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
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stringlengths 684
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If paul is either happy or not calm then someone is both happy and not tall. Everyone who is either not tall or not funny is not happy or not humble. If paul is not quiet then someone is humble or brave. Everyone who is funny is both happy and patient and vice versa. Everyone who is either wise or not creative is not curious. If alice is not strong or not rich then fred is not happy or patient. Everyone who is kind is not creative or not brave and vice versa. Everyone who is old is not kind or not humble and vice versa. If mary is either not strong or not quiet then someone is not strong or funny. Everyone who is either not rich or patient is funny or strong. Everyone who is not strong or strong is not old and vice versa. Everyone who is brave is either not old or rich and vice versa. If lucy is either funny or strong then someone is both rich and creative. Everyone who is not quiet is both patient and not brave and vice versa. Everyone who is either not kind or creative is both funny and not curious and vice versa. Everyone who is both not funny and tall is not humble or creative and vice versa. Someone is not strong. John is rich. Someone is not happy or generous. Someone is generous. Susan is kind. Someone is either not tall or creative. Someone is either quiet or not patient. | John is funny. | neutral | (((happy(paul)<~>~calm(paul)))=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~funny(X))=>(~happy(X)|~humble(X))))&
((~quiet(paul))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:(funny(X)<=>(happy(X)&patient(X))))&
(![X]:((wise(X)<~>~creative(X))=>~curious(X)))&
(((~strong(alice)|~rich(alice)))=>((~happy(fred)|patient(fred))))&
(![X]:(kind(X)<=>(~creative(X)|~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(![X]:(brave(X)<=>(~old(X)<~>rich(X))))&
(((funny(lucy)<~>strong(lucy)))=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~quiet(X)<=>(patient(X)&~brave(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(funny(X)&~curious(X))))&
(![X]:((~funny(X)&tall(X))<=>(~humble(X)|creative(X))))&
(?[X]:(~strong(X)))&
(rich(john))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:(generous(X)))&
(kind(susan))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | funny(john) | [] | null | 0 |
If john is both tall and brave then john is patient and vice versa. Everyone who is either curious or not funny is not kind and vice versa. Everyone who is rich or not wise is not kind or generous. Everyone who is kind is not creative or old and vice versa. Everyone who is not funny or not brave is both not happy and curious. Everyone who is not wise is generous and vice versa. Everyone who is tall or patient is both funny and kind and vice versa. If someone is tall or not calm then susan is either rich or not strong. Everyone who is either generous or not strong is not kind. If someone is not curious then alice is both patient and not wise and vice versa. Everyone who is patient is not old or creative. If paul is either tall or not kind then someone is not kind. Everyone who is wise or not strong is rich or not kind. Everyone who is happy or not humble is both humble and not patient and vice versa. If mary is humble then someone is either not humble or not patient. If mary is kind or not curious then john is either not funny or wise. Someone is not kind. Lucy is kind or not patient. Alice is both not happy and not tall. Someone is either not old or not patient. Fred is either quiet or not old. Someone is happy or curious. | Mary is not funny. | contradiction | (((tall(john)&brave(john)))<=>(patient(john)))&
(![X]:((curious(X)<~>~funny(X))<=>~kind(X)))&
(![X]:((rich(X)|~wise(X))=>(~kind(X)|generous(X))))&
(![X]:(kind(X)<=>(~creative(X)|old(X))))&
(![X]:((~funny(X)|~brave(X))=>(~happy(X)&curious(X))))&
(![X]:(~wise(X)<=>generous(X)))&
(![X]:((tall(X)|patient(X))<=>(funny(X)&kind(X))))&
((?[X]:((tall(X)|~calm(X))))=>((rich(susan)<~>~strong(susan))))&
(![X]:((generous(X)<~>~strong(X))=>~kind(X)))&
((?[X]:(~curious(X)))<=>((patient(alice)&~wise(alice))))&
(![X]:(patient(X)=>(~old(X)|creative(X))))&
(((tall(paul)<~>~kind(paul)))=>(?[X]:(~kind(X))))&
(![X]:((wise(X)|~strong(X))=>(rich(X)|~kind(X))))&
(![X]:((happy(X)|~humble(X))<=>(humble(X)&~patient(X))))&
((humble(mary))=>(?[X]:((~humble(X)<~>~patient(X)))))&
(((kind(mary)|~curious(mary)))=>((~funny(john)<~>wise(john))))&
(?[X]:(~kind(X)))&
((kind(lucy)|~patient(lucy)))&
((~happy(alice)&~tall(alice)))&
(?[X]:((~old(X)<~>~patient(X))))&
((quiet(fred)<~>~old(fred)))&
(?[X]:((happy(X)|curious(X)))) | ~funny(mary) | [
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6634352394694280046730953
% SZS output start Proof for 6634352394694280046730953
5. ! [X0] : ((~brave(X0) | ~funny(X0)) => (curious(X0) & ~happy(X0))) [input p4]
7. ! [X0] : ((patient(X0) | tall(X0)) <=> (kind(X0) & funny(X0))) [input p6]
14. ! [X0] : ((~humble(X0) | happy(X0)) <=> (~patient(X0) & humble(X0))) [input p13]
23. ~funny(mary) [input hypothesis]
27. ! [X0] : ((curious(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) [ennf transformation 5]
43. ! [X0] : (((patient(X0) | tall(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (~patient(X0) & ~tall(X0)))) [nnf transformation 7]
44. ! [X0] : ((patient(X0) | tall(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (~patient(X0) & ~tall(X0)))) [flattening 43]
55. ! [X0] : (((~humble(X0) | happy(X0)) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | (humble(X0) & ~happy(X0)))) [nnf transformation 14]
56. ! [X0] : ((~humble(X0) | happy(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | (humble(X0) & ~happy(X0)))) [flattening 55]
81. ~happy(X0) | funny(X0) [cnf transformation 27]
88. ~patient(X0) | funny(X0) [cnf transformation 44]
105. humble(X0) | humble(X0) [cnf transformation 56]
108. ~humble(X0) | happy(X0) | patient(X0) | ~humble(X0) [cnf transformation 56]
124. ~funny(mary) [cnf transformation 23]
125. humble(X0) [duplicate literal removal 105]
126. ~humble(X0) | happy(X0) | patient(X0) [duplicate literal removal 108]
370. happy(X0) | patient(X0) [resolution 126,125]
398. patient(X2) | funny(X2) [resolution 370,81]
399. funny(X2) [subsumption resolution 398,88]
434. $false [resolution 399,124]
% SZS output end Proof for 6634352394694280046730953
% ------------------------------
% 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 not patient or not generous then fred is happy and vice versa.
Everyone who is not patient is either not strong or funny.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious.
Someone is old.
Someone is not humble. | Lucy is patient. | neutral | ((?[X]:((~patient(X)<~>~generous(X))))<=>(happy(fred)))&
(![X]:(~patient(X)=>(~strong(X)<~>funny(X))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X)))&
(?[X]:(~humble(X))) | patient(lucy) | [] | null | 0 |
If someone is either quiet or not patient then someone is either not creative or quiet and vice versa. If john is both not generous and wise then fred is either not creative or not generous and vice versa. Everyone who is not strong or not brave is either not quiet or happy and vice versa. Everyone who is both patient and not old is either rich or humble and vice versa. Everyone who is patient or happy is strong or not curious and vice versa. If someone is either kind or wise then someone is curious and vice versa. Everyone who is either not humble or not creative is both not happy and kind and vice versa. Everyone who is not kind or tall is not old or rich and vice versa. Everyone who is both not calm and not quiet is both not humble and not kind and vice versa. Everyone who is both not brave and tall is not quiet or wise and vice versa. If someone is either not quiet or not humble then alice is either wise or patient and vice versa. Everyone who is either not curious or not happy is both funny and patient. If someone is both not curious and creative then mary is either rich or old. If someone is both not wise and old then someone is tall or quiet and vice versa. Everyone who is not patient is tall or humble. Everyone who is both not old and quiet is not old. Someone is not calm. Someone is not happy. Alice is not funny. Someone is tall. Lucy is either old or not tall. Lucy is either not humble or not tall. Someone is not brave or not wise. | Mary is humble. | neutral | ((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((~generous(john)&wise(john)))<=>((~creative(fred)<~>~generous(fred))))&
(![X]:((~strong(X)|~brave(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((patient(X)&~old(X))<=>(rich(X)<~>humble(X))))&
(![X]:((patient(X)|happy(X))<=>(strong(X)|~curious(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((~humble(X)<~>~creative(X))<=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|tall(X))<=>(~old(X)|rich(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~brave(X)&tall(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>((wise(alice)<~>patient(alice))))&
(![X]:((~curious(X)<~>~happy(X))=>(funny(X)&patient(X))))&
((?[X]:((~curious(X)&creative(X))))=>((rich(mary)<~>old(mary))))&
((?[X]:((~wise(X)&old(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:(~patient(X)=>(tall(X)|humble(X))))&
(![X]:((~old(X)&quiet(X))=>~old(X)))&
(?[X]:(~calm(X)))&
(?[X]:(~happy(X)))&
(~funny(alice))&
(?[X]:(tall(X)))&
((old(lucy)<~>~tall(lucy)))&
((~humble(lucy)<~>~tall(lucy)))&
(?[X]:((~brave(X)|~wise(X)))) | humble(mary) | [] | null | 0 |
Everyone who is both happy and quiet is both calm and happy and vice versa.
Everyone who is brave or quiet is both patient and strong and vice versa.
If someone is not brave or funny then someone is humble or not generous and vice versa.
Everyone who is both humble and not calm is either old or not strong.
If john is both not humble and not quiet then lucy is either not curious or not wise and vice versa.
Everyone who is both not humble and not strong is humble or not tall and vice versa.
If someone is both wise and quiet then someone is both humble and quiet and vice versa.
Everyone who is either quiet or not generous is both not wise and not happy and vice versa.
Everyone who is either not humble or not strong is tall or not old.
If someone is funny or not wise then someone is calm.
If paul is happy then lucy is kind or calm.
Everyone who is brave is either wise or creative and vice versa.
Everyone who is wise or happy is both curious and old and vice versa.
If someone is either not strong or curious then john is curious.
Everyone who is not happy is either not tall or not rich.
Everyone who is creative or kind is both not kind and rich and vice versa.
John is not happy or curious.
Lucy is not tall or humble.
Fred is rich or not quiet.
Alice is either not tall or not humble.
Alice is either not strong or not creative.
Fred is quiet.
John is not happy or not creative. | John is not funny. | neutral | (![X]:((happy(X)&quiet(X))<=>(calm(X)&happy(X))))&
(![X]:((brave(X)|quiet(X))<=>(patient(X)&strong(X))))&
((?[X]:((~brave(X)|funny(X))))<=>(?[X]:((humble(X)|~generous(X)))))&
(![X]:((humble(X)&~calm(X))=>(old(X)<~>~strong(X))))&
(((~humble(john)&~quiet(john)))<=>((~curious(lucy)<~>~wise(lucy))))&
(![X]:((~humble(X)&~strong(X))<=>(humble(X)|~tall(X))))&
((?[X]:((wise(X)&quiet(X))))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~wise(X)&~happy(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(tall(X)|~old(X))))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:(calm(X))))&
((happy(paul))=>((kind(lucy)|calm(lucy))))&
(![X]:(brave(X)<=>(wise(X)<~>creative(X))))&
(![X]:((wise(X)|happy(X))<=>(curious(X)&old(X))))&
((?[X]:((~strong(X)<~>curious(X))))=>(curious(john)))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((~happy(john)|curious(john)))&
((~tall(lucy)|humble(lucy)))&
((rich(fred)|~quiet(fred)))&
((~tall(alice)<~>~humble(alice)))&
((~strong(alice)<~>~creative(alice)))&
(quiet(fred))&
((~happy(john)|~creative(john))) | ~funny(john) | [] | null | 0 |
Everyone who is either not tall or quiet is not strong or creative and vice versa.
Everyone who is both humble and not happy is calm or humble and vice versa.
If someone is curious or not wise then someone is both patient and not humble and vice versa.
If someone is both patient and happy then john is both not rich and calm and vice versa.
Everyone who is not rich is both humble and calm and vice versa.
If someone is not humble then someone is wise or tall.
If someone is not wise then lucy is happy and vice versa.
Everyone who is creative or tall is either not rich or not strong.
Everyone who is not funny or not rich is either not generous or rich and vice versa.
If fred is not patient then john is both strong and not funny.
Everyone who is not wise is either not funny or quiet and vice versa.
Everyone who is both not brave and not tall is either calm or kind.
If someone is not strong then someone is humble or old.
Everyone who is both tall and strong is both happy and old and vice versa.
If someone is both not old and not tall then someone is not tall or funny and vice versa.
If someone is either not quiet or calm then someone is happy.
Alice is not wise or not strong.
Someone is not creative.
Fred is both brave and not funny.
Alice is not funny.
Someone is either not happy or humble.
Fred is happy or generous.
Someone is not wise or calm.
John is both not strong and tall. | Fred is quiet. | neutral | (![X]:((~tall(X)<~>quiet(X))<=>(~strong(X)|creative(X))))&
(![X]:((humble(X)&~happy(X))<=>(calm(X)|humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((~rich(john)&calm(john))))&
(![X]:(~rich(X)<=>(humble(X)&calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:(~wise(X)))<=>(happy(lucy)))&
(![X]:((creative(X)|tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~generous(X)<~>rich(X))))&
((~patient(fred))=>((strong(john)&~funny(john))))&
(![X]:(~wise(X)<=>(~funny(X)<~>quiet(X))))&
(![X]:((~brave(X)&~tall(X))=>(calm(X)<~>kind(X))))&
((?[X]:(~strong(X)))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((tall(X)&strong(X))<=>(happy(X)&old(X))))&
((?[X]:((~old(X)&~tall(X))))<=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:((~quiet(X)<~>calm(X))))=>(?[X]:(happy(X))))&
((~wise(alice)|~strong(alice)))&
(?[X]:(~creative(X)))&
((brave(fred)&~funny(fred)))&
(~funny(alice))&
(?[X]:((~happy(X)<~>humble(X))))&
((happy(fred)|generous(fred)))&
(?[X]:((~wise(X)|calm(X))))&
((~strong(john)&tall(john))) | quiet(fred) | [] | null | 0 |
If lucy is not tall or curious then fred is both wise and patient and vice versa.
If alice is not funny then someone is both not happy and funny.
Everyone who is not funny is not tall.
If susan is not funny or tall then paul is not humble or strong and vice versa.
Everyone who is either not humble or not funny is not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
If john is both curious and not creative then someone is either creative or not kind.
Someone is either wise or not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is not creative or curious.
Someone is not tall or patient.
Mary is either not strong or generous. | John is brave. | entailment | (((~tall(lucy)|curious(lucy)))<=>((wise(fred)&patient(fred))))&
((~funny(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~funny(X)=>~tall(X)))&
(((~funny(susan)|tall(susan)))<=>((~humble(paul)|strong(paul))))&
(![X]:((~humble(X)<~>~funny(X))<=>~tall(X)))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:((~tall(X)|patient(X))))&
((~strong(mary)<~>generous(mary))) | brave(john) | [
"p2",
"p4",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9107470874068633356909140
% SZS output start Proof for 9107470874068633356909140
3. ! [X0] : (~funny(X0) => ~tall(X0)) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p4]
10. ! [X0] : ((~strong(X0) <~> ~brave(X0)) => ~tall(X0)) [input p9]
13. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & ~calm(X0))) [input p12]
14. calm(mary) <=> ? [X0] : (strong(X0) <~> humble(X0)) [input p13]
23. ~brave(john) [input hypothesis]
27. ! [X0] : (~tall(X0) | funny(X0)) [ennf transformation 3]
31. ! [X0] : (~tall(X0) | (~strong(X0) <=> ~brave(X0))) [ennf transformation 10]
33. ! [X0] : ((tall(X0) & ~calm(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 13]
43. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | tall(X0)) & (~tall(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 5]
53. ! [X0] : (~tall(X0) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) [nnf transformation 31]
57. ! [X0] : ((tall(X0) & ~calm(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 33]
58. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~calm(mary)) [nnf transformation 14]
59. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) | ~calm(mary)) [rectify 58]
60. ? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) => ((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) [choice axiom]
61. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) | ~calm(mary)) [skolemisation 59,60]
82. ~tall(X0) | funny(X0) [cnf transformation 27]
87. ~tall(X0) | ~funny(X0) | humble(X0) [cnf transformation 43]
90. funny(X0) | humble(X0) | tall(X0) [cnf transformation 43]
104. ~strong(X0) | ~tall(X0) | brave(X0) [cnf transformation 53]
109. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
110. ~calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
111. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
112. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
116. calm(mary) | strong(X0) | ~humble(X0) [cnf transformation 61]
131. ~brave(john) [cnf transformation 23]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 109]
133. ~calm(X0) | ~quiet(X0) [duplicate literal removal 110]
134. tall(X0) | quiet(X0) [duplicate literal removal 111]
135. ~quiet(X0) | tall(X0) [duplicate literal removal 112]
191. humble(X0) | funny(X0) [subsumption resolution 90,82]
192. ~tall(X0) | humble(X0) [subsumption resolution 87,191]
267. tall(X0) [subsumption resolution 134,135]
268. ~calm(X0) [subsumption resolution 132,133]
269. ~humble(X0) | strong(X0) [subsumption resolution 116,268]
316. humble(X0) [resolution 192,267]
327. strong(X0) [resolution 269,316]
339. ~tall(X0) | brave(X0) [resolution 104,327]
341. brave(X0) [subsumption resolution 339,267]
343. $false [resolution 341,131]
% SZS output end Proof for 9107470874068633356909140
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or not creative then someone is both patient and wise and vice versa.
If someone is not kind or not patient then susan is both not brave and not funny.
If someone is rich then someone is either not brave or brave and vice versa.
Everyone who is not strong is quiet.
Everyone who is not tall or not funny is humble.
Everyone who is not generous or tall is brave.
Everyone who is not humble or not old is either calm or tall.
Everyone who is either not strong or not tall is funny or not rich and vice versa.
Everyone who is either generous or patient is patient and vice versa.
Everyone who is either tall or not generous is both old and wise.
Everyone who is brave or not calm is either funny or quiet and vice versa.
If someone is funny then someone is not generous.
If mary is both patient and generous then someone is not wise.
Everyone who is either not curious or happy is happy and vice versa.
If someone is both happy and not patient then someone is both not humble and strong and vice versa.
Fred is both not strong and tall.
Someone is either not happy or funny.
Alice is both strong and not generous.
John is either not happy or patient.
Someone is either not kind or not tall. | Mary is not strong. | neutral | ((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:((patient(X)&wise(X)))))&
((?[X]:((~kind(X)|~patient(X))))=>((~brave(susan)&~funny(susan))))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:(~strong(X)=>quiet(X)))&
(![X]:((~tall(X)|~funny(X))=>humble(X)))&
(![X]:((~generous(X)|tall(X))=>brave(X)))&
(![X]:((~humble(X)|~old(X))=>(calm(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>~generous(X))=>(old(X)&wise(X))))&
(![X]:((brave(X)|~calm(X))<=>(funny(X)<~>quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~generous(X))))&
(((patient(mary)&generous(mary)))=>(?[X]:(~wise(X))))&
(![X]:((~curious(X)<~>happy(X))<=>happy(X)))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((~humble(X)&strong(X)))))&
((~strong(fred)&tall(fred)))&
(?[X]:((~happy(X)<~>funny(X))))&
((strong(alice)&~generous(alice)))&
((~happy(john)<~>patient(john)))&
(?[X]:((~kind(X)<~>~tall(X)))) | ~strong(mary) | [] | null | 0 |
If susan is rich or not creative then someone is not funny. If fred is not wise or wise then fred is either curious or not brave and vice versa. If fred is quiet then someone is both not quiet and not generous. Everyone who is both not strong and rich is either not old or not patient. Everyone who is not curious is quiet. Everyone who is not curious is quiet or kind and vice versa. If lucy is funny or not rich then someone is not funny or tall and vice versa. If lucy is old then someone is wise or not brave and vice versa. Everyone who is quiet is both humble and not patient and vice versa. If someone is not old then someone is not wise and vice versa. Everyone who is not old or not tall is not patient. If someone is either not wise or humble then someone is not quiet or rich and vice versa. Everyone who is both funny and generous is not creative and vice versa. Everyone who is patient is both kind and generous. Everyone who is not rich is both not calm and not funny. If someone is not calm or not creative then someone is funny or not creative. Someone is both not strong and wise. John is curious. Lucy is either not patient or not old. Someone is either not curious or not happy. Lucy is both creative and kind. | John is not tall. | neutral | (((rich(susan)|~creative(susan)))=>(?[X]:(~funny(X))))&
(((~wise(fred)|wise(fred)))<=>((curious(fred)<~>~brave(fred))))&
((quiet(fred))=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:((~strong(X)&rich(X))=>(~old(X)<~>~patient(X))))&
(![X]:(~curious(X)=>quiet(X)))&
(![X]:(~curious(X)<=>(quiet(X)|kind(X))))&
(((funny(lucy)|~rich(lucy)))<=>(?[X]:((~funny(X)|tall(X)))))&
((old(lucy))<=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~patient(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~wise(X))))&
(![X]:((~old(X)|~tall(X))=>~patient(X)))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((funny(X)&generous(X))<=>~creative(X)))&
(![X]:(patient(X)=>(kind(X)&generous(X))))&
(![X]:(~rich(X)=>(~calm(X)&~funny(X))))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((funny(X)|~creative(X)))))&
(?[X]:((~strong(X)&wise(X))))&
(curious(john))&
((~patient(lucy)<~>~old(lucy)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((creative(lucy)&kind(lucy))) | ~tall(john) | [] | null | 0 |
Everyone who is not rich or not generous is both brave and not old and vice versa.
Everyone who is not quiet is not tall or patient and vice versa.
Everyone who is both kind and not brave is both not quiet and calm.
If someone is either not happy or happy then fred is old and vice versa.
If john is calm then fred is strong or not happy and vice versa.
If someone is both not quiet and quiet then someone is either not funny or not curious.
Everyone who is both humble and not wise is patient or not happy and vice versa.
If someone is either not strong or funny then mary is both rich and not calm.
Everyone who is not curious or rich is not quiet or not calm and vice versa.
Everyone who is patient or funny is patient and vice versa.
If alice is not strong or not tall then someone is not old or not funny.
If someone is either funny or rich then john is curious or kind.
Everyone who is happy or not quiet is rich or not quiet and vice versa.
Everyone who is either tall or not wise is not old.
Everyone who is not old is strong.
Everyone who is brave is tall or not old and vice versa.
Someone is humble or not kind.
John is curious.
John is either humble or wise.
Someone is both generous and brave.
Susan is curious or rich.
Someone is not rich or patient.
Mary is not humble.
Someone is both humble and not calm. | John is rich. | neutral | (![X]:((~rich(X)|~generous(X))<=>(brave(X)&~old(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|patient(X))))&
(![X]:((kind(X)&~brave(X))=>(~quiet(X)&calm(X))))&
((?[X]:((~happy(X)<~>happy(X))))<=>(old(fred)))&
((calm(john))<=>((strong(fred)|~happy(fred))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((humble(X)&~wise(X))<=>(patient(X)|~happy(X))))&
((?[X]:((~strong(X)<~>funny(X))))=>((rich(mary)&~calm(mary))))&
(![X]:((~curious(X)|rich(X))<=>(~quiet(X)|~calm(X))))&
(![X]:((patient(X)|funny(X))<=>patient(X)))&
(((~strong(alice)|~tall(alice)))=>(?[X]:((~old(X)|~funny(X)))))&
((?[X]:((funny(X)<~>rich(X))))=>((curious(john)|kind(john))))&
(![X]:((happy(X)|~quiet(X))<=>(rich(X)|~quiet(X))))&
(![X]:((tall(X)<~>~wise(X))=>~old(X)))&
(![X]:(~old(X)=>strong(X)))&
(![X]:(brave(X)<=>(tall(X)|~old(X))))&
(?[X]:((humble(X)|~kind(X))))&
(curious(john))&
((humble(john)<~>wise(john)))&
(?[X]:((generous(X)&brave(X))))&
((curious(susan)|rich(susan)))&
(?[X]:((~rich(X)|patient(X))))&
(~humble(mary))&
(?[X]:((humble(X)&~calm(X)))) | rich(john) | [] | null | 0 |
Everyone who is funny or quiet is creative or patient and vice versa.
Everyone who is not kind or calm is either curious or creative and vice versa.
If someone is not calm then someone is not strong.
Everyone who is both strong and old is kind or calm.
Everyone who is either funny or old is either not wise or not generous and vice versa.
If someone is either wise or brave then someone is either tall or curious.
If someone is not rich or rich then paul is either brave or not humble and vice versa.
If lucy is either funny or old then someone is not curious or kind and vice versa.
If someone is not happy or not old then paul is not patient.
Everyone who is either wise or not old is both wise and kind and vice versa.
Everyone who is both curious and strong is humble or not wise.
Everyone who is both not happy and tall is not creative or strong.
Everyone who is not old or not kind is both generous and old.
Everyone who is both funny and not humble is tall or not calm and vice versa.
Everyone who is either not wise or not creative is wise or not patient.
Everyone who is both generous and not wise is either not creative or patient and vice versa.
Mary is both wise and tall.
Someone is either generous or rich.
Lucy is either patient or quiet.
Someone is happy or not quiet.
Fred is both calm and strong.
Susan is either humble or kind.
Paul is not tall. | Lucy is wise. | entailment | (![X]:((funny(X)|quiet(X))<=>(creative(X)|patient(X))))&
(![X]:((~kind(X)|calm(X))<=>(curious(X)<~>creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~strong(X))))&
(![X]:((strong(X)&old(X))=>(kind(X)|calm(X))))&
(![X]:((funny(X)<~>old(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:((wise(X)<~>brave(X))))=>(?[X]:((tall(X)<~>curious(X)))))&
((?[X]:((~rich(X)|rich(X))))<=>((brave(paul)<~>~humble(paul))))&
(((funny(lucy)<~>old(lucy)))<=>(?[X]:((~curious(X)|kind(X)))))&
((?[X]:((~happy(X)|~old(X))))=>(~patient(paul)))&
(![X]:((wise(X)<~>~old(X))<=>(wise(X)&kind(X))))&
(![X]:((curious(X)&strong(X))=>(humble(X)|~wise(X))))&
(![X]:((~happy(X)&tall(X))=>(~creative(X)|strong(X))))&
(![X]:((~old(X)|~kind(X))=>(generous(X)&old(X))))&
(![X]:((funny(X)&~humble(X))<=>(tall(X)|~calm(X))))&
(![X]:((~wise(X)<~>~creative(X))=>(wise(X)|~patient(X))))&
(![X]:((generous(X)&~wise(X))<=>(~creative(X)<~>patient(X))))&
((wise(mary)&tall(mary)))&
(?[X]:((generous(X)<~>rich(X))))&
((patient(lucy)<~>quiet(lucy)))&
(?[X]:((happy(X)|~quiet(X))))&
((calm(fred)&strong(fred)))&
((humble(susan)<~>kind(susan)))&
(~tall(paul)) | wise(lucy) | [
"p0",
"p4",
"p7",
"p9",
"p12",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4087723388779920469426198
% SZS output start Proof for 4087723388779920469426198
1. ! [X0] : ((quiet(X0) | funny(X0)) <=> (patient(X0) | creative(X0))) [input p0]
5. ! [X0] : ((funny(X0) <~> old(X0)) <=> (~wise(X0) <~> ~generous(X0))) [input p4]
8. (funny(lucy) <~> old(lucy)) <=> ? [X0] : (kind(X0) | ~curious(X0)) [input p7]
10. ! [X0] : ((wise(X0) <~> ~old(X0)) <=> (kind(X0) & wise(X0))) [input p9]
13. ! [X0] : ((~kind(X0) | ~old(X0)) => (old(X0) & generous(X0))) [input p12]
15. ! [X0] : ((~wise(X0) <~> ~creative(X0)) => (~patient(X0) | wise(X0))) [input p14]
16. ! [X0] : ((~wise(X0) & generous(X0)) <=> (~creative(X0) <~> patient(X0))) [input p15]
17. tall(mary) & wise(mary) [input p16]
19. patient(lucy) <~> quiet(lucy) [input p18]
24. ~wise(lucy) [input hypothesis]
37. ! [X0] : ((old(X0) & generous(X0)) | (kind(X0) & old(X0))) [ennf transformation 13]
38. ! [X0] : ((~patient(X0) | wise(X0)) | (~wise(X0) <=> ~creative(X0))) [ennf transformation 15]
39. ! [X0] : (~patient(X0) | wise(X0) | (~wise(X0) <=> ~creative(X0))) [flattening 38]
40. ! [X0] : (((quiet(X0) | funny(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((quiet(X0) | funny(X0) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 40]
47. ! [X0] : ((((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) & (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0))))) [nnf transformation 5]
56. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & (? [X0] : (kind(X0) | ~curious(X0)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [nnf transformation 8]
57. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & (? [X1] : (kind(X1) | ~curious(X1)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [rectify 56]
58. ? [X1] : (kind(X1) | ~curious(X1)) => (kind(sK3) | ~curious(sK3)) [choice axiom]
59. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & ((kind(sK3) | ~curious(sK3)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [skolemisation 57,58]
60. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [nnf transformation 10]
61. ! [X0] : ((((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0))))) [flattening 60]
64. ! [X0] : (~patient(X0) | wise(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) [nnf transformation 39]
65. ! [X0] : (((~wise(X0) & generous(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (wise(X0) | ~generous(X0)))) [nnf transformation 16]
66. ! [X0] : (((~wise(X0) & generous(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | wise(X0) | ~generous(X0))) [flattening 65]
70. (~quiet(lucy) | ~patient(lucy)) & (quiet(lucy) | patient(lucy)) [nnf transformation 19]
73. ~quiet(X0) | creative(X0) | patient(X0) [cnf transformation 41]
75. ~patient(X0) | funny(X0) | quiet(X0) [cnf transformation 41]
87. ~old(X0) | wise(X0) | funny(X0) | generous(X0) [cnf transformation 47]
107. ~old(lucy) | ~funny(lucy) | ~kind(X0) [cnf transformation 59]
111. ~wise(X0) | ~old(X0) | kind(X0) [cnf transformation 61]
118. old(X0) | old(X0) [cnf transformation 37]
125. ~patient(X0) | wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 64]
127. patient(X0) | ~creative(X0) | wise(X0) | ~generous(X0) [cnf transformation 66]
128. ~patient(X0) | creative(X0) | wise(X0) | ~generous(X0) [cnf transformation 66]
133. wise(mary) [cnf transformation 17]
137. quiet(lucy) | patient(lucy) [cnf transformation 70]
138. ~quiet(lucy) | ~patient(lucy) [cnf transformation 70]
144. ~wise(lucy) [cnf transformation 24]
145. ~patient(X0) | wise(X0) | ~creative(X0) [duplicate literal removal 125]
146. old(X0) [duplicate literal removal 118]
194. 11 <=> ! [X0] : ~kind(X0) [avatar definition]
195. ~kind(X0) <- (11) [avatar component clause 194]
197. 12 <=> funny(lucy) [avatar definition]
199. ~funny(lucy) <- (~12) [avatar component clause 197]
201. 13 <=> old(lucy) [avatar definition]
203. ~old(lucy) <- (~13) [avatar component clause 201]
204. 11 | ~12 | ~13 [avatar split clause 107,201,197,194]
222. 17 <=> ! [X0] : old(X0) [avatar definition]
223. old(X0) <- (17) [avatar component clause 222]
229. 17 [avatar split clause 146,222]
231. ~generous(X0) | wise(X0) | ~patient(X0) [subsumption resolution 128,145]
232. ~generous(X0) | wise(X0) | ~creative(X0) [subsumption resolution 127,231]
244. 21 <=> patient(lucy) [avatar definition]
245. patient(lucy) <- (21) [avatar component clause 244]
246. ~patient(lucy) <- (~21) [avatar component clause 244]
248. 22 <=> quiet(lucy) [avatar definition]
249. quiet(lucy) <- (22) [avatar component clause 248]
250. ~quiet(lucy) <- (~22) [avatar component clause 248]
251. ~21 | ~22 [avatar split clause 138,248,244]
252. 21 | 22 [avatar split clause 137,248,244]
263. $false <- (~13, 17) [subsumption resolution 203,223]
264. 13 | ~17 [avatar contradiction clause 263]
293. funny(lucy) | quiet(lucy) <- (21) [resolution 75,245]
298. funny(lucy) <- (21, ~22) [subsumption resolution 293,250]
299. 12 | ~21 | 22 [avatar split clause 298,248,244,197]
305. creative(lucy) | patient(lucy) <- (22) [resolution 249,73]
306. creative(lucy) <- (~21, 22) [subsumption resolution 305,246]
373. ~old(mary) | kind(mary) [resolution 111,133]
375. kind(mary) <- (17) [subsumption resolution 373,223]
491. generous(X1) | funny(X1) | wise(X1) <- (17) [resolution 87,223]
603. funny(X4) | wise(X4) | wise(X4) | ~creative(X4) <- (17) [resolution 491,232]
606. ~creative(X4) | wise(X4) | funny(X4) <- (17) [duplicate literal removal 603]
642. wise(lucy) | funny(lucy) <- (17, ~21, 22) [resolution 606,306]
644. funny(lucy) <- (17, ~21, 22) [subsumption resolution 642,144]
645. $false <- (~12, 17, ~21, 22) [subsumption resolution 644,199]
646. 12 | ~17 | 21 | ~22 [avatar contradiction clause 645]
671. $false <- (11, 17) [resolution 195,375]
676. ~11 | ~17 [avatar contradiction clause 671]
677. $false [avatar sat refutation 204,229,251,252,264,299,646,676]
% SZS output end Proof for 4087723388779920469426198
% ------------------------------
% 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not creative is both quiet and rich and vice versa. If someone is not strong then someone is both not generous and quiet. If lucy is tall then paul is kind or not strong and vice versa. If mary is either not wise or strong then someone is either strong or kind and vice versa. Everyone who is not wise or brave is both not happy and not kind and vice versa. Everyone who is either humble or not curious is either not old or not calm and vice versa. Everyone who is either not strong or quiet is wise. Everyone who is not curious or brave is either not wise or patient. Everyone who is either creative or kind is not generous and vice versa. Everyone who is not tall is either not quiet or calm. If susan is both brave and not quiet then susan is either not calm or not funny and vice versa. If alice is not brave then someone is old or humble and vice versa. Everyone who is both brave and generous is both old and patient. If someone is either not humble or generous then mary is both strong and not calm and vice versa. Everyone who is either strong or patient is either wise or creative and vice versa. Everyone who is either not patient or brave is not tall and vice versa. Someone is either not rich or not tall. Mary is either kind or not curious. Lucy is both not humble and not brave. Susan is both funny and not old. Someone is either humble or strong. John is not strong or old. Mary is happy. Someone is either not kind or quiet. | Alice is not calm. | neutral | (![X]:((~calm(X)<~>~creative(X))<=>(quiet(X)&rich(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~generous(X)&quiet(X)))))&
((tall(lucy))<=>((kind(paul)|~strong(paul))))&
(((~wise(mary)<~>strong(mary)))<=>(?[X]:((strong(X)<~>kind(X)))))&
(![X]:((~wise(X)|brave(X))<=>(~happy(X)&~kind(X))))&
(![X]:((humble(X)<~>~curious(X))<=>(~old(X)<~>~calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>wise(X)))&
(![X]:((~curious(X)|brave(X))=>(~wise(X)<~>patient(X))))&
(![X]:((creative(X)<~>kind(X))<=>~generous(X)))&
(![X]:(~tall(X)=>(~quiet(X)<~>calm(X))))&
(((brave(susan)&~quiet(susan)))<=>((~calm(susan)<~>~funny(susan))))&
((~brave(alice))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:((brave(X)&generous(X))=>(old(X)&patient(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>((strong(mary)&~calm(mary))))&
(![X]:((strong(X)<~>patient(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)<~>brave(X))<=>~tall(X)))&
(?[X]:((~rich(X)<~>~tall(X))))&
((kind(mary)<~>~curious(mary)))&
((~humble(lucy)&~brave(lucy)))&
((funny(susan)&~old(susan)))&
(?[X]:((humble(X)<~>strong(X))))&
((~strong(john)|old(john)))&
(happy(mary))&
(?[X]:((~kind(X)<~>quiet(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is not strong is either strong or brave and vice versa. If someone is not happy or quiet then someone is old. If someone is humble or not happy then alice is curious or not funny. Everyone who is either not quiet or strong is either creative or humble. Everyone who is wise is both not brave and wise and vice versa. If someone is not quiet or funny then someone is strong or curious. If lucy is not kind then someone is not generous. If paul is not happy or not humble then mary is not rich and vice versa. Everyone who is both humble and old is both not calm and not kind and vice versa. If someone is not old then john is both happy and not patient and vice versa. Everyone who is brave is either not calm or kind and vice versa. If john is creative then someone is both happy and not kind and vice versa. If someone is happy or generous then paul is strong or not strong and vice versa. If someone is either not happy or not brave then fred is generous or not calm and vice versa. If someone is not creative or happy then someone is both not rich and happy. Everyone who is strong is not calm or tall and vice versa. Paul is old or not quiet. Mary is tall. Someone is both not curious and rich. Alice is not rich or not humble. Mary is either generous or old. Mary is both curious and not rich. | Alice is funny. | neutral | (![X]:(~strong(X)<=>(strong(X)<~>brave(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~happy(X))))=>((curious(alice)|~funny(alice))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~brave(X)&wise(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((strong(X)|curious(X)))))&
((~kind(lucy))=>(?[X]:(~generous(X))))&
(((~happy(paul)|~humble(paul)))<=>(~rich(mary)))&
(![X]:((humble(X)&old(X))<=>(~calm(X)&~kind(X))))&
((?[X]:(~old(X)))<=>((happy(john)&~patient(john))))&
(![X]:(brave(X)<=>(~calm(X)<~>kind(X))))&
((creative(john))<=>(?[X]:((happy(X)&~kind(X)))))&
((?[X]:((happy(X)|generous(X))))<=>((strong(paul)|~strong(paul))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>((generous(fred)|~calm(fred))))&
((?[X]:((~creative(X)|happy(X))))=>(?[X]:((~rich(X)&happy(X)))))&
(![X]:(strong(X)<=>(~calm(X)|tall(X))))&
((old(paul)|~quiet(paul)))&
(tall(mary))&
(?[X]:((~curious(X)&rich(X))))&
((~rich(alice)|~humble(alice)))&
((generous(mary)<~>old(mary)))&
((curious(mary)&~rich(mary))) | funny(alice) | [] | null | 0 |
Everyone who is either not curious or not old is tall or happy.
Everyone who is both not strong and not rich is wise or not brave and vice versa.
If someone is not calm or wise then lucy is curious.
Everyone who is patient or humble is funny.
If mary is not patient or not quiet then john is either kind or patient and vice versa.
Everyone who is not calm or not humble is both funny and not wise and vice versa.
Everyone who is not calm is both happy and not strong.
If someone is both kind and humble then lucy is both not old and old and vice versa.
Everyone who is both not brave and funny is both humble and curious.
Everyone who is both not funny and not tall is brave and vice versa.
Everyone who is strong is not creative and vice versa.
If someone is both tall and not calm then someone is tall and vice versa.
If someone is either creative or not wise then alice is either not calm or not patient.
If someone is not patient or not curious then someone is wise.
If mary is not creative then alice is humble.
Paul is curious.
Someone is both not calm and curious.
John is either quiet or not calm.
Paul is not calm or not creative.
Someone is either not tall or not patient.
Susan is not generous or generous. | Paul is not rich. | entailment | (![X]:((~curious(X)<~>~old(X))=>(tall(X)|happy(X))))&
(![X]:((~strong(X)&~rich(X))<=>(wise(X)|~brave(X))))&
((?[X]:((~calm(X)|wise(X))))=>(curious(lucy)))&
(![X]:((patient(X)|humble(X))=>funny(X)))&
(((~patient(mary)|~quiet(mary)))<=>((kind(john)<~>patient(john))))&
(![X]:((~calm(X)|~humble(X))<=>(funny(X)&~wise(X))))&
(![X]:(~calm(X)=>(happy(X)&~strong(X))))&
((?[X]:((kind(X)&humble(X))))<=>((~old(lucy)&old(lucy))))&
(![X]:((~brave(X)&funny(X))=>(humble(X)&curious(X))))&
(![X]:((~funny(X)&~tall(X))<=>brave(X)))&
(![X]:(strong(X)<=>~creative(X)))&
((?[X]:((tall(X)&~calm(X))))<=>(?[X]:(tall(X))))&
((?[X]:((creative(X)<~>~wise(X))))=>((~calm(alice)<~>~patient(alice))))&
((?[X]:((~patient(X)|~curious(X))))=>(?[X]:(wise(X))))&
((~creative(mary))=>(humble(alice)))&
(curious(paul))&
(?[X]:((~calm(X)&curious(X))))&
((quiet(john)<~>~calm(john)))&
((~calm(paul)|~creative(paul)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~generous(susan)|generous(susan))) | ~rich(paul) | [
"p1",
"p3",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 391330838803593487120619
% SZS output start Proof for 391330838803593487120619
2. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (~brave(X0) | wise(X0))) [input p1]
4. ! [X0] : ((humble(X0) | patient(X0)) => funny(X0)) [input p3]
6. ! [X0] : ((~humble(X0) | ~calm(X0)) <=> (~wise(X0) & funny(X0))) [input p5]
10. ! [X0] : ((~tall(X0) & ~funny(X0)) <=> brave(X0)) [input p9]
22. rich(paul) [input hypothesis]
32. ! [X0] : (funny(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 4]
39. ! [X0] : (((~rich(X0) & ~strong(X0)) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 2]
40. ! [X0] : (((~rich(X0) & ~strong(X0)) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | rich(X0) | strong(X0))) [flattening 39]
43. ! [X0] : (((~humble(X0) | ~calm(X0)) | (wise(X0) | ~funny(X0))) & ((~wise(X0) & funny(X0)) | (humble(X0) & calm(X0)))) [nnf transformation 6]
44. ! [X0] : ((~humble(X0) | ~calm(X0) | wise(X0) | ~funny(X0)) & ((~wise(X0) & funny(X0)) | (humble(X0) & calm(X0)))) [flattening 43]
50. ! [X0] : (((~tall(X0) & ~funny(X0)) | ~brave(X0)) & (brave(X0) | (tall(X0) | funny(X0)))) [nnf transformation 10]
51. ! [X0] : (((~tall(X0) & ~funny(X0)) | ~brave(X0)) & (brave(X0) | tall(X0) | funny(X0))) [flattening 50]
72. ~rich(X0) | brave(X0) [cnf transformation 40]
74. funny(X0) | ~humble(X0) [cnf transformation 32]
82. funny(X0) | humble(X0) [cnf transformation 44]
93. ~funny(X0) | ~brave(X0) [cnf transformation 51]
113. rich(paul) [cnf transformation 22]
137. funny(X0) [subsumption resolution 82,74]
148. ~brave(X0) [subsumption resolution 93,137]
242. brave(paul) [resolution 72,113]
243. $false [subsumption resolution 242,148]
% SZS output end Proof for 391330838803593487120619
% ------------------------------
% 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 strong or not old is both not creative and not happy and vice versa.
Everyone who is both not happy and tall is either calm or quiet and vice versa.
Everyone who is either happy or calm is either not old or not happy and vice versa.
If someone is both funny and creative then fred is either not patient or not happy.
Everyone who is not curious or not brave is either wise or not rich.
If someone is curious then someone is happy or calm.
Everyone who is not calm or happy is both wise and not rich.
Everyone who is not old is kind and vice versa.
Everyone who is both not old and not strong is quiet and vice versa.
Everyone who is funny is quiet or not strong and vice versa.
Everyone who is both creative and not wise is calm or not happy and vice versa.
If susan is calm then someone is not old or not generous and vice versa.
If someone is rich or generous then someone is both not old and wise.
Everyone who is either not quiet or kind is either not funny or happy and vice versa.
If someone is old then someone is either wise or not brave.
Lucy is not quiet.
John is not brave.
Someone is curious or not calm. | Fred is not brave. | neutral | (![X]:((~strong(X)|~old(X))<=>(~creative(X)&~happy(X))))&
(![X]:((~happy(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((funny(X)&creative(X))))=>((~patient(fred)<~>~happy(fred))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)<~>~rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~calm(X)|happy(X))=>(wise(X)&~rich(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~old(X)&~strong(X))<=>quiet(X)))&
(![X]:(funny(X)<=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)&~wise(X))<=>(calm(X)|~happy(X))))&
((calm(susan))<=>(?[X]:((~old(X)|~generous(X)))))&
((?[X]:((rich(X)|generous(X))))=>(?[X]:((~old(X)&wise(X)))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(old(X)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(~quiet(lucy))&
(~brave(john))&
(?[X]:((curious(X)|~calm(X)))) | ~brave(fred) | [] | null | 0 |
If alice is not old then someone is either rich or not curious and vice versa. If mary is brave or quiet then someone is either tall or rich and vice versa. Everyone who is both humble and not wise is happy or not old and vice versa. If someone is not wise or not happy then someone is either not kind or not happy. Everyone who is not strong is both strong and calm and vice versa. Everyone who is not creative is not calm and vice versa. If someone is strong then paul is happy and vice versa. If susan is patient or not quiet then lucy is not strong and vice versa. If mary is brave then john is both not calm and not patient. If someone is not patient then someone is not tall or strong and vice versa. Everyone who is both not happy and not humble is wise or not funny and vice versa. Everyone who is calm or not humble is brave. Everyone who is generous is not wise and vice versa. Everyone who is humble is either rich or not old and vice versa. If someone is either not funny or not strong then john is not strong or not humble. Everyone who is not generous is both not creative and not patient and vice versa. Someone is either quiet or humble. Someone is not funny or brave. Someone is both not tall and not creative. Lucy is both not rich and patient. Fred is humble. | John is not tall. | neutral | ((~old(alice))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(((brave(mary)|quiet(mary)))<=>(?[X]:((tall(X)<~>rich(X)))))&
(![X]:((humble(X)&~wise(X))<=>(happy(X)|~old(X))))&
((?[X]:((~wise(X)|~happy(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:(~strong(X)<=>(strong(X)&calm(X))))&
(![X]:(~creative(X)<=>~calm(X)))&
((?[X]:(strong(X)))<=>(happy(paul)))&
(((patient(susan)|~quiet(susan)))<=>(~strong(lucy)))&
((brave(mary))=>((~calm(john)&~patient(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((~happy(X)&~humble(X))<=>(wise(X)|~funny(X))))&
(![X]:((calm(X)|~humble(X))=>brave(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(humble(X)<=>(rich(X)<~>~old(X))))&
((?[X]:((~funny(X)<~>~strong(X))))=>((~strong(john)|~humble(john))))&
(![X]:(~generous(X)<=>(~creative(X)&~patient(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((~rich(lucy)&patient(lucy)))&
(humble(fred)) | ~tall(john) | [] | null | 0 |
Everyone who is curious is either curious or not kind.
If mary is either not quiet or strong then someone is both patient and not rich.
Everyone who is either not rich or generous is either not patient or strong and vice versa.
If mary is both happy and generous then susan is both old and curious and vice versa.
Everyone who is either not happy or calm is either generous or not creative and vice versa.
Everyone who is both not funny and not humble is humble or curious.
If fred is both not humble and wise then fred is both not brave and not calm.
If someone is both rich and calm then alice is both not old and wise and vice versa.
If someone is creative or wise then fred is either not brave or quiet and vice versa.
If someone is both not brave and not calm then someone is both funny and creative.
Everyone who is quiet or not creative is happy.
Everyone who is both generous and calm is either calm or happy and vice versa.
If someone is not brave then susan is happy or not funny.
Everyone who is both not generous and not happy is quiet and vice versa.
If susan is both not strong and not funny then someone is kind or not generous and vice versa.
If someone is both not curious and not patient then alice is both calm and kind and vice versa.
Paul is not humble.
Susan is both wise and strong.
Alice is either not brave or wise.
Someone is either brave or not kind.
Paul is generous.
Someone is both funny and old.
Fred is either not creative or not brave. | Paul is creative. | entailment | (![X]:(curious(X)=>(curious(X)<~>~kind(X))))&
(((~quiet(mary)<~>strong(mary)))=>(?[X]:((patient(X)&~rich(X)))))&
(![X]:((~rich(X)<~>generous(X))<=>(~patient(X)<~>strong(X))))&
(((happy(mary)&generous(mary)))<=>((old(susan)&curious(susan))))&
(![X]:((~happy(X)<~>calm(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((~funny(X)&~humble(X))=>(humble(X)|curious(X))))&
(((~humble(fred)&wise(fred)))=>((~brave(fred)&~calm(fred))))&
((?[X]:((rich(X)&calm(X))))<=>((~old(alice)&wise(alice))))&
((?[X]:((creative(X)|wise(X))))<=>((~brave(fred)<~>quiet(fred))))&
((?[X]:((~brave(X)&~calm(X))))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((quiet(X)|~creative(X))=>happy(X)))&
(![X]:((generous(X)&calm(X))<=>(calm(X)<~>happy(X))))&
((?[X]:(~brave(X)))=>((happy(susan)|~funny(susan))))&
(![X]:((~generous(X)&~happy(X))<=>quiet(X)))&
(((~strong(susan)&~funny(susan)))<=>(?[X]:((kind(X)|~generous(X)))))&
((?[X]:((~curious(X)&~patient(X))))<=>((calm(alice)&kind(alice))))&
(~humble(paul))&
((wise(susan)&strong(susan)))&
((~brave(alice)<~>wise(alice)))&
(?[X]:((brave(X)<~>~kind(X))))&
(generous(paul))&
(?[X]:((funny(X)&old(X))))&
((~creative(fred)<~>~brave(fred))) | creative(paul) | [
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2642764284658211794145987
% SZS output start Proof for 2642764284658211794145987
11. ! [X0] : ((~creative(X0) | quiet(X0)) => happy(X0)) [input p10]
12. ! [X0] : ((calm(X0) & generous(X0)) <=> (calm(X0) <~> happy(X0))) [input p11]
21. generous(paul) [input p20]
24. ~creative(paul) [input hypothesis]
33. ! [X0] : (happy(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 11]
56. ! [X0] : (((calm(X0) & generous(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 12]
57. ! [X0] : (((calm(X0) & generous(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ~calm(X0) | ~generous(X0))) [flattening 56]
119. creative(X0) | happy(X0) [cnf transformation 33]
121. ~happy(X0) | ~calm(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 57]
125. calm(X0) | calm(X0) | ~happy(X0) [cnf transformation 57]
146. generous(paul) [cnf transformation 21]
151. ~creative(paul) [cnf transformation 24]
152. ~happy(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 121]
153. ~happy(X0) | calm(X0) [duplicate literal removal 125]
274. ~happy(X0) | ~generous(X0) [subsumption resolution 152,153]
370. happy(paul) [resolution 119,151]
379. ~generous(paul) [resolution 274,370]
380. $false [subsumption resolution 379,146]
% SZS output end Proof for 2642764284658211794145987
% ------------------------------
% 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 wise is both not kind and not quiet.
Everyone who is not strong is either not patient or not quiet and vice versa.
If someone is both brave and humble then mary is wise or creative and vice versa.
Everyone who is quiet is either creative or tall and vice versa.
Everyone who is old is both kind and calm.
If someone is not creative then susan is either not curious or generous.
Everyone who is both strong and old is patient or not funny.
Everyone who is curious or not curious is either rich or not creative and vice versa.
If fred is not happy then alice is either happy or humble and vice versa.
Everyone who is kind or tall is either rich or not kind and vice versa.
If susan is patient or funny then someone is not strong and vice versa.
Everyone who is both not calm and funny is calm.
Everyone who is not kind or curious is both strong and not rich.
If someone is not old then someone is either rich or brave and vice versa.
If alice is both not humble and humble then john is not funny or not creative and vice versa.
Everyone who is either not happy or not kind is not old or quiet.
Mary is not rich.
Someone is either not humble or not rich.
Mary is either tall or not calm.
Someone is tall or generous.
Susan is either not patient or brave.
Paul is both happy and tall.
Alice is funny.
Someone is kind or curious. | Susan is not wise. | entailment | (![X]:(wise(X)=>(~kind(X)&~quiet(X))))&
(![X]:(~strong(X)<=>(~patient(X)<~>~quiet(X))))&
((?[X]:((brave(X)&humble(X))))<=>((wise(mary)|creative(mary))))&
(![X]:(quiet(X)<=>(creative(X)<~>tall(X))))&
(![X]:(old(X)=>(kind(X)&calm(X))))&
((?[X]:(~creative(X)))=>((~curious(susan)<~>generous(susan))))&
(![X]:((strong(X)&old(X))=>(patient(X)|~funny(X))))&
(![X]:((curious(X)|~curious(X))<=>(rich(X)<~>~creative(X))))&
((~happy(fred))<=>((happy(alice)<~>humble(alice))))&
(![X]:((kind(X)|tall(X))<=>(rich(X)<~>~kind(X))))&
(((patient(susan)|funny(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&funny(X))=>calm(X)))&
(![X]:((~kind(X)|curious(X))=>(strong(X)&~rich(X))))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>brave(X)))))&
(((~humble(alice)&humble(alice)))<=>((~funny(john)|~creative(john))))&
(![X]:((~happy(X)<~>~kind(X))=>(~old(X)|quiet(X))))&
(~rich(mary))&
(?[X]:((~humble(X)<~>~rich(X))))&
((tall(mary)<~>~calm(mary)))&
(?[X]:((tall(X)|generous(X))))&
((~patient(susan)<~>brave(susan)))&
((happy(paul)&tall(paul)))&
(funny(alice))&
(?[X]:((kind(X)|curious(X)))) | ~wise(susan) | [
"p0",
"p3",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3860026092567805737930514
% SZS output start Proof for 3860026092567805737930514
1. ! [X0] : (wise(X0) => (~quiet(X0) & ~kind(X0))) [input p0]
4. ! [X0] : (quiet(X0) <=> (creative(X0) <~> tall(X0))) [input p3]
8. ! [X0] : ((~curious(X0) | curious(X0)) <=> (rich(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : ((tall(X0) | kind(X0)) <=> (rich(X0) <~> ~kind(X0))) [input p9]
13. ! [X0] : ((curious(X0) | ~kind(X0)) => (~rich(X0) & strong(X0))) [input p12]
25. wise(susan) [input hypothesis]
27. ! [X0] : ((~quiet(X0) & ~kind(X0)) | ~wise(X0)) [ennf transformation 1]
34. ! [X0] : ((~rich(X0) & strong(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
43. ! [X0] : ((quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~quiet(X0))) [nnf transformation 4]
45. ! [X0] : (((~curious(X0) | curious(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | curious(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [flattening 45]
48. ! [X0] : (((tall(X0) | kind(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | kind(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [flattening 48]
72. ~kind(X0) | ~wise(X0) [cnf transformation 27]
73. ~quiet(X0) | ~wise(X0) [cnf transformation 27]
86. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 43]
92. ~creative(X0) | rich(X0) | ~curious(X0) [cnf transformation 46]
93. ~creative(X0) | rich(X0) | curious(X0) [cnf transformation 46]
102. ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 49]
105. ~rich(X0) | kind(X0) | ~tall(X0) [cnf transformation 49]
107. tall(X0) | kind(X0) | rich(X0) | kind(X0) [cnf transformation 49]
114. ~rich(X0) | kind(X0) [cnf transformation 34]
139. wise(susan) [cnf transformation 25]
141. ~kind(X0) | rich(X0) [duplicate literal removal 102]
142. rich(X0) | kind(X0) | tall(X0) [duplicate literal removal 107]
181. ~creative(X0) | rich(X0) [subsumption resolution 92,93]
446. kind(X4) | tall(X4) | kind(X4) [resolution 142,114]
447. tall(X4) | kind(X4) [duplicate literal removal 446]
522. creative(X1) | kind(X1) | quiet(X1) [resolution 447,86]
557. kind(X2) | quiet(X2) | rich(X2) [resolution 522,181]
564. rich(X2) | quiet(X2) [subsumption resolution 557,141]
578. quiet(X0) | kind(X0) | ~tall(X0) [resolution 564,105]
583. quiet(X0) | kind(X0) [subsumption resolution 578,447]
607. kind(X3) | ~wise(X3) [resolution 583,73]
610. ~wise(X3) [subsumption resolution 607,72]
619. $false [resolution 610,139]
% SZS output end Proof for 3860026092567805737930514
% ------------------------------
% 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 both not curious and not brave then someone is tall or not humble.
Everyone who is both quiet and not funny is not kind.
Everyone who is either creative or not quiet is curious.
If mary is both not strong and not rich then someone is generous.
Everyone who is not curious or happy is not curious.
Everyone who is patient is creative.
Everyone who is both happy and not creative is not quiet or patient and vice versa.
If mary is either wise or generous then susan is not patient and vice versa.
Everyone who is either not brave or not curious is not brave and vice versa.
If someone is either funny or not curious then susan is not patient or humble and vice versa.
Everyone who is old or wise is old or not kind and vice versa.
Everyone who is both not patient and creative is either patient or not humble.
Everyone who is brave or patient is kind or rich and vice versa.
Everyone who is not curious is tall and vice versa.
Everyone who is both happy and kind is creative or not curious and vice versa.
If someone is both not old and not strong then paul is either not generous or calm and vice versa.
Someone is either not funny or calm.
Lucy is brave.
Someone is either curious or generous.
Someone is either patient or not happy.
Someone is either not wise or brave.
Lucy is humble or not rich. | Susan is happy. | contradiction | ((?[X]:((~curious(X)&~brave(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((quiet(X)&~funny(X))=>~kind(X)))&
(![X]:((creative(X)<~>~quiet(X))=>curious(X)))&
(((~strong(mary)&~rich(mary)))=>(?[X]:(generous(X))))&
(![X]:((~curious(X)|happy(X))=>~curious(X)))&
(![X]:(patient(X)=>creative(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|patient(X))))&
(((wise(mary)<~>generous(mary)))<=>(~patient(susan)))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>((~patient(susan)|humble(susan))))&
(![X]:((old(X)|wise(X))<=>(old(X)|~kind(X))))&
(![X]:((~patient(X)&creative(X))=>(patient(X)<~>~humble(X))))&
(![X]:((brave(X)|patient(X))<=>(kind(X)|rich(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((happy(X)&kind(X))<=>(creative(X)|~curious(X))))&
((?[X]:((~old(X)&~strong(X))))<=>((~generous(paul)<~>calm(paul))))&
(?[X]:((~funny(X)<~>calm(X))))&
(brave(lucy))&
(?[X]:((curious(X)<~>generous(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~wise(X)<~>brave(X))))&
((humble(lucy)|~rich(lucy))) | happy(susan) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5706005540321981964778018
% SZS output start Proof for 5706005540321981964778018
5. ! [X0] : ((happy(X0) | ~curious(X0)) => ~curious(X0)) [input p4]
9. ! [X0] : ((~brave(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p8]
23. happy(susan) [input hypothesis]
31. ! [X0] : (~curious(X0) | (~happy(X0) & curious(X0))) [ennf transformation 5]
44. ! [X0] : ((((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | brave(X0)) & (~brave(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))))) [nnf transformation 9]
80. ~happy(X0) | ~curious(X0) [cnf transformation 31]
92. ~brave(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
94. curious(X0) | brave(X0) | brave(X0) [cnf transformation 44]
134. happy(susan) [cnf transformation 23]
136. ~brave(X0) | curious(X0) [duplicate literal removal 92]
137. curious(X0) | brave(X0) [duplicate literal removal 94]
139. 1 <=> ! [X1] : (brave(X1) | curious(X1)) [avatar definition]
140. brave(X1) | curious(X1) <- (1) [avatar component clause 139]
177. 1 [avatar split clause 137,139]
264. curious(X1) <- (1) [subsumption resolution 140,136]
267. ~curious(susan) [resolution 80,134]
268. $false <- (1) [subsumption resolution 267,264]
269. ~1 [avatar contradiction clause 268]
270. $false [avatar sat refutation 177,269]
% SZS output end Proof for 5706005540321981964778018
% ------------------------------
% 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 calm or not tall is calm or not funny.
Everyone who is funny or brave is not kind or not happy and vice versa.
Everyone who is either not funny or not rich is both not quiet and curious.
If someone is not calm then someone is both not generous and old.
If someone is brave or strong then paul is either not calm or not quiet and vice versa.
Everyone who is either old or humble is both brave and not patient.
Everyone who is humble is not calm or wise.
Everyone who is brave is either not quiet or not creative and vice versa.
If john is either not creative or curious then someone is both not quiet and not rich.
If fred is both not funny and not humble then someone is both not curious and not humble and vice versa.
Everyone who is funny is both not strong and not generous and vice versa.
Everyone who is happy is either not strong or not old and vice versa.
Everyone who is both funny and not creative is curious and vice versa.
Everyone who is calm is funny or not calm and vice versa.
Everyone who is either not old or not humble is either not rich or brave.
Everyone who is either funny or rich is brave.
Fred is both tall and creative.
Fred is not quiet.
Alice is both not patient and not kind.
Someone is both old and not quiet.
Someone is either brave or not rich.
Someone is both rich and not tall.
Paul is not strong or not quiet.
Someone is either creative or happy. | Fred is not rich. | contradiction | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~quiet(X)&curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~generous(X)&old(X)))))&
((?[X]:((brave(X)|strong(X))))<=>((~calm(paul)<~>~quiet(paul))))&
(![X]:((old(X)<~>humble(X))=>(brave(X)&~patient(X))))&
(![X]:(humble(X)=>(~calm(X)|wise(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~creative(X))))&
(((~creative(john)<~>curious(john)))=>(?[X]:((~quiet(X)&~rich(X)))))&
(((~funny(fred)&~humble(fred)))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:(funny(X)<=>(~strong(X)&~generous(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~old(X))))&
(![X]:((funny(X)&~creative(X))<=>curious(X)))&
(![X]:(calm(X)<=>(funny(X)|~calm(X))))&
(![X]:((~old(X)<~>~humble(X))=>(~rich(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>brave(X)))&
((tall(fred)&creative(fred)))&
(~quiet(fred))&
((~patient(alice)&~kind(alice)))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((rich(X)&~tall(X))))&
((~strong(paul)|~quiet(paul)))&
(?[X]:((creative(X)<~>happy(X)))) | ~rich(fred) | [
"p2",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4816094829742346445375963
% SZS output start Proof for 4816094829742346445375963
3. ! [X0] : ((~funny(X0) <~> ~rich(X0)) => (curious(X0) & ~quiet(X0))) [input p2]
13. ! [X0] : ((~creative(X0) & funny(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : (calm(X0) <=> (~calm(X0) | funny(X0))) [input p13]
17. creative(fred) & tall(fred) [input p16]
25. ~rich(fred) [input hypothesis]
32. ! [X0] : ((curious(X0) & ~quiet(X0)) | (~funny(X0) <=> ~rich(X0))) [ennf transformation 3]
40. ! [X0] : ((curious(X0) & ~quiet(X0)) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) [nnf transformation 32]
61. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | ~funny(X0)))) [nnf transformation 13]
62. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | ~funny(X0))) [flattening 61]
63. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ~calm(X0))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~calm(X0))) [flattening 63]
86. ~funny(X0) | curious(X0) | rich(X0) [cnf transformation 40]
118. ~creative(X0) | ~curious(X0) [cnf transformation 62]
119. ~calm(X0) | funny(X0) | ~calm(X0) [cnf transformation 64]
121. calm(X0) | calm(X0) [cnf transformation 64]
129. creative(fred) [cnf transformation 17]
141. ~rich(fred) [cnf transformation 25]
142. ~calm(X0) | funny(X0) [duplicate literal removal 119]
143. calm(X0) [duplicate literal removal 121]
146. 1 <=> ! [X1] : calm(X1) [avatar definition]
147. calm(X1) <- (1) [avatar component clause 146]
229. 1 [avatar split clause 143,146]
261. ~curious(fred) [resolution 118,129]
263. funny(X0) <- (1) [resolution 142,147]
283. curious(X0) | rich(X0) <- (1) [resolution 86,263]
398. rich(fred) <- (1) [resolution 283,261]
400. $false <- (1) [subsumption resolution 398,141]
401. ~1 [avatar contradiction clause 400]
402. $false [avatar sat refutation 229,401]
% SZS output end Proof for 4816094829742346445375963
% ------------------------------
% 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 |
If someone is both not funny and creative then someone is either not strong or not old and vice versa.
If someone is not kind then someone is both rich and not quiet.
Everyone who is quiet or creative is either funny or not patient and vice versa.
Everyone who is either creative or not humble is humble and vice versa.
Everyone who is wise is both not kind and tall and vice versa.
If someone is calm then lucy is either creative or not tall.
If someone is both generous and not creative then alice is happy or brave and vice versa.
If someone is funny then someone is not humble or not patient and vice versa.
Everyone who is not patient or not happy is either not old or humble.
If someone is not strong or humble then fred is either not wise or not calm.
Everyone who is both creative and not brave is kind.
If mary is brave then someone is either not rich or not strong.
If susan is either not rich or tall then someone is curious and vice versa.
If alice is both not old and humble then john is not kind.
If mary is both patient and happy then mary is generous.
Everyone who is strong or not humble is either not rich or not generous.
Someone is both creative and not quiet.
Paul is either not curious or curious.
Someone is both not curious and not old.
Someone is not tall or happy.
Someone is not old or strong.
Someone is either quiet or not strong.
Someone is happy.
John is not brave. | Alice is happy. | contradiction | ((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((~strong(X)<~>~old(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((quiet(X)|creative(X))<=>(funny(X)<~>~patient(X))))&
(![X]:((creative(X)<~>~humble(X))<=>humble(X)))&
(![X]:(wise(X)<=>(~kind(X)&tall(X))))&
((?[X]:(calm(X)))=>((creative(lucy)<~>~tall(lucy))))&
((?[X]:((generous(X)&~creative(X))))<=>((happy(alice)|brave(alice))))&
((?[X]:(funny(X)))<=>(?[X]:((~humble(X)|~patient(X)))))&
(![X]:((~patient(X)|~happy(X))=>(~old(X)<~>humble(X))))&
((?[X]:((~strong(X)|humble(X))))=>((~wise(fred)<~>~calm(fred))))&
(![X]:((creative(X)&~brave(X))=>kind(X)))&
((brave(mary))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(((~rich(susan)<~>tall(susan)))<=>(?[X]:(curious(X))))&
(((~old(alice)&humble(alice)))=>(~kind(john)))&
(((patient(mary)&happy(mary)))=>(generous(mary)))&
(![X]:((strong(X)|~humble(X))=>(~rich(X)<~>~generous(X))))&
(?[X]:((creative(X)&~quiet(X))))&
((~curious(paul)<~>curious(paul)))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:(happy(X)))&
(~brave(john)) | happy(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6559122602892731391224691
% SZS output start Proof for 6559122602892731391224691
4. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> humble(X0)) [input p3]
7. ? [X0] : (~creative(X0) & generous(X0)) <=> (brave(alice) | happy(alice)) [input p6]
25. happy(alice) [input hypothesis]
51. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ~humble(X0)) & (humble(X0) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 4]
55. (? [X0] : (~creative(X0) & generous(X0)) | (~brave(alice) & ~happy(alice))) & ((brave(alice) | happy(alice)) | ! [X0] : (creative(X0) | ~generous(X0))) [nnf transformation 7]
56. (? [X0] : (~creative(X0) & generous(X0)) | (~brave(alice) & ~happy(alice))) & (brave(alice) | happy(alice) | ! [X0] : (creative(X0) | ~generous(X0))) [flattening 55]
57. (? [X0] : (~creative(X0) & generous(X0)) | (~brave(alice) & ~happy(alice))) & (brave(alice) | happy(alice) | ! [X1] : (creative(X1) | ~generous(X1))) [rectify 56]
58. ? [X0] : (~creative(X0) & generous(X0)) => (~creative(sK3) & generous(sK3)) [choice axiom]
59. ((~creative(sK3) & generous(sK3)) | (~brave(alice) & ~happy(alice))) & (brave(alice) | happy(alice) | ! [X1] : (creative(X1) | ~generous(X1))) [skolemisation 57,58]
104. humble(X0) | creative(X0) | humble(X0) [cnf transformation 51]
105. ~humble(X0) | creative(X0) | ~humble(X0) [cnf transformation 51]
115. ~creative(sK3) | ~happy(alice) [cnf transformation 59]
153. happy(alice) [cnf transformation 25]
154. humble(X0) | creative(X0) [duplicate literal removal 104]
155. ~humble(X0) | creative(X0) [duplicate literal removal 105]
200. creative(X0) [subsumption resolution 154,155]
211. ~happy(alice) [subsumption resolution 115,200]
342. $false [subsumption resolution 153,211]
% SZS output end Proof for 6559122602892731391224691
% ------------------------------
% 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 tall is not happy or creative.
If someone is either old or not wise then someone is tall and vice versa.
If mary is rich then someone is rich and vice versa.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
If john is kind or not patient then someone is not creative or not strong and vice versa.
If john is not strong or rich then someone is either not kind or old and vice versa.
Everyone who is both strong and not wise is both not happy and calm and vice versa.
Everyone who is not wise or not patient is either humble or not strong.
If john is both not kind and strong then john is both quiet and not brave.
Someone is both tall and calm.
John is tall.
Someone is either not tall or not happy.
Alice is both not tall and not happy.
Someone is either not kind or brave.
Lucy is both not calm and brave.
Someone is brave or patient.
John is funny or quiet. | Alice is not humble. | contradiction | (![X]:(tall(X)=>(~happy(X)|creative(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:(tall(X))))&
((rich(mary))<=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
(((kind(john)|~patient(john)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(((~strong(john)|rich(john)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((strong(X)&~wise(X))<=>(~happy(X)&calm(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)<~>~strong(X))))&
(((~kind(john)&strong(john)))=>((quiet(john)&~brave(john))))&
(?[X]:((tall(X)&calm(X))))&
(tall(john))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~tall(alice)&~happy(alice)))&
(?[X]:((~kind(X)<~>brave(X))))&
((~calm(lucy)&brave(lucy)))&
(?[X]:((brave(X)|patient(X))))&
((funny(john)|quiet(john))) | ~humble(alice) | [
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 255653426588968983927960
% SZS output start Proof for 255653426588968983927960
10. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> happy(X0)) [input p9]
14. ! [X0] : ((~wise(X0) & strong(X0)) <=> (calm(X0) & ~happy(X0))) [input p13]
15. ! [X0] : ((~patient(X0) | ~wise(X0)) => (humble(X0) <~> ~strong(X0))) [input p14]
20. ~happy(alice) & ~tall(alice) [input p19]
25. ~humble(alice) [input hypothesis]
35. ! [X0] : ((humble(X0) <~> ~strong(X0)) | (patient(X0) & wise(X0))) [ennf transformation 15]
65. ! [X0] : (((~rich(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [nnf transformation 10]
66. ! [X0] : ((~rich(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [flattening 65]
77. ! [X0] : (((~wise(X0) & strong(X0)) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | (wise(X0) | ~strong(X0)))) [nnf transformation 14]
78. ! [X0] : (((~wise(X0) & strong(X0)) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | wise(X0) | ~strong(X0))) [flattening 77]
79. ! [X0] : (((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (patient(X0) & wise(X0))) [nnf transformation 35]
116. calm(X0) | happy(X0) [cnf transformation 66]
132. strong(X0) | ~calm(X0) | happy(X0) [cnf transformation 78]
133. ~wise(X0) | ~calm(X0) | happy(X0) [cnf transformation 78]
134. ~strong(X0) | humble(X0) | wise(X0) [cnf transformation 79]
146. ~happy(alice) [cnf transformation 20]
153. ~humble(alice) [cnf transformation 25]
319. ~wise(X0) | happy(X0) [subsumption resolution 133,116]
320. strong(X0) | happy(X0) [subsumption resolution 132,116]
456. humble(X0) | wise(X0) | happy(X0) [resolution 134,320]
458. humble(X0) | happy(X0) [subsumption resolution 456,319]
466. happy(alice) [resolution 458,153]
467. $false [subsumption resolution 466,146]
% SZS output end Proof for 255653426588968983927960
% ------------------------------
% 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 both humble and not quiet is old or wise and vice versa.
Everyone who is calm or quiet is both brave and tall and vice versa.
Everyone who is not strong is not happy.
Everyone who is not wise is both curious and not humble.
Everyone who is wise is either humble or wise.
Everyone who is happy is patient.
Everyone who is both patient and funny is either not strong or calm and vice versa.
Everyone who is creative is not curious or not tall.
Everyone who is not humble or old is both not generous and calm.
If john is both not calm and tall then someone is both not funny and brave and vice versa.
If someone is kind then mary is not patient and vice versa.
If lucy is either curious or funny then someone is not creative.
Everyone who is not strong is either curious or generous.
Everyone who is either generous or not tall is happy or not tall and vice versa.
Someone is either not strong or not humble.
Susan is not strong or calm.
Someone is either not strong or not quiet.
Susan is not wise or brave.
Someone is either not rich or not curious. | Susan is creative. | contradiction | (![X]:((humble(X)&~quiet(X))<=>(old(X)|wise(X))))&
(![X]:((calm(X)|quiet(X))<=>(brave(X)&tall(X))))&
(![X]:(~strong(X)=>~happy(X)))&
(![X]:(~wise(X)=>(curious(X)&~humble(X))))&
(![X]:(wise(X)=>(humble(X)<~>wise(X))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((patient(X)&funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(creative(X)=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)|old(X))=>(~generous(X)&calm(X))))&
(((~calm(john)&tall(john)))<=>(?[X]:((~funny(X)&brave(X)))))&
((?[X]:(kind(X)))<=>(~patient(mary)))&
(((curious(lucy)<~>funny(lucy)))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(happy(X)|~tall(X))))&
(?[X]:((~strong(X)<~>~humble(X))))&
((~strong(susan)|calm(susan)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~wise(susan)|brave(susan)))&
(?[X]:((~rich(X)<~>~curious(X)))) | creative(susan) | [
"p0",
"p1",
"p3",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 540157053425636727053665
% SZS output start Proof for 540157053425636727053665
1. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (wise(X0) | old(X0))) [input p0]
2. ! [X0] : ((quiet(X0) | calm(X0)) <=> (tall(X0) & brave(X0))) [input p1]
4. ! [X0] : (~wise(X0) => (~humble(X0) & curious(X0))) [input p3]
5. ! [X0] : (wise(X0) => (humble(X0) <~> wise(X0))) [input p4]
8. ! [X0] : (creative(X0) => (~tall(X0) | ~curious(X0))) [input p7]
9. ! [X0] : ((old(X0) | ~humble(X0)) => (calm(X0) & ~generous(X0))) [input p8]
20. creative(susan) [input hypothesis]
22. ! [X0] : ((~humble(X0) & curious(X0)) | wise(X0)) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> wise(X0)) | ~wise(X0)) [ennf transformation 5]
25. ! [X0] : ((~tall(X0) | ~curious(X0)) | ~creative(X0)) [ennf transformation 8]
26. ! [X0] : (~tall(X0) | ~curious(X0) | ~creative(X0)) [flattening 25]
27. ! [X0] : ((calm(X0) & ~generous(X0)) | (~old(X0) & humble(X0))) [ennf transformation 9]
30. ! [X0] : (((~quiet(X0) & humble(X0)) | (~wise(X0) & ~old(X0))) & ((wise(X0) | old(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 1]
31. ! [X0] : (((~quiet(X0) & humble(X0)) | (~wise(X0) & ~old(X0))) & (wise(X0) | old(X0) | quiet(X0) | ~humble(X0))) [flattening 30]
32. ! [X0] : (((quiet(X0) | calm(X0)) | (~tall(X0) | ~brave(X0))) & ((tall(X0) & brave(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 2]
33. ! [X0] : ((quiet(X0) | calm(X0) | ~tall(X0) | ~brave(X0)) & ((tall(X0) & brave(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 32]
34. ! [X0] : (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | ~wise(X0)) [nnf transformation 23]
63. ~wise(X0) | humble(X0) [cnf transformation 31]
68. ~calm(X0) | tall(X0) [cnf transformation 33]
72. curious(X0) | wise(X0) [cnf transformation 22]
73. ~humble(X0) | wise(X0) [cnf transformation 22]
75. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 34]
83. ~creative(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 26]
86. calm(X0) | humble(X0) [cnf transformation 27]
112. creative(susan) [cnf transformation 20]
115. ~wise(X0) | ~humble(X0) [duplicate literal removal 75]
116. ~humble(X0) [subsumption resolution 115,73]
117. calm(X0) [subsumption resolution 86,116]
170. 11 <=> wise(susan) [avatar definition]
171. wise(susan) <- (11) [avatar component clause 170]
189. tall(X0) [resolution 68,117]
203. ~curious(susan) | ~tall(susan) [resolution 83,112]
204. ~curious(susan) [subsumption resolution 203,189]
206. wise(susan) [resolution 204,72]
209. 11 [avatar split clause 206,170]
211. humble(susan) <- (11) [resolution 171,63]
212. $false <- (11) [subsumption resolution 211,116]
213. ~11 [avatar contradiction clause 212]
214. $false [avatar sat refutation 209,213]
% SZS output end Proof for 540157053425636727053665
% ------------------------------
% 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 old and funny is either wise or creative. If someone is either not wise or tall then someone is both generous and curious. Everyone who is either not strong or strong is tall or happy. Everyone who is brave or creative is either brave or not curious. Everyone who is not wise is not quiet or not tall and vice versa. Everyone who is generous or tall is not patient. If lucy is creative then lucy is both humble and funny. Everyone who is either not patient or not strong is both creative and not curious. If someone is both not kind and not quiet then someone is kind or calm and vice versa. If someone is both happy and not humble then lucy is generous and vice versa. Everyone who is not tall or creative is both not rich and wise and vice versa. Everyone who is humble or creative is either not old or not curious and vice versa. Everyone who is either not tall or not happy is either wise or tall and vice versa. If someone is both not brave and tall then someone is either not patient or not strong and vice versa. Everyone who is both not creative and humble is either old or not curious. If someone is not rich then susan is not patient or humble. Alice is both not curious and not creative. Someone is both strong and funny. Fred is not rich. Someone is either not quiet or creative. Fred is not old or wise. Someone is either strong or creative. | Alice is old. | contradiction | (![X]:((~old(X)&funny(X))=>(wise(X)<~>creative(X))))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(tall(X)|happy(X))))&
(![X]:((brave(X)|creative(X))=>(brave(X)<~>~curious(X))))&
(![X]:(~wise(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((generous(X)|tall(X))=>~patient(X)))&
((creative(lucy))=>((humble(lucy)&funny(lucy))))&
(![X]:((~patient(X)<~>~strong(X))=>(creative(X)&~curious(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>(generous(lucy)))&
(![X]:((~tall(X)|creative(X))<=>(~rich(X)&wise(X))))&
(![X]:((humble(X)|creative(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
(![X]:((~creative(X)&humble(X))=>(old(X)<~>~curious(X))))&
((?[X]:(~rich(X)))=>((~patient(susan)|humble(susan))))&
((~curious(alice)&~creative(alice)))&
(?[X]:((strong(X)&funny(X))))&
(~rich(fred))&
(?[X]:((~quiet(X)<~>creative(X))))&
((~old(fred)|wise(fred)))&
(?[X]:((strong(X)<~>creative(X)))) | old(alice) | [
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 181137189813827950595519
% SZS output start Proof for 181137189813827950595519
12. ! [X0] : ((creative(X0) | humble(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p11]
15. ! [X0] : ((humble(X0) & ~creative(X0)) => (old(X0) <~> ~curious(X0))) [input p14]
17. ~creative(alice) & ~curious(alice) [input p16]
23. old(alice) [input hypothesis]
36. ! [X0] : ((old(X0) <~> ~curious(X0)) | (~humble(X0) | creative(X0))) [ennf transformation 15]
37. ! [X0] : ((old(X0) <~> ~curious(X0)) | ~humble(X0) | creative(X0)) [flattening 36]
61. ! [X0] : (((creative(X0) | humble(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (~creative(X0) & ~humble(X0)))) [nnf transformation 12]
62. ! [X0] : ((creative(X0) | humble(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (~creative(X0) & ~humble(X0)))) [flattening 61]
69. ! [X0] : (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | ~humble(X0) | creative(X0)) [nnf transformation 37]
116. ~humble(X0) | old(X0) | curious(X0) [cnf transformation 62]
119. ~old(X0) | humble(X0) | creative(X0) | curious(X0) [cnf transformation 62]
135. curious(X0) | ~old(X0) | ~humble(X0) | creative(X0) [cnf transformation 69]
137. ~curious(alice) [cnf transformation 17]
138. ~creative(alice) [cnf transformation 17]
147. old(alice) [cnf transformation 23]
267. ~humble(X0) | curious(X0) | creative(X0) [subsumption resolution 135,116]
436. humble(alice) | creative(alice) | curious(alice) [resolution 119,147]
441. humble(alice) | curious(alice) [subsumption resolution 436,138]
442. humble(alice) [subsumption resolution 441,137]
444. curious(alice) | creative(alice) [resolution 442,267]
447. creative(alice) [subsumption resolution 444,137]
448. $false [subsumption resolution 447,138]
% SZS output end Proof for 181137189813827950595519
% ------------------------------
% 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 brave or old is either not generous or not old. Everyone who is either not humble or wise is either not rich or not kind. Everyone who is not calm or rich is humble or kind. If someone is both not wise and not rich then susan is both kind and strong. Everyone who is quiet or wise is either not kind or not brave. If someone is both wise and humble then someone is tall or not patient. If someone is not curious or strong then someone is old. Everyone who is not rich is either not patient or not funny and vice versa. Everyone who is not tall is either not kind or brave. Everyone who is either old or not brave is happy or strong and vice versa. If fred is both not brave and calm then someone is either humble or not patient and vice versa. If mary is either not wise or not strong then someone is either patient or not rich. Everyone who is both not tall and tall is strong and vice versa. If fred is not humble then someone is not curious or old and vice versa. Everyone who is either not calm or strong is both brave and patient. Everyone who is creative or not curious is not calm and vice versa. Someone is both not patient and not brave. Fred is both humble and kind. Someone is either not patient or generous. Someone is not funny or generous. Someone is generous. Someone is either strong or not kind. | Fred is creative. | contradiction | (![X]:((brave(X)|old(X))=>(~generous(X)<~>~old(X))))&
(![X]:((~humble(X)<~>wise(X))=>(~rich(X)<~>~kind(X))))&
(![X]:((~calm(X)|rich(X))=>(humble(X)|kind(X))))&
((?[X]:((~wise(X)&~rich(X))))=>((kind(susan)&strong(susan))))&
(![X]:((quiet(X)|wise(X))=>(~kind(X)<~>~brave(X))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:(old(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~funny(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>brave(X))))&
(![X]:((old(X)<~>~brave(X))<=>(happy(X)|strong(X))))&
(((~brave(fred)&calm(fred)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(((~wise(mary)<~>~strong(mary)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~tall(X)&tall(X))<=>strong(X)))&
((~humble(fred))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~calm(X)<~>strong(X))=>(brave(X)&patient(X))))&
(![X]:((creative(X)|~curious(X))<=>~calm(X)))&
(?[X]:((~patient(X)&~brave(X))))&
((humble(fred)&kind(fred)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>~kind(X)))) | creative(fred) | [
"p10",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1667456868766136800189
% SZS output start Proof for 1667456868766136800189
11. (calm(fred) & ~brave(fred)) <=> ? [X0] : (humble(X0) <~> ~patient(X0)) [input p10]
13. ! [X0] : ((tall(X0) & ~tall(X0)) <=> strong(X0)) [input p12]
15. ! [X0] : ((~calm(X0) <~> strong(X0)) => (patient(X0) & brave(X0))) [input p14]
16. ! [X0] : ((~curious(X0) | creative(X0)) <=> ~calm(X0)) [input p15]
18. kind(fred) & humble(fred) [input p17]
23. creative(fred) [input hypothesis]
37. ! [X0] : ((patient(X0) & brave(X0)) | (~calm(X0) <=> strong(X0))) [ennf transformation 15]
51. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X0] : ((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~calm(fred) | brave(fred))) [nnf transformation 11]
52. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X0] : ((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~calm(fred) | brave(fred)) [flattening 51]
53. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X1] : ((patient(X1) | ~humble(X1)) & (~patient(X1) | humble(X1))) | ~calm(fred) | brave(fred)) [rectify 52]
54. ? [X1] : ((patient(X1) | ~humble(X1)) & (~patient(X1) | humble(X1))) => ((patient(sK2) | ~humble(sK2)) & (~patient(sK2) | humble(sK2))) [choice axiom]
55. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(sK2) | ~humble(sK2)) & (~patient(sK2) | humble(sK2))) | ~calm(fred) | brave(fred)) [skolemisation 53,54]
59. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 13]
60. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | ~tall(X0) | tall(X0))) [flattening 59]
65. ! [X0] : ((patient(X0) & brave(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0)))) [nnf transformation 37]
66. ! [X0] : (((~curious(X0) | creative(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & ~creative(X0)))) [nnf transformation 16]
67. ! [X0] : ((~curious(X0) | creative(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & ~creative(X0)))) [flattening 66]
111. ~brave(fred) | ~patient(X0) | ~humble(X0) [cnf transformation 55]
120. ~tall(X0) | ~strong(X0) [cnf transformation 60]
121. ~strong(X0) | tall(X0) [cnf transformation 60]
125. strong(X0) | brave(X0) | calm(X0) [cnf transformation 65]
127. patient(X0) | strong(X0) | calm(X0) [cnf transformation 65]
129. ~creative(X0) | ~calm(X0) [cnf transformation 67]
134. humble(fred) [cnf transformation 18]
142. creative(fred) [cnf transformation 23]
170. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
171. ~strong(X1) <- (7) [avatar component clause 170]
185. 11 <=> calm(fred) [avatar definition]
186. ~calm(fred) <- (~11) [avatar component clause 185]
190. 12 <=> ! [X0] : (~patient(X0) | ~humble(X0)) [avatar definition]
191. ~patient(X0) | ~humble(X0) <- (12) [avatar component clause 190]
194. 13 <=> brave(fred) [avatar definition]
198. 12 | ~13 [avatar split clause 111,194,190]
229. ~strong(X0) [subsumption resolution 120,121]
230. 7 [avatar split clause 229,170]
235. 21 <=> humble(fred) [avatar definition]
236. humble(fred) <- (21) [avatar component clause 235]
249. 21 [avatar split clause 134,235]
281. ~calm(fred) [resolution 129,142]
284. ~11 [avatar split clause 281,185]
354. calm(X3) | brave(X3) <- (7) [resolution 125,171]
360. brave(fred) <- (7, ~11) [resolution 354,186]
364. 13 | ~7 | 11 [avatar split clause 360,185,170,194]
379. strong(X1) | calm(X1) | ~humble(X1) <- (12) [resolution 127,191]
386. ~humble(X1) | calm(X1) <- (7, 12) [subsumption resolution 379,171]
409. calm(fred) <- (7, 12, 21) [resolution 386,236]
415. $false <- (7, ~11, 12, 21) [subsumption resolution 409,186]
416. ~7 | 11 | ~12 | ~21 [avatar contradiction clause 415]
417. $false [avatar sat refutation 198,230,249,284,364,416]
% SZS output end Proof for 1667456868766136800189
% ------------------------------
% 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and rich then lucy is tall and vice versa.
Everyone who is both not creative and not tall is not funny and vice versa.
Everyone who is either not patient or kind is both not calm and not strong.
If susan is not wise or not curious then paul is not tall and vice versa.
Everyone who is either not humble or not generous is both not calm and humble.
If someone is not happy then lucy is not creative or generous and vice versa.
If lucy is patient or not rich then alice is either wise or quiet and vice versa.
Everyone who is strong is either funny or not brave and vice versa.
Everyone who is either not patient or not humble is not brave.
If someone is both not patient and not brave then paul is kind or rich and vice versa.
Everyone who is not strong is both not tall and tall and vice versa.
Everyone who is not old or kind is both not quiet and brave.
Everyone who is generous is tall or not happy and vice versa.
Everyone who is both strong and kind is creative.
Someone is funny or quiet.
Paul is strong or not kind.
Lucy is not humble.
Someone is either not creative or kind. | Alice is funny. | neutral | ((?[X]:((~creative(X)&rich(X))))<=>(tall(lucy)))&
(![X]:((~creative(X)&~tall(X))<=>~funny(X)))&
(![X]:((~patient(X)<~>kind(X))=>(~calm(X)&~strong(X))))&
(((~wise(susan)|~curious(susan)))<=>(~tall(paul)))&
(![X]:((~humble(X)<~>~generous(X))=>(~calm(X)&humble(X))))&
((?[X]:(~happy(X)))<=>((~creative(lucy)|generous(lucy))))&
(((patient(lucy)|~rich(lucy)))<=>((wise(alice)<~>quiet(alice))))&
(![X]:(strong(X)<=>(funny(X)<~>~brave(X))))&
(![X]:((~patient(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((kind(paul)|rich(paul))))&
(![X]:(~strong(X)<=>(~tall(X)&tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)&brave(X))))&
(![X]:(generous(X)<=>(tall(X)|~happy(X))))&
(![X]:((strong(X)&kind(X))=>creative(X)))&
(?[X]:((funny(X)|quiet(X))))&
((strong(paul)|~kind(paul)))&
(~humble(lucy))&
(?[X]:((~creative(X)<~>kind(X)))) | funny(alice) | [] | null | 0 |
If fred is not calm then someone is not calm.
Everyone who is not kind is not quiet and vice versa.
If alice is rich or not old then fred is both not humble and wise.
If someone is both calm and funny then john is generous or not happy and vice versa.
If paul is either not tall or old then someone is both generous and quiet and vice versa.
Everyone who is not strong or rich is either tall or creative.
Everyone who is not curious or happy is either old or not patient.
Everyone who is not wise is either funny or not patient.
If someone is either old or not wise then someone is curious or patient.
If paul is rich or not humble then someone is both not quiet and tall.
Everyone who is both not funny and not wise is old and vice versa.
If someone is both creative and not brave then fred is either not creative or humble.
Everyone who is not tall or wise is both kind and happy and vice versa.
Everyone who is old or not funny is both patient and not generous and vice versa.
If alice is quiet or not old then someone is both humble and happy.
If fred is both happy and not humble then someone is not happy or tall.
Lucy is not wise or wise.
Someone is not quiet or happy.
Lucy is both funny and happy.
Someone is both not patient and not brave.
Someone is not quiet or not old.
Paul is both rich and quiet. | Paul is not tall. | neutral | ((~calm(fred))=>(?[X]:(~calm(X))))&
(![X]:(~kind(X)<=>~quiet(X)))&
(((rich(alice)|~old(alice)))=>((~humble(fred)&wise(fred))))&
((?[X]:((calm(X)&funny(X))))<=>((generous(john)|~happy(john))))&
(((~tall(paul)<~>old(paul)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((~strong(X)|rich(X))=>(tall(X)<~>creative(X))))&
(![X]:((~curious(X)|happy(X))=>(old(X)<~>~patient(X))))&
(![X]:(~wise(X)=>(funny(X)<~>~patient(X))))&
((?[X]:((old(X)<~>~wise(X))))=>(?[X]:((curious(X)|patient(X)))))&
(((rich(paul)|~humble(paul)))=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~funny(X)&~wise(X))<=>old(X)))&
((?[X]:((creative(X)&~brave(X))))=>((~creative(fred)<~>humble(fred))))&
(![X]:((~tall(X)|wise(X))<=>(kind(X)&happy(X))))&
(![X]:((old(X)|~funny(X))<=>(patient(X)&~generous(X))))&
(((quiet(alice)|~old(alice)))=>(?[X]:((humble(X)&happy(X)))))&
(((happy(fred)&~humble(fred)))=>(?[X]:((~happy(X)|tall(X)))))&
((~wise(lucy)|wise(lucy)))&
(?[X]:((~quiet(X)|happy(X))))&
((funny(lucy)&happy(lucy)))&
(?[X]:((~patient(X)&~brave(X))))&
(?[X]:((~quiet(X)|~old(X))))&
((rich(paul)&quiet(paul))) | ~tall(paul) | [] | null | 0 |
Everyone who is not happy is humble or quiet and vice versa. Everyone who is brave is both kind and not curious. If someone is either not patient or not humble then paul is calm. If lucy is both not happy and brave then someone is wise. Everyone who is both kind and not old is creative or patient. Everyone who is not creative or not rich is both strong and not quiet. Everyone who is not curious is not brave or humble and vice versa. If mary is not brave then john is not kind. Everyone who is both not curious and not old is not generous and vice versa. Everyone who is both not happy and tall is not calm and vice versa. Everyone who is either quiet or not happy is not curious or patient. Everyone who is either tall or not creative is either wise or not kind and vice versa. If someone is strong or funny then john is not generous or calm and vice versa. Everyone who is not patient or wise is not wise or not creative. If paul is happy then someone is not creative and vice versa. If someone is patient or creative then susan is not wise and vice versa. Susan is both creative and not rich. Paul is either not brave or not generous. Susan is kind. Mary is not wise. Lucy is strong or not patient. Someone is both creative and not strong. Someone is not old. | Susan is tall. | contradiction | (![X]:(~happy(X)<=>(humble(X)|quiet(X))))&
(![X]:(brave(X)=>(kind(X)&~curious(X))))&
((?[X]:((~patient(X)<~>~humble(X))))=>(calm(paul)))&
(((~happy(lucy)&brave(lucy)))=>(?[X]:(wise(X))))&
(![X]:((kind(X)&~old(X))=>(creative(X)|patient(X))))&
(![X]:((~creative(X)|~rich(X))=>(strong(X)&~quiet(X))))&
(![X]:(~curious(X)<=>(~brave(X)|humble(X))))&
((~brave(mary))=>(~kind(john)))&
(![X]:((~curious(X)&~old(X))<=>~generous(X)))&
(![X]:((~happy(X)&tall(X))<=>~calm(X)))&
(![X]:((quiet(X)<~>~happy(X))=>(~curious(X)|patient(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(wise(X)<~>~kind(X))))&
((?[X]:((strong(X)|funny(X))))<=>((~generous(john)|calm(john))))&
(![X]:((~patient(X)|wise(X))=>(~wise(X)|~creative(X))))&
((happy(paul))<=>(?[X]:(~creative(X))))&
((?[X]:((patient(X)|creative(X))))<=>(~wise(susan)))&
((creative(susan)&~rich(susan)))&
((~brave(paul)<~>~generous(paul)))&
(kind(susan))&
(~wise(mary))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((creative(X)&~strong(X))))&
(?[X]:(~old(X))) | tall(susan) | [
"p11",
"p13",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7200044847022163699879224
% SZS output start Proof for 7200044847022163699879224
12. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> (wise(X0) <~> ~kind(X0))) [input p11]
14. ! [X0] : ((wise(X0) | ~patient(X0)) => (~creative(X0) | ~wise(X0))) [input p13]
17. ~rich(susan) & creative(susan) [input p16]
19. kind(susan) [input p18]
24. tall(susan) [input hypothesis]
35. ! [X0] : ((~creative(X0) | ~wise(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 14]
36. ! [X0] : (~creative(X0) | ~wise(X0) | (~wise(X0) & patient(X0))) [flattening 35]
49. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0)))) & (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 12]
93. ~tall(X0) | wise(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 49]
106. ~creative(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 36]
112. creative(susan) [cnf transformation 17]
116. kind(susan) [cnf transformation 19]
122. tall(susan) [cnf transformation 24]
123. ~creative(X0) | ~wise(X0) [duplicate literal removal 106]
201. 18 <=> wise(susan) [avatar definition]
202. ~wise(susan) <- (~18) [avatar component clause 201]
203. wise(susan) <- (18) [avatar component clause 201]
246. ~wise(susan) [resolution 123,112]
271. wise(susan) | ~creative(susan) | ~kind(susan) [resolution 93,122]
273. ~creative(susan) | ~kind(susan) <- (~18) [subsumption resolution 271,202]
274. ~kind(susan) <- (~18) [subsumption resolution 273,112]
275. $false <- (~18) [subsumption resolution 274,116]
276. 18 [avatar contradiction clause 275]
287. $false <- (18) [subsumption resolution 246,203]
288. ~18 [avatar contradiction clause 287]
290. $false [avatar sat refutation 276,288]
% SZS output end Proof for 7200044847022163699879224
% ------------------------------
% 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 fred is not creative then someone is either not brave or patient.
Everyone who is generous or not calm is not curious and vice versa.
If fred is either humble or not rich then john is either not generous or creative and vice versa.
If paul is both not creative and not rich then lucy is not humble and vice versa.
Everyone who is happy or not kind is both old and funny.
If mary is both calm and generous then fred is either patient or rich and vice versa.
If someone is either funny or not humble then paul is both not rich and not kind and vice versa.
If john is old then susan is generous and vice versa.
If someone is either not wise or not rich then susan is both not curious and creative and vice versa.
If someone is both happy and not old then mary is not quiet or not tall and vice versa.
If someone is humble then fred is both not calm and calm.
Everyone who is either not wise or strong is not rich or creative.
If someone is either not happy or funny then someone is either not kind or not wise.
Everyone who is either not humble or generous is both not strong and patient.
If someone is either not creative or creative then paul is strong.
Everyone who is either not funny or not old is both happy and not creative.
Paul is either tall or not generous.
Someone is either brave or old.
Lucy is patient or not kind.
Someone is generous or kind.
Alice is funny.
Alice is not tall. | Paul is not old. | contradiction | ((~creative(fred))=>(?[X]:((~brave(X)<~>patient(X)))))&
(![X]:((generous(X)|~calm(X))<=>~curious(X)))&
(((humble(fred)<~>~rich(fred)))<=>((~generous(john)<~>creative(john))))&
(((~creative(paul)&~rich(paul)))<=>(~humble(lucy)))&
(![X]:((happy(X)|~kind(X))=>(old(X)&funny(X))))&
(((calm(mary)&generous(mary)))<=>((patient(fred)<~>rich(fred))))&
((?[X]:((funny(X)<~>~humble(X))))<=>((~rich(paul)&~kind(paul))))&
((old(john))<=>(generous(susan)))&
((?[X]:((~wise(X)<~>~rich(X))))<=>((~curious(susan)&creative(susan))))&
((?[X]:((happy(X)&~old(X))))<=>((~quiet(mary)|~tall(mary))))&
((?[X]:(humble(X)))=>((~calm(fred)&calm(fred))))&
(![X]:((~wise(X)<~>strong(X))=>(~rich(X)|creative(X))))&
((?[X]:((~happy(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>~wise(X)))))&
(![X]:((~humble(X)<~>generous(X))=>(~strong(X)&patient(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(strong(paul)))&
(![X]:((~funny(X)<~>~old(X))=>(happy(X)&~creative(X))))&
((tall(paul)<~>~generous(paul)))&
(?[X]:((brave(X)<~>old(X))))&
((patient(lucy)|~kind(lucy)))&
(?[X]:((generous(X)|kind(X))))&
(funny(alice))&
(~tall(alice)) | ~old(paul) | [
"p4",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5145616704658846621114057
% SZS output start Proof for 5145616704658846621114057
5. ! [X0] : ((~kind(X0) | happy(X0)) => (funny(X0) & old(X0))) [input p4]
7. ? [X0] : (funny(X0) <~> ~humble(X0)) <=> (~kind(paul) & ~rich(paul)) [input p6]
11. ? [X0] : humble(X0) => (calm(fred) & ~calm(fred)) [input p10]
16. ! [X0] : ((~funny(X0) <~> ~old(X0)) => (~creative(X0) & happy(X0))) [input p15]
23. ~old(paul) [input hypothesis]
26. ! [X0] : ((funny(X0) & old(X0)) | (kind(X0) & ~happy(X0))) [ennf transformation 5]
27. (calm(fred) & ~calm(fred)) | ! [X0] : ~humble(X0) [ennf transformation 11]
33. ! [X0] : ((~creative(X0) & happy(X0)) | (~funny(X0) <=> ~old(X0))) [ennf transformation 16]
44. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (kind(paul) | rich(paul))) & ((~kind(paul) & ~rich(paul)) | ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0)))) [nnf transformation 7]
45. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | kind(paul) | rich(paul)) & ((~kind(paul) & ~rich(paul)) | ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0)))) [flattening 44]
46. (? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | kind(paul) | rich(paul)) & ((~kind(paul) & ~rich(paul)) | ! [X1] : ((funny(X1) | humble(X1)) & (~humble(X1) | ~funny(X1)))) [rectify 45]
47. ? [X0] : ((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) => ((humble(sK1) | ~funny(sK1)) & (~humble(sK1) | funny(sK1))) [choice axiom]
48. (((humble(sK1) | ~funny(sK1)) & (~humble(sK1) | funny(sK1))) | kind(paul) | rich(paul)) & ((~kind(paul) & ~rich(paul)) | ! [X1] : ((funny(X1) | humble(X1)) & (~humble(X1) | ~funny(X1)))) [skolemisation 46,47]
67. ! [X0] : ((~creative(X0) & happy(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) [nnf transformation 33]
90. ~happy(X0) | old(X0) [cnf transformation 26]
91. old(X0) | kind(X0) [cnf transformation 26]
103. ~kind(paul) | funny(X1) | humble(X1) [cnf transformation 48]
119. ~calm(fred) | ~humble(X0) [cnf transformation 27]
120. calm(fred) | ~humble(X0) [cnf transformation 27]
134. happy(X0) | ~funny(X0) | old(X0) [cnf transformation 67]
145. ~old(paul) [cnf transformation 23]
220. 14 <=> kind(paul) [avatar definition]
234. 17 <=> ! [X1] : (funny(X1) | humble(X1)) [avatar definition]
235. funny(X1) | humble(X1) <- (17) [avatar component clause 234]
236. 17 | ~14 [avatar split clause 103,220,234]
302. 31 <=> ! [X0] : ~humble(X0) [avatar definition]
303. ~humble(X0) <- (31) [avatar component clause 302]
305. 32 <=> calm(fred) [avatar definition]
308. 31 | 32 [avatar split clause 120,305,302]
309. 31 | ~32 [avatar split clause 119,305,302]
325. 36 <=> ! [X1] : funny(X1) [avatar definition]
326. funny(X1) <- (36) [avatar component clause 325]
344. ~funny(X0) | old(X0) [subsumption resolution 134,90]
384. kind(paul) [resolution 91,145]
389. 14 [avatar split clause 384,220]
390. funny(X1) <- (17, 31) [subsumption resolution 235,303]
391. 36 | ~17 | ~31 [avatar split clause 390,302,234,325]
396. old(X1) <- (36) [resolution 344,326]
401. $false <- (36) [resolution 396,145]
404. ~36 [avatar contradiction clause 401]
406. $false [avatar sat refutation 236,308,309,389,391,404]
% SZS output end Proof for 5145616704658846621114057
% ------------------------------
% 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 either old or not curious is both old and not old. Everyone who is both not tall and strong is either not brave or generous. If paul is either curious or quiet then alice is rich or wise. Everyone who is not humble is not generous or not quiet and vice versa. Everyone who is tall is not rich and vice versa. If someone is tall or not wise then someone is both rich and not quiet. If susan is brave then paul is both not funny and brave and vice versa. Everyone who is both not brave and patient is brave or curious. If mary is humble then someone is not creative or rich. If alice is both kind and creative then someone is both not kind and wise. Everyone who is wise is not creative. Everyone who is not happy is both brave and not humble. If someone is not rich or strong then someone is kind. Everyone who is either not quiet or curious is not happy or funny and vice versa. Everyone who is not curious or not calm is humble or quiet. If fred is old then paul is both not generous and not funny and vice versa. Alice is either not humble or not curious. Someone is rich. Someone is either patient or generous. Someone is either humble or kind. Fred is either not old or calm. John is both wise and not tall. Paul is not patient or humble. Someone is both not wise and kind. | Alice is not curious. | neutral | (![X]:((old(X)<~>~curious(X))=>(old(X)&~old(X))))&
(![X]:((~tall(X)&strong(X))=>(~brave(X)<~>generous(X))))&
(((curious(paul)<~>quiet(paul)))=>((rich(alice)|wise(alice))))&
(![X]:(~humble(X)<=>(~generous(X)|~quiet(X))))&
(![X]:(tall(X)<=>~rich(X)))&
((?[X]:((tall(X)|~wise(X))))=>(?[X]:((rich(X)&~quiet(X)))))&
((brave(susan))<=>((~funny(paul)&brave(paul))))&
(![X]:((~brave(X)&patient(X))=>(brave(X)|curious(X))))&
((humble(mary))=>(?[X]:((~creative(X)|rich(X)))))&
(((kind(alice)&creative(alice)))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(wise(X)=>~creative(X)))&
(![X]:(~happy(X)=>(brave(X)&~humble(X))))&
((?[X]:((~rich(X)|strong(X))))=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(~happy(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))=>(humble(X)|quiet(X))))&
((old(fred))<=>((~generous(paul)&~funny(paul))))&
((~humble(alice)<~>~curious(alice)))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((humble(X)<~>kind(X))))&
((~old(fred)<~>calm(fred)))&
((wise(john)&~tall(john)))&
((~patient(paul)|humble(paul)))&
(?[X]:((~wise(X)&kind(X)))) | ~curious(alice) | [] | null | 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is not quiet is kind and vice versa.
If susan is quiet or happy then john is either not old or funny and vice versa.
Everyone who is strong or old is either not humble or patient and vice versa.
Everyone who is either brave or not generous is calm or not wise.
If someone is not funny or wise then lucy is quiet or not funny.
Everyone who is brave is not quiet or not calm and vice versa.
If someone is not patient then susan is either wise or generous.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
Alice is both not tall and creative.
Someone is wise or not wise.
Someone is not funny.
Susan is not humble.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative.
Alice is both wise and happy. | Alice is strong. | contradiction | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(((quiet(susan)|happy(susan)))<=>((~old(john)<~>funny(john))))&
(![X]:((strong(X)|old(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((brave(X)<~>~generous(X))=>(calm(X)|~wise(X))))&
((?[X]:((~funny(X)|wise(X))))=>((quiet(lucy)|~funny(lucy))))&
(![X]:(brave(X)<=>(~quiet(X)|~calm(X))))&
((?[X]:(~patient(X)))=>((wise(susan)<~>generous(susan))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((~tall(alice)&creative(alice)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(~humble(susan))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy)))&
((wise(alice)&happy(alice))) | strong(alice) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 888004797776147102798528
% SZS output start Proof for 888004797776147102798528
11. ! [X0] : ((~old(X0) | funny(X0)) <=> (~strong(X0) & wise(X0))) [input p10]
12. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> tall(X0))) [input p11]
25. strong(alice) [input hypothesis]
59. ! [X0] : (((~old(X0) | funny(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 11]
60. ! [X0] : ((~old(X0) | funny(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [flattening 59]
61. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 12]
116. ~strong(X0) | ~funny(X0) [cnf transformation 60]
125. funny(X0) | ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 61]
126. funny(X0) | ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 61]
144. strong(alice) [cnf transformation 25]
147. funny(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 125]
148. funny(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 126]
236. ~strong(X0) | ~tall(X0) [subsumption resolution 148,116]
237. ~strong(X0) | tall(X0) [subsumption resolution 147,116]
238. ~strong(X0) [subsumption resolution 237,236]
308. $false [subsumption resolution 144,238]
% SZS output end Proof for 888004797776147102798528
% ------------------------------
% 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 happy is either not quiet or generous and vice versa.
Everyone who is either old or not brave is not humble or patient.
Everyone who is either not strong or not humble is either wise or not happy.
Everyone who is both kind and patient is quiet and vice versa.
Everyone who is either not funny or not rich is not wise or not creative.
Everyone who is curious or brave is both generous and not happy and vice versa.
Everyone who is either not brave or generous is rich or calm.
Everyone who is wise is not creative or not rich and vice versa.
If alice is not quiet or not wise then fred is either not tall or not humble.
Everyone who is brave is not wise.
Everyone who is both not creative and not rich is either happy or not old.
Everyone who is either not humble or brave is creative.
If lucy is either happy or curious then someone is not funny or funny.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Someone is patient or creative.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient.
Someone is happy.
Someone is either not humble or not curious. | Lucy is not curious. | neutral | (![X]:(happy(X)<=>(~quiet(X)<~>generous(X))))&
(![X]:((old(X)<~>~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)&patient(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~rich(X))=>(~wise(X)|~creative(X))))&
(![X]:((curious(X)|brave(X))<=>(generous(X)&~happy(X))))&
(![X]:((~brave(X)<~>generous(X))=>(rich(X)|calm(X))))&
(![X]:(wise(X)<=>(~creative(X)|~rich(X))))&
(((~quiet(alice)|~wise(alice)))=>((~tall(fred)<~>~humble(fred))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:((~creative(X)&~rich(X))=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>brave(X))=>creative(X)))&
(((happy(lucy)<~>curious(lucy)))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(?[X]:((patient(X)|creative(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~curious(lucy) | [] | null | 0 |
Everyone who is either generous or not calm is not creative.
If alice is happy then someone is both not happy and not old.
Everyone who is creative is both tall and not strong.
If mary is either not happy or not quiet then someone is wise or not funny and vice versa.
Everyone who is not calm or kind is not creative and vice versa.
If someone is both not rich and happy then someone is both not patient and calm.
Everyone who is both not funny and quiet is not kind and vice versa.
Everyone who is either quiet or not creative is both not patient and not tall and vice versa.
Everyone who is both kind and humble is either not calm or not tall.
If someone is both humble and not wise then someone is both not curious and curious and vice versa.
Everyone who is not humble or wise is not happy or not creative and vice versa.
If someone is not calm then someone is both patient and not patient and vice versa.
Everyone who is either not humble or not happy is either generous or not old and vice versa.
Everyone who is either kind or brave is not wise.
If paul is both generous and humble then someone is tall and vice versa.
Everyone who is both generous and not humble is both not humble and kind and vice versa.
Someone is not funny.
Lucy is both curious and strong.
Lucy is not creative or happy.
John is not quiet or not old.
Paul is either not strong or wise.
Someone is strong or funny.
Lucy is either not happy or old.
Fred is either old or not kind. | Mary is calm. | entailment | (![X]:((generous(X)<~>~calm(X))=>~creative(X)))&
((happy(alice))=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:(creative(X)=>(tall(X)&~strong(X))))&
(((~happy(mary)<~>~quiet(mary)))<=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:((~calm(X)|kind(X))<=>~creative(X)))&
((?[X]:((~rich(X)&happy(X))))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((~funny(X)&quiet(X))<=>~kind(X)))&
(![X]:((quiet(X)<~>~creative(X))<=>(~patient(X)&~tall(X))))&
(![X]:((kind(X)&humble(X))=>(~calm(X)<~>~tall(X))))&
((?[X]:((humble(X)&~wise(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~humble(X)|wise(X))<=>(~happy(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((patient(X)&~patient(X)))))&
(![X]:((~humble(X)<~>~happy(X))<=>(generous(X)<~>~old(X))))&
(![X]:((kind(X)<~>brave(X))=>~wise(X)))&
(((generous(paul)&humble(paul)))<=>(?[X]:(tall(X))))&
(![X]:((generous(X)&~humble(X))<=>(~humble(X)&kind(X))))&
(?[X]:(~funny(X)))&
((curious(lucy)&strong(lucy)))&
((~creative(lucy)|happy(lucy)))&
((~quiet(john)|~old(john)))&
((~strong(paul)<~>wise(paul)))&
(?[X]:((strong(X)|funny(X))))&
((~happy(lucy)<~>old(lucy)))&
((old(fred)<~>~kind(fred))) | calm(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2212944001633209791600409
% SZS output start Proof for 2212944001633209791600409
12. ? [X0] : ~calm(X0) <=> ? [X0] : (~patient(X0) & patient(X0)) [input p11]
25. ~calm(mary) [input hypothesis]
28. ? [X0] : ~calm(X0) <=> ? [X1] : (~patient(X1) & patient(X1)) [rectify 12]
57. (? [X0] : ~calm(X0) | ! [X1] : (patient(X1) | ~patient(X1))) & (? [X1] : (~patient(X1) & patient(X1)) | ! [X0] : calm(X0)) [nnf transformation 28]
58. (? [X0] : ~calm(X0) | ! [X1] : (patient(X1) | ~patient(X1))) & (? [X2] : (~patient(X2) & patient(X2)) | ! [X3] : calm(X3)) [rectify 57]
59. ? [X0] : ~calm(X0) => ~calm(sK4) [choice axiom]
60. ? [X2] : (~patient(X2) & patient(X2)) => (~patient(sK5) & patient(sK5)) [choice axiom]
61. (~calm(sK4) | ! [X1] : (patient(X1) | ~patient(X1))) & ((~patient(sK5) & patient(sK5)) | ! [X3] : calm(X3)) [skolemisation 58,60,59]
112. patient(sK5) | calm(X3) [cnf transformation 61]
113. ~patient(sK5) | calm(X3) [cnf transformation 61]
144. ~calm(mary) [cnf transformation 25]
199. 12 <=> ! [X3] : calm(X3) [avatar definition]
200. calm(X3) <- (12) [avatar component clause 199]
202. 13 <=> patient(sK5) [avatar definition]
205. 12 | ~13 [avatar split clause 113,202,199]
206. 12 | 13 [avatar split clause 112,202,199]
278. $false <- (12) [resolution 200,144]
279. ~12 [avatar contradiction clause 278]
280. $false [avatar sat refutation 205,206,279]
% SZS output end Proof for 2212944001633209791600409
% ------------------------------
% 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 |
If someone is both not calm and not funny then someone is both wise and not old. Everyone who is wise is not generous or happy. If someone is either not generous or not quiet then someone is kind and vice versa. Everyone who is not patient is not generous or calm. Everyone who is both strong and old is not happy or not funny and vice versa. Everyone who is not brave or not strong is both rich and not quiet and vice versa. If someone is not creative or quiet then someone is happy or not quiet and vice versa. Everyone who is both not generous and not rich is both tall and not rich. Everyone who is curious is both happy and humble and vice versa. Everyone who is both not rich and tall is either not brave or quiet. If someone is both humble and not patient then alice is both not wise and not creative and vice versa. If susan is both not generous and patient then someone is not quiet or happy and vice versa. If someone is generous then john is not generous or happy and vice versa. If mary is both not curious and humble then someone is not calm or not happy. Everyone who is both funny and not tall is not calm. Everyone who is brave or strong is curious or not tall. Someone is both not generous and creative. Someone is either old or humble. Someone is not brave or not humble. Mary is tall. John is both not funny and not quiet. Someone is either not strong or not old. Alice is both wise and not tall. | Mary is not calm. | neutral | ((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:(wise(X)=>(~generous(X)|happy(X))))&
((?[X]:((~generous(X)<~>~quiet(X))))<=>(?[X]:(kind(X))))&
(![X]:(~patient(X)=>(~generous(X)|calm(X))))&
(![X]:((strong(X)&old(X))<=>(~happy(X)|~funny(X))))&
(![X]:((~brave(X)|~strong(X))<=>(rich(X)&~quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~generous(X)&~rich(X))=>(tall(X)&~rich(X))))&
(![X]:(curious(X)<=>(happy(X)&humble(X))))&
(![X]:((~rich(X)&tall(X))=>(~brave(X)<~>quiet(X))))&
((?[X]:((humble(X)&~patient(X))))<=>((~wise(alice)&~creative(alice))))&
(((~generous(susan)&patient(susan)))<=>(?[X]:((~quiet(X)|happy(X)))))&
((?[X]:(generous(X)))<=>((~generous(john)|happy(john))))&
(((~curious(mary)&humble(mary)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((funny(X)&~tall(X))=>~calm(X)))&
(![X]:((brave(X)|strong(X))=>(curious(X)|~tall(X))))&
(?[X]:((~generous(X)&creative(X))))&
(?[X]:((old(X)<~>humble(X))))&
(?[X]:((~brave(X)|~humble(X))))&
(tall(mary))&
((~funny(john)&~quiet(john)))&
(?[X]:((~strong(X)<~>~old(X))))&
((wise(alice)&~tall(alice))) | ~calm(mary) | [] | null | 0 |
Everyone who is not calm is both patient and creative and vice versa.
Everyone who is both not tall and not kind is not happy or not quiet and vice versa.
Everyone who is not brave is either tall or creative.
Everyone who is not generous is either not old or funny and vice versa.
Everyone who is both old and not tall is both creative and patient.
If someone is humble then susan is either not creative or not happy.
If john is either not patient or calm then someone is old and vice versa.
If someone is not generous then someone is either not rich or creative and vice versa.
Everyone who is kind or not old is both strong and calm and vice versa.
Everyone who is either not happy or strong is not happy and vice versa.
If someone is either humble or patient then someone is either not strong or generous and vice versa.
Everyone who is humble is both humble and not kind.
Everyone who is both curious and quiet is either not rich or kind.
Everyone who is both creative and not quiet is humble or not strong.
Everyone who is either wise or not humble is not strong or not happy and vice versa.
Lucy is humble.
Someone is either generous or not humble.
Susan is tall or curious.
Paul is not happy.
Fred is not funny.
Mary is either tall or not tall.
Someone is not patient or not curious. | Paul is patient. | entailment | (![X]:(~calm(X)<=>(patient(X)&creative(X))))&
(![X]:((~tall(X)&~kind(X))<=>(~happy(X)|~quiet(X))))&
(![X]:(~brave(X)=>(tall(X)<~>creative(X))))&
(![X]:(~generous(X)<=>(~old(X)<~>funny(X))))&
(![X]:((old(X)&~tall(X))=>(creative(X)&patient(X))))&
((?[X]:(humble(X)))=>((~creative(susan)<~>~happy(susan))))&
(((~patient(john)<~>calm(john)))<=>(?[X]:(old(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((kind(X)|~old(X))<=>(strong(X)&calm(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~happy(X)))&
((?[X]:((humble(X)<~>patient(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(humble(X)=>(humble(X)&~kind(X))))&
(![X]:((curious(X)&quiet(X))=>(~rich(X)<~>kind(X))))&
(![X]:((creative(X)&~quiet(X))=>(humble(X)|~strong(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~strong(X)|~happy(X))))&
(humble(lucy))&
(?[X]:((generous(X)<~>~humble(X))))&
((tall(susan)|curious(susan)))&
(~happy(paul))&
(~funny(fred))&
((tall(mary)<~>~tall(mary)))&
(?[X]:((~patient(X)|~curious(X)))) | patient(paul) | [
"p1",
"p4",
"p8",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8802721438362526508696959
% SZS output start Proof for 8802721438362526508696959
2. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (~quiet(X0) | ~happy(X0))) [input p1]
5. ! [X0] : ((~tall(X0) & old(X0)) => (patient(X0) & creative(X0))) [input p4]
9. ! [X0] : ((~old(X0) | kind(X0)) <=> (calm(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> ~happy(X0)) [input p9]
19. ~happy(paul) [input p18]
23. ~patient(paul) [input hypothesis]
27. ! [X0] : ((patient(X0) & creative(X0)) | (tall(X0) | ~old(X0))) [ennf transformation 5]
28. ! [X0] : ((patient(X0) & creative(X0)) | tall(X0) | ~old(X0)) [flattening 27]
37. ! [X0] : (((~kind(X0) & ~tall(X0)) | (quiet(X0) & happy(X0))) & ((~quiet(X0) | ~happy(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 2]
38. ! [X0] : (((~kind(X0) & ~tall(X0)) | (quiet(X0) & happy(X0))) & (~quiet(X0) | ~happy(X0) | kind(X0) | tall(X0))) [flattening 37]
50. ! [X0] : (((~old(X0) | kind(X0)) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 9]
51. ! [X0] : ((~old(X0) | kind(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | (old(X0) & ~kind(X0)))) [flattening 50]
52. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | happy(X0)) & (~happy(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 10]
71. ~tall(X0) | happy(X0) [cnf transformation 38]
80. ~old(X0) | tall(X0) | patient(X0) [cnf transformation 28]
92. strong(X0) | old(X0) [cnf transformation 51]
97. ~happy(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 52]
99. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 52]
123. ~happy(paul) [cnf transformation 19]
128. ~patient(paul) [cnf transformation 23]
129. ~happy(X0) | ~strong(X0) [duplicate literal removal 97]
130. ~strong(X0) | happy(X0) [duplicate literal removal 99]
189. ~strong(X0) [subsumption resolution 129,130]
260. old(X0) [resolution 92,189]
296. tall(X1) | patient(X1) [resolution 80,260]
306. happy(X1) | patient(X1) [resolution 296,71]
335. patient(paul) [resolution 306,123]
337. $false [subsumption resolution 335,128]
% SZS output end Proof for 8802721438362526508696959
% ------------------------------
% 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 wise is not rich or humble.
Everyone who is not generous is both not tall and not quiet and vice versa.
Everyone who is not patient or not creative is not curious and vice versa.
Everyone who is humble or not brave is kind and vice versa.
If someone is strong then someone is both wise and not wise.
Everyone who is both not creative and funny is strong and vice versa.
If fred is calm then lucy is either not generous or generous.
Everyone who is both not strong and patient is both not patient and not quiet.
If someone is not tall or not funny then someone is not strong or brave and vice versa.
Everyone who is creative is either tall or humble and vice versa.
If someone is not happy then someone is quiet or not happy and vice versa.
Everyone who is either not happy or not funny is patient or not humble and vice versa.
If someone is creative then someone is not humble or creative.
If paul is not old then someone is either not calm or not happy.
Everyone who is both not kind and brave is both not quiet and old and vice versa.
If alice is either not generous or happy then lucy is both not generous and not humble.
Someone is either rich or curious.
Susan is both not strong and rich.
Alice is tall or not kind.
John is not rich.
Alice is both not funny and old.
Someone is not strong or wise. | Lucy is funny. | neutral | (![X]:(~wise(X)=>(~rich(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((~patient(X)|~creative(X))<=>~curious(X)))&
(![X]:((humble(X)|~brave(X))<=>kind(X)))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~creative(X)&funny(X))<=>strong(X)))&
((calm(fred))=>((~generous(lucy)<~>generous(lucy))))&
(![X]:((~strong(X)&patient(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:(creative(X)<=>(tall(X)<~>humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((~happy(X)<~>~funny(X))<=>(patient(X)|~humble(X))))&
((?[X]:(creative(X)))=>(?[X]:((~humble(X)|creative(X)))))&
((~old(paul))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)&old(X))))&
(((~generous(alice)<~>happy(alice)))=>((~generous(lucy)&~humble(lucy))))&
(?[X]:((rich(X)<~>curious(X))))&
((~strong(susan)&rich(susan)))&
((tall(alice)|~kind(alice)))&
(~rich(john))&
((~funny(alice)&old(alice)))&
(?[X]:((~strong(X)|wise(X)))) | funny(lucy) | [] | null | 0 |
Everyone who is old or patient is strong and vice versa.
Everyone who is old is either not brave or not tall and vice versa.
If someone is both not happy and brave then john is either happy or patient.
Everyone who is not calm or not rich is both old and not kind and vice versa.
Everyone who is kind or not quiet is both not patient and patient and vice versa.
Everyone who is not old is not quiet and vice versa.
Everyone who is either wise or happy is not patient and vice versa.
Everyone who is kind or old is calm.
Everyone who is wise or brave is not calm and vice versa.
Everyone who is rich or not funny is old and vice versa.
If mary is either calm or not happy then someone is both kind and not patient and vice versa.
Everyone who is not humble is both curious and not patient.
Everyone who is creative is either curious or not tall and vice versa.
Someone is both not brave and not kind.
Someone is either not generous or not wise.
Fred is either curious or rich.
Fred is kind or strong.
Paul is not rich or curious.
Paul is not calm or quiet.
Lucy is not humble. | Mary is strong. | entailment | (![X]:((old(X)|patient(X))<=>strong(X)))&
(![X]:(old(X)<=>(~brave(X)<~>~tall(X))))&
((?[X]:((~happy(X)&brave(X))))=>((happy(john)<~>patient(john))))&
(![X]:((~calm(X)|~rich(X))<=>(old(X)&~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~patient(X)&patient(X))))&
(![X]:(~old(X)<=>~quiet(X)))&
(![X]:((wise(X)<~>happy(X))<=>~patient(X)))&
(![X]:((kind(X)|old(X))=>calm(X)))&
(![X]:((wise(X)|brave(X))<=>~calm(X)))&
(![X]:((rich(X)|~funny(X))<=>old(X)))&
(((calm(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((curious(fred)<~>rich(fred)))&
((kind(fred)|strong(fred)))&
((~rich(paul)|curious(paul)))&
((~calm(paul)|quiet(paul)))&
(~humble(lucy)) | strong(mary) | [
"p0",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3016967182601861748570231
% SZS output start Proof for 3016967182601861748570231
1. ! [X0] : ((patient(X0) | old(X0)) <=> strong(X0)) [input p0]
5. ! [X0] : ((~quiet(X0) | kind(X0)) <=> (patient(X0) & ~patient(X0))) [input p4]
6. ! [X0] : (~old(X0) <=> ~quiet(X0)) [input p5]
21. ~strong(mary) [input hypothesis]
25. ! [X0] : (((patient(X0) | old(X0)) | ~strong(X0)) & (strong(X0) | (~patient(X0) & ~old(X0)))) [nnf transformation 1]
26. ! [X0] : ((patient(X0) | old(X0) | ~strong(X0)) & (strong(X0) | (~patient(X0) & ~old(X0)))) [flattening 25]
31. ! [X0] : (((~quiet(X0) | kind(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) & ~kind(X0)))) [nnf transformation 5]
32. ! [X0] : ((~quiet(X0) | kind(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (quiet(X0) & ~kind(X0)))) [flattening 31]
33. ! [X0] : ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))) [nnf transformation 6]
49. ~old(X0) | strong(X0) [cnf transformation 26]
64. ~patient(X0) | quiet(X0) [cnf transformation 32]
66. patient(X0) | quiet(X0) [cnf transformation 32]
68. ~quiet(X0) | old(X0) [cnf transformation 33]
100. ~strong(mary) [cnf transformation 21]
114. quiet(X0) [subsumption resolution 64,66]
116. old(X0) [subsumption resolution 68,114]
155. strong(X0) [resolution 49,116]
156. $false [resolution 155,100]
% SZS output end Proof for 3016967182601861748570231
% ------------------------------
% 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 |
If someone is both not wise and kind then someone is either not calm or not generous and vice versa. Everyone who is either generous or strong is both not calm and not tall and vice versa. If alice is either not generous or not rich then someone is both not funny and kind and vice versa. Everyone who is curious is either not creative or not tall. Everyone who is not brave or curious is either wise or calm and vice versa. If someone is old then lucy is patient. Everyone who is not generous or rich is either strong or not happy and vice versa. Everyone who is strong or quiet is not quiet. If someone is both not kind and not tall then alice is not calm or not humble and vice versa. Everyone who is either tall or generous is either wise or kind and vice versa. Everyone who is not kind or creative is not patient or funny. If someone is generous or curious then mary is wise. If lucy is not tall then someone is either not happy or not curious. If someone is not calm or not funny then someone is either not quiet or creative and vice versa. If alice is both brave and humble then someone is not happy or not patient and vice versa. Everyone who is both not calm and kind is wise. Paul is not brave. Someone is not calm or not funny. Someone is both creative and brave. Lucy is both not strong and not creative. Someone is curious or funny. Susan is either funny or not strong. Paul is rich or tall. | Mary is quiet. | contradiction | ((?[X]:((~wise(X)&kind(X))))<=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~calm(X)&~tall(X))))&
(((~generous(alice)<~>~rich(alice)))<=>(?[X]:((~funny(X)&kind(X)))))&
(![X]:(curious(X)=>(~creative(X)<~>~tall(X))))&
(![X]:((~brave(X)|curious(X))<=>(wise(X)<~>calm(X))))&
((?[X]:(old(X)))=>(patient(lucy)))&
(![X]:((~generous(X)|rich(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((strong(X)|quiet(X))=>~quiet(X)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(((brave(alice)&humble(alice)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(~brave(paul))&
(?[X]:((~calm(X)|~funny(X))))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul))) | quiet(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 928537767745800339355403
% SZS output start Proof for 928537767745800339355403
8. ! [X0] : ((quiet(X0) | strong(X0)) => ~quiet(X0)) [input p7]
24. quiet(mary) [input hypothesis]
29. ! [X0] : (~quiet(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 8]
111. ~quiet(X0) | ~quiet(X0) [cnf transformation 29]
153. quiet(mary) [cnf transformation 24]
154. ~quiet(X0) [duplicate literal removal 111]
348. $false [subsumption resolution 153,154]
% SZS output end Proof for 928537767745800339355403
% ------------------------------
% 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 |
Everyone who is not funny is curious or not tall. Everyone who is either not calm or rich is wise and vice versa. If susan is not generous then fred is both tall and not curious. If lucy is not generous then john is both not brave and creative. If paul is patient then someone is humble or patient and vice versa. Everyone who is generous is either not kind or not generous and vice versa. Everyone who is rich or wise is both brave and rich. Everyone who is either creative or not creative is not old or funny. If fred is both not tall and not humble then someone is brave or not rich and vice versa. Everyone who is both humble and funny is not funny or calm and vice versa. If someone is both calm and not funny then fred is patient or not generous and vice versa. Everyone who is not brave or not calm is curious and vice versa. Everyone who is both creative and not brave is either not tall or not humble. If mary is funny or not kind then someone is funny or not strong and vice versa. Someone is creative or not calm. Someone is either not patient or not creative. Lucy is curious or not calm. Someone is curious. Someone is calm. Someone is not brave. | Mary is not creative. | neutral | (![X]:(~funny(X)=>(curious(X)|~tall(X))))&
(![X]:((~calm(X)<~>rich(X))<=>wise(X)))&
((~generous(susan))=>((tall(fred)&~curious(fred))))&
((~generous(lucy))=>((~brave(john)&creative(john))))&
((patient(paul))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(generous(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:((rich(X)|wise(X))=>(brave(X)&rich(X))))&
(![X]:((creative(X)<~>~creative(X))=>(~old(X)|funny(X))))&
(((~tall(fred)&~humble(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
(![X]:((humble(X)&funny(X))<=>(~funny(X)|calm(X))))&
((?[X]:((calm(X)&~funny(X))))<=>((patient(fred)|~generous(fred))))&
(![X]:((~brave(X)|~calm(X))<=>curious(X)))&
(![X]:((creative(X)&~brave(X))=>(~tall(X)<~>~humble(X))))&
(((funny(mary)|~kind(mary)))<=>(?[X]:((funny(X)|~strong(X)))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((~patient(X)<~>~creative(X))))&
((curious(lucy)|~calm(lucy)))&
(?[X]:(curious(X)))&
(?[X]:(calm(X)))&
(?[X]:(~brave(X))) | ~creative(mary) | [] | null | 0 |
Everyone who is creative is not strong or happy.
Everyone who is either not generous or brave is both brave and not brave.
Everyone who is both patient and not brave is not calm or wise and vice versa.
If lucy is strong then john is both not patient and not old.
If someone is both not strong and rich then john is both not humble and not strong.
Everyone who is both not old and brave is both not generous and not creative and vice versa.
If paul is wise or not kind then susan is creative.
Everyone who is not creative is both calm and not quiet.
If someone is quiet or old then susan is both curious and funny and vice versa.
If lucy is both brave and rich then someone is not wise or not humble.
Everyone who is both not kind and wise is both kind and old and vice versa.
Everyone who is not patient or not curious is not patient or strong and vice versa.
Everyone who is either old or happy is not quiet and vice versa.
Everyone who is both not kind and calm is strong and vice versa.
If someone is both not kind and not old then someone is both strong and happy.
If someone is either creative or not curious then someone is not strong or not generous and vice versa.
Lucy is not brave or tall.
Mary is both not generous and not creative.
Someone is not strong.
Mary is not strong.
Alice is both brave and patient.
Someone is either not tall or creative.
Lucy is not generous.
Someone is both kind and calm. | Mary is kind. | entailment | (![X]:(creative(X)=>(~strong(X)|happy(X))))&
(![X]:((~generous(X)<~>brave(X))=>(brave(X)&~brave(X))))&
(![X]:((patient(X)&~brave(X))<=>(~calm(X)|wise(X))))&
((strong(lucy))=>((~patient(john)&~old(john))))&
((?[X]:((~strong(X)&rich(X))))=>((~humble(john)&~strong(john))))&
(![X]:((~old(X)&brave(X))<=>(~generous(X)&~creative(X))))&
(((wise(paul)|~kind(paul)))=>(creative(susan)))&
(![X]:(~creative(X)=>(calm(X)&~quiet(X))))&
((?[X]:((quiet(X)|old(X))))<=>((curious(susan)&funny(susan))))&
(((brave(lucy)&rich(lucy)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~kind(X)&wise(X))<=>(kind(X)&old(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)<~>happy(X))<=>~quiet(X)))&
(![X]:((~kind(X)&calm(X))<=>strong(X)))&
((?[X]:((~kind(X)&~old(X))))=>(?[X]:((strong(X)&happy(X)))))&
((?[X]:((creative(X)<~>~curious(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
((~brave(lucy)|tall(lucy)))&
((~generous(mary)&~creative(mary)))&
(?[X]:(~strong(X)))&
(~strong(mary))&
((brave(alice)&patient(alice)))&
(?[X]:((~tall(X)<~>creative(X))))&
(~generous(lucy))&
(?[X]:((kind(X)&calm(X)))) | kind(mary) | [
"p7",
"p13",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6110672097512286164516310
% SZS output start Proof for 6110672097512286164516310
8. ! [X0] : (~creative(X0) => (~quiet(X0) & calm(X0))) [input p7]
14. ! [X0] : ((calm(X0) & ~kind(X0)) <=> strong(X0)) [input p13]
18. ~creative(mary) & ~generous(mary) [input p17]
20. ~strong(mary) [input p19]
25. ~kind(mary) [input hypothesis]
36. ! [X0] : ((~quiet(X0) & calm(X0)) | creative(X0)) [ennf transformation 8]
53. ! [X0] : (((calm(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | (~calm(X0) | kind(X0)))) [nnf transformation 14]
54. ! [X0] : (((calm(X0) & ~kind(X0)) | ~strong(X0)) & (strong(X0) | ~calm(X0) | kind(X0))) [flattening 53]
88. calm(X0) | creative(X0) [cnf transformation 36]
107. ~calm(X0) | strong(X0) | kind(X0) [cnf transformation 54]
120. ~creative(mary) [cnf transformation 18]
122. ~strong(mary) [cnf transformation 20]
130. ~kind(mary) [cnf transformation 25]
340. kind(X1) | strong(X1) | creative(X1) [resolution 107,88]
444. strong(mary) | creative(mary) [resolution 340,130]
448. creative(mary) [subsumption resolution 444,122]
449. $false [subsumption resolution 448,120]
% SZS output end Proof for 6110672097512286164516310
% ------------------------------
% 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 |
If someone is either funny or not tall then someone is patient. If paul is not humble then paul is not strong. If fred is happy then someone is both funny and not curious and vice versa. Everyone who is both kind and not strong is curious or happy and vice versa. Everyone who is both strong and calm is not strong or not generous and vice versa. Everyone who is either not rich or not calm is both not humble and strong. Everyone who is not strong or not funny is rich or creative. Everyone who is humble or kind is quiet or not funny and vice versa. Everyone who is not strong or wise is either strong or not rich. Everyone who is not old is humble or tall. If someone is not old then someone is tall or calm. Everyone who is either not generous or not brave is either generous or creative. Everyone who is patient or rich is both not generous and not old and vice versa. Everyone who is both strong and not quiet is not quiet or not patient. Everyone who is kind is both quiet and funny. Everyone who is both creative and brave is both not tall and not happy. Someone is either strong or old. Someone is strong or not tall. Alice is either rich or wise. Someone is either humble or not wise. Someone is patient or not quiet. John is both not tall and not happy. Someone is humble or old. | John is humble. | entailment | ((?[X]:((funny(X)<~>~tall(X))))=>(?[X]:(patient(X))))&
((~humble(paul))=>(~strong(paul)))&
((happy(fred))<=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((kind(X)&~strong(X))<=>(curious(X)|happy(X))))&
(![X]:((strong(X)&calm(X))<=>(~strong(X)|~generous(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~humble(X)&strong(X))))&
(![X]:((~strong(X)|~funny(X))=>(rich(X)|creative(X))))&
(![X]:((humble(X)|kind(X))<=>(quiet(X)|~funny(X))))&
(![X]:((~strong(X)|wise(X))=>(strong(X)<~>~rich(X))))&
(![X]:(~old(X)=>(humble(X)|tall(X))))&
((?[X]:(~old(X)))=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((~generous(X)<~>~brave(X))=>(generous(X)<~>creative(X))))&
(![X]:((patient(X)|rich(X))<=>(~generous(X)&~old(X))))&
(![X]:((strong(X)&~quiet(X))=>(~quiet(X)|~patient(X))))&
(![X]:(kind(X)=>(quiet(X)&funny(X))))&
(![X]:((creative(X)&brave(X))=>(~tall(X)&~happy(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((strong(X)|~tall(X))))&
((rich(alice)<~>wise(alice)))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((patient(X)|~quiet(X))))&
((~tall(john)&~happy(john)))&
(?[X]:((humble(X)|old(X)))) | humble(john) | [
"p2",
"p3",
"p4",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9203734414459853096644607
% SZS output start Proof for 9203734414459853096644607
3. happy(fred) <=> ? [X0] : (~curious(X0) & funny(X0)) [input p2]
4. ! [X0] : ((~strong(X0) & kind(X0)) <=> (happy(X0) | curious(X0))) [input p3]
5. ! [X0] : ((calm(X0) & strong(X0)) <=> (~generous(X0) | ~strong(X0))) [input p4]
8. ! [X0] : ((kind(X0) | humble(X0)) <=> (~funny(X0) | quiet(X0))) [input p7]
15. ! [X0] : (kind(X0) => (funny(X0) & quiet(X0))) [input p14]
24. ~humble(john) [input hypothesis]
39. ! [X0] : ((funny(X0) & quiet(X0)) | ~kind(X0)) [ennf transformation 15]
46. (happy(fred) | ! [X0] : (curious(X0) | ~funny(X0))) & (? [X0] : (~curious(X0) & funny(X0)) | ~happy(fred)) [nnf transformation 3]
47. (happy(fred) | ! [X0] : (curious(X0) | ~funny(X0))) & (? [X1] : (~curious(X1) & funny(X1)) | ~happy(fred)) [rectify 46]
48. ? [X1] : (~curious(X1) & funny(X1)) => (~curious(sK1) & funny(sK1)) [choice axiom]
49. (happy(fred) | ! [X0] : (curious(X0) | ~funny(X0))) & ((~curious(sK1) & funny(sK1)) | ~happy(fred)) [skolemisation 47,48]
50. ! [X0] : (((~strong(X0) & kind(X0)) | (~happy(X0) & ~curious(X0))) & ((happy(X0) | curious(X0)) | (strong(X0) | ~kind(X0)))) [nnf transformation 4]
51. ! [X0] : (((~strong(X0) & kind(X0)) | (~happy(X0) & ~curious(X0))) & (happy(X0) | curious(X0) | strong(X0) | ~kind(X0))) [flattening 50]
52. ! [X0] : (((calm(X0) & strong(X0)) | (generous(X0) & strong(X0))) & ((~generous(X0) | ~strong(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 5]
53. ! [X0] : (((calm(X0) & strong(X0)) | (generous(X0) & strong(X0))) & (~generous(X0) | ~strong(X0) | ~calm(X0) | ~strong(X0))) [flattening 52]
55. ! [X0] : (((kind(X0) | humble(X0)) | (funny(X0) & ~quiet(X0))) & ((~funny(X0) | quiet(X0)) | (~kind(X0) & ~humble(X0)))) [nnf transformation 8]
56. ! [X0] : ((kind(X0) | humble(X0) | (funny(X0) & ~quiet(X0))) & (~funny(X0) | quiet(X0) | (~kind(X0) & ~humble(X0)))) [flattening 55]
82. happy(fred) | curious(X0) | ~funny(X0) [cnf transformation 49]
86. ~curious(X0) | ~strong(X0) [cnf transformation 51]
87. ~happy(X0) | ~strong(X0) [cnf transformation 51]
89. strong(X0) | strong(X0) [cnf transformation 53]
102. kind(X0) | humble(X0) | funny(X0) [cnf transformation 56]
120. ~kind(X0) | funny(X0) [cnf transformation 39]
134. ~humble(john) [cnf transformation 24]
139. strong(X0) [duplicate literal removal 89]
162. 6 <=> ! [X0] : (curious(X0) | ~funny(X0)) [avatar definition]
163. ~funny(X0) | curious(X0) <- (6) [avatar component clause 162]
165. 7 <=> happy(fred) [avatar definition]
167. happy(fred) <- (7) [avatar component clause 165]
168. 6 | 7 [avatar split clause 82,165,162]
270. humble(X1) | funny(X1) | funny(X1) [resolution 102,120]
272. humble(X1) | funny(X1) [duplicate literal removal 270]
274. funny(john) [resolution 272,134]
289. curious(john) <- (6) [resolution 274,163]
291. ~strong(john) <- (6) [resolution 289,86]
293. $false <- (6) [subsumption resolution 291,139]
294. ~6 [avatar contradiction clause 293]
295. ~strong(fred) <- (7) [resolution 167,87]
297. $false <- (7) [subsumption resolution 295,139]
298. ~7 [avatar contradiction clause 297]
299. $false [avatar sat refutation 168,294,298]
% SZS output end Proof for 9203734414459853096644607
% ------------------------------
% 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 funny is either brave or wise.
If fred is not creative or brave then someone is rich and vice versa.
If someone is not tall then someone is funny and vice versa.
Everyone who is brave is both curious and not generous and vice versa.
Everyone who is both not curious and not strong is either not brave or not wise and vice versa.
If someone is kind then someone is either not strong or kind and vice versa.
Everyone who is both not brave and funny is either not strong or not old.
Everyone who is both not creative and tall is not patient or not funny.
Everyone who is either not brave or curious is both curious and not kind and vice versa.
If someone is both not brave and funny then someone is brave or not humble and vice versa.
If paul is quiet then someone is either not wise or not creative.
If someone is either not patient or generous then lucy is either tall or creative and vice versa.
Everyone who is both creative and happy is either funny or rich and vice versa.
Everyone who is patient or quiet is both not brave and brave and vice versa.
Everyone who is both patient and not creative is not calm and vice versa.
If someone is either not strong or not funny then someone is not old.
Fred is either not brave or brave.
Lucy is not creative or not wise.
Someone is curious.
Someone is creative or not strong.
Someone is generous.
John is kind or not wise.
Someone is either calm or not tall.
Someone is humble or strong. | Lucy is not calm. | contradiction | (![X]:(funny(X)=>(brave(X)<~>wise(X))))&
(((~creative(fred)|brave(fred)))<=>(?[X]:(rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>(curious(X)&~generous(X))))&
(![X]:((~curious(X)&~strong(X))<=>(~brave(X)<~>~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:((~brave(X)&funny(X))=>(~strong(X)<~>~old(X))))&
(![X]:((~creative(X)&tall(X))=>(~patient(X)|~funny(X))))&
(![X]:((~brave(X)<~>curious(X))<=>(curious(X)&~kind(X))))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((brave(X)|~humble(X)))))&
((quiet(paul))=>(?[X]:((~wise(X)<~>~creative(X)))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((tall(lucy)<~>creative(lucy))))&
(![X]:((creative(X)&happy(X))<=>(funny(X)<~>rich(X))))&
(![X]:((patient(X)|quiet(X))<=>(~brave(X)&brave(X))))&
(![X]:((patient(X)&~creative(X))<=>~calm(X)))&
((?[X]:((~strong(X)<~>~funny(X))))=>(?[X]:(~old(X))))&
((~brave(fred)<~>brave(fred)))&
((~creative(lucy)|~wise(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:(generous(X)))&
((kind(john)|~wise(john)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((humble(X)|strong(X)))) | ~calm(lucy) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6464143826967521937720736
% SZS output start Proof for 6464143826967521937720736
14. ! [X0] : ((quiet(X0) | patient(X0)) <=> (brave(X0) & ~brave(X0))) [input p13]
15. ! [X0] : ((~creative(X0) & patient(X0)) <=> ~calm(X0)) [input p14]
25. ~calm(lucy) [input hypothesis]
74. ! [X0] : (((quiet(X0) | patient(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 14]
75. ! [X0] : ((quiet(X0) | patient(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (~quiet(X0) & ~patient(X0)))) [flattening 74]
76. ! [X0] : (((~creative(X0) & patient(X0)) | calm(X0)) & (~calm(X0) | (creative(X0) | ~patient(X0)))) [nnf transformation 15]
77. ! [X0] : (((~creative(X0) & patient(X0)) | calm(X0)) & (~calm(X0) | creative(X0) | ~patient(X0))) [flattening 76]
144. ~brave(X0) | ~patient(X0) [cnf transformation 75]
146. brave(X0) | ~patient(X0) [cnf transformation 75]
150. patient(X0) | calm(X0) [cnf transformation 77]
164. ~calm(lucy) [cnf transformation 25]
306. ~patient(X0) [subsumption resolution 144,146]
307. calm(X0) [subsumption resolution 150,306]
353. $false [subsumption resolution 164,307]
% SZS output end Proof for 6464143826967521937720736
% ------------------------------
% 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 wise or not humble is both tall and not rich and vice versa. Everyone who is either curious or not happy is both curious and calm. Everyone who is not kind is patient and vice versa. Everyone who is both not wise and not generous is humble or not patient and vice versa. Everyone who is strong or calm is either strong or not humble and vice versa. Everyone who is either not calm or not tall is not rich or wise. Everyone who is rich or not happy is both old and not funny. If someone is both not patient and not happy then mary is either not patient or old and vice versa. Everyone who is not funny is either not quiet or brave. If mary is quiet or wise then susan is both curious and not strong and vice versa. If someone is either not quiet or funny then someone is not kind and vice versa. Everyone who is both wise and not wise is not calm. If lucy is both calm and not rich then someone is not creative. If fred is wise or not funny then someone is either not happy or curious and vice versa. Everyone who is either not rich or rich is generous or wise. If john is not humble then someone is happy. Lucy is either not wise or not creative. Someone is both not creative and not brave. Someone is both not happy and not rich. Someone is happy. John is not quiet. Lucy is brave or calm. | Lucy is not wise. | neutral | (![X]:((~wise(X)|~humble(X))<=>(tall(X)&~rich(X))))&
(![X]:((curious(X)<~>~happy(X))=>(curious(X)&calm(X))))&
(![X]:(~kind(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))<=>(humble(X)|~patient(X))))&
(![X]:((strong(X)|calm(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((~calm(X)<~>~tall(X))=>(~rich(X)|wise(X))))&
(![X]:((rich(X)|~happy(X))=>(old(X)&~funny(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>((~patient(mary)<~>old(mary))))&
(![X]:(~funny(X)=>(~quiet(X)<~>brave(X))))&
(((quiet(mary)|wise(mary)))<=>((curious(susan)&~strong(susan))))&
((?[X]:((~quiet(X)<~>funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)&~wise(X))=>~calm(X)))&
(((calm(lucy)&~rich(lucy)))=>(?[X]:(~creative(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((~rich(X)<~>rich(X))=>(generous(X)|wise(X))))&
((~humble(john))=>(?[X]:(happy(X))))&
((~wise(lucy)<~>~creative(lucy)))&
(?[X]:((~creative(X)&~brave(X))))&
(?[X]:((~happy(X)&~rich(X))))&
(?[X]:(happy(X)))&
(~quiet(john))&
((brave(lucy)|calm(lucy))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either old or funny is not old or old and vice versa.
Everyone who is either not funny or not curious is both not curious and not brave and vice versa.
Everyone who is both brave and not creative is both not creative and creative and vice versa.
If someone is either not old or rich then someone is either not curious or humble.
If alice is wise or not generous then john is either kind or quiet.
Everyone who is patient is not humble and vice versa.
Everyone who is both not quiet and not tall is happy.
Everyone who is either not brave or strong is not old or not strong and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is strong or not kind is both old and calm.
Everyone who is either not strong or generous is both not wise and humble.
Everyone who is either not humble or not quiet is not brave and vice versa.
Everyone who is humble is strong or not quiet.
Everyone who is not happy is not wise and vice versa.
If someone is not curious then someone is either not creative or happy.
John is both not patient and not curious.
Paul is not patient or quiet.
Someone is wise or tall.
Someone is not brave or not rich.
Someone is either not funny or not quiet.
Mary is not humble.
Someone is either not kind or not curious. | John is quiet. | contradiction | (![X]:((old(X)<~>funny(X))<=>(~old(X)|old(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(~curious(X)&~brave(X))))&
(![X]:((brave(X)&~creative(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~old(X)<~>rich(X))))=>(?[X]:((~curious(X)<~>humble(X)))))&
(((wise(alice)|~generous(alice)))=>((kind(john)<~>quiet(john))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((~quiet(X)&~tall(X))=>happy(X)))&
(![X]:((~brave(X)<~>strong(X))<=>(~old(X)|~strong(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((strong(X)|~kind(X))=>(old(X)&calm(X))))&
(![X]:((~strong(X)<~>generous(X))=>(~wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>~brave(X)))&
(![X]:(humble(X)=>(strong(X)|~quiet(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)<~>happy(X)))))&
((~patient(john)&~curious(john)))&
((~patient(paul)|quiet(paul)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~funny(X)<~>~quiet(X))))&
(~humble(mary))&
(?[X]:((~kind(X)<~>~curious(X)))) | quiet(john) | [
"p5",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8688818516622621725204535
% SZS output start Proof for 8688818516622621725204535
6. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p5]
8. ! [X0] : ((~brave(X0) <~> strong(X0)) <=> (~strong(X0) | ~old(X0))) [input p7]
10. ! [X0] : ((~kind(X0) | strong(X0)) => (calm(X0) & old(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> ~quiet(X0)) <=> ~brave(X0)) [input p11]
16. ~curious(john) & ~patient(john) [input p15]
23. quiet(john) [input hypothesis]
26. ! [X0] : (~humble(X0) => patient(X0)) [unused predicate definition removal 6]
27. ! [X0] : ((~kind(X0) | strong(X0)) => old(X0)) [pure predicate removal 10]
32. ! [X0] : (patient(X0) | humble(X0)) [ennf transformation 26]
33. ! [X0] : (old(X0) | (kind(X0) & ~strong(X0))) [ennf transformation 27]
49. ! [X0] : ((((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (strong(X0) & old(X0))) & ((~strong(X0) | ~old(X0)) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (strong(X0) & old(X0))) & (~strong(X0) | ~old(X0) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))))) [flattening 49]
53. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | brave(X0)) & (~brave(X0) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [nnf transformation 12]
91. patient(X0) | humble(X0) [cnf transformation 32]
93. ~strong(X0) | ~old(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 50]
95. strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 50]
100. ~strong(X0) | old(X0) [cnf transformation 33]
108. ~quiet(X0) | ~humble(X0) | brave(X0) [cnf transformation 53]
115. ~patient(john) [cnf transformation 16]
124. quiet(john) [cnf transformation 23]
125. ~strong(X0) | ~old(X0) | ~brave(X0) [duplicate literal removal 93]
126. ~brave(X0) | strong(X0) [duplicate literal removal 95]
162. 7 <=> quiet(john) [avatar definition]
163. quiet(john) <- (7) [avatar component clause 162]
173. ~brave(X0) | ~old(X0) [subsumption resolution 125,126]
225. 7 [avatar split clause 124,162]
226. humble(john) [resolution 91,115]
251. ~humble(john) | brave(john) <- (7) [resolution 108,163]
252. brave(john) <- (7) [subsumption resolution 251,226]
255. ~old(john) <- (7) [resolution 252,173]
257. strong(john) <- (7) [resolution 252,126]
315. old(john) <- (7) [resolution 257,100]
325. $false <- (7) [subsumption resolution 315,255]
326. ~7 [avatar contradiction clause 325]
327. $false [avatar sat refutation 225,326]
% SZS output end Proof for 8688818516622621725204535
% ------------------------------
% 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 curious and not strong is rich and vice versa.
If someone is generous then paul is both generous and curious.
If john is not old then someone is old.
Everyone who is both not old and quiet is both not kind and not old.
If alice is quiet or calm then alice is not curious or curious and vice versa.
Everyone who is either curious or funny is either old or humble and vice versa.
Everyone who is funny or brave is either quiet or tall and vice versa.
Everyone who is both curious and funny is not patient and vice versa.
Everyone who is rich or wise is not patient or not rich.
Everyone who is both quiet and generous is both not calm and quiet.
If fred is happy or tall then someone is both tall and not funny and vice versa.
If john is either quiet or kind then lucy is tall or not quiet and vice versa.
Everyone who is both not strong and strong is quiet.
If alice is either not curious or not calm then someone is not kind or not old and vice versa.
Everyone who is not patient is both not brave and not funny and vice versa.
If fred is funny then someone is both not calm and wise.
John is brave.
John is not old or calm.
Someone is both tall and creative.
Someone is both generous and curious.
Someone is both not calm and strong.
Someone is curious.
Fred is both not quiet and not creative.
Someone is either not calm or wise. | Alice is not rich. | entailment | (![X]:((curious(X)&~strong(X))<=>rich(X)))&
((?[X]:(generous(X)))=>((generous(paul)&curious(paul))))&
((~old(john))=>(?[X]:(old(X))))&
(![X]:((~old(X)&quiet(X))=>(~kind(X)&~old(X))))&
(((quiet(alice)|calm(alice)))<=>((~curious(alice)|curious(alice))))&
(![X]:((curious(X)<~>funny(X))<=>(old(X)<~>humble(X))))&
(![X]:((funny(X)|brave(X))<=>(quiet(X)<~>tall(X))))&
(![X]:((curious(X)&funny(X))<=>~patient(X)))&
(![X]:((rich(X)|wise(X))=>(~patient(X)|~rich(X))))&
(![X]:((quiet(X)&generous(X))=>(~calm(X)&quiet(X))))&
(((happy(fred)|tall(fred)))<=>(?[X]:((tall(X)&~funny(X)))))&
(((quiet(john)<~>kind(john)))<=>((tall(lucy)|~quiet(lucy))))&
(![X]:((~strong(X)&strong(X))=>quiet(X)))&
(((~curious(alice)<~>~calm(alice)))<=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:(~patient(X)<=>(~brave(X)&~funny(X))))&
((funny(fred))=>(?[X]:((~calm(X)&wise(X)))))&
(brave(john))&
((~old(john)|calm(john)))&
(?[X]:((tall(X)&creative(X))))&
(?[X]:((generous(X)&curious(X))))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:(curious(X)))&
((~quiet(fred)&~creative(fred)))&
(?[X]:((~calm(X)<~>wise(X)))) | ~rich(alice) | [
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8290355926629267660389275
% SZS output start Proof for 8290355926629267660389275
8. ! [X0] : ((funny(X0) & curious(X0)) <=> ~patient(X0)) [input p7]
9. ! [X0] : ((wise(X0) | rich(X0)) => (~rich(X0) | ~patient(X0))) [input p8]
15. ! [X0] : (~patient(X0) <=> (~funny(X0) & ~brave(X0))) [input p14]
25. rich(alice) [input hypothesis]
30. ! [X0] : ((~rich(X0) | ~patient(X0)) | (~wise(X0) & ~rich(X0))) [ennf transformation 9]
31. ! [X0] : (~rich(X0) | ~patient(X0) | (~wise(X0) & ~rich(X0))) [flattening 30]
46. ! [X0] : (((funny(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | (~funny(X0) | ~curious(X0)))) [nnf transformation 8]
47. ! [X0] : (((funny(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | ~funny(X0) | ~curious(X0))) [flattening 46]
59. ! [X0] : ((~patient(X0) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 15]
60. ! [X0] : ((~patient(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | patient(X0))) [flattening 59]
102. patient(X0) | funny(X0) [cnf transformation 47]
103. ~rich(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 31]
126. ~funny(X0) | patient(X0) [cnf transformation 60]
143. rich(alice) [cnf transformation 25]
144. ~patient(X0) | ~rich(X0) [duplicate literal removal 103]
248. patient(X0) [subsumption resolution 126,102]
282. ~rich(X2) [resolution 144,248]
284. $false [resolution 282,143]
% SZS output end Proof for 8290355926629267660389275
% ------------------------------
% 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 kind or not generous is not kind or not old and vice versa.
If someone is not creative then fred is not curious.
If paul is rich or not creative then someone is either not tall or not creative.
If alice is not strong or not humble then alice is rich or not curious.
If someone is wise or generous then john is either not humble or rich and vice versa.
Everyone who is creative or not wise is rich and vice versa.
Everyone who is curious or not happy is not tall or not happy and vice versa.
Everyone who is either not curious or brave is both funny and tall and vice versa.
Everyone who is not curious is not kind or humble and vice versa.
Everyone who is old is humble or rich.
Everyone who is creative is either humble or not wise and vice versa.
Everyone who is either not tall or not generous is not happy or strong and vice versa.
If someone is both not strong and not humble then susan is either not generous or not quiet.
If john is both tall and not generous then someone is either brave or not wise and vice versa.
Everyone who is both not rich and not humble is both brave and not old and vice versa.
Everyone who is wise or not generous is either not curious or rich.
Someone is either calm or tall.
Fred is not tall.
Someone is old or not brave.
John is both not old and not calm.
Someone is not tall or generous. | Alice is not old. | entailment | (![X]:((kind(X)|~generous(X))<=>(~kind(X)|~old(X))))&
((?[X]:(~creative(X)))=>(~curious(fred)))&
(((rich(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(((~strong(alice)|~humble(alice)))=>((rich(alice)|~curious(alice))))&
((?[X]:((wise(X)|generous(X))))<=>((~humble(john)<~>rich(john))))&
(![X]:((creative(X)|~wise(X))<=>rich(X)))&
(![X]:((curious(X)|~happy(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(funny(X)&tall(X))))&
(![X]:(~curious(X)<=>(~kind(X)|humble(X))))&
(![X]:(old(X)=>(humble(X)|rich(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~strong(X)&~humble(X))))=>((~generous(susan)<~>~quiet(susan))))&
(((tall(john)&~generous(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)&~old(X))))&
(![X]:((wise(X)|~generous(X))=>(~curious(X)<~>rich(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(~tall(fred))&
(?[X]:((old(X)|~brave(X))))&
((~old(john)&~calm(john)))&
(?[X]:((~tall(X)|generous(X)))) | ~old(alice) | [
"p0",
"p5",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3597373093652682177518559
% SZS output start Proof for 3597373093652682177518559
1. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~old(X0) | ~kind(X0))) [input p0]
6. ! [X0] : ((~wise(X0) | creative(X0)) <=> rich(X0)) [input p5]
9. ! [X0] : (~curious(X0) <=> (humble(X0) | ~kind(X0))) [input p8]
10. ! [X0] : (old(X0) => (rich(X0) | humble(X0))) [input p9]
11. ! [X0] : (creative(X0) <=> (humble(X0) <~> ~wise(X0))) [input p10]
16. ! [X0] : ((~generous(X0) | wise(X0)) => (~curious(X0) <~> rich(X0))) [input p15]
22. old(alice) [input hypothesis]
27. ! [X0] : ((rich(X0) | humble(X0)) | ~old(X0)) [ennf transformation 10]
28. ! [X0] : (rich(X0) | humble(X0) | ~old(X0)) [flattening 27]
30. ! [X0] : ((~curious(X0) <~> rich(X0)) | (generous(X0) & ~wise(X0))) [ennf transformation 16]
31. ! [X0] : (((~generous(X0) | kind(X0)) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~generous(X0) | kind(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | (generous(X0) & ~kind(X0)))) [flattening 31]
40. ! [X0] : (((~wise(X0) | creative(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [nnf transformation 6]
41. ! [X0] : ((~wise(X0) | creative(X0) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [flattening 40]
46. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | curious(X0))) [flattening 46]
48. ! [X0] : ((creative(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ~creative(X0))) [nnf transformation 11]
59. ! [X0] : (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0))) [nnf transformation 30]
67. ~old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 32]
69. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 32]
84. ~creative(X0) | rich(X0) [cnf transformation 41]
85. wise(X0) | rich(X0) [cnf transformation 41]
98. ~curious(X0) | kind(X0) [cnf transformation 47]
100. ~old(X0) | humble(X0) | rich(X0) [cnf transformation 28]
103. ~wise(X0) | creative(X0) | ~humble(X0) [cnf transformation 48]
126. ~rich(X0) | curious(X0) | generous(X0) [cnf transformation 59]
134. old(alice) [cnf transformation 22]
135. ~old(X0) | ~kind(X0) [duplicate literal removal 67]
136. ~generous(X0) | kind(X0) [duplicate literal removal 69]
166. 7 <=> humble(alice) [avatar definition]
168. humble(alice) <- (7) [avatar component clause 166]
170. 8 <=> rich(alice) [avatar definition]
172. rich(alice) <- (8) [avatar component clause 170]
174. 9 <=> curious(alice) [avatar definition]
175. curious(alice) <- (9) [avatar component clause 174]
176. ~curious(alice) <- (~9) [avatar component clause 174]
282. ~kind(alice) [resolution 135,134]
330. humble(alice) | rich(alice) [resolution 100,134]
331. 8 | 7 [avatar split clause 330,166,170]
358. creative(X0) | ~humble(X0) | rich(X0) [resolution 103,85]
362. ~humble(X0) | rich(X0) [subsumption resolution 358,84]
515. rich(alice) <- (7) [resolution 362,168]
516. 8 | ~7 [avatar split clause 515,166,170]
517. curious(alice) | generous(alice) <- (8) [resolution 172,126]
518. generous(alice) <- (8, ~9) [subsumption resolution 517,176]
520. kind(alice) <- (8, ~9) [resolution 518,136]
521. $false <- (8, ~9) [subsumption resolution 520,282]
522. ~8 | 9 [avatar contradiction clause 521]
533. kind(alice) <- (9) [resolution 175,98]
534. $false <- (9) [subsumption resolution 533,282]
535. ~9 [avatar contradiction clause 534]
536. $false [avatar sat refutation 331,516,522,535]
% SZS output end Proof for 3597373093652682177518559
% ------------------------------
% 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is both not wise and not calm and vice versa.
Everyone who is not calm or not tall is either old or not humble and vice versa.
Everyone who is patient or wise is both humble and not old and vice versa.
Everyone who is creative or funny is creative or quiet.
If someone is both not tall and humble then susan is brave.
Everyone who is both not wise and not curious is both not happy and not calm and vice versa.
If john is old then someone is either not generous or curious and vice versa.
If someone is wise or not rich then someone is both not calm and not creative.
Everyone who is calm is both not calm and humble.
If someone is either happy or not funny then someone is not kind and vice versa.
Everyone who is calm or curious is both kind and not rich.
Everyone who is not strong or not kind is wise.
Everyone who is strong is old or not creative.
Everyone who is curious or not curious is not happy and vice versa.
Everyone who is either not happy or strong is either not happy or not generous and vice versa.
Everyone who is either funny or not brave is curious or not calm.
Someone is both brave and not tall.
John is not creative or happy.
Someone is not rich.
Lucy is kind.
Someone is rich or not curious. | Susan is not strong. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(old(X)<~>~humble(X))))&
(![X]:((patient(X)|wise(X))<=>(humble(X)&~old(X))))&
(![X]:((creative(X)|funny(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&humble(X))))=>(brave(susan)))&
(![X]:((~wise(X)&~curious(X))<=>(~happy(X)&~calm(X))))&
((old(john))<=>(?[X]:((~generous(X)<~>curious(X)))))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:(calm(X)=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((calm(X)|curious(X))=>(kind(X)&~rich(X))))&
(![X]:((~strong(X)|~kind(X))=>wise(X)))&
(![X]:(strong(X)=>(old(X)|~creative(X))))&
(![X]:((curious(X)|~curious(X))<=>~happy(X)))&
(![X]:((~happy(X)<~>strong(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((funny(X)<~>~brave(X))=>(curious(X)|~calm(X))))&
(?[X]:((brave(X)&~tall(X))))&
((~creative(john)|happy(john)))&
(?[X]:(~rich(X)))&
(kind(lucy))&
(?[X]:((rich(X)|~curious(X)))) | ~strong(susan) | [
"p1",
"p2",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3641342157940583356501028
% SZS output start Proof for 3641342157940583356501028
2. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> (old(X0) <~> ~humble(X0))) [input p1]
3. ! [X0] : ((wise(X0) | patient(X0)) <=> (~old(X0) & humble(X0))) [input p2]
9. ! [X0] : (calm(X0) => (humble(X0) & ~calm(X0))) [input p8]
12. ! [X0] : ((~kind(X0) | ~strong(X0)) => wise(X0)) [input p11]
22. ~strong(susan) [input hypothesis]
32. ! [X0] : ((humble(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 9]
34. ! [X0] : (wise(X0) | (kind(X0) & strong(X0))) [ennf transformation 12]
42. ! [X0] : (((~tall(X0) | ~calm(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (tall(X0) & calm(X0)))) [nnf transformation 2]
43. ! [X0] : ((~tall(X0) | ~calm(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (tall(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : (((wise(X0) | patient(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 3]
45. ! [X0] : ((wise(X0) | patient(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~wise(X0) & ~patient(X0)))) [flattening 44]
73. ~humble(X0) | old(X0) | calm(X0) [cnf transformation 43]
80. ~wise(X0) | humble(X0) [cnf transformation 45]
82. ~wise(X0) | ~old(X0) [cnf transformation 45]
95. ~calm(X0) | ~calm(X0) [cnf transformation 32]
105. strong(X0) | wise(X0) [cnf transformation 34]
125. ~strong(susan) [cnf transformation 22]
130. ~calm(X0) [duplicate literal removal 95]
223. wise(susan) [resolution 105,125]
225. ~old(susan) [resolution 223,82]
226. humble(susan) [resolution 223,80]
233. old(susan) | calm(susan) [resolution 73,226]
234. calm(susan) [subsumption resolution 233,225]
235. $false [subsumption resolution 234,130]
% SZS output end Proof for 3641342157940583356501028
% ------------------------------
% 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 brave and not tall then someone is either not quiet or not rich and vice versa.
If someone is either not curious or not rich then mary is generous and vice versa.
Everyone who is not kind or rich is patient and vice versa.
Everyone who is either not strong or not creative is both generous and not old and vice versa.
Everyone who is quiet or funny is humble or kind.
If someone is not wise then someone is either creative or not creative and vice versa.
If someone is not strong or patient then lucy is either not calm or generous and vice versa.
Everyone who is both happy and rich is both not quiet and humble.
If someone is tall or calm then mary is brave and vice versa.
Everyone who is wise or not kind is both wise and not tall and vice versa.
If alice is not strong or not brave then alice is not generous and vice versa.
If someone is patient or rich then john is not happy or not quiet.
If lucy is either quiet or kind then fred is not funny or not brave.
If someone is both not wise and not happy then someone is both happy and tall.
Everyone who is tall is not kind or not funny and vice versa.
If fred is either happy or tall then mary is not funny and vice versa.
Lucy is quiet or old.
Susan is either not old or not generous.
Fred is both tall and generous.
Someone is not happy or not generous.
Someone is either rich or not quiet.
John is not strong.
Susan is not tall or wise.
Someone is either happy or not brave. | Mary is not happy. | neutral | ((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
((?[X]:((~curious(X)<~>~rich(X))))<=>(generous(mary)))&
(![X]:((~kind(X)|rich(X))<=>patient(X)))&
(![X]:((~strong(X)<~>~creative(X))<=>(generous(X)&~old(X))))&
(![X]:((quiet(X)|funny(X))=>(humble(X)|kind(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
((?[X]:((~strong(X)|patient(X))))<=>((~calm(lucy)<~>generous(lucy))))&
(![X]:((happy(X)&rich(X))=>(~quiet(X)&humble(X))))&
((?[X]:((tall(X)|calm(X))))<=>(brave(mary)))&
(![X]:((wise(X)|~kind(X))<=>(wise(X)&~tall(X))))&
(((~strong(alice)|~brave(alice)))<=>(~generous(alice)))&
((?[X]:((patient(X)|rich(X))))=>((~happy(john)|~quiet(john))))&
(((quiet(lucy)<~>kind(lucy)))=>((~funny(fred)|~brave(fred))))&
((?[X]:((~wise(X)&~happy(X))))=>(?[X]:((happy(X)&tall(X)))))&
(![X]:(tall(X)<=>(~kind(X)|~funny(X))))&
(((happy(fred)<~>tall(fred)))<=>(~funny(mary)))&
((quiet(lucy)|old(lucy)))&
((~old(susan)<~>~generous(susan)))&
((tall(fred)&generous(fred)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
(~strong(john))&
((~tall(susan)|wise(susan)))&
(?[X]:((happy(X)<~>~brave(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is not rich is not generous or brave and vice versa. If john is wise or funny then john is not calm or creative. Everyone who is either old or happy is brave or humble and vice versa. Everyone who is calm is both curious and not curious. If john is not strong then someone is both old and tall. If someone is not calm or not brave then susan is either strong or patient and vice versa. Everyone who is both brave and calm is humble. Everyone who is either not curious or not happy is both rich and brave. If alice is either not funny or kind then alice is both old and quiet and vice versa. Everyone who is either curious or not patient is quiet. Everyone who is not quiet or humble is either not strong or not creative. Everyone who is patient is not patient or happy and vice versa. Everyone who is either not humble or generous is both humble and not happy. Everyone who is not strong or tall is either not kind or creative. Everyone who is either humble or not brave is both not humble and brave. If lucy is not humble then someone is not calm or not old and vice versa. Someone is not wise or not happy. Alice is generous. Fred is patient or wise. Alice is either not happy or not humble. Someone is not generous or not creative. | Alice is wise. | neutral | (![X]:(~rich(X)<=>(~generous(X)|brave(X))))&
(((wise(john)|funny(john)))=>((~calm(john)|creative(john))))&
(![X]:((old(X)<~>happy(X))<=>(brave(X)|humble(X))))&
(![X]:(calm(X)=>(curious(X)&~curious(X))))&
((~strong(john))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~calm(X)|~brave(X))))<=>((strong(susan)<~>patient(susan))))&
(![X]:((brave(X)&calm(X))=>humble(X)))&
(![X]:((~curious(X)<~>~happy(X))=>(rich(X)&brave(X))))&
(((~funny(alice)<~>kind(alice)))<=>((old(alice)&quiet(alice))))&
(![X]:((curious(X)<~>~patient(X))=>quiet(X)))&
(![X]:((~quiet(X)|humble(X))=>(~strong(X)<~>~creative(X))))&
(![X]:(patient(X)<=>(~patient(X)|happy(X))))&
(![X]:((~humble(X)<~>generous(X))=>(humble(X)&~happy(X))))&
(![X]:((~strong(X)|tall(X))=>(~kind(X)<~>creative(X))))&
(![X]:((humble(X)<~>~brave(X))=>(~humble(X)&brave(X))))&
((~humble(lucy))<=>(?[X]:((~calm(X)|~old(X)))))&
(?[X]:((~wise(X)|~happy(X))))&
(generous(alice))&
((patient(fred)|wise(fred)))&
((~happy(alice)<~>~humble(alice)))&
(?[X]:((~generous(X)|~creative(X)))) | wise(alice) | [] | null | 0 |
Everyone who is humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not calm.
Everyone who is either generous or calm is rich and vice versa.
If someone is either creative or strong then mary is not brave.
Everyone who is both humble and happy is either not kind or funny and vice versa.
Everyone who is not quiet is not brave or not rich and vice versa.
Everyone who is old is generous or not old and vice versa.
Everyone who is not rich is both strong and quiet.
Everyone who is both not rich and not tall is both patient and happy.
Everyone who is quiet or not funny is curious or generous.
If someone is humble or not kind then someone is not brave or not old and vice versa.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
If someone is not quiet then someone is strong and vice versa.
If someone is either not brave or curious then someone is both happy and not creative.
If john is both tall and not patient then someone is either not funny or not generous.
If someone is wise or not wise then someone is happy or not kind.
Susan is either not quiet or not funny.
Someone is not happy or not humble.
Someone is kind or not patient.
Fred is both patient and not tall.
Someone is not tall.
Alice is not funny or creative.
Someone is not happy or old.
Fred is old. | Susan is funny. | contradiction | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~calm(X)))&
(![X]:((generous(X)<~>calm(X))<=>rich(X)))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(((tall(john)&~patient(john)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((happy(X)|~kind(X)))))&
((~quiet(susan)<~>~funny(susan)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((kind(X)|~patient(X))))&
((patient(fred)&~tall(fred)))&
(?[X]:(~tall(X)))&
((~funny(alice)|creative(alice)))&
(?[X]:((~happy(X)|old(X))))&
(old(fred)) | funny(susan) | [
"p0",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 770796538600287598423450
% SZS output start Proof for 770796538600287598423450
1. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~strong(X0)) [input p0]
13. ? [X0] : ~quiet(X0) <=> ? [X0] : strong(X0) [input p12]
17. ~quiet(susan) <~> ~funny(susan) [input p16]
25. funny(susan) [input hypothesis]
27. ? [X0] : ~quiet(X0) <=> ? [X1] : strong(X1) [rectify 13]
41. ! [X0] : (((~humble(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 1]
42. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [flattening 41]
62. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : quiet(X0)) [nnf transformation 27]
63. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : quiet(X3)) [rectify 62]
64. ? [X0] : ~quiet(X0) => ~quiet(sK3) [choice axiom]
65. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
66. (~quiet(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : quiet(X3)) [skolemisation 63,65,64]
77. (funny(susan) | quiet(susan)) & (~funny(susan) | ~quiet(susan)) [nnf transformation 17]
86. ~strong(X0) | ~humble(X0) [cnf transformation 42]
87. ~strong(X0) | humble(X0) [cnf transformation 42]
125. strong(sK4) | quiet(X3) [cnf transformation 66]
135. ~funny(susan) | ~quiet(susan) [cnf transformation 77]
145. funny(susan) [cnf transformation 25]
149. ~strong(X0) [subsumption resolution 86,87]
211. quiet(X3) [subsumption resolution 125,149]
260. ~funny(susan) [subsumption resolution 135,211]
288. $false [subsumption resolution 145,260]
% SZS output end Proof for 770796538600287598423450
% ------------------------------
% 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 happy is creative or not old and vice versa.
If fred is not quiet or not calm then lucy is not rich.
If mary is either calm or patient then someone is not rich and vice versa.
Everyone who is creative is either not curious or tall and vice versa.
Everyone who is both not brave and not old is not old.
Everyone who is either brave or not wise is either not old or not brave and vice versa.
Everyone who is both generous and not tall is either not strong or funny and vice versa.
If john is both not calm and not strong then alice is both kind and curious.
Everyone who is either humble or not calm is both patient and not happy and vice versa.
If alice is kind or not calm then lucy is both rich and not creative and vice versa.
If someone is either not old or calm then someone is either not generous or not calm.
Everyone who is both strong and calm is quiet and vice versa.
Everyone who is rich or strong is not brave and vice versa.
Everyone who is either not tall or not patient is both curious and not tall and vice versa.
If john is not rich or not calm then paul is patient or creative.
Everyone who is both curious and not old is both not old and not generous and vice versa.
Someone is either generous or tall.
Someone is curious.
Alice is either not humble or calm.
Mary is not tall or curious.
Fred is creative or calm.
Someone is either humble or calm.
Someone is both not brave and not tall.
Alice is humble or not happy. | Alice is wise. | contradiction | (![X]:(happy(X)<=>(creative(X)|~old(X))))&
(((~quiet(fred)|~calm(fred)))=>(~rich(lucy)))&
(((calm(mary)<~>patient(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(creative(X)<=>(~curious(X)<~>tall(X))))&
(![X]:((~brave(X)&~old(X))=>~old(X)))&
(![X]:((brave(X)<~>~wise(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((generous(X)&~tall(X))<=>(~strong(X)<~>funny(X))))&
(((~calm(john)&~strong(john)))=>((kind(alice)&curious(alice))))&
(![X]:((humble(X)<~>~calm(X))<=>(patient(X)&~happy(X))))&
(((kind(alice)|~calm(alice)))<=>((rich(lucy)&~creative(lucy))))&
((?[X]:((~old(X)<~>calm(X))))=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((strong(X)&calm(X))<=>quiet(X)))&
(![X]:((rich(X)|strong(X))<=>~brave(X)))&
(![X]:((~tall(X)<~>~patient(X))<=>(curious(X)&~tall(X))))&
(((~rich(john)|~calm(john)))=>((patient(paul)|creative(paul))))&
(![X]:((curious(X)&~old(X))<=>(~old(X)&~generous(X))))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:(curious(X)))&
((~humble(alice)<~>calm(alice)))&
((~tall(mary)|curious(mary)))&
((creative(fred)|calm(fred)))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:((~brave(X)&~tall(X))))&
((humble(alice)|~happy(alice))) | wise(alice) | [
"p0",
"p5",
"p8",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3806504035464364160393558
% SZS output start Proof for 3806504035464364160393558
1. ! [X0] : (happy(X0) <=> (~old(X0) | creative(X0))) [input p0]
6. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (~old(X0) <~> ~brave(X0))) [input p5]
9. ! [X0] : ((humble(X0) <~> ~calm(X0)) <=> (~happy(X0) & patient(X0))) [input p8]
19. ~humble(alice) <~> calm(alice) [input p18]
24. ~happy(alice) | humble(alice) [input p23]
25. wise(alice) [input hypothesis]
37. ! [X0] : ((happy(X0) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ~happy(X0))) [nnf transformation 1]
38. ! [X0] : ((happy(X0) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ~happy(X0))) [flattening 37]
44. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 6]
47. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (happy(X0) | ~patient(X0))) & ((~happy(X0) & patient(X0)) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [nnf transformation 9]
48. ! [X0] : ((((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | happy(X0) | ~patient(X0)) & ((~happy(X0) & patient(X0)) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))))) [flattening 47]
66. (~calm(alice) | humble(alice)) & (calm(alice) | ~humble(alice)) [nnf transformation 19]
74. old(X0) | happy(X0) [cnf transformation 38]
86. ~brave(X0) | ~old(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 44]
91. ~wise(X0) | brave(X0) | ~old(X0) | brave(X0) [cnf transformation 44]
104. ~humble(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 48]
137. calm(alice) | ~humble(alice) [cnf transformation 66]
145. ~happy(alice) | humble(alice) [cnf transformation 24]
146. wise(alice) [cnf transformation 25]
149. ~brave(X0) | ~old(X0) | ~wise(X0) [duplicate literal removal 86]
151. ~wise(X0) | brave(X0) | ~old(X0) [duplicate literal removal 91]
187. ~wise(X0) | ~old(X0) [subsumption resolution 149,151]
211. 13 <=> calm(alice) [avatar definition]
212. calm(alice) <- (13) [avatar component clause 211]
262. 23 <=> humble(alice) [avatar definition]
264. humble(alice) <- (23) [avatar component clause 262]
266. ~23 | 13 [avatar split clause 137,211,262]
292. 29 <=> happy(alice) [avatar definition]
293. happy(alice) <- (29) [avatar component clause 292]
295. 23 | ~29 [avatar split clause 145,292,262]
299. ~old(alice) [resolution 187,146]
302. happy(alice) [resolution 299,74]
303. 29 [avatar split clause 302,292]
377. ~calm(alice) | ~happy(alice) <- (23) [resolution 104,264]
380. ~happy(alice) <- (13, 23) [subsumption resolution 377,212]
381. $false <- (13, 23, 29) [subsumption resolution 380,293]
382. ~13 | ~23 | ~29 [avatar contradiction clause 381]
383. $false [avatar sat refutation 266,295,303,382]
% SZS output end Proof for 3806504035464364160393558
% ------------------------------
% 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and funny then someone is tall or calm. Everyone who is brave is both not calm and tall and vice versa. Everyone who is happy or not brave is humble. Everyone who is both not rich and patient is both not brave and not tall and vice versa. Everyone who is creative is rich and vice versa. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Everyone who is either not old or not funny is both kind and not strong and vice versa. Everyone who is quiet is generous and vice versa. If fred is either creative or not wise then someone is both brave and not patient. Susan is not humble. Someone is both not rich and funny. Someone is humble or brave. Mary is either funny or patient. Someone is wise. Someone is either not rich or rich. Paul is both strong and not kind. Someone is not brave or calm. | Fred is wise. | entailment | ((?[X]:((generous(X)&funny(X))))=>(?[X]:((tall(X)|calm(X)))))&
(![X]:(brave(X)<=>(~calm(X)&tall(X))))&
(![X]:((happy(X)|~brave(X))=>humble(X)))&
(![X]:((~rich(X)&patient(X))<=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((humble(X)|brave(X))))&
((funny(mary)<~>patient(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | wise(fred) | [
"p1",
"p3",
"p4",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4232865505161129713951298
% SZS output start Proof for 4232865505161129713951298
2. ! [X0] : (brave(X0) <=> (tall(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((patient(X0) & ~rich(X0)) <=> (~tall(X0) & ~brave(X0))) [input p3]
5. ! [X0] : (creative(X0) <=> rich(X0)) [input p4]
9. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (funny(X0) <~> patient(X0))) [input p8]
10. ! [X0] : ((~tall(X0) & quiet(X0)) <=> (~wise(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p12]
16. (creative(fred) <~> ~wise(fred)) => ? [X0] : (~patient(X0) & brave(X0)) [input p15]
25. ~wise(fred) [input hypothesis]
32. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
35. ? [X0] : (~patient(X0) & brave(X0)) | (creative(fred) <=> ~wise(fred)) [ennf transformation 16]
39. ! [X0] : ((brave(X0) | (~tall(X0) | calm(X0))) & ((tall(X0) & ~calm(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | ~tall(X0) | calm(X0)) & ((tall(X0) & ~calm(X0)) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((patient(X0) & ~rich(X0)) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | (~patient(X0) | rich(X0)))) [nnf transformation 4]
42. ! [X0] : (((patient(X0) & ~rich(X0)) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ~patient(X0) | rich(X0))) [flattening 41]
43. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 5]
48. ! [X0] : (((~calm(X0) | ~generous(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | ~generous(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [flattening 48]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | (tall(X0) | ~quiet(X0)))) [nnf transformation 10]
51. ! [X0] : (((~tall(X0) & quiet(X0)) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | tall(X0) | ~quiet(X0))) [flattening 50]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 13]
54. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 53]
58. ? [X0] : (~patient(X0) & brave(X0)) | ((creative(fred) | wise(fred)) & (~wise(fred) | ~creative(fred))) [nnf transformation 35]
59. ? [X0] : (~patient(X0) & brave(X0)) => (~patient(sK2) & brave(sK2)) [choice axiom]
60. (~patient(sK2) & brave(sK2)) | ((creative(fred) | wise(fred)) & (~wise(fred) | ~creative(fred))) [skolemisation 58,59]
74. ~brave(X0) | ~calm(X0) [cnf transformation 40]
75. ~brave(X0) | tall(X0) [cnf transformation 40]
81. ~rich(X0) | tall(X0) | brave(X0) [cnf transformation 42]
83. ~creative(X0) | rich(X0) [cnf transformation 43]
92. patient(X0) | funny(X0) | calm(X0) [cnf transformation 49]
100. ~tall(X0) | wise(X0) | ~generous(X0) [cnf transformation 51]
102. generous(X0) | generous(X0) [cnf transformation 32]
108. ~funny(X0) | patient(X0) [cnf transformation 54]
119. brave(sK2) | creative(fred) | wise(fred) [cnf transformation 60]
121. ~patient(sK2) | creative(fred) | wise(fred) [cnf transformation 60]
134. ~wise(fred) [cnf transformation 25]
136. generous(X0) [duplicate literal removal 102]
150. ~rich(X0) | tall(X0) [subsumption resolution 81,75]
182. 10 <=> wise(fred) [avatar definition]
183. ~wise(fred) <- (~10) [avatar component clause 182]
186. 11 <=> creative(fred) [avatar definition]
188. creative(fred) <- (11) [avatar component clause 186]
190. 12 <=> patient(sK2) [avatar definition]
192. ~patient(sK2) <- (~12) [avatar component clause 190]
193. 10 | 11 | ~12 [avatar split clause 121,190,186,182]
196. 13 <=> brave(sK2) [avatar definition]
198. brave(sK2) <- (13) [avatar component clause 196]
199. 10 | 11 | 13 [avatar split clause 119,196,186,182]
205. ~10 [avatar split clause 134,182]
234. ~calm(sK2) <- (13) [resolution 198,74]
286. funny(sK2) | calm(sK2) <- (~12) [resolution 92,192]
289. funny(sK2) <- (~12, 13) [subsumption resolution 286,234]
306. patient(sK2) <- (~12, 13) [resolution 289,108]
307. $false <- (~12, 13) [subsumption resolution 306,192]
308. 12 | ~13 [avatar contradiction clause 307]
319. rich(fred) <- (11) [resolution 188,83]
323. tall(fred) <- (11) [resolution 319,150]
394. wise(fred) | ~generous(fred) <- (11) [resolution 323,100]
396. ~generous(fred) <- (~10, 11) [subsumption resolution 394,183]
397. $false <- (~10, 11) [subsumption resolution 396,136]
398. 10 | ~11 [avatar contradiction clause 397]
399. $false [avatar sat refutation 193,199,205,308,398]
% SZS output end Proof for 4232865505161129713951298
% ------------------------------
% 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 not strong or not humble then someone is not rich or not tall. Everyone who is both humble and tall is wise or not tall. Everyone who is either rich or not humble is wise or not old. If someone is not brave then paul is either rich or not funny. If someone is not rich then someone is either not old or funny and vice versa. If fred is old or not rich then someone is either not tall or wise. Everyone who is not quiet or kind is both not wise and patient. Everyone who is happy or strong is strong or not brave and vice versa. If someone is humble then someone is not wise or happy and vice versa. Everyone who is either brave or rich is generous and vice versa. Everyone who is not kind is both not humble and generous. If someone is patient or not quiet then someone is both creative and generous and vice versa. Everyone who is both rich and quiet is not humble or not calm and vice versa. Everyone who is either rich or not calm is calm or not strong. Everyone who is both not old and not creative is either not strong or humble and vice versa. Everyone who is not old or patient is not funny or not old. Susan is either not funny or calm. Alice is either not funny or not wise. Someone is not happy. John is calm or not calm. John is not kind or funny. Paul is wise. Someone is both not old and not wise. Someone is either not brave or kind. | Paul is not brave. | entailment | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(wise(X)|~tall(X))))&
(![X]:((rich(X)<~>~humble(X))=>(wise(X)|~old(X))))&
((?[X]:(~brave(X)))=>((rich(paul)<~>~funny(paul))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(((old(fred)|~rich(fred)))=>(?[X]:((~tall(X)<~>wise(X)))))&
(![X]:((~quiet(X)|kind(X))=>(~wise(X)&patient(X))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)|~brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((brave(X)<~>rich(X))<=>generous(X)))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~humble(X)|~calm(X))))&
(![X]:((rich(X)<~>~calm(X))=>(calm(X)|~strong(X))))&
(![X]:((~old(X)&~creative(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|patient(X))=>(~funny(X)|~old(X))))&
((~funny(susan)<~>calm(susan)))&
((~funny(alice)<~>~wise(alice)))&
(?[X]:(~happy(X)))&
((calm(john)|~calm(john)))&
((~kind(john)|funny(john)))&
(wise(paul))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | ~brave(paul) | [
"p6",
"p9",
"p10",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6897685314787568367811902
% SZS output start Proof for 6897685314787568367811902
7. ! [X0] : ((kind(X0) | ~quiet(X0)) => (patient(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> rich(X0)) <=> generous(X0)) [input p9]
11. ! [X0] : (~kind(X0) => (generous(X0) & ~humble(X0))) [input p10]
13. ! [X0] : ((quiet(X0) & rich(X0)) <=> (~calm(X0) | ~humble(X0))) [input p12]
22. wise(paul) [input p21]
25. brave(paul) [input hypothesis]
37. ! [X0] : ((patient(X0) & ~wise(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 7]
38. ! [X0] : ((generous(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 11]
63. ! [X0] : ((((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ~generous(X0)) & (generous(X0) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0))))) [nnf transformation 10]
69. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~quiet(X0) | ~rich(X0)))) [nnf transformation 13]
70. ! [X0] : (((quiet(X0) & rich(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~quiet(X0) | ~rich(X0))) [flattening 69]
99. ~kind(X0) | ~wise(X0) [cnf transformation 37]
112. ~generous(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 63]
113. ~humble(X0) | kind(X0) [cnf transformation 38]
114. generous(X0) | kind(X0) [cnf transformation 38]
121. rich(X0) | humble(X0) [cnf transformation 70]
142. wise(paul) [cnf transformation 22]
147. brave(paul) [cnf transformation 25]
170. 6 <=> rich(paul) [avatar definition]
171. rich(paul) <- (6) [avatar component clause 170]
172. ~rich(paul) <- (~6) [avatar component clause 170]
332. humble(paul) <- (~6) [resolution 121,172]
338. kind(paul) <- (~6) [resolution 332,113]
392. ~brave(X0) | ~rich(X0) | kind(X0) [resolution 112,114]
435. ~wise(paul) <- (~6) [resolution 338,99]
436. $false <- (~6) [subsumption resolution 435,142]
437. 6 [avatar contradiction clause 436]
588. ~rich(paul) | kind(paul) [resolution 392,147]
591. kind(paul) <- (6) [subsumption resolution 588,171]
634. ~wise(paul) <- (6) [resolution 591,99]
635. $false <- (6) [subsumption resolution 634,142]
636. ~6 [avatar contradiction clause 635]
637. $false [avatar sat refutation 437,636]
% SZS output end Proof for 6897685314787568367811902
% ------------------------------
% 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 |
If someone is not funny then fred is kind and vice versa.
If someone is not patient then someone is not quiet or not rich.
Everyone who is both kind and tall is either not creative or patient.
If paul is not strong or tall then lucy is old or not quiet.
If someone is both wise and kind then lucy is both wise and generous.
Everyone who is brave or quiet is both calm and not old.
Everyone who is both not calm and not funny is both wise and not creative and vice versa.
If someone is both humble and happy then someone is not brave and vice versa.
Everyone who is both humble and not brave is both old and patient.
Everyone who is quiet is both generous and not creative.
Everyone who is not creative is either not generous or not strong and vice versa.
Everyone who is not patient is both not humble and quiet and vice versa.
If someone is both not kind and creative then alice is either not strong or not rich and vice versa.
If alice is quiet or not creative then john is kind.
Everyone who is both not calm and not funny is wise or kind.
If someone is either rich or calm then lucy is strong.
Fred is humble or not funny.
John is rich or kind.
Fred is not happy.
Someone is both not humble and generous.
Mary is not curious or not strong.
Someone is either not calm or not curious.
Alice is either not patient or not quiet.
John is both kind and not wise. | Mary is not strong. | neutral | ((?[X]:(~funny(X)))<=>(kind(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((~quiet(X)|~rich(X)))))&
(![X]:((kind(X)&tall(X))=>(~creative(X)<~>patient(X))))&
(((~strong(paul)|tall(paul)))=>((old(lucy)|~quiet(lucy))))&
((?[X]:((wise(X)&kind(X))))=>((wise(lucy)&generous(lucy))))&
(![X]:((brave(X)|quiet(X))=>(calm(X)&~old(X))))&
(![X]:((~calm(X)&~funny(X))<=>(wise(X)&~creative(X))))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:(~brave(X))))&
(![X]:((humble(X)&~brave(X))=>(old(X)&patient(X))))&
(![X]:(quiet(X)=>(generous(X)&~creative(X))))&
(![X]:(~creative(X)<=>(~generous(X)<~>~strong(X))))&
(![X]:(~patient(X)<=>(~humble(X)&quiet(X))))&
((?[X]:((~kind(X)&creative(X))))<=>((~strong(alice)<~>~rich(alice))))&
(((quiet(alice)|~creative(alice)))=>(kind(john)))&
(![X]:((~calm(X)&~funny(X))=>(wise(X)|kind(X))))&
((?[X]:((rich(X)<~>calm(X))))=>(strong(lucy)))&
((humble(fred)|~funny(fred)))&
((rich(john)|kind(john)))&
(~happy(fred))&
(?[X]:((~humble(X)&generous(X))))&
((~curious(mary)|~strong(mary)))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~patient(alice)<~>~quiet(alice)))&
((kind(john)&~wise(john))) | ~strong(mary) | [] | null | 0 |
Everyone who is both not strong and patient is either funny or not humble.
Everyone who is both not strong and calm is either wise or not brave and vice versa.
If susan is either not old or not brave then someone is brave and vice versa.
Everyone who is kind is not generous and vice versa.
Everyone who is not generous is humble or tall.
If someone is both not quiet and not tall then someone is both not rich and creative and vice versa.
If someone is either quiet or humble then john is not calm and vice versa.
Everyone who is happy is either quiet or not rich and vice versa.
Everyone who is funny is not funny or brave and vice versa.
Everyone who is happy or tall is not tall and vice versa.
Everyone who is either not calm or not patient is humble.
If someone is both kind and funny then someone is not old and vice versa.
Everyone who is either not happy or not old is either not humble or tall and vice versa.
Everyone who is either tall or not humble is either not rich or strong.
If mary is either not old or quiet then someone is old.
If mary is not happy then john is not tall.
Mary is not curious.
John is either funny or generous.
Someone is funny.
Mary is either humble or not quiet.
Paul is both not generous and not creative.
Someone is not rich or not brave.
Someone is patient or not old.
Someone is both creative and rich. | John is generous. | contradiction | (![X]:((~strong(X)&patient(X))=>(funny(X)<~>~humble(X))))&
(![X]:((~strong(X)&calm(X))<=>(wise(X)<~>~brave(X))))&
(((~old(susan)<~>~brave(susan)))<=>(?[X]:(brave(X))))&
(![X]:(kind(X)<=>~generous(X)))&
(![X]:(~generous(X)=>(humble(X)|tall(X))))&
((?[X]:((~quiet(X)&~tall(X))))<=>(?[X]:((~rich(X)&creative(X)))))&
((?[X]:((quiet(X)<~>humble(X))))<=>(~calm(john)))&
(![X]:(happy(X)<=>(quiet(X)<~>~rich(X))))&
(![X]:(funny(X)<=>(~funny(X)|brave(X))))&
(![X]:((happy(X)|tall(X))<=>~tall(X)))&
(![X]:((~calm(X)<~>~patient(X))=>humble(X)))&
((?[X]:((kind(X)&funny(X))))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((tall(X)<~>~humble(X))=>(~rich(X)<~>strong(X))))&
(((~old(mary)<~>quiet(mary)))=>(?[X]:(old(X))))&
((~happy(mary))=>(~tall(john)))&
(~curious(mary))&
((funny(john)<~>generous(john)))&
(?[X]:(funny(X)))&
((humble(mary)<~>~quiet(mary)))&
((~generous(paul)&~creative(paul)))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:((patient(X)|~old(X))))&
(?[X]:((creative(X)&rich(X)))) | generous(john) | [
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1517799146682421490105377
% SZS output start Proof for 1517799146682421490105377
9. ! [X0] : (funny(X0) <=> (brave(X0) | ~funny(X0))) [input p8]
18. funny(john) <~> generous(john) [input p17]
25. generous(john) [input hypothesis]
55. ! [X0] : ((funny(X0) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
56. ! [X0] : ((funny(X0) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | ~funny(X0))) [flattening 55]
70. (~generous(john) | ~funny(john)) & (generous(john) | funny(john)) [nnf transformation 18]
108. funny(X0) | funny(X0) [cnf transformation 56]
134. ~generous(john) | ~funny(john) [cnf transformation 70]
144. generous(john) [cnf transformation 25]
148. funny(X0) [duplicate literal removal 108]
252. ~generous(john) [subsumption resolution 134,148]
269. $false [subsumption resolution 144,252]
% SZS output end Proof for 1517799146682421490105377
% ------------------------------
% 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 kind then lucy is wise or funny. If mary is tall or quiet then lucy is either not rich or not creative. Everyone who is creative is both not happy and curious. Everyone who is both not quiet and patient is rich and vice versa. If someone is kind then alice is both not happy and humble. Everyone who is either patient or not strong is either not generous or curious and vice versa. If lucy is either tall or not rich then alice is both not humble and not tall and vice versa. If mary is either strong or kind then fred is patient and vice versa. If alice is not curious then someone is not rich and vice versa. Everyone who is both not wise and not happy is either not patient or not quiet. If lucy is not brave or not humble then someone is not generous or not calm. If alice is old then someone is not funny and vice versa. If paul is either not tall or quiet then someone is not wise or strong and vice versa. Everyone who is rich is not curious and vice versa. Everyone who is both not curious and not generous is either brave or happy. Everyone who is funny or tall is either rich or wise and vice versa. Someone is not wise or not generous. Fred is either rich or not kind. Someone is happy. Fred is either not old or not brave. Paul is not kind or not funny. Someone is not quiet or not kind. Alice is brave. Someone is not calm or not strong. | Alice is not quiet. | entailment | ((?[X]:(kind(X)))=>((wise(lucy)|funny(lucy))))&
(((tall(mary)|quiet(mary)))=>((~rich(lucy)<~>~creative(lucy))))&
(![X]:(creative(X)=>(~happy(X)&curious(X))))&
(![X]:((~quiet(X)&patient(X))<=>rich(X)))&
((?[X]:(kind(X)))=>((~happy(alice)&humble(alice))))&
(![X]:((patient(X)<~>~strong(X))<=>(~generous(X)<~>curious(X))))&
(((tall(lucy)<~>~rich(lucy)))<=>((~humble(alice)&~tall(alice))))&
(((strong(mary)<~>kind(mary)))<=>(patient(fred)))&
((~curious(alice))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(~patient(X)<~>~quiet(X))))&
(((~brave(lucy)|~humble(lucy)))=>(?[X]:((~generous(X)|~calm(X)))))&
((old(alice))<=>(?[X]:(~funny(X))))&
(((~tall(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)|strong(X)))))&
(![X]:(rich(X)<=>~curious(X)))&
(![X]:((~curious(X)&~generous(X))=>(brave(X)<~>happy(X))))&
(![X]:((funny(X)|tall(X))<=>(rich(X)<~>wise(X))))&
(?[X]:((~wise(X)|~generous(X))))&
((rich(fred)<~>~kind(fred)))&
(?[X]:(happy(X)))&
((~old(fred)<~>~brave(fred)))&
((~kind(paul)|~funny(paul)))&
(?[X]:((~quiet(X)|~kind(X))))&
(brave(alice))&
(?[X]:((~calm(X)|~strong(X)))) | ~quiet(alice) | [
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7220487565886578814376718
% SZS output start Proof for 7220487565886578814376718
4. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> rich(X0)) [input p3]
9. ~curious(alice) <=> ? [X0] : ~rich(X0) [input p8]
14. ! [X0] : (rich(X0) <=> ~curious(X0)) [input p13]
25. quiet(alice) [input hypothesis]
38. ! [X0] : (((patient(X0) & ~quiet(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) | quiet(X0)))) [nnf transformation 4]
39. ! [X0] : (((patient(X0) & ~quiet(X0)) | ~rich(X0)) & (rich(X0) | ~patient(X0) | quiet(X0))) [flattening 38]
44. (~curious(alice) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | curious(alice)) [nnf transformation 9]
45. (~curious(alice) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | curious(alice)) [rectify 44]
46. ? [X1] : ~rich(X1) => ~rich(sK0) [choice axiom]
47. (~curious(alice) | ! [X0] : rich(X0)) & (~rich(sK0) | curious(alice)) [skolemisation 45,46]
57. ! [X0] : ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))) [nnf transformation 14]
77. ~rich(X0) | ~quiet(X0) [cnf transformation 39]
100. ~curious(alice) | rich(X0) [cnf transformation 47]
111. ~curious(X0) | ~rich(X0) [cnf transformation 57]
112. curious(X0) | rich(X0) [cnf transformation 57]
130. quiet(alice) [cnf transformation 25]
204. 15 <=> ! [X0] : rich(X0) [avatar definition]
205. rich(X0) <- (15) [avatar component clause 204]
207. 16 <=> curious(alice) [avatar definition]
208. curious(alice) <- (16) [avatar component clause 207]
209. ~curious(alice) <- (~16) [avatar component clause 207]
210. 15 | ~16 [avatar split clause 100,207,204]
309. rich(alice) <- (~16) [resolution 112,209]
313. ~quiet(alice) <- (~16) [resolution 309,77]
314. $false <- (~16) [subsumption resolution 313,130]
315. 16 [avatar contradiction clause 314]
322. ~rich(alice) <- (16) [resolution 208,111]
323. $false <- (15, 16) [subsumption resolution 322,205]
324. ~15 | ~16 [avatar contradiction clause 323]
325. $false [avatar sat refutation 210,315,324]
% SZS output end Proof for 7220487565886578814376718
% ------------------------------
% 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 either not humble or generous then john is not creative and vice versa.
Everyone who is generous or not quiet is either not strong or not funny.
If someone is both not creative and wise then john is quiet and vice versa.
Everyone who is not rich is not calm or not wise.
Everyone who is both generous and not patient is patient and vice versa.
If someone is not strong or not brave then john is both not patient and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
Someone is not wise or creative.
Alice is both not old and funny.
Susan is either happy or old.
Someone is both not rich and strong.
Someone is quiet or old. | John is tall. | neutral | ((?[X]:((~humble(X)<~>generous(X))))<=>(~creative(john)))&
(![X]:((generous(X)|~quiet(X))=>(~strong(X)<~>~funny(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(quiet(john)))&
(![X]:(~rich(X)=>(~calm(X)|~wise(X))))&
(![X]:((generous(X)&~patient(X))<=>patient(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>((~patient(john)&creative(john))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
(?[X]:((~wise(X)|creative(X))))&
((~old(alice)&funny(alice)))&
((happy(susan)<~>old(susan)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((quiet(X)|old(X)))) | tall(john) | [] | null | 0 |
Everyone who is not generous is patient and vice versa.
If paul is either curious or calm then lucy is both humble and tall.
Everyone who is both funny and generous is wise or not creative and vice versa.
Everyone who is both not wise and not creative is either rich or wise.
If someone is not generous then someone is both tall and not rich.
If someone is funny then someone is both not brave and rich and vice versa.
If someone is kind or not rich then someone is old.
If fred is either not quiet or happy then lucy is not funny.
Everyone who is either not quiet or humble is not creative or kind.
If someone is not funny or not old then someone is either not happy or happy and vice versa.
If paul is either quiet or calm then someone is either not tall or calm.
Everyone who is humble is both old and not humble and vice versa.
Everyone who is both not old and kind is either rich or creative and vice versa.
Everyone who is both not funny and funny is patient or wise and vice versa.
If someone is either not generous or not humble then lucy is not happy.
If someone is not brave then someone is both curious and calm and vice versa.
Someone is not curious.
John is rich.
Mary is either not brave or not humble.
Someone is either not strong or old.
Someone is both not curious and tall.
Paul is creative. | Paul is wise. | contradiction | (![X]:(~generous(X)<=>patient(X)))&
(((curious(paul)<~>calm(paul)))=>((humble(lucy)&tall(lucy))))&
(![X]:((funny(X)&generous(X))<=>(wise(X)|~creative(X))))&
(![X]:((~wise(X)&~creative(X))=>(rich(X)<~>wise(X))))&
((?[X]:(~generous(X)))=>(?[X]:((tall(X)&~rich(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((~brave(X)&rich(X)))))&
((?[X]:((kind(X)|~rich(X))))=>(?[X]:(old(X))))&
(((~quiet(fred)<~>happy(fred)))=>(~funny(lucy)))&
(![X]:((~quiet(X)<~>humble(X))=>(~creative(X)|kind(X))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(((quiet(paul)<~>calm(paul)))=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:(humble(X)<=>(old(X)&~humble(X))))&
(![X]:((~old(X)&kind(X))<=>(rich(X)<~>creative(X))))&
(![X]:((~funny(X)&funny(X))<=>(patient(X)|wise(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(~happy(lucy)))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)&calm(X)))))&
(?[X]:(~curious(X)))&
(rich(john))&
((~brave(mary)<~>~humble(mary)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((~curious(X)&tall(X))))&
(creative(paul)) | wise(paul) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 515927893306997398482772
% SZS output start Proof for 515927893306997398482772
3. ! [X0] : ((generous(X0) & funny(X0)) <=> (~creative(X0) | wise(X0))) [input p2]
14. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (wise(X0) | patient(X0))) [input p13]
23. wise(paul) [input hypothesis]
41. ! [X0] : (((generous(X0) & funny(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (~generous(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((generous(X0) & funny(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | ~generous(X0) | ~funny(X0))) [flattening 41]
69. ! [X0] : (((funny(X0) & ~funny(X0)) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | (~funny(X0) | funny(X0)))) [nnf transformation 14]
70. ! [X0] : (((funny(X0) & ~funny(X0)) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | ~funny(X0) | funny(X0))) [flattening 69]
92. funny(X0) | ~wise(X0) [cnf transformation 42]
130. ~funny(X0) | ~wise(X0) [cnf transformation 70]
147. wise(paul) [cnf transformation 23]
265. ~wise(X0) [subsumption resolution 130,92]
308. $false [subsumption resolution 147,265]
% SZS output end Proof for 515927893306997398482772
% ------------------------------
% 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 either curious or funny then someone is either calm or not humble.
Everyone who is patient is not curious or not brave.
Everyone who is not humble or not funny is either tall or old.
If lucy is not brave then alice is either humble or patient and vice versa.
If someone is tall or not patient then paul is either not happy or happy.
If someone is not calm or generous then fred is generous and vice versa.
Everyone who is not happy is both not funny and happy.
If someone is patient or not happy then fred is either not old or not curious and vice versa.
Everyone who is kind or humble is not humble.
If someone is either wise or curious then someone is either not brave or strong.
If someone is not wise or funny then mary is both old and tall and vice versa.
If someone is not old then paul is both not generous and tall.
If someone is rich or creative then paul is old and vice versa.
Everyone who is wise or strong is not old or not wise.
Everyone who is either funny or not patient is not kind or not old.
Everyone who is happy or old is both brave and wise.
Someone is not creative or kind.
Fred is not strong or generous.
Someone is either not happy or curious.
Fred is not generous.
Someone is brave.
Lucy is either not tall or not generous.
Mary is calm or not brave.
Fred is both brave and not curious. | Lucy is not generous. | entailment | (((curious(mary)<~>funny(mary)))=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:(patient(X)=>(~curious(X)|~brave(X))))&
(![X]:((~humble(X)|~funny(X))=>(tall(X)<~>old(X))))&
((~brave(lucy))<=>((humble(alice)<~>patient(alice))))&
((?[X]:((tall(X)|~patient(X))))=>((~happy(paul)<~>happy(paul))))&
((?[X]:((~calm(X)|generous(X))))<=>(generous(fred)))&
(![X]:(~happy(X)=>(~funny(X)&happy(X))))&
((?[X]:((patient(X)|~happy(X))))<=>((~old(fred)<~>~curious(fred))))&
(![X]:((kind(X)|humble(X))=>~humble(X)))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:((~wise(X)|funny(X))))<=>((old(mary)&tall(mary))))&
((?[X]:(~old(X)))=>((~generous(paul)&tall(paul))))&
((?[X]:((rich(X)|creative(X))))<=>(old(paul)))&
(![X]:((wise(X)|strong(X))=>(~old(X)|~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~kind(X)|~old(X))))&
(![X]:((happy(X)|old(X))=>(brave(X)&wise(X))))&
(?[X]:((~creative(X)|kind(X))))&
((~strong(fred)|generous(fred)))&
(?[X]:((~happy(X)<~>curious(X))))&
(~generous(fred))&
(?[X]:(brave(X)))&
((~tall(lucy)<~>~generous(lucy)))&
((calm(mary)|~brave(mary)))&
((brave(fred)&~curious(fred))) | ~generous(lucy) | [
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1060076267678838980931881
% SZS output start Proof for 1060076267678838980931881
6. ? [X0] : (generous(X0) | ~calm(X0)) <=> generous(fred) [input p5]
20. ~generous(fred) [input p19]
25. generous(lucy) [input hypothesis]
47. (? [X0] : (generous(X0) | ~calm(X0)) | ~generous(fred)) & (generous(fred) | ! [X0] : (~generous(X0) & calm(X0))) [nnf transformation 6]
48. (? [X0] : (generous(X0) | ~calm(X0)) | ~generous(fred)) & (generous(fred) | ! [X1] : (~generous(X1) & calm(X1))) [rectify 47]
49. ? [X0] : (generous(X0) | ~calm(X0)) => (generous(sK1) | ~calm(sK1)) [choice axiom]
50. ((generous(sK1) | ~calm(sK1)) | ~generous(fred)) & (generous(fred) | ! [X1] : (~generous(X1) & calm(X1))) [skolemisation 48,49]
95. generous(fred) | ~generous(X1) [cnf transformation 50]
133. ~generous(fred) [cnf transformation 20]
140. generous(lucy) [cnf transformation 25]
181. 8 <=> generous(fred) [avatar definition]
194. 11 <=> ! [X1] : ~generous(X1) [avatar definition]
195. ~generous(X1) <- (11) [avatar component clause 194]
196. 11 | 8 [avatar split clause 95,181,194]
320. ~8 [avatar split clause 133,181]
326. 39 <=> generous(lucy) [avatar definition]
328. generous(lucy) <- (39) [avatar component clause 326]
333. 39 [avatar split clause 140,326]
352. $false <- (11, 39) [resolution 328,195]
353. ~11 | ~39 [avatar contradiction clause 352]
354. $false [avatar sat refutation 196,320,333,353]
% SZS output end Proof for 1060076267678838980931881
% ------------------------------
% 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy then john is curious or not calm.
Everyone who is both not rich and not creative is both not curious and calm.
Everyone who is either brave or quiet is funny or not generous.
Everyone who is not curious or humble is kind and vice versa.
Everyone who is funny or not brave is quiet or not strong.
Everyone who is patient or kind is not old.
Everyone who is not calm or not funny is either not patient or not generous.
If someone is either not brave or not calm then someone is funny and vice versa.
Everyone who is either not creative or not patient is happy or not rich.
Everyone who is both generous and not humble is both happy and not creative and vice versa.
If someone is either not generous or not patient then someone is not old and vice versa.
If john is strong then someone is curious or not strong.
If someone is either kind or not curious then paul is both not wise and not generous and vice versa.
If mary is brave then someone is not patient and vice versa.
If someone is creative or not old then someone is quiet or rich.
If mary is both patient and not wise then someone is not patient or not happy and vice versa.
Susan is not rich.
Someone is both not strong and generous.
John is either strong or not creative.
Someone is happy.
Fred is either not happy or old.
Someone is both generous and funny.
Mary is not curious.
Someone is humble. | Paul is wise. | neutral | ((happy(mary))=>((curious(john)|~calm(john))))&
(![X]:((~rich(X)&~creative(X))=>(~curious(X)&calm(X))))&
(![X]:((brave(X)<~>quiet(X))=>(funny(X)|~generous(X))))&
(![X]:((~curious(X)|humble(X))<=>kind(X)))&
(![X]:((funny(X)|~brave(X))=>(quiet(X)|~strong(X))))&
(![X]:((patient(X)|kind(X))=>~old(X)))&
(![X]:((~calm(X)|~funny(X))=>(~patient(X)<~>~generous(X))))&
((?[X]:((~brave(X)<~>~calm(X))))<=>(?[X]:(funny(X))))&
(![X]:((~creative(X)<~>~patient(X))=>(happy(X)|~rich(X))))&
(![X]:((generous(X)&~humble(X))<=>(happy(X)&~creative(X))))&
((?[X]:((~generous(X)<~>~patient(X))))<=>(?[X]:(~old(X))))&
((strong(john))=>(?[X]:((curious(X)|~strong(X)))))&
((?[X]:((kind(X)<~>~curious(X))))<=>((~wise(paul)&~generous(paul))))&
((brave(mary))<=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)|~old(X))))=>(?[X]:((quiet(X)|rich(X)))))&
(((patient(mary)&~wise(mary)))<=>(?[X]:((~patient(X)|~happy(X)))))&
(~rich(susan))&
(?[X]:((~strong(X)&generous(X))))&
((strong(john)<~>~creative(john)))&
(?[X]:(happy(X)))&
((~happy(fred)<~>old(fred)))&
(?[X]:((generous(X)&funny(X))))&
(~curious(mary))&
(?[X]:(humble(X))) | wise(paul) | [] | null | 0 |
If someone is not patient or not happy then mary is both generous and not funny and vice versa.
If john is not generous or not happy then susan is both quiet and not creative.
If susan is both curious and not old then someone is either not creative or rich and vice versa.
If alice is not kind then someone is not curious or not humble.
If someone is not kind or not curious then someone is either not funny or creative.
If someone is either kind or not happy then lucy is both not rich and old and vice versa.
Everyone who is rich or not kind is both not happy and not creative and vice versa.
If someone is curious or generous then susan is either patient or old.
Everyone who is humble or not old is not humble or happy.
If paul is not rich then paul is either not patient or not kind.
Everyone who is calm or not happy is humble or wise.
If someone is strong or wise then someone is either not calm or calm and vice versa.
Everyone who is not old or rich is patient.
Everyone who is either patient or not patient is both not brave and not wise and vice versa.
Everyone who is kind or not creative is both happy and not calm.
If lucy is both not quiet and wise then someone is not wise.
Someone is either kind or not quiet.
Someone is not rich or not generous.
Someone is funny or not generous.
Mary is funny or not old.
Mary is either curious or not strong.
Someone is curious. | John is not happy. | contradiction | ((?[X]:((~patient(X)|~happy(X))))<=>((generous(mary)&~funny(mary))))&
(((~generous(john)|~happy(john)))=>((quiet(susan)&~creative(susan))))&
(((curious(susan)&~old(susan)))<=>(?[X]:((~creative(X)<~>rich(X)))))&
((~kind(alice))=>(?[X]:((~curious(X)|~humble(X)))))&
((?[X]:((~kind(X)|~curious(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((funny(X)|~generous(X))))&
((funny(mary)|~old(mary)))&
((curious(mary)<~>~strong(mary)))&
(?[X]:(curious(X))) | ~happy(john) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8498137477485611382162544
% SZS output start Proof for 8498137477485611382162544
7. ! [X0] : ((~kind(X0) | rich(X0)) <=> (~creative(X0) & ~happy(X0))) [input p6]
15. ! [X0] : ((~creative(X0) | kind(X0)) => (~calm(X0) & happy(X0))) [input p14]
23. ~happy(john) [input hypothesis]
36. ! [X0] : ((~calm(X0) & happy(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 15]
60. ! [X0] : (((~kind(X0) | rich(X0)) | (creative(X0) | happy(X0))) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [nnf transformation 7]
61. ! [X0] : ((~kind(X0) | rich(X0) | creative(X0) | happy(X0)) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [flattening 60]
110. ~happy(X0) | kind(X0) [cnf transformation 61]
112. ~creative(X0) | kind(X0) [cnf transformation 61]
138. ~kind(X0) | happy(X0) [cnf transformation 36]
139. creative(X0) | happy(X0) [cnf transformation 36]
151. ~happy(john) [cnf transformation 23]
177. 5 <=> ! [X1] : happy(X1) [avatar definition]
178. happy(X1) <- (5) [avatar component clause 177]
187. 7 <=> happy(john) [avatar definition]
188. ~happy(john) <- (~7) [avatar component clause 187]
260. 23 <=> ! [X1] : kind(X1) [avatar definition]
261. kind(X1) <- (23) [avatar component clause 260]
384. ~7 [avatar split clause 151,187]
387. $false <- (5, ~7) [resolution 188,178]
388. ~5 | 7 [avatar contradiction clause 387]
399. happy(X0) | kind(X0) [resolution 139,112]
400. kind(X0) [subsumption resolution 399,110]
401. 23 [avatar split clause 400,260]
404. happy(X0) <- (23) [resolution 261,138]
407. 5 | ~23 [avatar split clause 404,260,177]
408. $false [avatar sat refutation 384,388,401,407]
% SZS output end Proof for 8498137477485611382162544
% ------------------------------
% 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 both patient and not old is not tall or not patient.
If someone is both wise and brave then mary is either happy or generous.
Everyone who is either kind or not kind is happy.
If someone is tall then someone is both tall and not patient and vice versa.
If someone is both not rich and not wise then john is both patient and strong.
If someone is both quiet and not calm then someone is either brave or not quiet and vice versa.
Everyone who is happy or quiet is curious or generous.
If fred is either not wise or not rich then someone is both humble and not patient.
Everyone who is either patient or quiet is happy or wise and vice versa.
Everyone who is not quiet is both wise and not funny.
Everyone who is not patient is not generous.
If susan is creative then lucy is not kind and vice versa.
If someone is not wise then alice is not old and vice versa.
If mary is not old or not generous then someone is both creative and not humble and vice versa.
Everyone who is both kind and rich is not quiet or not calm.
Everyone who is not curious is both not strong and funny and vice versa.
Lucy is brave or not quiet.
Someone is not rich.
Someone is happy.
Someone is either wise or not old.
Someone is not old.
Paul is not curious or humble.
Someone is either wise or not brave. | Alice is curious. | entailment | (![X]:((patient(X)&~old(X))=>(~tall(X)|~patient(X))))&
((?[X]:((wise(X)&brave(X))))=>((happy(mary)<~>generous(mary))))&
(![X]:((kind(X)<~>~kind(X))=>happy(X)))&
((?[X]:(tall(X)))<=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((~rich(X)&~wise(X))))=>((patient(john)&strong(john))))&
((?[X]:((quiet(X)&~calm(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((happy(X)|quiet(X))=>(curious(X)|generous(X))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((humble(X)&~patient(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(happy(X)|wise(X))))&
(![X]:(~quiet(X)=>(wise(X)&~funny(X))))&
(![X]:(~patient(X)=>~generous(X)))&
((creative(susan))<=>(~kind(lucy)))&
((?[X]:(~wise(X)))<=>(~old(alice)))&
(((~old(mary)|~generous(mary)))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((kind(X)&rich(X))=>(~quiet(X)|~calm(X))))&
(![X]:(~curious(X)<=>(~strong(X)&funny(X))))&
((brave(lucy)|~quiet(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:(~old(X)))&
((~curious(paul)|humble(paul)))&
(?[X]:((wise(X)<~>~brave(X)))) | curious(alice) | [
"p2",
"p6",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3777299416881831832551223
% SZS output start Proof for 3777299416881831832551223
3. ! [X0] : ((kind(X0) <~> ~kind(X0)) => happy(X0)) [input p2]
7. ! [X0] : ((quiet(X0) | happy(X0)) => (generous(X0) | curious(X0))) [input p6]
9. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (wise(X0) | happy(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~funny(X0) & wise(X0))) [input p9]
11. ! [X0] : (~patient(X0) => ~generous(X0)) [input p10]
16. ! [X0] : (~curious(X0) <=> (funny(X0) & ~strong(X0))) [input p15]
24. ~curious(alice) [input hypothesis]
30. ! [X0] : (happy(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 3]
32. ! [X0] : ((generous(X0) | curious(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 7]
33. ! [X0] : (generous(X0) | curious(X0) | (~quiet(X0) & ~happy(X0))) [flattening 32]
35. ! [X0] : ((~funny(X0) & wise(X0)) | quiet(X0)) [ennf transformation 10]
36. ! [X0] : (~generous(X0) | patient(X0)) [ennf transformation 11]
40. ! [X0] : (happy(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
54. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 54]
66. ! [X0] : ((~curious(X0) | (~funny(X0) | strong(X0))) & ((funny(X0) & ~strong(X0)) | curious(X0))) [nnf transformation 16]
67. ! [X0] : ((~curious(X0) | ~funny(X0) | strong(X0)) & ((funny(X0) & ~strong(X0)) | curious(X0))) [flattening 66]
83. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
84. happy(X0) | kind(X0) | kind(X0) [cnf transformation 40]
96. generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 33]
106. ~quiet(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 55]
109. ~funny(X0) | quiet(X0) [cnf transformation 35]
110. ~generous(X0) | patient(X0) [cnf transformation 36]
122. funny(X0) | curious(X0) [cnf transformation 67]
133. ~curious(alice) [cnf transformation 24]
134. happy(X0) | ~kind(X0) [duplicate literal removal 83]
135. kind(X0) | happy(X0) [duplicate literal removal 84]
150. happy(X0) [subsumption resolution 134,135]
216. curious(X0) | generous(X0) [subsumption resolution 96,150]
237. ~quiet(X0) | ~patient(X0) [subsumption resolution 106,150]
324. curious(X0) | quiet(X0) [resolution 122,109]
337. generous(alice) [resolution 216,133]
341. patient(alice) [resolution 337,110]
359. quiet(alice) [resolution 324,133]
363. ~patient(alice) [resolution 359,237]
366. $false [subsumption resolution 363,341]
% SZS output end Proof for 3777299416881831832551223
% ------------------------------
% 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 |
Everyone who is not quiet or brave is curious or generous.
Everyone who is both not brave and generous is not rich and vice versa.
If someone is either not quiet or creative then someone is patient and vice versa.
Everyone who is not funny or strong is strong or not generous and vice versa.
If someone is not quiet or curious then lucy is humble or happy.
Everyone who is either humble or curious is not humble.
Everyone who is calm or strong is both strong and not strong.
Everyone who is both brave and not funny is not strong or creative and vice versa.
Everyone who is wise is rich.
Everyone who is either creative or old is patient or not creative and vice versa.
Everyone who is both not strong and not old is either rich or creative and vice versa.
If paul is both not kind and brave then paul is either strong or not patient.
If mary is not happy or not calm then someone is kind.
Everyone who is not rich is both not calm and kind.
If paul is curious then susan is calm or old.
If someone is wise then mary is happy.
Someone is both not wise and humble.
Someone is either old or not kind.
Someone is both not humble and curious.
Someone is not wise or not humble.
Someone is both not happy and not kind. | Mary is not curious. | contradiction | (![X]:((~quiet(X)|brave(X))=>(curious(X)|generous(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~quiet(X)|curious(X))))=>((humble(lucy)|happy(lucy))))&
(![X]:((humble(X)<~>curious(X))=>~humble(X)))&
(![X]:((calm(X)|strong(X))=>(strong(X)&~strong(X))))&
(![X]:((brave(X)&~funny(X))<=>(~strong(X)|creative(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((creative(X)<~>old(X))<=>(patient(X)|~creative(X))))&
(![X]:((~strong(X)&~old(X))<=>(rich(X)<~>creative(X))))&
(((~kind(paul)&brave(paul)))=>((strong(paul)<~>~patient(paul))))&
(((~happy(mary)|~calm(mary)))=>(?[X]:(kind(X))))&
(![X]:(~rich(X)=>(~calm(X)&kind(X))))&
((curious(paul))=>((calm(susan)|old(susan))))&
((?[X]:(wise(X)))=>(happy(mary)))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~happy(X)&~kind(X)))) | ~curious(mary) | [
"p0",
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2960005195526841555234416
% SZS output start Proof for 2960005195526841555234416
1. ! [X0] : ((brave(X0) | ~quiet(X0)) => (generous(X0) | curious(X0))) [input p0]
4. ! [X0] : ((strong(X0) | ~funny(X0)) <=> (~generous(X0) | strong(X0))) [input p3]
7. ! [X0] : ((strong(X0) | calm(X0)) => (~strong(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & brave(X0)) <=> (creative(X0) | ~strong(X0))) [input p7]
22. ~curious(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) | curious(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 1]
29. ! [X0] : (generous(X0) | curious(X0) | (~brave(X0) & quiet(X0))) [flattening 28]
33. ! [X0] : ((~strong(X0) & strong(X0)) | (~strong(X0) & ~calm(X0))) [ennf transformation 7]
47. ! [X0] : (((strong(X0) | ~funny(X0)) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | (~strong(X0) & funny(X0)))) [nnf transformation 4]
48. ! [X0] : ((strong(X0) | ~funny(X0) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | (~strong(X0) & funny(X0)))) [flattening 47]
50. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | funny(X0) | ~brave(X0))) [flattening 50]
69. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 29]
77. ~generous(X0) | strong(X0) | funny(X0) [cnf transformation 48]
88. ~strong(X0) | ~strong(X0) [cnf transformation 33]
90. brave(X0) | strong(X0) [cnf transformation 51]
92. ~funny(X0) | strong(X0) [cnf transformation 51]
120. ~curious(mary) [cnf transformation 22]
123. ~strong(X0) [duplicate literal removal 88]
167. ~funny(X0) [subsumption resolution 92,123]
168. brave(X0) [subsumption resolution 90,123]
226. generous(X0) | curious(X0) [resolution 69,168]
229. strong(X0) | funny(X0) | curious(X0) [resolution 77,226]
231. funny(X0) | curious(X0) [subsumption resolution 229,123]
232. curious(X0) [subsumption resolution 231,167]
233. $false [resolution 232,120]
% SZS output end Proof for 2960005195526841555234416
% ------------------------------
% 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 quiet then someone is both not humble and not curious.
Everyone who is both not rich and happy is not calm and vice versa.
If someone is either not curious or humble then mary is not tall or not brave.
Everyone who is both creative and rich is not patient and vice versa.
If lucy is both tall and strong then lucy is not patient or not wise and vice versa.
If mary is not strong or not wise then mary is old or strong and vice versa.
If lucy is not generous or not humble then someone is both kind and creative.
Everyone who is both strong and humble is not humble or kind.
If john is either not rich or not generous then mary is happy and vice versa.
Everyone who is humble is brave and vice versa.
Everyone who is either not kind or not curious is curious and vice versa.
If fred is kind or happy then someone is both curious and generous.
Everyone who is either rich or calm is not calm.
If mary is both kind and tall then someone is not tall or not calm and vice versa.
If someone is not rich then someone is both not strong and not quiet and vice versa.
Everyone who is wise or not funny is tall and vice versa.
Paul is not patient.
Fred is either not strong or funny.
Alice is brave or not quiet.
Someone is either not tall or humble.
John is happy or not strong.
Mary is generous. | Fred is not generous. | neutral | ((?[X]:(~quiet(X)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:((~rich(X)&happy(X))<=>~calm(X)))&
((?[X]:((~curious(X)<~>humble(X))))=>((~tall(mary)|~brave(mary))))&
(![X]:((creative(X)&rich(X))<=>~patient(X)))&
(((tall(lucy)&strong(lucy)))<=>((~patient(lucy)|~wise(lucy))))&
(((~strong(mary)|~wise(mary)))<=>((old(mary)|strong(mary))))&
(((~generous(lucy)|~humble(lucy)))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:((strong(X)&humble(X))=>(~humble(X)|kind(X))))&
(((~rich(john)<~>~generous(john)))<=>(happy(mary)))&
(![X]:(humble(X)<=>brave(X)))&
(![X]:((~kind(X)<~>~curious(X))<=>curious(X)))&
(((kind(fred)|happy(fred)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:((rich(X)<~>calm(X))=>~calm(X)))&
(((kind(mary)&tall(mary)))<=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((wise(X)|~funny(X))<=>tall(X)))&
(~patient(paul))&
((~strong(fred)<~>funny(fred)))&
((brave(alice)|~quiet(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
((happy(john)|~strong(john)))&
(generous(mary)) | ~generous(fred) | [] | null | 0 |
Everyone who is kind or not calm is curious or not wise. If alice is not patient or wise then fred is either not happy or not generous and vice versa. Everyone who is either brave or not creative is both not quiet and quiet. Everyone who is both not kind and strong is not brave or not rich. If someone is funny or not humble then someone is not strong or not tall. If someone is old or humble then susan is not creative. Everyone who is both old and strong is not creative or creative. If someone is both not brave and curious then someone is either not happy or creative and vice versa. Everyone who is both funny and kind is not strong. Everyone who is tall or calm is both not calm and creative and vice versa. If john is not kind or not patient then lucy is both humble and creative and vice versa. Everyone who is happy or not funny is both not strong and not happy and vice versa. Everyone who is both brave and not generous is both curious and quiet and vice versa. If someone is both not curious and not wise then paul is wise or patient. If alice is rich then someone is either funny or brave and vice versa. If someone is patient or not funny then someone is not humble or not happy. Fred is both not quiet and not generous. John is either not old or strong. Alice is either not calm or kind. Someone is not brave. Susan is not happy or patient. Someone is either creative or not quiet. Paul is either not curious or not generous. | Susan is not calm. | entailment | (![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
(![X]:((brave(X)<~>~creative(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~kind(X)&strong(X))=>(~brave(X)|~rich(X))))&
((?[X]:((funny(X)|~humble(X))))=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:((old(X)|humble(X))))=>(~creative(susan)))&
(![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
((~quiet(fred)&~generous(fred)))&
((~old(john)<~>strong(john)))&
((~calm(alice)<~>kind(alice)))&
(?[X]:(~brave(X)))&
((~happy(susan)|patient(susan)))&
(?[X]:((creative(X)<~>~quiet(X))))&
((~curious(paul)<~>~generous(paul))) | ~calm(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5353008881850717960651603
% SZS output start Proof for 5353008881850717960651603
10. ! [X0] : ((calm(X0) | tall(X0)) <=> (creative(X0) & ~calm(X0))) [input p9]
24. calm(susan) [input hypothesis]
53. ! [X0] : (((calm(X0) | tall(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [nnf transformation 10]
54. ! [X0] : ((calm(X0) | tall(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [flattening 53]
102. ~calm(X0) | ~calm(X0) [cnf transformation 54]
139. calm(susan) [cnf transformation 24]
142. ~calm(X0) [duplicate literal removal 102]
314. $false [subsumption resolution 139,142]
% SZS output end Proof for 5353008881850717960651603
% ------------------------------
% 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 funny and not humble is tall or rich.
Everyone who is either not humble or brave is generous and vice versa.
Everyone who is either not kind or kind is brave or wise and vice versa.
Everyone who is both not funny and not strong is calm and vice versa.
If someone is not funny then susan is either not brave or curious and vice versa.
If susan is not generous then someone is both patient and humble and vice versa.
If someone is old or strong then mary is funny and vice versa.
If john is not happy then susan is either curious or not brave.
Everyone who is quiet is both wise and not humble.
Everyone who is either not rich or rich is both not happy and not creative.
If someone is not tall or humble then someone is funny or not calm and vice versa.
Everyone who is both funny and creative is both not humble and brave and vice versa.
Everyone who is not brave is either funny or humble.
If paul is both not happy and not wise then fred is kind and vice versa.
Everyone who is both not curious and old is either not calm or humble and vice versa.
Everyone who is either generous or old is happy or not happy and vice versa.
Someone is either not kind or not curious.
Someone is either humble or not calm.
Alice is wise or not tall.
Someone is both not brave and patient.
Lucy is not kind. | Mary is quiet. | contradiction | (![X]:((~funny(X)&~humble(X))=>(tall(X)|rich(X))))&
(![X]:((~humble(X)<~>brave(X))<=>generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(brave(X)|wise(X))))&
(![X]:((~funny(X)&~strong(X))<=>calm(X)))&
((?[X]:(~funny(X)))<=>((~brave(susan)<~>curious(susan))))&
((~generous(susan))<=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:((old(X)|strong(X))))<=>(funny(mary)))&
((~happy(john))=>((curious(susan)<~>~brave(susan))))&
(![X]:(quiet(X)=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((wise(alice)|~tall(alice)))&
(?[X]:((~brave(X)&patient(X))))&
(~kind(lucy)) | quiet(mary) | [
"p1",
"p3",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 17184502758847810468365
% SZS output start Proof for 17184502758847810468365
2. ! [X0] : ((~humble(X0) <~> brave(X0)) <=> generous(X0)) [input p1]
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
9. ! [X0] : (quiet(X0) => (~humble(X0) & wise(X0))) [input p8]
10. ! [X0] : ((~rich(X0) <~> rich(X0)) => (~creative(X0) & ~happy(X0))) [input p9]
12. ! [X0] : ((creative(X0) & funny(X0)) <=> (brave(X0) & ~humble(X0))) [input p11]
13. ! [X0] : (~brave(X0) => (funny(X0) <~> humble(X0))) [input p12]
15. ! [X0] : ((old(X0) & ~curious(X0)) <=> (~calm(X0) <~> humble(X0))) [input p14]
16. ! [X0] : ((generous(X0) <~> old(X0)) <=> (~happy(X0) | happy(X0))) [input p15]
22. quiet(mary) [input hypothesis]
27. ! [X0] : ((~humble(X0) & wise(X0)) | ~quiet(X0)) [ennf transformation 9]
28. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~rich(X0) <=> rich(X0))) [ennf transformation 10]
29. ! [X0] : ((funny(X0) <~> humble(X0)) | brave(X0)) [ennf transformation 13]
30. ! [X0] : ((((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | ~generous(X0)) & (generous(X0) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0))))) [nnf transformation 2]
33. ! [X0] : (((~strong(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (strong(X0) | funny(X0)))) [nnf transformation 4]
34. ! [X0] : (((~strong(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | strong(X0) | funny(X0))) [flattening 33]
48. ! [X0] : ((~creative(X0) & ~happy(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 28]
54. ! [X0] : (((creative(X0) & funny(X0)) | (~brave(X0) | humble(X0))) & ((brave(X0) & ~humble(X0)) | (~creative(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((creative(X0) & funny(X0)) | ~brave(X0) | humble(X0)) & ((brave(X0) & ~humble(X0)) | ~creative(X0) | ~funny(X0))) [flattening 54]
56. ! [X0] : (((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | brave(X0)) [nnf transformation 29]
59. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~old(X0) | curious(X0)))) [nnf transformation 15]
60. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | ~old(X0) | curious(X0))) [flattening 59]
61. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 61]
72. generous(X0) | brave(X0) | humble(X0) [cnf transformation 30]
83. ~calm(X0) | ~funny(X0) [cnf transformation 34]
98. ~quiet(X0) | ~humble(X0) [cnf transformation 27]
99. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 48]
100. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
101. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 48]
102. ~creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
110. creative(X0) | ~brave(X0) | humble(X0) [cnf transformation 55]
111. humble(X0) | funny(X0) | brave(X0) [cnf transformation 56]
120. old(X0) | humble(X0) | calm(X0) [cnf transformation 60]
127. ~old(X0) | ~generous(X0) | happy(X0) [cnf transformation 62]
136. quiet(mary) [cnf transformation 22]
137. ~happy(X0) | rich(X0) [duplicate literal removal 99]
138. ~happy(X0) | ~rich(X0) [duplicate literal removal 100]
139. ~creative(X0) | rich(X0) [duplicate literal removal 101]
140. ~creative(X0) | ~rich(X0) [duplicate literal removal 102]
208. ~creative(X0) [subsumption resolution 139,140]
209. ~happy(X0) [subsumption resolution 137,138]
240. ~brave(X0) | humble(X0) [subsumption resolution 110,208]
241. humble(X0) | funny(X0) [subsumption resolution 111,240]
253. ~old(X0) | ~generous(X0) [subsumption resolution 127,209]
285. ~humble(mary) [resolution 98,136]
354. ~generous(X0) | calm(X0) | humble(X0) [resolution 120,253]
360. calm(X0) | humble(X0) | brave(X0) | humble(X0) [resolution 354,72]
362. calm(X0) | humble(X0) | brave(X0) [duplicate literal removal 360]
364. calm(X0) | humble(X0) [subsumption resolution 362,240]
435. humble(X2) | ~funny(X2) [resolution 364,83]
438. humble(X2) [subsumption resolution 435,241]
445. $false [resolution 438,285]
% SZS output end Proof for 17184502758847810468365
% ------------------------------
% 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 not curious or old is not funny and vice versa. Everyone who is either not patient or curious is calm or kind. Everyone who is not strong or not curious is happy or calm and vice versa. Everyone who is not tall or tall is either rich or not wise. Everyone who is not funny is both not happy and not generous. If someone is both not happy and not wise then fred is either rich or kind. If someone is either patient or not rich then someone is not generous or not curious. Everyone who is either not brave or creative is both not creative and not patient and vice versa. If susan is brave or not brave then lucy is old and vice versa. If fred is either not patient or not curious then someone is kind and vice versa. Everyone who is either not quiet or not brave is kind or not old. Everyone who is both quiet and not strong is not happy or not old and vice versa. Everyone who is both not curious and quiet is calm or not tall. Everyone who is not happy or not quiet is kind or not calm. Everyone who is not rich is either not old or calm. If someone is both quiet and not old then someone is quiet and vice versa. Lucy is not happy. Alice is not funny or not calm. John is not happy. Susan is either old or strong. Someone is not patient. Lucy is not old or calm. Alice is either not rich or not curious. Someone is both not patient and calm. | Lucy is kind. | entailment | (![X]:((~curious(X)|old(X))<=>~funny(X)))&
(![X]:((~patient(X)<~>curious(X))=>(calm(X)|kind(X))))&
(![X]:((~strong(X)|~curious(X))<=>(happy(X)|calm(X))))&
(![X]:((~tall(X)|tall(X))=>(rich(X)<~>~wise(X))))&
(![X]:(~funny(X)=>(~happy(X)&~generous(X))))&
((?[X]:((~happy(X)&~wise(X))))=>((rich(fred)<~>kind(fred))))&
((?[X]:((patient(X)<~>~rich(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:((~brave(X)<~>creative(X))<=>(~creative(X)&~patient(X))))&
(((brave(susan)|~brave(susan)))<=>(old(lucy)))&
(((~patient(fred)<~>~curious(fred)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~brave(X))=>(kind(X)|~old(X))))&
(![X]:((quiet(X)&~strong(X))<=>(~happy(X)|~old(X))))&
(![X]:((~curious(X)&quiet(X))=>(calm(X)|~tall(X))))&
(![X]:((~happy(X)|~quiet(X))=>(kind(X)|~calm(X))))&
(![X]:(~rich(X)=>(~old(X)<~>calm(X))))&
((?[X]:((quiet(X)&~old(X))))<=>(?[X]:(quiet(X))))&
(~happy(lucy))&
((~funny(alice)|~calm(alice)))&
(~happy(john))&
((old(susan)<~>strong(susan)))&
(?[X]:(~patient(X)))&
((~old(lucy)|calm(lucy)))&
((~rich(alice)<~>~curious(alice)))&
(?[X]:((~patient(X)&calm(X)))) | kind(lucy) | [
"p8",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5417598736965384211683889
% SZS output start Proof for 5417598736965384211683889
9. (~brave(susan) | brave(susan)) <=> old(lucy) [input p8]
14. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~calm(X0) | kind(X0))) [input p13]
17. ~happy(lucy) [input p16]
22. calm(lucy) | ~old(lucy) [input p21]
25. ~kind(lucy) [input hypothesis]
39. ! [X0] : ((~calm(X0) | kind(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 14]
40. ! [X0] : (~calm(X0) | kind(X0) | (quiet(X0) & happy(X0))) [flattening 39]
51. ((~brave(susan) | brave(susan)) | ~old(lucy)) & (old(lucy) | (brave(susan) & ~brave(susan))) [nnf transformation 9]
52. (~brave(susan) | brave(susan) | ~old(lucy)) & (old(lucy) | (brave(susan) & ~brave(susan))) [flattening 51]
94. old(lucy) | ~brave(susan) [cnf transformation 52]
95. old(lucy) | brave(susan) [cnf transformation 52]
109. ~calm(X0) | kind(X0) | happy(X0) [cnf transformation 40]
116. ~happy(lucy) [cnf transformation 17]
122. calm(lucy) | ~old(lucy) [cnf transformation 22]
127. ~kind(lucy) [cnf transformation 25]
146. 4 <=> brave(susan) [avatar definition]
150. 5 <=> old(lucy) [avatar definition]
153. 4 | 5 [avatar split clause 95,150,146]
154. ~4 | 5 [avatar split clause 94,150,146]
208. 17 <=> calm(lucy) [avatar definition]
210. calm(lucy) <- (17) [avatar component clause 208]
211. ~5 | 17 [avatar split clause 122,208,150]
270. kind(lucy) | happy(lucy) <- (17) [resolution 109,210]
275. happy(lucy) <- (17) [subsumption resolution 270,127]
276. $false <- (17) [subsumption resolution 275,116]
277. ~17 [avatar contradiction clause 276]
283. $false [avatar sat refutation 153,154,211,277]
% SZS output end Proof for 5417598736965384211683889
% ------------------------------
% 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 |
Everyone who is both curious and not rich is not creative or not tall.
Everyone who is not humble or not wise is old.
If alice is both funny and not curious then fred is both quiet and wise and vice versa.
Everyone who is not generous is both creative and not humble.
Everyone who is both generous and not old is both calm and kind.
Everyone who is not quiet or not generous is either happy or generous.
If susan is both kind and creative then fred is both happy and not curious and vice versa.
If someone is happy then someone is either happy or not curious.
If lucy is funny or patient then susan is not tall.
If mary is curious then mary is both generous and patient and vice versa.
Everyone who is both kind and happy is either strong or quiet and vice versa.
Everyone who is both curious and not calm is both wise and not kind and vice versa.
If mary is calm or not happy then lucy is either not funny or happy.
If fred is both humble and not kind then someone is not quiet.
Everyone who is not rich is not patient or generous and vice versa.
Everyone who is either calm or not happy is not creative or rich.
Lucy is not rich or not wise.
John is either tall or calm.
Someone is either not quiet or tall.
Someone is not patient.
Mary is both not humble and old.
Lucy is either not kind or strong.
Susan is not strong or not tall.
Lucy is both quiet and not old. | Lucy is patient. | neutral | (![X]:((curious(X)&~rich(X))=>(~creative(X)|~tall(X))))&
(![X]:((~humble(X)|~wise(X))=>old(X)))&
(((funny(alice)&~curious(alice)))<=>((quiet(fred)&wise(fred))))&
(![X]:(~generous(X)=>(creative(X)&~humble(X))))&
(![X]:((generous(X)&~old(X))=>(calm(X)&kind(X))))&
(![X]:((~quiet(X)|~generous(X))=>(happy(X)<~>generous(X))))&
(((kind(susan)&creative(susan)))<=>((happy(fred)&~curious(fred))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((funny(lucy)|patient(lucy)))=>(~tall(susan)))&
((curious(mary))<=>((generous(mary)&patient(mary))))&
(![X]:((kind(X)&happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((curious(X)&~calm(X))<=>(wise(X)&~kind(X))))&
(((calm(mary)|~happy(mary)))=>((~funny(lucy)<~>happy(lucy))))&
(((humble(fred)&~kind(fred)))=>(?[X]:(~quiet(X))))&
(![X]:(~rich(X)<=>(~patient(X)|generous(X))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)|rich(X))))&
((~rich(lucy)|~wise(lucy)))&
((tall(john)<~>calm(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~humble(mary)&old(mary)))&
((~kind(lucy)<~>strong(lucy)))&
((~strong(susan)|~tall(susan)))&
((quiet(lucy)&~old(lucy))) | patient(lucy) | [] | null | 0 |
If alice is both brave and quiet then mary is not patient and vice versa.
If someone is not old then someone is strong and vice versa.
Everyone who is not funny or not wise is happy and vice versa.
Everyone who is not creative or old is either humble or not brave.
Everyone who is either not brave or not creative is either not humble or not wise.
If someone is not kind or creative then someone is both not rich and not patient.
Everyone who is either funny or happy is quiet or not strong.
Everyone who is either creative or not humble is not tall or not rich and vice versa.
Everyone who is not kind is humble.
If someone is creative or humble then mary is quiet.
If mary is not wise then mary is either not humble or old and vice versa.
If fred is both not happy and not kind then someone is either not wise or not humble and vice versa.
Everyone who is both not tall and kind is either not strong or patient and vice versa.
Everyone who is brave is either not rich or not kind.
If someone is both not rich and wise then mary is kind and vice versa.
If someone is not happy or tall then someone is both not rich and not happy.
Fred is not curious or not quiet.
Someone is both old and quiet.
Someone is either patient or not quiet.
Someone is not old or not wise.
Someone is not strong or not wise.
John is both humble and curious.
Mary is rich.
Someone is both funny and not creative. | Fred is not happy. | neutral | (((brave(alice)&quiet(alice)))<=>(~patient(mary)))&
((?[X]:(~old(X)))<=>(?[X]:(strong(X))))&
(![X]:((~funny(X)|~wise(X))<=>happy(X)))&
(![X]:((~creative(X)|old(X))=>(humble(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((~kind(X)|creative(X))))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((funny(X)<~>happy(X))=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(~tall(X)|~rich(X))))&
(![X]:(~kind(X)=>humble(X)))&
((?[X]:((creative(X)|humble(X))))=>(quiet(mary)))&
((~wise(mary))<=>((~humble(mary)<~>old(mary))))&
(((~happy(fred)&~kind(fred)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~tall(X)&kind(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~kind(X))))&
((?[X]:((~rich(X)&wise(X))))<=>(kind(mary)))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((~rich(X)&~happy(X)))))&
((~curious(fred)|~quiet(fred)))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((~old(X)|~wise(X))))&
(?[X]:((~strong(X)|~wise(X))))&
((humble(john)&curious(john)))&
(rich(mary))&
(?[X]:((funny(X)&~creative(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is both generous and not funny is humble or not kind and vice versa.
Everyone who is funny or calm is both not rich and strong and vice versa.
Everyone who is either generous or not strong is not wise or old and vice versa.
If someone is humble or not rich then susan is both generous and not tall and vice versa.
If paul is not old then someone is not old or tall and vice versa.
Everyone who is either rich or curious is strong or generous.
Everyone who is quiet is either not wise or not creative.
Everyone who is both generous and old is humble or wise.
If someone is both not wise and not brave then someone is either not humble or not quiet.
Everyone who is happy or not happy is both not humble and kind.
Everyone who is both not funny and quiet is curious or strong and vice versa.
If someone is either generous or not quiet then paul is both not generous and not quiet and vice versa.
If someone is both humble and not creative then someone is not old or not humble.
Everyone who is either not humble or not kind is both not wise and not patient and vice versa.
Everyone who is not kind or curious is either humble or not brave and vice versa.
Lucy is curious or humble.
Susan is either not wise or not rich.
Someone is brave or quiet.
Someone is not tall or generous.
Mary is humble or not patient.
Mary is not humble or not old. | Mary is rich. | entailment | (![X]:((generous(X)&~funny(X))<=>(humble(X)|~kind(X))))&
(![X]:((funny(X)|calm(X))<=>(~rich(X)&strong(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(~wise(X)|old(X))))&
((?[X]:((humble(X)|~rich(X))))<=>((generous(susan)&~tall(susan))))&
((~old(paul))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((rich(X)<~>curious(X))=>(strong(X)|generous(X))))&
(![X]:(quiet(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((generous(X)&old(X))=>(humble(X)|wise(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((happy(X)|~happy(X))=>(~humble(X)&kind(X))))&
(![X]:((~funny(X)&quiet(X))<=>(curious(X)|strong(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>((~generous(paul)&~quiet(paul))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~kind(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
((curious(lucy)|humble(lucy)))&
((~wise(susan)<~>~rich(susan)))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:((~tall(X)|generous(X))))&
((humble(mary)|~patient(mary)))&
((~humble(mary)|~old(mary))) | rich(mary) | [
"p0",
"p1",
"p3",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4363092738115849791127494
% SZS output start Proof for 4363092738115849791127494
1. ! [X0] : ((~funny(X0) & generous(X0)) <=> (~kind(X0) | humble(X0))) [input p0]
2. ! [X0] : ((calm(X0) | funny(X0)) <=> (strong(X0) & ~rich(X0))) [input p1]
4. ? [X0] : (~rich(X0) | humble(X0)) <=> (~tall(susan) & generous(susan)) [input p3]
10. ! [X0] : ((~happy(X0) | happy(X0)) => (kind(X0) & ~humble(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (strong(X0) | curious(X0))) [input p10]
22. ~rich(mary) [input hypothesis]
31. ! [X0] : ((kind(X0) & ~humble(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 10]
33. ! [X0] : (((~funny(X0) & generous(X0)) | (kind(X0) & ~humble(X0))) & ((~kind(X0) | humble(X0)) | (funny(X0) | ~generous(X0)))) [nnf transformation 1]
34. ! [X0] : (((~funny(X0) & generous(X0)) | (kind(X0) & ~humble(X0))) & (~kind(X0) | humble(X0) | funny(X0) | ~generous(X0))) [flattening 33]
35. ! [X0] : (((calm(X0) | funny(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : ((calm(X0) | funny(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [flattening 35]
39. (? [X0] : (~rich(X0) | humble(X0)) | (tall(susan) | ~generous(susan))) & ((~tall(susan) & generous(susan)) | ! [X0] : (rich(X0) & ~humble(X0))) [nnf transformation 4]
40. (? [X0] : (~rich(X0) | humble(X0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X0] : (rich(X0) & ~humble(X0))) [flattening 39]
41. (? [X0] : (~rich(X0) | humble(X0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X1] : (rich(X1) & ~humble(X1))) [rectify 40]
42. ? [X0] : (~rich(X0) | humble(X0)) => (~rich(sK0) | humble(sK0)) [choice axiom]
43. ((~rich(sK0) | humble(sK0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X1] : (rich(X1) & ~humble(X1))) [skolemisation 41,42]
54. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~strong(X0) & ~curious(X0))) & ((strong(X0) | curious(X0)) | (~quiet(X0) | funny(X0)))) [nnf transformation 11]
55. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~strong(X0) & ~curious(X0))) & (strong(X0) | curious(X0) | ~quiet(X0) | funny(X0))) [flattening 54]
73. ~kind(X0) | humble(X0) | funny(X0) | ~generous(X0) [cnf transformation 34]
80. ~funny(X0) | strong(X0) [cnf transformation 36]
90. generous(susan) | rich(X1) [cnf transformation 43]
104. ~humble(X0) | ~happy(X0) [cnf transformation 31]
105. ~humble(X0) | happy(X0) [cnf transformation 31]
106. kind(X0) | ~happy(X0) [cnf transformation 31]
107. happy(X0) | kind(X0) [cnf transformation 31]
110. ~funny(X0) | ~strong(X0) [cnf transformation 55]
139. ~rich(mary) [cnf transformation 22]
141. 1 <=> generous(susan) [avatar definition]
142. generous(susan) <- (1) [avatar component clause 141]
158. 5 <=> ! [X1] : rich(X1) [avatar definition]
159. rich(X1) <- (5) [avatar component clause 158]
162. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
163. ~humble(X1) <- (6) [avatar component clause 162]
165. 5 | 1 [avatar split clause 90,141,158]
201. kind(X0) [subsumption resolution 106,107]
202. ~humble(X0) [subsumption resolution 104,105]
203. 6 [avatar split clause 202,162]
204. ~funny(X0) [subsumption resolution 110,80]
297. $false <- (5) [resolution 159,139]
298. ~5 [avatar contradiction clause 297]
384. humble(X1) | funny(X1) | ~generous(X1) [resolution 73,201]
385. funny(X1) | ~generous(X1) <- (6) [subsumption resolution 384,163]
386. ~generous(X1) <- (6) [subsumption resolution 385,204]
394. $false <- (1, 6) [resolution 386,142]
395. ~1 | ~6 [avatar contradiction clause 394]
396. $false [avatar sat refutation 165,203,298,395]
% SZS output end Proof for 4363092738115849791127494
% ------------------------------
% 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not creative or not generous then someone is not brave and vice versa. If paul is not old or old then someone is strong and vice versa. If someone is either not creative or creative then alice is either rich or kind and vice versa. Everyone who is both not rich and not happy is strong. If fred is kind or patient then susan is both wise and not generous. Everyone who is tall is both not rich and not humble. Everyone who is both not humble and strong is not wise or creative. If lucy is both kind and not tall then john is curious and vice versa. If fred is quiet then someone is either curious or wise. Everyone who is both not brave and not happy is creative or quiet. If someone is both not tall and not wise then someone is not humble or creative and vice versa. Everyone who is both kind and not curious is not old or rich and vice versa. Everyone who is both strong and not tall is not calm. Everyone who is both not humble and not quiet is not kind. If mary is either happy or not calm then someone is either brave or not rich. Everyone who is humble is curious or not strong and vice versa. Someone is not funny. Lucy is both curious and not calm. Someone is either generous or tall. Someone is both funny and not generous. Someone is not tall or patient. Someone is either funny or not wise. Paul is both old and calm. Someone is rich. | Paul is not generous. | neutral | (((~creative(susan)|~generous(susan)))<=>(?[X]:(~brave(X))))&
(((~old(paul)|old(paul)))<=>(?[X]:(strong(X))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
(![X]:((~humble(X)&~quiet(X))=>~kind(X)))&
(((happy(mary)<~>~calm(mary)))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(humble(X)<=>(curious(X)|~strong(X))))&
(?[X]:(~funny(X)))&
((curious(lucy)&~calm(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X))) | ~generous(paul) | [] | null | 0 |
Everyone who is not happy or creative is either brave or not kind and vice versa. Everyone who is old or not creative is either curious or quiet. Everyone who is either not humble or not tall is both not curious and not brave and vice versa. Everyone who is either not curious or not strong is not rich or old. Everyone who is either not wise or wise is either not humble or brave. If mary is either generous or calm then paul is not calm. Everyone who is not creative is either generous or happy. Everyone who is either funny or humble is both not happy and not rich and vice versa. If someone is either tall or old then someone is either happy or not happy and vice versa. Everyone who is curious or generous is not kind. If john is either wise or generous then someone is funny. Everyone who is not kind or not humble is either not happy or not brave. Everyone who is either not funny or not patient is both not quiet and happy and vice versa. Everyone who is either calm or not creative is either not generous or not wise and vice versa. Everyone who is either funny or not tall is either strong or kind and vice versa. Everyone who is either brave or not quiet is rich. Lucy is both humble and patient. Susan is calm. Someone is both generous and not rich. Lucy is either not patient or funny. Fred is either funny or not brave. Susan is either rich or not strong. | Lucy is quiet. | neutral | (![X]:((~happy(X)|creative(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((old(X)|~creative(X))=>(curious(X)<~>quiet(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>(~curious(X)&~brave(X))))&
(![X]:((~curious(X)<~>~strong(X))=>(~rich(X)|old(X))))&
(![X]:((~wise(X)<~>wise(X))=>(~humble(X)<~>brave(X))))&
(((generous(mary)<~>calm(mary)))=>(~calm(paul)))&
(![X]:(~creative(X)=>(generous(X)<~>happy(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((curious(X)|generous(X))=>~kind(X)))&
(((wise(john)<~>generous(john)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~quiet(X)&happy(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(strong(X)<~>kind(X))))&
(![X]:((brave(X)<~>~quiet(X))=>rich(X)))&
((humble(lucy)&patient(lucy)))&
(calm(susan))&
(?[X]:((generous(X)&~rich(X))))&
((~patient(lucy)<~>funny(lucy)))&
((funny(fred)<~>~brave(fred)))&
((rich(susan)<~>~strong(susan))) | quiet(lucy) | [] | null | 0 |
If someone is humble or not happy then someone is both not quiet and kind and vice versa.
Everyone who is either creative or not brave is not brave and vice versa.
If someone is both not strong and calm then someone is either kind or humble.
If someone is strong then lucy is both funny and happy.
Everyone who is either not tall or not rich is not brave.
If someone is either wise or curious then someone is either not calm or not patient and vice versa.
Everyone who is old or not generous is old and vice versa.
If susan is both not happy and not quiet then susan is both brave and calm.
Everyone who is either not patient or not rich is either not brave or not happy.
Everyone who is wise is either curious or rich and vice versa.
Everyone who is not old is old or not wise and vice versa.
Everyone who is both funny and calm is both patient and not old and vice versa.
Everyone who is either funny or humble is either old or quiet.
If susan is either happy or not rich then john is patient or humble.
Everyone who is not generous or calm is both not creative and not happy.
Everyone who is either humble or creative is either not strong or not humble and vice versa.
Someone is either not patient or strong.
Someone is either kind or old.
Someone is both not kind and not wise.
Lucy is both not kind and not tall.
Someone is brave or curious. | Lucy is not strong. | entailment | ((?[X]:((humble(X)|~happy(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>~brave(X)))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:((kind(X)<~>humble(X)))))&
((?[X]:(strong(X)))=>((funny(lucy)&happy(lucy))))&
(![X]:((~tall(X)<~>~rich(X))=>~brave(X)))&
((?[X]:((wise(X)<~>curious(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((old(X)|~generous(X))<=>old(X)))&
(((~happy(susan)&~quiet(susan)))=>((brave(susan)&calm(susan))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>~happy(X))))&
(![X]:(wise(X)<=>(curious(X)<~>rich(X))))&
(![X]:(~old(X)<=>(old(X)|~wise(X))))&
(![X]:((funny(X)&calm(X))<=>(patient(X)&~old(X))))&
(![X]:((funny(X)<~>humble(X))=>(old(X)<~>quiet(X))))&
(((happy(susan)<~>~rich(susan)))=>((patient(john)|humble(john))))&
(![X]:((~generous(X)|calm(X))=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~strong(X)<~>~humble(X))))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((kind(X)<~>old(X))))&
(?[X]:((~kind(X)&~wise(X))))&
((~kind(lucy)&~tall(lucy)))&
(?[X]:((brave(X)|curious(X)))) | ~strong(lucy) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3788826104711261494255957
% SZS output start Proof for 3788826104711261494255957
2. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> ~brave(X0)) [input p1]
16. ! [X0] : ((humble(X0) <~> creative(X0)) <=> (~strong(X0) <~> ~humble(X0))) [input p15]
22. strong(lucy) [input hypothesis]
41. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | brave(X0)) & (~brave(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 2]
62. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 16]
78. ~brave(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 41]
81. brave(X0) | ~creative(X0) | brave(X0) [cnf transformation 41]
126. ~humble(X0) | ~strong(X0) | creative(X0) | ~humble(X0) [cnf transformation 62]
131. creative(X0) | humble(X0) | ~strong(X0) | humble(X0) [cnf transformation 62]
143. strong(lucy) [cnf transformation 22]
144. ~humble(X0) | ~strong(X0) | creative(X0) [duplicate literal removal 126]
146. creative(X0) | humble(X0) | ~strong(X0) [duplicate literal removal 131]
150. ~brave(X0) | ~creative(X0) [duplicate literal removal 78]
151. brave(X0) | ~creative(X0) [duplicate literal removal 81]
182. ~creative(X0) [subsumption resolution 150,151]
197. 11 <=> ! [X0] : ~strong(X0) [avatar definition]
198. ~strong(X0) <- (11) [avatar component clause 197]
283. humble(X0) | ~strong(X0) [subsumption resolution 146,182]
284. ~humble(X0) | ~strong(X0) [subsumption resolution 144,182]
285. ~strong(X0) [subsumption resolution 284,283]
286. 11 [avatar split clause 285,197]
308. $false <- (11) [resolution 198,143]
309. ~11 [avatar contradiction clause 308]
310. $false [avatar sat refutation 286,309]
% SZS output end Proof for 3788826104711261494255957
% ------------------------------
% 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 both wise and kind is either rich or old. Everyone who is rich or not strong is quiet or not funny and vice versa. Everyone who is both brave and strong is rich. If paul is curious or not tall then someone is strong. Everyone who is rich or humble is either wise or generous and vice versa. If susan is either patient or not happy then someone is both not tall and not old and vice versa. Everyone who is brave or not old is not strong. If paul is either not creative or old then susan is both not curious and not strong. If paul is either strong or generous then paul is both not creative and patient. If someone is funny then mary is not calm or creative. Everyone who is funny is either rich or not strong and vice versa. Everyone who is not tall is both not humble and old. If someone is not quiet or not rich then someone is patient or tall and vice versa. Everyone who is both quiet and funny is quiet and vice versa. Everyone who is either patient or not happy is wise or not brave. If someone is both strong and curious then susan is not funny. Someone is either not rich or kind. Paul is either creative or kind. Someone is both generous and not rich. Someone is either tall or not brave. Lucy is not funny. Someone is strong. Fred is both not rich and not brave. Paul is either wise or not tall. | Fred is not quiet. | contradiction | (![X]:((wise(X)&kind(X))=>(rich(X)<~>old(X))))&
(![X]:((rich(X)|~strong(X))<=>(quiet(X)|~funny(X))))&
(![X]:((brave(X)&strong(X))=>rich(X)))&
(((curious(paul)|~tall(paul)))=>(?[X]:(strong(X))))&
(![X]:((rich(X)|humble(X))<=>(wise(X)<~>generous(X))))&
(((patient(susan)<~>~happy(susan)))<=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((brave(X)|~old(X))=>~strong(X)))&
(((~creative(paul)<~>old(paul)))=>((~curious(susan)&~strong(susan))))&
(((strong(paul)<~>generous(paul)))=>((~creative(paul)&patient(paul))))&
((?[X]:(funny(X)))=>((~calm(mary)|creative(mary))))&
(![X]:(funny(X)<=>(rich(X)<~>~strong(X))))&
(![X]:(~tall(X)=>(~humble(X)&old(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((quiet(X)&funny(X))<=>quiet(X)))&
(![X]:((patient(X)<~>~happy(X))=>(wise(X)|~brave(X))))&
((?[X]:((strong(X)&curious(X))))=>(~funny(susan)))&
(?[X]:((~rich(X)<~>kind(X))))&
((creative(paul)<~>kind(paul)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
(~funny(lucy))&
(?[X]:(strong(X)))&
((~rich(fred)&~brave(fred)))&
((wise(paul)<~>~tall(paul))) | ~quiet(fred) | [
"p1",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8986308384941571673383974
% SZS output start Proof for 8986308384941571673383974
2. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~funny(X0) | quiet(X0))) [input p1]
11. ! [X0] : (funny(X0) <=> (rich(X0) <~> ~strong(X0))) [input p10]
23. ~brave(fred) & ~rich(fred) [input p22]
25. ~quiet(fred) [input hypothesis]
43. ! [X0] : (((~strong(X0) | rich(X0)) | (funny(X0) & ~quiet(X0))) & ((~funny(X0) | quiet(X0)) | (strong(X0) & ~rich(X0)))) [nnf transformation 2]
44. ! [X0] : ((~strong(X0) | rich(X0) | (funny(X0) & ~quiet(X0))) & (~funny(X0) | quiet(X0) | (strong(X0) & ~rich(X0)))) [flattening 43]
55. ! [X0] : ((funny(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | ~funny(X0))) [nnf transformation 11]
79. ~funny(X0) | quiet(X0) | strong(X0) [cnf transformation 44]
81. ~strong(X0) | rich(X0) | funny(X0) [cnf transformation 44]
104. ~strong(X0) | rich(X0) | ~funny(X0) [cnf transformation 55]
106. funny(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 55]
107. funny(X0) | rich(X0) | strong(X0) [cnf transformation 55]
129. ~rich(fred) [cnf transformation 23]
133. ~quiet(fred) [cnf transformation 25]
198. funny(X0) | rich(X0) [subsumption resolution 107,81]
199. ~strong(X0) | funny(X0) [subsumption resolution 106,81]
200. ~strong(X0) | rich(X0) [subsumption resolution 104,199]
287. quiet(X0) | strong(X0) | rich(X0) [resolution 79,198]
290. quiet(X0) | rich(X0) [subsumption resolution 287,200]
297. rich(fred) [resolution 290,133]
302. $false [subsumption resolution 297,129]
% SZS output end Proof for 8986308384941571673383974
% ------------------------------
% 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 strong or old is both not curious and funny and vice versa. Everyone who is not funny is both not calm and not curious and vice versa. Everyone who is either kind or old is quiet and vice versa. If someone is both quiet and creative then someone is not kind and vice versa. Everyone who is brave or not humble is quiet. Everyone who is either not rich or strong is calm or not generous and vice versa. Everyone who is both not wise and brave is patient or funny and vice versa. If fred is either strong or happy then someone is either not rich or not old and vice versa. Everyone who is not creative or not generous is not brave or wise and vice versa. Everyone who is quiet is both not generous and old. If someone is both quiet and tall then paul is both tall and old and vice versa. Everyone who is either tall or generous is either creative or tall. If john is both not brave and patient then lucy is both curious and patient and vice versa. If susan is both not curious and not strong then alice is both wise and not patient. Everyone who is not funny or calm is either calm or not happy and vice versa. Everyone who is either not kind or humble is funny or not funny and vice versa. Someone is either brave or not humble. Mary is either happy or strong. Someone is not creative. Someone is old. | Alice is happy. | contradiction | (![X]:((strong(X)<~>old(X))<=>(~curious(X)&funny(X))))&
(![X]:(~funny(X)<=>(~calm(X)&~curious(X))))&
(![X]:((kind(X)<~>old(X))<=>quiet(X)))&
((?[X]:((quiet(X)&creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:((brave(X)|~humble(X))=>quiet(X)))&
(![X]:((~rich(X)<~>strong(X))<=>(calm(X)|~generous(X))))&
(![X]:((~wise(X)&brave(X))<=>(patient(X)|funny(X))))&
(((strong(fred)<~>happy(fred)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(![X]:((~creative(X)|~generous(X))<=>(~brave(X)|wise(X))))&
(![X]:(quiet(X)=>(~generous(X)&old(X))))&
((?[X]:((quiet(X)&tall(X))))<=>((tall(paul)&old(paul))))&
(![X]:((tall(X)<~>generous(X))=>(creative(X)<~>tall(X))))&
(((~brave(john)&patient(john)))<=>((curious(lucy)&patient(lucy))))&
(((~curious(susan)&~strong(susan)))=>((wise(alice)&~patient(alice))))&
(![X]:((~funny(X)|calm(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(funny(X)|~funny(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
((happy(mary)<~>strong(mary)))&
(?[X]:(~creative(X)))&
(?[X]:(old(X))) | happy(alice) | [
"p1",
"p4",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 720414407292566365387630
% SZS output start Proof for 720414407292566365387630
2. ! [X0] : (~funny(X0) <=> (~curious(X0) & ~calm(X0))) [input p1]
5. ! [X0] : ((~humble(X0) | brave(X0)) => quiet(X0)) [input p4]
7. ! [X0] : ((brave(X0) & ~wise(X0)) <=> (funny(X0) | patient(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | ~creative(X0)) <=> (wise(X0) | ~brave(X0))) [input p8]
10. ! [X0] : (quiet(X0) => (old(X0) & ~generous(X0))) [input p9]
15. ! [X0] : ((calm(X0) | ~funny(X0)) <=> (calm(X0) <~> ~happy(X0))) [input p14]
21. happy(alice) [input hypothesis]
23. ! [X0] : (quiet(X0) | (humble(X0) & ~brave(X0))) [ennf transformation 5]
24. ! [X0] : ((old(X0) & ~generous(X0)) | ~quiet(X0)) [ennf transformation 10]
30. ! [X0] : ((~funny(X0) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | funny(X0))) [nnf transformation 2]
31. ! [X0] : ((~funny(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | funny(X0))) [flattening 30]
40. ! [X0] : (((brave(X0) & ~wise(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (~brave(X0) | wise(X0)))) [nnf transformation 7]
41. ! [X0] : (((brave(X0) & ~wise(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | ~brave(X0) | wise(X0))) [flattening 40]
46. ! [X0] : (((~generous(X0) | ~creative(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (generous(X0) & creative(X0)))) [nnf transformation 9]
47. ! [X0] : ((~generous(X0) | ~creative(X0) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | (generous(X0) & creative(X0)))) [flattening 46]
56. ! [X0] : (((calm(X0) | ~funny(X0)) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) & (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~calm(X0) & funny(X0)))) [nnf transformation 15]
57. ! [X0] : ((calm(X0) | ~funny(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0)))) & (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (~calm(X0) & funny(X0)))) [flattening 56]
74. ~calm(X0) | funny(X0) [cnf transformation 31]
84. ~brave(X0) | quiet(X0) [cnf transformation 23]
94. ~wise(X0) | ~funny(X0) [cnf transformation 41]
96. ~funny(X0) | brave(X0) [cnf transformation 41]
106. ~brave(X0) | wise(X0) | generous(X0) [cnf transformation 47]
109. ~generous(X0) | ~quiet(X0) [cnf transformation 24]
125. ~happy(X0) | calm(X0) | funny(X0) [cnf transformation 57]
143. happy(alice) [cnf transformation 21]
254. 24 <=> wise(alice) [avatar definition]
256. wise(alice) <- (24) [avatar component clause 254]
258. ~happy(X0) | funny(X0) [subsumption resolution 125,74]
295. funny(alice) [resolution 258,143]
299. brave(alice) [resolution 295,96]
398. quiet(alice) [resolution 299,84]
470. wise(alice) | generous(alice) [resolution 106,299]
475. 53 <=> generous(alice) [avatar definition]
477. generous(alice) <- (53) [avatar component clause 475]
478. 53 | 24 [avatar split clause 470,254,475]
712. ~quiet(alice) <- (53) [resolution 477,109]
719. $false <- (53) [subsumption resolution 712,398]
720. ~53 [avatar contradiction clause 719]
722. ~funny(alice) <- (24) [resolution 256,94]
723. $false <- (24) [subsumption resolution 722,295]
724. ~24 [avatar contradiction clause 723]
725. $false [avatar sat refutation 478,720,724]
% SZS output end Proof for 720414407292566365387630
% ------------------------------
% 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 both not calm and brave is both not rich and not brave and vice versa.
If lucy is not quiet or rich then alice is not rich or not funny.
Everyone who is either not kind or not humble is not brave or creative and vice versa.
If susan is both not wise and calm then someone is either generous or humble and vice versa.
Everyone who is not calm is creative.
Everyone who is brave is either not brave or funny.
Everyone who is either creative or curious is not humble and vice versa.
If someone is not rich or not creative then someone is both kind and happy.
Everyone who is not quiet or not kind is not strong and vice versa.
Everyone who is generous or not curious is both not quiet and creative and vice versa.
Everyone who is either not happy or wise is generous and vice versa.
If lucy is either not rich or not tall then someone is either generous or not funny and vice versa.
Everyone who is either not generous or not creative is both kind and not brave and vice versa.
Everyone who is both not rich and calm is both not wise and happy and vice versa.
If someone is both curious and creative then fred is not patient or not old.
If paul is both strong and not old then someone is patient and vice versa.
Alice is not kind or not wise.
Mary is either not kind or not happy.
Someone is not rich or not patient.
Susan is not calm or rich.
Lucy is brave.
Lucy is either not kind or patient.
John is both not tall and curious. | Fred is curious. | neutral | (![X]:((~calm(X)&brave(X))<=>(~rich(X)&~brave(X))))&
(((~quiet(lucy)|rich(lucy)))=>((~rich(alice)|~funny(alice))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)|creative(X))))&
(((~wise(susan)&calm(susan)))<=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:(~calm(X)=>creative(X)))&
(![X]:(brave(X)=>(~brave(X)<~>funny(X))))&
(![X]:((creative(X)<~>curious(X))<=>~humble(X)))&
((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~curious(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~happy(X)<~>wise(X))<=>generous(X)))&
(((~rich(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))<=>(kind(X)&~brave(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&happy(X))))&
((?[X]:((curious(X)&creative(X))))=>((~patient(fred)|~old(fred))))&
(((strong(paul)&~old(paul)))<=>(?[X]:(patient(X))))&
((~kind(alice)|~wise(alice)))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~rich(X)|~patient(X))))&
((~calm(susan)|rich(susan)))&
(brave(lucy))&
((~kind(lucy)<~>patient(lucy)))&
((~tall(john)&curious(john))) | curious(fred) | [] | null | 0 |
If someone is both not curious and quiet then lucy is brave or not wise.
Everyone who is not calm is either not curious or kind.
Everyone who is patient is both not patient and calm and vice versa.
If alice is not old then someone is quiet and vice versa.
If someone is either curious or not funny then lucy is both generous and creative and vice versa.
If someone is both not rich and not kind then alice is both curious and generous.
If someone is either not generous or tall then someone is not curious or generous and vice versa.
Everyone who is not rich is either quiet or humble.
Everyone who is either funny or patient is not quiet or generous.
Everyone who is both generous and calm is both old and kind and vice versa.
If fred is brave then someone is brave and vice versa.
If mary is humble or not old then someone is not quiet.
Everyone who is both not old and not brave is both not happy and not generous and vice versa.
If john is both rich and not generous then paul is not old.
If someone is not quiet then someone is not funny and vice versa.
If someone is brave then someone is either curious or not curious.
Someone is either not happy or not patient.
Lucy is both brave and old.
Paul is generous or not tall.
Someone is not funny.
Alice is not rich.
Lucy is both generous and not humble.
Someone is both generous and funny.
Someone is either old or creative. | Paul is not patient. | entailment | ((?[X]:((~curious(X)&quiet(X))))=>((brave(lucy)|~wise(lucy))))&
(![X]:(~calm(X)=>(~curious(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&calm(X))))&
((~old(alice))<=>(?[X]:(quiet(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((generous(lucy)&creative(lucy))))&
((?[X]:((~rich(X)&~kind(X))))=>((curious(alice)&generous(alice))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~rich(X)=>(quiet(X)<~>humble(X))))&
(![X]:((funny(X)<~>patient(X))=>(~quiet(X)|generous(X))))&
(![X]:((generous(X)&calm(X))<=>(old(X)&kind(X))))&
((brave(fred))<=>(?[X]:(brave(X))))&
(((humble(mary)|~old(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~old(X)&~brave(X))<=>(~happy(X)&~generous(X))))&
(((rich(john)&~generous(john)))=>(~old(paul)))&
((?[X]:(~quiet(X)))<=>(?[X]:(~funny(X))))&
((?[X]:(brave(X)))=>(?[X]:((curious(X)<~>~curious(X)))))&
(?[X]:((~happy(X)<~>~patient(X))))&
((brave(lucy)&old(lucy)))&
((generous(paul)|~tall(paul)))&
(?[X]:(~funny(X)))&
(~rich(alice))&
((generous(lucy)&~humble(lucy)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((old(X)<~>creative(X)))) | ~patient(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4419366175237845244725920
% SZS output start Proof for 4419366175237845244725920
3. ! [X0] : (patient(X0) <=> (calm(X0) & ~patient(X0))) [input p2]
25. patient(paul) [input hypothesis]
40. ! [X0] : ((patient(X0) | (~calm(X0) | patient(X0))) & ((calm(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 3]
41. ! [X0] : ((patient(X0) | ~calm(X0) | patient(X0)) & ((calm(X0) & ~patient(X0)) | ~patient(X0))) [flattening 40]
89. ~patient(X0) | ~patient(X0) [cnf transformation 41]
142. patient(paul) [cnf transformation 25]
143. ~patient(X0) [duplicate literal removal 89]
311. $false [subsumption resolution 142,143]
% SZS output end Proof for 4419366175237845244725920
% ------------------------------
% 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 both not curious and not rich then someone is either not rich or not humble and vice versa.
Everyone who is either not creative or kind is not patient.
Everyone who is not happy is both not wise and not old.
If fred is humble then someone is either not humble or not tall.
If someone is both not quiet and tall then someone is quiet and vice versa.
Everyone who is not creative is not tall or creative and vice versa.
Everyone who is not quiet or not old is both not quiet and calm.
Everyone who is both calm and not generous is both kind and not rich and vice versa.
Everyone who is either generous or patient is both old and not old.
Everyone who is curious or not funny is not brave or strong.
If lucy is rich or generous then someone is either not old or not humble and vice versa.
Everyone who is not humble or kind is either not curious or brave and vice versa.
Everyone who is not wise is both not humble and kind and vice versa.
If someone is both humble and not quiet then someone is not quiet.
If fred is either generous or not patient then susan is not patient or tall and vice versa.
Someone is strong or happy.
Someone is either curious or not quiet.
Susan is either funny or generous.
Someone is curious or not rich.
John is wise.
Alice is not rich or humble.
Fred is not creative or happy. | Susan is not kind. | contradiction | ((?[X]:((~curious(X)&~rich(X))))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~creative(X)<~>kind(X))=>~patient(X)))&
(![X]:(~happy(X)=>(~wise(X)&~old(X))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(![X]:(~wise(X)<=>(~humble(X)&kind(X))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:(~quiet(X))))&
(((generous(fred)<~>~patient(fred)))<=>((~patient(susan)|tall(susan))))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((funny(susan)<~>generous(susan)))&
(?[X]:((curious(X)|~rich(X))))&
(wise(john))&
((~rich(alice)|humble(alice)))&
((~creative(fred)|happy(fred))) | ~kind(susan) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3390354038434324964613341
% SZS output start Proof for 3390354038434324964613341
5. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : quiet(X0) [input p4]
6. ! [X0] : (~creative(X0) <=> (creative(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~quiet(X0)) => (calm(X0) & ~quiet(X0))) [input p6]
8. ! [X0] : ((~generous(X0) & calm(X0)) <=> (~rich(X0) & kind(X0))) [input p7]
9. ! [X0] : ((generous(X0) <~> patient(X0)) => (~old(X0) & old(X0))) [input p8]
15. (generous(fred) <~> ~patient(fred)) <=> (tall(susan) | ~patient(susan)) [input p14]
23. ~kind(susan) [input hypothesis]
25. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : quiet(X1) [rectify 5]
34. ! [X0] : ((calm(X0) & ~quiet(X0)) | (old(X0) & quiet(X0))) [ennf transformation 7]
35. ! [X0] : ((~old(X0) & old(X0)) | (generous(X0) <=> patient(X0))) [ennf transformation 9]
48. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 25]
49. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 48]
50. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK3) & ~quiet(sK3)) [choice axiom]
51. ? [X2] : quiet(X2) => quiet(sK4) [choice axiom]
52. ((tall(sK3) & ~quiet(sK3)) | ! [X1] : ~quiet(X1)) & (quiet(sK4) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | creative(X0))) [nnf transformation 6]
54. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | creative(X0))) [flattening 53]
55. ! [X0] : (((~generous(X0) & calm(X0)) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | (generous(X0) | ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((~generous(X0) & calm(X0)) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | generous(X0) | ~calm(X0))) [flattening 55]
57. ! [X0] : ((~old(X0) & old(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) [nnf transformation 35]
68. (((patient(fred) | ~generous(fred)) & (~patient(fred) | generous(fred))) | (~tall(susan) & patient(susan))) & ((tall(susan) | ~patient(susan)) | ((generous(fred) | patient(fred)) & (~patient(fred) | ~generous(fred)))) [nnf transformation 15]
69. (((patient(fred) | ~generous(fred)) & (~patient(fred) | generous(fred))) | (~tall(susan) & patient(susan))) & (tall(susan) | ~patient(susan) | ((generous(fred) | patient(fred)) & (~patient(fred) | ~generous(fred)))) [flattening 68]
88. tall(sK3) | ~quiet(X1) [cnf transformation 52]
89. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 54]
91. ~creative(X0) | ~creative(X0) [cnf transformation 54]
94. calm(X0) | quiet(X0) [cnf transformation 34]
96. ~calm(X0) | generous(X0) | kind(X0) [cnf transformation 56]
100. old(X0) | patient(X0) | ~generous(X0) [cnf transformation 57]
101. old(X0) | generous(X0) | ~patient(X0) [cnf transformation 57]
102. ~old(X0) | patient(X0) | ~generous(X0) [cnf transformation 57]
103. ~old(X0) | generous(X0) | ~patient(X0) [cnf transformation 57]
118. tall(susan) | ~patient(susan) | ~patient(fred) | ~generous(fred) [cnf transformation 69]
119. tall(susan) | ~patient(susan) | generous(fred) | patient(fred) [cnf transformation 69]
131. ~kind(susan) [cnf transformation 23]
132. creative(X0) | ~tall(X0) [duplicate literal removal 89]
133. ~creative(X0) [duplicate literal removal 91]
180. 11 <=> ! [X1] : ~quiet(X1) [avatar definition]
181. ~quiet(X1) <- (11) [avatar component clause 180]
183. 12 <=> tall(sK3) [avatar definition]
185. tall(sK3) <- (12) [avatar component clause 183]
186. 11 | 12 [avatar split clause 88,183,180]
200. ~tall(X0) [subsumption resolution 132,133]
201. ~patient(X0) | generous(X0) [subsumption resolution 101,103]
202. ~generous(X0) | patient(X0) [subsumption resolution 100,102]
239. ~patient(susan) | generous(fred) | patient(fred) [subsumption resolution 119,200]
240. ~patient(susan) | generous(fred) [subsumption resolution 239,201]
242. 24 <=> generous(fred) [avatar definition]
246. 25 <=> patient(susan) [avatar definition]
248. ~patient(susan) <- (~25) [avatar component clause 246]
249. 24 | ~25 [avatar split clause 240,246,242]
250. ~patient(susan) | ~patient(fred) | ~generous(fred) [subsumption resolution 118,200]
251. ~patient(susan) | ~generous(fred) [subsumption resolution 250,202]
252. ~24 | ~25 [avatar split clause 251,246,242]
268. 29 <=> generous(susan) [avatar definition]
269. generous(susan) <- (29) [avatar component clause 268]
270. ~generous(susan) <- (~29) [avatar component clause 268]
299. generous(X1) | kind(X1) | quiet(X1) [resolution 96,94]
300. generous(X1) | kind(X1) <- (11) [subsumption resolution 299,181]
302. kind(susan) <- (11, ~29) [resolution 300,270]
304. $false <- (11, ~29) [subsumption resolution 302,131]
305. ~11 | 29 [avatar contradiction clause 304]
306. $false <- (12) [subsumption resolution 185,200]
307. ~12 [avatar contradiction clause 306]
308. patient(susan) <- (29) [resolution 269,202]
309. $false <- (~25, 29) [subsumption resolution 308,248]
310. 25 | ~29 [avatar contradiction clause 309]
311. $false [avatar sat refutation 186,249,252,305,307,310]
% SZS output end Proof for 3390354038434324964613341
% ------------------------------
% 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 curious or not curious then susan is funny or tall and vice versa. Everyone who is strong or not quiet is not quiet. Everyone who is either not old or not quiet is both not rich and wise. Everyone who is strong or not happy is both rich and patient. Everyone who is not kind or not tall is not happy and vice versa. Everyone who is not funny is not old and vice versa. If lucy is both generous and not happy then lucy is rich or patient and vice versa. Everyone who is not strong or not funny is not creative and vice versa. If someone is not curious or calm then mary is patient or not humble. If mary is both not humble and old then lucy is quiet or rich. Everyone who is either quiet or brave is not humble or wise and vice versa. If alice is either generous or rich then john is either tall or rich and vice versa. If someone is strong then someone is not rich. Everyone who is both not old and not tall is happy. If susan is funny or not rich then someone is either quiet or funny. Everyone who is generous or patient is not patient and vice versa. Someone is either not patient or not kind. Mary is either tall or not kind. Someone is either not rich or not kind. Someone is not brave or tall. Someone is not funny or humble. Someone is creative or not old. | Lucy is not humble. | neutral | ((?[X]:((curious(X)|~curious(X))))<=>((funny(susan)|tall(susan))))&
(![X]:((strong(X)|~quiet(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~quiet(X))=>(~rich(X)&wise(X))))&
(![X]:((strong(X)|~happy(X))=>(rich(X)&patient(X))))&
(![X]:((~kind(X)|~tall(X))<=>~happy(X)))&
(![X]:(~funny(X)<=>~old(X)))&
(((generous(lucy)&~happy(lucy)))<=>((rich(lucy)|patient(lucy))))&
(![X]:((~strong(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~curious(X)|calm(X))))=>((patient(mary)|~humble(mary))))&
(((~humble(mary)&old(mary)))=>((quiet(lucy)|rich(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(~humble(X)|wise(X))))&
(((generous(alice)<~>rich(alice)))<=>((tall(john)<~>rich(john))))&
((?[X]:(strong(X)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&~tall(X))=>happy(X)))&
(((funny(susan)|~rich(susan)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((generous(X)|patient(X))<=>~patient(X)))&
(?[X]:((~patient(X)<~>~kind(X))))&
((tall(mary)<~>~kind(mary)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((creative(X)|~old(X)))) | ~humble(lucy) | [] | null | 0 |
If alice is not strong or not curious then someone is either not wise or creative and vice versa.
If lucy is not generous then someone is quiet or rich and vice versa.
If mary is both not happy and not generous then alice is either strong or happy and vice versa.
If someone is either happy or not humble then lucy is brave or not rich.
Everyone who is both not curious and calm is either not generous or not brave and vice versa.
Everyone who is kind is not calm and vice versa.
Everyone who is both happy and calm is both happy and not rich.
Everyone who is both brave and not humble is not brave.
Everyone who is both not rich and kind is not creative or not happy and vice versa.
If someone is either not brave or creative then someone is brave.
Everyone who is funny is quiet or not curious and vice versa.
Everyone who is funny is not creative and vice versa.
If someone is quiet then paul is not curious or kind and vice versa.
Everyone who is not kind or not brave is rich.
If lucy is tall then someone is creative.
Everyone who is either not creative or not old is both funny and creative and vice versa.
Alice is not curious.
Lucy is quiet or not funny.
Fred is both not funny and not calm.
Someone is patient or generous.
Lucy is either not wise or happy.
Alice is both humble and not curious.
Mary is tall.
Paul is not happy or not curious. | Alice is brave. | entailment | (((~strong(alice)|~curious(alice)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
((~generous(lucy))<=>(?[X]:((quiet(X)|rich(X)))))&
(((~happy(mary)&~generous(mary)))<=>((strong(alice)<~>happy(alice))))&
((?[X]:((happy(X)<~>~humble(X))))=>((brave(lucy)|~rich(lucy))))&
(![X]:((~curious(X)&calm(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(![X]:((happy(X)&calm(X))=>(happy(X)&~rich(X))))&
(![X]:((brave(X)&~humble(X))=>~brave(X)))&
(![X]:((~rich(X)&kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((?[X]:(quiet(X)))<=>((~curious(paul)|kind(paul))))&
(![X]:((~kind(X)|~brave(X))=>rich(X)))&
((tall(lucy))=>(?[X]:(creative(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(funny(X)&creative(X))))&
(~curious(alice))&
((quiet(lucy)|~funny(lucy)))&
((~funny(fred)&~calm(fred)))&
(?[X]:((patient(X)|generous(X))))&
((~wise(lucy)<~>happy(lucy)))&
((humble(alice)&~curious(alice)))&
(tall(mary))&
((~happy(paul)|~curious(paul))) | brave(alice) | [
"p8",
"p10",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2003162009654294952724410
% SZS output start Proof for 2003162009654294952724410
9. ! [X0] : ((kind(X0) & ~rich(X0)) <=> (~happy(X0) | ~creative(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p10]
12. ! [X0] : (funny(X0) <=> ~creative(X0)) [input p11]
14. ! [X0] : ((~brave(X0) | ~kind(X0)) => rich(X0)) [input p13]
22. ~curious(alice) & humble(alice) [input p21]
25. ~brave(alice) [input hypothesis]
35. ! [X0] : (rich(X0) | (brave(X0) & kind(X0))) [ennf transformation 14]
52. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~kind(X0) | rich(X0)))) [nnf transformation 9]
53. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~kind(X0) | rich(X0))) [flattening 52]
58. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 11]
59. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))) [nnf transformation 12]
100. ~rich(X0) | creative(X0) [cnf transformation 53]
108. funny(X0) | curious(X0) [cnf transformation 59]
109. ~funny(X0) | ~creative(X0) [cnf transformation 60]
115. brave(X0) | rich(X0) [cnf transformation 35]
130. ~curious(alice) [cnf transformation 22]
133. ~brave(alice) [cnf transformation 25]
145. 3 <=> curious(alice) [avatar definition]
147. ~curious(alice) <- (~3) [avatar component clause 145]
277. ~3 [avatar split clause 130,145]
292. ~creative(X0) | curious(X0) [resolution 109,108]
300. rich(alice) [resolution 115,133]
306. creative(alice) [resolution 300,100]
350. curious(alice) [resolution 292,306]
354. $false <- (~3) [subsumption resolution 350,147]
355. 3 [avatar contradiction clause 354]
358. $false [avatar sat refutation 277,355]
% SZS output end Proof for 2003162009654294952724410
% ------------------------------
% 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 curious or quiet then alice is both brave and curious.
If someone is either not calm or not quiet then someone is not strong.
If lucy is not brave then alice is strong or tall and vice versa.
Everyone who is both brave and patient is either not strong or wise and vice versa.
Everyone who is both brave and not old is not rich or not old and vice versa.
Everyone who is both not curious and not strong is patient and vice versa.
Everyone who is generous or wise is both strong and not quiet.
Everyone who is tall is both rich and not humble and vice versa.
If someone is not funny or not tall then someone is either not creative or funny and vice versa.
If someone is calm or patient then lucy is strong or kind.
If someone is both creative and not curious then mary is either not calm or old.
Everyone who is either not brave or not tall is not old and vice versa.
If mary is not calm then john is either not patient or curious and vice versa.
Everyone who is not rich or old is not calm and vice versa.
If someone is calm or not brave then lucy is curious or wise.
John is either happy or quiet.
Mary is not tall or quiet.
Someone is not happy or not wise.
Someone is strong or rich.
Paul is both creative and kind.
Someone is both generous and rich. | Lucy is brave. | contradiction | ((?[X]:((~curious(X)|quiet(X))))=>((brave(alice)&curious(alice))))&
((?[X]:((~calm(X)<~>~quiet(X))))=>(?[X]:(~strong(X))))&
((~brave(lucy))<=>((strong(alice)|tall(alice))))&
(![X]:((brave(X)&patient(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((brave(X)&~old(X))<=>(~rich(X)|~old(X))))&
(![X]:((~curious(X)&~strong(X))<=>patient(X)))&
(![X]:((generous(X)|wise(X))=>(strong(X)&~quiet(X))))&
(![X]:(tall(X)<=>(rich(X)&~humble(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((calm(X)|patient(X))))=>((strong(lucy)|kind(lucy))))&
((?[X]:((creative(X)&~curious(X))))=>((~calm(mary)<~>old(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>~old(X)))&
((~calm(mary))<=>((~patient(john)<~>curious(john))))&
(![X]:((~rich(X)|old(X))<=>~calm(X)))&
((?[X]:((calm(X)|~brave(X))))=>((curious(lucy)|wise(lucy))))&
((happy(john)<~>quiet(john)))&
((~tall(mary)|quiet(mary)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((strong(X)|rich(X))))&
((creative(paul)&kind(paul)))&
(?[X]:((generous(X)&rich(X)))) | brave(lucy) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2960168446749259123428872
% SZS output start Proof for 2960168446749259123428872
1. ? [X0] : (quiet(X0) | ~curious(X0)) => (curious(alice) & brave(alice)) [input p0]
3. ~brave(lucy) <=> (tall(alice) | strong(alice)) [input p2]
4. ! [X0] : ((patient(X0) & brave(X0)) <=> (~strong(X0) <~> wise(X0))) [input p3]
6. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((wise(X0) | generous(X0)) => (~quiet(X0) & strong(X0))) [input p6]
22. brave(lucy) [input hypothesis]
27. (curious(alice) & brave(alice)) | ! [X0] : (~quiet(X0) & curious(X0)) [ennf transformation 1]
29. ! [X0] : ((~quiet(X0) & strong(X0)) | (~wise(X0) & ~generous(X0))) [ennf transformation 7]
37. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & ((tall(alice) | strong(alice)) | brave(lucy)) [nnf transformation 3]
38. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & (tall(alice) | strong(alice) | brave(lucy)) [flattening 37]
39. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (~patient(X0) | ~brave(X0)))) [nnf transformation 4]
40. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (strong(X0) | curious(X0)))) [nnf transformation 6]
44. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | strong(X0) | curious(X0))) [flattening 43]
66. curious(alice) | curious(X0) [cnf transformation 27]
71. ~brave(lucy) | ~strong(alice) [cnf transformation 38]
77. wise(X0) | patient(X0) | strong(X0) [cnf transformation 40]
85. ~patient(X0) | ~curious(X0) [cnf transformation 44]
88. ~wise(X0) | strong(X0) [cnf transformation 29]
123. brave(lucy) [cnf transformation 22]
128. 2 <=> curious(alice) [avatar definition]
129. ~curious(alice) <- (~2) [avatar component clause 128]
130. curious(alice) <- (2) [avatar component clause 128]
133. 3 <=> ! [X0] : curious(X0) [avatar definition]
134. curious(X0) <- (3) [avatar component clause 133]
135. 3 | 2 [avatar split clause 66,128,133]
159. 9 <=> brave(lucy) [avatar definition]
164. 10 <=> strong(alice) [avatar definition]
166. ~strong(alice) <- (~10) [avatar component clause 164]
167. ~10 | ~9 [avatar split clause 71,159,164]
284. 9 [avatar split clause 123,159]
313. patient(X2) | strong(X2) | strong(X2) [resolution 77,88]
314. patient(X2) | strong(X2) [duplicate literal removal 313]
361. ~curious(X2) | strong(X2) [resolution 314,85]
363. strong(alice) <- (2) [resolution 361,130]
365. $false <- (2, ~10) [subsumption resolution 363,166]
366. ~2 | 10 [avatar contradiction clause 365]
367. $false <- (~2, 3) [subsumption resolution 129,134]
368. 2 | ~3 [avatar contradiction clause 367]
369. $false [avatar sat refutation 135,167,284,366,368]
% SZS output end Proof for 2960168446749259123428872
% ------------------------------
% 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 strong or brave is brave and vice versa.
If susan is either wise or humble then mary is both strong and brave.
Everyone who is humble is either tall or brave.
Everyone who is not quiet or creative is quiet or not quiet and vice versa.
Everyone who is both creative and patient is both not brave and rich and vice versa.
Everyone who is both wise and not brave is both not brave and calm.
If someone is brave then alice is either not curious or tall and vice versa.
If susan is either strong or not rich then someone is not old or funny.
Everyone who is either not brave or not funny is either kind or not calm.
Everyone who is not tall or kind is either not generous or brave.
Everyone who is not wise or brave is not funny and vice versa.
Everyone who is not tall is either kind or not quiet.
Everyone who is not tall or old is funny.
If someone is both rich and not humble then alice is either curious or not quiet and vice versa.
Everyone who is generous or not patient is not creative.
Everyone who is both not creative and not brave is brave and vice versa.
Lucy is not generous or creative.
Lucy is both kind and curious.
Mary is both old and strong.
Someone is either quiet or not strong.
Fred is both quiet and not old.
Someone is either happy or not brave. | Mary is not wise. | contradiction | (![X]:((~strong(X)<~>brave(X))<=>brave(X)))&
(((wise(susan)<~>humble(susan)))=>((strong(mary)&brave(mary))))&
(![X]:(humble(X)=>(tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|creative(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((creative(X)&patient(X))<=>(~brave(X)&rich(X))))&
(![X]:((wise(X)&~brave(X))=>(~brave(X)&calm(X))))&
((?[X]:(brave(X)))<=>((~curious(alice)<~>tall(alice))))&
(((strong(susan)<~>~rich(susan)))=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((~brave(X)<~>~funny(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~tall(X)|kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~wise(X)|brave(X))<=>~funny(X)))&
(![X]:(~tall(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((~tall(X)|old(X))=>funny(X)))&
((?[X]:((rich(X)&~humble(X))))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((generous(X)|~patient(X))=>~creative(X)))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
((~generous(lucy)|creative(lucy)))&
((kind(lucy)&curious(lucy)))&
((old(mary)&strong(mary)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((quiet(fred)&~old(fred)))&
(?[X]:((happy(X)<~>~brave(X)))) | ~wise(mary) | [
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 543459694830267945628023
% SZS output start Proof for 543459694830267945628023
11. ! [X0] : ((brave(X0) | ~wise(X0)) <=> ~funny(X0)) [input p10]
13. ! [X0] : ((old(X0) | ~tall(X0)) => funny(X0)) [input p12]
19. strong(mary) & old(mary) [input p18]
23. ~wise(mary) [input hypothesis]
32. ! [X0] : (funny(X0) | (~old(X0) & tall(X0))) [ennf transformation 13]
50. ! [X0] : (((brave(X0) | ~wise(X0)) | funny(X0)) & (~funny(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 11]
51. ! [X0] : ((brave(X0) | ~wise(X0) | funny(X0)) & (~funny(X0) | (~brave(X0) & wise(X0)))) [flattening 50]
99. ~funny(X0) | wise(X0) [cnf transformation 51]
105. ~old(X0) | funny(X0) [cnf transformation 32]
120. old(mary) [cnf transformation 19]
128. ~wise(mary) [cnf transformation 23]
221. funny(mary) [resolution 105,120]
223. wise(mary) [resolution 221,99]
224. $false [subsumption resolution 223,128]
% SZS output end Proof for 543459694830267945628023
% ------------------------------
% 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 |
If someone is patient then someone is not creative.
Everyone who is either not old or tall is both not quiet and not humble and vice versa.
If susan is either not strong or not calm then susan is either strong or brave and vice versa.
If someone is both patient and not quiet then someone is either not quiet or brave and vice versa.
Everyone who is not old is either not rich or not creative.
If john is either not wise or patient then john is both not calm and generous and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
Alice is either quiet or not happy.
Susan is either strong or not generous.
Someone is happy.
Lucy is generous or not brave.
Susan is not creative. | John is not tall. | entailment | ((?[X]:(patient(X)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&~humble(X))))&
(((~strong(susan)<~>~calm(susan)))<=>((strong(susan)<~>brave(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:(~old(X)=>(~rich(X)<~>~creative(X))))&
(((~wise(john)<~>patient(john)))<=>((~calm(john)&generous(john))))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((quiet(alice)<~>~happy(alice)))&
((strong(susan)<~>~generous(susan)))&
(?[X]:(happy(X)))&
((generous(lucy)|~brave(lucy)))&
(~creative(susan)) | ~tall(john) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8833178973995690457261077
% SZS output start Proof for 8833178973995690457261077
10. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (old(X0) & ~tall(X0))) [input p12]
21. tall(john) [input hypothesis]
30. ! [X0] : ((old(X0) & ~tall(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 13]
31. ! [X0] : ((old(X0) & ~tall(X0)) | patient(X0) | quiet(X0)) [flattening 30]
58. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 10]
59. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 58]
110. ~patient(X0) | ~patient(X0) [cnf transformation 59]
112. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 59]
116. ~tall(X0) | patient(X0) | quiet(X0) [cnf transformation 31]
133. tall(john) [cnf transformation 21]
134. ~patient(X0) [duplicate literal removal 110]
135. ~quiet(X0) | patient(X0) [duplicate literal removal 112]
141. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
142. ~patient(X1) <- (1) [avatar component clause 141]
259. 1 [avatar split clause 134,141]
284. ~tall(X0) | patient(X0) [subsumption resolution 116,135]
349. patient(john) [resolution 284,133]
352. $false <- (1) [subsumption resolution 349,142]
353. ~1 [avatar contradiction clause 352]
356. $false [avatar sat refutation 259,353]
% SZS output end Proof for 8833178973995690457261077
% ------------------------------
% 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 |
If fred is both generous and wise then alice is either not curious or happy and vice versa. Everyone who is both creative and quiet is quiet or happy and vice versa. If susan is either creative or not rich then lucy is both kind and not brave and vice versa. Everyone who is either not rich or funny is both patient and not patient and vice versa. Everyone who is not kind or funny is both not brave and not patient and vice versa. If someone is not wise or old then mary is not rich or patient and vice versa. If alice is both old and kind then john is creative and vice versa. If john is both not brave and not creative then alice is both not kind and wise. If someone is quiet or not creative then someone is either not funny or not curious. If fred is not funny or humble then someone is not happy or quiet and vice versa. Everyone who is both kind and old is not tall or humble. Everyone who is not wise is old or patient. If fred is both happy and rich then mary is both rich and not brave and vice versa. If someone is kind or patient then lucy is both not humble and creative and vice versa. If susan is not quiet or patient then someone is wise and vice versa. Everyone who is kind or not calm is both not patient and happy. John is either creative or brave. Someone is creative. Someone is patient or funny. Mary is not happy. Someone is either brave or funny. Someone is not quiet. Someone is quiet or happy. | Alice is funny. | neutral | (((generous(fred)&wise(fred)))<=>((~curious(alice)<~>happy(alice))))&
(![X]:((creative(X)&quiet(X))<=>(quiet(X)|happy(X))))&
(((creative(susan)<~>~rich(susan)))<=>((kind(lucy)&~brave(lucy))))&
(![X]:((~rich(X)<~>funny(X))<=>(patient(X)&~patient(X))))&
(![X]:((~kind(X)|funny(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~wise(X)|old(X))))<=>((~rich(mary)|patient(mary))))&
(((old(alice)&kind(alice)))<=>(creative(john)))&
(((~brave(john)&~creative(john)))=>((~kind(alice)&wise(alice))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~funny(fred)|humble(fred)))<=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((kind(X)&old(X))=>(~tall(X)|humble(X))))&
(![X]:(~wise(X)=>(old(X)|patient(X))))&
(((happy(fred)&rich(fred)))<=>((rich(mary)&~brave(mary))))&
((?[X]:((kind(X)|patient(X))))<=>((~humble(lucy)&creative(lucy))))&
(((~quiet(susan)|patient(susan)))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~calm(X))=>(~patient(X)&happy(X))))&
((creative(john)<~>brave(john)))&
(?[X]:(creative(X)))&
(?[X]:((patient(X)|funny(X))))&
(~happy(mary))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)|happy(X)))) | funny(alice) | [] | null | 0 |
Everyone who is not rich is not kind and vice versa.
Everyone who is either not brave or not creative is not tall and vice versa.
Everyone who is either happy or not patient is not generous or not kind and vice versa.
Everyone who is either rich or not curious is not happy and vice versa.
Everyone who is generous is generous or not happy.
Everyone who is either rich or patient is both strong and not curious.
Everyone who is both not patient and not curious is either not funny or not calm and vice versa.
If john is either not rich or generous then fred is both wise and not creative.
If mary is wise or not quiet then someone is not kind.
If john is both not generous and curious then someone is not curious and vice versa.
Everyone who is both quiet and not rich is both wise and quiet.
If lucy is calm then someone is kind or humble.
If susan is both not old and old then fred is brave or old and vice versa.
Everyone who is either not wise or wise is not old or not patient.
If alice is either patient or not happy then someone is humble.
Lucy is either generous or not quiet.
Lucy is wise or generous.
Someone is either not happy or not strong.
Someone is either not funny or not old.
Someone is both not strong and calm. | Susan is not happy. | entailment | (![X]:(~rich(X)<=>~kind(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>~tall(X)))&
(![X]:((happy(X)<~>~patient(X))<=>(~generous(X)|~kind(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~happy(X)))&
(![X]:(generous(X)=>(generous(X)|~happy(X))))&
(![X]:((rich(X)<~>patient(X))=>(strong(X)&~curious(X))))&
(![X]:((~patient(X)&~curious(X))<=>(~funny(X)<~>~calm(X))))&
(((~rich(john)<~>generous(john)))=>((wise(fred)&~creative(fred))))&
(((wise(mary)|~quiet(mary)))=>(?[X]:(~kind(X))))&
(((~generous(john)&curious(john)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)&~rich(X))=>(wise(X)&quiet(X))))&
((calm(lucy))=>(?[X]:((kind(X)|humble(X)))))&
(((~old(susan)&old(susan)))<=>((brave(fred)|old(fred))))&
(![X]:((~wise(X)<~>wise(X))=>(~old(X)|~patient(X))))&
(((patient(alice)<~>~happy(alice)))=>(?[X]:(humble(X))))&
((generous(lucy)<~>~quiet(lucy)))&
((wise(lucy)|generous(lucy)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((~strong(X)&calm(X)))) | ~happy(susan) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9175616116022498190958237
% SZS output start Proof for 9175616116022498190958237
1. ! [X0] : (~rich(X0) <=> ~kind(X0)) [input p0]
3. ! [X0] : ((happy(X0) <~> ~patient(X0)) <=> (~kind(X0) | ~generous(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~happy(X0)) [input p3]
6. ! [X0] : ((rich(X0) <~> patient(X0)) => (~curious(X0) & strong(X0))) [input p5]
10. (curious(john) & ~generous(john)) <=> ? [X0] : ~curious(X0) [input p9]
21. happy(susan) [input hypothesis]
27. ! [X0] : ((~curious(X0) & strong(X0)) | (rich(X0) <=> patient(X0))) [ennf transformation 6]
34. ! [X0] : ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0))) [nnf transformation 1]
35. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [nnf transformation 3]
36. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [flattening 35]
37. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | happy(X0)) & (~happy(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 4]
38. ! [X0] : ((~curious(X0) & strong(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) [nnf transformation 27]
44. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~curious(john) | generous(john))) [nnf transformation 10]
45. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~curious(john) | generous(john)) [flattening 44]
46. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~curious(john) | generous(john)) [rectify 45]
47. ? [X1] : ~curious(X1) => ~curious(sK1) [choice axiom]
48. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (~curious(sK1) | ~curious(john) | generous(john)) [skolemisation 46,47]
61. ~kind(X0) | rich(X0) [cnf transformation 34]
65. ~patient(X0) | happy(X0) | generous(X0) [cnf transformation 36]
67. ~happy(X0) | patient(X0) | generous(X0) [cnf transformation 36]
68. ~happy(X0) | patient(X0) | kind(X0) [cnf transformation 36]
69. ~curious(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 37]
71. ~curious(X0) | rich(X0) | happy(X0) [cnf transformation 37]
76. ~curious(X0) | patient(X0) | ~rich(X0) [cnf transformation 38]
77. ~curious(X0) | rich(X0) | ~patient(X0) [cnf transformation 38]
89. ~generous(john) | curious(X0) [cnf transformation 48]
90. curious(john) | curious(X0) [cnf transformation 48]
109. happy(susan) [cnf transformation 21]
113. 1 <=> generous(john) [avatar definition]
115. ~generous(john) <- (~1) [avatar component clause 113]
117. 2 <=> rich(john) [avatar definition]
141. 7 <=> ! [X0] : curious(X0) [avatar definition]
142. curious(X0) <- (7) [avatar component clause 141]
144. 8 <=> curious(john) [avatar definition]
146. curious(john) <- (8) [avatar component clause 144]
147. 7 | 8 [avatar split clause 90,144,141]
148. 7 | ~1 [avatar split clause 89,113,141]
217. 21 <=> patient(susan) [avatar definition]
230. patient(susan) | kind(susan) [resolution 68,109]
232. 24 <=> kind(susan) [avatar definition]
234. kind(susan) <- (24) [avatar component clause 232]
235. 24 | 21 [avatar split clause 230,217,232]
242. 25 <=> curious(susan) [avatar definition]
243. ~curious(susan) <- (~25) [avatar component clause 242]
244. curious(susan) <- (25) [avatar component clause 242]
246. 26 <=> rich(susan) [avatar definition]
247. ~rich(susan) <- (~26) [avatar component clause 246]
250. ~happy(susan) | ~rich(susan) <- (25) [resolution 244,69]
251. ~rich(susan) <- (25) [subsumption resolution 250,109]
252. ~26 | ~25 [avatar split clause 251,242,246]
262. 28 <=> patient(john) [avatar definition]
263. ~patient(john) <- (~28) [avatar component clause 262]
264. patient(john) <- (28) [avatar component clause 262]
267. 29 <=> happy(john) [avatar definition]
268. ~happy(john) <- (~29) [avatar component clause 267]
269. happy(john) <- (29) [avatar component clause 267]
287. rich(susan) | ~patient(susan) <- (25) [resolution 77,244]
290. ~patient(susan) <- (25, ~26) [subsumption resolution 287,247]
293. ~21 | ~25 | 26 [avatar split clause 290,246,242,217]
304. rich(susan) <- (24) [resolution 234,61]
307. 26 | ~24 [avatar split clause 304,232,246]
308. $false <- (7, ~25) [subsumption resolution 243,142]
309. ~7 | 25 [avatar contradiction clause 308]
312. rich(john) | ~patient(john) <- (8) [resolution 146,77]
313. patient(john) | ~rich(john) <- (8) [resolution 146,76]
314. rich(john) | happy(john) <- (8) [resolution 146,71]
315. ~happy(john) | ~rich(john) <- (8) [resolution 146,69]
340. happy(john) | generous(john) <- (28) [resolution 264,65]
341. generous(john) <- (28, ~29) [subsumption resolution 340,268]
342. $false <- (~1, 28, ~29) [subsumption resolution 341,115]
343. 1 | ~28 | 29 [avatar contradiction clause 342]
344. 29 | 2 | ~8 [avatar split clause 314,144,117,267]
345. ~2 | 28 | ~8 [avatar split clause 313,144,262,117]
346. ~28 | 2 | ~8 [avatar split clause 312,144,117,262]
347. ~2 | ~29 | ~8 [avatar split clause 315,144,267,117]
356. patient(john) | generous(john) <- (29) [resolution 269,67]
358. generous(john) <- (~28, 29) [subsumption resolution 356,263]
359. $false <- (~1, ~28, 29) [subsumption resolution 358,115]
360. 1 | 28 | ~29 [avatar contradiction clause 359]
361. $false [avatar sat refutation 147,148,235,252,293,307,309,343,344,345,346,347,360]
% SZS output end Proof for 9175616116022498190958237
% ------------------------------
% 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 funny and old is not patient or strong and vice versa.
If someone is both tall and not curious then someone is not strong or not happy and vice versa.
Everyone who is calm or kind is both tall and not rich and vice versa.
If susan is both not wise and not happy then someone is not strong.
If fred is curious or kind then someone is both not old and not funny.
Everyone who is both not old and happy is rich.
If susan is either creative or calm then lucy is both creative and wise and vice versa.
Everyone who is not strong or happy is both creative and not wise and vice versa.
Everyone who is kind is not generous or creative.
If someone is both not strong and kind then someone is kind and vice versa.
If someone is both generous and not generous then someone is kind or not calm.
If someone is strong or old then fred is humble.
Everyone who is generous or not wise is either happy or not wise.
Everyone who is not patient is quiet or not curious.
Everyone who is either not kind or old is both not brave and not old and vice versa.
Everyone who is brave or not curious is both not wise and not brave and vice versa.
Lucy is either not strong or not humble.
Someone is not rich.
Alice is not creative.
Someone is not generous.
Susan is both old and not tall.
John is calm. | Fred is not tall. | neutral | (![X]:((funny(X)&old(X))<=>(~patient(X)|strong(X))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((calm(X)|kind(X))<=>(tall(X)&~rich(X))))&
(((~wise(susan)&~happy(susan)))=>(?[X]:(~strong(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((~old(X)&happy(X))=>rich(X)))&
(((creative(susan)<~>calm(susan)))<=>((creative(lucy)&wise(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(creative(X)&~wise(X))))&
(![X]:(kind(X)=>(~generous(X)|creative(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~generous(X))))=>(?[X]:((kind(X)|~calm(X)))))&
((?[X]:((strong(X)|old(X))))=>(humble(fred)))&
(![X]:((generous(X)|~wise(X))=>(happy(X)<~>~wise(X))))&
(![X]:(~patient(X)=>(quiet(X)|~curious(X))))&
(![X]:((~kind(X)<~>old(X))<=>(~brave(X)&~old(X))))&
(![X]:((brave(X)|~curious(X))<=>(~wise(X)&~brave(X))))&
((~strong(lucy)<~>~humble(lucy)))&
(?[X]:(~rich(X)))&
(~creative(alice))&
(?[X]:(~generous(X)))&
((old(susan)&~tall(susan)))&
(calm(john)) | ~tall(fred) | [] | null | 0 |
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
If mary is either not happy or not calm then susan is not tall.
Everyone who is curious or not curious is generous.
If someone is strong or humble then someone is both kind and generous and vice versa.
Everyone who is not curious or not generous is both patient and not funny.
If someone is funny then someone is not creative or not calm and vice versa.
Everyone who is either not tall or not generous is not creative or creative and vice versa.
If fred is both not creative and not funny then someone is both not wise and kind and vice versa.
If someone is humble or wise then fred is not rich and vice versa.
If someone is not happy or funny then mary is creative.
Everyone who is both not happy and patient is either not patient or not calm.
Everyone who is old or not happy is either generous or not tall and vice versa.
Everyone who is not kind or not strong is calm or not quiet and vice versa.
Lucy is calm or rich.
Someone is both not kind and not brave.
Someone is creative or humble.
Someone is rich or curious.
John is brave or not humble.
Someone is creative or not kind.
Someone is wise or not wise. | Mary is not humble. | entailment | (![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((humble(X)|wise(X))))<=>(~rich(fred)))&
((?[X]:((~happy(X)|funny(X))))=>(creative(mary)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((old(X)|~happy(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~kind(X)|~strong(X))<=>(calm(X)|~quiet(X))))&
((calm(lucy)|rich(lucy)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((rich(X)|curious(X))))&
((brave(john)|~humble(john)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((wise(X)|~wise(X)))) | ~humble(mary) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 365802867571702322464737
% SZS output start Proof for 365802867571702322464737
1. ! [X0] : ((rich(X0) & ~quiet(X0)) <=> (~brave(X0) | brave(X0))) [input p0]
11. ? [X0] : (wise(X0) | humble(X0)) <=> ~rich(fred) [input p10]
23. humble(mary) [input hypothesis]
33. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (~rich(X0) | quiet(X0)))) [nnf transformation 1]
34. ! [X0] : (((rich(X0) & ~quiet(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ~rich(X0) | quiet(X0))) [flattening 33]
56. (? [X0] : (wise(X0) | humble(X0)) | rich(fred)) & (~rich(fred) | ! [X0] : (~wise(X0) & ~humble(X0))) [nnf transformation 11]
57. (? [X0] : (wise(X0) | humble(X0)) | rich(fred)) & (~rich(fred) | ! [X1] : (~wise(X1) & ~humble(X1))) [rectify 56]
58. ? [X0] : (wise(X0) | humble(X0)) => (wise(sK5) | humble(sK5)) [choice axiom]
59. ((wise(sK5) | humble(sK5)) | rich(fred)) & (~rich(fred) | ! [X1] : (~wise(X1) & ~humble(X1))) [skolemisation 57,58]
78. rich(X0) | ~brave(X0) [cnf transformation 34]
79. rich(X0) | brave(X0) [cnf transformation 34]
112. ~rich(fred) | ~humble(X1) [cnf transformation 59]
137. humble(mary) [cnf transformation 23]
139. rich(X0) [subsumption resolution 78,79]
170. 7 <=> ! [X3] : ~humble(X3) [avatar definition]
171. ~humble(X3) <- (7) [avatar component clause 170]
232. ~humble(X1) [subsumption resolution 112,139]
233. 7 [avatar split clause 232,170]
280. $false <- (7) [resolution 171,137]
281. ~7 [avatar contradiction clause 280]
282. $false [avatar sat refutation 233,281]
% SZS output end Proof for 365802867571702322464737
% ------------------------------
% 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 not strong then mary is both not humble and not brave.
If someone is either old or wise then alice is not curious and vice versa.
Everyone who is generous is either not tall or old and vice versa.
Everyone who is wise or creative is both funny and not old and vice versa.
If paul is not humble or not tall then mary is not patient.
If paul is not happy or generous then fred is both not quiet and not strong and vice versa.
Everyone who is either not kind or funny is either calm or funny and vice versa.
Everyone who is kind is happy or not brave.
Everyone who is not curious or humble is both not brave and happy and vice versa.
Everyone who is not wise or not brave is creative and vice versa.
Everyone who is either not patient or not strong is both quiet and happy.
Everyone who is either creative or not happy is not generous and vice versa.
If someone is both not quiet and not happy then john is either creative or quiet and vice versa.
If fred is happy then someone is both not calm and not generous.
Everyone who is patient is both not curious and not strong and vice versa.
If someone is humble then susan is both brave and patient and vice versa.
Someone is either patient or not curious.
Lucy is happy.
Someone is not quiet or not rich.
Someone is not strong.
Susan is not generous or not funny.
Lucy is not old or not rich. | Mary is not funny. | contradiction | ((?[X]:((~happy(X)<~>~strong(X))))=>((~humble(mary)&~brave(mary))))&
((?[X]:((old(X)<~>wise(X))))<=>(~curious(alice)))&
(![X]:(generous(X)<=>(~tall(X)<~>old(X))))&
(![X]:((wise(X)|creative(X))<=>(funny(X)&~old(X))))&
(((~humble(paul)|~tall(paul)))=>(~patient(mary)))&
(((~happy(paul)|generous(paul)))<=>((~quiet(fred)&~strong(fred))))&
(![X]:((~kind(X)<~>funny(X))<=>(calm(X)<~>funny(X))))&
(![X]:(kind(X)=>(happy(X)|~brave(X))))&
(![X]:((~curious(X)|humble(X))<=>(~brave(X)&happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>creative(X)))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((?[X]:(humble(X)))<=>((brave(susan)&patient(susan))))&
(?[X]:((patient(X)<~>~curious(X))))&
(happy(lucy))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:(~strong(X)))&
((~generous(susan)|~funny(susan)))&
((~old(lucy)|~rich(lucy))) | ~funny(mary) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6017585120812540994211657
% SZS output start Proof for 6017585120812540994211657
4. ! [X0] : ((creative(X0) | wise(X0)) <=> (~old(X0) & funny(X0))) [input p3]
10. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> creative(X0)) [input p9]
23. ~funny(mary) [input hypothesis]
38. ! [X0] : (((creative(X0) | wise(X0)) | (old(X0) | ~funny(X0))) & ((~old(X0) & funny(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 4]
39. ! [X0] : ((creative(X0) | wise(X0) | old(X0) | ~funny(X0)) & ((~old(X0) & funny(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 38]
45. ! [X0] : (((~brave(X0) | ~wise(X0)) | ~creative(X0)) & (creative(X0) | (brave(X0) & wise(X0)))) [nnf transformation 10]
46. ! [X0] : ((~brave(X0) | ~wise(X0) | ~creative(X0)) & (creative(X0) | (brave(X0) & wise(X0)))) [flattening 45]
79. ~wise(X0) | funny(X0) [cnf transformation 39]
80. ~creative(X0) | funny(X0) [cnf transformation 39]
105. creative(X0) | wise(X0) [cnf transformation 46]
135. ~funny(mary) [cnf transformation 23]
292. wise(X1) | funny(X1) [resolution 105,80]
294. funny(X1) [subsumption resolution 292,79]
309. $false [resolution 294,135]
% SZS output end Proof for 6017585120812540994211657
% ------------------------------
% 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 wise or not strong is calm or not humble and vice versa. If someone is strong or wise then someone is generous or quiet and vice versa. Everyone who is either not old or not creative is both not humble and old. Everyone who is either not calm or not kind is rich. Everyone who is strong is both not old and not quiet and vice versa. If fred is both quiet and funny then someone is not curious and vice versa. Everyone who is either rich or not happy is either creative or not tall. If someone is either funny or creative then lucy is humble or not generous and vice versa. If someone is either generous or not old then someone is old or not kind. If someone is either humble or patient then someone is both not old and kind and vice versa. Everyone who is either humble or not brave is old. If alice is both strong and kind then susan is strong. If someone is patient then someone is not brave or not creative. If lucy is not tall then someone is quiet. Everyone who is both not tall and not curious is either brave or wise. Everyone who is both tall and not brave is either tall or not happy. Someone is not kind or not humble. Fred is old or not brave. Susan is either patient or not creative. Someone is not strong or tall. Someone is both strong and not old. Susan is both strong and not happy. Someone is not calm. Someone is either quiet or not curious. | Susan is not strong. | contradiction | (![X]:((~wise(X)|~strong(X))<=>(calm(X)|~humble(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((generous(X)|quiet(X)))))&
(![X]:((~old(X)<~>~creative(X))=>(~humble(X)&old(X))))&
(![X]:((~calm(X)<~>~kind(X))=>rich(X)))&
(![X]:(strong(X)<=>(~old(X)&~quiet(X))))&
(((quiet(fred)&funny(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((rich(X)<~>~happy(X))=>(creative(X)<~>~tall(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>((humble(lucy)|~generous(lucy))))&
((?[X]:((generous(X)<~>~old(X))))=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((humble(X)<~>patient(X))))<=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((humble(X)<~>~brave(X))=>old(X)))&
(((strong(alice)&kind(alice)))=>(strong(susan)))&
((?[X]:(patient(X)))=>(?[X]:((~brave(X)|~creative(X)))))&
((~tall(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)&~curious(X))=>(brave(X)<~>wise(X))))&
(![X]:((tall(X)&~brave(X))=>(tall(X)<~>~happy(X))))&
(?[X]:((~kind(X)|~humble(X))))&
((old(fred)|~brave(fred)))&
((patient(susan)<~>~creative(susan)))&
(?[X]:((~strong(X)|tall(X))))&
(?[X]:((strong(X)&~old(X))))&
((strong(susan)&~happy(susan)))&
(?[X]:(~calm(X)))&
(?[X]:((quiet(X)<~>~curious(X)))) | ~strong(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4023479485047802825900701
% SZS output start Proof for 4023479485047802825900701
22. ~happy(susan) & strong(susan) [input p21]
25. ~strong(susan) [input hypothesis]
148. strong(susan) [cnf transformation 22]
153. ~strong(susan) [cnf transformation 25]
290. 32 <=> strong(susan) [avatar definition]
352. 32 [avatar split clause 148,290]
363. ~32 [avatar split clause 153,290]
364. $false [avatar sat refutation 352,363]
% SZS output end Proof for 4023479485047802825900701
% ------------------------------
% 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 brave or not strong then someone is both not tall and not wise and vice versa. Everyone who is not quiet is not creative. Everyone who is calm or not tall is not calm or not kind and vice versa. If susan is either creative or not wise then someone is either not happy or generous and vice versa. If someone is strong or not rich then someone is tall. If lucy is both not kind and rich then someone is either kind or funny. If mary is not calm then alice is both not calm and strong. Everyone who is either strong or tall is both tall and strong. Everyone who is not brave or kind is not kind and vice versa. Everyone who is curious or creative is both brave and happy and vice versa. If someone is not calm then lucy is either creative or not brave. If someone is not strong then alice is not brave and vice versa. If someone is both rich and calm then someone is not brave and vice versa. If someone is both not brave and not wise then susan is not strong or not rich. Everyone who is either rich or not strong is both not generous and not kind and vice versa. Everyone who is calm or not curious is not humble. Someone is not wise or happy. Someone is quiet or humble. Someone is not humble or strong. Someone is humble or wise. Someone is either generous or not old. Mary is both not strong and not old. John is generous. | John is brave. | contradiction | ((?[X]:((~brave(X)<~>~strong(X))))<=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:(~quiet(X)=>~creative(X)))&
(![X]:((calm(X)|~tall(X))<=>(~calm(X)|~kind(X))))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(tall(X))))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>funny(X)))))&
((~calm(mary))=>((~calm(alice)&strong(alice))))&
(![X]:((strong(X)<~>tall(X))=>(tall(X)&strong(X))))&
(![X]:((~brave(X)|kind(X))<=>~kind(X)))&
(![X]:((curious(X)|creative(X))<=>(brave(X)&happy(X))))&
((?[X]:(~calm(X)))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(~strong(X)))<=>(~brave(alice)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)&~wise(X))))=>((~strong(susan)|~rich(susan))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~kind(X))))&
(![X]:((calm(X)|~curious(X))=>~humble(X)))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((quiet(X)|humble(X))))&
(?[X]:((~humble(X)|strong(X))))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((generous(X)<~>~old(X))))&
((~strong(mary)&~old(mary)))&
(generous(john)) | brave(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7229779054028224540914060
% SZS output start Proof for 7229779054028224540914060
9. ! [X0] : ((kind(X0) | ~brave(X0)) <=> ~kind(X0)) [input p8]
24. brave(john) [input hypothesis]
57. ! [X0] : (((kind(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) & brave(X0)))) [nnf transformation 9]
58. ! [X0] : ((kind(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (~kind(X0) & brave(X0)))) [flattening 57]
111. ~kind(X0) | ~kind(X0) [cnf transformation 58]
112. kind(X0) | ~brave(X0) | kind(X0) [cnf transformation 58]
142. brave(john) [cnf transformation 24]
143. ~kind(X0) [duplicate literal removal 111]
144. ~brave(X0) | kind(X0) [duplicate literal removal 112]
367. kind(john) [resolution 144,142]
370. $false [subsumption resolution 367,143]
% SZS output end Proof for 7229779054028224540914060
% ------------------------------
% 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 not patient then someone is both not rich and not kind.
Everyone who is not calm or generous is both tall and not patient.
If someone is kind then someone is either happy or kind.
If someone is curious then someone is not kind and vice versa.
Everyone who is not generous or kind is not calm.
If someone is not patient or brave then john is either not old or not generous and vice versa.
Everyone who is humble is both brave and not wise.
If someone is kind then someone is both wise and tall and vice versa.
If mary is calm or brave then someone is patient and vice versa.
If someone is both generous and not brave then someone is wise and vice versa.
Everyone who is either curious or not kind is not tall and vice versa.
Everyone who is kind is not humble.
If someone is both not curious and not rich then lucy is quiet and vice versa.
Everyone who is either not strong or brave is not happy.
Everyone who is both brave and calm is generous or not creative.
Someone is both not old and not strong.
Mary is both creative and not happy.
Someone is brave or not rich.
Mary is either not old or not tall.
Mary is patient or not kind.
Alice is not funny.
Someone is wise or happy. | Mary is not brave. | entailment | ((?[X]:(~patient(X)))=>(?[X]:((~rich(X)&~kind(X)))))&
(![X]:((~calm(X)|generous(X))=>(tall(X)&~patient(X))))&
((?[X]:(kind(X)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:(curious(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~generous(X)|kind(X))=>~calm(X)))&
((?[X]:((~patient(X)|brave(X))))<=>((~old(john)<~>~generous(john))))&
(![X]:(humble(X)=>(brave(X)&~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)&tall(X)))))&
(((calm(mary)|brave(mary)))<=>(?[X]:(patient(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(?[X]:(wise(X))))&
(![X]:((curious(X)<~>~kind(X))<=>~tall(X)))&
(![X]:(kind(X)=>~humble(X)))&
((?[X]:((~curious(X)&~rich(X))))<=>(quiet(lucy)))&
(![X]:((~strong(X)<~>brave(X))=>~happy(X)))&
(![X]:((brave(X)&calm(X))=>(generous(X)|~creative(X))))&
(?[X]:((~old(X)&~strong(X))))&
((creative(mary)&~happy(mary)))&
(?[X]:((brave(X)|~rich(X))))&
((~old(mary)<~>~tall(mary)))&
((patient(mary)|~kind(mary)))&
(~funny(alice))&
(?[X]:((wise(X)|happy(X)))) | ~brave(mary) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2110440093913789330836429
% SZS output start Proof for 2110440093913789330836429
2. ! [X0] : ((generous(X0) | ~calm(X0)) => (~patient(X0) & tall(X0))) [input p1]
5. ! [X0] : ((kind(X0) | ~generous(X0)) => ~calm(X0)) [input p4]
9. (brave(mary) | calm(mary)) <=> ? [X0] : patient(X0) [input p8]
23. brave(mary) [input hypothesis]
33. ! [X0] : ((~patient(X0) & tall(X0)) | (~generous(X0) & calm(X0))) [ennf transformation 2]
35. ! [X0] : (~calm(X0) | (~kind(X0) & generous(X0))) [ennf transformation 5]
60. ((brave(mary) | calm(mary)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~brave(mary) & ~calm(mary))) [nnf transformation 9]
61. (brave(mary) | calm(mary) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~brave(mary) & ~calm(mary))) [flattening 60]
62. (brave(mary) | calm(mary) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | (~brave(mary) & ~calm(mary))) [rectify 61]
63. ? [X1] : patient(X1) => patient(sK7) [choice axiom]
64. (brave(mary) | calm(mary) | ! [X0] : ~patient(X0)) & (patient(sK7) | (~brave(mary) & ~calm(mary))) [skolemisation 62,63]
87. ~patient(X0) | calm(X0) [cnf transformation 33]
88. ~generous(X0) | ~patient(X0) [cnf transformation 33]
93. ~calm(X0) | generous(X0) [cnf transformation 35]
105. patient(sK7) | ~brave(mary) [cnf transformation 64]
129. brave(mary) [cnf transformation 23]
223. 22 <=> brave(mary) [avatar definition]
228. 23 <=> patient(sK7) [avatar definition]
230. patient(sK7) <- (23) [avatar component clause 228]
231. ~22 | 23 [avatar split clause 105,228,223]
309. 22 [avatar split clause 129,223]
320. calm(sK7) <- (23) [resolution 87,230]
324. generous(sK7) <- (23) [resolution 93,320]
343. ~patient(sK7) <- (23) [resolution 324,88]
345. $false <- (23) [subsumption resolution 343,230]
346. ~23 [avatar contradiction clause 345]
347. $false [avatar sat refutation 231,309,346]
% SZS output end Proof for 2110440093913789330836429
% ------------------------------
% 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not tall is either old or curious.
If mary is both not old and strong then someone is not old or not calm and vice versa.
If john is tall then paul is not brave or not humble and vice versa.
If alice is not rich or not curious then lucy is both not happy and not quiet and vice versa.
Everyone who is either curious or not patient is not humble or not brave and vice versa.
Everyone who is brave or not rich is not creative or wise and vice versa.
Everyone who is not patient is both not humble and quiet and vice versa.
Everyone who is either curious or wise is not quiet or not curious.
If someone is either not creative or strong then susan is not creative.
If susan is both not rich and humble then alice is kind and vice versa.
Everyone who is wise is not brave or not happy.
If alice is strong or funny then alice is either not quiet or generous and vice versa.
Everyone who is either creative or not happy is both strong and wise and vice versa.
Everyone who is either not brave or creative is either not quiet or curious and vice versa.
Everyone who is rich or not funny is either happy or curious.
If someone is not tall or not happy then susan is both not funny and not tall.
Alice is not brave.
Someone is calm.
Someone is both not kind and not calm.
Susan is both strong and not humble.
Someone is both old and curious.
Someone is tall or not old.
Someone is calm or brave.
Someone is strong or kind. | Mary is strong. | entailment | (![X]:((~funny(X)|~tall(X))=>(old(X)<~>curious(X))))&
(((~old(mary)&strong(mary)))<=>(?[X]:((~old(X)|~calm(X)))))&
((tall(john))<=>((~brave(paul)|~humble(paul))))&
(((~rich(alice)|~curious(alice)))<=>((~happy(lucy)&~quiet(lucy))))&
(![X]:((curious(X)<~>~patient(X))<=>(~humble(X)|~brave(X))))&
(![X]:((brave(X)|~rich(X))<=>(~creative(X)|wise(X))))&
(![X]:(~patient(X)<=>(~humble(X)&quiet(X))))&
(![X]:((curious(X)<~>wise(X))=>(~quiet(X)|~curious(X))))&
((?[X]:((~creative(X)<~>strong(X))))=>(~creative(susan)))&
(((~rich(susan)&humble(susan)))<=>(kind(alice)))&
(![X]:(wise(X)=>(~brave(X)|~happy(X))))&
(((strong(alice)|funny(alice)))<=>((~quiet(alice)<~>generous(alice))))&
(![X]:((creative(X)<~>~happy(X))<=>(strong(X)&wise(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((rich(X)|~funny(X))=>(happy(X)<~>curious(X))))&
((?[X]:((~tall(X)|~happy(X))))=>((~funny(susan)&~tall(susan))))&
(~brave(alice))&
(?[X]:(calm(X)))&
(?[X]:((~kind(X)&~calm(X))))&
((strong(susan)&~humble(susan)))&
(?[X]:((old(X)&curious(X))))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((strong(X)|kind(X)))) | strong(mary) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 139823349656692764459159
% SZS output start Proof for 139823349656692764459159
2. (strong(mary) & ~old(mary)) <=> ? [X0] : (~calm(X0) | ~old(X0)) [input p1]
19. ? [X0] : (~calm(X0) & ~kind(X0)) [input p18]
25. ~strong(mary) [input hypothesis]
35. ((strong(mary) & ~old(mary)) | ! [X0] : (calm(X0) & old(X0))) & (? [X0] : (~calm(X0) | ~old(X0)) | (~strong(mary) | old(mary))) [nnf transformation 2]
36. ((strong(mary) & ~old(mary)) | ! [X0] : (calm(X0) & old(X0))) & (? [X0] : (~calm(X0) | ~old(X0)) | ~strong(mary) | old(mary)) [flattening 35]
37. ((strong(mary) & ~old(mary)) | ! [X0] : (calm(X0) & old(X0))) & (? [X1] : (~calm(X1) | ~old(X1)) | ~strong(mary) | old(mary)) [rectify 36]
38. ? [X1] : (~calm(X1) | ~old(X1)) => (~calm(sK0) | ~old(sK0)) [choice axiom]
39. ((strong(mary) & ~old(mary)) | ! [X0] : (calm(X0) & old(X0))) & ((~calm(sK0) | ~old(sK0)) | ~strong(mary) | old(mary)) [skolemisation 37,38]
62. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
63. ~calm(sK2) & ~kind(sK2) [skolemisation 19,62]
80. strong(mary) | calm(X0) [cnf transformation 39]
141. ~calm(sK2) [cnf transformation 63]
149. ~strong(mary) [cnf transformation 25]
152. 1 <=> ! [X0] : calm(X0) [avatar definition]
153. calm(X0) <- (1) [avatar component clause 152]
155. 2 <=> strong(mary) [avatar definition]
158. 1 | 2 [avatar split clause 80,155,152]
309. ~2 [avatar split clause 149,155]
310. $false <- (1) [resolution 153,141]
311. ~1 [avatar contradiction clause 310]
312. $false [avatar sat refutation 158,309,311]
% SZS output end Proof for 139823349656692764459159
% ------------------------------
% 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 fred is both calm and patient then someone is quiet or tall and vice versa.
Everyone who is creative or not strong is both patient and happy and vice versa.
Everyone who is wise or not rich is either not creative or not rich.
If john is both not humble and tall then john is either not funny or creative and vice versa.
If someone is either patient or not quiet then someone is either rich or not wise and vice versa.
Everyone who is not calm is not happy or strong.
Everyone who is happy or not rich is both not brave and quiet.
Everyone who is both brave and not creative is wise or not calm and vice versa.
Everyone who is not wise or funny is not humble or not generous.
Everyone who is either rich or wise is not creative or generous.
If someone is brave or not creative then fred is not brave and vice versa.
If someone is brave or not strong then alice is brave or not tall and vice versa.
Everyone who is calm or not funny is either tall or creative.
Everyone who is funny or humble is either happy or not funny and vice versa.
Everyone who is funny is not patient.
Everyone who is happy or quiet is either not calm or not old.
Paul is calm.
Susan is brave.
Someone is not humble or rich.
Someone is not strong or happy.
Someone is both humble and brave.
Someone is both creative and not funny.
Someone is not calm. | Fred is not brave. | entailment | (((calm(fred)&patient(fred)))<=>(?[X]:((quiet(X)|tall(X)))))&
(![X]:((creative(X)|~strong(X))<=>(patient(X)&happy(X))))&
(![X]:((wise(X)|~rich(X))=>(~creative(X)<~>~rich(X))))&
(((~humble(john)&tall(john)))<=>((~funny(john)<~>creative(john))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((rich(X)<~>~wise(X)))))&
(![X]:(~calm(X)=>(~happy(X)|strong(X))))&
(![X]:((happy(X)|~rich(X))=>(~brave(X)&quiet(X))))&
(![X]:((brave(X)&~creative(X))<=>(wise(X)|~calm(X))))&
(![X]:((~wise(X)|funny(X))=>(~humble(X)|~generous(X))))&
(![X]:((rich(X)<~>wise(X))=>(~creative(X)|generous(X))))&
((?[X]:((brave(X)|~creative(X))))<=>(~brave(fred)))&
((?[X]:((brave(X)|~strong(X))))<=>((brave(alice)|~tall(alice))))&
(![X]:((calm(X)|~funny(X))=>(tall(X)<~>creative(X))))&
(![X]:((funny(X)|humble(X))<=>(happy(X)<~>~funny(X))))&
(![X]:(funny(X)=>~patient(X)))&
(![X]:((happy(X)|quiet(X))=>(~calm(X)<~>~old(X))))&
(calm(paul))&
(brave(susan))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((humble(X)&brave(X))))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:(~calm(X))) | ~brave(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 557414839619652661861543
% SZS output start Proof for 557414839619652661861543
11. ? [X0] : (~creative(X0) | brave(X0)) <=> ~brave(fred) [input p10]
24. brave(fred) [input hypothesis]
55. (? [X0] : (~creative(X0) | brave(X0)) | brave(fred)) & (~brave(fred) | ! [X0] : (creative(X0) & ~brave(X0))) [nnf transformation 11]
56. (? [X0] : (~creative(X0) | brave(X0)) | brave(fred)) & (~brave(fred) | ! [X1] : (creative(X1) & ~brave(X1))) [rectify 55]
57. ? [X0] : (~creative(X0) | brave(X0)) => (~creative(sK3) | brave(sK3)) [choice axiom]
58. ((~creative(sK3) | brave(sK3)) | brave(fred)) & (~brave(fred) | ! [X1] : (creative(X1) & ~brave(X1))) [skolemisation 56,57]
120. ~brave(fred) | ~brave(X1) [cnf transformation 58]
151. brave(fred) [cnf transformation 24]
243. 19 <=> brave(fred) [avatar definition]
245. brave(fred) <- (19) [avatar component clause 243]
260. 23 <=> ! [X1] : ~brave(X1) [avatar definition]
261. ~brave(X1) <- (23) [avatar component clause 260]
262. 23 | ~19 [avatar split clause 120,243,260]
297. 19 [avatar split clause 151,243]
298. $false <- (19, 23) [subsumption resolution 245,261]
299. ~19 | ~23 [avatar contradiction clause 298]
300. $false [avatar sat refutation 262,297,299]
% SZS output end Proof for 557414839619652661861543
% ------------------------------
% 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 wise or curious then lucy is rich.
If someone is strong or not calm then alice is rich or generous and vice versa.
Everyone who is either not rich or happy is not tall or not kind and vice versa.
Everyone who is old or not old is both not kind and not happy.
If paul is both happy and not quiet then mary is brave or wise.
Everyone who is both creative and generous is curious.
If lucy is not humble or not generous then someone is either curious or not patient.
Everyone who is either not creative or rich is either not creative or wise.
If lucy is not happy or curious then lucy is both not kind and not brave.
If someone is not strong or old then someone is either not funny or strong and vice versa.
Everyone who is either not wise or not old is either brave or not funny and vice versa.
If paul is either not rich or not happy then someone is both old and not creative.
Everyone who is either not humble or tall is both quiet and not wise and vice versa.
If someone is not humble then susan is both not curious and happy.
If someone is patient then someone is rich or calm and vice versa.
Someone is patient.
Someone is quiet or generous.
Fred is kind or not rich.
Someone is either curious or not generous. | Susan is not creative. | contradiction | ((?[X]:((~wise(X)|curious(X))))=>(rich(lucy)))&
((?[X]:((strong(X)|~calm(X))))<=>((rich(alice)|generous(alice))))&
(![X]:((~rich(X)<~>happy(X))<=>(~tall(X)|~kind(X))))&
(![X]:((old(X)|~old(X))=>(~kind(X)&~happy(X))))&
(((happy(paul)&~quiet(paul)))=>((brave(mary)|wise(mary))))&
(![X]:((creative(X)&generous(X))=>curious(X)))&
(((~humble(lucy)|~generous(lucy)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~creative(X)<~>wise(X))))&
(((~happy(lucy)|curious(lucy)))=>((~kind(lucy)&~brave(lucy))))&
((?[X]:((~strong(X)|old(X))))<=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~wise(X)<~>~old(X))<=>(brave(X)<~>~funny(X))))&
(((~rich(paul)<~>~happy(paul)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~humble(X)<~>tall(X))<=>(quiet(X)&~wise(X))))&
((?[X]:(~humble(X)))=>((~curious(susan)&happy(susan))))&
((?[X]:(patient(X)))<=>(?[X]:((rich(X)|calm(X)))))&
(?[X]:(patient(X)))&
(?[X]:((quiet(X)|generous(X))))&
((kind(fred)|~rich(fred)))&
(?[X]:((curious(X)<~>~generous(X)))) | ~creative(susan) | [
"p0",
"p2",
"p3",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8864907374839085751555236
% SZS output start Proof for 8864907374839085751555236
1. ? [X0] : (curious(X0) | ~wise(X0)) => rich(lucy) [input p0]
3. ! [X0] : ((~rich(X0) <~> happy(X0)) <=> (~kind(X0) | ~tall(X0))) [input p2]
4. ! [X0] : ((~old(X0) | old(X0)) => (~happy(X0) & ~kind(X0))) [input p3]
8. ! [X0] : ((~creative(X0) <~> rich(X0)) => (~creative(X0) <~> wise(X0))) [input p7]
13. ! [X0] : ((~humble(X0) <~> tall(X0)) <=> (~wise(X0) & quiet(X0))) [input p12]
14. ? [X0] : ~humble(X0) => (happy(susan) & ~curious(susan)) [input p13]
20. ~creative(susan) [input hypothesis]
23. rich(lucy) | ! [X0] : (~curious(X0) & wise(X0)) [ennf transformation 1]
24. ! [X0] : ((~happy(X0) & ~kind(X0)) | (old(X0) & ~old(X0))) [ennf transformation 4]
30. ! [X0] : ((~creative(X0) <~> wise(X0)) | (~creative(X0) <=> rich(X0))) [ennf transformation 8]
33. (happy(susan) & ~curious(susan)) | ! [X0] : humble(X0) [ennf transformation 14]
39. ! [X0] : ((((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0))))) [flattening 39]
44. ! [X0] : (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) [nnf transformation 30]
54. ! [X0] : ((((~tall(X0) | humble(X0)) & (tall(X0) | ~humble(X0))) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | ((~humble(X0) | ~tall(X0)) & (tall(X0) | humble(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~tall(X0) | humble(X0)) & (tall(X0) | ~humble(X0))) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | ((~humble(X0) | ~tall(X0)) & (tall(X0) | humble(X0))))) [flattening 54]
68. rich(lucy) | wise(X0) [cnf transformation 23]
76. ~rich(X0) | happy(X0) | tall(X0) [cnf transformation 40]
77. ~rich(X0) | happy(X0) | kind(X0) [cnf transformation 40]
80. ~kind(X0) | ~old(X0) [cnf transformation 24]
81. ~kind(X0) | old(X0) [cnf transformation 24]
82. ~happy(X0) | ~old(X0) [cnf transformation 24]
83. ~happy(X0) | old(X0) [cnf transformation 24]
92. ~wise(X0) | creative(X0) | rich(X0) | creative(X0) [cnf transformation 44]
119. ~humble(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 55]
123. happy(susan) | humble(X0) [cnf transformation 33]
132. ~creative(susan) [cnf transformation 20]
134. ~wise(X0) | creative(X0) | rich(X0) [duplicate literal removal 92]
139. 2 <=> rich(lucy) [avatar definition]
141. rich(lucy) <- (2) [avatar component clause 139]
144. 3 <=> ! [X0] : wise(X0) [avatar definition]
145. wise(X0) <- (3) [avatar component clause 144]
146. 3 | 2 [avatar split clause 68,139,144]
173. ~happy(X0) [subsumption resolution 82,83]
174. ~kind(X0) [subsumption resolution 80,81]
256. humble(X0) [subsumption resolution 123,173]
309. happy(lucy) | kind(lucy) <- (2) [resolution 77,141]
311. kind(lucy) <- (2) [subsumption resolution 309,173]
312. $false <- (2) [subsumption resolution 311,174]
313. ~2 [avatar contradiction clause 312]
326. ~wise(X1) | ~tall(X1) [resolution 119,256]
327. ~tall(X1) <- (3) [subsumption resolution 326,145]
328. creative(X0) | rich(X0) <- (3) [resolution 134,145]
335. rich(susan) <- (3) [resolution 328,132]
340. happy(susan) | tall(susan) <- (3) [resolution 335,76]
344. tall(susan) <- (3) [subsumption resolution 340,173]
345. $false <- (3) [subsumption resolution 344,327]
346. ~3 [avatar contradiction clause 345]
347. $false [avatar sat refutation 146,313,346]
% SZS output end Proof for 8864907374839085751555236
% ------------------------------
% 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not brave is either not brave or old and vice versa.
Everyone who is tall or wise is both rich and curious and vice versa.
Everyone who is quiet or happy is either not happy or creative.
Everyone who is creative or not calm is both not generous and kind.
Everyone who is not happy is funny or not strong.
If someone is both creative and not quiet then mary is not generous and vice versa.
Everyone who is both not wise and kind is not generous and vice versa.
If someone is not humble or not calm then someone is tall or not old and vice versa.
Everyone who is not calm is both patient and not wise.
Everyone who is either not rich or happy is brave or strong and vice versa.
Everyone who is either not wise or kind is either not kind or creative and vice versa.
Everyone who is not calm is not generous.
Everyone who is either not funny or strong is both brave and old and vice versa.
If someone is not humble or old then alice is either kind or strong.
If paul is rich then alice is not calm.
If someone is not brave then alice is old or not old.
Someone is both not tall and patient.
Someone is either creative or rich.
Lucy is not strong or not tall.
Susan is either not humble or not quiet.
Lucy is either humble or curious.
Someone is rich or not generous.
Paul is quiet.
John is not brave or old. | Alice is not old. | contradiction | (![X]:((~generous(X)<~>~brave(X))<=>(~brave(X)<~>old(X))))&
(![X]:((tall(X)|wise(X))<=>(rich(X)&curious(X))))&
(![X]:((quiet(X)|happy(X))=>(~happy(X)<~>creative(X))))&
(![X]:((creative(X)|~calm(X))=>(~generous(X)&kind(X))))&
(![X]:(~happy(X)=>(funny(X)|~strong(X))))&
((?[X]:((creative(X)&~quiet(X))))<=>(~generous(mary)))&
(![X]:((~wise(X)&kind(X))<=>~generous(X)))&
((?[X]:((~humble(X)|~calm(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:(~calm(X)=>(patient(X)&~wise(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~kind(X)<~>creative(X))))&
(![X]:(~calm(X)=>~generous(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(brave(X)&old(X))))&
((?[X]:((~humble(X)|old(X))))=>((kind(alice)<~>strong(alice))))&
((rich(paul))=>(~calm(alice)))&
((?[X]:(~brave(X)))=>((old(alice)|~old(alice))))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((creative(X)<~>rich(X))))&
((~strong(lucy)|~tall(lucy)))&
((~humble(susan)<~>~quiet(susan)))&
((humble(lucy)<~>curious(lucy)))&
(?[X]:((rich(X)|~generous(X))))&
(quiet(paul))&
((~brave(john)|old(john))) | ~old(alice) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3097238019895854235800845
% SZS output start Proof for 3097238019895854235800845
1. ! [X0] : ((~generous(X0) <~> ~brave(X0)) <=> (~brave(X0) <~> old(X0))) [input p0]
3. ! [X0] : ((happy(X0) | quiet(X0)) => (~happy(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((~calm(X0) | creative(X0)) => (kind(X0) & ~generous(X0))) [input p3]
5. ! [X0] : (~happy(X0) => (~strong(X0) | funny(X0))) [input p4]
7. ! [X0] : ((kind(X0) & ~wise(X0)) <=> ~generous(X0)) [input p6]
8. ? [X0] : (~calm(X0) | ~humble(X0)) <=> ? [X0] : (~old(X0) | tall(X0)) [input p7]
11. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (~kind(X0) <~> creative(X0))) [input p10]
13. ! [X0] : ((~funny(X0) <~> strong(X0)) <=> (old(X0) & brave(X0))) [input p12]
14. ? [X0] : (old(X0) | ~humble(X0)) => (kind(alice) <~> strong(alice)) [input p13]
25. ~old(alice) [input hypothesis]
26. ? [X0] : (~calm(X0) | ~humble(X0)) <=> ? [X1] : (~old(X1) | tall(X1)) [rectify 8]
29. ! [X0] : ((~happy(X0) <~> creative(X0)) | (~happy(X0) & ~quiet(X0))) [ennf transformation 3]
30. ! [X0] : ((kind(X0) & ~generous(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 4]
31. ! [X0] : ((~strong(X0) | funny(X0)) | happy(X0)) [ennf transformation 5]
32. ! [X0] : (~strong(X0) | funny(X0) | happy(X0)) [flattening 31]
35. (kind(alice) <~> strong(alice)) | ! [X0] : (~old(X0) & humble(X0)) [ennf transformation 14]
39. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [nnf transformation 1]
42. ! [X0] : (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~happy(X0) & ~quiet(X0))) [nnf transformation 29]
47. ! [X0] : (((kind(X0) & ~wise(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | wise(X0)))) [nnf transformation 7]
48. ! [X0] : (((kind(X0) & ~wise(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | wise(X0))) [flattening 47]
49. (? [X0] : (~calm(X0) | ~humble(X0)) | ! [X1] : (old(X1) & ~tall(X1))) & (? [X1] : (~old(X1) | tall(X1)) | ! [X0] : (calm(X0) & humble(X0))) [nnf transformation 26]
50. (? [X0] : (~calm(X0) | ~humble(X0)) | ! [X1] : (old(X1) & ~tall(X1))) & (? [X2] : (~old(X2) | tall(X2)) | ! [X3] : (calm(X3) & humble(X3))) [rectify 49]
51. ? [X0] : (~calm(X0) | ~humble(X0)) => (~calm(sK1) | ~humble(sK1)) [choice axiom]
52. ? [X2] : (~old(X2) | tall(X2)) => (~old(sK2) | tall(sK2)) [choice axiom]
53. ((~calm(sK1) | ~humble(sK1)) | ! [X1] : (old(X1) & ~tall(X1))) & ((~old(sK2) | tall(sK2)) | ! [X3] : (calm(X3) & humble(X3))) [skolemisation 50,52,51]
56. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 11]
57. ! [X0] : ((((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0))))) [nnf transformation 13]
58. ! [X0] : ((((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0))))) [flattening 57]
59. ((~strong(alice) | ~kind(alice)) & (strong(alice) | kind(alice))) | ! [X0] : (~old(X0) & humble(X0)) [nnf transformation 35]
69. old(X0) | ~brave(X0) | ~brave(X0) | generous(X0) [cnf transformation 39]
75. brave(X0) | generous(X0) | old(X0) | brave(X0) [cnf transformation 39]
83. creative(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 42]
86. ~creative(X0) | ~generous(X0) [cnf transformation 30]
87. ~generous(X0) | calm(X0) [cnf transformation 30]
88. ~creative(X0) | kind(X0) [cnf transformation 30]
90. ~strong(X0) | funny(X0) | happy(X0) [cnf transformation 32]
94. ~kind(X0) | ~generous(X0) | wise(X0) [cnf transformation 48]
100. ~calm(sK1) | ~humble(sK1) | old(X1) [cnf transformation 53]
109. creative(X0) | ~kind(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 56]
112. kind(X0) | ~wise(X0) | creative(X0) | kind(X0) [cnf transformation 56]
120. ~strong(X0) | ~funny(X0) | old(X0) [cnf transformation 58]
123. strong(alice) | kind(alice) | humble(X0) [cnf transformation 59]
124. strong(alice) | kind(alice) | ~old(X0) [cnf transformation 59]
140. ~old(alice) [cnf transformation 25]
141. creative(X0) | ~kind(X0) | ~wise(X0) [duplicate literal removal 109]
143. kind(X0) | ~wise(X0) | creative(X0) [duplicate literal removal 112]
145. ~happy(X0) | creative(X0) [duplicate literal removal 83]
146. old(X0) | ~brave(X0) | generous(X0) [duplicate literal removal 69]
149. brave(X0) | generous(X0) | old(X0) [duplicate literal removal 75]
151. old(X0) | generous(X0) [subsumption resolution 146,149]
171. 5 <=> ! [X1] : old(X1) [avatar definition]
172. old(X1) <- (5) [avatar component clause 171]
174. 6 <=> humble(sK1) [avatar definition]
176. ~humble(sK1) <- (~6) [avatar component clause 174]
178. 7 <=> calm(sK1) [avatar definition]
180. ~calm(sK1) <- (~7) [avatar component clause 178]
181. 5 | ~6 | ~7 [avatar split clause 100,178,174,171]
187. 9 <=> ! [X3] : calm(X3) [avatar definition]
188. calm(X3) <- (9) [avatar component clause 187]
199. 12 <=> ! [X3] : humble(X3) [avatar definition]
200. humble(X3) <- (12) [avatar component clause 199]
203. ~wise(X0) | kind(X0) [subsumption resolution 143,88]
204. ~wise(X0) | creative(X0) [subsumption resolution 141,203]
206. 13 <=> ! [X0] : ~old(X0) [avatar definition]
207. ~old(X0) <- (13) [avatar component clause 206]
209. 14 <=> kind(alice) [avatar definition]
210. kind(alice) <- (14) [avatar component clause 209]
213. 15 <=> strong(alice) [avatar definition]
214. strong(alice) <- (15) [avatar component clause 213]
218. 13 | 14 | 15 [avatar split clause 124,213,209,206]
219. 12 | 14 | 15 [avatar split clause 123,213,209,199]
286. $false <- (~6, 12) [subsumption resolution 176,200]
287. 6 | ~12 [avatar contradiction clause 286]
292. generous(alice) [resolution 151,140]
294. generous(X1) <- (13) [resolution 151,207]
301. calm(X0) <- (13) [resolution 294,87]
310. 9 | ~13 [avatar split clause 301,206,187]
333. ~generous(alice) | wise(alice) <- (14) [resolution 94,210]
334. wise(alice) <- (14) [subsumption resolution 333,292]
335. creative(alice) <- (14) [resolution 334,204]
355. ~generous(alice) <- (14) [resolution 335,86]
361. 33 <=> happy(alice) [avatar definition]
363. happy(alice) <- (33) [avatar component clause 361]
366. $false <- (14) [subsumption resolution 355,292]
367. ~14 [avatar contradiction clause 366]
371. funny(alice) | happy(alice) <- (15) [resolution 214,90]
378. 35 <=> funny(alice) [avatar definition]
381. 33 | 35 | ~15 [avatar split clause 371,213,378,361]
382. $false <- (~7, 9) [resolution 188,180]
383. 7 | ~9 [avatar contradiction clause 382]
424. creative(alice) <- (33) [resolution 363,145]
425. ~funny(alice) | old(alice) <- (15) [resolution 120,214]
433. ~generous(alice) <- (33) [resolution 424,86]
437. $false <- (33) [subsumption resolution 433,292]
438. ~33 [avatar contradiction clause 437]
441. ~funny(alice) <- (15) [subsumption resolution 425,140]
442. ~35 | ~15 [avatar split clause 441,213,378]
443. $false <- (5, 13) [subsumption resolution 172,207]
444. ~5 | ~13 [avatar contradiction clause 443]
445. $false [avatar sat refutation 181,218,219,287,310,367,381,383,438,442,444]
% SZS output end Proof for 3097238019895854235800845
% ------------------------------
% 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then mary is kind or old and vice versa. Everyone who is not old is both patient and not tall. Everyone who is not happy is both wise and not funny. Everyone who is brave is wise or patient and vice versa. If someone is either humble or funny then someone is patient or not brave. If susan is brave or not rich then someone is not brave or not kind. Everyone who is not strong or funny is not wise or happy and vice versa. Everyone who is either not patient or not quiet is either quiet or happy and vice versa. If susan is either not generous or not humble then someone is not wise and vice versa. If someone is both patient and not tall then someone is not strong and vice versa. If someone is either not tall or curious then someone is not old or strong and vice versa. If paul is brave or generous then alice is either not curious or not humble. Everyone who is both brave and strong is either funny or not creative and vice versa. Everyone who is creative or not quiet is both old and not creative and vice versa. If someone is not curious then someone is generous and vice versa. Someone is both brave and not patient. Lucy is either not humble or generous. Someone is either humble or quiet. Someone is both wise and not happy. Someone is brave. Lucy is either generous or not tall. Someone is not rich. John is not calm. | Mary is brave. | entailment | ((?[X]:(~kind(X)))<=>((kind(mary)|old(mary))))&
(![X]:(~old(X)=>(patient(X)&~tall(X))))&
(![X]:(~happy(X)=>(wise(X)&~funny(X))))&
(![X]:(brave(X)<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((brave(susan)|~rich(susan)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)|funny(X))<=>(~wise(X)|happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(quiet(X)<~>happy(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((brave(paul)|generous(paul)))=>((~curious(alice)<~>~humble(alice))))&
(![X]:((brave(X)&strong(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~quiet(X))<=>(old(X)&~creative(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(generous(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~humble(lucy)<~>generous(lucy)))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:(brave(X)))&
((generous(lucy)<~>~tall(lucy)))&
(?[X]:(~rich(X)))&
(~calm(john)) | brave(mary) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2433755267944732037303073
% SZS output start Proof for 2433755267944732037303073
3. ! [X0] : (~happy(X0) => (~funny(X0) & wise(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (patient(X0) | wise(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (quiet(X0) <~> happy(X0))) [input p7]
24. ~brave(mary) [input hypothesis]
31. ! [X0] : ((~funny(X0) & wise(X0)) | happy(X0)) [ennf transformation 3]
40. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ~brave(X0))) [nnf transformation 4]
41. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~brave(X0))) [flattening 40]
50. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 8]
93. wise(X0) | happy(X0) [cnf transformation 31]
96. ~wise(X0) | brave(X0) [cnf transformation 41]
97. ~patient(X0) | brave(X0) [cnf transformation 41]
108. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 50]
113. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 50]
156. ~brave(mary) [cnf transformation 24]
160. ~happy(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 108]
162. ~happy(X0) | patient(X0) | quiet(X0) [duplicate literal removal 113]
216. ~happy(X0) | patient(X0) [subsumption resolution 160,162]
368. brave(X0) | happy(X0) [resolution 96,93]
416. happy(mary) [resolution 368,156]
421. patient(mary) [resolution 416,216]
528. brave(mary) [resolution 421,97]
529. $false [subsumption resolution 528,156]
% SZS output end Proof for 2433755267944732037303073
% ------------------------------
% 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or not happy then someone is both curious and strong and vice versa.
Everyone who is generous is both rich and humble.
If lucy is rich then someone is both not calm and not kind and vice versa.
If someone is not wise then someone is curious or not brave and vice versa.
Everyone who is not wise is both kind and quiet.
Everyone who is not quiet or not happy is calm or happy and vice versa.
Everyone who is both not strong and not tall is both strong and brave and vice versa.
If someone is tall or generous then susan is happy.
Everyone who is not happy is not patient or happy.
Everyone who is either wise or not patient is not quiet.
If someone is both not tall and patient then someone is both not old and not funny.
If someone is both not funny and kind then fred is both not quiet and not kind and vice versa.
Everyone who is not strong is happy or not generous and vice versa.
Everyone who is both quiet and humble is both not calm and not rich.
If john is either not generous or humble then susan is either not humble or not kind.
If paul is both strong and not kind then someone is generous.
Alice is not quiet or not kind.
Someone is either not creative or rich.
Someone is either brave or curious.
Alice is brave or calm.
Lucy is not quiet or not generous.
Alice is kind or not old.
Someone is tall. | Paul is not strong. | entailment | ((?[X]:((strong(X)<~>~happy(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(generous(X)=>(rich(X)&humble(X))))&
((rich(lucy))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(~wise(X)=>(kind(X)&quiet(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&~tall(X))<=>(strong(X)&brave(X))))&
((?[X]:((tall(X)|generous(X))))=>(happy(susan)))&
(![X]:(~happy(X)=>(~patient(X)|happy(X))))&
(![X]:((wise(X)<~>~patient(X))=>~quiet(X)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((~funny(X)&kind(X))))<=>((~quiet(fred)&~kind(fred))))&
(![X]:(~strong(X)<=>(happy(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>(~calm(X)&~rich(X))))&
(((~generous(john)<~>humble(john)))=>((~humble(susan)<~>~kind(susan))))&
(((strong(paul)&~kind(paul)))=>(?[X]:(generous(X))))&
((~quiet(alice)|~kind(alice)))&
(?[X]:((~creative(X)<~>rich(X))))&
(?[X]:((brave(X)<~>curious(X))))&
((brave(alice)|calm(alice)))&
((~quiet(lucy)|~generous(lucy)))&
((kind(alice)|~old(alice)))&
(?[X]:(tall(X))) | ~strong(paul) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6202498764819787328614090
% SZS output start Proof for 6202498764819787328614090
4. ? [X0] : ~wise(X0) <=> ? [X0] : (~brave(X0) | curious(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (quiet(X0) & kind(X0))) [input p4]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (happy(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (brave(X0) & strong(X0))) [input p6]
9. ! [X0] : (~happy(X0) => (happy(X0) | ~patient(X0))) [input p8]
10. ! [X0] : ((wise(X0) <~> ~patient(X0)) => ~quiet(X0)) [input p9]
24. strong(paul) [input hypothesis]
26. ? [X0] : ~wise(X0) <=> ? [X1] : (~brave(X1) | curious(X1)) [rectify 4]
31. ! [X0] : ((quiet(X0) & kind(X0)) | wise(X0)) [ennf transformation 5]
33. ! [X0] : ((happy(X0) | ~patient(X0)) | happy(X0)) [ennf transformation 9]
34. ! [X0] : (happy(X0) | ~patient(X0) | happy(X0)) [flattening 33]
35. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~patient(X0))) [ennf transformation 10]
51. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X1] : (~brave(X1) | curious(X1)) | ! [X0] : wise(X0)) [nnf transformation 26]
52. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X2] : (~brave(X2) | curious(X2)) | ! [X3] : wise(X3)) [rectify 51]
53. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
54. ? [X2] : (~brave(X2) | curious(X2)) => (~brave(sK4) | curious(sK4)) [choice axiom]
55. (~wise(sK3) | ! [X1] : (brave(X1) & ~curious(X1))) & ((~brave(sK4) | curious(sK4)) | ! [X3] : wise(X3)) [skolemisation 52,54,53]
56. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
57. ! [X0] : ((~happy(X0) | ~quiet(X0) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | (happy(X0) & quiet(X0)))) [flattening 56]
58. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 7]
59. ! [X0] : (((~tall(X0) & ~strong(X0)) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | tall(X0) | strong(X0))) [flattening 58]
60. ! [X0] : (~quiet(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) [nnf transformation 35]
95. ~wise(sK3) | brave(X1) [cnf transformation 55]
97. quiet(X0) | wise(X0) [cnf transformation 31]
101. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 57]
104. ~strong(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 59]
108. happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 34]
110. ~quiet(X0) | wise(X0) | patient(X0) [cnf transformation 60]
134. strong(paul) [cnf transformation 24]
135. ~patient(X0) | happy(X0) [duplicate literal removal 108]
137. ~brave(X0) | ~strong(X0) [duplicate literal removal 104]
139. ~quiet(X0) | ~happy(X0) [duplicate literal removal 101]
190. 12 <=> ! [X1] : brave(X1) [avatar definition]
191. brave(X1) <- (12) [avatar component clause 190]
193. 13 <=> wise(sK3) [avatar definition]
195. ~wise(sK3) <- (~13) [avatar component clause 193]
196. 12 | ~13 [avatar split clause 95,193,190]
202. 15 <=> ! [X3] : wise(X3) [avatar definition]
203. wise(X3) <- (15) [avatar component clause 202]
225. patient(X0) | wise(X0) [subsumption resolution 110,97]
283. 32 <=> strong(paul) [avatar definition]
284. strong(paul) <- (32) [avatar component clause 283]
342. 32 [avatar split clause 134,283]
351. ~happy(X0) | wise(X0) [resolution 139,97]
364. wise(X0) | happy(X0) [resolution 225,135]
365. wise(X0) [subsumption resolution 364,351]
366. 15 [avatar split clause 365,202]
367. $false <- (~13, 15) [resolution 203,195]
368. 13 | ~15 [avatar contradiction clause 367]
370. ~strong(X0) <- (12) [resolution 191,137]
379. $false <- (12, 32) [resolution 370,284]
382. ~12 | ~32 [avatar contradiction clause 379]
383. $false [avatar sat refutation 196,342,366,368,382]
% SZS output end Proof for 6202498764819787328614090
% ------------------------------
% 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 creative or old is both not patient and quiet and vice versa.
Everyone who is not happy is humble.
Everyone who is either quiet or not creative is not tall or not brave.
If john is not calm or brave then someone is either not brave or generous and vice versa.
If fred is both not strong and tall then someone is humble and vice versa.
If someone is both funny and wise then mary is either not creative or not happy and vice versa.
Everyone who is not generous or old is either not wise or rich.
Everyone who is calm is kind or tall.
Everyone who is not happy or patient is either not generous or tall.
Everyone who is both humble and not wise is either not funny or rich and vice versa.
If alice is both not calm and not patient then someone is not rich and vice versa.
If fred is both old and rich then mary is rich or not tall.
Everyone who is either kind or happy is both not calm and not tall.
If someone is calm then someone is both old and not patient and vice versa.
Everyone who is not wise is either generous or not calm.
Everyone who is either curious or not old is not curious and vice versa.
Paul is either not patient or not creative.
Someone is either not happy or generous.
Someone is not brave or not happy.
Someone is either wise or tall.
Someone is calm or not old.
Lucy is creative or not curious.
Someone is patient.
Someone is old or not strong. | Lucy is calm. | contradiction | (![X]:((creative(X)|old(X))<=>(~patient(X)&quiet(X))))&
(![X]:(~happy(X)=>humble(X)))&
(![X]:((quiet(X)<~>~creative(X))=>(~tall(X)|~brave(X))))&
(((~calm(john)|brave(john)))<=>(?[X]:((~brave(X)<~>generous(X)))))&
(((~strong(fred)&tall(fred)))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&wise(X))))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:((~generous(X)|old(X))=>(~wise(X)<~>rich(X))))&
(![X]:(calm(X)=>(kind(X)|tall(X))))&
(![X]:((~happy(X)|patient(X))=>(~generous(X)<~>tall(X))))&
(![X]:((humble(X)&~wise(X))<=>(~funny(X)<~>rich(X))))&
(((~calm(alice)&~patient(alice)))<=>(?[X]:(~rich(X))))&
(((old(fred)&rich(fred)))=>((rich(mary)|~tall(mary))))&
(![X]:((kind(X)<~>happy(X))=>(~calm(X)&~tall(X))))&
((?[X]:(calm(X)))<=>(?[X]:((old(X)&~patient(X)))))&
(![X]:(~wise(X)=>(generous(X)<~>~calm(X))))&
(![X]:((curious(X)<~>~old(X))<=>~curious(X)))&
((~patient(paul)<~>~creative(paul)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((~brave(X)|~happy(X))))&
(?[X]:((wise(X)<~>tall(X))))&
(?[X]:((calm(X)|~old(X))))&
((creative(lucy)|~curious(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((old(X)|~strong(X)))) | calm(lucy) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7671758852839717817807343
% SZS output start Proof for 7671758852839717817807343
14. ? [X0] : calm(X0) <=> ? [X0] : (~patient(X0) & old(X0)) [input p13]
16. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> ~curious(X0)) [input p15]
25. calm(lucy) [input hypothesis]
26. ? [X0] : calm(X0) <=> ? [X1] : (~patient(X1) & old(X1)) [rectify 14]
65. (? [X0] : calm(X0) | ! [X1] : (patient(X1) | ~old(X1))) & (? [X1] : (~patient(X1) & old(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 26]
66. (? [X0] : calm(X0) | ! [X1] : (patient(X1) | ~old(X1))) & (? [X2] : (~patient(X2) & old(X2)) | ! [X3] : ~calm(X3)) [rectify 65]
67. ? [X0] : calm(X0) => calm(sK4) [choice axiom]
68. ? [X2] : (~patient(X2) & old(X2)) => (~patient(sK5) & old(sK5)) [choice axiom]
69. (calm(sK4) | ! [X1] : (patient(X1) | ~old(X1))) & ((~patient(sK5) & old(sK5)) | ! [X3] : ~calm(X3)) [skolemisation 66,68,67]
71. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | curious(X0)) & (~curious(X0) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 16]
133. old(sK5) | ~calm(X3) [cnf transformation 69]
138. ~curious(X0) | ~old(X0) | ~curious(X0) [cnf transformation 71]
140. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 71]
153. calm(lucy) [cnf transformation 25]
154. ~curious(X0) | ~old(X0) [duplicate literal removal 138]
155. ~old(X0) | curious(X0) [duplicate literal removal 140]
266. 24 <=> ! [X1] : ~old(X1) [avatar definition]
267. ~old(X1) <- (24) [avatar component clause 266]
274. 26 <=> ! [X3] : ~calm(X3) [avatar definition]
275. ~calm(X3) <- (26) [avatar component clause 274]
282. 28 <=> old(sK5) [avatar definition]
284. old(sK5) <- (28) [avatar component clause 282]
285. 26 | 28 [avatar split clause 133,282,274]
286. ~old(X0) [subsumption resolution 154,155]
287. 24 [avatar split clause 286,266]
353. $false <- (26) [resolution 275,153]
354. ~26 [avatar contradiction clause 353]
355. $false <- (24, 28) [subsumption resolution 284,267]
356. ~24 | ~28 [avatar contradiction clause 355]
357. $false [avatar sat refutation 285,287,354,356]
% SZS output end Proof for 7671758852839717817807343
% ------------------------------
% 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 kind is generous and vice versa.
If someone is rich then someone is not funny.
Everyone who is both not calm and not generous is not brave or quiet.
If alice is either not wise or strong then paul is both brave and creative.
Everyone who is both calm and patient is both not generous and not patient.
Everyone who is kind or not strong is both quiet and not happy.
If mary is not old or strong then someone is not brave or tall and vice versa.
If alice is either calm or not curious then john is strong.
If alice is happy then someone is either not kind or patient and vice versa.
Everyone who is both happy and generous is both happy and curious and vice versa.
Everyone who is either wise or not humble is both humble and not patient.
Everyone who is either funny or strong is either not tall or funny.
Everyone who is not happy is brave.
Everyone who is not strong or not quiet is both rich and happy.
Everyone who is both calm and not curious is either strong or kind and vice versa.
If mary is not funny then mary is either not humble or creative.
Someone is rich.
Someone is either not wise or not strong.
Someone is wise.
Someone is not quiet or creative.
Alice is either not wise or not creative.
Mary is not creative or not old.
Susan is both not generous and not humble. | Mary is not patient. | entailment | (![X]:(~kind(X)<=>generous(X)))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)&~generous(X))=>(~brave(X)|quiet(X))))&
(((~wise(alice)<~>strong(alice)))=>((brave(paul)&creative(paul))))&
(![X]:((calm(X)&patient(X))=>(~generous(X)&~patient(X))))&
(![X]:((kind(X)|~strong(X))=>(quiet(X)&~happy(X))))&
(((~old(mary)|strong(mary)))<=>(?[X]:((~brave(X)|tall(X)))))&
(((calm(alice)<~>~curious(alice)))=>(strong(john)))&
((happy(alice))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((happy(X)&generous(X))<=>(happy(X)&curious(X))))&
(![X]:((wise(X)<~>~humble(X))=>(humble(X)&~patient(X))))&
(![X]:((funny(X)<~>strong(X))=>(~tall(X)<~>funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((~strong(X)|~quiet(X))=>(rich(X)&happy(X))))&
(![X]:((calm(X)&~curious(X))<=>(strong(X)<~>kind(X))))&
((~funny(mary))=>((~humble(mary)<~>creative(mary))))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|creative(X))))&
((~wise(alice)<~>~creative(alice)))&
((~creative(mary)|~old(mary)))&
((~generous(susan)&~humble(susan))) | ~patient(mary) | [
"p0",
"p4",
"p5",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1567930272204362067525973
% SZS output start Proof for 1567930272204362067525973
1. ! [X0] : (~kind(X0) <=> generous(X0)) [input p0]
5. ! [X0] : ((patient(X0) & calm(X0)) => (~patient(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~strong(X0) | kind(X0)) => (~happy(X0) & quiet(X0))) [input p5]
9. happy(alice) <=> ? [X0] : (~kind(X0) <~> patient(X0)) [input p8]
10. ! [X0] : ((generous(X0) & happy(X0)) <=> (curious(X0) & happy(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) | ~strong(X0)) => (happy(X0) & rich(X0))) [input p13]
15. ! [X0] : ((~curious(X0) & calm(X0)) <=> (strong(X0) <~> kind(X0))) [input p14]
24. patient(mary) [input hypothesis]
30. ! [X0] : ((~patient(X0) & ~generous(X0)) | (~patient(X0) | ~calm(X0))) [ennf transformation 5]
31. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~patient(X0) | ~calm(X0)) [flattening 30]
32. ! [X0] : ((~happy(X0) & quiet(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 6]
37. ! [X0] : ((happy(X0) & rich(X0)) | (quiet(X0) & strong(X0))) [ennf transformation 14]
39. ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))) [nnf transformation 1]
50. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (? [X0] : ((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | ~happy(alice)) [nnf transformation 9]
51. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (? [X1] : ((~patient(X1) | kind(X1)) & (patient(X1) | ~kind(X1))) | ~happy(alice)) [rectify 50]
52. ? [X1] : ((~patient(X1) | kind(X1)) & (patient(X1) | ~kind(X1))) => ((~patient(sK2) | kind(sK2)) & (patient(sK2) | ~kind(sK2))) [choice axiom]
53. (happy(alice) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(sK2) | kind(sK2)) & (patient(sK2) | ~kind(sK2))) | ~happy(alice)) [skolemisation 51,52]
54. ! [X0] : (((generous(X0) & happy(X0)) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 10]
55. ! [X0] : (((generous(X0) & happy(X0)) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | ~generous(X0) | ~happy(X0))) [flattening 54]
58. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (curious(X0) | ~calm(X0)))) [nnf transformation 15]
59. ! [X0] : (((~curious(X0) & calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | curious(X0) | ~calm(X0))) [flattening 58]
71. generous(X0) | kind(X0) [cnf transformation 39]
80. ~patient(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 31]
83. ~happy(X0) | ~kind(X0) [cnf transformation 32]
84. ~happy(X0) | strong(X0) [cnf transformation 32]
94. happy(alice) | ~kind(X0) | ~patient(X0) [cnf transformation 53]
96. ~happy(X0) | ~generous(X0) | curious(X0) [cnf transformation 55]
110. happy(X0) | strong(X0) [cnf transformation 37]
114. calm(X0) | kind(X0) | ~strong(X0) [cnf transformation 59]
116. ~curious(X0) | kind(X0) | ~strong(X0) [cnf transformation 59]
130. patient(mary) [cnf transformation 24]
134. ~patient(X0) | ~calm(X0) [duplicate literal removal 80]
190. 13 <=> curious(alice) [avatar definition]
191. ~curious(alice) <- (~13) [avatar component clause 190]
192. curious(alice) <- (13) [avatar component clause 190]
204. 16 <=> ! [X0] : (~kind(X0) | ~patient(X0)) [avatar definition]
205. ~patient(X0) | ~kind(X0) <- (16) [avatar component clause 204]
207. 17 <=> happy(alice) [avatar definition]
209. happy(alice) <- (17) [avatar component clause 207]
210. 16 | 17 [avatar split clause 94,207,204]
225. strong(X0) [subsumption resolution 110,84]
226. ~curious(X0) | kind(X0) [subsumption resolution 116,225]
227. calm(X0) | kind(X0) [subsumption resolution 114,225]
265. ~kind(alice) <- (17) [resolution 83,209]
274. ~calm(mary) [resolution 134,130]
275. kind(alice) <- (13) [resolution 226,192]
276. $false <- (13, 17) [subsumption resolution 275,265]
277. ~13 | ~17 [avatar contradiction clause 276]
278. kind(mary) [resolution 227,274]
280. ~generous(alice) | curious(alice) <- (17) [resolution 96,209]
283. ~generous(alice) <- (~13, 17) [subsumption resolution 280,191]
284. kind(alice) <- (~13, 17) [resolution 283,71]
285. $false <- (~13, 17) [subsumption resolution 284,265]
286. 13 | ~17 [avatar contradiction clause 285]
289. ~kind(mary) <- (16) [resolution 205,130]
290. $false <- (16) [subsumption resolution 289,278]
291. ~16 [avatar contradiction clause 290]
292. $false [avatar sat refutation 210,277,286,291]
% SZS output end Proof for 1567930272204362067525973
% ------------------------------
% 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 creative is both old and not rich.
Everyone who is either funny or not humble is not humble.
Everyone who is rich is both patient and wise.
Everyone who is funny or not funny is either not strong or rich.
If someone is both not patient and not happy then someone is curious or happy and vice versa.
Everyone who is either tall or not creative is either not kind or not old.
Everyone who is either not humble or not kind is either kind or not happy and vice versa.
Everyone who is both curious and not wise is either calm or old.
Everyone who is tall is either not rich or wise.
If someone is either not brave or not curious then mary is strong and vice versa.
If someone is not curious then susan is not wise or creative.
Everyone who is not rich or not wise is not funny.
Everyone who is patient is either not strong or not wise and vice versa.
Everyone who is both not old and happy is patient.
Everyone who is both happy and not tall is not calm or not quiet and vice versa.
Alice is kind.
Mary is either generous or creative.
John is either not creative or patient.
Someone is not funny or not strong.
John is calm.
Mary is not strong or not funny.
Someone is both humble and not kind.
Alice is either not rich or old. | Alice is funny. | contradiction | (![X]:(~creative(X)=>(old(X)&~rich(X))))&
(![X]:((funny(X)<~>~humble(X))=>~humble(X)))&
(![X]:(rich(X)=>(patient(X)&wise(X))))&
(![X]:((funny(X)|~funny(X))=>(~strong(X)<~>rich(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:((tall(X)<~>~creative(X))=>(~kind(X)<~>~old(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((curious(X)&~wise(X))=>(calm(X)<~>old(X))))&
(![X]:(tall(X)=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(strong(mary)))&
((?[X]:(~curious(X)))=>((~wise(susan)|creative(susan))))&
(![X]:((~rich(X)|~wise(X))=>~funny(X)))&
(![X]:(patient(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:((~old(X)&happy(X))=>patient(X)))&
(![X]:((happy(X)&~tall(X))<=>(~calm(X)|~quiet(X))))&
(kind(alice))&
((generous(mary)<~>creative(mary)))&
((~creative(john)<~>patient(john)))&
(?[X]:((~funny(X)|~strong(X))))&
(calm(john))&
((~strong(mary)|~funny(mary)))&
(?[X]:((humble(X)&~kind(X))))&
((~rich(alice)<~>old(alice))) | funny(alice) | [
"p2",
"p3",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6886085953787690156684572
% SZS output start Proof for 6886085953787690156684572
3. ! [X0] : (rich(X0) => (wise(X0) & patient(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | funny(X0)) => (~strong(X0) <~> rich(X0))) [input p3]
12. ! [X0] : ((~wise(X0) | ~rich(X0)) => ~funny(X0)) [input p11]
13. ! [X0] : (patient(X0) <=> (~strong(X0) <~> ~wise(X0))) [input p12]
24. funny(alice) [input hypothesis]
28. ! [X0] : ((wise(X0) & patient(X0)) | ~rich(X0)) [ennf transformation 3]
29. ! [X0] : ((~strong(X0) <~> rich(X0)) | (funny(X0) & ~funny(X0))) [ennf transformation 4]
36. ! [X0] : (~funny(X0) | (wise(X0) & rich(X0))) [ennf transformation 12]
40. ! [X0] : (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | (funny(X0) & ~funny(X0))) [nnf transformation 29]
54. ! [X0] : ((patient(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | ~patient(X0))) [nnf transformation 13]
68. ~rich(X0) | patient(X0) [cnf transformation 28]
69. ~rich(X0) | wise(X0) [cnf transformation 28]
72. ~rich(X0) | strong(X0) | ~funny(X0) [cnf transformation 40]
73. ~rich(X0) | strong(X0) | funny(X0) [cnf transformation 40]
100. ~funny(X0) | rich(X0) [cnf transformation 36]
102. ~strong(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 54]
124. funny(alice) [cnf transformation 24]
130. ~rich(X0) | strong(X0) [subsumption resolution 72,73]
235. 23 <=> rich(alice) [avatar definition]
237. rich(alice) <- (23) [avatar component clause 235]
245. rich(alice) [resolution 100,124]
248. 23 [avatar split clause 245,235]
249. wise(alice) <- (23) [resolution 237,69]
250. patient(alice) <- (23) [resolution 237,68]
254. strong(alice) <- (23) [resolution 130,237]
291. ~wise(alice) | ~patient(alice) <- (23) [resolution 102,254]
292. ~patient(alice) <- (23) [subsumption resolution 291,249]
293. $false <- (23) [subsumption resolution 292,250]
294. ~23 [avatar contradiction clause 293]
295. $false [avatar sat refutation 248,294]
% SZS output end Proof for 6886085953787690156684572
% ------------------------------
% 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 |
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