X0) [cnf transformation 38]
109. ~wise(X0) | humble(X0) | ~creative(X0) [cnf transformation 41]
110. ~old(X0) | ~tall(X0) [cnf transformation 42]
112. tall(lucy) | happy(X1) | ~strong(X1) [cnf transformation 69]
116. ~generous(X0) | brave(X0) [cnf transformation 43]
120. old(lucy) [cnf transformation 18]
121. ~wise(alice) | ~funny(alice) [cnf transformation 72]
126. strong(alice) | funny(alice) [cnf transformation 76]
133. wise(alice) [cnf transformation 25]
222. 21 <=> ! [X1] : (happy(X1) | ~strong(X1)) [avatar definition]
223. ~strong(X1) | happy(X1) <- (21) [avatar component clause 222]
230. 23 <=> tall(lucy) [avatar definition]
233. 21 | 23 [avatar split clause 112,230,222]
236. 24 <=> funny(alice) [avatar definition]
240. 25 <=> wise(alice) [avatar definition]
242. wise(alice) <- (25) [avatar component clause 240]
244. ~24 | ~25 [avatar split clause 121,240,236]
256. 28 <=> strong(alice) [avatar definition]
258. strong(alice) <- (28) [avatar component clause 256]
259. 24 | 28 [avatar split clause 126,256,236]
261. 25 [avatar split clause 133,240]
262. ~tall(lucy) [resolution 110,120]
264. ~23 [avatar split clause 262,230]
272. happy(alice) <- (21, 28) [resolution 223,258]
286. 31 <=> brave(alice) [avatar definition]
298. generous(alice) | brave(alice) <- (25) [resolution 90,242]
302. calm(alice) | ~strong(alice) <- (21, 28) [resolution 104,272]
304. calm(alice) <- (21, 28) [subsumption resolution 302,258]
310. humble(alice) | ~creative(alice) <- (25) [resolution 109,242]
313. 33 <=> creative(alice) [avatar definition]
317. 34 <=> humble(alice) [avatar definition]
319. humble(alice) <- (34) [avatar component clause 317]
320. ~33 | 34 | ~25 [avatar split clause 310,240,317,313]
331. ~calm(alice) | ~strong(alice) | creative(alice) <- (21, 28) [resolution 83,272]
334. ~strong(alice) | creative(alice) <- (21, 28) [subsumption resolution 331,304]
335. creative(alice) <- (21, 28) [subsumption resolution 334,258]
338. 33 | ~21 | ~28 [avatar split clause 335,256,222,313]
342. ~brave(alice) <- (34) [resolution 319,97]
346. ~31 | ~34 [avatar split clause 342,317,286]
347. brave(alice) <- (25) [subsumption resolution 298,116]
348. 31 | ~25 [avatar split clause 347,240,286]
349. $false [avatar sat refutation 233,244,259,261,264,320,338,346,348]
% SZS output end Proof for 4551699644868743873412787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either kind or old then susan is not rich or not tall.
Everyone who is generous or funny is old or happy.
Everyone who is either not quiet or creative is either wise or not calm.
Everyone who is creative or not wise is either not tall or humble and vice versa.
Everyone who is both not tall and old is either creative or brave and vice versa.
Everyone who is not wise or generous is not generous.
Everyone who is either patient or kind is not humble and vice versa.
Everyone who is calm or creative is either strong or wise.
If alice is either not wise or not funny then someone is patient or generous and vice versa.
Everyone who is either not quiet or not tall is not funny.
Everyone who is either curious or not old is not kind or not tall.
Everyone who is either not funny or kind is either not wise or not calm.
Everyone who is both not tall and humble is both tall and funny and vice versa.
Everyone who is either not wise or not rich is either not funny or not calm and vice versa.
If susan is either not creative or wise then someone is curious and vice versa.
If someone is not patient or happy then alice is not curious and vice versa.
Someone is strong or quiet.
Susan is both not generous and not happy.
Susan is either not tall or quiet.
Someone is creative or patient.
Paul is both rich and strong.
Someone is brave or not calm. | Paul is not happy. | neutral | (((kind(fred)<~>old(fred)))=>((~rich(susan)|~tall(susan))))&
(![X]:((generous(X)|funny(X))=>(old(X)|happy(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(wise(X)<~>~calm(X))))&
(![X]:((creative(X)|~wise(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((~tall(X)&old(X))<=>(creative(X)<~>brave(X))))&
(![X]:((~wise(X)|generous(X))=>~generous(X)))&
(![X]:((patient(X)<~>kind(X))<=>~humble(X)))&
(![X]:((calm(X)|creative(X))=>(strong(X)<~>wise(X))))&
(((~wise(alice)<~>~funny(alice)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~quiet(X)<~>~tall(X))=>~funny(X)))&
(![X]:((curious(X)<~>~old(X))=>(~kind(X)|~tall(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((~tall(X)&humble(X))<=>(tall(X)&funny(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>(~funny(X)<~>~calm(X))))&
(((~creative(susan)<~>wise(susan)))<=>(?[X]:(curious(X))))&
((?[X]:((~patient(X)|happy(X))))<=>(~curious(alice)))&
(?[X]:((strong(X)|quiet(X))))&
((~generous(susan)&~happy(susan)))&
((~tall(susan)<~>quiet(susan)))&
(?[X]:((creative(X)|patient(X))))&
((rich(paul)&strong(paul)))&
(?[X]:((brave(X)|~calm(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is humble or curious is strong.
Everyone who is not brave or humble is not generous or curious and vice versa.
Everyone who is both not strong and rich is both not curious and not strong and vice versa.
Everyone who is happy or funny is either not strong or patient.
Everyone who is strong or patient is not wise and vice versa.
Everyone who is not patient or not kind is both funny and not happy and vice versa.
Everyone who is either not old or not rich is both not creative and old and vice versa.
Everyone who is both not happy and quiet is not wise.
If paul is quiet then susan is both rich and humble.
Everyone who is either not curious or not quiet is happy.
Everyone who is generous is creative or not happy and vice versa.
If mary is both creative and not quiet then someone is either not generous or not humble.
If lucy is quiet or brave then someone is both not humble and quiet and vice versa.
If lucy is both not kind and not brave then alice is either happy or old and vice versa.
Everyone who is either generous or not old is either rich or quiet and vice versa.
Someone is not humble.
Someone is both brave and not quiet.
Susan is not kind.
Lucy is not tall or humble.
Alice is not patient or brave.
Someone is curious or not quiet.
Lucy is wise.
Someone is brave or not rich. | Alice is wise. | contradiction | (![X]:((humble(X)|curious(X))=>strong(X)))&
(![X]:((~brave(X)|humble(X))<=>(~generous(X)|curious(X))))&
(![X]:((~strong(X)&rich(X))<=>(~curious(X)&~strong(X))))&
(![X]:((happy(X)|funny(X))=>(~strong(X)<~>patient(X))))&
(![X]:((strong(X)|patient(X))<=>~wise(X)))&
(![X]:((~patient(X)|~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)&old(X))))&
(![X]:((~happy(X)&quiet(X))=>~wise(X)))&
((quiet(paul))=>((rich(susan)&humble(susan))))&
(![X]:((~curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:(generous(X)<=>(creative(X)|~happy(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((quiet(lucy)|brave(lucy)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((~kind(lucy)&~brave(lucy)))<=>((happy(alice)<~>old(alice))))&
(![X]:((generous(X)<~>~old(X))<=>(rich(X)<~>quiet(X))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&~quiet(X))))&
(~kind(susan))&
((~tall(lucy)|humble(lucy)))&
((~patient(alice)|brave(alice)))&
(?[X]:((curious(X)|~quiet(X))))&
(wise(lucy))&
(?[X]:((brave(X)|~rich(X)))) | wise(alice) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7643914894336804519176922
% SZS output start Proof for 7643914894336804519176922
1. ! [X0] : ((curious(X0) | humble(X0)) => strong(X0)) [input p0]
2. ! [X0] : ((humble(X0) | ~brave(X0)) <=> (curious(X0) | ~generous(X0))) [input p1]
3. ! [X0] : ((rich(X0) & ~strong(X0)) <=> (~strong(X0) & ~curious(X0))) [input p2]
5. ! [X0] : ((patient(X0) | strong(X0)) <=> ~wise(X0)) [input p4]
6. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (~happy(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (old(X0) & ~creative(X0))) [input p6]
11. ! [X0] : (generous(X0) <=> (~happy(X0) | creative(X0))) [input p10]
14. (~brave(lucy) & ~kind(lucy)) <=> (happy(alice) <~> old(alice)) [input p13]
22. wise(lucy) [input p21]
24. wise(alice) [input hypothesis]
26. ! [X0] : (strong(X0) | (~curious(X0) & ~humble(X0))) [ennf transformation 1]
34. ! [X0] : (((humble(X0) | ~brave(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (~humble(X0) & brave(X0)))) [nnf transformation 2]
35. ! [X0] : ((humble(X0) | ~brave(X0) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | (~humble(X0) & brave(X0)))) [flattening 34]
36. ! [X0] : (((rich(X0) & ~strong(X0)) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | (~rich(X0) | strong(X0)))) [nnf transformation 3]
37. ! [X0] : (((rich(X0) & ~strong(X0)) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~rich(X0) | strong(X0))) [flattening 36]
39. ! [X0] : (((patient(X0) | strong(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [nnf transformation 5]
40. ! [X0] : ((patient(X0) | strong(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [flattening 39]
41. ! [X0] : (((~kind(X0) | ~patient(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 6]
42. ! [X0] : ((~kind(X0) | ~patient(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [flattening 41]
43. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 7]
44. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 43]
46. ! [X0] : ((generous(X0) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | ~generous(X0))) [nnf transformation 11]
47. ! [X0] : ((generous(X0) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | ~generous(X0))) [flattening 46]
56. ((~brave(lucy) & ~kind(lucy)) | ((happy(alice) | ~old(alice)) & (old(alice) | ~happy(alice)))) & (((~old(alice) | ~happy(alice)) & (old(alice) | happy(alice))) | (brave(lucy) | kind(lucy))) [nnf transformation 14]
57. ((~brave(lucy) & ~kind(lucy)) | ((happy(alice) | ~old(alice)) & (old(alice) | ~happy(alice)))) & (((~old(alice) | ~happy(alice)) & (old(alice) | happy(alice))) | brave(lucy) | kind(lucy)) [flattening 56]
68. ~curious(X0) | strong(X0) [cnf transformation 26]
69. ~generous(X0) | curious(X0) | brave(X0) [cnf transformation 35]
76. rich(X0) | strong(X0) | curious(X0) [cnf transformation 37]
81. ~wise(X0) | ~strong(X0) [cnf transformation 40]
82. ~wise(X0) | ~patient(X0) [cnf transformation 40]
86. ~happy(X0) | patient(X0) [cnf transformation 42]
87. ~happy(X0) | kind(X0) [cnf transformation 42]
91. old(X0) | ~rich(X0) | old(X0) [cnf transformation 44]
102. happy(X0) | generous(X0) [cnf transformation 47]
113. ~kind(lucy) | happy(alice) | ~old(alice) [cnf transformation 57]
115. ~brave(lucy) | happy(alice) | ~old(alice) [cnf transformation 57]
130. wise(lucy) [cnf transformation 22]
132. wise(alice) [cnf transformation 24]
133. ~rich(X0) | old(X0) [duplicate literal removal 91]
135. rich(X0) | strong(X0) [subsumption resolution 76,68]
176. 10 <=> brave(lucy) [avatar definition]
177. ~brave(lucy) <- (~10) [avatar component clause 176]
193. 13 <=> old(alice) [avatar definition]
197. 14 <=> happy(alice) [avatar definition]
199. happy(alice) <- (14) [avatar component clause 197]
200. ~13 | 14 | ~10 [avatar split clause 115,176,197,193]
203. 15 <=> kind(lucy) [avatar definition]
205. ~kind(lucy) <- (~15) [avatar component clause 203]
206. ~13 | 14 | ~15 [avatar split clause 113,203,197,193]
215. 16 <=> patient(alice) [avatar definition]
241. ~strong(lucy) [resolution 81,130]
242. ~strong(alice) [resolution 81,132]
244. ~patient(alice) [resolution 82,132]
249. kind(X0) | generous(X0) [resolution 102,87]
260. patient(alice) <- (14) [resolution 199,86]
263. 16 | ~14 [avatar split clause 260,197,215]
264. ~16 [avatar split clause 244,215]
291. 26 <=> generous(lucy) [avatar definition]
293. generous(lucy) <- (26) [avatar component clause 291]
380. 37 <=> rich(alice) [avatar definition]
381. rich(alice) <- (37) [avatar component clause 380]
382. ~rich(alice) <- (~37) [avatar component clause 380]
384. strong(alice) <- (~37) [resolution 382,135]
385. $false <- (~37) [subsumption resolution 384,242]
386. 37 [avatar contradiction clause 385]
391. old(alice) <- (37) [resolution 381,133]
393. generous(lucy) <- (~15) [resolution 249,205]
394. 26 | 15 [avatar split clause 393,203,291]
395. 13 | ~37 [avatar split clause 391,380,193]
482. curious(lucy) | brave(lucy) <- (26) [resolution 293,69]
483. curious(lucy) <- (~10, 26) [subsumption resolution 482,177]
554. strong(lucy) <- (~10, 26) [resolution 483,68]
556. $false <- (~10, 26) [subsumption resolution 554,241]
557. 10 | ~26 [avatar contradiction clause 556]
558. $false [avatar sat refutation 200,206,263,264,386,394,395,557]
% SZS output end Proof for 7643914894336804519176922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not brave is humble and vice versa.
Everyone who is strong is either not calm or quiet.
Everyone who is either happy or not tall is either humble or not patient and vice versa.
Everyone who is either not rich or curious is not strong or patient and vice versa.
If someone is curious or not generous then someone is both not brave and not curious.
Everyone who is humble or not funny is not strong or rich and vice versa.
Everyone who is both not patient and generous is wise.
If someone is not happy or not calm then someone is both not brave and patient and vice versa.
If someone is rich then john is tall.
Everyone who is kind or not happy is not quiet and vice versa.
If someone is not wise or not old then someone is not tall or generous and vice versa.
If someone is either not wise or wise then lucy is kind or wise and vice versa.
Everyone who is not old or generous is not old.
Everyone who is both patient and not happy is either not tall or not rich.
If someone is either generous or not patient then someone is both not kind and curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
John is either not old or humble.
Mary is both not funny and not patient.
Lucy is humble.
Someone is either not rich or not creative.
Someone is either strong or old.
Someone is not patient or not quiet.
Someone is generous or not funny.
Lucy is either creative or not kind. | Mary is generous. | neutral | (![X]:((happy(X)|~brave(X))<=>humble(X)))&
(![X]:(strong(X)=>(~calm(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)|patient(X))))&
((?[X]:((curious(X)|~generous(X))))=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((humble(X)|~funny(X))<=>(~strong(X)|rich(X))))&
(![X]:((~patient(X)&generous(X))=>wise(X)))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((~brave(X)&patient(X)))))&
((?[X]:(rich(X)))=>(tall(john)))&
(![X]:((kind(X)|~happy(X))<=>~quiet(X)))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((kind(lucy)|wise(lucy))))&
(![X]:((~old(X)|generous(X))=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(~tall(X)<~>~rich(X))))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
((~old(john)<~>humble(john)))&
((~funny(mary)&~patient(mary)))&
(humble(lucy))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((generous(X)|~funny(X))))&
((creative(lucy)<~>~kind(lucy))) | generous(mary) | [] | null | 0 |
If alice is both not rich and kind then someone is both not old and tall and vice versa.
Everyone who is not creative is not strong and vice versa.
If mary is either rich or humble then someone is either brave or not generous.
If john is not happy then john is brave and vice versa.
If mary is either patient or wise then fred is brave or not generous.
Everyone who is not curious is either tall or strong.
Everyone who is not kind or not old is old or wise.
Everyone who is not wise or not generous is not strong or humble and vice versa.
If paul is both rich and not generous then someone is not humble and vice versa.
If paul is both humble and tall then someone is either rich or tall.
Everyone who is both strong and creative is not funny or not old.
Everyone who is old or not wise is either generous or humble.
If susan is both creative and generous then someone is either not curious or not happy and vice versa.
If alice is not old then lucy is either humble or rich.
Everyone who is not brave is both kind and generous and vice versa.
Everyone who is both not curious and not kind is creative or not strong.
Someone is happy.
Someone is quiet or not wise.
John is not creative or not wise.
Someone is both not funny and not old.
Someone is both not calm and wise.
Paul is either not rich or not generous.
Someone is not wise. | John is creative. | neutral | (((~rich(alice)&kind(alice)))<=>(?[X]:((~old(X)&tall(X)))))&
(![X]:(~creative(X)<=>~strong(X)))&
(((rich(mary)<~>humble(mary)))=>(?[X]:((brave(X)<~>~generous(X)))))&
((~happy(john))<=>(brave(john)))&
(((patient(mary)<~>wise(mary)))=>((brave(fred)|~generous(fred))))&
(![X]:(~curious(X)=>(tall(X)<~>strong(X))))&
(![X]:((~kind(X)|~old(X))=>(old(X)|wise(X))))&
(![X]:((~wise(X)|~generous(X))<=>(~strong(X)|humble(X))))&
(((rich(paul)&~generous(paul)))<=>(?[X]:(~humble(X))))&
(((humble(paul)&tall(paul)))=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((strong(X)&creative(X))=>(~funny(X)|~old(X))))&
(![X]:((old(X)|~wise(X))=>(generous(X)<~>humble(X))))&
(((creative(susan)&generous(susan)))<=>(?[X]:((~curious(X)<~>~happy(X)))))&
((~old(alice))=>((humble(lucy)<~>rich(lucy))))&
(![X]:(~brave(X)<=>(kind(X)&generous(X))))&
(![X]:((~curious(X)&~kind(X))=>(creative(X)|~strong(X))))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)|~wise(X))))&
((~creative(john)|~wise(john)))&
(?[X]:((~funny(X)&~old(X))))&
(?[X]:((~calm(X)&wise(X))))&
((~rich(paul)<~>~generous(paul)))&
(?[X]:(~wise(X))) | creative(john) | [] | null | 0 |
Everyone who is strong is both curious and not quiet and vice versa.
If someone is old or not old then someone is quiet and vice versa.
Everyone who is not funny or not rich is both humble and not curious and vice versa.
If someone is not creative or strong then mary is not strong or not funny and vice versa.
Everyone who is either happy or wise is both kind and not patient and vice versa.
Everyone who is either not happy or not creative is not funny and vice versa.
Everyone who is not strong is both creative and kind and vice versa.
Everyone who is both not patient and not creative is curious or not curious.
If mary is either not strong or not wise then fred is not wise or strong and vice versa.
If mary is strong or not strong then paul is either not tall or brave and vice versa.
Everyone who is kind is both not patient and quiet and vice versa.
If someone is either not calm or quiet then someone is wise.
If lucy is both not calm and happy then fred is both not patient and funny.
If paul is not funny then someone is either not kind or not funny and vice versa.
John is either quiet or not wise.
Someone is not patient.
Fred is both not calm and not generous.
Someone is either rich or old.
Someone is both not generous and not brave.
Someone is patient or old.
Someone is creative. | Paul is not humble. | contradiction | (![X]:(strong(X)<=>(curious(X)&~quiet(X))))&
((?[X]:((old(X)|~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(humble(X)&~curious(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~strong(mary)|~funny(mary))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)&~patient(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>~funny(X)))&
(![X]:(~strong(X)<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~creative(X))=>(curious(X)|~curious(X))))&
(((~strong(mary)<~>~wise(mary)))<=>((~wise(fred)|strong(fred))))&
(((strong(mary)|~strong(mary)))<=>((~tall(paul)<~>brave(paul))))&
(![X]:(kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~calm(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(((~calm(lucy)&happy(lucy)))=>((~patient(fred)&funny(fred))))&
((~funny(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((quiet(john)<~>~wise(john)))&
(?[X]:(~patient(X)))&
((~calm(fred)&~generous(fred)))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(creative(X))) | ~humble(paul) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7053036711619553213374472
% SZS output start Proof for 7053036711619553213374472
1. ! [X0] : (strong(X0) <=> (~quiet(X0) & curious(X0))) [input p0]
3. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~curious(X0) & humble(X0))) [input p2]
4. ? [X0] : (strong(X0) | ~creative(X0)) <=> (~funny(mary) | ~strong(mary)) [input p3]
5. ! [X0] : ((happy(X0) <~> wise(X0)) <=> (~patient(X0) & kind(X0))) [input p4]
6. ! [X0] : ((~happy(X0) <~> ~creative(X0)) <=> ~funny(X0)) [input p5]
7. ! [X0] : (~strong(X0) <=> (kind(X0) & creative(X0))) [input p6]
9. (~strong(mary) <~> ~wise(mary)) <=> (strong(fred) | ~wise(fred)) [input p8]
11. ! [X0] : (kind(X0) <=> (quiet(X0) & ~patient(X0))) [input p10]
14. ~funny(paul) <=> ? [X0] : (~kind(X0) <~> ~funny(X0)) [input p13]
22. ~humble(paul) [input hypothesis]
32. ! [X0] : ((strong(X0) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [nnf transformation 1]
33. ! [X0] : ((strong(X0) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | ~strong(X0))) [flattening 32]
39. ! [X0] : (((~rich(X0) | ~funny(X0)) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~rich(X0) | ~funny(X0) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | (rich(X0) & funny(X0)))) [flattening 39]
41. (? [X0] : (strong(X0) | ~creative(X0)) | (funny(mary) & strong(mary))) & ((~funny(mary) | ~strong(mary)) | ! [X0] : (~strong(X0) & creative(X0))) [nnf transformation 4]
42. (? [X0] : (strong(X0) | ~creative(X0)) | (funny(mary) & strong(mary))) & (~funny(mary) | ~strong(mary) | ! [X0] : (~strong(X0) & creative(X0))) [flattening 41]
43. (? [X0] : (strong(X0) | ~creative(X0)) | (funny(mary) & strong(mary))) & (~funny(mary) | ~strong(mary) | ! [X1] : (~strong(X1) & creative(X1))) [rectify 42]
44. ? [X0] : (strong(X0) | ~creative(X0)) => (strong(sK2) | ~creative(sK2)) [choice axiom]
45. ((strong(sK2) | ~creative(sK2)) | (funny(mary) & strong(mary))) & (~funny(mary) | ~strong(mary) | ! [X1] : (~strong(X1) & creative(X1))) [skolemisation 43,44]
46. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [nnf transformation 5]
47. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [flattening 46]
48. ! [X0] : ((((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | funny(X0)) & (~funny(X0) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0))))) [nnf transformation 6]
49. ! [X0] : ((~strong(X0) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | strong(X0))) [nnf transformation 7]
50. ! [X0] : ((~strong(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | strong(X0))) [flattening 49]
51. (((wise(mary) | strong(mary)) & (~wise(mary) | ~strong(mary))) | (~strong(fred) & wise(fred))) & ((strong(fred) | ~wise(fred)) | ((~strong(mary) | wise(mary)) & (~wise(mary) | strong(mary)))) [nnf transformation 9]
52. (((wise(mary) | strong(mary)) & (~wise(mary) | ~strong(mary))) | (~strong(fred) & wise(fred))) & (strong(fred) | ~wise(fred) | ((~strong(mary) | wise(mary)) & (~wise(mary) | strong(mary)))) [flattening 51]
55. ! [X0] : ((kind(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [nnf transformation 11]
56. ! [X0] : ((kind(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~kind(X0))) [flattening 55]
61. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X0] : ((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | funny(paul)) [nnf transformation 14]
62. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) | funny(paul)) [rectify 61]
63. ? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) => ((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) [choice axiom]
64. (~funny(paul) | ! [X0] : ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(sK4) | kind(sK4)) & (~funny(sK4) | ~kind(sK4))) | funny(paul)) [skolemisation 62,63]
77. ~strong(X0) | curious(X0) [cnf transformation 33]
83. humble(X0) | funny(X0) [cnf transformation 40]
85. ~curious(X0) | funny(X0) [cnf transformation 40]
89. ~funny(mary) | ~strong(mary) | ~strong(X1) [cnf transformation 45]
97. ~kind(X0) | ~happy(X0) | patient(X0) | ~wise(X0) [cnf transformation 47]
98. ~creative(X0) | ~funny(X0) | happy(X0) [cnf transformation 48]
102. creative(X0) | strong(X0) [cnf transformation 50]
103. kind(X0) | strong(X0) [cnf transformation 50]
110. wise(mary) | strong(mary) | wise(fred) [cnf transformation 52]
111. wise(mary) | strong(mary) | ~strong(fred) [cnf transformation 52]
118. ~patient(X0) | ~kind(X0) [cnf transformation 56]
127. ~funny(paul) | ~funny(X0) | kind(X0) [cnf transformation 64]
128. ~funny(paul) | ~kind(X0) | funny(X0) [cnf transformation 64]
138. ~humble(paul) [cnf transformation 22]
152. 4 <=> funny(mary) [avatar definition]
153. ~funny(mary) <- (~4) [avatar component clause 152]
154. funny(mary) <- (4) [avatar component clause 152]
165. 7 <=> strong(mary) [avatar definition]
166. ~strong(mary) <- (~7) [avatar component clause 165]
167. strong(mary) <- (7) [avatar component clause 165]
170. 8 <=> ! [X1] : ~strong(X1) [avatar definition]
171. ~strong(X1) <- (8) [avatar component clause 170]
172. 8 | ~7 | ~4 [avatar split clause 89,152,165,170]
178. 10 <=> strong(fred) [avatar definition]
180. ~strong(fred) <- (~10) [avatar component clause 178]
182. 11 <=> wise(mary) [avatar definition]
184. wise(mary) <- (11) [avatar component clause 182]
185. ~10 | 7 | 11 [avatar split clause 111,182,165,178]
187. 12 <=> wise(fred) [avatar definition]
189. wise(fred) <- (12) [avatar component clause 187]
190. 12 | 7 | 11 [avatar split clause 110,182,165,187]
233. 21 <=> patient(fred) [avatar definition]
234. patient(fred) <- (21) [avatar component clause 233]
238. 22 <=> ! [X0] : (~kind(X0) | funny(X0)) [avatar definition]
239. ~kind(X0) | funny(X0) <- (22) [avatar component clause 238]
241. 23 <=> funny(paul) [avatar definition]
244. 22 | ~23 [avatar split clause 128,241,238]
246. 24 <=> ! [X0] : (~funny(X0) | kind(X0)) [avatar definition]
247. ~funny(X0) | kind(X0) <- (24) [avatar component clause 246]
248. 24 | ~23 [avatar split clause 127,241,246]
288. curious(mary) <- (7) [resolution 77,167]
290. funny(paul) [resolution 83,138]
292. funny(mary) <- (7) [resolution 85,288]
295. 4 | ~7 [avatar split clause 292,165,152]
296. $false <- (7, 8) [resolution 171,167]
297. ~7 | ~8 [avatar contradiction clause 296]
308. funny(X0) | strong(X0) <- (22) [resolution 239,103]
310. kind(mary) <- (4, 24) [resolution 247,154]
344. ~funny(X0) | happy(X0) | strong(X0) [resolution 98,102]
354. happy(X0) | strong(X0) <- (22) [subsumption resolution 344,308]
458. 23 [avatar split clause 290,241]
506. ~happy(X0) | patient(X0) | ~wise(X0) | strong(X0) [resolution 97,103]
510. ~wise(X0) | patient(X0) | strong(X0) <- (22) [subsumption resolution 506,354]
513. 61 <=> patient(mary) [avatar definition]
515. patient(mary) <- (61) [avatar component clause 513]
560. patient(mary) | strong(mary) <- (11, 22) [resolution 510,184]
564. patient(mary) <- (~7, 11, 22) [subsumption resolution 560,166]
565. 61 | 7 | ~11 | ~22 [avatar split clause 564,238,182,165,513]
601. ~kind(mary) <- (61) [resolution 515,118]
605. $false <- (4, 24, 61) [subsumption resolution 601,310]
606. ~4 | ~24 | ~61 [avatar contradiction clause 605]
612. patient(fred) | strong(fred) <- (12, 22) [resolution 189,510]
614. patient(fred) <- (~10, 12, 22) [subsumption resolution 612,180]
615. 21 | 10 | ~12 | ~22 [avatar split clause 614,238,187,178,233]
617. 63 <=> kind(fred) [avatar definition]
618. ~kind(fred) <- (~63) [avatar component clause 617]
627. ~kind(fred) <- (21) [resolution 234,118]
628. ~63 | ~21 [avatar split clause 627,233,617]
630. strong(fred) <- (~63) [resolution 618,103]
631. $false <- (~10, ~63) [subsumption resolution 630,180]
632. 10 | 63 [avatar contradiction clause 631]
633. strong(mary) <- (~4, 22) [resolution 153,308]
634. $false <- (~4, ~7, 22) [subsumption resolution 633,166]
635. 4 | 7 | ~22 [avatar contradiction clause 634]
636. $false [avatar sat refutation 172,185,190,244,248,295,297,458,565,606,615,628,632,635]
% SZS output end Proof for 7053036711619553213374472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is funny or humble and vice versa.
Everyone who is both wise and not strong is both funny and not rich.
Everyone who is strong is both old and not funny.
Everyone who is humble is not brave or old.
If someone is both curious and not quiet then paul is either kind or not curious.
If lucy is quiet or not rich then paul is creative or not calm and vice versa.
Everyone who is either generous or not strong is not tall and vice versa.
If someone is tall or brave then alice is generous or not curious and vice versa.
Everyone who is both not humble and not calm is not rich.
If paul is both not humble and rich then lucy is not generous or not brave and vice versa.
If mary is not curious then john is not old and vice versa.
Everyone who is either not wise or not humble is not strong or rich.
If someone is funny or not humble then fred is tall and vice versa.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
If fred is both not old and calm then susan is either not happy or not humble and vice versa.
Lucy is not calm or creative.
Someone is both not generous and rich.
Someone is not rich or not creative.
Someone is either wise or funny.
Lucy is both not kind and not rich.
Alice is both not patient and tall.
Mary is not calm or not humble.
John is not patient or not generous. | Mary is funny. | neutral | (![X]:(happy(X)<=>(funny(X)|humble(X))))&
(![X]:((wise(X)&~strong(X))=>(funny(X)&~rich(X))))&
(![X]:(strong(X)=>(old(X)&~funny(X))))&
(![X]:(humble(X)=>(~brave(X)|old(X))))&
((?[X]:((curious(X)&~quiet(X))))=>((kind(paul)<~>~curious(paul))))&
(((quiet(lucy)|~rich(lucy)))<=>((creative(paul)|~calm(paul))))&
(![X]:((generous(X)<~>~strong(X))<=>~tall(X)))&
((?[X]:((tall(X)|brave(X))))<=>((generous(alice)|~curious(alice))))&
(![X]:((~humble(X)&~calm(X))=>~rich(X)))&
(((~humble(paul)&rich(paul)))<=>((~generous(lucy)|~brave(lucy))))&
((~curious(mary))<=>(~old(john)))&
(![X]:((~wise(X)<~>~humble(X))=>(~strong(X)|rich(X))))&
((?[X]:((funny(X)|~humble(X))))<=>(tall(fred)))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
(((~old(fred)&calm(fred)))<=>((~happy(susan)<~>~humble(susan))))&
((~calm(lucy)|creative(lucy)))&
(?[X]:((~generous(X)&rich(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~kind(lucy)&~rich(lucy)))&
((~patient(alice)&tall(alice)))&
((~calm(mary)|~humble(mary)))&
((~patient(john)|~generous(john))) | funny(mary) | [] | null | 0 |
Everyone who is quiet is either not calm or creative and vice versa.
Everyone who is not patient is both not curious and wise.
If lucy is generous then someone is both calm and generous.
Everyone who is not happy or not funny is either calm or patient.
Everyone who is old or humble is either old or humble and vice versa.
Everyone who is patient is not patient.
Everyone who is both humble and not tall is curious and vice versa.
If lucy is both not quiet and not rich then susan is curious or old and vice versa.
If someone is creative then susan is both curious and not wise.
Everyone who is wise is not generous.
If susan is old or patient then susan is either not quiet or happy.
If susan is both not patient and funny then mary is both not funny and not kind.
If fred is both not quiet and kind then someone is both not happy and happy and vice versa.
Everyone who is kind or happy is both not tall and not calm and vice versa.
Everyone who is both not humble and not generous is either funny or rich.
Everyone who is not generous is calm and vice versa.
Someone is not funny.
Someone is not creative.
Susan is not generous or not patient.
Someone is both not tall and not quiet.
Susan is patient or not patient. | Fred is not kind. | entailment | (![X]:(quiet(X)<=>(~calm(X)<~>creative(X))))&
(![X]:(~patient(X)=>(~curious(X)&wise(X))))&
((generous(lucy))=>(?[X]:((calm(X)&generous(X)))))&
(![X]:((~happy(X)|~funny(X))=>(calm(X)<~>patient(X))))&
(![X]:((old(X)|humble(X))<=>(old(X)<~>humble(X))))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:((humble(X)&~tall(X))<=>curious(X)))&
(((~quiet(lucy)&~rich(lucy)))<=>((curious(susan)|old(susan))))&
((?[X]:(creative(X)))=>((curious(susan)&~wise(susan))))&
(![X]:(wise(X)=>~generous(X)))&
(((old(susan)|patient(susan)))=>((~quiet(susan)<~>happy(susan))))&
(((~patient(susan)&funny(susan)))=>((~funny(mary)&~kind(mary))))&
(((~quiet(fred)&kind(fred)))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((kind(X)|happy(X))<=>(~tall(X)&~calm(X))))&
(![X]:((~humble(X)&~generous(X))=>(funny(X)<~>rich(X))))&
(![X]:(~generous(X)<=>calm(X)))&
(?[X]:(~funny(X)))&
(?[X]:(~creative(X)))&
((~generous(susan)|~patient(susan)))&
(?[X]:((~tall(X)&~quiet(X))))&
((patient(susan)|~patient(susan))) | ~kind(fred) | [
"p1",
"p5",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6510037961048488953705915
% SZS output start Proof for 6510037961048488953705915
2. ! [X0] : (~patient(X0) => (wise(X0) & ~curious(X0))) [input p1]
6. ! [X0] : (patient(X0) => ~patient(X0)) [input p5]
10. ! [X0] : (wise(X0) => ~generous(X0)) [input p9]
14. ! [X0] : ((happy(X0) | kind(X0)) <=> (~calm(X0) & ~tall(X0))) [input p13]
16. ! [X0] : (~generous(X0) <=> calm(X0)) [input p15]
22. kind(fred) [input hypothesis]
23. ! [X0] : ((wise(X0) & ~curious(X0)) | patient(X0)) [ennf transformation 2]
26. ! [X0] : (~patient(X0) | ~patient(X0)) [ennf transformation 6]
28. ! [X0] : (~generous(X0) | ~wise(X0)) [ennf transformation 10]
50. ! [X0] : (((happy(X0) | kind(X0)) | (calm(X0) | tall(X0))) & ((~calm(X0) & ~tall(X0)) | (~happy(X0) & ~kind(X0)))) [nnf transformation 14]
51. ! [X0] : ((happy(X0) | kind(X0) | calm(X0) | tall(X0)) & ((~calm(X0) & ~tall(X0)) | (~happy(X0) & ~kind(X0)))) [flattening 50]
53. ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))) [nnf transformation 16]
65. wise(X0) | patient(X0) [cnf transformation 23]
78. ~patient(X0) | ~patient(X0) [cnf transformation 26]
89. ~generous(X0) | ~wise(X0) [cnf transformation 28]
102. ~kind(X0) | ~calm(X0) [cnf transformation 51]
107. generous(X0) | calm(X0) [cnf transformation 53]
115. kind(fred) [cnf transformation 22]
116. ~patient(X0) [duplicate literal removal 78]
196. 16 <=> kind(fred) [avatar definition]
197. kind(fred) <- (16) [avatar component clause 196]
205. 16 [avatar split clause 115,196]
213. ~calm(fred) <- (16) [resolution 102,197]
215. ~wise(X0) | calm(X0) [resolution 107,89]
218. calm(X0) | patient(X0) [resolution 215,65]
220. calm(X0) [subsumption resolution 218,116]
221. $false <- (16) [resolution 220,213]
223. ~16 [avatar contradiction clause 221]
225. $false [avatar sat refutation 205,223]
% SZS output end Proof for 6510037961048488953705915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then mary is curious and vice versa.
If someone is not quiet or not wise then someone is wise or not tall.
If someone is tall or curious then someone is not creative or calm.
If mary is wise or creative then fred is not calm or not funny and vice versa.
If paul is not wise or not humble then paul is curious or not rich and vice versa.
If susan is both not tall and wise then susan is tall or patient and vice versa.
If someone is both not kind and rich then mary is kind.
Everyone who is either humble or rich is either strong or not old.
If someone is both not creative and not calm then someone is generous or calm and vice versa.
Everyone who is not curious or curious is not wise or humble.
Everyone who is not rich is not brave and vice versa.
Everyone who is rich is both strong and old and vice versa.
Everyone who is brave or calm is wise or not humble and vice versa.
Everyone who is both quiet and not tall is curious or not patient.
Everyone who is happy or not brave is both not funny and funny.
If alice is not quiet then john is either quiet or not calm and vice versa.
Fred is not creative.
Fred is brave.
Someone is both not curious and humble.
Lucy is both wise and not creative.
Someone is both not curious and not calm.
Someone is either not calm or funny.
Paul is not kind or tall. | Fred is not old. | contradiction | ((?[X]:(~calm(X)))<=>(curious(mary)))&
((?[X]:((~quiet(X)|~wise(X))))=>(?[X]:((wise(X)|~tall(X)))))&
((?[X]:((tall(X)|curious(X))))=>(?[X]:((~creative(X)|calm(X)))))&
(((wise(mary)|creative(mary)))<=>((~calm(fred)|~funny(fred))))&
(((~wise(paul)|~humble(paul)))<=>((curious(paul)|~rich(paul))))&
(((~tall(susan)&wise(susan)))<=>((tall(susan)|patient(susan))))&
((?[X]:((~kind(X)&rich(X))))=>(kind(mary)))&
(![X]:((humble(X)<~>rich(X))=>(strong(X)<~>~old(X))))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~curious(X)|curious(X))=>(~wise(X)|humble(X))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:(rich(X)<=>(strong(X)&old(X))))&
(![X]:((brave(X)|calm(X))<=>(wise(X)|~humble(X))))&
(![X]:((quiet(X)&~tall(X))=>(curious(X)|~patient(X))))&
(![X]:((happy(X)|~brave(X))=>(~funny(X)&funny(X))))&
((~quiet(alice))<=>((quiet(john)<~>~calm(john))))&
(~creative(fred))&
(brave(fred))&
(?[X]:((~curious(X)&humble(X))))&
((wise(lucy)&~creative(lucy)))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:((~calm(X)<~>funny(X))))&
((~kind(paul)|tall(paul))) | ~old(fred) | [
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7214034173022090141128229
% SZS output start Proof for 7214034173022090141128229
11. ! [X0] : (~rich(X0) <=> ~brave(X0)) [input p10]
12. ! [X0] : (rich(X0) <=> (old(X0) & strong(X0))) [input p11]
15. ! [X0] : ((~brave(X0) | happy(X0)) => (funny(X0) & ~funny(X0))) [input p14]
24. ~old(fred) [input hypothesis]
28. ! [X0] : (~brave(X0) => (funny(X0) & ~funny(X0))) [pure predicate removal 15]
37. ! [X0] : ((funny(X0) & ~funny(X0)) | brave(X0)) [ennf transformation 28]
60. ! [X0] : ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0))) [nnf transformation 11]
61. ! [X0] : ((rich(X0) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 12]
62. ! [X0] : ((rich(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | ~rich(X0))) [flattening 61]
104. ~brave(X0) | rich(X0) [cnf transformation 60]
107. ~rich(X0) | old(X0) [cnf transformation 62]
114. ~funny(X0) | brave(X0) [cnf transformation 37]
115. brave(X0) | funny(X0) [cnf transformation 37]
131. ~old(fred) [cnf transformation 24]
275. brave(X0) [subsumption resolution 114,115]
313. rich(X0) [resolution 104,275]
318. old(X0) [resolution 107,313]
320. $false [resolution 318,131]
% SZS output end Proof for 7214034173022090141128229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious or kind then someone is old.
If paul is either not humble or calm then someone is both not brave and not rich and vice versa.
If paul is strong or creative then someone is strong.
Everyone who is either strong or old is either not brave or happy and vice versa.
Everyone who is not humble or creative is either tall or not curious.
Everyone who is rich is either humble or wise.
If someone is both patient and not humble then fred is generous.
If mary is either not old or not quiet then fred is not patient or patient and vice versa.
Everyone who is not generous or patient is either tall or not brave and vice versa.
If mary is not patient or humble then mary is rich and vice versa.
Everyone who is both patient and happy is both not happy and kind and vice versa.
Everyone who is not quiet is both not quiet and old and vice versa.
If someone is both tall and not patient then fred is quiet.
If fred is not old then someone is both not kind and not rich and vice versa.
Everyone who is calm or not rich is old.
Everyone who is both curious and happy is not happy and vice versa.
Someone is happy or patient.
Someone is either not happy or not rich.
Lucy is not curious or funny.
Someone is not rich.
Someone is either quiet or old.
Alice is either not strong or not generous.
Someone is kind or not old. | Lucy is curious. | contradiction | (((~curious(paul)|kind(paul)))=>(?[X]:(old(X))))&
(((~humble(paul)<~>calm(paul)))<=>(?[X]:((~brave(X)&~rich(X)))))&
(((strong(paul)|creative(paul)))=>(?[X]:(strong(X))))&
(![X]:((strong(X)<~>old(X))<=>(~brave(X)<~>happy(X))))&
(![X]:((~humble(X)|creative(X))=>(tall(X)<~>~curious(X))))&
(![X]:(rich(X)=>(humble(X)<~>wise(X))))&
((?[X]:((patient(X)&~humble(X))))=>(generous(fred)))&
(((~old(mary)<~>~quiet(mary)))<=>((~patient(fred)|patient(fred))))&
(![X]:((~generous(X)|patient(X))<=>(tall(X)<~>~brave(X))))&
(((~patient(mary)|humble(mary)))<=>(rich(mary)))&
(![X]:((patient(X)&happy(X))<=>(~happy(X)&kind(X))))&
(![X]:(~quiet(X)<=>(~quiet(X)&old(X))))&
((?[X]:((tall(X)&~patient(X))))=>(quiet(fred)))&
((~old(fred))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((calm(X)|~rich(X))=>old(X)))&
(![X]:((curious(X)&happy(X))<=>~happy(X)))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((~happy(X)<~>~rich(X))))&
((~curious(lucy)|funny(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:((quiet(X)<~>old(X))))&
((~strong(alice)<~>~generous(alice)))&
(?[X]:((kind(X)|~old(X)))) | curious(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9045281166047620149337137
% SZS output start Proof for 9045281166047620149337137
16. ! [X0] : ((happy(X0) & curious(X0)) <=> ~happy(X0)) [input p15]
24. curious(lucy) [input hypothesis]
60. ! [X0] : (((happy(X0) & curious(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | ~curious(X0)))) [nnf transformation 16]
61. ! [X0] : (((happy(X0) & curious(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | ~curious(X0))) [flattening 60]
125. ~happy(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 61]
127. happy(X0) | happy(X0) [cnf transformation 61]
137. curious(lucy) [cnf transformation 24]
138. ~happy(X0) | ~curious(X0) [duplicate literal removal 125]
139. happy(X0) [duplicate literal removal 127]
255. ~curious(X0) [subsumption resolution 138,139]
285. $false [subsumption resolution 137,255]
% SZS output end Proof for 9045281166047620149337137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or strong then john is curious or not humble and vice versa.
Everyone who is not funny is both not creative and not tall and vice versa.
Everyone who is not tall or old is both creative and old and vice versa.
If lucy is either curious or not tall then someone is either not wise or not kind and vice versa.
Everyone who is not creative is curious or not humble and vice versa.
Everyone who is kind or curious is not kind.
If paul is both not rich and not quiet then someone is either brave or creative and vice versa.
If lucy is both calm and not tall then someone is both wise and not curious and vice versa.
Everyone who is either brave or wise is either not calm or tall.
Everyone who is both not patient and not wise is funny or old and vice versa.
If mary is either not happy or funny then someone is both not creative and not happy and vice versa.
Everyone who is creative is old.
If lucy is not rich or strong then lucy is either not brave or brave and vice versa.
Everyone who is both funny and not quiet is not rich.
If mary is both not tall and quiet then someone is calm or creative and vice versa.
Lucy is not funny or calm.
Someone is strong or not generous.
Someone is not curious or wise. | John is brave. | neutral | ((?[X]:((~generous(X)|strong(X))))<=>((curious(john)|~humble(john))))&
(![X]:(~funny(X)<=>(~creative(X)&~tall(X))))&
(![X]:((~tall(X)|old(X))<=>(creative(X)&old(X))))&
(((curious(lucy)<~>~tall(lucy)))<=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:(~creative(X)<=>(curious(X)|~humble(X))))&
(![X]:((kind(X)|curious(X))=>~kind(X)))&
(((~rich(paul)&~quiet(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(((calm(lucy)&~tall(lucy)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((brave(X)<~>wise(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&~wise(X))<=>(funny(X)|old(X))))&
(((~happy(mary)<~>funny(mary)))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:(creative(X)=>old(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~brave(lucy)<~>brave(lucy))))&
(![X]:((funny(X)&~quiet(X))=>~rich(X)))&
(((~tall(mary)&quiet(mary)))<=>(?[X]:((calm(X)|creative(X)))))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((strong(X)|~generous(X))))&
(?[X]:((~curious(X)|wise(X)))) | brave(john) | [] | null | 0 |
Everyone who is tall or not old is rich or not tall and vice versa. Everyone who is either not humble or humble is not funny and vice versa. Everyone who is either patient or not brave is not brave. If someone is not brave or not humble then lucy is either not humble or not calm. If john is calm or not wise then paul is either calm or patient. Everyone who is not curious or strong is old and vice versa. If someone is kind then someone is both not quiet and not patient and vice versa. If john is both not calm and humble then someone is generous. If someone is both not tall and not rich then someone is both old and happy and vice versa. Everyone who is both kind and rich is not wise and vice versa. Everyone who is both funny and not generous is both not wise and happy. Everyone who is both not calm and strong is either old or not calm and vice versa. Everyone who is tall is patient or not quiet and vice versa. Everyone who is not rich is humble and vice versa. Everyone who is either brave or rich is either curious or not quiet. Everyone who is both not generous and not funny is not rich. Someone is either not humble or not tall. Fred is not wise or not curious. Alice is rich or not curious. Someone is both not old and not strong. Paul is strong or not generous. Alice is rich. Mary is either not patient or not calm. | Lucy is calm. | entailment | (![X]:((tall(X)|~old(X))<=>(rich(X)|~tall(X))))&
(![X]:((~humble(X)<~>humble(X))<=>~funny(X)))&
(![X]:((patient(X)<~>~brave(X))=>~brave(X)))&
((?[X]:((~brave(X)|~humble(X))))=>((~humble(lucy)<~>~calm(lucy))))&
(((calm(john)|~wise(john)))=>((calm(paul)<~>patient(paul))))&
(![X]:((~curious(X)|strong(X))<=>old(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(((~calm(john)&humble(john)))=>(?[X]:(generous(X))))&
((?[X]:((~tall(X)&~rich(X))))<=>(?[X]:((old(X)&happy(X)))))&
(![X]:((kind(X)&rich(X))<=>~wise(X)))&
(![X]:((funny(X)&~generous(X))=>(~wise(X)&happy(X))))&
(![X]:((~calm(X)&strong(X))<=>(old(X)<~>~calm(X))))&
(![X]:(tall(X)<=>(patient(X)|~quiet(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((brave(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~funny(X))=>~rich(X)))&
(?[X]:((~humble(X)<~>~tall(X))))&
((~wise(fred)|~curious(fred)))&
((rich(alice)|~curious(alice)))&
(?[X]:((~old(X)&~strong(X))))&
((strong(paul)|~generous(paul)))&
(rich(alice))&
((~patient(mary)<~>~calm(mary))) | calm(lucy) | [
"p0",
"p3",
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4740313793353917343500715
% SZS output start Proof for 4740313793353917343500715
1. ! [X0] : ((~old(X0) | tall(X0)) <=> (~tall(X0) | rich(X0))) [input p0]
4. ? [X0] : (~humble(X0) | ~brave(X0)) => (~humble(lucy) <~> ~calm(lucy)) [input p3]
6. ! [X0] : ((strong(X0) | ~curious(X0)) <=> old(X0)) [input p5]
12. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (old(X0) <~> ~calm(X0))) [input p11]
14. ! [X0] : (~rich(X0) <=> humble(X0)) [input p13]
24. ~calm(lucy) [input hypothesis]
28. (~humble(lucy) <~> ~calm(lucy)) | ! [X0] : (humble(X0) & brave(X0)) [ennf transformation 4]
37. ! [X0] : (((~old(X0) | tall(X0)) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | (old(X0) & ~tall(X0)))) [nnf transformation 1]
38. ! [X0] : ((~old(X0) | tall(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | (old(X0) & ~tall(X0)))) [flattening 37]
41. ((calm(lucy) | humble(lucy)) & (~calm(lucy) | ~humble(lucy))) | ! [X0] : (humble(X0) & brave(X0)) [nnf transformation 28]
43. ! [X0] : (((strong(X0) | ~curious(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & curious(X0)))) [nnf transformation 6]
44. ! [X0] : ((strong(X0) | ~curious(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & curious(X0)))) [flattening 43]
59. ! [X0] : (((strong(X0) & ~calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (~strong(X0) | calm(X0)))) [nnf transformation 12]
60. ! [X0] : (((strong(X0) & ~calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ~strong(X0) | calm(X0))) [flattening 59]
63. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 14]
71. ~tall(X0) | rich(X0) | ~tall(X0) [cnf transformation 38]
74. ~old(X0) | tall(X0) | tall(X0) [cnf transformation 38]
84. calm(lucy) | humble(lucy) | humble(X0) [cnf transformation 41]
90. ~strong(X0) | old(X0) [cnf transformation 44]
110. strong(X0) | old(X0) | calm(X0) [cnf transformation 60]
115. ~humble(X0) | ~rich(X0) [cnf transformation 63]
131. ~calm(lucy) [cnf transformation 24]
137. ~tall(X0) | rich(X0) [duplicate literal removal 71]
138. ~old(X0) | tall(X0) [duplicate literal removal 74]
141. 1 <=> ! [X0] : humble(X0) [avatar definition]
142. humble(X0) <- (1) [avatar component clause 141]
144. 2 <=> humble(lucy) [avatar definition]
145. ~humble(lucy) <- (~2) [avatar component clause 144]
146. humble(lucy) <- (2) [avatar component clause 144]
148. 3 <=> calm(lucy) [avatar definition]
149. ~calm(lucy) <- (~3) [avatar component clause 148]
151. 1 | 2 | 3 [avatar split clause 84,148,144,141]
236. calm(X0) | old(X0) [subsumption resolution 110,90]
287. ~3 [avatar split clause 131,148]
294. ~rich(lucy) <- (2) [resolution 115,146]
312. old(lucy) <- (~3) [resolution 236,149]
315. tall(lucy) <- (~3) [resolution 312,138]
347. rich(lucy) <- (~3) [resolution 315,137]
348. $false <- (2, ~3) [subsumption resolution 347,294]
349. ~2 | 3 [avatar contradiction clause 348]
353. $false <- (1, ~2) [resolution 145,142]
355. ~1 | 2 [avatar contradiction clause 353]
356. $false [avatar sat refutation 151,287,349,355]
% SZS output end Proof for 4740313793353917343500715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not wise is either not generous or not brave. If someone is kind or curious then someone is kind. If mary is either not patient or not generous then paul is either not patient or brave and vice versa. Everyone who is funny or humble is either not happy or brave and vice versa. Everyone who is both not quiet and patient is patient or not humble and vice versa. If fred is not generous or patient then mary is both not wise and not rich. If fred is rich or not calm then someone is either calm or happy and vice versa. Everyone who is not quiet is both wise and not funny and vice versa. If mary is not brave then mary is humble or not calm and vice versa. If someone is not brave or not humble then lucy is either wise or not quiet and vice versa. If someone is not quiet then alice is calm. Everyone who is both not rich and curious is both not strong and not calm and vice versa. If lucy is either humble or not wise then someone is both not calm and not rich. Everyone who is either tall or happy is tall. If susan is not humble then someone is not calm or not happy. Everyone who is not old is both strong and generous. Someone is both not kind and patient. Someone is both not wise and not curious. Fred is not humble. Fred is both happy and creative. Someone is either humble or brave. Someone is not funny or curious. Susan is not humble or creative. Someone is not rich or curious. | Mary is rich. | contradiction | (![X]:((rich(X)<~>~wise(X))=>(~generous(X)<~>~brave(X))))&
((?[X]:((kind(X)|curious(X))))=>(?[X]:(kind(X))))&
(((~patient(mary)<~>~generous(mary)))<=>((~patient(paul)<~>brave(paul))))&
(![X]:((funny(X)|humble(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~quiet(X)&patient(X))<=>(patient(X)|~humble(X))))&
(((~generous(fred)|patient(fred)))=>((~wise(mary)&~rich(mary))))&
(((rich(fred)|~calm(fred)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(~quiet(X)<=>(wise(X)&~funny(X))))&
((~brave(mary))<=>((humble(mary)|~calm(mary))))&
((?[X]:((~brave(X)|~humble(X))))<=>((wise(lucy)<~>~quiet(lucy))))&
((?[X]:(~quiet(X)))=>(calm(alice)))&
(![X]:((~rich(X)&curious(X))<=>(~strong(X)&~calm(X))))&
(((humble(lucy)<~>~wise(lucy)))=>(?[X]:((~calm(X)&~rich(X)))))&
(![X]:((tall(X)<~>happy(X))=>tall(X)))&
((~humble(susan))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~old(X)=>(strong(X)&generous(X))))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((~wise(X)&~curious(X))))&
(~humble(fred))&
((happy(fred)&creative(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((~funny(X)|curious(X))))&
((~humble(susan)|creative(susan)))&
(?[X]:((~rich(X)|curious(X)))) | rich(mary) | [
"p4",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6720826187503817488626657
% SZS output start Proof for 6720826187503817488626657
5. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (~humble(X0) | patient(X0))) [input p4]
6. (patient(fred) | ~generous(fred)) => (~rich(mary) & ~wise(mary)) [input p5]
19. ~humble(fred) [input p18]
25. rich(mary) [input hypothesis]
32. (~rich(mary) & ~wise(mary)) | (~patient(fred) & generous(fred)) [ennf transformation 6]
44. ! [X0] : (((patient(X0) & ~quiet(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (~patient(X0) | quiet(X0)))) [nnf transformation 5]
45. ! [X0] : (((patient(X0) & ~quiet(X0)) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | ~patient(X0) | quiet(X0))) [flattening 44]
102. humble(X0) | patient(X0) [cnf transformation 45]
106. ~rich(mary) | ~patient(fred) [cnf transformation 32]
141. ~humble(fred) [cnf transformation 19]
147. rich(mary) [cnf transformation 25]
186. 8 <=> patient(fred) [avatar definition]
188. ~patient(fred) <- (~8) [avatar component clause 186]
190. 9 <=> rich(mary) [avatar definition]
193. ~8 | ~9 [avatar split clause 106,190,186]
344. 9 [avatar split clause 147,190]
364. patient(fred) [resolution 102,141]
366. $false <- (~8) [subsumption resolution 364,188]
367. 8 [avatar contradiction clause 366]
368. $false [avatar sat refutation 193,344,367]
% SZS output end Proof for 6720826187503817488626657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both curious and not quiet and vice versa.
Everyone who is either not strong or old is both not humble and old and vice versa.
If someone is either calm or generous then alice is not funny.
If someone is generous or not patient then lucy is generous.
If someone is either strong or not funny then mary is rich or quiet.
Everyone who is generous or brave is not generous.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Everyone who is either not brave or generous is both not old and rich and vice versa.
If john is not patient then lucy is not funny or not quiet.
Everyone who is either creative or curious is wise.
If alice is both not happy and old then someone is either old or curious and vice versa.
If mary is either wise or not funny then someone is not patient and vice versa.
If john is happy or tall then mary is both brave and not creative and vice versa.
Someone is happy or not quiet.
Someone is both kind and not quiet.
Someone is both creative and not humble.
Someone is not strong.
Someone is not funny or creative.
Someone is not humble.
Alice is not calm or rich.
Mary is not generous or not creative. | Mary is generous. | contradiction | (![X]:(calm(X)<=>(curious(X)&~quiet(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~humble(X)&old(X))))&
((?[X]:((calm(X)<~>generous(X))))=>(~funny(alice)))&
((?[X]:((generous(X)|~patient(X))))=>(generous(lucy)))&
((?[X]:((strong(X)<~>~funny(X))))=>((rich(mary)|quiet(mary))))&
(![X]:((generous(X)|brave(X))=>~generous(X)))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
((~patient(john))=>((~funny(lucy)|~quiet(lucy))))&
(![X]:((creative(X)<~>curious(X))=>wise(X)))&
(((~happy(alice)&old(alice)))<=>(?[X]:((old(X)<~>curious(X)))))&
(((wise(mary)<~>~funny(mary)))<=>(?[X]:(~patient(X))))&
(((happy(john)|tall(john)))<=>((brave(mary)&~creative(mary))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:((creative(X)&~humble(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:(~humble(X)))&
((~calm(alice)|rich(alice)))&
((~generous(mary)|~creative(mary))) | generous(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6252702135114244831994
% SZS output start Proof for 6252702135114244831994
6. ! [X0] : ((brave(X0) | generous(X0)) => ~generous(X0)) [input p5]
24. generous(mary) [input hypothesis]
29. ! [X0] : (~generous(X0) | (~brave(X0) & ~generous(X0))) [ennf transformation 6]
89. ~generous(X0) | ~generous(X0) [cnf transformation 29]
137. generous(mary) [cnf transformation 24]
138. ~generous(X0) [duplicate literal removal 89]
162. 6 <=> ! [X0] : ~generous(X0) [avatar definition]
163. ~generous(X0) <- (6) [avatar component clause 162]
181. 6 [avatar split clause 138,162]
304. 36 <=> generous(mary) [avatar definition]
305. generous(mary) <- (36) [avatar component clause 304]
308. 36 [avatar split clause 137,304]
313. $false <- (6, 36) [resolution 305,163]
314. ~6 | ~36 [avatar contradiction clause 313]
315. $false [avatar sat refutation 181,308,314]
% SZS output end Proof for 6252702135114244831994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is rich or humble and vice versa.
If susan is humble or curious then someone is not rich or not kind and vice versa.
Everyone who is not brave or rich is not wise or happy and vice versa.
If john is both wise and generous then someone is either patient or not brave and vice versa.
If someone is not wise or humble then lucy is happy or not rich and vice versa.
Everyone who is not tall is either old or not strong and vice versa.
If someone is both not curious and quiet then mary is tall.
Everyone who is both not kind and not rich is both happy and not curious and vice versa.
If john is not rich then lucy is either creative or not patient.
Everyone who is not happy or not quiet is not kind or happy.
Everyone who is either kind or not quiet is not rich or old.
If susan is both funny and quiet then someone is both not patient and not creative and vice versa.
Everyone who is happy or tall is either kind or not curious and vice versa.
Everyone who is not strong is either kind or not old and vice versa.
Everyone who is not strong or not old is either not old or not strong and vice versa.
Everyone who is tall or patient is either not creative or tall and vice versa.
Someone is both old and creative.
Lucy is both tall and not patient.
Someone is not generous or not creative.
Someone is both not strong and not generous.
Lucy is generous or not curious.
Alice is either tall or not wise.
Alice is not humble or not happy.
Someone is both not rich and not quiet. | John is not patient. | neutral | (![X]:(calm(X)<=>(rich(X)|humble(X))))&
(((humble(susan)|curious(susan)))<=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((~brave(X)|rich(X))<=>(~wise(X)|happy(X))))&
(((wise(john)&generous(john)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
((?[X]:((~wise(X)|humble(X))))<=>((happy(lucy)|~rich(lucy))))&
(![X]:(~tall(X)<=>(old(X)<~>~strong(X))))&
((?[X]:((~curious(X)&quiet(X))))=>(tall(mary)))&
(![X]:((~kind(X)&~rich(X))<=>(happy(X)&~curious(X))))&
((~rich(john))=>((creative(lucy)<~>~patient(lucy))))&
(![X]:((~happy(X)|~quiet(X))=>(~kind(X)|happy(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(~rich(X)|old(X))))&
(((funny(susan)&quiet(susan)))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((happy(X)|tall(X))<=>(kind(X)<~>~curious(X))))&
(![X]:(~strong(X)<=>(kind(X)<~>~old(X))))&
(![X]:((~strong(X)|~old(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((tall(X)|patient(X))<=>(~creative(X)<~>tall(X))))&
(?[X]:((old(X)&creative(X))))&
((tall(lucy)&~patient(lucy)))&
(?[X]:((~generous(X)|~creative(X))))&
(?[X]:((~strong(X)&~generous(X))))&
((generous(lucy)|~curious(lucy)))&
((tall(alice)<~>~wise(alice)))&
((~humble(alice)|~happy(alice)))&
(?[X]:((~rich(X)&~quiet(X)))) | ~patient(john) | [] | null | 0 |
If someone is not patient or not calm then someone is either humble or old. If john is both not rich and not kind then fred is not creative. Everyone who is not creative or not quiet is both not strong and not quiet and vice versa. Everyone who is both kind and not strong is strong. Everyone who is not old or not humble is both quiet and curious and vice versa. Everyone who is both rich and not kind is strong and vice versa. Everyone who is either not patient or not wise is rich or not creative and vice versa. If someone is wise then someone is humble or not patient and vice versa. If someone is wise or humble then someone is not quiet or funny and vice versa. Everyone who is either not kind or kind is strong or not creative. If john is either quiet or patient then someone is generous or not calm. If mary is either rich or not quiet then mary is either curious or not tall and vice versa. If someone is both not quiet and not calm then someone is not patient or calm and vice versa. If someone is both curious and not rich then lucy is both not brave and not wise and vice versa. Everyone who is both patient and old is both not old and happy and vice versa. If alice is wise then john is rich or not curious and vice versa. John is happy. Someone is both not funny and not quiet. Alice is either old or strong. Someone is not rich. Fred is not rich. John is either not rich or not patient. Susan is both not kind and not brave. | Alice is kind. | contradiction | ((?[X]:((~patient(X)|~calm(X))))=>(?[X]:((humble(X)<~>old(X)))))&
(((~rich(john)&~kind(john)))=>(~creative(fred)))&
(![X]:((~creative(X)|~quiet(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((kind(X)&~strong(X))=>strong(X)))&
(![X]:((~old(X)|~humble(X))<=>(quiet(X)&curious(X))))&
(![X]:((rich(X)&~kind(X))<=>strong(X)))&
(![X]:((~patient(X)<~>~wise(X))<=>(rich(X)|~creative(X))))&
((?[X]:(wise(X)))<=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((~kind(X)<~>kind(X))=>(strong(X)|~creative(X))))&
(((quiet(john)<~>patient(john)))=>(?[X]:((generous(X)|~calm(X)))))&
(((rich(mary)<~>~quiet(mary)))<=>((curious(mary)<~>~tall(mary))))&
((?[X]:((~quiet(X)&~calm(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((curious(X)&~rich(X))))<=>((~brave(lucy)&~wise(lucy))))&
(![X]:((patient(X)&old(X))<=>(~old(X)&happy(X))))&
((wise(alice))<=>((rich(john)|~curious(john))))&
(happy(john))&
(?[X]:((~funny(X)&~quiet(X))))&
((old(alice)<~>strong(alice)))&
(?[X]:(~rich(X)))&
(~rich(fred))&
((~rich(john)<~>~patient(john)))&
((~kind(susan)&~brave(susan))) | kind(alice) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2694482020370988816250205
% SZS output start Proof for 2694482020370988816250205
4. ! [X0] : ((~strong(X0) & kind(X0)) => strong(X0)) [input p3]
6. ! [X0] : ((~kind(X0) & rich(X0)) <=> strong(X0)) [input p5]
24. kind(alice) [input hypothesis]
33. ! [X0] : (strong(X0) | (strong(X0) | ~kind(X0))) [ennf transformation 4]
34. ! [X0] : (strong(X0) | strong(X0) | ~kind(X0)) [flattening 33]
45. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | (kind(X0) | ~rich(X0)))) [nnf transformation 6]
46. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0)) & (strong(X0) | kind(X0) | ~rich(X0))) [flattening 45]
91. strong(X0) | strong(X0) | ~kind(X0) [cnf transformation 34]
99. ~kind(X0) | ~strong(X0) [cnf transformation 46]
150. kind(alice) [cnf transformation 24]
155. strong(X0) | ~kind(X0) [duplicate literal removal 91]
187. ~kind(X0) [subsumption resolution 99,155]
338. $false [subsumption resolution 150,187]
% SZS output end Proof for 2694482020370988816250205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and not brave then paul is either not quiet or not generous and vice versa.
Everyone who is both not happy and not funny is either tall or not happy.
If john is calm or not generous then someone is both not kind and patient and vice versa.
Everyone who is both not brave and not kind is both creative and wise and vice versa.
If paul is either not creative or not calm then someone is both happy and not kind.
If someone is both not generous and not curious then someone is both calm and not tall and vice versa.
If someone is both brave and curious then someone is kind or not curious and vice versa.
If someone is tall or old then fred is old and vice versa.
Everyone who is quiet is both not patient and quiet.
Everyone who is calm is quiet.
If alice is strong then paul is either calm or not funny and vice versa.
Everyone who is both not tall and rich is both kind and patient.
If mary is not generous then fred is calm.
Everyone who is both not calm and patient is brave.
Everyone who is either not old or old is funny or not generous.
Everyone who is not curious is patient.
Someone is either not old or funny.
Alice is not generous.
Lucy is both not happy and tall.
Someone is not kind.
Someone is both not humble and not generous.
John is both not happy and funny.
Mary is generous.
Lucy is funny or not generous. | Mary is not generous. | contradiction | (((quiet(paul)&~brave(paul)))<=>((~quiet(paul)<~>~generous(paul))))&
(![X]:((~happy(X)&~funny(X))=>(tall(X)<~>~happy(X))))&
(((calm(john)|~generous(john)))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)&wise(X))))&
(((~creative(paul)<~>~calm(paul)))=>(?[X]:((happy(X)&~kind(X)))))&
((?[X]:((~generous(X)&~curious(X))))<=>(?[X]:((calm(X)&~tall(X)))))&
((?[X]:((brave(X)&curious(X))))<=>(?[X]:((kind(X)|~curious(X)))))&
((?[X]:((tall(X)|old(X))))<=>(old(fred)))&
(![X]:(quiet(X)=>(~patient(X)&quiet(X))))&
(![X]:(calm(X)=>quiet(X)))&
((strong(alice))<=>((calm(paul)<~>~funny(paul))))&
(![X]:((~tall(X)&rich(X))=>(kind(X)&patient(X))))&
((~generous(mary))=>(calm(fred)))&
(![X]:((~calm(X)&patient(X))=>brave(X)))&
(![X]:((~old(X)<~>old(X))=>(funny(X)|~generous(X))))&
(![X]:(~curious(X)=>patient(X)))&
(?[X]:((~old(X)<~>funny(X))))&
(~generous(alice))&
((~happy(lucy)&tall(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~humble(X)&~generous(X))))&
((~happy(john)&funny(john)))&
(generous(mary))&
((funny(lucy)|~generous(lucy))) | ~generous(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6005374505450306202611368
% SZS output start Proof for 6005374505450306202611368
23. generous(mary) [input p22]
25. ~generous(mary) [input hypothesis]
131. generous(mary) [cnf transformation 23]
133. ~generous(mary) [cnf transformation 25]
289. 33 <=> generous(mary) [avatar definition]
308. 33 [avatar split clause 131,289]
309. ~33 [avatar split clause 133,289]
310. $false [avatar sat refutation 308,309]
% SZS output end Proof for 6005374505450306202611368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either curious or generous then someone is both not patient and funny. If someone is either rich or not creative then someone is not calm or strong. If someone is both not curious and wise then fred is kind or rich and vice versa. Everyone who is brave or creative is not humble or not quiet. Everyone who is not humble or calm is strong or not wise and vice versa. If someone is both not curious and not funny then someone is rich. If someone is not funny or creative then someone is either not old or not patient and vice versa. Everyone who is either kind or not quiet is rich or humble and vice versa. If someone is both kind and not brave then someone is tall or wise. If someone is both brave and not calm then someone is both not strong and not creative. If someone is either rich or patient then susan is old or calm. If fred is both patient and humble then someone is both not calm and kind and vice versa. Everyone who is not generous is either wise or not wise and vice versa. Everyone who is both not brave and not quiet is not rich. Everyone who is not rich or calm is either funny or not strong. Everyone who is both not humble and happy is both old and not humble. Mary is kind or patient. Someone is both tall and not brave. Someone is creative or wise. Someone is either not strong or curious. Lucy is either not calm or not generous. Susan is wise or not patient. Someone is tall. Someone is either not humble or not rich. | Mary is generous. | contradiction | (((curious(alice)<~>generous(alice)))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~calm(X)|strong(X)))))&
((?[X]:((~curious(X)&wise(X))))<=>((kind(fred)|rich(fred))))&
(![X]:((brave(X)|creative(X))=>(~humble(X)|~quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(strong(X)|~wise(X))))&
((?[X]:((~curious(X)&~funny(X))))=>(?[X]:(rich(X))))&
((?[X]:((~funny(X)|creative(X))))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((kind(X)<~>~quiet(X))<=>(rich(X)|humble(X))))&
((?[X]:((kind(X)&~brave(X))))=>(?[X]:((tall(X)|wise(X)))))&
((?[X]:((brave(X)&~calm(X))))=>(?[X]:((~strong(X)&~creative(X)))))&
((?[X]:((rich(X)<~>patient(X))))=>((old(susan)|calm(susan))))&
(((patient(fred)&humble(fred)))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:(~generous(X)<=>(wise(X)<~>~wise(X))))&
(![X]:((~brave(X)&~quiet(X))=>~rich(X)))&
(![X]:((~rich(X)|calm(X))=>(funny(X)<~>~strong(X))))&
(![X]:((~humble(X)&happy(X))=>(old(X)&~humble(X))))&
((kind(mary)|patient(mary)))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
((~calm(lucy)<~>~generous(lucy)))&
((wise(susan)|~patient(susan)))&
(?[X]:(tall(X)))&
(?[X]:((~humble(X)<~>~rich(X)))) | generous(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8332135732620072883277792
% SZS output start Proof for 8332135732620072883277792
13. ! [X0] : (~generous(X0) <=> (wise(X0) <~> ~wise(X0))) [input p12]
25. generous(mary) [input hypothesis]
79. ! [X0] : ((~generous(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | generous(X0))) [nnf transformation 13]
132. ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 79]
133. ~generous(X0) | wise(X0) | wise(X0) [cnf transformation 79]
149. generous(mary) [cnf transformation 25]
150. ~generous(X0) | ~wise(X0) [duplicate literal removal 132]
151. ~generous(X0) | wise(X0) [duplicate literal removal 133]
306. ~generous(X0) [subsumption resolution 150,151]
355. $false [subsumption resolution 149,306]
% SZS output end Proof for 8332135732620072883277792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not tall is patient and vice versa.
If mary is not rich or happy then someone is not funny.
Everyone who is either happy or patient is not funny and vice versa.
If someone is not patient or not generous then someone is rich or not happy and vice versa.
Everyone who is not kind is either patient or generous.
Everyone who is both not brave and strong is either generous or not old.
Everyone who is either strong or not brave is either not calm or happy and vice versa.
Everyone who is both quiet and not creative is creative.
Everyone who is both not humble and wise is both brave and patient.
If alice is not happy then lucy is either rich or not brave and vice versa.
If susan is both strong and not quiet then someone is brave or not kind and vice versa.
If someone is either generous or tall then john is both not kind and not wise and vice versa.
Everyone who is either calm or creative is either wise or old and vice versa.
If mary is both not wise and not old then someone is not tall.
Everyone who is either calm or generous is either not wise or not happy and vice versa.
Everyone who is not wise or not patient is either funny or kind.
Someone is either tall or not tall.
Susan is both old and brave.
Someone is rich or strong.
Alice is both creative and humble.
Someone is either not funny or old.
John is not funny.
Lucy is not rich. | Susan is not kind. | neutral | (![X]:((~humble(X)|~tall(X))<=>patient(X)))&
(((~rich(mary)|happy(mary)))=>(?[X]:(~funny(X))))&
(![X]:((happy(X)<~>patient(X))<=>~funny(X)))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:(~kind(X)=>(patient(X)<~>generous(X))))&
(![X]:((~brave(X)&strong(X))=>(generous(X)<~>~old(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))=>creative(X)))&
(![X]:((~humble(X)&wise(X))=>(brave(X)&patient(X))))&
((~happy(alice))<=>((rich(lucy)<~>~brave(lucy))))&
(((strong(susan)&~quiet(susan)))<=>(?[X]:((brave(X)|~kind(X)))))&
((?[X]:((generous(X)<~>tall(X))))<=>((~kind(john)&~wise(john))))&
(![X]:((calm(X)<~>creative(X))<=>(wise(X)<~>old(X))))&
(((~wise(mary)&~old(mary)))=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((~wise(X)|~patient(X))=>(funny(X)<~>kind(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((old(susan)&brave(susan)))&
(?[X]:((rich(X)|strong(X))))&
((creative(alice)&humble(alice)))&
(?[X]:((~funny(X)<~>old(X))))&
(~funny(john))&
(~rich(lucy)) | ~kind(susan) | [] | null | 0 |
Everyone who is both not humble and brave is both humble and old and vice versa.
If someone is wise then mary is both curious and kind.
If lucy is either not rich or not happy then someone is both not quiet and not happy.
Everyone who is both rich and not quiet is either tall or not quiet.
Everyone who is tall is both rich and old.
Everyone who is calm or not calm is both brave and wise.
If john is both not happy and funny then someone is either quiet or wise and vice versa.
Everyone who is both not patient and creative is both old and wise and vice versa.
Everyone who is both not funny and calm is both not wise and creative.
Everyone who is not generous is both creative and generous and vice versa.
If someone is both rich and tall then alice is not quiet or creative.
Everyone who is both not happy and humble is either not calm or funny and vice versa.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Lucy is either not happy or not strong.
Someone is rich or not happy.
Fred is not brave or not creative.
Someone is strong or wise.
Someone is both not kind and not rich.
Someone is either rich or not tall. | Fred is patient. | neutral | (![X]:((~humble(X)&brave(X))<=>(humble(X)&old(X))))&
((?[X]:(wise(X)))=>((curious(mary)&kind(mary))))&
(((~rich(lucy)<~>~happy(lucy)))=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((rich(X)&~quiet(X))=>(tall(X)<~>~quiet(X))))&
(![X]:(tall(X)=>(rich(X)&old(X))))&
(![X]:((calm(X)|~calm(X))=>(brave(X)&wise(X))))&
(((~happy(john)&funny(john)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((~patient(X)&creative(X))<=>(old(X)&wise(X))))&
(![X]:((~funny(X)&calm(X))=>(~wise(X)&creative(X))))&
(![X]:(~generous(X)<=>(creative(X)&generous(X))))&
((?[X]:((rich(X)&tall(X))))=>((~quiet(alice)|creative(alice))))&
(![X]:((~happy(X)&humble(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
((~happy(lucy)<~>~strong(lucy)))&
(?[X]:((rich(X)|~happy(X))))&
((~brave(fred)|~creative(fred)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((rich(X)<~>~tall(X)))) | patient(fred) | [] | null | 0 |
Everyone who is either generous or wise is either not humble or not brave.
Everyone who is either not funny or strong is either not patient or rich and vice versa.
Everyone who is either funny or humble is brave or happy and vice versa.
Everyone who is brave is not funny and vice versa.
If someone is both not rich and not creative then someone is both curious and old and vice versa.
Everyone who is either not rich or funny is calm or not curious.
If someone is both not curious and not generous then someone is not generous or old.
If someone is either wise or not old then mary is either not humble or patient and vice versa.
Everyone who is curious is either quiet or not calm and vice versa.
If someone is either not curious or tall then someone is curious.
Everyone who is both happy and calm is humble or tall and vice versa.
Everyone who is rich is both quiet and wise and vice versa.
Everyone who is humble is not generous or not creative and vice versa.
If fred is both humble and not brave then someone is not curious or not patient and vice versa.
Everyone who is not funny is both not generous and not strong and vice versa.
If someone is both brave and creative then someone is patient or not patient.
Someone is not funny or quiet.
Someone is both not kind and wise.
Fred is not strong.
Paul is not quiet.
Someone is not quiet.
Someone is calm.
Someone is not happy or not humble. | Paul is tall. | contradiction | (![X]:((generous(X)<~>wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((funny(X)<~>humble(X))<=>(brave(X)|happy(X))))&
(![X]:(brave(X)<=>~funny(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(calm(X)|~curious(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~generous(X)|old(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>((~humble(mary)<~>patient(mary))))&
(![X]:(curious(X)<=>(quiet(X)<~>~calm(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:(curious(X))))&
(![X]:((happy(X)&calm(X))<=>(humble(X)|tall(X))))&
(![X]:(rich(X)<=>(quiet(X)&wise(X))))&
(![X]:(humble(X)<=>(~generous(X)|~creative(X))))&
(((humble(fred)&~brave(fred)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:(~funny(X)<=>(~generous(X)&~strong(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((patient(X)|~patient(X)))))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((~kind(X)&wise(X))))&
(~strong(fred))&
(~quiet(paul))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)|~humble(X)))) | tall(paul) | [
"p2",
"p3",
"p8",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 881744688654503181739337
% SZS output start Proof for 881744688654503181739337
3. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (happy(X0) | brave(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> ~funny(X0)) [input p3]
9. ! [X0] : (curious(X0) <=> (quiet(X0) <~> ~calm(X0))) [input p8]
11. ! [X0] : ((calm(X0) & happy(X0)) <=> (tall(X0) | humble(X0))) [input p10]
14. (~brave(fred) & humble(fred)) <=> ? [X0] : (~patient(X0) | ~curious(X0)) [input p13]
20. ~quiet(paul) [input p19]
24. tall(paul) [input hypothesis]
38. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [flattening 38]
40. ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))) [nnf transformation 4]
54. ! [X0] : ((curious(X0) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~curious(X0))) [nnf transformation 9]
59. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 11]
60. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ~calm(X0) | ~happy(X0))) [flattening 59]
65. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | (brave(fred) | ~humble(fred))) [nnf transformation 14]
66. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | brave(fred) | ~humble(fred)) [flattening 65]
67. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X1] : (~patient(X1) | ~curious(X1)) | brave(fred) | ~humble(fred)) [rectify 66]
68. ? [X1] : (~patient(X1) | ~curious(X1)) => (~patient(sK5) | ~curious(sK5)) [choice axiom]
69. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & ((~patient(sK5) | ~curious(sK5)) | brave(fred) | ~humble(fred)) [skolemisation 67,68]
102. ~happy(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 39]
104. funny(X0) | brave(X0) [cnf transformation 40]
120. ~calm(X0) | quiet(X0) | ~curious(X0) [cnf transformation 54]
127. ~humble(X0) | happy(X0) [cnf transformation 60]
130. ~tall(X0) | calm(X0) [cnf transformation 60]
138. humble(fred) | curious(X0) [cnf transformation 69]
140. ~brave(fred) | curious(X0) [cnf transformation 69]
149. ~quiet(paul) [cnf transformation 20]
153. tall(paul) [cnf transformation 24]
238. 20 <=> brave(fred) [avatar definition]
240. ~brave(fred) <- (~20) [avatar component clause 238]
243. 21 <=> ! [X0] : curious(X0) [avatar definition]
244. curious(X0) <- (21) [avatar component clause 243]
245. 21 | ~20 [avatar split clause 140,238,243]
247. 22 <=> humble(fred) [avatar definition]
249. humble(fred) <- (22) [avatar component clause 247]
251. 21 | 22 [avatar split clause 138,247,243]
278. happy(fred) <- (22) [resolution 127,249]
282. calm(paul) [resolution 130,153]
316. ~funny(fred) | ~humble(fred) <- (22) [resolution 102,278]
319. ~funny(fred) <- (22) [subsumption resolution 316,249]
325. quiet(paul) | ~curious(paul) [resolution 120,282]
329. ~curious(paul) [subsumption resolution 325,149]
330. $false <- (21) [subsumption resolution 329,244]
331. ~21 [avatar contradiction clause 330]
361. brave(fred) <- (22) [resolution 319,104]
362. $false <- (~20, 22) [subsumption resolution 361,240]
363. 20 | ~22 [avatar contradiction clause 362]
364. $false [avatar sat refutation 245,251,331,363]
% SZS output end Proof for 881744688654503181739337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is tall or happy and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is both not generous and tall then someone is either not rich or curious.
If mary is either not brave or not humble then someone is either generous or funny.
If someone is not calm then paul is both rich and not tall and vice versa.
If someone is wise then susan is happy or not old and vice versa.
If someone is not happy or not funny then lucy is not kind or not funny.
Everyone who is quiet is both not happy and not brave and vice versa.
Everyone who is brave is both not generous and humble.
Everyone who is either not curious or not happy is calm or not generous and vice versa.
Everyone who is both kind and humble is wise or quiet and vice versa.
Everyone who is either funny or rich is not creative and vice versa.
Everyone who is not patient is either old or kind and vice versa.
If someone is either kind or not generous then john is both not wise and happy and vice versa.
If someone is not humble then someone is curious or generous.
If lucy is both quiet and not kind then someone is either not strong or generous and vice versa.
Someone is either not funny or kind.
Lucy is both strong and humble.
Someone is not funny.
Someone is strong.
Alice is either not brave or happy.
Mary is patient or not strong. | Lucy is funny. | contradiction | (![X]:(~strong(X)<=>(tall(X)|happy(X))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:((~generous(X)&tall(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(((~brave(mary)<~>~humble(mary)))=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:(~calm(X)))<=>((rich(paul)&~tall(paul))))&
((?[X]:(wise(X)))<=>((happy(susan)|~old(susan))))&
((?[X]:((~happy(X)|~funny(X))))=>((~kind(lucy)|~funny(lucy))))&
(![X]:(quiet(X)<=>(~happy(X)&~brave(X))))&
(![X]:(brave(X)=>(~generous(X)&humble(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>(calm(X)|~generous(X))))&
(![X]:((kind(X)&humble(X))<=>(wise(X)|quiet(X))))&
(![X]:((funny(X)<~>rich(X))<=>~creative(X)))&
(![X]:(~patient(X)<=>(old(X)<~>kind(X))))&
((?[X]:((kind(X)<~>~generous(X))))<=>((~wise(john)&happy(john))))&
((?[X]:(~humble(X)))=>(?[X]:((curious(X)|generous(X)))))&
(((quiet(lucy)&~kind(lucy)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(?[X]:((~funny(X)<~>kind(X))))&
((strong(lucy)&humble(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:(strong(X)))&
((~brave(alice)<~>happy(alice)))&
((patient(mary)|~strong(mary))) | funny(lucy) | [
"p1",
"p6",
"p10",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1881638879799707752330815
% SZS output start Proof for 1881638879799707752330815
2. ! [X0] : ((funny(X0) | strong(X0)) <=> quiet(X0)) [input p1]
7. ? [X0] : (~funny(X0) | ~happy(X0)) => (~funny(lucy) | ~kind(lucy)) [input p6]
11. ! [X0] : ((humble(X0) & kind(X0)) <=> (quiet(X0) | wise(X0))) [input p10]
18. humble(lucy) & strong(lucy) [input p17]
19. ? [X0] : ~funny(X0) [input p18]
23. funny(lucy) [input hypothesis]
29. (~funny(lucy) | ~kind(lucy)) | ! [X0] : (funny(X0) & happy(X0)) [ennf transformation 7]
30. ~funny(lucy) | ~kind(lucy) | ! [X0] : (funny(X0) & happy(X0)) [flattening 29]
36. ! [X0] : (((funny(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 2]
37. ! [X0] : ((funny(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [flattening 36]
59. ! [X0] : (((humble(X0) & kind(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 11]
60. ! [X0] : (((humble(X0) & kind(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~humble(X0) | ~kind(X0))) [flattening 59]
78. ? [X0] : ~funny(X0) => ~funny(sK8) [choice axiom]
79. ~funny(sK8) [skolemisation 19,78]
86. ~strong(X0) | quiet(X0) [cnf transformation 37]
102. ~funny(lucy) | ~kind(lucy) | funny(X0) [cnf transformation 30]
116. ~quiet(X0) | kind(X0) [cnf transformation 60]
136. strong(lucy) [cnf transformation 18]
138. ~funny(sK8) [cnf transformation 79]
143. funny(lucy) [cnf transformation 23]
214. 16 <=> ! [X0] : funny(X0) [avatar definition]
215. funny(X0) <- (16) [avatar component clause 214]
217. 17 <=> kind(lucy) [avatar definition]
221. 18 <=> funny(lucy) [avatar definition]
224. 16 | ~17 | ~18 [avatar split clause 102,221,217,214]
278. 31 <=> quiet(lucy) [avatar definition]
280. quiet(lucy) <- (31) [avatar component clause 278]
312. 18 [avatar split clause 143,221]
316. quiet(lucy) [resolution 86,136]
318. 31 [avatar split clause 316,278]
326. kind(lucy) <- (31) [resolution 116,280]
330. 17 | ~31 [avatar split clause 326,278,217]
331. $false <- (16) [resolution 215,138]
335. ~16 [avatar contradiction clause 331]
336. $false [avatar sat refutation 224,312,318,330,335]
% SZS output end Proof for 1881638879799707752330815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not old or quiet then susan is either not wise or brave and vice versa.
Everyone who is either happy or not rich is wise and vice versa.
If someone is creative or wise then someone is not quiet or not wise.
Everyone who is not brave is happy.
If someone is either not wise or tall then someone is both not old and creative.
Everyone who is either not tall or not brave is generous and vice versa.
If someone is not quiet then someone is both not happy and rich and vice versa.
Everyone who is patient is either not curious or not happy and vice versa.
If someone is tall then someone is old or kind and vice versa.
Everyone who is not humble or quiet is both kind and not quiet and vice versa.
Everyone who is not brave or not quiet is humble or curious and vice versa.
Everyone who is not brave or brave is not creative.
If someone is creative then susan is curious and vice versa.
Everyone who is calm is not calm or strong and vice versa.
Everyone who is both quiet and not tall is not calm.
If paul is both not happy and curious then someone is patient.
Someone is both tall and happy.
John is either not quiet or not funny.
Alice is either creative or calm.
Fred is either happy or not humble.
Someone is both old and not wise.
Someone is tall or humble.
Fred is not quiet or not happy. | Alice is not curious. | neutral | (((~old(susan)<~>quiet(susan)))<=>((~wise(susan)<~>brave(susan))))&
(![X]:((happy(X)<~>~rich(X))<=>wise(X)))&
((?[X]:((creative(X)|wise(X))))=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:(~brave(X)=>happy(X)))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((~old(X)&creative(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>generous(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:(patient(X)<=>(~curious(X)<~>~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~humble(X)|quiet(X))<=>(kind(X)&~quiet(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(humble(X)|curious(X))))&
(![X]:((~brave(X)|brave(X))=>~creative(X)))&
((?[X]:(creative(X)))<=>(curious(susan)))&
(![X]:(calm(X)<=>(~calm(X)|strong(X))))&
(![X]:((quiet(X)&~tall(X))=>~calm(X)))&
(((~happy(paul)&curious(paul)))=>(?[X]:(patient(X))))&
(?[X]:((tall(X)&happy(X))))&
((~quiet(john)<~>~funny(john)))&
((creative(alice)<~>calm(alice)))&
((happy(fred)<~>~humble(fred)))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((tall(X)|humble(X))))&
((~quiet(fred)|~happy(fred))) | ~curious(alice) | [] | null | 0 |
Everyone who is not tall is kind or strong.
If lucy is not curious or not calm then lucy is generous and vice versa.
If someone is strong then someone is either generous or not wise.
Everyone who is either not funny or tall is both not calm and creative and vice versa.
If paul is either wise or humble then alice is strong or rich and vice versa.
If someone is not calm then someone is not quiet.
If fred is either generous or brave then john is both calm and not quiet.
If paul is not brave or rich then someone is either not curious or old.
Everyone who is calm or not kind is not happy.
If paul is not rich or humble then someone is both not humble and funny.
If someone is curious or brave then someone is both quiet and not old.
Everyone who is brave or not strong is tall or not kind.
If someone is either brave or not strong then someone is not old or not brave.
Everyone who is both not strong and curious is not happy.
Everyone who is creative is not quiet or not tall.
If alice is not strong then fred is either not happy or not brave and vice versa.
Someone is not old or not generous.
Someone is kind or not rich.
Someone is either brave or not funny.
Someone is funny or not kind.
Someone is not humble.
Someone is kind or curious.
Lucy is either old or not old.
Someone is happy or not creative. | John is quiet. | neutral | (![X]:(~tall(X)=>(kind(X)|strong(X))))&
(((~curious(lucy)|~calm(lucy)))<=>(generous(lucy)))&
((?[X]:(strong(X)))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((~funny(X)<~>tall(X))<=>(~calm(X)&creative(X))))&
(((wise(paul)<~>humble(paul)))<=>((strong(alice)|rich(alice))))&
((?[X]:(~calm(X)))=>(?[X]:(~quiet(X))))&
(((generous(fred)<~>brave(fred)))=>((calm(john)&~quiet(john))))&
(((~brave(paul)|rich(paul)))=>(?[X]:((~curious(X)<~>old(X)))))&
(![X]:((calm(X)|~kind(X))=>~happy(X)))&
(((~rich(paul)|humble(paul)))=>(?[X]:((~humble(X)&funny(X)))))&
((?[X]:((curious(X)|brave(X))))=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((brave(X)|~strong(X))=>(tall(X)|~kind(X))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((~old(X)|~brave(X)))))&
(![X]:((~strong(X)&curious(X))=>~happy(X)))&
(![X]:(creative(X)=>(~quiet(X)|~tall(X))))&
((~strong(alice))<=>((~happy(fred)<~>~brave(fred))))&
(?[X]:((~old(X)|~generous(X))))&
(?[X]:((kind(X)|~rich(X))))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((funny(X)|~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)|curious(X))))&
((old(lucy)<~>~old(lucy)))&
(?[X]:((happy(X)|~creative(X)))) | quiet(john) | [] | null | 0 |
Everyone who is not kind is happy or not creative. If susan is not wise or calm then mary is both patient and wise. If lucy is quiet then someone is patient. Everyone who is either not funny or not calm is both not generous and not kind and vice versa. If someone is not curious or tall then someone is both not wise and not old and vice versa. Everyone who is tall is both not rich and brave. Everyone who is both tall and not rich is both not tall and quiet. If someone is both creative and not brave then someone is either funny or patient. Everyone who is humble or not wise is either not strong or not generous. Everyone who is both funny and quiet is tall and vice versa. Everyone who is both not funny and patient is happy. If someone is both tall and not creative then someone is strong or not humble. If alice is quiet then john is either tall or curious. If someone is both not quiet and not humble then someone is either not generous or rich and vice versa. Everyone who is humble is both not old and patient. If mary is either not calm or not quiet then someone is kind and vice versa. Lucy is either not creative or not generous. Lucy is calm. Someone is either brave or strong. Someone is not funny or strong. Someone is brave. Lucy is rich or not curious. Paul is either kind or not creative. Someone is both rich and quiet. | Mary is patient. | neutral | (![X]:(~kind(X)=>(happy(X)|~creative(X))))&
(((~wise(susan)|calm(susan)))=>((patient(mary)&wise(mary))))&
((quiet(lucy))=>(?[X]:(patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~generous(X)&~kind(X))))&
((?[X]:((~curious(X)|tall(X))))<=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:(tall(X)=>(~rich(X)&brave(X))))&
(![X]:((tall(X)&~rich(X))=>(~tall(X)&quiet(X))))&
((?[X]:((creative(X)&~brave(X))))=>(?[X]:((funny(X)<~>patient(X)))))&
(![X]:((humble(X)|~wise(X))=>(~strong(X)<~>~generous(X))))&
(![X]:((funny(X)&quiet(X))<=>tall(X)))&
(![X]:((~funny(X)&patient(X))=>happy(X)))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:((strong(X)|~humble(X)))))&
((quiet(alice))=>((tall(john)<~>curious(john))))&
((?[X]:((~quiet(X)&~humble(X))))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:(humble(X)=>(~old(X)&patient(X))))&
(((~calm(mary)<~>~quiet(mary)))<=>(?[X]:(kind(X))))&
((~creative(lucy)<~>~generous(lucy)))&
(calm(lucy))&
(?[X]:((brave(X)<~>strong(X))))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:(brave(X)))&
((rich(lucy)|~curious(lucy)))&
((kind(paul)<~>~creative(paul)))&
(?[X]:((rich(X)&quiet(X)))) | patient(mary) | [] | null | 0 |
Everyone who is not curious is not brave or old. Everyone who is either strong or not brave is both not patient and kind. If someone is both creative and wise then paul is either not humble or generous. Everyone who is either brave or humble is creative. If alice is both creative and calm then fred is old. If susan is either not funny or not generous then fred is kind and vice versa. If someone is either not curious or creative then someone is quiet and vice versa. Everyone who is not brave or not calm is both brave and not brave. If someone is not old then someone is either not wise or happy. If someone is both humble and not funny then alice is both not humble and tall and vice versa. If someone is either not brave or not patient then fred is either not brave or quiet and vice versa. Everyone who is either not curious or not kind is either not rich or creative. Everyone who is both not generous and kind is funny or creative and vice versa. If someone is either not funny or funny then someone is either quiet or not brave and vice versa. Everyone who is not generous or funny is not creative. Everyone who is both strong and not old is not happy or wise. Someone is either not kind or patient. Paul is not happy. Someone is either creative or not rich. Susan is either kind or old. Someone is humble. | Susan is not humble. | contradiction | (![X]:(~curious(X)=>(~brave(X)|old(X))))&
(![X]:((strong(X)<~>~brave(X))=>(~patient(X)&kind(X))))&
((?[X]:((creative(X)&wise(X))))=>((~humble(paul)<~>generous(paul))))&
(![X]:((brave(X)<~>humble(X))=>creative(X)))&
(((creative(alice)&calm(alice)))=>(old(fred)))&
(((~funny(susan)<~>~generous(susan)))<=>(kind(fred)))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))=>(brave(X)&~brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((humble(X)&~funny(X))))<=>((~humble(alice)&tall(alice))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((~brave(fred)<~>quiet(fred))))&
(![X]:((~curious(X)<~>~kind(X))=>(~rich(X)<~>creative(X))))&
(![X]:((~generous(X)&kind(X))<=>(funny(X)|creative(X))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(![X]:((strong(X)&~old(X))=>(~happy(X)|wise(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
(~happy(paul))&
(?[X]:((creative(X)<~>~rich(X))))&
((kind(susan)<~>old(susan)))&
(?[X]:(humble(X))) | ~humble(susan) | [
"p3",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 370961065040298251113053
% SZS output start Proof for 370961065040298251113053
4. ! [X0] : ((brave(X0) <~> humble(X0)) => creative(X0)) [input p3]
8. ! [X0] : ((~calm(X0) | ~brave(X0)) => (~brave(X0) & brave(X0))) [input p7]
13. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (creative(X0) | funny(X0))) [input p12]
15. ! [X0] : ((funny(X0) | ~generous(X0)) => ~creative(X0)) [input p14]
22. ~humble(susan) [input hypothesis]
30. ! [X0] : (creative(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 4]
33. ! [X0] : ((~brave(X0) & brave(X0)) | (calm(X0) & brave(X0))) [ennf transformation 8]
36. ! [X0] : (~creative(X0) | (~funny(X0) & generous(X0))) [ennf transformation 15]
41. ! [X0] : (creative(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 30]
62. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & ((creative(X0) | funny(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 13]
63. ! [X0] : (((kind(X0) & ~generous(X0)) | (~creative(X0) & ~funny(X0))) & (creative(X0) | funny(X0) | ~kind(X0) | generous(X0))) [flattening 62]
85. ~brave(X0) | humble(X0) | creative(X0) [cnf transformation 41]
96. brave(X0) | brave(X0) [cnf transformation 33]
120. ~generous(X0) | ~creative(X0) [cnf transformation 63]
131. ~creative(X0) | generous(X0) [cnf transformation 36]
142. ~humble(susan) [cnf transformation 22]
147. brave(X0) [duplicate literal removal 96]
283. ~creative(X0) [subsumption resolution 131,120]
312. humble(X0) | creative(X0) [resolution 85,147]
313. humble(X0) [subsumption resolution 312,283]
319. $false [resolution 313,142]
% SZS output end Proof for 370961065040298251113053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or generous is calm or not rich. If fred is not old then alice is not patient and vice versa. Everyone who is both not brave and not curious is not strong. Everyone who is either not generous or rich is rich and vice versa. If someone is both not old and not generous then alice is not generous. Everyone who is either not strong or curious is either not quiet or not curious. Everyone who is kind or not kind is kind. Everyone who is humble is calm or kind and vice versa. If someone is not rich then someone is creative. Everyone who is not creative or tall is not old and vice versa. Everyone who is rich is either not strong or not brave. If fred is rich then someone is either brave or happy and vice versa. Everyone who is both not old and not kind is both not patient and not funny and vice versa. Everyone who is either old or not funny is happy and vice versa. If alice is both not tall and wise then someone is happy and vice versa. Everyone who is old or funny is both patient and not tall. Paul is either not old or not calm. Someone is both funny and not happy. Someone is both quiet and not wise. Alice is generous. Someone is both not rich and tall. John is patient or rich. Someone is either wise or not funny. | Fred is not tall. | entailment | (![X]:((~tall(X)<~>generous(X))=>(calm(X)|~rich(X))))&
((~old(fred))<=>(~patient(alice)))&
(![X]:((~brave(X)&~curious(X))=>~strong(X)))&
(![X]:((~generous(X)<~>rich(X))<=>rich(X)))&
((?[X]:((~old(X)&~generous(X))))=>(~generous(alice)))&
(![X]:((~strong(X)<~>curious(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((kind(X)|~kind(X))=>kind(X)))&
(![X]:(humble(X)<=>(calm(X)|kind(X))))&
((?[X]:(~rich(X)))=>(?[X]:(creative(X))))&
(![X]:((~creative(X)|tall(X))<=>~old(X)))&
(![X]:(rich(X)=>(~strong(X)<~>~brave(X))))&
((rich(fred))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~patient(X)&~funny(X))))&
(![X]:((old(X)<~>~funny(X))<=>happy(X)))&
(((~tall(alice)&wise(alice)))<=>(?[X]:(happy(X))))&
(![X]:((old(X)|funny(X))=>(patient(X)&~tall(X))))&
((~old(paul)<~>~calm(paul)))&
(?[X]:((funny(X)&~happy(X))))&
(?[X]:((quiet(X)&~wise(X))))&
(generous(alice))&
(?[X]:((~rich(X)&tall(X))))&
((patient(john)|rich(john)))&
(?[X]:((wise(X)<~>~funny(X)))) | ~tall(fred) | [
"p1",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2688775349810027468910792
% SZS output start Proof for 2688775349810027468910792
2. ~old(fred) <=> ~patient(alice) [input p1]
7. ! [X0] : ((~kind(X0) | kind(X0)) => kind(X0)) [input p6]
10. ! [X0] : ((tall(X0) | ~creative(X0)) <=> ~old(X0)) [input p9]
13. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~funny(X0) & ~patient(X0))) [input p12]
16. ! [X0] : ((funny(X0) | old(X0)) => (~tall(X0) & patient(X0))) [input p15]
24. tall(fred) [input hypothesis]
32. ! [X0] : (kind(X0) | (kind(X0) & ~kind(X0))) [ennf transformation 7]
35. ! [X0] : ((~tall(X0) & patient(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 16]
37. (~old(fred) | patient(alice)) & (~patient(alice) | old(fred)) [nnf transformation 2]
43. ! [X0] : (((tall(X0) | ~creative(X0)) | old(X0)) & (~old(X0) | (~tall(X0) & creative(X0)))) [nnf transformation 10]
44. ! [X0] : ((tall(X0) | ~creative(X0) | old(X0)) & (~old(X0) | (~tall(X0) & creative(X0)))) [flattening 43]
50. ! [X0] : (((~kind(X0) & ~old(X0)) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | (kind(X0) | old(X0)))) [nnf transformation 13]
51. ! [X0] : (((~kind(X0) & ~old(X0)) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | kind(X0) | old(X0))) [flattening 50]
70. ~patient(alice) | old(fred) [cnf transformation 37]
83. kind(X0) | kind(X0) [cnf transformation 32]
86. ~old(X0) | ~tall(X0) [cnf transformation 44]
97. ~kind(X0) | funny(X0) | patient(X0) [cnf transformation 51]
106. patient(X0) | ~funny(X0) [cnf transformation 35]
121. tall(fred) [cnf transformation 24]
122. kind(X0) [duplicate literal removal 83]
128. 1 <=> patient(alice) [avatar definition]
129. ~patient(alice) <- (~1) [avatar component clause 128]
132. 2 <=> old(fred) [avatar definition]
133. old(fred) <- (2) [avatar component clause 132]
136. 2 | ~1 [avatar split clause 70,128,132]
168. funny(X0) | patient(X0) [subsumption resolution 97,122]
187. patient(X0) [subsumption resolution 106,168]
209. $false <- (~1) [subsumption resolution 129,187]
210. 1 [avatar contradiction clause 209]
215. ~tall(fred) <- (2) [resolution 86,133]
217. $false <- (2) [subsumption resolution 215,121]
218. ~2 [avatar contradiction clause 217]
219. $false [avatar sat refutation 136,210,218]
% SZS output end Proof for 2688775349810027468910792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is funny or generous then fred is both not funny and not creative.
Everyone who is not patient is calm or not calm.
Everyone who is not humble or strong is both creative and brave and vice versa.
Everyone who is wise is either not curious or not happy and vice versa.
Everyone who is both not kind and brave is both old and not humble and vice versa.
If lucy is humble then john is both funny and not kind.
Everyone who is both patient and generous is both curious and not generous and vice versa.
Everyone who is not creative is both not quiet and not curious and vice versa.
Everyone who is both not calm and kind is not creative or not funny and vice versa.
If mary is funny or old then someone is not calm and vice versa.
Everyone who is both not humble and not wise is both calm and not wise and vice versa.
If john is both not brave and quiet then mary is either not funny or calm and vice versa.
Everyone who is either old or calm is both not tall and humble and vice versa.
If someone is either old or wise then someone is curious or not tall and vice versa.
If someone is generous then lucy is either strong or not curious and vice versa.
Everyone who is rich or not strong is both quiet and patient.
Someone is both not generous and creative.
Someone is either not old or quiet.
John is both funny and calm.
Someone is generous.
Lucy is not kind or not rich.
Someone is either not wise or not happy.
Someone is not wise or not kind. | Mary is not calm. | entailment | (((funny(mary)|generous(mary)))=>((~funny(fred)&~creative(fred))))&
(![X]:(~patient(X)=>(calm(X)|~calm(X))))&
(![X]:((~humble(X)|strong(X))<=>(creative(X)&brave(X))))&
(![X]:(wise(X)<=>(~curious(X)<~>~happy(X))))&
(![X]:((~kind(X)&brave(X))<=>(old(X)&~humble(X))))&
((humble(lucy))=>((funny(john)&~kind(john))))&
(![X]:((patient(X)&generous(X))<=>(curious(X)&~generous(X))))&
(![X]:(~creative(X)<=>(~quiet(X)&~curious(X))))&
(![X]:((~calm(X)&kind(X))<=>(~creative(X)|~funny(X))))&
(((funny(mary)|old(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((~humble(X)&~wise(X))<=>(calm(X)&~wise(X))))&
(((~brave(john)&quiet(john)))<=>((~funny(mary)<~>calm(mary))))&
(![X]:((old(X)<~>calm(X))<=>(~tall(X)&humble(X))))&
((?[X]:((old(X)<~>wise(X))))<=>(?[X]:((curious(X)|~tall(X)))))&
((?[X]:(generous(X)))<=>((strong(lucy)<~>~curious(lucy))))&
(![X]:((rich(X)|~strong(X))=>(quiet(X)&patient(X))))&
(?[X]:((~generous(X)&creative(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
((funny(john)&calm(john)))&
(?[X]:(generous(X)))&
((~kind(lucy)|~rich(lucy)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((~wise(X)|~kind(X)))) | ~calm(mary) | [
"p0",
"p2",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7095018217201126161544469
% SZS output start Proof for 7095018217201126161544469
1. (generous(mary) | funny(mary)) => (~creative(fred) & ~funny(fred)) [input p0]
3. ! [X0] : ((strong(X0) | ~humble(X0)) <=> (brave(X0) & creative(X0))) [input p2]
8. ! [X0] : (~creative(X0) <=> (~curious(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (~funny(X0) | ~creative(X0))) [input p8]
16. ! [X0] : ((~strong(X0) | rich(X0)) => (patient(X0) & quiet(X0))) [input p15]
24. calm(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) => (patient(X0) & quiet(X0))) [pure predicate removal 16]
28. (~creative(fred) & ~funny(fred)) | (~generous(mary) & ~funny(mary)) [ennf transformation 1]
32. ! [X0] : ((patient(X0) & quiet(X0)) | strong(X0)) [ennf transformation 27]
33. ! [X0] : (((strong(X0) | ~humble(X0)) | (~brave(X0) | ~creative(X0))) & ((brave(X0) & creative(X0)) | (~strong(X0) & humble(X0)))) [nnf transformation 3]
34. ! [X0] : ((strong(X0) | ~humble(X0) | ~brave(X0) | ~creative(X0)) & ((brave(X0) & creative(X0)) | (~strong(X0) & humble(X0)))) [flattening 33]
40. ! [X0] : ((~creative(X0) | (curious(X0) | quiet(X0))) & ((~curious(X0) & ~quiet(X0)) | creative(X0))) [nnf transformation 8]
41. ! [X0] : ((~creative(X0) | curious(X0) | quiet(X0)) & ((~curious(X0) & ~quiet(X0)) | creative(X0))) [flattening 40]
42. ! [X0] : (((kind(X0) & ~calm(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 9]
43. ! [X0] : (((kind(X0) & ~calm(X0)) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | ~kind(X0) | calm(X0))) [flattening 42]
78. ~creative(fred) | ~funny(mary) [cnf transformation 28]
82. ~strong(X0) | creative(X0) [cnf transformation 34]
100. ~quiet(X0) | creative(X0) [cnf transformation 41]
105. ~calm(X0) | funny(X0) [cnf transformation 43]
137. quiet(X0) | strong(X0) [cnf transformation 32]
149. calm(mary) [cnf transformation 24]
157. 2 <=> creative(fred) [avatar definition]
159. ~creative(fred) <- (~2) [avatar component clause 157]
162. 3 <=> funny(mary) [avatar definition]
165. ~3 | ~2 [avatar split clause 78,157,162]
202. 11 <=> calm(mary) [avatar definition]
203. calm(mary) <- (11) [avatar component clause 202]
304. 11 [avatar split clause 149,202]
310. funny(mary) <- (11) [resolution 105,203]
314. strong(X0) | creative(X0) [resolution 137,100]
315. creative(X0) [subsumption resolution 314,82]
321. $false <- (~2) [resolution 315,159]
322. 2 [avatar contradiction clause 321]
323. 3 | ~11 [avatar split clause 310,202,162]
324. $false [avatar sat refutation 165,304,322,323]
% SZS output end Proof for 7095018217201126161544469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then lucy is old.
Everyone who is both not strong and not generous is not quiet or generous.
If lucy is not brave or not humble then someone is not tall and vice versa.
Everyone who is either not quiet or rich is old or kind.
If fred is both not old and rich then someone is both not kind and wise and vice versa.
If someone is not curious then someone is creative or rich and vice versa.
Everyone who is not rich or not curious is tall.
If susan is either wise or generous then lucy is either not funny or tall and vice versa.
Everyone who is not patient or not humble is either creative or tall and vice versa.
Everyone who is both humble and strong is both humble and not patient and vice versa.
Everyone who is either humble or quiet is both not funny and not kind.
Everyone who is tall or rich is both not patient and not happy.
If someone is either not brave or calm then susan is not generous and vice versa.
If john is both calm and funny then someone is funny.
If john is patient or not happy then someone is happy or not strong and vice versa.
If fred is both quiet and not curious then alice is not kind or not curious and vice versa.
Fred is brave or not funny.
Alice is not tall.
Susan is strong.
Someone is quiet or not rich.
John is both strong and quiet.
Alice is not tall or not wise.
Lucy is not curious or humble. | Lucy is not generous. | neutral | ((?[X]:((kind(X)<~>~creative(X))))=>(old(lucy)))&
(![X]:((~strong(X)&~generous(X))=>(~quiet(X)|generous(X))))&
(((~brave(lucy)|~humble(lucy)))<=>(?[X]:(~tall(X))))&
(![X]:((~quiet(X)<~>rich(X))=>(old(X)|kind(X))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)&strong(X))<=>(humble(X)&~patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)|rich(X))=>(~patient(X)&~happy(X))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(~generous(susan)))&
(((calm(john)&funny(john)))=>(?[X]:(funny(X))))&
(((patient(john)|~happy(john)))<=>(?[X]:((happy(X)|~strong(X)))))&
(((quiet(fred)&~curious(fred)))<=>((~kind(alice)|~curious(alice))))&
((brave(fred)|~funny(fred)))&
(~tall(alice))&
(strong(susan))&
(?[X]:((quiet(X)|~rich(X))))&
((strong(john)&quiet(john)))&
((~tall(alice)|~wise(alice)))&
((~curious(lucy)|humble(lucy))) | ~generous(lucy) | [] | null | 0 |
If lucy is happy or kind then someone is humble or not rich and vice versa. Everyone who is both not quiet and funny is not brave or patient and vice versa. Everyone who is tall or rich is rich or quiet and vice versa. If alice is either not creative or humble then someone is either humble or old and vice versa. Everyone who is generous or not quiet is either happy or strong and vice versa. Everyone who is either not funny or not humble is strong or generous. Everyone who is not happy or not kind is either tall or not happy and vice versa. If someone is either not calm or not rich then lucy is both quiet and calm and vice versa. Everyone who is either not tall or funny is happy and vice versa. Everyone who is not strong or not kind is brave and vice versa. If someone is either funny or happy then fred is not funny or not generous and vice versa. If someone is not quiet or patient then mary is either tall or generous. Everyone who is either old or generous is not calm and vice versa. If alice is calm then someone is calm. Everyone who is both not quiet and calm is old or tall. Everyone who is both brave and not calm is both wise and calm and vice versa. Someone is not kind or not brave. Someone is tall or not kind. Someone is both not creative and old. Mary is not generous or creative. Someone is kind. Mary is either old or not tall. John is both not strong and not tall. John is either tall or not generous. | John is quiet. | entailment | (((happy(lucy)|kind(lucy)))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(~brave(X)|patient(X))))&
(![X]:((tall(X)|rich(X))<=>(rich(X)|quiet(X))))&
(((~creative(alice)<~>humble(alice)))<=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(happy(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(strong(X)|generous(X))))&
(![X]:((~happy(X)|~kind(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((quiet(lucy)&calm(lucy))))&
(![X]:((~tall(X)<~>funny(X))<=>happy(X)))&
(![X]:((~strong(X)|~kind(X))<=>brave(X)))&
((?[X]:((funny(X)<~>happy(X))))<=>((~funny(fred)|~generous(fred))))&
((?[X]:((~quiet(X)|patient(X))))=>((tall(mary)<~>generous(mary))))&
(![X]:((old(X)<~>generous(X))<=>~calm(X)))&
((calm(alice))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)&calm(X))=>(old(X)|tall(X))))&
(![X]:((brave(X)&~calm(X))<=>(wise(X)&calm(X))))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((~creative(X)&old(X))))&
((~generous(mary)|creative(mary)))&
(?[X]:(kind(X)))&
((old(mary)<~>~tall(mary)))&
((~strong(john)&~tall(john)))&
((tall(john)<~>~generous(john))) | quiet(john) | [
"p9",
"p12",
"p14",
"p15",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5258313820987561018200968
% SZS output start Proof for 5258313820987561018200968
10. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> brave(X0)) [input p9]
13. ! [X0] : ((old(X0) <~> generous(X0)) <=> ~calm(X0)) [input p12]
15. ! [X0] : ((calm(X0) & ~quiet(X0)) => (tall(X0) | old(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & brave(X0)) <=> (calm(X0) & wise(X0))) [input p15]
23. ~tall(john) & ~strong(john) [input p22]
24. tall(john) <~> ~generous(john) [input p23]
25. ~quiet(john) [input hypothesis]
30. ! [X0] : ((tall(X0) | old(X0)) | (~calm(X0) | quiet(X0))) [ennf transformation 15]
31. ! [X0] : (tall(X0) | old(X0) | ~calm(X0) | quiet(X0)) [flattening 30]
56. ! [X0] : (((~kind(X0) | ~strong(X0)) | ~brave(X0)) & (brave(X0) | (kind(X0) & strong(X0)))) [nnf transformation 10]
57. ! [X0] : ((~kind(X0) | ~strong(X0) | ~brave(X0)) & (brave(X0) | (kind(X0) & strong(X0)))) [flattening 56]
64. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | calm(X0)) & (~calm(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [nnf transformation 13]
67. ! [X0] : (((~calm(X0) & brave(X0)) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 16]
68. ! [X0] : (((~calm(X0) & brave(X0)) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | calm(X0) | ~brave(X0))) [flattening 67]
78. (generous(john) | ~tall(john)) & (~generous(john) | tall(john)) [nnf transformation 24]
124. strong(X0) | brave(X0) [cnf transformation 57]
137. ~calm(X0) | generous(X0) | ~old(X0) [cnf transformation 64]
142. ~calm(X0) | old(X0) | tall(X0) | quiet(X0) [cnf transformation 31]
144. calm(X0) | calm(X0) | ~brave(X0) [cnf transformation 68]
155. ~strong(john) [cnf transformation 23]
156. ~tall(john) [cnf transformation 23]
157. ~generous(john) | tall(john) [cnf transformation 78]
159. ~quiet(john) [cnf transformation 25]
160. ~brave(X0) | calm(X0) [duplicate literal removal 144]
334. ~generous(john) [subsumption resolution 157,156]
339. brave(john) [resolution 124,155]
345. calm(john) [resolution 339,160]
416. generous(john) | ~old(john) [resolution 137,345]
430. ~old(john) [subsumption resolution 416,334]
529. old(john) | tall(john) | quiet(john) [resolution 142,345]
532. tall(john) | quiet(john) [subsumption resolution 529,430]
533. quiet(john) [subsumption resolution 532,156]
534. $false [subsumption resolution 533,159]
% SZS output end Proof for 5258313820987561018200968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or creative is not old or not funny.
Everyone who is wise or patient is both not tall and strong and vice versa.
Everyone who is either not tall or patient is generous or tall.
If paul is rich then someone is either quiet or creative.
Everyone who is both not strong and not patient is not humble or calm.
Everyone who is brave is either not humble or not wise.
If someone is either wise or not quiet then fred is both not brave and calm.
Everyone who is old or not kind is both curious and not happy and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is either old or not patient is either not old or tall and vice versa.
Everyone who is rich or generous is both not creative and wise and vice versa.
Everyone who is not wise is either not tall or wise.
If john is both generous and happy then someone is kind or not old.
Everyone who is not old is not humble or calm.
Everyone who is not quiet or not generous is both tall and happy.
Everyone who is either not funny or humble is not tall or quiet.
Someone is either not quiet or not rich.
Mary is either not patient or old.
Lucy is not patient or happy.
Someone is either not curious or curious.
Someone is either generous or rich.
Paul is strong.
Someone is either not quiet or not calm. | Lucy is not brave. | entailment | (![X]:((calm(X)|creative(X))=>(~old(X)|~funny(X))))&
(![X]:((wise(X)|patient(X))<=>(~tall(X)&strong(X))))&
(![X]:((~tall(X)<~>patient(X))=>(generous(X)|tall(X))))&
((rich(paul))=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~humble(X)|calm(X))))&
(![X]:(brave(X)=>(~humble(X)<~>~wise(X))))&
((?[X]:((wise(X)<~>~quiet(X))))=>((~brave(fred)&calm(fred))))&
(![X]:((old(X)|~kind(X))<=>(curious(X)&~happy(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:((old(X)<~>~patient(X))<=>(~old(X)<~>tall(X))))&
(![X]:((rich(X)|generous(X))<=>(~creative(X)&wise(X))))&
(![X]:(~wise(X)=>(~tall(X)<~>wise(X))))&
(((generous(john)&happy(john)))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:(~old(X)=>(~humble(X)|calm(X))))&
(![X]:((~quiet(X)|~generous(X))=>(tall(X)&happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>(~tall(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
((~patient(mary)<~>old(mary)))&
((~patient(lucy)|happy(lucy)))&
(?[X]:((~curious(X)<~>curious(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(strong(paul))&
(?[X]:((~quiet(X)<~>~calm(X)))) | ~brave(lucy) | [
"p1",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6891446588000287097977389
% SZS output start Proof for 6891446588000287097977389
2. ! [X0] : ((patient(X0) | wise(X0)) <=> (strong(X0) & ~tall(X0))) [input p1]
9. ! [X0] : (brave(X0) <=> ~quiet(X0)) [input p8]
10. ! [X0] : ((old(X0) <~> ~patient(X0)) <=> (~old(X0) <~> tall(X0))) [input p9]
15. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (happy(X0) & tall(X0))) [input p14]
24. brave(lucy) [input hypothesis]
39. ! [X0] : ((happy(X0) & tall(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 15]
42. ! [X0] : (((patient(X0) | wise(X0)) | (~strong(X0) | tall(X0))) & ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 2]
43. ! [X0] : ((patient(X0) | wise(X0) | ~strong(X0) | tall(X0)) & ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~wise(X0)))) [flattening 42]
52. ! [X0] : ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))) [nnf transformation 9]
53. ! [X0] : ((((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) & (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))))) [nnf transformation 10]
76. ~tall(X0) | ~patient(X0) [cnf transformation 43]
96. ~brave(X0) | ~quiet(X0) [cnf transformation 52]
101. ~tall(X0) | old(X0) | old(X0) | patient(X0) [cnf transformation 53]
105. patient(X0) | ~old(X0) | ~old(X0) | ~tall(X0) [cnf transformation 53]
115. tall(X0) | quiet(X0) [cnf transformation 39]
133. brave(lucy) [cnf transformation 24]
136. ~tall(X0) | old(X0) | patient(X0) [duplicate literal removal 101]
138. patient(X0) | ~old(X0) | ~tall(X0) [duplicate literal removal 105]
173. ~old(X0) | ~tall(X0) [subsumption resolution 138,76]
175. ~tall(X0) | patient(X0) [subsumption resolution 136,173]
176. ~tall(X0) [subsumption resolution 175,76]
197. quiet(X0) [subsumption resolution 115,176]
202. ~quiet(lucy) [resolution 96,133]
203. $false [subsumption resolution 202,197]
% SZS output end Proof for 6891446588000287097977389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and strong is quiet or not creative and vice versa.
Everyone who is happy is not creative or patient and vice versa.
Everyone who is either old or not brave is not kind and vice versa.
Everyone who is both not happy and not kind is both funny and happy.
Everyone who is happy is both not old and wise.
Everyone who is not quiet is not kind.
Everyone who is either generous or wise is both not happy and calm and vice versa.
If mary is both patient and not humble then someone is either not calm or creative.
Everyone who is both not tall and wise is either not patient or not calm and vice versa.
Everyone who is either not calm or funny is either not old or not wise and vice versa.
If susan is both generous and not wise then someone is old and vice versa.
If alice is curious or not quiet then someone is both not tall and quiet and vice versa.
Everyone who is not tall or generous is either rich or calm and vice versa.
If someone is not rich or tall then someone is both not generous and not funny.
Everyone who is either rich or not kind is either not brave or calm.
Everyone who is quiet is wise and vice versa.
Someone is quiet.
Alice is either funny or rich.
Mary is rich.
Lucy is either not humble or old.
Someone is not kind. | Susan is old. | contradiction | (![X]:((rich(X)&strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>~kind(X)))&
(![X]:((~happy(X)&~kind(X))=>(funny(X)&happy(X))))&
(![X]:(happy(X)=>(~old(X)&wise(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((generous(X)<~>wise(X))<=>(~happy(X)&calm(X))))&
(((patient(mary)&~humble(mary)))=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~tall(X)&wise(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~old(X)<~>~wise(X))))&
(((generous(susan)&~wise(susan)))<=>(?[X]:(old(X))))&
(((curious(alice)|~quiet(alice)))<=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:((~tall(X)|generous(X))<=>(rich(X)<~>calm(X))))&
((?[X]:((~rich(X)|tall(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((rich(X)<~>~kind(X))=>(~brave(X)<~>calm(X))))&
(![X]:(quiet(X)<=>wise(X)))&
(?[X]:(quiet(X)))&
((funny(alice)<~>rich(alice)))&
(rich(mary))&
((~humble(lucy)<~>old(lucy)))&
(?[X]:(~kind(X))) | old(susan) | [
"p3",
"p4",
"p5",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6665418930807544073645182
% SZS output start Proof for 6665418930807544073645182
4. ! [X0] : ((~kind(X0) & ~happy(X0)) => (happy(X0) & funny(X0))) [input p3]
5. ! [X0] : (happy(X0) => (wise(X0) & ~old(X0))) [input p4]
6. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p5]
11. (~wise(susan) & generous(susan)) <=> ? [X0] : old(X0) [input p10]
16. ! [X0] : (quiet(X0) <=> wise(X0)) [input p15]
22. old(susan) [input hypothesis]
24. ! [X0] : ((happy(X0) & funny(X0)) | (kind(X0) | happy(X0))) [ennf transformation 4]
25. ! [X0] : ((happy(X0) & funny(X0)) | kind(X0) | happy(X0)) [flattening 24]
26. ! [X0] : ((wise(X0) & ~old(X0)) | ~happy(X0)) [ennf transformation 5]
27. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 6]
45. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (wise(susan) | ~generous(susan))) [nnf transformation 11]
46. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | wise(susan) | ~generous(susan)) [flattening 45]
47. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | wise(susan) | ~generous(susan)) [rectify 46]
48. ? [X1] : old(X1) => old(sK1) [choice axiom]
49. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (old(sK1) | wise(susan) | ~generous(susan)) [skolemisation 47,48]
61. ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 16]
81. happy(X0) | kind(X0) | happy(X0) [cnf transformation 25]
82. ~old(X0) | ~happy(X0) [cnf transformation 26]
84. ~kind(X0) | quiet(X0) [cnf transformation 27]
109. ~wise(susan) | ~old(X0) [cnf transformation 49]
129. ~quiet(X0) | wise(X0) [cnf transformation 61]
138. old(susan) [cnf transformation 22]
139. kind(X0) | happy(X0) [duplicate literal removal 81]
161. 5 <=> ! [X0] : ~old(X0) [avatar definition]
162. ~old(X0) <- (5) [avatar component clause 161]
164. 6 <=> wise(susan) [avatar definition]
166. ~wise(susan) <- (~6) [avatar component clause 164]
167. 5 | ~6 [avatar split clause 109,164,161]
240. $false <- (5) [resolution 162,138]
241. ~5 [avatar contradiction clause 240]
249. ~happy(susan) [resolution 82,138]
290. 24 <=> kind(susan) [avatar definition]
291. ~kind(susan) <- (~24) [avatar component clause 290]
292. kind(susan) <- (24) [avatar component clause 290]
309. quiet(susan) <- (24) [resolution 292,84]
361. wise(susan) <- (24) [resolution 309,129]
364. $false <- (~6, 24) [subsumption resolution 361,166]
365. 6 | ~24 [avatar contradiction clause 364]
370. happy(susan) <- (~24) [resolution 291,139]
371. $false <- (~24) [subsumption resolution 370,249]
372. 24 [avatar contradiction clause 371]
373. $false [avatar sat refutation 167,241,365,372]
% SZS output end Proof for 6665418930807544073645182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not patient is not kind and vice versa. Everyone who is curious is either not curious or not humble and vice versa. Everyone who is not calm or not tall is either quiet or not old. If someone is both strong and not creative then someone is both patient and wise. If someone is calm then someone is either not creative or calm. If someone is not rich then someone is brave. Everyone who is curious is both generous and not humble. If someone is not kind then alice is generous or not patient and vice versa. Everyone who is either not wise or brave is not calm. Everyone who is funny or not quiet is not brave and vice versa. Everyone who is quiet is happy or creative and vice versa. If someone is either curious or not funny then mary is rich or brave. Everyone who is either not creative or not old is not rich. Everyone who is quiet is tall and vice versa. If someone is both kind and not happy then someone is calm. If lucy is either not creative or brave then paul is either not patient or not strong. Someone is not tall or generous. Paul is not curious. Someone is either not humble or not happy. Paul is not patient. John is kind. Someone is either not quiet or rich. Someone is both not creative and brave. Someone is not quiet or not tall. | Paul is humble. | contradiction | (![X]:((humble(X)&~patient(X))<=>~kind(X)))&
(![X]:(curious(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:((~calm(X)|~tall(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((patient(X)&wise(X)))))&
((?[X]:(calm(X)))=>(?[X]:((~creative(X)<~>calm(X)))))&
((?[X]:(~rich(X)))=>(?[X]:(brave(X))))&
(![X]:(curious(X)=>(generous(X)&~humble(X))))&
((?[X]:(~kind(X)))<=>((generous(alice)|~patient(alice))))&
(![X]:((~wise(X)<~>brave(X))=>~calm(X)))&
(![X]:((funny(X)|~quiet(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(happy(X)|creative(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>((rich(mary)|brave(mary))))&
(![X]:((~creative(X)<~>~old(X))=>~rich(X)))&
(![X]:(quiet(X)<=>tall(X)))&
((?[X]:((kind(X)&~happy(X))))=>(?[X]:(calm(X))))&
(((~creative(lucy)<~>brave(lucy)))=>((~patient(paul)<~>~strong(paul))))&
(?[X]:((~tall(X)|generous(X))))&
(~curious(paul))&
(?[X]:((~humble(X)<~>~happy(X))))&
(~patient(paul))&
(kind(john))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~quiet(X)|~tall(X)))) | humble(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1095132662391257965893038
% SZS output start Proof for 1095132662391257965893038
2. ! [X0] : (curious(X0) <=> (~curious(X0) <~> ~humble(X0))) [input p1]
25. humble(paul) [input hypothesis]
43. ! [X0] : ((curious(X0) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | ~curious(X0))) [nnf transformation 2]
87. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
89. curious(X0) | ~humble(X0) | curious(X0) [cnf transformation 43]
135. humble(paul) [cnf transformation 25]
136. ~humble(X0) | ~curious(X0) [duplicate literal removal 87]
137. curious(X0) | ~humble(X0) [duplicate literal removal 89]
138. ~humble(X0) [subsumption resolution 136,137]
257. $false [subsumption resolution 135,138]
% SZS output end Proof for 1095132662391257965893038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or kind then someone is humble or creative and vice versa.
Everyone who is happy is either not rich or not patient.
Everyone who is both not rich and not tall is not wise.
If someone is both strong and humble then someone is either not humble or rich.
Everyone who is either not curious or strong is not curious or old.
Everyone who is not curious is not patient or brave and vice versa.
Everyone who is not brave is both not wise and not strong.
If someone is curious then someone is rich.
If someone is both not quiet and not strong then someone is both strong and curious and vice versa.
Everyone who is both tall and not generous is funny and vice versa.
Everyone who is either quiet or not kind is not curious and vice versa.
Everyone who is both curious and not happy is both tall and brave.
If paul is both not kind and not strong then someone is patient or strong and vice versa.
Everyone who is curious or not old is either not strong or funny and vice versa.
If someone is either strong or not brave then susan is both generous and calm and vice versa.
If someone is not kind or not patient then someone is patient or funny and vice versa.
Alice is not generous.
Someone is both not strong and not funny.
Alice is both curious and not old.
Someone is either patient or creative.
John is either not wise or rich.
Someone is both generous and rich.
Paul is either tall or not old. | Susan is funny. | contradiction | ((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:(happy(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~curious(X)<~>strong(X))=>(~curious(X)|old(X))))&
(![X]:(~curious(X)<=>(~patient(X)|brave(X))))&
(![X]:(~brave(X)=>(~wise(X)&~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)&~generous(X))<=>funny(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~curious(X)))&
(![X]:((curious(X)&~happy(X))=>(tall(X)&brave(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((curious(X)|~old(X))<=>(~strong(X)<~>funny(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>((generous(susan)&calm(susan))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((patient(X)|funny(X)))))&
(~generous(alice))&
(?[X]:((~strong(X)&~funny(X))))&
((curious(alice)&~old(alice)))&
(?[X]:((patient(X)<~>creative(X))))&
((~wise(john)<~>rich(john)))&
(?[X]:((generous(X)&rich(X))))&
((tall(paul)<~>~old(paul))) | funny(susan) | [
"p5",
"p6",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4744698182912287963576151
% SZS output start Proof for 4744698182912287963576151
6. ! [X0] : (~curious(X0) <=> (brave(X0) | ~patient(X0))) [input p5]
7. ! [X0] : (~brave(X0) => (~strong(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((~generous(X0) & tall(X0)) <=> funny(X0)) [input p9]
15. ? [X0] : (strong(X0) <~> ~brave(X0)) <=> (calm(susan) & generous(susan)) [input p14]
19. ~old(alice) & curious(alice) [input p18]
24. funny(susan) [input hypothesis]
36. ! [X0] : ((~strong(X0) & ~wise(X0)) | brave(X0)) [ennf transformation 7]
51. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | curious(X0))) [nnf transformation 6]
52. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | curious(X0))) [flattening 51]
61. ! [X0] : (((~generous(X0) & tall(X0)) | ~funny(X0)) & (funny(X0) | (generous(X0) | ~tall(X0)))) [nnf transformation 10]
62. ! [X0] : (((~generous(X0) & tall(X0)) | ~funny(X0)) & (funny(X0) | generous(X0) | ~tall(X0))) [flattening 61]
71. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~calm(susan) | ~generous(susan))) & ((calm(susan) & generous(susan)) | ! [X0] : ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) [nnf transformation 15]
72. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X0] : ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) [flattening 71]
73. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X1] : ((strong(X1) | brave(X1)) & (~brave(X1) | ~strong(X1)))) [rectify 72]
74. ? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) => ((brave(sK7) | ~strong(sK7)) & (~brave(sK7) | strong(sK7))) [choice axiom]
75. (((brave(sK7) | ~strong(sK7)) & (~brave(sK7) | strong(sK7))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X1] : ((strong(X1) | brave(X1)) & (~brave(X1) | ~strong(X1)))) [skolemisation 73,74]
105. ~brave(X0) | ~curious(X0) [cnf transformation 52]
107. ~strong(X0) | brave(X0) [cnf transformation 36]
115. ~funny(X0) | ~generous(X0) [cnf transformation 62]
134. generous(susan) | strong(X1) | brave(X1) [cnf transformation 75]
146. curious(alice) [cnf transformation 19]
156. funny(susan) [cnf transformation 24]
206. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
207. ~curious(X1) <- (12) [avatar component clause 206]
268. 26 <=> generous(susan) [avatar definition]
286. 30 <=> ! [X1] : brave(X1) [avatar definition]
287. brave(X1) <- (30) [avatar component clause 286]
291. generous(susan) | brave(X1) [subsumption resolution 134,107]
292. 30 | 26 [avatar split clause 291,268,286]
365. $false <- (12) [resolution 207,146]
366. ~12 [avatar contradiction clause 365]
369. ~generous(susan) [resolution 115,156]
372. ~26 [avatar split clause 369,268]
376. ~curious(X0) <- (30) [resolution 287,105]
378. 12 | ~30 [avatar split clause 376,286,206]
379. $false [avatar sat refutation 292,366,372,378]
% SZS output end Proof for 4744698182912287963576151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is both old and not wise and vice versa. Everyone who is not old or brave is both calm and not funny and vice versa. Everyone who is not calm is either not strong or not happy and vice versa. If alice is not quiet then susan is not wise. If john is not kind then someone is patient and vice versa. Everyone who is either brave or not rich is either quiet or not old and vice versa. Everyone who is both not quiet and strong is both funny and not patient. Everyone who is both not brave and not generous is either patient or old and vice versa. Everyone who is wise or not strong is both not brave and wise. Everyone who is humble is either not happy or not generous. If susan is not quiet or not kind then mary is not humble and vice versa. Everyone who is not kind or brave is both not quiet and creative. If lucy is tall then someone is not happy or not quiet. If someone is both rich and tall then alice is both not funny and humble. Everyone who is old is both strong and brave. Everyone who is not old is either kind or happy and vice versa. Someone is either not patient or funny. Someone is both calm and kind. Someone is wise or not calm. Paul is not funny. Someone is not quiet. John is both rich and not old. Lucy is either not generous or humble. | Lucy is brave. | contradiction | (![X]:(tall(X)<=>(old(X)&~wise(X))))&
(![X]:((~old(X)|brave(X))<=>(calm(X)&~funny(X))))&
(![X]:(~calm(X)<=>(~strong(X)<~>~happy(X))))&
((~quiet(alice))=>(~wise(susan)))&
((~kind(john))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~quiet(X)&strong(X))=>(funny(X)&~patient(X))))&
(![X]:((~brave(X)&~generous(X))<=>(patient(X)<~>old(X))))&
(![X]:((wise(X)|~strong(X))=>(~brave(X)&wise(X))))&
(![X]:(humble(X)=>(~happy(X)<~>~generous(X))))&
(((~quiet(susan)|~kind(susan)))<=>(~humble(mary)))&
(![X]:((~kind(X)|brave(X))=>(~quiet(X)&creative(X))))&
((tall(lucy))=>(?[X]:((~happy(X)|~quiet(X)))))&
((?[X]:((rich(X)&tall(X))))=>((~funny(alice)&humble(alice))))&
(![X]:(old(X)=>(strong(X)&brave(X))))&
(![X]:(~old(X)<=>(kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:((wise(X)|~calm(X))))&
(~funny(paul))&
(?[X]:(~quiet(X)))&
((rich(john)&~old(john)))&
((~generous(lucy)<~>humble(lucy))) | brave(lucy) | [
"p1",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4043190161394404404615386
% SZS output start Proof for 4043190161394404404615386
2. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~funny(X0) & calm(X0))) [input p1]
7. ! [X0] : ((strong(X0) & ~quiet(X0)) => (~patient(X0) & funny(X0))) [input p6]
9. ! [X0] : ((~strong(X0) | wise(X0)) => (wise(X0) & ~brave(X0))) [input p8]
12. ! [X0] : ((brave(X0) | ~kind(X0)) => (creative(X0) & ~quiet(X0))) [input p11]
24. brave(lucy) [input hypothesis]
26. ! [X0] : ((brave(X0) | ~kind(X0)) => ~quiet(X0)) [pure predicate removal 12]
30. ! [X0] : ((~patient(X0) & funny(X0)) | (~strong(X0) | quiet(X0))) [ennf transformation 7]
31. ! [X0] : ((~patient(X0) & funny(X0)) | ~strong(X0) | quiet(X0)) [flattening 30]
32. ! [X0] : ((wise(X0) & ~brave(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 9]
34. ! [X0] : (~quiet(X0) | (~brave(X0) & kind(X0))) [ennf transformation 26]
38. ! [X0] : (((brave(X0) | ~old(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~old(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (~brave(X0) & old(X0)))) [flattening 38]
68. ~funny(X0) | ~brave(X0) [cnf transformation 39]
85. ~strong(X0) | funny(X0) | quiet(X0) [cnf transformation 31]
94. ~brave(X0) | strong(X0) [cnf transformation 32]
103. ~quiet(X0) | ~brave(X0) [cnf transformation 34]
124. brave(lucy) [cnf transformation 24]
220. strong(lucy) [resolution 94,124]
240. funny(lucy) | quiet(lucy) [resolution 85,220]
242. 21 <=> quiet(lucy) [avatar definition]
244. quiet(lucy) <- (21) [avatar component clause 242]
246. 22 <=> funny(lucy) [avatar definition]
248. funny(lucy) <- (22) [avatar component clause 246]
249. 21 | 22 [avatar split clause 240,246,242]
250. ~brave(lucy) <- (21) [resolution 244,103]
252. $false <- (21) [subsumption resolution 250,124]
253. ~21 [avatar contradiction clause 252]
254. ~brave(lucy) <- (22) [resolution 248,68]
256. $false <- (22) [subsumption resolution 254,124]
257. ~22 [avatar contradiction clause 256]
258. $false [avatar sat refutation 249,253,257]
% SZS output end Proof for 4043190161394404404615386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both creative and humble. Everyone who is not rich or not calm is strong. If someone is either brave or not calm then someone is either old or not kind and vice versa. Everyone who is funny is both not old and rich and vice versa. If someone is both not strong and not creative then john is either not funny or strong. If someone is both humble and patient then john is both not calm and generous. Everyone who is not wise is both calm and not old and vice versa. Everyone who is not creative is not calm or not strong. Everyone who is both brave and not tall is not creative or humble and vice versa. Everyone who is both kind and happy is not rich or not quiet. Everyone who is both funny and not wise is either generous or wise and vice versa. If someone is both not generous and funny then someone is patient or not generous and vice versa. Everyone who is either not funny or happy is either not funny or not humble and vice versa. If someone is old then someone is kind or rich. If alice is not tall or brave then lucy is either kind or not humble. Everyone who is either not patient or rich is not strong and vice versa. Lucy is both not happy and old. Paul is strong. John is both old and wise. John is either patient or not quiet. Mary is both rich and not quiet. John is either not curious or rich. Someone is not quiet or funny. | Lucy is not humble. | contradiction | (![X]:(~rich(X)=>(creative(X)&humble(X))))&
(![X]:((~rich(X)|~calm(X))=>strong(X)))&
((?[X]:((brave(X)<~>~calm(X))))<=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:(funny(X)<=>(~old(X)&rich(X))))&
((?[X]:((~strong(X)&~creative(X))))=>((~funny(john)<~>strong(john))))&
((?[X]:((humble(X)&patient(X))))=>((~calm(john)&generous(john))))&
(![X]:(~wise(X)<=>(calm(X)&~old(X))))&
(![X]:(~creative(X)=>(~calm(X)|~strong(X))))&
(![X]:((brave(X)&~tall(X))<=>(~creative(X)|humble(X))))&
(![X]:((kind(X)&happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:((funny(X)&~wise(X))<=>(generous(X)<~>wise(X))))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((~funny(X)<~>happy(X))<=>(~funny(X)<~>~humble(X))))&
((?[X]:(old(X)))=>(?[X]:((kind(X)|rich(X)))))&
(((~tall(alice)|brave(alice)))=>((kind(lucy)<~>~humble(lucy))))&
(![X]:((~patient(X)<~>rich(X))<=>~strong(X)))&
((~happy(lucy)&old(lucy)))&
(strong(paul))&
((old(john)&wise(john)))&
((patient(john)<~>~quiet(john)))&
((rich(mary)&~quiet(mary)))&
((~curious(john)<~>rich(john)))&
(?[X]:((~quiet(X)|funny(X)))) | ~humble(lucy) | [
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5668556894780376390227216
% SZS output start Proof for 5668556894780376390227216
13. ! [X0] : ((~funny(X0) <~> happy(X0)) <=> (~funny(X0) <~> ~humble(X0))) [input p12]
17. old(lucy) & ~happy(lucy) [input p16]
24. ~humble(lucy) [input hypothesis]
57. ! [X0] : ((((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) & (((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))))) [nnf transformation 13]
109. humble(X0) | funny(X0) | happy(X0) | funny(X0) [cnf transformation 57]
112. happy(X0) | ~funny(X0) | ~funny(X0) | humble(X0) [cnf transformation 57]
124. ~happy(lucy) [cnf transformation 17]
136. ~humble(lucy) [cnf transformation 24]
138. humble(X0) | funny(X0) | happy(X0) [duplicate literal removal 109]
139. happy(X0) | ~funny(X0) | humble(X0) [duplicate literal removal 112]
224. happy(X0) | humble(X0) [subsumption resolution 138,139]
247. 24 <=> humble(lucy) [avatar definition]
248. ~humble(lucy) <- (~24) [avatar component clause 247]
289. ~24 [avatar split clause 136,247]
313. humble(lucy) [resolution 224,124]
314. $false <- (~24) [subsumption resolution 313,248]
315. 24 [avatar contradiction clause 314]
316. $false [avatar sat refutation 289,315]
% SZS output end Proof for 5668556894780376390227216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not kind is either kind or not kind and vice versa.
Everyone who is both wise and not curious is both tall and brave and vice versa.
Everyone who is kind or tall is not humble or not strong.
Everyone who is calm or humble is curious.
Everyone who is not calm is calm or strong and vice versa.
Everyone who is not rich or not patient is brave or not happy.
Everyone who is either wise or not calm is both not patient and not humble.
If lucy is not brave then lucy is either kind or tall.
Everyone who is old or brave is not quiet or strong and vice versa.
Everyone who is funny or rich is either not wise or brave.
If alice is either creative or not calm then someone is creative.
If someone is humble or not creative then someone is old.
If lucy is not patient or not happy then someone is both rich and not kind and vice versa.
If someone is both rich and generous then someone is not happy or not strong.
If john is not humble or not calm then someone is not calm and vice versa.
Everyone who is both kind and not generous is not calm or not generous.
Paul is not brave or rich.
Fred is both not funny and not tall.
Lucy is not rich or humble.
Paul is not tall.
Someone is not tall.
Susan is either strong or not rich.
Someone is quiet. | Alice is not calm. | entailment | (![X]:((~generous(X)|~kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((wise(X)&~curious(X))<=>(tall(X)&brave(X))))&
(![X]:((kind(X)|tall(X))=>(~humble(X)|~strong(X))))&
(![X]:((calm(X)|humble(X))=>curious(X)))&
(![X]:(~calm(X)<=>(calm(X)|strong(X))))&
(![X]:((~rich(X)|~patient(X))=>(brave(X)|~happy(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~patient(X)&~humble(X))))&
((~brave(lucy))=>((kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)|brave(X))<=>(~quiet(X)|strong(X))))&
(![X]:((funny(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(((creative(alice)<~>~calm(alice)))=>(?[X]:(creative(X))))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:(old(X))))&
(((~patient(lucy)|~happy(lucy)))<=>(?[X]:((rich(X)&~kind(X)))))&
((?[X]:((rich(X)&generous(X))))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~humble(john)|~calm(john)))<=>(?[X]:(~calm(X))))&
(![X]:((kind(X)&~generous(X))=>(~calm(X)|~generous(X))))&
((~brave(paul)|rich(paul)))&
((~funny(fred)&~tall(fred)))&
((~rich(lucy)|humble(lucy)))&
(~tall(paul))&
(?[X]:(~tall(X)))&
((strong(susan)<~>~rich(susan)))&
(?[X]:(quiet(X))) | ~calm(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4871671258154559244158090
% SZS output start Proof for 4871671258154559244158090
5. ! [X0] : (~calm(X0) <=> (strong(X0) | calm(X0))) [input p4]
24. calm(alice) [input hypothesis]
46. ! [X0] : ((~calm(X0) | (~strong(X0) & ~calm(X0))) & ((strong(X0) | calm(X0)) | calm(X0))) [nnf transformation 5]
47. ! [X0] : ((~calm(X0) | (~strong(X0) & ~calm(X0))) & (strong(X0) | calm(X0) | calm(X0))) [flattening 46]
92. ~calm(X0) | ~calm(X0) [cnf transformation 47]
130. calm(alice) [cnf transformation 24]
132. ~calm(X0) [duplicate literal removal 92]
229. $false [subsumption resolution 130,132]
% SZS output end Proof for 4871671258154559244158090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and happy is happy or patient.
If susan is curious or not patient then someone is either tall or not tall and vice versa.
Everyone who is not happy or happy is not old.
If mary is generous then susan is creative and vice versa.
Everyone who is either old or not funny is patient or quiet and vice versa.
If someone is both not generous and not patient then paul is either calm or rich.
If someone is either funny or not patient then mary is both creative and generous.
Everyone who is not calm is both funny and creative.
If someone is either kind or not strong then someone is either not strong or not humble and vice versa.
If fred is either not funny or humble then someone is not quiet or not wise.
If someone is both generous and wise then someone is both quiet and not happy.
Everyone who is either strong or not rich is either not tall or old and vice versa.
Everyone who is creative or not humble is kind or humble and vice versa.
Everyone who is both not creative and brave is humble and vice versa.
If alice is either quiet or humble then someone is either rich or quiet and vice versa.
If someone is calm or not old then someone is not calm or humble.
John is both patient and wise.
John is both patient and happy.
Someone is both not patient and not old.
Fred is not tall.
Fred is either brave or not creative.
Susan is both not strong and not rich. | Mary is not kind. | contradiction | (![X]:((~calm(X)&happy(X))=>(happy(X)|patient(X))))&
(((curious(susan)|~patient(susan)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~happy(X)|happy(X))=>~old(X)))&
((generous(mary))<=>(creative(susan)))&
(![X]:((old(X)<~>~funny(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((calm(paul)<~>rich(paul))))&
((?[X]:((funny(X)<~>~patient(X))))=>((creative(mary)&generous(mary))))&
(![X]:(~calm(X)=>(funny(X)&creative(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(((~funny(fred)<~>humble(fred)))=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((generous(X)&wise(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:((strong(X)<~>~rich(X))<=>(~tall(X)<~>old(X))))&
(![X]:((creative(X)|~humble(X))<=>(kind(X)|humble(X))))&
(![X]:((~creative(X)&brave(X))<=>humble(X)))&
(((quiet(alice)<~>humble(alice)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((~calm(X)|humble(X)))))&
((patient(john)&wise(john)))&
((patient(john)&happy(john)))&
(?[X]:((~patient(X)&~old(X))))&
(~tall(fred))&
((brave(fred)<~>~creative(fred)))&
((~strong(susan)&~rich(susan))) | ~kind(mary) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5652781383024489326961004
% SZS output start Proof for 5652781383024489326961004
13. ! [X0] : ((~humble(X0) | creative(X0)) <=> (humble(X0) | kind(X0))) [input p12]
14. ! [X0] : ((brave(X0) & ~creative(X0)) <=> humble(X0)) [input p13]
23. ~kind(mary) [input hypothesis]
58. ! [X0] : (((~humble(X0) | creative(X0)) | (~humble(X0) & ~kind(X0))) & ((humble(X0) | kind(X0)) | (humble(X0) & ~creative(X0)))) [nnf transformation 13]
59. ! [X0] : ((~humble(X0) | creative(X0) | (~humble(X0) & ~kind(X0))) & (humble(X0) | kind(X0) | (humble(X0) & ~creative(X0)))) [flattening 58]
60. ! [X0] : (((brave(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) | creative(X0)))) [nnf transformation 14]
61. ! [X0] : (((brave(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | ~brave(X0) | creative(X0))) [flattening 60]
118. humble(X0) | kind(X0) | humble(X0) [cnf transformation 59]
120. ~humble(X0) | creative(X0) | ~humble(X0) [cnf transformation 59]
122. ~creative(X0) | ~humble(X0) [cnf transformation 61]
145. ~kind(mary) [cnf transformation 23]
146. humble(X0) | kind(X0) [duplicate literal removal 118]
147. ~humble(X0) | creative(X0) [duplicate literal removal 120]
273. ~humble(X0) [subsumption resolution 122,147]
315. kind(X1) [resolution 146,273]
317. $false [resolution 315,145]
% SZS output end Proof for 5652781383024489326961004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not patient is kind or not brave and vice versa.
If mary is creative or not generous then mary is both not curious and rich.
Everyone who is both not generous and not quiet is strong or creative and vice versa.
If alice is not wise or happy then alice is patient and vice versa.
If someone is not kind or calm then someone is not happy and vice versa.
Everyone who is both generous and kind is old or not wise and vice versa.
Everyone who is both happy and not patient is funny or curious.
Everyone who is both curious and not kind is kind or quiet and vice versa.
Everyone who is either curious or not wise is both not patient and happy.
If someone is either strong or not funny then fred is brave and vice versa.
If susan is either creative or not kind then someone is not rich.
Everyone who is humble is both not kind and creative.
If someone is both tall and patient then someone is not kind.
If someone is not curious then someone is either kind or not happy.
Everyone who is both brave and funny is happy or not patient and vice versa.
Everyone who is either not creative or quiet is both not funny and patient.
Paul is not generous or patient.
Susan is either not tall or strong.
Fred is not curious or old.
Mary is either not old or tall.
Someone is either not happy or brave.
Susan is not funny.
Someone is either kind or generous. | Alice is wise. | entailment | (![X]:((~funny(X)|~patient(X))<=>(kind(X)|~brave(X))))&
(((creative(mary)|~generous(mary)))=>((~curious(mary)&rich(mary))))&
(![X]:((~generous(X)&~quiet(X))<=>(strong(X)|creative(X))))&
(((~wise(alice)|happy(alice)))<=>(patient(alice)))&
((?[X]:((~kind(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(![X]:((generous(X)&kind(X))<=>(old(X)|~wise(X))))&
(![X]:((happy(X)&~patient(X))=>(funny(X)|curious(X))))&
(![X]:((curious(X)&~kind(X))<=>(kind(X)|quiet(X))))&
(![X]:((curious(X)<~>~wise(X))=>(~patient(X)&happy(X))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(brave(fred)))&
(((creative(susan)<~>~kind(susan)))=>(?[X]:(~rich(X))))&
(![X]:(humble(X)=>(~kind(X)&creative(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((brave(X)&funny(X))<=>(happy(X)|~patient(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(~funny(X)&patient(X))))&
((~generous(paul)|patient(paul)))&
((~tall(susan)<~>strong(susan)))&
((~curious(fred)|old(fred)))&
((~old(mary)<~>tall(mary)))&
(?[X]:((~happy(X)<~>brave(X))))&
(~funny(susan))&
(?[X]:((kind(X)<~>generous(X)))) | wise(alice) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 555652160493927852704866
% SZS output start Proof for 555652160493927852704866
6. ! [X0] : ((kind(X0) & generous(X0)) <=> (~wise(X0) | old(X0))) [input p5]
8. ! [X0] : ((~kind(X0) & curious(X0)) <=> (quiet(X0) | kind(X0))) [input p7]
24. ~wise(alice) [input hypothesis]
48. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~kind(X0) | ~generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | ~kind(X0) | ~generous(X0))) [flattening 48]
50. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 8]
51. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | kind(X0) | ~curious(X0))) [flattening 50]
101. wise(X0) | kind(X0) [cnf transformation 49]
106. ~kind(X0) | ~kind(X0) [cnf transformation 51]
141. ~wise(alice) [cnf transformation 24]
143. ~kind(X0) [duplicate literal removal 106]
169. 6 <=> wise(alice) [avatar definition]
171. ~wise(alice) <- (~6) [avatar component clause 169]
294. ~6 [avatar split clause 141,169]
298. kind(alice) <- (~6) [resolution 101,171]
299. $false <- (~6) [subsumption resolution 298,143]
300. 6 [avatar contradiction clause 299]
301. $false [avatar sat refutation 294,300]
% SZS output end Proof for 555652160493927852704866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not calm is wise and vice versa.
If john is wise or not brave then someone is both kind and not generous and vice versa.
If paul is patient or not brave then lucy is not old and vice versa.
Everyone who is tall is either generous or creative and vice versa.
If someone is both not strong and patient then susan is both not wise and not happy and vice versa.
If someone is not creative then john is creative or patient.
Everyone who is brave or not humble is humble.
Everyone who is calm is both humble and not happy and vice versa.
If someone is either not humble or happy then fred is not tall and vice versa.
Everyone who is both wise and not happy is both not patient and not strong.
Everyone who is not happy or kind is both curious and not brave.
Everyone who is wise is either not quiet or brave.
Everyone who is not funny or old is not patient.
Everyone who is either not generous or brave is either not creative or not calm.
Everyone who is both patient and quiet is not generous or kind.
Everyone who is both funny and not patient is curious or brave and vice versa.
Mary is not old.
Alice is both not patient and not creative.
Fred is either creative or humble.
Paul is either not brave or tall.
Mary is wise.
Paul is happy.
Fred is quiet.
Susan is not curious. | Fred is not generous. | entailment | (![X]:((~curious(X)|~calm(X))<=>wise(X)))&
(((wise(john)|~brave(john)))<=>(?[X]:((kind(X)&~generous(X)))))&
(((patient(paul)|~brave(paul)))<=>(~old(lucy)))&
(![X]:(tall(X)<=>(generous(X)<~>creative(X))))&
((?[X]:((~strong(X)&patient(X))))<=>((~wise(susan)&~happy(susan))))&
((?[X]:(~creative(X)))=>((creative(john)|patient(john))))&
(![X]:((brave(X)|~humble(X))=>humble(X)))&
(![X]:(calm(X)<=>(humble(X)&~happy(X))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(~tall(fred)))&
(![X]:((wise(X)&~happy(X))=>(~patient(X)&~strong(X))))&
(![X]:((~happy(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:(wise(X)=>(~quiet(X)<~>brave(X))))&
(![X]:((~funny(X)|old(X))=>~patient(X)))&
(![X]:((~generous(X)<~>brave(X))=>(~creative(X)<~>~calm(X))))&
(![X]:((patient(X)&quiet(X))=>(~generous(X)|kind(X))))&
(![X]:((funny(X)&~patient(X))<=>(curious(X)|brave(X))))&
(~old(mary))&
((~patient(alice)&~creative(alice)))&
((creative(fred)<~>humble(fred)))&
((~brave(paul)<~>tall(paul)))&
(wise(mary))&
(happy(paul))&
(quiet(fred))&
(~curious(susan)) | ~generous(fred) | [
"p3",
"p6",
"p8",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6812124262348011295243773
% SZS output start Proof for 6812124262348011295243773
4. ! [X0] : (tall(X0) <=> (generous(X0) <~> creative(X0))) [input p3]
7. ! [X0] : ((~humble(X0) | brave(X0)) => humble(X0)) [input p6]
9. ? [X0] : (~humble(X0) <~> happy(X0)) <=> ~tall(fred) [input p8]
19. creative(fred) <~> humble(fred) [input p18]
22. happy(paul) [input p21]
25. generous(fred) [input hypothesis]
28. ! [X0] : (humble(X0) | (humble(X0) & ~brave(X0))) [ennf transformation 7]
46. ! [X0] : ((tall(X0) | ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | ~tall(X0))) [nnf transformation 4]
54. (? [X0] : ((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | tall(fred)) & (~tall(fred) | ! [X0] : ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) [nnf transformation 9]
55. (? [X0] : ((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | tall(fred)) & (~tall(fred) | ! [X1] : ((~humble(X1) | ~happy(X1)) & (happy(X1) | humble(X1)))) [rectify 54]
56. ? [X0] : ((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) => ((~happy(sK2) | humble(sK2)) & (happy(sK2) | ~humble(sK2))) [choice axiom]
57. (((~happy(sK2) | humble(sK2)) & (happy(sK2) | ~humble(sK2))) | tall(fred)) & (~tall(fred) | ! [X1] : ((~humble(X1) | ~happy(X1)) & (happy(X1) | humble(X1)))) [skolemisation 55,56]
62. (~humble(fred) | ~creative(fred)) & (humble(fred) | creative(fred)) [nnf transformation 19]
77. ~generous(X0) | creative(X0) | tall(X0) [cnf transformation 46]
85. humble(X0) | humble(X0) [cnf transformation 28]
90. ~tall(fred) | ~humble(X1) | ~happy(X1) [cnf transformation 57]
117. ~humble(fred) | ~creative(fred) [cnf transformation 62]
121. happy(paul) [cnf transformation 22]
124. generous(fred) [cnf transformation 25]
125. humble(X0) [duplicate literal removal 85]
203. 17 <=> tall(fred) [avatar definition]
211. ~tall(fred) | ~happy(X1) [subsumption resolution 90,125]
213. 19 <=> ! [X1] : ~happy(X1) [avatar definition]
214. ~happy(X1) <- (19) [avatar component clause 213]
215. 19 | ~17 [avatar split clause 211,203,213]
216. ~creative(fred) [subsumption resolution 117,125]
264. creative(fred) | tall(fred) [resolution 77,124]
265. tall(fred) [subsumption resolution 264,216]
268. 17 [avatar split clause 265,203]
272. $false <- (19) [resolution 214,121]
277. ~19 [avatar contradiction clause 272]
278. $false [avatar sat refutation 215,268,277]
% SZS output end Proof for 6812124262348011295243773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and kind is both not creative and rich and vice versa. Everyone who is not quiet is wise or not calm and vice versa. Everyone who is either tall or calm is not quiet and vice versa. Everyone who is tall is not funny or not rich and vice versa. Everyone who is not strong is either rich or wise. Everyone who is not old is not kind. If paul is either calm or not rich then john is not humble or kind. If lucy is not funny then someone is rich. Everyone who is rich or not tall is both tall and old. Everyone who is both happy and humble is not generous. Everyone who is both generous and not creative is not old or not humble. Everyone who is either generous or not generous is either not curious or funny and vice versa. Everyone who is both not strong and humble is not humble and vice versa. If someone is either tall or funny then someone is both kind and strong. If someone is old or not patient then fred is not patient. If alice is happy then fred is not rich and vice versa. Mary is not funny or not brave. Someone is either not generous or humble. Someone is both happy and not generous. Paul is both not curious and not old. Mary is wise or tall. Susan is either not wise or happy. | John is not happy. | neutral | (![X]:((rich(X)&kind(X))<=>(~creative(X)&rich(X))))&
(![X]:(~quiet(X)<=>(wise(X)|~calm(X))))&
(![X]:((tall(X)<~>calm(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~funny(X)|~rich(X))))&
(![X]:(~strong(X)=>(rich(X)<~>wise(X))))&
(![X]:(~old(X)=>~kind(X)))&
(((calm(paul)<~>~rich(paul)))=>((~humble(john)|kind(john))))&
((~funny(lucy))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>~generous(X)))&
(![X]:((generous(X)&~creative(X))=>(~old(X)|~humble(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~strong(X)&humble(X))<=>~humble(X)))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:((kind(X)&strong(X)))))&
((?[X]:((old(X)|~patient(X))))=>(~patient(fred)))&
((happy(alice))<=>(~rich(fred)))&
((~funny(mary)|~brave(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((happy(X)&~generous(X))))&
((~curious(paul)&~old(paul)))&
((wise(mary)|tall(mary)))&
((~wise(susan)<~>happy(susan))) | ~happy(john) | [] | null | 0 |
If someone is both not humble and happy then lucy is wise and vice versa.
If john is not funny or funny then john is wise.
Everyone who is both not tall and humble is both not funny and not rich.
If someone is either not patient or not happy then someone is tall and vice versa.
Everyone who is not patient or kind is not quiet or happy and vice versa.
Everyone who is not brave is not funny and vice versa.
Everyone who is strong is curious.
Everyone who is curious or strong is both happy and not creative.
If alice is happy or wise then fred is both not calm and patient.
If paul is both not curious and not rich then paul is generous or strong.
If fred is patient or rich then someone is both not tall and rich.
Everyone who is not generous or tall is both not curious and not generous.
Everyone who is either not happy or not tall is both quiet and not curious and vice versa.
Everyone who is both funny and not rich is not kind and vice versa.
Everyone who is curious is both not humble and not curious and vice versa.
Everyone who is generous or not patient is both kind and not generous.
Someone is kind or calm.
Lucy is calm or not funny.
Someone is rich.
Susan is quiet or not calm.
Alice is both quiet and not curious.
Someone is not wise. | Lucy is not strong. | entailment | ((?[X]:((~humble(X)&happy(X))))<=>(wise(lucy)))&
(((~funny(john)|funny(john)))=>(wise(john)))&
(![X]:((~tall(X)&humble(X))=>(~funny(X)&~rich(X))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((~patient(X)|kind(X))<=>(~quiet(X)|happy(X))))&
(![X]:(~brave(X)<=>~funny(X)))&
(![X]:(strong(X)=>curious(X)))&
(![X]:((curious(X)|strong(X))=>(happy(X)&~creative(X))))&
(((happy(alice)|wise(alice)))=>((~calm(fred)&patient(fred))))&
(((~curious(paul)&~rich(paul)))=>((generous(paul)|strong(paul))))&
(((patient(fred)|rich(fred)))=>(?[X]:((~tall(X)&rich(X)))))&
(![X]:((~generous(X)|tall(X))=>(~curious(X)&~generous(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>(quiet(X)&~curious(X))))&
(![X]:((funny(X)&~rich(X))<=>~kind(X)))&
(![X]:(curious(X)<=>(~humble(X)&~curious(X))))&
(![X]:((generous(X)|~patient(X))=>(kind(X)&~generous(X))))&
(?[X]:((kind(X)|calm(X))))&
((calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
((quiet(susan)|~calm(susan)))&
((quiet(alice)&~curious(alice)))&
(?[X]:(~wise(X))) | ~strong(lucy) | [
"p6",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3254288324424355959467435
% SZS output start Proof for 3254288324424355959467435
7. ! [X0] : (strong(X0) => curious(X0)) [input p6]
8. ! [X0] : ((strong(X0) | curious(X0)) => (~creative(X0) & happy(X0))) [input p7]
12. ! [X0] : ((tall(X0) | ~generous(X0)) => (~generous(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (~curious(X0) & quiet(X0))) [input p12]
23. strong(lucy) [input hypothesis]
25. ! [X0] : ((strong(X0) | curious(X0)) => happy(X0)) [pure predicate removal 8]
29. ! [X0] : (curious(X0) | ~strong(X0)) [ennf transformation 7]
30. ! [X0] : (happy(X0) | (~strong(X0) & ~curious(X0))) [ennf transformation 25]
35. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 12]
50. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 13]
51. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 50]
77. ~strong(X0) | curious(X0) [cnf transformation 29]
78. happy(X0) | ~curious(X0) [cnf transformation 30]
90. ~curious(X0) | ~tall(X0) [cnf transformation 35]
96. ~curious(X0) | ~happy(X0) | tall(X0) [cnf transformation 51]
116. strong(lucy) [cnf transformation 23]
225. ~curious(X0) | tall(X0) [subsumption resolution 96,78]
226. ~curious(X0) [subsumption resolution 225,90]
259. curious(lucy) [resolution 77,116]
260. $false [subsumption resolution 259,226]
% SZS output end Proof for 3254288324424355959467435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not kind then someone is old or curious.
If someone is both humble and curious then someone is rich or happy.
Everyone who is either not calm or happy is not patient or happy and vice versa.
Everyone who is tall or happy is either patient or quiet and vice versa.
If susan is not generous then someone is both rich and brave and vice versa.
Everyone who is both not rich and not wise is either strong or not calm.
Everyone who is both tall and humble is either humble or not calm.
Everyone who is either rich or happy is both wise and not creative.
Everyone who is either old or not calm is both not rich and not tall.
Everyone who is kind or not rich is both calm and brave and vice versa.
If lucy is both not patient and brave then mary is not patient and vice versa.
If lucy is both not generous and not kind then john is funny.
If mary is either not happy or quiet then someone is not rich.
If lucy is not strong or patient then someone is either not quiet or not patient and vice versa.
Everyone who is not old or curious is both rich and wise and vice versa.
If someone is either not quiet or curious then someone is either not curious or not brave and vice versa.
Susan is curious.
Alice is both not humble and not kind.
Alice is creative or not humble.
Someone is either not patient or not brave.
Paul is not curious.
Lucy is quiet.
Fred is both not creative and happy.
Susan is not brave. | Fred is not happy. | contradiction | ((?[X]:((old(X)&~kind(X))))=>(?[X]:((old(X)|curious(X)))))&
((?[X]:((humble(X)&curious(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(~patient(X)|happy(X))))&
(![X]:((tall(X)|happy(X))<=>(patient(X)<~>quiet(X))))&
((~generous(susan))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~rich(X)&~wise(X))=>(strong(X)<~>~calm(X))))&
(![X]:((tall(X)&humble(X))=>(humble(X)<~>~calm(X))))&
(![X]:((rich(X)<~>happy(X))=>(wise(X)&~creative(X))))&
(![X]:((old(X)<~>~calm(X))=>(~rich(X)&~tall(X))))&
(![X]:((kind(X)|~rich(X))<=>(calm(X)&brave(X))))&
(((~patient(lucy)&brave(lucy)))<=>(~patient(mary)))&
(((~generous(lucy)&~kind(lucy)))=>(funny(john)))&
(((~happy(mary)<~>quiet(mary)))=>(?[X]:(~rich(X))))&
(((~strong(lucy)|patient(lucy)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:((~old(X)|curious(X))<=>(rich(X)&wise(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(curious(susan))&
((~humble(alice)&~kind(alice)))&
((creative(alice)|~humble(alice)))&
(?[X]:((~patient(X)<~>~brave(X))))&
(~curious(paul))&
(quiet(lucy))&
((~creative(fred)&happy(fred)))&
(~brave(susan)) | ~happy(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8100633789281719409267755
% SZS output start Proof for 8100633789281719409267755
23. happy(fred) & ~creative(fred) [input p22]
25. ~happy(fred) [input hypothesis]
146. happy(fred) [cnf transformation 23]
148. ~happy(fred) [cnf transformation 25]
294. $false [subsumption resolution 148,146]
% SZS output end Proof for 8100633789281719409267755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not happy is either not rich or patient and vice versa.
If someone is either not strong or not happy then mary is both creative and not rich and vice versa.
If susan is not creative then someone is brave or not tall and vice versa.
If someone is both old and generous then susan is funny or not quiet and vice versa.
Everyone who is not rich or not brave is both quiet and not generous and vice versa.
Everyone who is not calm or not rich is both not strong and rich.
Everyone who is not funny is either old or not kind and vice versa.
If someone is either rich or not old then paul is both not curious and not kind.
Everyone who is not brave or happy is not strong or not wise and vice versa.
Everyone who is both curious and not generous is either not generous or not brave and vice versa.
Everyone who is both not curious and not quiet is strong or not quiet.
Everyone who is both not kind and not old is not funny.
If lucy is both not curious and old then someone is either not strong or not rich.
If fred is funny then someone is not quiet.
If fred is not calm or patient then paul is both not humble and not creative.
Someone is both not generous and not brave.
Someone is not patient.
Someone is either not humble or creative.
Someone is not wise or not quiet.
Someone is either kind or humble.
Alice is either not wise or quiet. | Fred is happy. | entailment | (![X]:((patient(X)<~>~happy(X))<=>(~rich(X)<~>patient(X))))&
((?[X]:((~strong(X)<~>~happy(X))))<=>((creative(mary)&~rich(mary))))&
((~creative(susan))<=>(?[X]:((brave(X)|~tall(X)))))&
((?[X]:((old(X)&generous(X))))<=>((funny(susan)|~quiet(susan))))&
(![X]:((~rich(X)|~brave(X))<=>(quiet(X)&~generous(X))))&
(![X]:((~calm(X)|~rich(X))=>(~strong(X)&rich(X))))&
(![X]:(~funny(X)<=>(old(X)<~>~kind(X))))&
((?[X]:((rich(X)<~>~old(X))))=>((~curious(paul)&~kind(paul))))&
(![X]:((~brave(X)|happy(X))<=>(~strong(X)|~wise(X))))&
(![X]:((curious(X)&~generous(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:((~curious(X)&~quiet(X))=>(strong(X)|~quiet(X))))&
(![X]:((~kind(X)&~old(X))=>~funny(X)))&
(((~curious(lucy)&old(lucy)))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((funny(fred))=>(?[X]:(~quiet(X))))&
(((~calm(fred)|patient(fred)))=>((~humble(paul)&~creative(paul))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((kind(X)<~>humble(X))))&
((~wise(alice)<~>quiet(alice))) | happy(fred) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3239282498211797765209378
% SZS output start Proof for 3239282498211797765209378
1. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (~rich(X0) <~> patient(X0))) [input p0]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) => (rich(X0) & ~strong(X0))) [input p5]
22. ~happy(fred) [input hypothesis]
23. ! [X0] : (~rich(X0) => (rich(X0) & ~strong(X0))) [pure predicate removal 6]
25. ! [X0] : ((rich(X0) & ~strong(X0)) | rich(X0)) [ennf transformation 23]
35. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0)))) & (((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 1]
77. patient(X0) | ~rich(X0) | patient(X0) | happy(X0) [cnf transformation 35]
83. happy(X0) | ~patient(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 35]
104. rich(X0) | rich(X0) [cnf transformation 25]
140. ~happy(fred) [cnf transformation 22]
143. rich(X0) [duplicate literal removal 104]
144. patient(X0) | ~rich(X0) | happy(X0) [duplicate literal removal 77]
147. happy(X0) | ~patient(X0) | ~rich(X0) [duplicate literal removal 83]
149. ~rich(X0) | happy(X0) [subsumption resolution 144,147]
323. happy(X0) [resolution 149,143]
324. $false [resolution 323,140]
% SZS output end Proof for 3239282498211797765209378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is both not curious and curious.
Everyone who is not rich is either not wise or funny.
Everyone who is patient or calm is humble or not wise.
Everyone who is both calm and not generous is not strong and vice versa.
If fred is not strong then mary is strong or not happy and vice versa.
If someone is patient or curious then someone is funny or kind.
If susan is humble or not strong then susan is not funny or not kind.
Everyone who is old or not curious is either generous or funny.
Everyone who is wise is either not strong or quiet.
Everyone who is old or not calm is kind and vice versa.
Everyone who is not brave or not strong is not curious and vice versa.
Everyone who is not patient or not happy is rich or quiet.
Everyone who is either not kind or humble is either not humble or not brave and vice versa.
Lucy is not happy or not old.
Mary is both creative and not wise.
Susan is not funny.
Someone is either not kind or wise.
Paul is either creative or tall.
Someone is generous or not funny. | Susan is curious. | contradiction | ((?[X]:(~old(X)))=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:(~rich(X)=>(~wise(X)<~>funny(X))))&
(![X]:((patient(X)|calm(X))=>(humble(X)|~wise(X))))&
(![X]:((calm(X)&~generous(X))<=>~strong(X)))&
((~strong(fred))<=>((strong(mary)|~happy(mary))))&
((?[X]:((patient(X)|curious(X))))=>(?[X]:((funny(X)|kind(X)))))&
(((humble(susan)|~strong(susan)))=>((~funny(susan)|~kind(susan))))&
(![X]:((old(X)|~curious(X))=>(generous(X)<~>funny(X))))&
(![X]:(wise(X)=>(~strong(X)<~>quiet(X))))&
(![X]:((old(X)|~calm(X))<=>kind(X)))&
(![X]:((~brave(X)|~strong(X))<=>~curious(X)))&
(![X]:((~patient(X)|~happy(X))=>(rich(X)|quiet(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(~humble(X)<~>~brave(X))))&
((~happy(lucy)|~old(lucy)))&
((creative(mary)&~wise(mary)))&
(~funny(susan))&
(?[X]:((~kind(X)<~>wise(X))))&
((creative(paul)<~>tall(paul)))&
(?[X]:((generous(X)|~funny(X)))) | curious(susan) | [
"p0",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7399152598290219722800265
% SZS output start Proof for 7399152598290219722800265
1. ? [X0] : ~old(X0) => ? [X0] : (curious(X0) & ~curious(X0)) [input p0]
10. ! [X0] : ((~calm(X0) | old(X0)) <=> kind(X0)) [input p9]
11. ! [X0] : ((~strong(X0) | ~brave(X0)) <=> ~curious(X0)) [input p10]
13. ! [X0] : ((~kind(X0) <~> humble(X0)) <=> (~humble(X0) <~> ~brave(X0))) [input p12]
20. curious(susan) [input hypothesis]
21. ? [X0] : ~old(X0) => ? [X1] : (curious(X1) & ~curious(X1)) [rectify 1]
27. ? [X1] : (curious(X1) & ~curious(X1)) | ! [X0] : old(X0) [ennf transformation 21]
35. ? [X0] : (curious(X0) & ~curious(X0)) | ! [X1] : old(X1) [rectify 27]
36. ? [X0] : (curious(X0) & ~curious(X0)) => (curious(sK0) & ~curious(sK0)) [choice axiom]
37. (curious(sK0) & ~curious(sK0)) | ! [X1] : old(X1) [skolemisation 35,36]
47. ! [X0] : (((~calm(X0) | old(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~old(X0)))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | old(X0) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~old(X0)))) [flattening 47]
49. ! [X0] : (((~strong(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (strong(X0) & brave(X0)))) [nnf transformation 11]
50. ! [X0] : ((~strong(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (strong(X0) & brave(X0)))) [flattening 49]
51. ! [X0] : ((((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))))) [nnf transformation 13]
58. ~curious(sK0) | old(X1) [cnf transformation 37]
59. curious(sK0) | old(X1) [cnf transformation 37]
76. ~old(X0) | kind(X0) [cnf transformation 48]
79. ~curious(X0) | brave(X0) [cnf transformation 50]
83. ~brave(X0) | ~humble(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 51]
86. humble(X0) | ~kind(X0) | ~brave(X0) | humble(X0) [cnf transformation 51]
99. curious(susan) [cnf transformation 20]
100. ~brave(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 83]
102. humble(X0) | ~kind(X0) | ~brave(X0) [duplicate literal removal 86]
105. 1 <=> ! [X1] : old(X1) [avatar definition]
106. old(X1) <- (1) [avatar component clause 105]
108. 2 <=> curious(sK0) [avatar definition]
111. 1 | 2 [avatar split clause 59,108,105]
112. 1 | ~2 [avatar split clause 58,108,105]
159. ~brave(X0) | ~kind(X0) [subsumption resolution 100,102]
202. kind(X0) <- (1) [resolution 76,106]
206. brave(susan) [resolution 79,99]
210. ~kind(susan) [resolution 159,206]
211. $false <- (1) [subsumption resolution 210,202]
212. ~1 [avatar contradiction clause 211]
213. $false [avatar sat refutation 111,112,212]
% SZS output end Proof for 7399152598290219722800265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both wise and not happy and vice versa. Everyone who is not calm or not old is both quiet and not curious and vice versa. If someone is both humble and calm then mary is kind or not patient and vice versa. Everyone who is wise or strong is both not strong and humble. Everyone who is both not humble and not calm is patient or rich and vice versa. Everyone who is both not humble and generous is not patient and vice versa. If someone is not creative then susan is both not brave and happy and vice versa. Everyone who is both creative and not quiet is either not old or not tall and vice versa. Everyone who is either not creative or not wise is either patient or tall and vice versa. If alice is both funny and not kind then alice is not quiet or not strong and vice versa. If someone is both not tall and tall then someone is calm. Everyone who is not brave is both creative and not tall and vice versa. Everyone who is not calm is not kind. If susan is either not creative or rich then someone is strong or not rich. Someone is curious or not funny. Someone is not creative or not humble. Mary is either not wise or not funny. Lucy is not wise or strong. Fred is not curious. | Fred is not happy. | neutral | (![X]:(~quiet(X)<=>(wise(X)&~happy(X))))&
(![X]:((~calm(X)|~old(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((humble(X)&calm(X))))<=>((kind(mary)|~patient(mary))))&
(![X]:((wise(X)|strong(X))=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)|rich(X))))&
(![X]:((~humble(X)&generous(X))<=>~patient(X)))&
((?[X]:(~creative(X)))<=>((~brave(susan)&happy(susan))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(((funny(alice)&~kind(alice)))<=>((~quiet(alice)|~strong(alice))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:(~brave(X)<=>(creative(X)&~tall(X))))&
(![X]:(~calm(X)=>~kind(X)))&
(((~creative(susan)<~>rich(susan)))=>(?[X]:((strong(X)|~rich(X)))))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~creative(X)|~humble(X))))&
((~wise(mary)<~>~funny(mary)))&
((~wise(lucy)|strong(lucy)))&
(~curious(fred)) | ~happy(fred) | [] | null | 0 |
Everyone who is not quiet or not happy is either wise or quiet and vice versa. If someone is both not curious and not calm then someone is either not quiet or not rich and vice versa. Everyone who is tall or brave is both not funny and funny and vice versa. If fred is both wise and not rich then someone is both calm and not rich. If lucy is kind or wise then mary is patient or humble. If someone is either not creative or humble then john is both not rich and not patient. If someone is either rich or not brave then paul is either not funny or not humble. Everyone who is either not old or wise is both patient and not funny and vice versa. If john is not tall then alice is not tall. Everyone who is either not old or patient is either patient or not tall and vice versa. Everyone who is happy or old is funny or not calm. Everyone who is both old and not patient is funny or not wise and vice versa. Everyone who is happy is both wise and not old. Everyone who is not humble is both not generous and humble. If lucy is rich or not generous then fred is generous or kind and vice versa. If someone is quiet or not calm then someone is kind and vice versa. John is not curious. Someone is not funny. Someone is either not kind or kind. Paul is either calm or old. Paul is not curious or humble. Someone is kind or generous. Someone is curious or strong. | Mary is not patient. | entailment | (![X]:((~quiet(X)|~happy(X))<=>(wise(X)<~>quiet(X))))&
((?[X]:((~curious(X)&~calm(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((tall(X)|brave(X))<=>(~funny(X)&funny(X))))&
(((wise(fred)&~rich(fred)))=>(?[X]:((calm(X)&~rich(X)))))&
(((kind(lucy)|wise(lucy)))=>((patient(mary)|humble(mary))))&
((?[X]:((~creative(X)<~>humble(X))))=>((~rich(john)&~patient(john))))&
((?[X]:((rich(X)<~>~brave(X))))=>((~funny(paul)<~>~humble(paul))))&
(![X]:((~old(X)<~>wise(X))<=>(patient(X)&~funny(X))))&
((~tall(john))=>(~tall(alice)))&
(![X]:((~old(X)<~>patient(X))<=>(patient(X)<~>~tall(X))))&
(![X]:((happy(X)|old(X))=>(funny(X)|~calm(X))))&
(![X]:((old(X)&~patient(X))<=>(funny(X)|~wise(X))))&
(![X]:(happy(X)=>(wise(X)&~old(X))))&
(![X]:(~humble(X)=>(~generous(X)&humble(X))))&
(((rich(lucy)|~generous(lucy)))<=>((generous(fred)|kind(fred))))&
((?[X]:((quiet(X)|~calm(X))))<=>(?[X]:(kind(X))))&
(~curious(john))&
(?[X]:(~funny(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
((calm(paul)<~>old(paul)))&
((~curious(paul)|humble(paul)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((curious(X)|strong(X)))) | ~patient(mary) | [
"p2",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 647897767790355489767561
% SZS output start Proof for 647897767790355489767561
3. ! [X0] : ((brave(X0) | tall(X0)) <=> (funny(X0) & ~funny(X0))) [input p2]
8. ! [X0] : ((~old(X0) <~> wise(X0)) <=> (~funny(X0) & patient(X0))) [input p7]
10. ! [X0] : ((~old(X0) <~> patient(X0)) <=> (patient(X0) <~> ~tall(X0))) [input p9]
12. ! [X0] : ((~patient(X0) & old(X0)) <=> (~wise(X0) | funny(X0))) [input p11]
24. patient(mary) [input hypothesis]
46. ! [X0] : (((brave(X0) | tall(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (~brave(X0) & ~tall(X0)))) [nnf transformation 3]
47. ! [X0] : ((brave(X0) | tall(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (~brave(X0) & ~tall(X0)))) [flattening 46]
52. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [nnf transformation 8]
53. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [flattening 52]
54. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [nnf transformation 10]
55. ! [X0] : (((~patient(X0) & old(X0)) | (wise(X0) & ~funny(X0))) & ((~wise(X0) | funny(X0)) | (patient(X0) | ~old(X0)))) [nnf transformation 12]
56. ! [X0] : (((~patient(X0) & old(X0)) | (wise(X0) & ~funny(X0))) & (~wise(X0) | funny(X0) | patient(X0) | ~old(X0))) [flattening 55]
84. ~funny(X0) | ~tall(X0) [cnf transformation 47]
86. ~tall(X0) | funny(X0) [cnf transformation 47]
106. ~patient(X0) | old(X0) | funny(X0) | ~wise(X0) [cnf transformation 53]
111. tall(X0) | ~patient(X0) | ~old(X0) | ~patient(X0) [cnf transformation 54]
113. patient(X0) | ~old(X0) | patient(X0) | tall(X0) [cnf transformation 54]
119. old(X0) | ~funny(X0) [cnf transformation 56]
120. old(X0) | wise(X0) [cnf transformation 56]
142. patient(mary) [cnf transformation 24]
145. tall(X0) | ~patient(X0) | ~old(X0) [duplicate literal removal 111]
146. patient(X0) | ~old(X0) | tall(X0) [duplicate literal removal 113]
182. ~tall(X0) [subsumption resolution 84,86]
206. 13 <=> patient(mary) [avatar definition]
208. patient(mary) <- (13) [avatar component clause 206]
252. ~old(X0) | patient(X0) [subsumption resolution 146,182]
253. ~patient(X0) | ~old(X0) [subsumption resolution 145,182]
254. ~old(X0) [subsumption resolution 253,252]
255. wise(X0) [subsumption resolution 120,254]
256. ~funny(X0) [subsumption resolution 119,254]
311. 13 [avatar split clause 142,206]
339. old(mary) | funny(mary) | ~wise(mary) <- (13) [resolution 106,208]
340. funny(mary) | ~wise(mary) <- (13) [subsumption resolution 339,254]
341. ~wise(mary) <- (13) [subsumption resolution 340,256]
342. $false <- (13) [subsumption resolution 341,255]
343. ~13 [avatar contradiction clause 342]
344. $false [avatar sat refutation 311,343]
% SZS output end Proof for 647897767790355489767561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not kind is old.
If mary is not humble then john is not quiet or not curious.
If susan is either not quiet or not rich then alice is either brave or not strong.
If someone is either not calm or not patient then someone is calm or rich and vice versa.
Everyone who is not wise or not kind is tall and vice versa.
Everyone who is not quiet is either not generous or not quiet.
If susan is both not wise and rich then mary is both calm and rich and vice versa.
If someone is old then someone is not funny or not generous.
If susan is not calm then someone is not creative and vice versa.
Everyone who is not old is either old or not quiet and vice versa.
Everyone who is both not generous and not funny is wise or strong and vice versa.
Everyone who is both generous and funny is happy and vice versa.
If lucy is either not patient or generous then lucy is old or not rich and vice versa.
Everyone who is both not brave and not curious is not kind.
Everyone who is not wise is either not tall or not wise.
Paul is not happy.
Someone is either not strong or not happy.
Someone is either not strong or not calm.
Someone is curious.
Someone is patient.
Susan is not strong or not generous.
Alice is not creative or strong. | Alice is wise. | contradiction | (![X]:((kind(X)<~>~kind(X))=>old(X)))&
((~humble(mary))=>((~quiet(john)|~curious(john))))&
(((~quiet(susan)<~>~rich(susan)))=>((brave(alice)<~>~strong(alice))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~wise(X)|~kind(X))<=>tall(X)))&
(![X]:(~quiet(X)=>(~generous(X)<~>~quiet(X))))&
(((~wise(susan)&rich(susan)))<=>((calm(mary)&rich(mary))))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)|~generous(X)))))&
((~calm(susan))<=>(?[X]:(~creative(X))))&
(![X]:(~old(X)<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)|strong(X))))&
(![X]:((generous(X)&funny(X))<=>happy(X)))&
(((~patient(lucy)<~>generous(lucy)))<=>((old(lucy)|~rich(lucy))))&
(![X]:((~brave(X)&~curious(X))=>~kind(X)))&
(![X]:(~wise(X)=>(~tall(X)<~>~wise(X))))&
(~happy(paul))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:(curious(X)))&
(?[X]:(patient(X)))&
((~strong(susan)|~generous(susan)))&
((~creative(alice)|strong(alice))) | wise(alice) | [
"p0",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5351087110994405706974531
% SZS output start Proof for 5351087110994405706974531
1. ! [X0] : ((kind(X0) <~> ~kind(X0)) => old(X0)) [input p0]
6. ! [X0] : (~quiet(X0) => (~generous(X0) <~> ~quiet(X0))) [input p5]
10. ! [X0] : (~old(X0) <=> (old(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~funny(X0) & ~generous(X0)) <=> (strong(X0) | wise(X0))) [input p10]
23. wise(alice) [input hypothesis]
29. ! [X0] : (old(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 1]
31. ! [X0] : ((~generous(X0) <~> ~quiet(X0)) | quiet(X0)) [ennf transformation 6]
34. ! [X0] : (old(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 29]
43. ! [X0] : (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | quiet(X0)) [nnf transformation 31]
53. ! [X0] : ((~old(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | old(X0))) [nnf transformation 10]
54. ! [X0] : (((~funny(X0) & ~generous(X0)) | (~strong(X0) & ~wise(X0))) & ((strong(X0) | wise(X0)) | (funny(X0) | generous(X0)))) [nnf transformation 11]
55. ! [X0] : (((~funny(X0) & ~generous(X0)) | (~strong(X0) & ~wise(X0))) & (strong(X0) | wise(X0) | funny(X0) | generous(X0))) [flattening 54]
69. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 34]
70. old(X0) | kind(X0) | kind(X0) [cnf transformation 34]
85. quiet(X0) | generous(X0) | quiet(X0) [cnf transformation 43]
95. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 53]
98. ~generous(X0) | ~wise(X0) [cnf transformation 55]
121. wise(alice) [cnf transformation 23]
124. ~old(X0) | ~quiet(X0) [duplicate literal removal 95]
125. generous(X0) | quiet(X0) [duplicate literal removal 85]
126. old(X0) | ~kind(X0) [duplicate literal removal 69]
127. old(X0) | kind(X0) [duplicate literal removal 70]
128. old(X0) [subsumption resolution 126,127]
222. ~quiet(X0) [subsumption resolution 124,128]
268. quiet(X1) | ~wise(X1) [resolution 125,98]
272. ~wise(X1) [subsumption resolution 268,222]
283. $false [resolution 272,121]
% SZS output end Proof for 5351087110994405706974531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not strong or quiet then paul is both not strong and not quiet and vice versa.
If lucy is creative or happy then alice is both kind and not tall and vice versa.
If someone is both curious and not happy then mary is not kind and vice versa.
If someone is rich or not tall then lucy is either funny or not rich and vice versa.
If alice is not kind or not happy then paul is wise.
Everyone who is not quiet or not funny is strong and vice versa.
If someone is not calm then someone is both not old and not rich and vice versa.
If someone is not humble or not funny then someone is both patient and not generous and vice versa.
Everyone who is generous or quiet is either not calm or not wise and vice versa.
Everyone who is both old and not funny is both not patient and not wise.
Everyone who is not curious or not kind is brave.
Everyone who is either happy or not funny is both not old and not calm.
Everyone who is not old is funny.
Everyone who is either old or not strong is either curious or strong.
If someone is calm or not quiet then someone is rich.
Everyone who is not humble or kind is both not tall and funny and vice versa.
Fred is creative or not humble.
Someone is not funny.
Someone is both patient and humble.
Alice is both patient and not tall.
Lucy is both brave and curious.
Someone is either generous or not generous.
Someone is not humble.
Someone is kind or old. | Lucy is rich. | entailment | (((~strong(paul)|quiet(paul)))<=>((~strong(paul)&~quiet(paul))))&
(((creative(lucy)|happy(lucy)))<=>((kind(alice)&~tall(alice))))&
((?[X]:((curious(X)&~happy(X))))<=>(~kind(mary)))&
((?[X]:((rich(X)|~tall(X))))<=>((funny(lucy)<~>~rich(lucy))))&
(((~kind(alice)|~happy(alice)))=>(wise(paul)))&
(![X]:((~quiet(X)|~funny(X))<=>strong(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)&~rich(X)))))&
((?[X]:((~humble(X)|~funny(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((generous(X)|quiet(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((old(X)&~funny(X))=>(~patient(X)&~wise(X))))&
(![X]:((~curious(X)|~kind(X))=>brave(X)))&
(![X]:((happy(X)<~>~funny(X))=>(~old(X)&~calm(X))))&
(![X]:(~old(X)=>funny(X)))&
(![X]:((old(X)<~>~strong(X))=>(curious(X)<~>strong(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:(rich(X))))&
(![X]:((~humble(X)|kind(X))<=>(~tall(X)&funny(X))))&
((creative(fred)|~humble(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)&humble(X))))&
((patient(alice)&~tall(alice)))&
((brave(lucy)&curious(lucy)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)|old(X)))) | rich(lucy) | [
"p3",
"p5",
"p12",
"p13",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2548780469890194826822421
% SZS output start Proof for 2548780469890194826822421
4. ? [X0] : (~tall(X0) | rich(X0)) <=> (funny(lucy) <~> ~rich(lucy)) [input p3]
6. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> strong(X0)) [input p5]
13. ! [X0] : (~old(X0) => funny(X0)) [input p12]
14. ! [X0] : ((old(X0) <~> ~strong(X0)) => (curious(X0) <~> strong(X0))) [input p13]
20. ~tall(alice) & patient(alice) [input p19]
21. curious(lucy) & brave(lucy) [input p20]
25. ~rich(lucy) [input hypothesis]
29. curious(lucy) [pure predicate removal 21]
35. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 13]
36. ! [X0] : ((curious(X0) <~> strong(X0)) | (old(X0) <=> ~strong(X0))) [ennf transformation 14]
46. (? [X0] : (~tall(X0) | rich(X0)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X0] : (tall(X0) & ~rich(X0))) [nnf transformation 4]
47. (? [X0] : (~tall(X0) | rich(X0)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X1] : (tall(X1) & ~rich(X1))) [rectify 46]
48. ? [X0] : (~tall(X0) | rich(X0)) => (~tall(sK1) | rich(sK1)) [choice axiom]
49. ((~tall(sK1) | rich(sK1)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X1] : (tall(X1) & ~rich(X1))) [skolemisation 47,48]
50. ! [X0] : (((~funny(X0) | ~quiet(X0)) | ~strong(X0)) & (strong(X0) | (funny(X0) & quiet(X0)))) [nnf transformation 6]
51. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~strong(X0)) & (strong(X0) | (funny(X0) & quiet(X0)))) [flattening 50]
65. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) [nnf transformation 36]
98. rich(lucy) | ~funny(lucy) | tall(X1) [cnf transformation 49]
104. funny(X0) | strong(X0) [cnf transformation 51]
126. old(X0) | funny(X0) [cnf transformation 35]
129. ~strong(X0) | ~curious(X0) | ~strong(X0) | ~old(X0) [cnf transformation 65]
143. ~tall(alice) [cnf transformation 20]
144. curious(lucy) [cnf transformation 29]
149. ~rich(lucy) [cnf transformation 25]
151. ~old(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 129]
159. 2 <=> tall(alice) [avatar definition]
160. ~tall(alice) <- (~2) [avatar component clause 159]
194. 9 <=> rich(lucy) [avatar definition]
198. 10 <=> funny(lucy) [avatar definition]
199. ~funny(lucy) <- (~10) [avatar component clause 198]
212. 13 <=> ! [X1] : tall(X1) [avatar definition]
213. tall(X1) <- (13) [avatar component clause 212]
214. 13 | ~10 | 9 [avatar split clause 98,194,198,212]
303. ~2 [avatar split clause 143,159]
313. ~9 [avatar split clause 149,194]
320. $false <- (~2, 13) [resolution 213,160]
323. 2 | ~13 [avatar contradiction clause 320]
445. ~curious(X1) | ~strong(X1) | funny(X1) [resolution 151,126]
446. ~curious(X1) | funny(X1) [subsumption resolution 445,104]
480. funny(lucy) [resolution 446,144]
483. $false <- (~10) [subsumption resolution 480,199]
484. 10 [avatar contradiction clause 483]
485. $false [avatar sat refutation 214,303,313,323,484]
% SZS output end Proof for 2548780469890194826822421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not tall is both generous and strong and vice versa. Everyone who is either not calm or not generous is either not kind or brave. Everyone who is either happy or not rich is both not brave and not strong. Everyone who is both not rich and not quiet is curious and vice versa. Everyone who is either happy or humble is brave. If fred is both not rich and tall then someone is quiet or not patient and vice versa. If someone is both not curious and not strong then someone is happy or not quiet. Everyone who is not funny or generous is not kind and vice versa. Everyone who is both not brave and wise is happy and vice versa. If lucy is curious then john is patient or not old. Everyone who is creative is either strong or not happy. If lucy is creative or not funny then fred is either creative or not generous and vice versa. Everyone who is not creative is rich and vice versa. Everyone who is not rich is both not strong and not patient and vice versa. If paul is quiet then someone is both not generous and quiet. Everyone who is old is either not kind or generous. Someone is not brave or not calm. Someone is either humble or old. Someone is kind. Someone is brave. Paul is either kind or humble. Someone is either happy or humble. | John is quiet. | contradiction | (![X]:((~humble(X)|~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(![X]:(old(X)=>(~kind(X)<~>generous(X))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
((kind(paul)<~>humble(paul)))&
(?[X]:((happy(X)<~>humble(X)))) | quiet(john) | [
"p0",
"p2",
"p4",
"p5",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3596890917491455354184287
% SZS output start Proof for 3596890917491455354184287
1. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (strong(X0) & generous(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~rich(X0)) => (~strong(X0) & ~brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) <~> humble(X0)) => brave(X0)) [input p4]
6. (tall(fred) & ~rich(fred)) <=> ? [X0] : (~patient(X0) | quiet(X0)) [input p5]
11. ! [X0] : (creative(X0) => (strong(X0) <~> ~happy(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> rich(X0)) [input p12]
14. ! [X0] : (~rich(X0) <=> (~patient(X0) & ~strong(X0))) [input p13]
23. quiet(john) [input hypothesis]
26. ! [X0] : ((~strong(X0) & ~brave(X0)) | (happy(X0) <=> ~rich(X0))) [ennf transformation 3]
27. ! [X0] : (brave(X0) | (happy(X0) <=> humble(X0))) [ennf transformation 5]
31. ! [X0] : ((strong(X0) <~> ~happy(X0)) | ~creative(X0)) [ennf transformation 11]
34. ! [X0] : (((~tall(X0) | ~humble(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 1]
35. ! [X0] : ((~tall(X0) | ~humble(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | (tall(X0) & humble(X0)))) [flattening 34]
37. ! [X0] : ((~strong(X0) & ~brave(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) [nnf transformation 26]
40. ! [X0] : (brave(X0) | ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0)))) [nnf transformation 27]
41. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (~tall(fred) | rich(fred))) [nnf transformation 6]
42. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | ~tall(fred) | rich(fred)) [flattening 41]
43. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X1] : (~patient(X1) | quiet(X1)) | ~tall(fred) | rich(fred)) [rectify 42]
44. ? [X1] : (~patient(X1) | quiet(X1)) => (~patient(sK0) | quiet(sK0)) [choice axiom]
45. ((tall(fred) & ~rich(fred)) | ! [X0] : (patient(X0) & ~quiet(X0))) & ((~patient(sK0) | quiet(sK0)) | ~tall(fred) | rich(fred)) [skolemisation 43,44]
53. ! [X0] : (((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~creative(X0)) [nnf transformation 31]
56. ! [X0] : ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0))) [nnf transformation 13]
57. ! [X0] : ((~rich(X0) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [nnf transformation 14]
58. ! [X0] : ((~rich(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | rich(X0))) [flattening 57]
77. strong(X0) | humble(X0) [cnf transformation 35]
85. ~brave(X0) | happy(X0) | rich(X0) [cnf transformation 37]
92. ~humble(X0) | happy(X0) | brave(X0) [cnf transformation 40]
94. ~rich(fred) | ~quiet(X0) [cnf transformation 45]
106. ~creative(X0) | strong(X0) | ~happy(X0) [cnf transformation 53]
114. creative(X0) | rich(X0) [cnf transformation 56]
116. ~strong(X0) | rich(X0) [cnf transformation 58]
132. quiet(john) [cnf transformation 23]
142. 3 <=> ! [X0] : ~quiet(X0) [avatar definition]
143. ~quiet(X0) <- (3) [avatar component clause 142]
146. 4 <=> rich(fred) [avatar definition]
148. ~rich(fred) <- (~4) [avatar component clause 146]
150. 3 | ~4 [avatar split clause 94,146,142]
190. 14 <=> creative(fred) [avatar definition]
191. ~creative(fred) <- (~14) [avatar component clause 190]
192. creative(fred) <- (14) [avatar component clause 190]
272. rich(fred) <- (~14) [resolution 114,191]
273. $false <- (~4, ~14) [subsumption resolution 272,148]
274. 4 | 14 [avatar contradiction clause 273]
282. rich(X1) | humble(X1) [resolution 116,77]
285. humble(fred) <- (~4) [resolution 282,148]
332. happy(fred) | brave(fred) <- (~4) [resolution 92,285]
338. 33 <=> brave(fred) [avatar definition]
340. brave(fred) <- (33) [avatar component clause 338]
342. 34 <=> happy(fred) [avatar definition]
345. 33 | 34 | 4 [avatar split clause 332,146,342,338]
388. strong(X0) | ~happy(X0) | rich(X0) [resolution 106,114]
389. strong(fred) | ~happy(fred) <- (14) [resolution 106,192]
390. ~happy(X0) | rich(X0) [subsumption resolution 388,116]
392. 42 <=> strong(fred) [avatar definition]
394. strong(fred) <- (42) [avatar component clause 392]
395. ~34 | 42 | ~14 [avatar split clause 389,190,392,342]
551. happy(fred) | rich(fred) <- (33) [resolution 340,85]
570. rich(fred) <- (42) [resolution 394,116]
575. $false <- (~4, 42) [subsumption resolution 570,148]
576. 4 | ~42 [avatar contradiction clause 575]
577. rich(fred) <- (33) [subsumption resolution 551,390]
578. 4 | ~33 [avatar split clause 577,338,146]
583. $false <- (3) [resolution 143,132]
584. ~3 [avatar contradiction clause 583]
585. $false [avatar sat refutation 150,274,345,395,576,578,584]
% SZS output end Proof for 3596890917491455354184287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is creative.
If susan is not patient then lucy is either not brave or wise and vice versa.
Everyone who is both not rich and not happy is funny and vice versa.
If lucy is either strong or patient then someone is generous and vice versa.
Everyone who is either not generous or not curious is tall or not brave.
Everyone who is brave is either rich or wise and vice versa.
If someone is both happy and tall then someone is strong and vice versa.
Everyone who is both not curious and wise is calm and vice versa.
If paul is strong or not calm then fred is either rich or not kind and vice versa.
If susan is humble then alice is either old or kind.
Everyone who is not humble or not happy is not tall or not strong and vice versa.
Everyone who is either funny or not curious is not strong or happy.
Everyone who is both happy and not strong is both quiet and calm and vice versa.
Everyone who is wise or quiet is not humble or not tall and vice versa.
If someone is not kind then someone is brave or not tall and vice versa.
Everyone who is either not calm or not funny is quiet or strong.
Susan is either not generous or not creative.
Lucy is creative.
Paul is brave.
Someone is both patient and curious.
Someone is happy or not funny.
Fred is either brave or generous.
Someone is not generous.
Fred is either not strong or not calm. | Susan is not generous. | neutral | (![X]:(tall(X)=>creative(X)))&
((~patient(susan))<=>((~brave(lucy)<~>wise(lucy))))&
(![X]:((~rich(X)&~happy(X))<=>funny(X)))&
(((strong(lucy)<~>patient(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)<~>~curious(X))=>(tall(X)|~brave(X))))&
(![X]:(brave(X)<=>(rich(X)<~>wise(X))))&
((?[X]:((happy(X)&tall(X))))<=>(?[X]:(strong(X))))&
(![X]:((~curious(X)&wise(X))<=>calm(X)))&
(((strong(paul)|~calm(paul)))<=>((rich(fred)<~>~kind(fred))))&
((humble(susan))=>((old(alice)<~>kind(alice))))&
(![X]:((~humble(X)|~happy(X))<=>(~tall(X)|~strong(X))))&
(![X]:((funny(X)<~>~curious(X))=>(~strong(X)|happy(X))))&
(![X]:((happy(X)&~strong(X))<=>(quiet(X)&calm(X))))&
(![X]:((wise(X)|quiet(X))<=>(~humble(X)|~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)|~tall(X)))))&
(![X]:((~calm(X)<~>~funny(X))=>(quiet(X)|strong(X))))&
((~generous(susan)<~>~creative(susan)))&
(creative(lucy))&
(brave(paul))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:((happy(X)|~funny(X))))&
((brave(fred)<~>generous(fred)))&
(?[X]:(~generous(X)))&
((~strong(fred)<~>~calm(fred))) | ~generous(susan) | [] | null | 0 |
Everyone who is both not strong and not curious is both not humble and not tall and vice versa. If lucy is creative or quiet then john is not creative or happy. If john is not tall or not brave then john is not happy or generous. If john is humble then someone is happy or not old and vice versa. Everyone who is curious is either old or not wise and vice versa. If lucy is not quiet then someone is happy and vice versa. If fred is both not patient and not tall then mary is not kind or not wise. If paul is humble then lucy is either curious or not brave and vice versa. If someone is both funny and not strong then lucy is not generous or funny. If fred is not funny then someone is either funny or not funny and vice versa. Everyone who is either not calm or not happy is either not funny or wise. Everyone who is kind is quiet or not quiet. If someone is not old then susan is not funny or not curious. Everyone who is either not generous or patient is kind or not old. If susan is both happy and not calm then someone is either not brave or wise and vice versa. If someone is not curious or tall then someone is both not generous and happy. John is creative. John is both quiet and rich. Mary is not tall. Someone is not calm or not curious. Alice is not kind. John is both creative and generous. Someone is either strong or not tall. Someone is patient. | John is generous. | entailment | (![X]:((~strong(X)&~curious(X))<=>(~humble(X)&~tall(X))))&
(((creative(lucy)|quiet(lucy)))=>((~creative(john)|happy(john))))&
(((~tall(john)|~brave(john)))=>((~happy(john)|generous(john))))&
((humble(john))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:(curious(X)<=>(old(X)<~>~wise(X))))&
((~quiet(lucy))<=>(?[X]:(happy(X))))&
(((~patient(fred)&~tall(fred)))=>((~kind(mary)|~wise(mary))))&
((humble(paul))<=>((curious(lucy)<~>~brave(lucy))))&
((?[X]:((funny(X)&~strong(X))))=>((~generous(lucy)|funny(lucy))))&
((~funny(fred))<=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((~calm(X)<~>~happy(X))=>(~funny(X)<~>wise(X))))&
(![X]:(kind(X)=>(quiet(X)|~quiet(X))))&
((?[X]:(~old(X)))=>((~funny(susan)|~curious(susan))))&
(![X]:((~generous(X)<~>patient(X))=>(kind(X)|~old(X))))&
(((happy(susan)&~calm(susan)))<=>(?[X]:((~brave(X)<~>wise(X)))))&
((?[X]:((~curious(X)|tall(X))))=>(?[X]:((~generous(X)&happy(X)))))&
(creative(john))&
((quiet(john)&rich(john)))&
(~tall(mary))&
(?[X]:((~calm(X)|~curious(X))))&
(~kind(alice))&
((creative(john)&generous(john)))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:(patient(X))) | generous(john) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 570782456071708320423977
% SZS output start Proof for 570782456071708320423977
22. generous(john) & creative(john) [input p21]
25. ~generous(john) [input hypothesis]
128. generous(john) [cnf transformation 22]
132. ~generous(john) [cnf transformation 25]
158. 6 <=> generous(john) [avatar definition]
316. 6 [avatar split clause 128,158]
328. ~6 [avatar split clause 132,158]
329. $false [avatar sat refutation 316,328]
% SZS output end Proof for 570782456071708320423977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not creative then paul is not generous.
If someone is either generous or kind then someone is tall.
If someone is both strong and not humble then paul is rich.
Everyone who is not patient is not tall.
If fred is either strong or not wise then someone is either not brave or quiet and vice versa.
If someone is either not rich or funny then someone is both quiet and curious.
Everyone who is kind or not rich is both not rich and old and vice versa.
Everyone who is not kind or not happy is not brave or strong and vice versa.
If someone is not patient or tall then susan is both not rich and humble.
Everyone who is either not tall or not creative is happy.
If someone is calm then someone is not rich.
If someone is both calm and not brave then someone is either tall or not calm and vice versa.
If john is both not funny and not quiet then fred is tall or humble and vice versa.
Everyone who is either strong or not tall is not patient or rich and vice versa.
Everyone who is happy or patient is not creative.
If someone is either old or not creative then someone is either old or not rich and vice versa.
Someone is not happy or humble.
Mary is funny.
Someone is both not kind and not creative.
Someone is both calm and not quiet.
Someone is either not curious or kind.
Someone is curious or not curious.
Someone is either not calm or not quiet.
Susan is not creative or not calm. | John is not creative. | entailment | ((?[X]:((~old(X)&~creative(X))))=>(~generous(paul)))&
((?[X]:((generous(X)<~>kind(X))))=>(?[X]:(tall(X))))&
((?[X]:((strong(X)&~humble(X))))=>(rich(paul)))&
(![X]:(~patient(X)=>~tall(X)))&
(((strong(fred)<~>~wise(fred)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
((?[X]:((~rich(X)<~>funny(X))))=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((kind(X)|~rich(X))<=>(~rich(X)&old(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~brave(X)|strong(X))))&
((?[X]:((~patient(X)|tall(X))))=>((~rich(susan)&humble(susan))))&
(![X]:((~tall(X)<~>~creative(X))=>happy(X)))&
((?[X]:(calm(X)))=>(?[X]:(~rich(X))))&
((?[X]:((calm(X)&~brave(X))))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((~funny(john)&~quiet(john)))<=>((tall(fred)|humble(fred))))&
(![X]:((strong(X)<~>~tall(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|patient(X))=>~creative(X)))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((old(X)<~>~rich(X)))))&
(?[X]:((~happy(X)|humble(X))))&
(funny(mary))&
(?[X]:((~kind(X)&~creative(X))))&
(?[X]:((calm(X)&~quiet(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((~creative(susan)|~calm(susan))) | ~creative(john) | [
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 57989329265084156932988
% SZS output start Proof for 57989329265084156932988
4. ! [X0] : (~patient(X0) => ~tall(X0)) [input p3]
10. ! [X0] : ((~tall(X0) <~> ~creative(X0)) => happy(X0)) [input p9]
15. ! [X0] : ((patient(X0) | happy(X0)) => ~creative(X0)) [input p14]
25. creative(john) [input hypothesis]
34. ! [X0] : (~tall(X0) | patient(X0)) [ennf transformation 4]
37. ! [X0] : (happy(X0) | (~tall(X0) <=> ~creative(X0))) [ennf transformation 10]
39. ! [X0] : (~creative(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 15]
56. ! [X0] : (happy(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) [nnf transformation 37]
92. ~tall(X0) | patient(X0) [cnf transformation 34]
118. ~creative(X0) | happy(X0) | tall(X0) [cnf transformation 56]
138. ~happy(X0) | ~creative(X0) [cnf transformation 39]
139. ~patient(X0) | ~creative(X0) [cnf transformation 39]
160. creative(john) [cnf transformation 25]
404. happy(john) | tall(john) [resolution 118,160]
406. 49 <=> tall(john) [avatar definition]
408. tall(john) <- (49) [avatar component clause 406]
410. 50 <=> happy(john) [avatar definition]
412. happy(john) <- (50) [avatar component clause 410]
413. 49 | 50 [avatar split clause 404,410,406]
417. patient(john) <- (49) [resolution 408,92]
455. ~creative(john) <- (49) [resolution 417,139]
456. $false <- (49) [subsumption resolution 455,160]
457. ~49 [avatar contradiction clause 456]
466. ~creative(john) <- (50) [resolution 412,138]
467. $false <- (50) [subsumption resolution 466,160]
468. ~50 [avatar contradiction clause 467]
469. $false [avatar sat refutation 413,457,468]
% SZS output end Proof for 57989329265084156932988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either wise or not curious then someone is not patient and vice versa.
Everyone who is either not brave or brave is strong or not old and vice versa.
Everyone who is either calm or generous is either not rich or kind.
Everyone who is not strong is not generous.
Everyone who is either wise or curious is not kind.
Everyone who is not brave or not happy is curious and vice versa.
Everyone who is either not humble or not generous is either not curious or not rich.
If someone is either rich or wise then someone is tall.
Everyone who is both not curious and tall is both curious and calm.
If someone is either rich or not brave then someone is both happy and not quiet and vice versa.
If alice is calm or not happy then alice is quiet or wise.
Everyone who is not rich or generous is rich.
Everyone who is either not happy or humble is either not brave or not curious and vice versa.
Everyone who is both not patient and creative is patient or not humble and vice versa.
Everyone who is both not humble and not happy is not kind or not tall.
Everyone who is wise or funny is either not happy or creative and vice versa.
Someone is not tall or not wise.
Someone is not brave or tall.
Someone is both tall and brave.
Someone is calm or wise.
Someone is either not rich or calm.
Someone is funny.
Fred is not funny or not humble. | Fred is humble. | entailment | (((wise(fred)<~>~curious(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(strong(X)|~old(X))))&
(![X]:((calm(X)<~>generous(X))=>(~rich(X)<~>kind(X))))&
(![X]:(~strong(X)=>~generous(X)))&
(![X]:((wise(X)<~>curious(X))=>~kind(X)))&
(![X]:((~brave(X)|~happy(X))<=>curious(X)))&
(![X]:((~humble(X)<~>~generous(X))=>(~curious(X)<~>~rich(X))))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:(tall(X))))&
(![X]:((~curious(X)&tall(X))=>(curious(X)&calm(X))))&
((?[X]:((rich(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(((calm(alice)|~happy(alice)))=>((quiet(alice)|wise(alice))))&
(![X]:((~rich(X)|generous(X))=>rich(X)))&
(![X]:((~happy(X)<~>humble(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~patient(X)&creative(X))<=>(patient(X)|~humble(X))))&
(![X]:((~humble(X)&~happy(X))=>(~kind(X)|~tall(X))))&
(![X]:((wise(X)|funny(X))<=>(~happy(X)<~>creative(X))))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((tall(X)&brave(X))))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((~rich(X)<~>calm(X))))&
(?[X]:(funny(X)))&
((~funny(fred)|~humble(fred))) | humble(fred) | [
"p0",
"p5",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8640272185173354113548890
% SZS output start Proof for 8640272185173354113548890
1. (wise(fred) <~> ~curious(fred)) <=> ? [X0] : ~patient(X0) [input p0]
6. ! [X0] : ((~happy(X0) | ~brave(X0)) <=> curious(X0)) [input p5]
13. ! [X0] : ((~happy(X0) <~> humble(X0)) <=> (~brave(X0) <~> ~curious(X0))) [input p12]
14. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (~humble(X0) | patient(X0))) [input p13]
16. ! [X0] : ((funny(X0) | wise(X0)) <=> (~happy(X0) <~> creative(X0))) [input p15]
24. ~humble(fred) [input hypothesis]
39. (((curious(fred) | ~wise(fred)) & (~curious(fred) | wise(fred))) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ((wise(fred) | curious(fred)) & (~curious(fred) | ~wise(fred)))) [nnf transformation 1]
40. (((curious(fred) | ~wise(fred)) & (~curious(fred) | wise(fred))) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ((wise(fred) | curious(fred)) & (~curious(fred) | ~wise(fred)))) [rectify 39]
41. ? [X1] : ~patient(X1) => ~patient(sK0) [choice axiom]
42. (((curious(fred) | ~wise(fred)) & (~curious(fred) | wise(fred))) | ! [X0] : patient(X0)) & (~patient(sK0) | ((wise(fred) | curious(fred)) & (~curious(fred) | ~wise(fred)))) [skolemisation 40,41]
47. ! [X0] : (((~happy(X0) | ~brave(X0)) | ~curious(X0)) & (curious(X0) | (happy(X0) & brave(X0)))) [nnf transformation 6]
48. ! [X0] : ((~happy(X0) | ~brave(X0) | ~curious(X0)) & (curious(X0) | (happy(X0) & brave(X0)))) [flattening 47]
59. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [nnf transformation 13]
60. ! [X0] : (((creative(X0) & ~patient(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (~creative(X0) | patient(X0)))) [nnf transformation 14]
61. ! [X0] : (((creative(X0) & ~patient(X0)) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | ~creative(X0) | patient(X0))) [flattening 60]
62. ! [X0] : (((funny(X0) | wise(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~funny(X0) & ~wise(X0)))) [nnf transformation 16]
63. ! [X0] : ((funny(X0) | wise(X0) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~funny(X0) & ~wise(X0)))) [flattening 62]
79. ~curious(fred) | wise(fred) | patient(X0) [cnf transformation 42]
94. brave(X0) | curious(X0) [cnf transformation 48]
95. happy(X0) | curious(X0) [cnf transformation 48]
96. ~happy(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 48]
119. humble(X0) | ~happy(X0) | ~curious(X0) | brave(X0) [cnf transformation 59]
120. humble(X0) | ~happy(X0) | ~brave(X0) | curious(X0) [cnf transformation 59]
124. ~patient(X0) | ~patient(X0) [cnf transformation 61]
127. creative(X0) | humble(X0) [cnf transformation 61]
131. ~creative(X0) | happy(X0) | ~wise(X0) [cnf transformation 63]
144. ~humble(fred) [cnf transformation 24]
146. ~patient(X0) [duplicate literal removal 124]
152. 1 <=> ! [X0] : patient(X0) [avatar definition]
153. patient(X0) <- (1) [avatar component clause 152]
155. 2 <=> wise(fred) [avatar definition]
156. wise(fred) <- (2) [avatar component clause 155]
159. 3 <=> curious(fred) [avatar definition]
163. 1 | 2 | ~3 [avatar split clause 79,159,155,152]
233. humble(X0) | ~happy(X0) | curious(X0) [subsumption resolution 120,94]
234. humble(X0) | curious(X0) [subsumption resolution 233,95]
235. humble(X0) | ~happy(X0) | ~curious(X0) [subsumption resolution 119,96]
236. ~happy(X0) | humble(X0) [subsumption resolution 235,234]
274. 26 <=> humble(fred) [avatar definition]
276. ~humble(fred) <- (~26) [avatar component clause 274]
278. ~26 [avatar split clause 144,274]
294. curious(fred) <- (~26) [resolution 234,276]
297. 3 | 26 [avatar split clause 294,274,159]
357. happy(X0) | ~wise(X0) | humble(X0) [resolution 131,127]
358. ~wise(X0) | humble(X0) [subsumption resolution 357,236]
385. humble(fred) <- (2) [resolution 358,156]
386. $false <- (2, ~26) [subsumption resolution 385,276]
387. ~2 | 26 [avatar contradiction clause 386]
388. $false <- (1) [subsumption resolution 153,146]
389. ~1 [avatar contradiction clause 388]
390. $false [avatar sat refutation 163,278,297,387,389]
% SZS output end Proof for 8640272185173354113548890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall then someone is not curious and vice versa.
Everyone who is either tall or not calm is either not rich or calm and vice versa.
Everyone who is both not strong and rich is curious and vice versa.
Everyone who is not tall or not old is either brave or not old and vice versa.
If susan is calm or happy then paul is either not funny or kind.
If someone is either kind or happy then someone is not brave.
If alice is not strong or not quiet then mary is patient.
If mary is rich or tall then mary is both not brave and curious.
Everyone who is not rich or not calm is not tall and vice versa.
If john is either quiet or calm then alice is either not happy or strong.
If someone is both calm and not wise then susan is either quiet or happy and vice versa.
Everyone who is not humble is both generous and brave.
If fred is wise or tall then someone is both not curious and not tall and vice versa.
If someone is both calm and strong then john is both rich and not brave.
Everyone who is either tall or not patient is both kind and not rich.
Everyone who is either quiet or generous is both funny and not funny and vice versa.
Someone is not creative.
Someone is both rich and not funny.
Someone is old.
Susan is not funny.
Alice is either wise or not funny.
Someone is not brave.
Someone is either not happy or not wise.
Lucy is brave. | Lucy is not old. | contradiction | ((tall(alice))<=>(?[X]:(~curious(X))))&
(![X]:((tall(X)<~>~calm(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((~strong(X)&rich(X))<=>curious(X)))&
(![X]:((~tall(X)|~old(X))<=>(brave(X)<~>~old(X))))&
(((calm(susan)|happy(susan)))=>((~funny(paul)<~>kind(paul))))&
((?[X]:((kind(X)<~>happy(X))))=>(?[X]:(~brave(X))))&
(((~strong(alice)|~quiet(alice)))=>(patient(mary)))&
(((rich(mary)|tall(mary)))=>((~brave(mary)&curious(mary))))&
(![X]:((~rich(X)|~calm(X))<=>~tall(X)))&
(((quiet(john)<~>calm(john)))=>((~happy(alice)<~>strong(alice))))&
((?[X]:((calm(X)&~wise(X))))<=>((quiet(susan)<~>happy(susan))))&
(![X]:(~humble(X)=>(generous(X)&brave(X))))&
(((wise(fred)|tall(fred)))<=>(?[X]:((~curious(X)&~tall(X)))))&
((?[X]:((calm(X)&strong(X))))=>((rich(john)&~brave(john))))&
(![X]:((tall(X)<~>~patient(X))=>(kind(X)&~rich(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(funny(X)&~funny(X))))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)&~funny(X))))&
(?[X]:(old(X)))&
(~funny(susan))&
((wise(alice)<~>~funny(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(brave(lucy)) | ~old(lucy) | [
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5051920735307345265712059
% SZS output start Proof for 5051920735307345265712059
4. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (brave(X0) <~> ~old(X0))) [input p3]
24. brave(lucy) [input p23]
25. ~old(lucy) [input hypothesis]
43. ! [X0] : (((~old(X0) | ~tall(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (old(X0) & tall(X0)))) [nnf transformation 4]
44. ! [X0] : ((~old(X0) | ~tall(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) & (((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (old(X0) & tall(X0)))) [flattening 43]
91. old(X0) | ~brave(X0) | old(X0) [cnf transformation 44]
145. brave(lucy) [cnf transformation 24]
146. ~old(lucy) [cnf transformation 25]
147. ~brave(X0) | old(X0) [duplicate literal removal 91]
332. old(lucy) [resolution 147,145]
333. $false [subsumption resolution 332,146]
% SZS output end Proof for 5051920735307345265712059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not happy then paul is old.
Everyone who is not creative or not calm is either not rich or tall and vice versa.
Everyone who is either quiet or funny is not calm.
If someone is either rich or humble then alice is either curious or generous.
Everyone who is both not patient and not brave is both creative and not quiet and vice versa.
If susan is generous then someone is either not patient or not brave.
If paul is not old then someone is either not quiet or not generous.
If someone is both not calm and quiet then someone is either happy or tall and vice versa.
If someone is strong then lucy is not kind and vice versa.
Everyone who is not creative or not funny is both not creative and not happy and vice versa.
If paul is not old or happy then john is either not rich or strong and vice versa.
Everyone who is curious is either not strong or not calm and vice versa.
If someone is either not kind or not generous then someone is not tall or not brave and vice versa.
Everyone who is old is either not creative or not calm.
Everyone who is both not creative and not wise is both calm and not tall and vice versa.
If john is either not generous or generous then someone is either not old or not calm.
Susan is either not creative or quiet.
Paul is brave.
Someone is either not curious or quiet.
Someone is either not creative or brave.
Fred is both not kind and quiet.
Susan is either wise or creative. | Fred is quiet. | entailment | ((?[X]:((~creative(X)&~happy(X))))=>(old(paul)))&
(![X]:((~creative(X)|~calm(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((quiet(X)<~>funny(X))=>~calm(X)))&
((?[X]:((rich(X)<~>humble(X))))=>((curious(alice)<~>generous(alice))))&
(![X]:((~patient(X)&~brave(X))<=>(creative(X)&~quiet(X))))&
((generous(susan))=>(?[X]:((~patient(X)<~>~brave(X)))))&
((~old(paul))=>(?[X]:((~quiet(X)<~>~generous(X)))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((happy(X)<~>tall(X)))))&
((?[X]:(strong(X)))<=>(~kind(lucy)))&
(![X]:((~creative(X)|~funny(X))<=>(~creative(X)&~happy(X))))&
(((~old(paul)|happy(paul)))<=>((~rich(john)<~>strong(john))))&
(![X]:(curious(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(old(X)=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)&~wise(X))<=>(calm(X)&~tall(X))))&
(((~generous(john)<~>generous(john)))=>(?[X]:((~old(X)<~>~calm(X)))))&
((~creative(susan)<~>quiet(susan)))&
(brave(paul))&
(?[X]:((~curious(X)<~>quiet(X))))&
(?[X]:((~creative(X)<~>brave(X))))&
((~kind(fred)&quiet(fred)))&
((wise(susan)<~>creative(susan))) | quiet(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 605196383709597302327511
% SZS output start Proof for 605196383709597302327511
21. quiet(fred) & ~kind(fred) [input p20]
23. ~quiet(fred) [input hypothesis]
146. quiet(fred) [cnf transformation 21]
149. ~quiet(fred) [cnf transformation 23]
352. $false [subsumption resolution 149,146]
% SZS output end Proof for 605196383709597302327511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or patient is wise or tall.
Everyone who is both not happy and brave is either not calm or not kind and vice versa.
Everyone who is either patient or calm is either not patient or not strong and vice versa.
Everyone who is both not quiet and not wise is calm.
Everyone who is not happy or not strong is rich or not rich.
Everyone who is not curious or humble is both not funny and not humble.
If someone is not rich then someone is both not tall and not patient and vice versa.
If someone is not calm or happy then mary is not humble or not kind.
If someone is either funny or not humble then someone is both tall and not generous.
If john is either funny or wise then mary is not curious or curious.
Everyone who is generous or curious is rich or wise and vice versa.
If someone is both funny and not tall then lucy is both wise and not strong and vice versa.
If someone is both rich and not creative then someone is either funny or humble.
Everyone who is happy is either not humble or not brave and vice versa.
Everyone who is either not humble or not funny is both not kind and rich and vice versa.
Everyone who is both strong and tall is generous and vice versa.
Someone is not happy or calm.
Someone is both not patient and creative.
Mary is curious.
Alice is not strong.
Mary is both rich and not calm.
Someone is not brave or tall.
Paul is both not brave and not generous. | Mary is not funny. | contradiction | (![X]:((curious(X)|patient(X))=>(wise(X)|tall(X))))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>~kind(X))))&
(![X]:((patient(X)<~>calm(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((~quiet(X)&~wise(X))=>calm(X)))&
(![X]:((~happy(X)|~strong(X))=>(rich(X)|~rich(X))))&
(![X]:((~curious(X)|humble(X))=>(~funny(X)&~humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
((?[X]:((~calm(X)|happy(X))))=>((~humble(mary)|~kind(mary))))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((tall(X)&~generous(X)))))&
(((funny(john)<~>wise(john)))=>((~curious(mary)|curious(mary))))&
(![X]:((generous(X)|curious(X))<=>(rich(X)|wise(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((wise(lucy)&~strong(lucy))))&
((?[X]:((rich(X)&~creative(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:(happy(X)<=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~kind(X)&rich(X))))&
(![X]:((strong(X)&tall(X))<=>generous(X)))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((~patient(X)&creative(X))))&
(curious(mary))&
(~strong(alice))&
((rich(mary)&~calm(mary)))&
(?[X]:((~brave(X)|tall(X))))&
((~brave(paul)&~generous(paul))) | ~funny(mary) | [
"p1",
"p5",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 319870199656683524871174
% SZS output start Proof for 319870199656683524871174
2. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (~calm(X0) <~> ~kind(X0))) [input p1]
6. ! [X0] : ((humble(X0) | ~curious(X0)) => (~humble(X0) & ~funny(X0))) [input p5]
14. ! [X0] : (happy(X0) <=> (~humble(X0) <~> ~brave(X0))) [input p13]
15. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> (rich(X0) & ~kind(X0))) [input p14]
21. ~calm(mary) & rich(mary) [input p20]
24. ~funny(mary) [input hypothesis]
35. ! [X0] : ((~humble(X0) & ~funny(X0)) | (~humble(X0) & curious(X0))) [ennf transformation 6]
41. ! [X0] : (((brave(X0) & ~happy(X0)) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) & (((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 2]
42. ! [X0] : (((brave(X0) & ~happy(X0)) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) & (((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~brave(X0) | happy(X0))) [flattening 41]
61. ! [X0] : ((happy(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) & (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ~happy(X0))) [nnf transformation 14]
62. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | (~rich(X0) | kind(X0))) & ((rich(X0) & ~kind(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 15]
63. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | ~rich(X0) | kind(X0)) & ((rich(X0) & ~kind(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [flattening 62]
76. ~kind(X0) | ~happy(X0) | calm(X0) [cnf transformation 42]
78. ~kind(X0) | brave(X0) | calm(X0) [cnf transformation 42]
93. ~humble(X0) | ~humble(X0) [cnf transformation 35]
115. happy(X0) | ~brave(X0) | humble(X0) [cnf transformation 61]
122. funny(X0) | humble(X0) | ~rich(X0) | kind(X0) [cnf transformation 63]
130. rich(mary) [cnf transformation 21]
131. ~calm(mary) [cnf transformation 21]
135. ~funny(mary) [cnf transformation 24]
136. ~humble(X0) [duplicate literal removal 93]
202. ~brave(X0) | happy(X0) [subsumption resolution 115,136]
204. ~rich(X0) | funny(X0) | kind(X0) [subsumption resolution 122,136]
266. funny(mary) | kind(mary) [resolution 204,130]
268. kind(mary) [subsumption resolution 266,135]
269. brave(mary) | calm(mary) [resolution 268,78]
270. ~happy(mary) | calm(mary) [resolution 268,76]
271. brave(mary) [subsumption resolution 269,131]
272. ~happy(mary) [subsumption resolution 270,131]
274. happy(mary) [resolution 271,202]
275. $false [subsumption resolution 274,272]
% SZS output end Proof for 319870199656683524871174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or curious is not generous or creative.
If someone is either not happy or not wise then someone is either old or wise.
Everyone who is not rich or generous is brave and vice versa.
Everyone who is generous is not strong or not brave and vice versa.
If lucy is kind then susan is either curious or strong.
If mary is creative then alice is not patient or not rich and vice versa.
Everyone who is both strong and not generous is both not tall and not strong and vice versa.
If someone is either not patient or quiet then lucy is either wise or not old.
Everyone who is kind or not brave is both not happy and not kind.
If someone is both humble and not brave then alice is both rich and not strong and vice versa.
Everyone who is either creative or not creative is not patient or not funny.
Everyone who is both not creative and humble is either wise or not old.
Everyone who is both not kind and funny is both humble and not old and vice versa.
If john is both old and not tall then john is either creative or not humble and vice versa.
Everyone who is quiet is not creative.
Everyone who is not brave is either strong or creative.
Someone is not happy.
Fred is kind or not funny.
Someone is both not old and not wise.
Someone is not old.
Alice is not creative.
Susan is both not happy and not patient.
Someone is both not old and not rich. | Alice is rich. | contradiction | (![X]:((~wise(X)|curious(X))=>(~generous(X)|creative(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~rich(X)|generous(X))<=>brave(X)))&
(![X]:(generous(X)<=>(~strong(X)|~brave(X))))&
((kind(lucy))=>((curious(susan)<~>strong(susan))))&
((creative(mary))<=>((~patient(alice)|~rich(alice))))&
(![X]:((strong(X)&~generous(X))<=>(~tall(X)&~strong(X))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((wise(lucy)<~>~old(lucy))))&
(![X]:((kind(X)|~brave(X))=>(~happy(X)&~kind(X))))&
((?[X]:((humble(X)&~brave(X))))<=>((rich(alice)&~strong(alice))))&
(![X]:((creative(X)<~>~creative(X))=>(~patient(X)|~funny(X))))&
(![X]:((~creative(X)&humble(X))=>(wise(X)<~>~old(X))))&
(![X]:((~kind(X)&funny(X))<=>(humble(X)&~old(X))))&
(((old(john)&~tall(john)))<=>((creative(john)<~>~humble(john))))&
(![X]:(quiet(X)=>~creative(X)))&
(![X]:(~brave(X)=>(strong(X)<~>creative(X))))&
(?[X]:(~happy(X)))&
((kind(fred)|~funny(fred)))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:(~old(X)))&
(~creative(alice))&
((~happy(susan)&~patient(susan)))&
(?[X]:((~old(X)&~rich(X)))) | rich(alice) | [
"p2",
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 501245809712227690689396
% SZS output start Proof for 501245809712227690689396
3. ! [X0] : ((generous(X0) | ~rich(X0)) <=> brave(X0)) [input p2]
4. ! [X0] : (generous(X0) <=> (~brave(X0) | ~strong(X0))) [input p3]
7. ! [X0] : ((~generous(X0) & strong(X0)) <=> (~strong(X0) & ~tall(X0))) [input p6]
10. ? [X0] : (~brave(X0) & humble(X0)) <=> (~strong(alice) & rich(alice)) [input p9]
24. rich(alice) [input hypothesis]
42. ! [X0] : (((generous(X0) | ~rich(X0)) | ~brave(X0)) & (brave(X0) | (~generous(X0) & rich(X0)))) [nnf transformation 3]
43. ! [X0] : ((generous(X0) | ~rich(X0) | ~brave(X0)) & (brave(X0) | (~generous(X0) & rich(X0)))) [flattening 42]
44. ! [X0] : ((generous(X0) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | ~generous(X0))) [nnf transformation 4]
45. ! [X0] : ((generous(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | ~generous(X0))) [flattening 44]
49. ! [X0] : (((~generous(X0) & strong(X0)) | (strong(X0) | tall(X0))) & ((~strong(X0) & ~tall(X0)) | (generous(X0) | ~strong(X0)))) [nnf transformation 7]
50. ! [X0] : (((~generous(X0) & strong(X0)) | strong(X0) | tall(X0)) & ((~strong(X0) & ~tall(X0)) | generous(X0) | ~strong(X0))) [flattening 49]
52. (? [X0] : (~brave(X0) & humble(X0)) | (strong(alice) | ~rich(alice))) & ((~strong(alice) & rich(alice)) | ! [X0] : (brave(X0) | ~humble(X0))) [nnf transformation 10]
53. (? [X0] : (~brave(X0) & humble(X0)) | strong(alice) | ~rich(alice)) & ((~strong(alice) & rich(alice)) | ! [X0] : (brave(X0) | ~humble(X0))) [flattening 52]
54. (? [X0] : (~brave(X0) & humble(X0)) | strong(alice) | ~rich(alice)) & ((~strong(alice) & rich(alice)) | ! [X1] : (brave(X1) | ~humble(X1))) [rectify 53]
55. ? [X0] : (~brave(X0) & humble(X0)) => (~brave(sK1) & humble(sK1)) [choice axiom]
56. ((~brave(sK1) & humble(sK1)) | strong(alice) | ~rich(alice)) & ((~strong(alice) & rich(alice)) | ! [X1] : (brave(X1) | ~humble(X1))) [skolemisation 54,55]
79. brave(X0) | ~generous(X0) [cnf transformation 43]
81. ~brave(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 45]
83. generous(X0) | brave(X0) [cnf transformation 45]
90. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 50]
104. ~brave(sK1) | strong(alice) | ~rich(alice) [cnf transformation 56]
132. rich(alice) [cnf transformation 24]
136. ~strong(X0) | generous(X0) [duplicate literal removal 90]
156. brave(X0) [subsumption resolution 83,79]
157. ~strong(X0) | ~generous(X0) [subsumption resolution 81,156]
173. 8 <=> rich(alice) [avatar definition]
188. ~strong(X0) [subsumption resolution 136,157]
207. strong(alice) | ~rich(alice) [subsumption resolution 104,156]
208. ~rich(alice) [subsumption resolution 207,188]
209. ~8 [avatar split clause 208,173]
242. 8 [avatar split clause 132,173]
243. $false [avatar sat refutation 209,242]
% SZS output end Proof for 501245809712227690689396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is brave then someone is not curious and vice versa.
If someone is brave or not old then someone is curious.
If fred is not humble or not generous then someone is old.
Everyone who is either not creative or brave is either old or curious and vice versa.
If someone is either not patient or rich then someone is either not brave or happy.
If someone is both curious and happy then someone is patient or tall and vice versa.
If fred is funny then fred is kind.
Everyone who is not calm is either brave or curious and vice versa.
If fred is both rich and not humble then someone is either not patient or curious.
Everyone who is happy is generous and vice versa.
Everyone who is creative or not patient is either old or brave.
If susan is both funny and not generous then someone is patient or not generous.
Everyone who is both happy and not quiet is both happy and not patient and vice versa.
If john is not kind or old then susan is not humble and vice versa.
Everyone who is either not happy or not quiet is brave.
Everyone who is either not curious or not creative is either not wise or not kind.
Someone is both not old and not quiet.
Mary is both wise and not quiet.
Lucy is both not creative and quiet.
Someone is either creative or not brave.
John is funny or not patient.
Someone is both not patient and wise.
Someone is quiet.
Someone is both not old and calm. | Fred is generous. | neutral | ((brave(susan))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:(curious(X))))&
(((~humble(fred)|~generous(fred)))=>(?[X]:(old(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:((~brave(X)<~>happy(X)))))&
((?[X]:((curious(X)&happy(X))))<=>(?[X]:((patient(X)|tall(X)))))&
((funny(fred))=>(kind(fred)))&
(![X]:(~calm(X)<=>(brave(X)<~>curious(X))))&
(((rich(fred)&~humble(fred)))=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>(old(X)<~>brave(X))))&
(((funny(susan)&~generous(susan)))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(happy(X)&~patient(X))))&
(((~kind(john)|old(john)))<=>(~humble(susan)))&
(![X]:((~happy(X)<~>~quiet(X))=>brave(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~wise(X)<~>~kind(X))))&
(?[X]:((~old(X)&~quiet(X))))&
((wise(mary)&~quiet(mary)))&
((~creative(lucy)&quiet(lucy)))&
(?[X]:((creative(X)<~>~brave(X))))&
((funny(john)|~patient(john)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)&calm(X)))) | generous(fred) | [] | null | 0 |
Everyone who is either not kind or wise is either kind or humble. If lucy is either not curious or humble then alice is kind or not tall. If susan is both not patient and not humble then paul is either rich or not happy and vice versa. Everyone who is not strong is patient and vice versa. If susan is either tall or wise then lucy is humble or not kind. Everyone who is patient or funny is both not humble and not tall. Everyone who is both not happy and not old is both not patient and generous and vice versa. Everyone who is either not brave or old is either wise or patient. Everyone who is both old and not brave is tall or happy and vice versa. Everyone who is either not creative or generous is either not creative or kind and vice versa. If fred is both not tall and not wise then lucy is both humble and patient. Everyone who is either strong or not rich is both not quiet and happy and vice versa. If someone is either not patient or not tall then fred is humble or not tall and vice versa. Everyone who is both kind and curious is both not wise and not kind and vice versa. If someone is both not brave and not humble then paul is not humble. If lucy is generous then someone is either not creative or old. Someone is not humble or not happy. John is both not happy and not generous. Susan is not kind or not humble. John is both not generous and humble. Someone is either not generous or not patient. Someone is either quiet or not patient. Susan is not creative or rich. | Fred is not wise. | contradiction | (![X]:((~kind(X)<~>wise(X))=>(kind(X)<~>humble(X))))&
(((~curious(lucy)<~>humble(lucy)))=>((kind(alice)|~tall(alice))))&
(((~patient(susan)&~humble(susan)))<=>((rich(paul)<~>~happy(paul))))&
(![X]:(~strong(X)<=>patient(X)))&
(((tall(susan)<~>wise(susan)))=>((humble(lucy)|~kind(lucy))))&
(![X]:((patient(X)|funny(X))=>(~humble(X)&~tall(X))))&
(![X]:((~happy(X)&~old(X))<=>(~patient(X)&generous(X))))&
(![X]:((~brave(X)<~>old(X))=>(wise(X)<~>patient(X))))&
(![X]:((old(X)&~brave(X))<=>(tall(X)|happy(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~creative(X)<~>kind(X))))&
(((~tall(fred)&~wise(fred)))=>((humble(lucy)&patient(lucy))))&
(![X]:((strong(X)<~>~rich(X))<=>(~quiet(X)&happy(X))))&
((?[X]:((~patient(X)<~>~tall(X))))<=>((humble(fred)|~tall(fred))))&
(![X]:((kind(X)&curious(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~brave(X)&~humble(X))))=>(~humble(paul)))&
((generous(lucy))=>(?[X]:((~creative(X)<~>old(X)))))&
(?[X]:((~humble(X)|~happy(X))))&
((~happy(john)&~generous(john)))&
((~kind(susan)|~humble(susan)))&
((~generous(john)&humble(john)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(?[X]:((quiet(X)<~>~patient(X))))&
((~creative(susan)|rich(susan))) | ~wise(fred) | [
"p5",
"p6",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3529807142047507071762174
% SZS output start Proof for 3529807142047507071762174
6. ! [X0] : ((funny(X0) | patient(X0)) => (~tall(X0) & ~humble(X0))) [input p5]
7. ! [X0] : ((~old(X0) & ~happy(X0)) <=> (generous(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((~brave(X0) & old(X0)) <=> (happy(X0) | tall(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (~creative(X0) <~> kind(X0))) [input p9]
11. (~wise(fred) & ~tall(fred)) => (patient(lucy) & humble(lucy)) [input p10]
14. ! [X0] : ((curious(X0) & kind(X0)) <=> (~kind(X0) & ~wise(X0))) [input p13]
24. ~wise(fred) [input hypothesis]
25. ! [X0] : (patient(X0) => (~tall(X0) & ~humble(X0))) [pure predicate removal 6]
31. ! [X0] : ((~tall(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 25]
33. (patient(lucy) & humble(lucy)) | (wise(fred) | tall(fred)) [ennf transformation 11]
34. (patient(lucy) & humble(lucy)) | wise(fred) | tall(fred) [flattening 33]
43. ! [X0] : (((~old(X0) & ~happy(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (old(X0) | happy(X0)))) [nnf transformation 7]
44. ! [X0] : (((~old(X0) & ~happy(X0)) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | old(X0) | happy(X0))) [flattening 43]
46. ! [X0] : (((~brave(X0) & old(X0)) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 9]
47. ! [X0] : (((~brave(X0) & old(X0)) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | brave(X0) | ~old(X0))) [flattening 46]
48. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 10]
56. ! [X0] : (((curious(X0) & kind(X0)) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | (~curious(X0) | ~kind(X0)))) [nnf transformation 14]
57. ! [X0] : (((curious(X0) & kind(X0)) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | ~curious(X0) | ~kind(X0))) [flattening 56]
85. ~patient(X0) | ~humble(X0) [cnf transformation 31]
86. ~patient(X0) | ~tall(X0) [cnf transformation 31]
90. ~generous(X0) | ~old(X0) | patient(X0) [cnf transformation 44]
96. ~tall(X0) | old(X0) [cnf transformation 47]
102. ~kind(X0) | creative(X0) | generous(X0) | creative(X0) [cnf transformation 48]
105. generous(X0) | ~creative(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 48]
108. humble(lucy) | wise(fred) | tall(fred) [cnf transformation 34]
109. patient(lucy) | wise(fred) | tall(fred) [cnf transformation 34]
124. kind(X0) | kind(X0) | wise(X0) [cnf transformation 57]
140. ~wise(fred) [cnf transformation 24]
142. wise(X0) | kind(X0) [duplicate literal removal 124]
144. ~kind(X0) | creative(X0) | generous(X0) [duplicate literal removal 102]
145. generous(X0) | ~creative(X0) | ~kind(X0) [duplicate literal removal 105]
150. 1 <=> humble(lucy) [avatar definition]
151. humble(lucy) <- (1) [avatar component clause 150]
203. ~kind(X0) | generous(X0) [subsumption resolution 144,145]
206. 12 <=> tall(fred) [avatar definition]
208. tall(fred) <- (12) [avatar component clause 206]
210. 13 <=> wise(fred) [avatar definition]
211. ~wise(fred) <- (~13) [avatar component clause 210]
214. 14 <=> patient(lucy) [avatar definition]
216. patient(lucy) <- (14) [avatar component clause 214]
217. 12 | 13 | 14 [avatar split clause 109,214,210,206]
218. 12 | 13 | 1 [avatar split clause 108,150,210,206]
308. ~13 [avatar split clause 140,210]
313. old(fred) <- (12) [resolution 96,208]
314. kind(fred) <- (~13) [resolution 142,211]
315. generous(fred) <- (~13) [resolution 203,314]
332. 34 <=> patient(fred) [avatar definition]
334. patient(fred) <- (34) [avatar component clause 332]
341. ~old(fred) | patient(fred) <- (~13) [resolution 90,315]
344. patient(fred) <- (12, ~13) [subsumption resolution 341,313]
345. 34 | ~12 | 13 [avatar split clause 344,210,206,332]
353. ~humble(lucy) <- (14) [resolution 216,85]
354. $false <- (1, 14) [subsumption resolution 353,151]
355. ~1 | ~14 [avatar contradiction clause 354]
362. ~tall(fred) <- (34) [resolution 334,86]
364. $false <- (12, 34) [subsumption resolution 362,208]
365. ~12 | ~34 [avatar contradiction clause 364]
368. $false [avatar sat refutation 217,218,308,345,355,365]
% SZS output end Proof for 3529807142047507071762174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and funny is both funny and not generous.
If lucy is both not old and not funny then someone is both brave and not generous and vice versa.
If someone is either not patient or not funny then someone is both not strong and not happy and vice versa.
If someone is either brave or not tall then someone is not rich.
Everyone who is both patient and funny is generous and vice versa.
Everyone who is not brave is not creative or not brave.
If mary is either not tall or happy then someone is not rich or not wise.
Everyone who is not old is either creative or not calm.
If someone is either not creative or creative then someone is wise or not tall.
Everyone who is not strong is old or not rich.
If paul is both not generous and calm then someone is either not quiet or old and vice versa.
If lucy is kind or not old then someone is strong or kind.
If fred is creative or curious then susan is not quiet or not tall.
Everyone who is both not curious and old is not calm and vice versa.
Everyone who is creative is quiet and vice versa.
Everyone who is calm is both rich and not rich and vice versa.
Someone is not kind.
Someone is either not rich or not funny.
Alice is both not humble and not curious.
Someone is rich.
Lucy is curious or brave.
Someone is either not rich or not kind. | Lucy is generous. | entailment | (![X]:((~humble(X)&funny(X))=>(funny(X)&~generous(X))))&
(((~old(lucy)&~funny(lucy)))<=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((~strong(X)&~happy(X)))))&
((?[X]:((brave(X)<~>~tall(X))))=>(?[X]:(~rich(X))))&
(![X]:((patient(X)&funny(X))<=>generous(X)))&
(![X]:(~brave(X)=>(~creative(X)|~brave(X))))&
(((~tall(mary)<~>happy(mary)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~old(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~strong(X)=>(old(X)|~rich(X))))&
(((~generous(paul)&calm(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((kind(lucy)|~old(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(((creative(fred)|curious(fred)))=>((~quiet(susan)|~tall(susan))))&
(![X]:((~curious(X)&old(X))<=>~calm(X)))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:(calm(X)<=>(rich(X)&~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((~humble(alice)&~curious(alice)))&
(?[X]:(rich(X)))&
((curious(lucy)|brave(lucy)))&
(?[X]:((~rich(X)<~>~kind(X)))) | generous(lucy) | [
"p1",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4494030457602796527775123
% SZS output start Proof for 4494030457602796527775123
2. (~funny(lucy) & ~old(lucy)) <=> ? [X0] : (~generous(X0) & brave(X0)) [input p1]
14. ! [X0] : ((old(X0) & ~curious(X0)) <=> ~calm(X0)) [input p13]
16. ! [X0] : (calm(X0) <=> (~rich(X0) & rich(X0))) [input p15]
21. brave(lucy) | curious(lucy) [input p20]
23. ~generous(lucy) [input hypothesis]
40. ((~funny(lucy) & ~old(lucy)) | ! [X0] : (generous(X0) | ~brave(X0))) & (? [X0] : (~generous(X0) & brave(X0)) | (funny(lucy) | old(lucy))) [nnf transformation 2]
41. ((~funny(lucy) & ~old(lucy)) | ! [X0] : (generous(X0) | ~brave(X0))) & (? [X0] : (~generous(X0) & brave(X0)) | funny(lucy) | old(lucy)) [flattening 40]
42. ((~funny(lucy) & ~old(lucy)) | ! [X0] : (generous(X0) | ~brave(X0))) & (? [X1] : (~generous(X1) & brave(X1)) | funny(lucy) | old(lucy)) [rectify 41]
43. ? [X1] : (~generous(X1) & brave(X1)) => (~generous(sK0) & brave(sK0)) [choice axiom]
44. ((~funny(lucy) & ~old(lucy)) | ! [X0] : (generous(X0) | ~brave(X0))) & ((~generous(sK0) & brave(sK0)) | funny(lucy) | old(lucy)) [skolemisation 42,43]
71. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~old(X0) | curious(X0)))) [nnf transformation 14]
72. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~old(X0) | curious(X0))) [flattening 71]
74. ! [X0] : ((calm(X0) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 16]
75. ! [X0] : ((calm(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [flattening 74]
90. ~old(lucy) | generous(X0) | ~brave(X0) [cnf transformation 44]
122. ~curious(X0) | calm(X0) [cnf transformation 72]
123. calm(X0) | old(X0) [cnf transformation 72]
126. rich(X0) | ~calm(X0) [cnf transformation 75]
127. ~calm(X0) | ~rich(X0) [cnf transformation 75]
135. brave(lucy) | curious(lucy) [cnf transformation 21]
138. ~generous(lucy) [cnf transformation 23]
142. 1 <=> ! [X0] : (generous(X0) | ~brave(X0)) [avatar definition]
143. ~brave(X0) | generous(X0) <- (1) [avatar component clause 142]
150. 3 <=> old(lucy) [avatar definition]
152. ~old(lucy) <- (~3) [avatar component clause 150]
153. 1 | ~3 [avatar split clause 90,150,142]
301. ~calm(X0) [subsumption resolution 126,127]
313. 39 <=> curious(lucy) [avatar definition]
315. curious(lucy) <- (39) [avatar component clause 313]
317. 40 <=> brave(lucy) [avatar definition]
319. brave(lucy) <- (40) [avatar component clause 317]
320. 39 | 40 [avatar split clause 135,317,313]
333. calm(lucy) <- (39) [resolution 122,315]
334. $false <- (39) [subsumption resolution 333,301]
335. ~39 [avatar contradiction clause 334]
336. old(X0) [resolution 123,301]
337. $false <- (~3) [resolution 336,152]
340. 3 [avatar contradiction clause 337]
343. generous(lucy) <- (1, 40) [resolution 143,319]
346. $false <- (1, 40) [subsumption resolution 343,138]
347. ~1 | ~40 [avatar contradiction clause 346]
348. $false [avatar sat refutation 153,320,335,340,347]
% SZS output end Proof for 4494030457602796527775123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either rich or not curious and vice versa.
Everyone who is either brave or funny is not kind.
Everyone who is not funny or generous is both not humble and not kind and vice versa.
Everyone who is either not rich or curious is both not humble and not curious and vice versa.
If susan is wise or creative then lucy is either not tall or not patient and vice versa.
Everyone who is creative is either not kind or not patient and vice versa.
Everyone who is either not old or not kind is either rich or brave.
Everyone who is either not quiet or brave is not quiet or creative and vice versa.
If alice is rich then susan is either wise or generous.
Everyone who is calm or not patient is both rich and not happy and vice versa.
Everyone who is not calm is not wise or not humble.
Everyone who is not rich or rich is either not tall or brave and vice versa.
If mary is both not patient and curious then someone is brave or not old.
Everyone who is both funny and not creative is both not curious and not humble and vice versa.
Everyone who is not wise is either calm or not tall and vice versa.
If someone is brave or rich then fred is strong and vice versa.
Fred is tall or patient.
Someone is not curious.
Alice is humble or not humble.
Paul is either curious or not brave.
Someone is not generous.
Lucy is happy.
Someone is either not old or not wise. | Alice is curious. | neutral | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>funny(X))=>~kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~humble(X)&~curious(X))))&
(((wise(susan)|creative(susan)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:(creative(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)<~>~kind(X))=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>brave(X))<=>(~quiet(X)|creative(X))))&
((rich(alice))=>((wise(susan)<~>generous(susan))))&
(![X]:((calm(X)|~patient(X))<=>(rich(X)&~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|rich(X))<=>(~tall(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((brave(X)|rich(X))))<=>(strong(fred)))&
((tall(fred)|patient(fred)))&
(?[X]:(~curious(X)))&
((humble(alice)|~humble(alice)))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~generous(X)))&
(happy(lucy))&
(?[X]:((~old(X)<~>~wise(X)))) | curious(alice) | [] | null | 0 |
Everyone who is old is not tall or old.
If someone is both old and not tall then someone is both calm and curious and vice versa.
If john is not wise then lucy is both not happy and calm.
Everyone who is either not wise or brave is patient.
If someone is not funny or not quiet then john is wise or not creative and vice versa.
Everyone who is both calm and not patient is not funny and vice versa.
Everyone who is not rich is not old and vice versa.
Everyone who is quiet or brave is either strong or wise and vice versa.
If alice is either rich or not tall then alice is both strong and quiet.
If lucy is either not tall or quiet then someone is not tall or generous and vice versa.
If fred is both old and quiet then alice is not kind or not humble and vice versa.
If susan is tall then someone is not creative.
Everyone who is not happy is both brave and quiet and vice versa.
If someone is happy or tall then alice is both not kind and not brave.
Everyone who is not wise is both wise and rich.
If alice is either not patient or brave then someone is either not creative or brave.
John is not tall or quiet.
Lucy is not quiet.
Paul is both not tall and not brave.
Someone is not generous.
Someone is kind.
Someone is not strong.
Lucy is either not wise or not rich.
Someone is both tall and old. | Paul is wise. | entailment | (![X]:(old(X)=>(~tall(X)|old(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:((calm(X)&curious(X)))))&
((~wise(john))=>((~happy(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>brave(X))=>patient(X)))&
((?[X]:((~funny(X)|~quiet(X))))<=>((wise(john)|~creative(john))))&
(![X]:((calm(X)&~patient(X))<=>~funny(X)))&
(![X]:(~rich(X)<=>~old(X)))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)<~>wise(X))))&
(((rich(alice)<~>~tall(alice)))=>((strong(alice)&quiet(alice))))&
(((~tall(lucy)<~>quiet(lucy)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((old(fred)&quiet(fred)))<=>((~kind(alice)|~humble(alice))))&
((tall(susan))=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)<=>(brave(X)&quiet(X))))&
((?[X]:((happy(X)|tall(X))))=>((~kind(alice)&~brave(alice))))&
(![X]:(~wise(X)=>(wise(X)&rich(X))))&
(((~patient(alice)<~>brave(alice)))=>(?[X]:((~creative(X)<~>brave(X)))))&
((~tall(john)|quiet(john)))&
(~quiet(lucy))&
((~tall(paul)&~brave(paul)))&
(?[X]:(~generous(X)))&
(?[X]:(kind(X)))&
(?[X]:(~strong(X)))&
((~wise(lucy)<~>~rich(lucy)))&
(?[X]:((tall(X)&old(X)))) | wise(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4539472120847963756790738
% SZS output start Proof for 4539472120847963756790738
15. ! [X0] : (~wise(X0) => (rich(X0) & wise(X0))) [input p14]
25. ~wise(paul) [input hypothesis]
36. ! [X0] : ((rich(X0) & wise(X0)) | wise(X0)) [ennf transformation 15]
121. wise(X0) | wise(X0) [cnf transformation 36]
138. ~wise(paul) [cnf transformation 25]
139. wise(X0) [duplicate literal removal 121]
321. $false [subsumption resolution 138,139]
% SZS output end Proof for 4539472120847963756790738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not happy is old or not creative and vice versa. Everyone who is not kind is either calm or wise. Everyone who is rich or not wise is curious or not calm and vice versa. Everyone who is both rich and not quiet is both patient and not rich and vice versa. If someone is quiet then someone is both not tall and happy. If alice is generous or not tall then someone is generous and vice versa. Everyone who is not wise or not generous is funny. If susan is either wise or not wise then someone is either curious or brave and vice versa. If someone is both patient and not generous then someone is tall or kind. Everyone who is both kind and humble is either tall or happy. Everyone who is creative is kind and vice versa. Everyone who is rich or not tall is not old. If someone is calm or patient then someone is not curious and vice versa. If someone is wise or not curious then susan is both not humble and not old and vice versa. If paul is either not tall or not patient then someone is either not quiet or wise and vice versa. If paul is either not generous or funny then someone is either tall or kind. John is not wise or not happy. Fred is both not generous and not creative. Someone is both not creative and not strong. Alice is either not kind or brave. Someone is not generous or not tall. Susan is not tall or patient. John is either creative or curious. Someone is both not funny and humble. | Fred is not curious. | contradiction | (![X]:((kind(X)<~>~happy(X))<=>(old(X)|~creative(X))))&
(![X]:(~kind(X)=>(calm(X)<~>wise(X))))&
(![X]:((rich(X)|~wise(X))<=>(curious(X)|~calm(X))))&
(![X]:((rich(X)&~quiet(X))<=>(patient(X)&~rich(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~tall(X)&happy(X)))))&
(((generous(alice)|~tall(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|~generous(X))=>funny(X)))&
(((wise(susan)<~>~wise(susan)))<=>(?[X]:((curious(X)<~>brave(X)))))&
((?[X]:((patient(X)&~generous(X))))=>(?[X]:((tall(X)|kind(X)))))&
(![X]:((kind(X)&humble(X))=>(tall(X)<~>happy(X))))&
(![X]:(creative(X)<=>kind(X)))&
(![X]:((rich(X)|~tall(X))=>~old(X)))&
((?[X]:((calm(X)|patient(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|~curious(X))))<=>((~humble(susan)&~old(susan))))&
(((~tall(paul)<~>~patient(paul)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(((~generous(paul)<~>funny(paul)))=>(?[X]:((tall(X)<~>kind(X)))))&
((~wise(john)|~happy(john)))&
((~generous(fred)&~creative(fred)))&
(?[X]:((~creative(X)&~strong(X))))&
((~kind(alice)<~>brave(alice)))&
(?[X]:((~generous(X)|~tall(X))))&
((~tall(susan)|patient(susan)))&
((creative(john)<~>curious(john)))&
(?[X]:((~funny(X)&humble(X)))) | ~curious(fred) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 641148146440149132553210
% SZS output start Proof for 641148146440149132553210
1. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (~creative(X0) | old(X0))) [input p0]
2. ! [X0] : (~kind(X0) => (calm(X0) <~> wise(X0))) [input p1]
3. ! [X0] : ((~wise(X0) | rich(X0)) <=> (~calm(X0) | curious(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & rich(X0)) <=> (~rich(X0) & patient(X0))) [input p3]
5. ? [X0] : quiet(X0) => ? [X0] : (happy(X0) & ~tall(X0)) [input p4]
11. ! [X0] : (creative(X0) <=> kind(X0)) [input p10]
12. ! [X0] : ((~tall(X0) | rich(X0)) => ~old(X0)) [input p11]
18. ~creative(fred) & ~generous(fred) [input p17]
25. ~curious(fred) [input hypothesis]
26. ? [X0] : quiet(X0) => ? [X1] : (happy(X1) & ~tall(X1)) [rectify 5]
30. ! [X0] : ((calm(X0) <~> wise(X0)) | kind(X0)) [ennf transformation 2]
31. ? [X1] : (happy(X1) & ~tall(X1)) | ! [X0] : ~quiet(X0) [ennf transformation 26]
36. ! [X0] : (~old(X0) | (tall(X0) & ~rich(X0))) [ennf transformation 12]
38. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (creative(X0) & ~old(X0))) & ((~creative(X0) | old(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 1]
39. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (creative(X0) & ~old(X0))) & (~creative(X0) | old(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 38]
40. ! [X0] : (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | kind(X0)) [nnf transformation 30]
41. ! [X0] : (((~wise(X0) | rich(X0)) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | (wise(X0) & ~rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((~wise(X0) | rich(X0) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | (wise(X0) & ~rich(X0)))) [flattening 41]
43. ! [X0] : (((~quiet(X0) & rich(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (quiet(X0) | ~rich(X0)))) [nnf transformation 4]
44. ! [X0] : (((~quiet(X0) & rich(X0)) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | quiet(X0) | ~rich(X0))) [flattening 43]
45. ? [X0] : (happy(X0) & ~tall(X0)) | ! [X1] : ~quiet(X1) [rectify 31]
46. ? [X0] : (happy(X0) & ~tall(X0)) => (happy(sK0) & ~tall(sK0)) [choice axiom]
47. (happy(sK0) & ~tall(sK0)) | ! [X1] : ~quiet(X1) [skolemisation 45,46]
61. ! [X0] : ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))) [nnf transformation 11]
87. ~creative(X0) | old(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 39]
90. ~happy(X0) | kind(X0) | creative(X0) [cnf transformation 39]
93. wise(X0) | calm(X0) | kind(X0) [cnf transformation 40]
94. ~wise(X0) | ~calm(X0) | kind(X0) [cnf transformation 40]
96. ~calm(X0) | curious(X0) | wise(X0) [cnf transformation 42]
98. ~wise(X0) | rich(X0) | calm(X0) [cnf transformation 42]
100. ~rich(X0) | quiet(X0) | ~rich(X0) [cnf transformation 44]
103. ~tall(sK0) | ~quiet(X1) [cnf transformation 47]
104. happy(sK0) | ~quiet(X1) [cnf transformation 47]
121. ~creative(X0) | kind(X0) [cnf transformation 61]
122. ~kind(X0) | creative(X0) [cnf transformation 61]
124. ~old(X0) | tall(X0) [cnf transformation 36]
147. ~creative(fred) [cnf transformation 18]
157. ~curious(fred) [cnf transformation 25]
162. ~rich(X0) | quiet(X0) [duplicate literal removal 100]
165. 1 <=> ! [X1] : ~quiet(X1) [avatar definition]
166. ~quiet(X1) <- (1) [avatar component clause 165]
168. 2 <=> happy(sK0) [avatar definition]
170. happy(sK0) <- (2) [avatar component clause 168]
171. 1 | 2 [avatar split clause 104,168,165]
173. 3 <=> tall(sK0) [avatar definition]
175. ~tall(sK0) <- (~3) [avatar component clause 173]
176. 1 | ~3 [avatar split clause 103,173,165]
379. kind(sK0) | creative(sK0) <- (2) [resolution 90,170]
380. creative(sK0) <- (2) [subsumption resolution 379,122]
381. kind(sK0) <- (2) [resolution 380,121]
453. rich(X0) | calm(X0) | calm(X0) | kind(X0) [resolution 98,93]
455. rich(X0) | calm(X0) | kind(X0) [duplicate literal removal 453]
482. old(sK0) | ~happy(sK0) | ~kind(sK0) <- (2) [resolution 87,380]
484. old(sK0) | ~kind(sK0) <- (2) [subsumption resolution 482,170]
485. old(sK0) <- (2) [subsumption resolution 484,381]
508. quiet(X1) | kind(X1) | calm(X1) [resolution 455,162]
515. tall(sK0) <- (2) [resolution 485,124]
516. $false <- (2, ~3) [subsumption resolution 515,175]
517. ~2 | 3 [avatar contradiction clause 516]
528. calm(X0) | kind(X0) <- (1) [resolution 508,166]
558. curious(X0) | kind(X0) | wise(X0) <- (1) [resolution 528,96]
561. kind(fred) | wise(fred) <- (1) [resolution 558,157]
565. 67 <=> wise(fred) [avatar definition]
567. wise(fred) <- (67) [avatar component clause 565]
569. 68 <=> kind(fred) [avatar definition]
571. kind(fred) <- (68) [avatar component clause 569]
572. 67 | 68 | ~1 [avatar split clause 561,165,569,565]
602. ~calm(fred) | kind(fred) <- (67) [resolution 567,94]
612. kind(fred) <- (1, 67) [subsumption resolution 602,528]
613. 68 | ~1 | ~67 [avatar split clause 612,565,165,569]
616. creative(fred) <- (68) [resolution 571,122]
618. $false <- (68) [subsumption resolution 616,147]
619. ~68 [avatar contradiction clause 618]
620. $false [avatar sat refutation 171,176,517,572,613,619]
% SZS output end Proof for 641148146440149132553210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either brave or strong.
Everyone who is not tall or not brave is not tall or not quiet and vice versa.
Everyone who is either not quiet or not generous is not patient or not old and vice versa.
If paul is both not quiet and not patient then mary is both curious and old.
Everyone who is both not rich and curious is not calm or humble.
Everyone who is both strong and brave is both patient and not tall.
If fred is not tall then lucy is either not brave or humble.
If susan is either happy or not tall then someone is both not wise and not creative and vice versa.
If fred is both calm and not strong then someone is either strong or not patient.
If fred is funny or not strong then alice is both not old and not funny.
Everyone who is either not funny or creative is not creative and vice versa.
If someone is generous or old then paul is either not calm or calm and vice versa.
Everyone who is both brave and not tall is either not curious or funny and vice versa.
Everyone who is both not calm and not happy is quiet or not kind and vice versa.
Everyone who is not brave is either not happy or not tall and vice versa.
Everyone who is funny or not patient is both wise and creative and vice versa.
Susan is not brave or humble.
Paul is both not brave and not quiet.
John is both patient and not calm.
Susan is both not calm and strong.
Someone is both happy and not generous.
Someone is either not strong or not quiet.
Alice is wise or patient.
Alice is not old. | John is patient. | entailment | (![X]:(~funny(X)=>(brave(X)<~>strong(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~tall(X)|~quiet(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~patient(X)|~old(X))))&
(((~quiet(paul)&~patient(paul)))=>((curious(mary)&old(mary))))&
(![X]:((~rich(X)&curious(X))=>(~calm(X)|humble(X))))&
(![X]:((strong(X)&brave(X))=>(patient(X)&~tall(X))))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~calm(X)&~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~tall(X))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&creative(X))))&
((~brave(susan)|humble(susan)))&
((~brave(paul)&~quiet(paul)))&
((patient(john)&~calm(john)))&
((~calm(susan)&strong(susan)))&
(?[X]:((happy(X)&~generous(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((wise(alice)|patient(alice)))&
(~old(alice)) | patient(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1131311440160558381254285
% SZS output start Proof for 1131311440160558381254285
19. ~calm(john) & patient(john) [input p18]
25. ~patient(john) [input hypothesis]
129. patient(john) [cnf transformation 19]
139. ~patient(john) [cnf transformation 25]
275. $false [subsumption resolution 139,129]
% SZS output end Proof for 1131311440160558381254285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then john is not brave.
If someone is either not brave or not strong then mary is both happy and not generous and vice versa.
If mary is quiet then someone is both brave and rich.
Everyone who is either not brave or happy is both not happy and humble.
Everyone who is either not humble or creative is both patient and not old and vice versa.
If someone is not funny then someone is calm and vice versa.
If alice is either not kind or not rich then john is not creative or not old and vice versa.
If paul is both not rich and curious then someone is both quiet and tall and vice versa.
If susan is both rich and not kind then someone is not calm.
If someone is both not rich and not quiet then someone is not old.
Everyone who is both not quiet and not strong is old.
Everyone who is not patient or not funny is not rich or not creative.
Everyone who is both curious and rich is tall and vice versa.
If someone is strong then someone is patient or old.
Everyone who is either rich or quiet is both not kind and funny.
Someone is happy or calm.
Lucy is either not humble or rich.
Someone is either not kind or patient.
Lucy is rich.
Someone is curious or humble.
Susan is either not tall or curious.
Susan is both not humble and not funny.
John is either humble or not funny. | Susan is humble. | contradiction | ((?[X]:(kind(X)))=>(~brave(john)))&
((?[X]:((~brave(X)<~>~strong(X))))<=>((happy(mary)&~generous(mary))))&
((quiet(mary))=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~brave(X)<~>happy(X))=>(~happy(X)&humble(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(patient(X)&~old(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(calm(X))))&
(((~kind(alice)<~>~rich(alice)))<=>((~creative(john)|~old(john))))&
(((~rich(paul)&curious(paul)))<=>(?[X]:((quiet(X)&tall(X)))))&
(((rich(susan)&~kind(susan)))=>(?[X]:(~calm(X))))&
((?[X]:((~rich(X)&~quiet(X))))=>(?[X]:(~old(X))))&
(![X]:((~quiet(X)&~strong(X))=>old(X)))&
(![X]:((~patient(X)|~funny(X))=>(~rich(X)|~creative(X))))&
(![X]:((curious(X)&rich(X))<=>tall(X)))&
((?[X]:(strong(X)))=>(?[X]:((patient(X)|old(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(~kind(X)&funny(X))))&
(?[X]:((happy(X)|calm(X))))&
((~humble(lucy)<~>rich(lucy)))&
(?[X]:((~kind(X)<~>patient(X))))&
(rich(lucy))&
(?[X]:((curious(X)|humble(X))))&
((~tall(susan)<~>curious(susan)))&
((~humble(susan)&~funny(susan)))&
((humble(john)<~>~funny(john))) | humble(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6147958600610808795478059
% SZS output start Proof for 6147958600610808795478059
22. ~funny(susan) & ~humble(susan) [input p21]
24. humble(susan) [input hypothesis]
136. ~humble(susan) [cnf transformation 22]
140. humble(susan) [cnf transformation 24]
344. $false [subsumption resolution 140,136]
% SZS output end Proof for 6147958600610808795478059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not curious is either not rich or not creative. Everyone who is kind or not brave is not rich or not strong. If mary is either not patient or generous then john is both calm and not kind and vice versa. Everyone who is both not quiet and not wise is strong or not strong. Everyone who is not wise is not old or strong and vice versa. Everyone who is both patient and strong is both not generous and humble. Everyone who is not brave or not patient is either patient or not brave and vice versa. Everyone who is not calm is strong. Everyone who is both not creative and not rich is both funny and not wise. Everyone who is both not calm and not humble is both brave and old and vice versa. Everyone who is both not creative and not rich is either patient or humble and vice versa. Everyone who is old is quiet and vice versa. Everyone who is either not creative or calm is both tall and not wise and vice versa. Everyone who is kind or old is not wise or calm and vice versa. Everyone who is both not humble and strong is not creative or not generous. Everyone who is rich or kind is rich or patient. Mary is either rich or not calm. Susan is curious or not funny. Susan is both wise and not happy. Someone is either kind or old. Lucy is both strong and quiet. John is happy. Fred is not strong. John is not patient. | Mary is not patient. | entailment | (![X]:((~creative(X)|~curious(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((kind(X)|~brave(X))=>(~rich(X)|~strong(X))))&
(((~patient(mary)<~>generous(mary)))<=>((calm(john)&~kind(john))))&
(![X]:((~quiet(X)&~wise(X))=>(strong(X)|~strong(X))))&
(![X]:(~wise(X)<=>(~old(X)|strong(X))))&
(![X]:((patient(X)&strong(X))=>(~generous(X)&humble(X))))&
(![X]:((~brave(X)|~patient(X))<=>(patient(X)<~>~brave(X))))&
(![X]:(~calm(X)=>strong(X)))&
(![X]:((~creative(X)&~rich(X))=>(funny(X)&~wise(X))))&
(![X]:((~calm(X)&~humble(X))<=>(brave(X)&old(X))))&
(![X]:((~creative(X)&~rich(X))<=>(patient(X)<~>humble(X))))&
(![X]:(old(X)<=>quiet(X)))&
(![X]:((~creative(X)<~>calm(X))<=>(tall(X)&~wise(X))))&
(![X]:((kind(X)|old(X))<=>(~wise(X)|calm(X))))&
(![X]:((~humble(X)&strong(X))=>(~creative(X)|~generous(X))))&
(![X]:((rich(X)|kind(X))=>(rich(X)|patient(X))))&
((rich(mary)<~>~calm(mary)))&
((curious(susan)|~funny(susan)))&
((wise(susan)&~happy(susan)))&
(?[X]:((kind(X)<~>old(X))))&
((strong(lucy)&quiet(lucy)))&
(happy(john))&
(~strong(fred))&
(~patient(john)) | ~patient(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 195496712220199001792833
% SZS output start Proof for 195496712220199001792833
7. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> (patient(X0) <~> ~brave(X0))) [input p6]
25. patient(mary) [input hypothesis]
48. ! [X0] : (((~patient(X0) | ~brave(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (patient(X0) & brave(X0)))) [nnf transformation 7]
49. ! [X0] : ((~patient(X0) | ~brave(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (patient(X0) & brave(X0)))) [flattening 48]
81. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 49]
83. ~patient(X0) | ~brave(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 49]
123. patient(mary) [cnf transformation 25]
125. brave(X0) | ~patient(X0) [duplicate literal removal 81]
126. ~patient(X0) | ~brave(X0) [duplicate literal removal 83]
150. ~patient(X0) [subsumption resolution 125,126]
178. $false [subsumption resolution 123,150]
% SZS output end Proof for 195496712220199001792833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not tall is humble or generous and vice versa. Everyone who is rich or curious is generous and vice versa. Everyone who is calm or not funny is not old and vice versa. If susan is not rich or not calm then susan is not tall. Everyone who is not patient is not quiet or not patient and vice versa. Everyone who is both not strong and wise is both not brave and not kind. If lucy is either not creative or funny then lucy is not old. If someone is either curious or tall then someone is humble or creative. If john is quiet or not funny then someone is not kind. Everyone who is both not patient and not funny is creative. If someone is happy then alice is both not wise and tall. Everyone who is both not calm and rich is either not funny or not curious and vice versa. Everyone who is either not tall or not brave is both funny and not kind and vice versa. If fred is funny or humble then lucy is funny and vice versa. Everyone who is not rich or strong is either funny or not patient. Everyone who is both not happy and wise is tall or quiet and vice versa. John is both curious and not calm. Lucy is not patient or not strong. Someone is not curious. Someone is rich. Someone is either old or creative. John is either old or creative. Someone is both generous and not curious. Someone is not patient. | John is not calm. | entailment | (![X]:((~humble(X)&~tall(X))<=>(humble(X)|generous(X))))&
(![X]:((rich(X)|curious(X))<=>generous(X)))&
(![X]:((calm(X)|~funny(X))<=>~old(X)))&
(((~rich(susan)|~calm(susan)))=>(~tall(susan)))&
(![X]:(~patient(X)<=>(~quiet(X)|~patient(X))))&
(![X]:((~strong(X)&wise(X))=>(~brave(X)&~kind(X))))&
(((~creative(lucy)<~>funny(lucy)))=>(~old(lucy)))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:((humble(X)|creative(X)))))&
(((quiet(john)|~funny(john)))=>(?[X]:(~kind(X))))&
(![X]:((~patient(X)&~funny(X))=>creative(X)))&
((?[X]:(happy(X)))=>((~wise(alice)&tall(alice))))&
(![X]:((~calm(X)&rich(X))<=>(~funny(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>~brave(X))<=>(funny(X)&~kind(X))))&
(((funny(fred)|humble(fred)))<=>(funny(lucy)))&
(![X]:((~rich(X)|strong(X))=>(funny(X)<~>~patient(X))))&
(![X]:((~happy(X)&wise(X))<=>(tall(X)|quiet(X))))&
((curious(john)&~calm(john)))&
((~patient(lucy)|~strong(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:(rich(X)))&
(?[X]:((old(X)<~>creative(X))))&
((old(john)<~>creative(john)))&
(?[X]:((generous(X)&~curious(X))))&
(?[X]:(~patient(X))) | ~calm(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1164854574671097314912281
% SZS output start Proof for 1164854574671097314912281
17. ~calm(john) & curious(john) [input p16]
25. calm(john) [input hypothesis]
125. ~calm(john) [cnf transformation 17]
136. calm(john) [cnf transformation 25]
245. $false [subsumption resolution 136,125]
% SZS output end Proof for 1164854574671097314912281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not patient is both rich and not creative and vice versa. Everyone who is both humble and not kind is not wise or not rich. Everyone who is not tall is not happy. If john is both not quiet and not wise then someone is both not strong and not brave and vice versa. Everyone who is either patient or creative is either humble or tall and vice versa. Everyone who is tall or not generous is generous. If someone is old then lucy is curious. If someone is quiet then susan is both not rich and not creative and vice versa. Everyone who is either happy or not generous is either not kind or wise and vice versa. Everyone who is curious is creative or not rich. If someone is either curious or old then someone is both calm and not old and vice versa. Everyone who is not creative or not generous is either not happy or wise. If someone is generous or not generous then someone is not wise and vice versa. Everyone who is not brave is either not wise or generous and vice versa. If someone is tall then paul is both not kind and not quiet and vice versa. Everyone who is patient is not happy or not humble and vice versa. Alice is either wise or patient. Someone is brave. Someone is either tall or not funny. Someone is humble. Mary is not calm. Paul is either not quiet or not funny. Susan is not quiet or curious. | John is strong. | neutral | (![X]:((old(X)|~patient(X))<=>(rich(X)&~creative(X))))&
(![X]:((humble(X)&~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:(~tall(X)=>~happy(X)))&
(((~quiet(john)&~wise(john)))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((patient(X)<~>creative(X))<=>(humble(X)<~>tall(X))))&
(![X]:((tall(X)|~generous(X))=>generous(X)))&
((?[X]:(old(X)))=>(curious(lucy)))&
((?[X]:(quiet(X)))<=>((~rich(susan)&~creative(susan))))&
(![X]:((happy(X)<~>~generous(X))<=>(~kind(X)<~>wise(X))))&
(![X]:(curious(X)=>(creative(X)|~rich(X))))&
((?[X]:((curious(X)<~>old(X))))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((~creative(X)|~generous(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((generous(X)|~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)<~>generous(X))))&
((?[X]:(tall(X)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:(patient(X)<=>(~happy(X)|~humble(X))))&
((wise(alice)<~>patient(alice)))&
(?[X]:(brave(X)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:(humble(X)))&
(~calm(mary))&
((~quiet(paul)<~>~funny(paul)))&
((~quiet(susan)|curious(susan))) | strong(john) | [] | null | 0 |
Everyone who is not humble or not funny is not strong and vice versa. Everyone who is not rich or not creative is both generous and patient and vice versa. Everyone who is either not happy or not brave is both not curious and old. Everyone who is funny is rich and vice versa. Everyone who is not happy is not wise. Everyone who is not happy or not quiet is both brave and not old and vice versa. If someone is not tall then lucy is either not generous or not rich and vice versa. Everyone who is both not strong and not curious is both not calm and not funny and vice versa. If alice is both quiet and strong then someone is both not strong and not funny. If someone is both not calm and generous then someone is both not wise and brave and vice versa. Everyone who is funny or patient is both not strong and curious. If someone is both funny and calm then paul is not humble or calm and vice versa. If susan is old then susan is either strong or not creative. Everyone who is wise is both not patient and not generous. If someone is either generous or funny then lucy is funny. Everyone who is both wise and funny is not humble or quiet and vice versa. Alice is both old and creative. Someone is either not generous or not old. Alice is not patient. Lucy is not patient or strong. Someone is either funny or not calm. | Alice is rich. | entailment | (![X]:((~humble(X)|~funny(X))<=>~strong(X)))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
((?[X]:((generous(X)<~>funny(X))))=>(funny(lucy)))&
(![X]:((wise(X)&funny(X))<=>(~humble(X)|quiet(X))))&
((old(alice)&creative(alice)))&
(?[X]:((~generous(X)<~>~old(X))))&
(~patient(alice))&
((~patient(lucy)|strong(lucy)))&
(?[X]:((funny(X)<~>~calm(X)))) | rich(alice) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 554291764948108942445455
% SZS output start Proof for 554291764948108942445455
2. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p1]
19. ~patient(alice) [input p18]
22. ~rich(alice) [input hypothesis]
34. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 2]
35. ! [X0] : ((~creative(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [flattening 34]
73. patient(X0) | rich(X0) [cnf transformation 35]
126. ~patient(alice) [cnf transformation 19]
130. ~rich(alice) [cnf transformation 22]
264. rich(alice) [resolution 73,126]
266. $false [subsumption resolution 264,130]
% SZS output end Proof for 554291764948108942445455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not funny then someone is both not calm and patient and vice versa.
Everyone who is both patient and not curious is either not kind or wise and vice versa.
If susan is not brave then susan is both not brave and not funny.
If someone is not patient or generous then someone is both creative and wise and vice versa.
If mary is not strong then someone is both old and wise.
Everyone who is not kind or not curious is either calm or not funny.
If someone is not humble then someone is either humble or rich and vice versa.
Everyone who is either not calm or patient is not patient or kind and vice versa.
Everyone who is either not rich or curious is not calm or curious.
If someone is both not tall and curious then someone is not calm or not curious and vice versa.
If someone is not quiet or wise then someone is not happy and vice versa.
Everyone who is both old and not old is not calm or not curious and vice versa.
If john is not curious or not patient then john is both not calm and tall and vice versa.
Everyone who is either not generous or not happy is either not funny or quiet and vice versa.
Everyone who is not tall or not brave is either not creative or rich and vice versa.
Everyone who is not creative is either not creative or rich and vice versa.
Someone is not old.
Paul is both not rich and humble.
Someone is kind or not strong.
Lucy is either patient or rich.
Someone is calm.
Someone is either rich or not brave. | Paul is calm. | entailment | ((~funny(mary))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((patient(X)&~curious(X))<=>(~kind(X)<~>wise(X))))&
((~brave(susan))=>((~brave(susan)&~funny(susan))))&
((?[X]:((~patient(X)|generous(X))))<=>(?[X]:((creative(X)&wise(X)))))&
((~strong(mary))=>(?[X]:((old(X)&wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)<~>rich(X)))))&
(![X]:((~calm(X)<~>patient(X))<=>(~patient(X)|kind(X))))&
(![X]:((~rich(X)<~>curious(X))=>(~calm(X)|curious(X))))&
((?[X]:((~tall(X)&curious(X))))<=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:(~happy(X))))&
(![X]:((old(X)&~old(X))<=>(~calm(X)|~curious(X))))&
(((~curious(john)|~patient(john)))<=>((~calm(john)&tall(john))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~creative(X)<~>rich(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>rich(X))))&
(?[X]:(~old(X)))&
((~rich(paul)&humble(paul)))&
(?[X]:((kind(X)|~strong(X))))&
((patient(lucy)<~>rich(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((rich(X)<~>~brave(X)))) | calm(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7031564418971587203755752
% SZS output start Proof for 7031564418971587203755752
12. ! [X0] : ((~old(X0) & old(X0)) <=> (~curious(X0) | ~calm(X0))) [input p11]
23. ~calm(paul) [input hypothesis]
65. ! [X0] : (((~old(X0) & old(X0)) | (curious(X0) & calm(X0))) & ((~curious(X0) | ~calm(X0)) | (old(X0) | ~old(X0)))) [nnf transformation 12]
66. ! [X0] : (((~old(X0) & old(X0)) | (curious(X0) & calm(X0))) & (~curious(X0) | ~calm(X0) | old(X0) | ~old(X0))) [flattening 65]
126. old(X0) | calm(X0) [cnf transformation 66]
128. ~old(X0) | calm(X0) [cnf transformation 66]
162. ~calm(paul) [cnf transformation 23]
274. 25 <=> ! [X1] : calm(X1) [avatar definition]
275. calm(X1) <- (25) [avatar component clause 274]
321. calm(X0) [subsumption resolution 126,128]
322. 25 [avatar split clause 321,274]
364. $false <- (25) [resolution 275,162]
365. ~25 [avatar contradiction clause 364]
366. $false [avatar sat refutation 322,365]
% SZS output end Proof for 7031564418971587203755752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is creative or brave then someone is either old or kind and vice versa. Everyone who is tall is both quiet and not rich and vice versa. Everyone who is not calm is not patient and vice versa. If paul is either not quiet or patient then fred is both brave and not kind. If someone is quiet or tall then someone is not brave or humble. Everyone who is tall or happy is not wise. Everyone who is strong or not rich is not quiet or not funny and vice versa. Everyone who is calm or generous is wise or not creative. Everyone who is rich or curious is both not brave and not funny and vice versa. Everyone who is not creative or not kind is either not happy or humble and vice versa. Everyone who is humble or not rich is either old or not funny. Everyone who is not funny or patient is not old and vice versa. If fred is either not quiet or generous then someone is both humble and not funny and vice versa. Everyone who is not funny is both tall and not patient. If paul is happy then someone is either old or patient. Everyone who is generous is wise or not calm. Someone is patient or tall. John is either curious or tall. Someone is not tall or not happy. Someone is not wise or rich. Fred is both happy and not old. Paul is old or rich. | Paul is not patient. | entailment | (((creative(paul)|brave(paul)))<=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(quiet(X)&~rich(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(((~quiet(paul)<~>patient(paul)))=>((brave(fred)&~kind(fred))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((tall(X)|happy(X))=>~wise(X)))&
(![X]:((strong(X)|~rich(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((calm(X)|generous(X))=>(wise(X)|~creative(X))))&
(![X]:((rich(X)|curious(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((humble(X)|~rich(X))=>(old(X)<~>~funny(X))))&
(![X]:((~funny(X)|patient(X))<=>~old(X)))&
(((~quiet(fred)<~>generous(fred)))<=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:(~funny(X)=>(tall(X)&~patient(X))))&
((happy(paul))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(generous(X)=>(wise(X)|~calm(X))))&
(?[X]:((patient(X)|tall(X))))&
((curious(john)<~>tall(john)))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~wise(X)|rich(X))))&
((happy(fred)&~old(fred)))&
((old(paul)|rich(paul))) | ~patient(paul) | [
"p1",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1293805753216121810936849
% SZS output start Proof for 1293805753216121810936849
2. ! [X0] : (tall(X0) <=> (~rich(X0) & quiet(X0))) [input p1]
9. ! [X0] : ((curious(X0) | rich(X0)) <=> (~funny(X0) & ~brave(X0))) [input p8]
12. ! [X0] : ((patient(X0) | ~funny(X0)) <=> ~old(X0)) [input p11]
14. ! [X0] : (~funny(X0) => (~patient(X0) & tall(X0))) [input p13]
22. rich(paul) | old(paul) [input p21]
23. patient(paul) [input hypothesis]
33. ! [X0] : ((~patient(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
42. ! [X0] : ((tall(X0) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 2]
43. ! [X0] : ((tall(X0) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [flattening 42]
50. ! [X0] : (((curious(X0) | rich(X0)) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 9]
51. ! [X0] : ((curious(X0) | rich(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 50]
55. ! [X0] : (((patient(X0) | ~funny(X0)) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((patient(X0) | ~funny(X0) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [flattening 55]
78. ~rich(X0) | ~tall(X0) [cnf transformation 43]
97. ~funny(X0) | ~rich(X0) [cnf transformation 51]
111. ~patient(X0) | ~old(X0) [cnf transformation 56]
119. funny(X0) | tall(X0) [cnf transformation 33]
131. rich(paul) | old(paul) [cnf transformation 22]
132. patient(paul) [cnf transformation 23]
162. 7 <=> patient(paul) [avatar definition]
163. patient(paul) <- (7) [avatar component clause 162]
274. 31 <=> old(paul) [avatar definition]
278. 32 <=> rich(paul) [avatar definition]
280. rich(paul) <- (32) [avatar component clause 278]
281. 31 | 32 [avatar split clause 131,278,274]
282. 7 [avatar split clause 132,162]
289. ~old(paul) <- (7) [resolution 111,163]
293. ~31 | ~7 [avatar split clause 289,162,274]
299. tall(X0) | ~rich(X0) [resolution 119,97]
301. ~rich(X0) [subsumption resolution 299,78]
313. $false <- (32) [resolution 301,280]
314. ~32 [avatar contradiction clause 313]
315. $false [avatar sat refutation 281,282,293,314]
% SZS output end Proof for 1293805753216121810936849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not creative or not strong then someone is not curious or humble and vice versa.
Everyone who is humble or happy is either not happy or not wise and vice versa.
If someone is both creative and not strong then susan is not creative and vice versa.
Everyone who is both wise and calm is both not curious and not calm.
Everyone who is either rich or creative is not wise and vice versa.
Everyone who is not old or happy is either patient or curious and vice versa.
If alice is not strong then paul is calm or tall and vice versa.
Everyone who is not calm is both old and calm.
If someone is not generous or not old then someone is not old.
Everyone who is old is humble and vice versa.
Everyone who is wise or not funny is strong and vice versa.
Everyone who is curious is not rich or tall.
Everyone who is not tall or wise is either not funny or happy.
If fred is humble or not curious then someone is not tall.
Everyone who is funny is either not humble or rich and vice versa.
Everyone who is either tall or patient is either not curious or not patient.
Someone is not brave or happy.
Alice is old or not patient.
Mary is not rich or quiet.
Alice is generous.
Susan is both not tall and not brave.
Paul is both patient and not kind.
Susan is not brave.
Paul is either happy or not calm. | Susan is not funny. | neutral | (((~creative(mary)<~>~strong(mary)))<=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((humble(X)|happy(X))<=>(~happy(X)<~>~wise(X))))&
((?[X]:((creative(X)&~strong(X))))<=>(~creative(susan)))&
(![X]:((wise(X)&calm(X))=>(~curious(X)&~calm(X))))&
(![X]:((rich(X)<~>creative(X))<=>~wise(X)))&
(![X]:((~old(X)|happy(X))<=>(patient(X)<~>curious(X))))&
((~strong(alice))<=>((calm(paul)|tall(paul))))&
(![X]:(~calm(X)=>(old(X)&calm(X))))&
((?[X]:((~generous(X)|~old(X))))=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>humble(X)))&
(![X]:((wise(X)|~funny(X))<=>strong(X)))&
(![X]:(curious(X)=>(~rich(X)|tall(X))))&
(![X]:((~tall(X)|wise(X))=>(~funny(X)<~>happy(X))))&
(((humble(fred)|~curious(fred)))=>(?[X]:(~tall(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>rich(X))))&
(![X]:((tall(X)<~>patient(X))=>(~curious(X)<~>~patient(X))))&
(?[X]:((~brave(X)|happy(X))))&
((old(alice)|~patient(alice)))&
((~rich(mary)|quiet(mary)))&
(generous(alice))&
((~tall(susan)&~brave(susan)))&
((patient(paul)&~kind(paul)))&
(~brave(susan))&
((happy(paul)<~>~calm(paul))) | ~funny(susan) | [] | null | 0 |
If susan is brave then someone is not brave and vice versa.
If fred is both not calm and patient then lucy is tall or not calm.
Everyone who is not brave is not funny or not brave and vice versa.
Everyone who is either not humble or not tall is both creative and not brave and vice versa.
If paul is both quiet and not calm then someone is happy and vice versa.
Everyone who is both not wise and humble is both tall and not wise.
If someone is not strong or not rich then alice is either not curious or tall and vice versa.
Everyone who is calm or not funny is both calm and strong.
If someone is both tall and not kind then susan is both funny and not happy.
If susan is strong then someone is both happy and quiet.
If fred is either not happy or creative then mary is both quiet and not wise and vice versa.
Everyone who is both tall and patient is both not curious and tall.
Everyone who is not quiet or not funny is both not strong and not brave.
Everyone who is both not kind and not strong is rich and vice versa.
Everyone who is both not creative and patient is both kind and not funny.
Everyone who is both not old and quiet is not wise and vice versa.
Alice is both not patient and kind.
Someone is either not creative or creative.
Lucy is not generous.
Mary is both curious and creative.
Someone is both not brave and not creative.
Susan is rich or not tall. | Mary is not brave. | neutral | ((brave(susan))<=>(?[X]:(~brave(X))))&
(((~calm(fred)&patient(fred)))=>((tall(lucy)|~calm(lucy))))&
(![X]:(~brave(X)<=>(~funny(X)|~brave(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>(creative(X)&~brave(X))))&
(((quiet(paul)&~calm(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)&humble(X))=>(tall(X)&~wise(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((~curious(alice)<~>tall(alice))))&
(![X]:((calm(X)|~funny(X))=>(calm(X)&strong(X))))&
((?[X]:((tall(X)&~kind(X))))=>((funny(susan)&~happy(susan))))&
((strong(susan))=>(?[X]:((happy(X)&quiet(X)))))&
(((~happy(fred)<~>creative(fred)))<=>((quiet(mary)&~wise(mary))))&
(![X]:((tall(X)&patient(X))=>(~curious(X)&tall(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~strong(X)&~brave(X))))&
(![X]:((~kind(X)&~strong(X))<=>rich(X)))&
(![X]:((~creative(X)&patient(X))=>(kind(X)&~funny(X))))&
(![X]:((~old(X)&quiet(X))<=>~wise(X)))&
((~patient(alice)&kind(alice)))&
(?[X]:((~creative(X)<~>creative(X))))&
(~generous(lucy))&
((curious(mary)&creative(mary)))&
(?[X]:((~brave(X)&~creative(X))))&
((rich(susan)|~tall(susan))) | ~brave(mary) | [] | null | 0 |
Everyone who is patient is either not happy or generous and vice versa.
Everyone who is either quiet or happy is not wise or calm.
If susan is both not quiet and old then lucy is either not old or not kind and vice versa.
If lucy is both generous and not humble then fred is not quiet or wise and vice versa.
If paul is both not calm and humble then someone is not tall and vice versa.
Everyone who is both patient and creative is either not strong or funny.
Everyone who is funny is not wise or not humble.
If alice is happy then susan is kind or not strong and vice versa.
If someone is both not creative and not calm then someone is not happy or generous.
Everyone who is either not creative or funny is either calm or not quiet.
Everyone who is not generous or not happy is funny and vice versa.
If fred is either curious or not curious then paul is both not curious and creative and vice versa.
Everyone who is either humble or generous is patient or not tall and vice versa.
If lucy is not humble or brave then fred is either not strong or happy and vice versa.
If someone is both old and quiet then fred is either quiet or not generous.
Everyone who is not wise or creative is not strong.
Susan is either patient or not rich.
Someone is both curious and funny.
Lucy is both not strong and not wise.
Someone is not strong.
Susan is both kind and not wise.
Someone is not tall or not wise.
John is either patient or wise.
John is curious or funny. | Paul is strong. | contradiction | (![X]:(patient(X)<=>(~happy(X)<~>generous(X))))&
(![X]:((quiet(X)<~>happy(X))=>(~wise(X)|calm(X))))&
(((~quiet(susan)&old(susan)))<=>((~old(lucy)<~>~kind(lucy))))&
(((generous(lucy)&~humble(lucy)))<=>((~quiet(fred)|wise(fred))))&
(((~calm(paul)&humble(paul)))<=>(?[X]:(~tall(X))))&
(![X]:((patient(X)&creative(X))=>(~strong(X)<~>funny(X))))&
(![X]:(funny(X)=>(~wise(X)|~humble(X))))&
((happy(alice))<=>((kind(susan)|~strong(susan))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((~creative(X)<~>funny(X))=>(calm(X)<~>~quiet(X))))&
(![X]:((~generous(X)|~happy(X))<=>funny(X)))&
(((curious(fred)<~>~curious(fred)))<=>((~curious(paul)&creative(paul))))&
(![X]:((humble(X)<~>generous(X))<=>(patient(X)|~tall(X))))&
(((~humble(lucy)|brave(lucy)))<=>((~strong(fred)<~>happy(fred))))&
((?[X]:((old(X)&quiet(X))))=>((quiet(fred)<~>~generous(fred))))&
(![X]:((~wise(X)|creative(X))=>~strong(X)))&
((patient(susan)<~>~rich(susan)))&
(?[X]:((curious(X)&funny(X))))&
((~strong(lucy)&~wise(lucy)))&
(?[X]:(~strong(X)))&
((kind(susan)&~wise(susan)))&
(?[X]:((~tall(X)|~wise(X))))&
((patient(john)<~>wise(john)))&
((curious(john)|funny(john))) | strong(paul) | [
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5342943220322114029289198
% SZS output start Proof for 5342943220322114029289198
12. (curious(fred) <~> ~curious(fred)) <=> (creative(paul) & ~curious(paul)) [input p11]
16. ! [X0] : ((creative(X0) | ~wise(X0)) => ~strong(X0)) [input p15]
25. strong(paul) [input hypothesis]
36. ! [X0] : (~strong(X0) | (~creative(X0) & wise(X0))) [ennf transformation 16]
57. (((curious(fred) | ~curious(fred)) & (~curious(fred) | curious(fred))) | (~creative(paul) | curious(paul))) & ((creative(paul) & ~curious(paul)) | ((curious(fred) | curious(fred)) & (~curious(fred) | ~curious(fred)))) [nnf transformation 12]
58. (((curious(fred) | ~curious(fred)) & (~curious(fred) | curious(fred))) | ~creative(paul) | curious(paul)) & ((creative(paul) & ~curious(paul)) | ((curious(fred) | curious(fred)) & (~curious(fred) | ~curious(fred)))) [flattening 57]
108. creative(paul) | ~curious(fred) | ~curious(fred) [cnf transformation 58]
109. creative(paul) | curious(fred) | curious(fred) [cnf transformation 58]
127. ~strong(X0) | ~creative(X0) [cnf transformation 36]
141. strong(paul) [cnf transformation 25]
144. creative(paul) | ~curious(fred) [duplicate literal removal 108]
145. creative(paul) | curious(fred) [duplicate literal removal 109]
235. 19 <=> curious(fred) [avatar definition]
239. 20 <=> creative(paul) [avatar definition]
241. creative(paul) <- (20) [avatar component clause 239]
242. 19 | 20 [avatar split clause 145,239,235]
243. ~19 | 20 [avatar split clause 144,239,235]
319. ~creative(paul) [resolution 127,141]
320. $false <- (20) [subsumption resolution 319,241]
321. ~20 [avatar contradiction clause 320]
322. $false [avatar sat refutation 242,243,321]
% SZS output end Proof for 5342943220322114029289198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then susan is either funny or brave and vice versa.
Everyone who is humble is old or funny and vice versa.
If someone is both not strong and not curious then susan is not happy.
Everyone who is either brave or not wise is humble.
Everyone who is both brave and funny is old and vice versa.
Everyone who is calm or curious is creative and vice versa.
Everyone who is rich or not patient is not wise.
If someone is not rich or not old then someone is not calm or not curious and vice versa.
If someone is either creative or not quiet then someone is quiet or creative.
If someone is not happy or not humble then susan is not brave or not strong and vice versa.
If someone is both not curious and wise then someone is funny and vice versa.
Everyone who is not wise or happy is brave or not kind.
Everyone who is not brave is not humble.
Everyone who is calm or not generous is not funny or not strong.
If alice is not happy then someone is kind or rich and vice versa.
Everyone who is either not tall or not brave is either not curious or not rich and vice versa.
Someone is not creative or humble.
Paul is not generous or not kind.
Mary is not patient.
Someone is either creative or rich.
Someone is calm or not patient.
Someone is both brave and calm.
Fred is brave.
Someone is humble. | Mary is wise. | contradiction | ((?[X]:(wise(X)))<=>((funny(susan)<~>brave(susan))))&
(![X]:(humble(X)<=>(old(X)|funny(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(~happy(susan)))&
(![X]:((brave(X)<~>~wise(X))=>humble(X)))&
(![X]:((brave(X)&funny(X))<=>old(X)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(![X]:((rich(X)|~patient(X))=>~wise(X)))&
((?[X]:((~rich(X)|~old(X))))<=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((quiet(X)|creative(X)))))&
((?[X]:((~happy(X)|~humble(X))))<=>((~brave(susan)|~strong(susan))))&
((?[X]:((~curious(X)&wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|happy(X))=>(brave(X)|~kind(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((calm(X)|~generous(X))=>(~funny(X)|~strong(X))))&
((~happy(alice))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>(~curious(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
((~generous(paul)|~kind(paul)))&
(~patient(mary))&
(?[X]:((creative(X)<~>rich(X))))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((brave(X)&calm(X))))&
(brave(fred))&
(?[X]:(humble(X))) | wise(mary) | [
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 842879021851724886979790
% SZS output start Proof for 842879021851724886979790
7. ! [X0] : ((~patient(X0) | rich(X0)) => ~wise(X0)) [input p6]
19. ~patient(mary) [input p18]
25. wise(mary) [input hypothesis]
31. ! [X0] : (~wise(X0) | (patient(X0) & ~rich(X0))) [ennf transformation 7]
101. ~wise(X0) | patient(X0) [cnf transformation 31]
133. ~patient(mary) [cnf transformation 19]
141. wise(mary) [cnf transformation 25]
326. patient(mary) [resolution 101,141]
329. $false [subsumption resolution 326,133]
% SZS output end Proof for 842879021851724886979790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or funny is not quiet and vice versa.
Everyone who is not happy or kind is either creative or happy.
Everyone who is either curious or brave is not old or not generous and vice versa.
Everyone who is kind or humble is not curious and vice versa.
If someone is not curious then mary is both creative and kind and vice versa.
If paul is patient then john is humble and vice versa.
Everyone who is either not funny or not brave is quiet.
If someone is both not patient and not calm then alice is either not happy or not wise.
If john is not old then mary is either not patient or kind and vice versa.
Everyone who is not happy or patient is either brave or rich.
Everyone who is old or not tall is tall or patient and vice versa.
If mary is both not patient and not curious then someone is wise or not old and vice versa.
If someone is not quiet then paul is not tall or not strong and vice versa.
If someone is either not calm or not funny then someone is both funny and not creative.
Everyone who is not creative or not wise is both not calm and calm.
Everyone who is either patient or kind is both not strong and generous and vice versa.
John is humble.
Someone is not calm or calm.
Someone is both strong and not happy.
Alice is both strong and patient.
Someone is humble or not strong. | Mary is not generous. | contradiction | (![X]:((~brave(X)<~>funny(X))<=>~quiet(X)))&
(![X]:((~happy(X)|kind(X))=>(creative(X)<~>happy(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~old(X)|~generous(X))))&
(![X]:((kind(X)|humble(X))<=>~curious(X)))&
((?[X]:(~curious(X)))<=>((creative(mary)&kind(mary))))&
((patient(paul))<=>(humble(john)))&
(![X]:((~funny(X)<~>~brave(X))=>quiet(X)))&
((?[X]:((~patient(X)&~calm(X))))=>((~happy(alice)<~>~wise(alice))))&
((~old(john))<=>((~patient(mary)<~>kind(mary))))&
(![X]:((~happy(X)|patient(X))=>(brave(X)<~>rich(X))))&
(![X]:((old(X)|~tall(X))<=>(tall(X)|patient(X))))&
(((~patient(mary)&~curious(mary)))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:(~quiet(X)))<=>((~tall(paul)|~strong(paul))))&
((?[X]:((~calm(X)<~>~funny(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:((~creative(X)|~wise(X))=>(~calm(X)&calm(X))))&
(![X]:((patient(X)<~>kind(X))<=>(~strong(X)&generous(X))))&
(humble(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((strong(X)&~happy(X))))&
((strong(alice)&patient(alice)))&
(?[X]:((humble(X)|~strong(X)))) | ~generous(mary) | [
"p4",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6247795038552334696777621
% SZS output start Proof for 6247795038552334696777621
5. ? [X0] : ~curious(X0) <=> (kind(mary) & creative(mary)) [input p4]
12. (~curious(mary) & ~patient(mary)) <=> ? [X0] : (~old(X0) | wise(X0)) [input p11]
15. ! [X0] : ((~wise(X0) | ~creative(X0)) => (calm(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((patient(X0) <~> kind(X0)) <=> (generous(X0) & ~strong(X0))) [input p15]
22. ~generous(mary) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~calm(X0)) | (wise(X0) & creative(X0))) [ennf transformation 15]
36. (? [X0] : ~curious(X0) | (~kind(mary) | ~creative(mary))) & ((kind(mary) & creative(mary)) | ! [X0] : curious(X0)) [nnf transformation 5]
37. (? [X0] : ~curious(X0) | ~kind(mary) | ~creative(mary)) & ((kind(mary) & creative(mary)) | ! [X0] : curious(X0)) [flattening 36]
38. (? [X0] : ~curious(X0) | ~kind(mary) | ~creative(mary)) & ((kind(mary) & creative(mary)) | ! [X1] : curious(X1)) [rectify 37]
39. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
40. (~curious(sK0) | ~kind(mary) | ~creative(mary)) & ((kind(mary) & creative(mary)) | ! [X1] : curious(X1)) [skolemisation 38,39]
48. ((~curious(mary) & ~patient(mary)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X0] : (~old(X0) | wise(X0)) | (curious(mary) | patient(mary))) [nnf transformation 12]
49. ((~curious(mary) & ~patient(mary)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X0] : (~old(X0) | wise(X0)) | curious(mary) | patient(mary)) [flattening 48]
50. ((~curious(mary) & ~patient(mary)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X1] : (~old(X1) | wise(X1)) | curious(mary) | patient(mary)) [rectify 49]
51. ? [X1] : (~old(X1) | wise(X1)) => (~old(sK1) | wise(sK1)) [choice axiom]
52. ((~curious(mary) & ~patient(mary)) | ! [X0] : (old(X0) & ~wise(X0))) & ((~old(sK1) | wise(sK1)) | curious(mary) | patient(mary)) [skolemisation 50,51]
62. ! [X0] : ((((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (~generous(X0) | strong(X0))) & ((generous(X0) & ~strong(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))))) [nnf transformation 16]
63. ! [X0] : ((((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | ~generous(X0) | strong(X0)) & ((generous(X0) & ~strong(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))))) [flattening 62]
88. kind(mary) | curious(X1) [cnf transformation 40]
109. ~patient(mary) | ~wise(X0) [cnf transformation 52]
111. ~curious(mary) | ~wise(X0) [cnf transformation 52]
121. ~calm(X0) | wise(X0) [cnf transformation 29]
123. wise(X0) | calm(X0) [cnf transformation 29]
127. ~kind(X0) | patient(X0) | generous(X0) [cnf transformation 63]
137. ~generous(mary) [cnf transformation 22]
146. 2 <=> kind(mary) [avatar definition]
147. kind(mary) <- (2) [avatar component clause 146]
155. 4 <=> ! [X1] : curious(X1) [avatar definition]
156. curious(X1) <- (4) [avatar component clause 155]
157. 4 | 2 [avatar split clause 88,146,155]
183. 10 <=> patient(mary) [avatar definition]
185. ~patient(mary) <- (~10) [avatar component clause 183]
198. 13 <=> curious(mary) [avatar definition]
200. ~curious(mary) <- (~13) [avatar component clause 198]
203. 14 <=> ! [X0] : ~wise(X0) [avatar definition]
204. ~wise(X0) <- (14) [avatar component clause 203]
205. 14 | ~13 [avatar split clause 111,198,203]
207. 14 | ~10 [avatar split clause 109,183,203]
253. wise(X0) [subsumption resolution 121,123]
267. $false <- (4, ~13) [resolution 200,156]
268. ~4 | 13 [avatar contradiction clause 267]
269. $false <- (14) [subsumption resolution 204,253]
270. ~14 [avatar contradiction clause 269]
401. patient(mary) | generous(mary) <- (2) [resolution 127,147]
403. generous(mary) <- (2, ~10) [subsumption resolution 401,185]
404. $false <- (2, ~10) [subsumption resolution 403,137]
405. ~2 | 10 [avatar contradiction clause 404]
406. $false [avatar sat refutation 157,205,207,268,270,405]
% SZS output end Proof for 6247795038552334696777621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is funny and vice versa.
Everyone who is not brave is not creative and vice versa.
Everyone who is calm or humble is both calm and humble.
If someone is either generous or not creative then someone is both tall and not humble.
Everyone who is not curious or happy is strong or curious.
Everyone who is either not tall or not strong is not rich or not creative and vice versa.
If someone is either humble or curious then mary is not rich and vice versa.
If susan is either not rich or not old then someone is not quiet or rich.
If susan is strong or not old then susan is not humble or not old and vice versa.
If mary is rich then john is both not humble and tall and vice versa.
Everyone who is not humble is either humble or not tall.
If someone is both calm and not creative then john is tall or not old.
Everyone who is tall or strong is either not humble or not kind.
Everyone who is brave is not tall.
Everyone who is wise is both not patient and not tall and vice versa.
Everyone who is both not creative and funny is funny and vice versa.
Mary is both not calm and not tall.
Lucy is wise or generous.
Someone is both wise and happy.
Susan is not rich or not kind.
Someone is quiet.
Susan is funny or generous.
Someone is both not humble and not generous.
Someone is either patient or not funny. | Susan is generous. | entailment | ((?[X]:(~happy(X)))<=>(?[X]:(funny(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((calm(X)|humble(X))=>(calm(X)&humble(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((tall(X)&~humble(X)))))&
(![X]:((~curious(X)|happy(X))=>(strong(X)|curious(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(~rich(X)|~creative(X))))&
((?[X]:((humble(X)<~>curious(X))))<=>(~rich(mary)))&
(((~rich(susan)<~>~old(susan)))=>(?[X]:((~quiet(X)|rich(X)))))&
(((strong(susan)|~old(susan)))<=>((~humble(susan)|~old(susan))))&
((rich(mary))<=>((~humble(john)&tall(john))))&
(![X]:(~humble(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((calm(X)&~creative(X))))=>((tall(john)|~old(john))))&
(![X]:((tall(X)|strong(X))=>(~humble(X)<~>~kind(X))))&
(![X]:(brave(X)=>~tall(X)))&
(![X]:(wise(X)<=>(~patient(X)&~tall(X))))&
(![X]:((~creative(X)&funny(X))<=>funny(X)))&
((~calm(mary)&~tall(mary)))&
((wise(lucy)|generous(lucy)))&
(?[X]:((wise(X)&happy(X))))&
((~rich(susan)|~kind(susan)))&
(?[X]:(quiet(X)))&
((funny(susan)|generous(susan)))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:((patient(X)<~>~funny(X)))) | generous(susan) | [
"p3",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6176468344973271926773062
% SZS output start Proof for 6176468344973271926773062
4. ? [X0] : (generous(X0) <~> ~creative(X0)) => ? [X0] : (~humble(X0) & tall(X0)) [input p3]
11. ! [X0] : (~humble(X0) => (humble(X0) <~> ~tall(X0))) [input p10]
16. ! [X0] : ((funny(X0) & ~creative(X0)) <=> funny(X0)) [input p15]
22. generous(susan) | funny(susan) [input p21]
25. ~generous(susan) [input hypothesis]
27. ? [X0] : (generous(X0) <~> ~creative(X0)) => ? [X1] : (~humble(X1) & tall(X1)) [rectify 4]
32. ? [X1] : (~humble(X1) & tall(X1)) | ! [X0] : (generous(X0) <=> ~creative(X0)) [ennf transformation 27]
36. ! [X0] : ((humble(X0) <~> ~tall(X0)) | humble(X0)) [ennf transformation 11]
47. ? [X1] : (~humble(X1) & tall(X1)) | ! [X0] : ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))) [nnf transformation 32]
48. ? [X0] : (~humble(X0) & tall(X0)) | ! [X1] : ((generous(X1) | creative(X1)) & (~creative(X1) | ~generous(X1))) [rectify 47]
49. ? [X0] : (~humble(X0) & tall(X0)) => (~humble(sK2) & tall(sK2)) [choice axiom]
50. (~humble(sK2) & tall(sK2)) | ! [X1] : ((generous(X1) | creative(X1)) & (~creative(X1) | ~generous(X1))) [skolemisation 48,49]
64. ! [X0] : (((tall(X0) | ~humble(X0)) & (~tall(X0) | humble(X0))) | humble(X0)) [nnf transformation 36]
66. ! [X0] : (((funny(X0) & ~creative(X0)) | ~funny(X0)) & (funny(X0) | (~funny(X0) | creative(X0)))) [nnf transformation 16]
67. ! [X0] : (((funny(X0) & ~creative(X0)) | ~funny(X0)) & (funny(X0) | ~funny(X0) | creative(X0))) [flattening 66]
85. tall(sK2) | generous(X1) | creative(X1) [cnf transformation 50]
87. ~humble(sK2) | generous(X1) | creative(X1) [cnf transformation 50]
109. ~tall(X0) | humble(X0) | humble(X0) [cnf transformation 64]
120. ~creative(X0) | ~funny(X0) [cnf transformation 67]
129. generous(susan) | funny(susan) [cnf transformation 22]
134. ~generous(susan) [cnf transformation 25]
135. ~tall(X0) | humble(X0) [duplicate literal removal 109]
154. 5 <=> ! [X1] : (generous(X1) | creative(X1)) [avatar definition]
155. generous(X1) | creative(X1) <- (5) [avatar component clause 154]
157. 6 <=> humble(sK2) [avatar definition]
159. ~humble(sK2) <- (~6) [avatar component clause 157]
160. 5 | ~6 [avatar split clause 87,157,154]
166. 8 <=> tall(sK2) [avatar definition]
168. tall(sK2) <- (8) [avatar component clause 166]
169. 5 | 8 [avatar split clause 85,166,154]
256. 27 <=> funny(susan) [avatar definition]
258. funny(susan) <- (27) [avatar component clause 256]
260. 28 <=> generous(susan) [avatar definition]
261. ~generous(susan) <- (~28) [avatar component clause 260]
263. 27 | 28 [avatar split clause 129,260,256]
274. ~28 [avatar split clause 134,260]
284. creative(susan) <- (5, ~28) [resolution 155,261]
288. ~funny(susan) <- (5, ~28) [resolution 284,120]
290. $false <- (5, 27, ~28) [subsumption resolution 288,258]
291. ~5 | ~27 | 28 [avatar contradiction clause 290]
292. humble(sK2) <- (8) [resolution 168,135]
294. $false <- (~6, 8) [subsumption resolution 292,159]
295. 6 | ~8 [avatar contradiction clause 294]
296. $false [avatar sat refutation 160,169,263,274,291,295]
% SZS output end Proof for 6176468344973271926773062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not brave and not quiet then john is either curious or not old and vice versa. If someone is humble then susan is both calm and strong and vice versa. If paul is quiet or not old then mary is old and vice versa. If someone is either not brave or calm then mary is either not happy or brave and vice versa. Everyone who is not brave is kind and vice versa. If john is humble or not patient then someone is either not generous or not curious and vice versa. If lucy is not funny or wise then lucy is either not wise or tall. If someone is happy then someone is not strong. Everyone who is rich or not tall is both curious and not creative and vice versa. Everyone who is not humble or not strong is strong and vice versa. If someone is happy or kind then someone is either not curious or funny and vice versa. Everyone who is generous is either happy or not tall and vice versa. Everyone who is not old or curious is brave and vice versa. Everyone who is both not wise and creative is not tall or not funny and vice versa. Everyone who is either not curious or wise is not wise and vice versa. Someone is creative. Susan is either tall or calm. Lucy is both not brave and kind. Paul is either brave or not tall. Fred is old or calm. Susan is not kind or strong. Susan is old or not curious. | Susan is kind. | neutral | (((~brave(paul)&~quiet(paul)))<=>((curious(john)<~>~old(john))))&
((?[X]:(humble(X)))<=>((calm(susan)&strong(susan))))&
(((quiet(paul)|~old(paul)))<=>(old(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((~happy(mary)<~>brave(mary))))&
(![X]:(~brave(X)<=>kind(X)))&
(((humble(john)|~patient(john)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~funny(lucy)|wise(lucy)))=>((~wise(lucy)<~>tall(lucy))))&
((?[X]:(happy(X)))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~humble(X)|~strong(X))<=>strong(X)))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
(![X]:((~old(X)|curious(X))<=>brave(X)))&
(![X]:((~wise(X)&creative(X))<=>(~tall(X)|~funny(X))))&
(![X]:((~curious(X)<~>wise(X))<=>~wise(X)))&
(?[X]:(creative(X)))&
((tall(susan)<~>calm(susan)))&
((~brave(lucy)&kind(lucy)))&
((brave(paul)<~>~tall(paul)))&
((old(fred)|calm(fred)))&
((~kind(susan)|strong(susan)))&
((old(susan)|~curious(susan))) | kind(susan) | [] | null | 0 |
Everyone who is not curious or not calm is either humble or calm and vice versa. Everyone who is either not quiet or not happy is strong or not quiet and vice versa. Everyone who is either not curious or not quiet is either old or tall. Everyone who is both not strong and not creative is both generous and not kind and vice versa. If someone is either creative or not rich then someone is either not old or not strong. If mary is either patient or not humble then someone is both not kind and calm and vice versa. Everyone who is both rich and happy is both not patient and not strong. Everyone who is either not happy or brave is quiet and vice versa. Everyone who is happy or calm is either rich or humble. Everyone who is either kind or rich is strong. Everyone who is either funny or happy is either brave or funny and vice versa. Everyone who is both not happy and tall is not generous. If lucy is wise then john is either calm or not patient. If someone is both not happy and not creative then someone is rich or calm and vice versa. If lucy is either not tall or calm then someone is patient or not funny. Everyone who is either creative or strong is both not kind and not creative and vice versa. Fred is either strong or tall. Lucy is either not wise or not tall. John is not kind. Lucy is both not happy and not wise. Lucy is not curious or not creative. Someone is old or not creative. Alice is not happy. Someone is generous. | Fred is happy. | contradiction | (![X]:((~curious(X)|~calm(X))<=>(humble(X)<~>calm(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(strong(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~quiet(X))=>(old(X)<~>tall(X))))&
(![X]:((~strong(X)&~creative(X))<=>(generous(X)&~kind(X))))&
((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((~old(X)<~>~strong(X)))))&
(((patient(mary)<~>~humble(mary)))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((rich(X)&happy(X))=>(~patient(X)&~strong(X))))&
(![X]:((~happy(X)<~>brave(X))<=>quiet(X)))&
(![X]:((happy(X)|calm(X))=>(rich(X)<~>humble(X))))&
(![X]:((kind(X)<~>rich(X))=>strong(X)))&
(![X]:((funny(X)<~>happy(X))<=>(brave(X)<~>funny(X))))&
(![X]:((~happy(X)&tall(X))=>~generous(X)))&
((wise(lucy))=>((calm(john)<~>~patient(john))))&
((?[X]:((~happy(X)&~creative(X))))<=>(?[X]:((rich(X)|calm(X)))))&
(((~tall(lucy)<~>calm(lucy)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((creative(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
((strong(fred)<~>tall(fred)))&
((~wise(lucy)<~>~tall(lucy)))&
(~kind(john))&
((~happy(lucy)&~wise(lucy)))&
((~curious(lucy)|~creative(lucy)))&
(?[X]:((old(X)|~creative(X))))&
(~happy(alice))&
(?[X]:(generous(X))) | happy(fred) | [
"p1",
"p3",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 408974101305877177951813
% SZS output start Proof for 408974101305877177951813
2. ! [X0] : ((~quiet(X0) <~> ~happy(X0)) <=> (~quiet(X0) | strong(X0))) [input p1]
4. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (~kind(X0) & generous(X0))) [input p3]
8. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> quiet(X0)) [input p7]
11. ! [X0] : ((funny(X0) <~> happy(X0)) <=> (brave(X0) <~> funny(X0))) [input p10]
16. ! [X0] : ((creative(X0) <~> strong(X0)) <=> (~creative(X0) & ~kind(X0))) [input p15]
25. happy(fred) [input hypothesis]
40. ! [X0] : ((((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))))) [nnf transformation 2]
41. ! [X0] : ((((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))))) [flattening 40]
43. ! [X0] : (((~creative(X0) & ~strong(X0)) | (kind(X0) | ~generous(X0))) & ((~kind(X0) & generous(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 4]
44. ! [X0] : (((~creative(X0) & ~strong(X0)) | kind(X0) | ~generous(X0)) & ((~kind(X0) & generous(X0)) | creative(X0) | strong(X0))) [flattening 43]
53. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~quiet(X0)) & (quiet(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [nnf transformation 11]
66. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | (creative(X0) | kind(X0))) & ((~creative(X0) & ~kind(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 16]
67. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | creative(X0) | kind(X0)) & ((~creative(X0) & ~kind(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [flattening 66]
82. ~strong(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 41]
85. happy(X0) | quiet(X0) | quiet(X0) [cnf transformation 41]
91. ~kind(X0) | creative(X0) | strong(X0) [cnf transformation 44]
107. quiet(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 53]
109. ~brave(X0) | happy(X0) | ~quiet(X0) [cnf transformation 53]
117. funny(X0) | brave(X0) | funny(X0) | ~happy(X0) [cnf transformation 56]
123. ~happy(X0) | ~funny(X0) | brave(X0) | ~funny(X0) [cnf transformation 56]
136. ~creative(X0) | strong(X0) | ~creative(X0) [cnf transformation 67]
138. strong(X0) | creative(X0) | creative(X0) | kind(X0) [cnf transformation 67]
151. happy(fred) [cnf transformation 25]
152. ~creative(X0) | strong(X0) [duplicate literal removal 136]
153. strong(X0) | creative(X0) | kind(X0) [duplicate literal removal 138]
154. funny(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 117]
157. ~happy(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 123]
159. happy(X0) | quiet(X0) [duplicate literal removal 85]
206. ~brave(X0) | happy(X0) [subsumption resolution 109,159]
207. ~brave(X0) | quiet(X0) [subsumption resolution 107,206]
209. ~happy(X0) | brave(X0) [subsumption resolution 154,157]
272. creative(X0) | strong(X0) [subsumption resolution 153,91]
273. strong(X0) [subsumption resolution 152,272]
307. brave(X0) | quiet(X0) [resolution 209,159]
308. quiet(X0) [subsumption resolution 307,207]
325. ~quiet(X1) | ~happy(X1) [resolution 82,273]
326. ~happy(X1) [subsumption resolution 325,308]
331. $false [resolution 326,151]
% SZS output end Proof for 408974101305877177951813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
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