premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If susan is not humble then lucy is either strong or rich and vice versa.
If someone is funny then someone is patient or wise.
Everyone who is either not humble or not quiet is calm or not strong and vice versa.
Everyone who is humble or not calm is not happy or not wise.
Everyone who is not quiet or wise is curious or not tall.
If someone is not quiet or calm then someone is happy or funny.
Everyone who is not strong is not rich and vice versa.
Everyone who is not humble is brave.
Everyone who is wise or not kind is not patient and vice versa.
Everyone who is creative is patient.
If someone is not generous or rich then someone is not patient or not funny.
Everyone who is either quiet or not happy is generous or not generous and vice versa.
Everyone who is curious or not patient is both not happy and happy and vice versa.
Everyone who is quiet is not wise or not curious.
If someone is not creative or quiet then someone is both happy and calm and vice versa.
Everyone who is not calm or not quiet is happy.
Someone is not wise.
Someone is both happy and not funny.
Alice is patient.
Someone is not brave.
Paul is both old and not wise.
Mary is generous or not wise. | Lucy is old. | neutral | ((~humble(susan))<=>((strong(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(calm(X)|~strong(X))))&
(![X]:((humble(X)|~calm(X))=>(~happy(X)|~wise(X))))&
(![X]:((~quiet(X)|wise(X))=>(curious(X)|~tall(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((happy(X)|funny(X)))))&
(![X]:(~strong(X)<=>~rich(X)))&
(![X]:(~humble(X)=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((curious(X)|~patient(X))<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~wise(X)|~curious(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~calm(X)|~quiet(X))=>happy(X)))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)&~funny(X))))&
(patient(alice))&
(?[X]:(~brave(X)))&
((old(paul)&~wise(paul)))&
((generous(mary)|~wise(mary))) | old(lucy) | [] | null | 0 |
Everyone who is either tall or quiet is either wise or not creative and vice versa.
Everyone who is either old or strong is strong and vice versa.
Everyone who is not curious or not creative is patient or not generous and vice versa.
Everyone who is rich or patient is not funny.
Everyone who is both not wise and not generous is funny and vice versa.
Everyone who is either not rich or humble is both not tall and quiet.
If someone is creative or not old then lucy is both not kind and wise and vice versa.
Everyone who is both creative and happy is both not kind and patient and vice versa.
If mary is either not rich or not creative then susan is not kind and vice versa.
If john is not funny then lucy is both tall and calm.
Everyone who is both generous and not brave is funny or calm and vice versa.
If someone is quiet then susan is not patient.
If lucy is both not patient and not brave then someone is humble or happy.
If susan is creative or not wise then john is rich or not rich.
If mary is either not kind or curious then someone is either old or creative.
Everyone who is brave or kind is either rich or not humble.
Susan is both happy and not kind.
Someone is either not curious or not creative.
Lucy is either not curious or wise.
Someone is not wise.
John is not strong.
Someone is curious or not happy.
Susan is not strong. | Mary is tall. | neutral | (![X]:((tall(X)<~>quiet(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((old(X)<~>strong(X))<=>strong(X)))&
(![X]:((~curious(X)|~creative(X))<=>(patient(X)|~generous(X))))&
(![X]:((rich(X)|patient(X))=>~funny(X)))&
(![X]:((~wise(X)&~generous(X))<=>funny(X)))&
(![X]:((~rich(X)<~>humble(X))=>(~tall(X)&quiet(X))))&
((?[X]:((creative(X)|~old(X))))<=>((~kind(lucy)&wise(lucy))))&
(![X]:((creative(X)&happy(X))<=>(~kind(X)&patient(X))))&
(((~rich(mary)<~>~creative(mary)))<=>(~kind(susan)))&
((~funny(john))=>((tall(lucy)&calm(lucy))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)|calm(X))))&
((?[X]:(quiet(X)))=>(~patient(susan)))&
(((~patient(lucy)&~brave(lucy)))=>(?[X]:((humble(X)|happy(X)))))&
(((creative(susan)|~wise(susan)))=>((rich(john)|~rich(john))))&
(((~kind(mary)<~>curious(mary)))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((brave(X)|kind(X))=>(rich(X)<~>~humble(X))))&
((happy(susan)&~kind(susan)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~curious(lucy)<~>wise(lucy)))&
(?[X]:(~wise(X)))&
(~strong(john))&
(?[X]:((curious(X)|~happy(X))))&
(~strong(susan)) | tall(mary) | [] | null | 0 |
Everyone who is humble or not tall is either happy or not tall.
If someone is either kind or generous then lucy is patient or rich and vice versa.
If someone is both not calm and not creative then fred is wise.
Everyone who is wise or not generous is patient.
If lucy is either not tall or not patient then someone is not humble and vice versa.
Everyone who is both not patient and not happy is not creative and vice versa.
Everyone who is both not creative and tall is both wise and happy.
Everyone who is not calm is either humble or calm.
If someone is brave or not wise then someone is not kind or quiet.
If susan is happy then susan is not brave and vice versa.
If someone is either not creative or not patient then john is generous or brave and vice versa.
Everyone who is kind or not creative is both tall and not tall.
Everyone who is happy is either not generous or patient and vice versa.
Everyone who is both humble and not wise is happy and vice versa.
Everyone who is not happy is both not brave and old.
Lucy is either strong or humble.
Someone is kind or not funny.
Fred is wise.
Fred is funny.
Alice is tall or strong.
Paul is either creative or funny. | Alice is happy. | neutral | (![X]:((humble(X)|~tall(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((kind(X)<~>generous(X))))<=>((patient(lucy)|rich(lucy))))&
((?[X]:((~calm(X)&~creative(X))))=>(wise(fred)))&
(![X]:((wise(X)|~generous(X))=>patient(X)))&
(((~tall(lucy)<~>~patient(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~happy(X))<=>~creative(X)))&
(![X]:((~creative(X)&tall(X))=>(wise(X)&happy(X))))&
(![X]:(~calm(X)=>(humble(X)<~>calm(X))))&
((?[X]:((brave(X)|~wise(X))))=>(?[X]:((~kind(X)|quiet(X)))))&
((happy(susan))<=>(~brave(susan)))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(john)|brave(john))))&
(![X]:((kind(X)|~creative(X))=>(tall(X)&~tall(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>patient(X))))&
(![X]:((humble(X)&~wise(X))<=>happy(X)))&
(![X]:(~happy(X)=>(~brave(X)&old(X))))&
((strong(lucy)<~>humble(lucy)))&
(?[X]:((kind(X)|~funny(X))))&
(wise(fred))&
(funny(fred))&
((tall(alice)|strong(alice)))&
((creative(paul)<~>funny(paul))) | happy(alice) | [] | null | 0 |
If mary is creative or not funny then someone is either patient or not brave and vice versa. Everyone who is humble or not wise is not brave. If susan is not tall or not humble then alice is both generous and not rich and vice versa. Everyone who is not strong is both not humble and rich and vice versa. If mary is not quiet then mary is quiet or not rich. If paul is both not brave and creative then john is wise and vice versa. If someone is not funny then someone is not curious or old and vice versa. Everyone who is either not brave or strong is happy or not wise and vice versa. Everyone who is either happy or not curious is both not rich and kind. Everyone who is both not patient and creative is both not old and creative and vice versa. If someone is both humble and quiet then someone is not funny or tall and vice versa. Everyone who is either not strong or happy is not funny or not rich. Everyone who is either not happy or kind is both brave and rich. Alice is both not tall and calm. Someone is not wise or not quiet. Susan is either not humble or not creative. Lucy is not old. | John is kind. | neutral | (((creative(mary)|~funny(mary)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((humble(X)|~wise(X))=>~brave(X)))&
(((~tall(susan)|~humble(susan)))<=>((generous(alice)&~rich(alice))))&
(![X]:(~strong(X)<=>(~humble(X)&rich(X))))&
((~quiet(mary))=>((quiet(mary)|~rich(mary))))&
(((~brave(paul)&creative(paul)))<=>(wise(john)))&
((?[X]:(~funny(X)))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(happy(X)|~wise(X))))&
(![X]:((happy(X)<~>~curious(X))=>(~rich(X)&kind(X))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
((~tall(alice)&calm(alice)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~humble(susan)<~>~creative(susan)))&
(~old(lucy)) | kind(john) | [] | null | 0 |
Everyone who is both not creative and not happy is both humble and not humble. If someone is both not calm and calm then susan is either not kind or not patient and vice versa. If someone is both not tall and creative then someone is either funny or strong. If alice is strong or funny then paul is not curious or not humble and vice versa. Everyone who is not tall is not creative or tall. Everyone who is either not generous or not patient is not strong or wise and vice versa. Everyone who is both humble and happy is brave. If mary is both not strong and old then someone is not rich or patient. If someone is either kind or generous then susan is either not generous or creative and vice versa. Everyone who is both not calm and patient is either not kind or generous and vice versa. If paul is not kind or not quiet then susan is not calm and vice versa. Everyone who is not happy is both old and not patient. Everyone who is rich is not creative. Everyone who is calm is not old or not patient and vice versa. If someone is not humble or not old then someone is generous and vice versa. If someone is either not curious or brave then paul is either quiet or not rich. Alice is not tall or not creative. Someone is both not kind and patient. Someone is either rich or not brave. Mary is curious or not creative. Paul is both wise and not kind. John is not generous. Mary is both not patient and not old. | Alice is rich. | neutral | (![X]:((~creative(X)&~happy(X))=>(humble(X)&~humble(X))))&
((?[X]:((~calm(X)&calm(X))))<=>((~kind(susan)<~>~patient(susan))))&
((?[X]:((~tall(X)&creative(X))))=>(?[X]:((funny(X)<~>strong(X)))))&
(((strong(alice)|funny(alice)))<=>((~curious(paul)|~humble(paul))))&
(![X]:(~tall(X)=>(~creative(X)|tall(X))))&
(![X]:((~generous(X)<~>~patient(X))<=>(~strong(X)|wise(X))))&
(![X]:((humble(X)&happy(X))=>brave(X)))&
(((~strong(mary)&old(mary)))=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((kind(X)<~>generous(X))))<=>((~generous(susan)<~>creative(susan))))&
(![X]:((~calm(X)&patient(X))<=>(~kind(X)<~>generous(X))))&
(((~kind(paul)|~quiet(paul)))<=>(~calm(susan)))&
(![X]:(~happy(X)=>(old(X)&~patient(X))))&
(![X]:(rich(X)=>~creative(X)))&
(![X]:(calm(X)<=>(~old(X)|~patient(X))))&
((?[X]:((~humble(X)|~old(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~curious(X)<~>brave(X))))=>((quiet(paul)<~>~rich(paul))))&
((~tall(alice)|~creative(alice)))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((rich(X)<~>~brave(X))))&
((curious(mary)|~creative(mary)))&
((wise(paul)&~kind(paul)))&
(~generous(john))&
((~patient(mary)&~old(mary))) | rich(alice) | [] | null | 0 |
If john is both brave and not old then lucy is either not quiet or not funny and vice versa. Everyone who is both old and tall is brave or not old and vice versa. If paul is both not rich and strong then fred is old. Everyone who is both rich and not happy is generous. Everyone who is wise or brave is not quiet and vice versa. Everyone who is curious or not creative is not kind and vice versa. If someone is both not brave and not strong then lucy is both not wise and curious. If john is both wise and generous then someone is happy. If someone is both quiet and rich then someone is creative and vice versa. If fred is either humble or calm then someone is either kind or happy and vice versa. Everyone who is both not kind and not rich is both not creative and generous and vice versa. Everyone who is either wise or not happy is not wise. Everyone who is strong is not quiet. Everyone who is both not funny and not wise is funny or not funny and vice versa. If someone is either not kind or not happy then someone is either not wise or wise. Someone is not strong or not humble. John is tall or wise. Alice is both happy and old. Someone is either generous or not patient. Mary is generous or not curious. Someone is curious or happy. | Mary is quiet. | neutral | (((brave(john)&~old(john)))<=>((~quiet(lucy)<~>~funny(lucy))))&
(![X]:((old(X)&tall(X))<=>(brave(X)|~old(X))))&
(((~rich(paul)&strong(paul)))=>(old(fred)))&
(![X]:((rich(X)&~happy(X))=>generous(X)))&
(![X]:((wise(X)|brave(X))<=>~quiet(X)))&
(![X]:((curious(X)|~creative(X))<=>~kind(X)))&
((?[X]:((~brave(X)&~strong(X))))=>((~wise(lucy)&curious(lucy))))&
(((wise(john)&generous(john)))=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:(creative(X))))&
(((humble(fred)<~>calm(fred)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(~creative(X)&generous(X))))&
(![X]:((wise(X)<~>~happy(X))=>~wise(X)))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((~funny(X)&~wise(X))<=>(funny(X)|~funny(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(?[X]:((~strong(X)|~humble(X))))&
((tall(john)|wise(john)))&
((happy(alice)&old(alice)))&
(?[X]:((generous(X)<~>~patient(X))))&
((generous(mary)|~curious(mary)))&
(?[X]:((curious(X)|happy(X)))) | quiet(mary) | [] | null | 0 |
If susan is both happy and not generous then john is either not humble or not patient and vice versa.
Everyone who is rich or happy is not happy or kind.
If alice is strong then fred is humble and vice versa.
If someone is not old then someone is both not curious and kind and vice versa.
Everyone who is both creative and not funny is both tall and generous and vice versa.
Everyone who is both curious and old is either generous or not rich.
Everyone who is both rich and strong is not kind or not old.
If someone is both tall and not quiet then someone is not strong.
If mary is either kind or not strong then fred is both wise and not humble and vice versa.
If someone is both not tall and patient then alice is either tall or not creative and vice versa.
If someone is both rich and not wise then someone is generous.
If someone is either not funny or not creative then susan is either happy or not curious.
If someone is funny or creative then alice is either strong or wise and vice versa.
Everyone who is humble is creative or happy and vice versa.
Everyone who is both patient and tall is curious.
Everyone who is calm is either not kind or not brave.
Susan is wise or not creative.
Someone is either humble or not creative.
Susan is happy.
Fred is funny.
Fred is either not humble or quiet.
Someone is not kind.
Paul is either tall or not strong. | Fred is humble. | neutral | (((happy(susan)&~generous(susan)))<=>((~humble(john)<~>~patient(john))))&
(![X]:((rich(X)|happy(X))=>(~happy(X)|kind(X))))&
((strong(alice))<=>(humble(fred)))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((creative(X)&~funny(X))<=>(tall(X)&generous(X))))&
(![X]:((curious(X)&old(X))=>(generous(X)<~>~rich(X))))&
(![X]:((rich(X)&strong(X))=>(~kind(X)|~old(X))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:(~strong(X))))&
(((kind(mary)<~>~strong(mary)))<=>((wise(fred)&~humble(fred))))&
((?[X]:((~tall(X)&patient(X))))<=>((tall(alice)<~>~creative(alice))))&
((?[X]:((rich(X)&~wise(X))))=>(?[X]:(generous(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((happy(susan)<~>~curious(susan))))&
((?[X]:((funny(X)|creative(X))))<=>((strong(alice)<~>wise(alice))))&
(![X]:(humble(X)<=>(creative(X)|happy(X))))&
(![X]:((patient(X)&tall(X))=>curious(X)))&
(![X]:(calm(X)=>(~kind(X)<~>~brave(X))))&
((wise(susan)|~creative(susan)))&
(?[X]:((humble(X)<~>~creative(X))))&
(happy(susan))&
(funny(fred))&
((~humble(fred)<~>quiet(fred)))&
(?[X]:(~kind(X)))&
((tall(paul)<~>~strong(paul))) | humble(fred) | [] | null | 0 |
Everyone who is both not generous and not funny is not patient. Everyone who is either old or not strong is not strong or happy. If someone is creative then susan is not calm and vice versa. Everyone who is both quiet and not creative is quiet and vice versa. Everyone who is either strong or tall is old and vice versa. If someone is either not funny or not wise then fred is both generous and not happy and vice versa. If mary is either rich or not strong then someone is not wise and vice versa. Everyone who is both patient and old is both not old and not calm. If someone is not patient or curious then someone is creative. If someone is both not rich and not wise then someone is rich or funny and vice versa. If someone is both patient and happy then paul is both creative and not generous and vice versa. Everyone who is both kind and rich is either patient or not humble and vice versa. If someone is not generous then someone is not strong and vice versa. Everyone who is generous is not happy or strong and vice versa. Everyone who is not calm or not tall is not calm or not quiet. Everyone who is both not tall and not old is patient or not happy. Lucy is not humble or not happy. Someone is not creative or not wise. Someone is not kind or rich. Paul is either not tall or tall. Someone is either not rich or not happy. Someone is both creative and not calm. Fred is either not happy or calm. Someone is either rich or calm. | Lucy is rich. | neutral | (![X]:((~generous(X)&~funny(X))=>~patient(X)))&
(![X]:((old(X)<~>~strong(X))=>(~strong(X)|happy(X))))&
((?[X]:(creative(X)))<=>(~calm(susan)))&
(![X]:((quiet(X)&~creative(X))<=>quiet(X)))&
(![X]:((strong(X)<~>tall(X))<=>old(X)))&
((?[X]:((~funny(X)<~>~wise(X))))<=>((generous(fred)&~happy(fred))))&
(((rich(mary)<~>~strong(mary)))<=>(?[X]:(~wise(X))))&
(![X]:((patient(X)&old(X))=>(~old(X)&~calm(X))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:(creative(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>(?[X]:((rich(X)|funny(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((creative(paul)&~generous(paul))))&
(![X]:((kind(X)&rich(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(~happy(X)|strong(X))))&
(![X]:((~calm(X)|~tall(X))=>(~calm(X)|~quiet(X))))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~happy(X))))&
((~humble(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~wise(X))))&
(?[X]:((~kind(X)|rich(X))))&
((~tall(paul)<~>tall(paul)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~happy(fred)<~>calm(fred)))&
(?[X]:((rich(X)<~>calm(X)))) | rich(lucy) | [] | null | 0 |
Everyone who is both not strong and curious is both not curious and not brave.
Everyone who is generous or not rich is tall.
If someone is either not rich or not creative then alice is happy and vice versa.
Everyone who is both wise and rich is creative.
If someone is generous then someone is both calm and strong.
If mary is either calm or not strong then alice is both not wise and old and vice versa.
If lucy is either tall or not patient then susan is strong or brave and vice versa.
If someone is not tall then someone is brave or not quiet.
Everyone who is generous is either humble or old.
Everyone who is not rich or not generous is either curious or strong.
If mary is not kind then fred is generous or not wise and vice versa.
Everyone who is either not brave or calm is not calm and vice versa.
If someone is patient or not creative then mary is creative.
Everyone who is not creative is either curious or creative and vice versa.
If someone is humble then susan is either not old or not rich and vice versa.
Everyone who is both not quiet and not generous is happy and vice versa.
Someone is either not generous or quiet.
Lucy is either not patient or curious.
Someone is either not kind or not strong.
Someone is both not old and not brave.
Paul is either rich or kind. | Paul is not kind. | entailment | (![X]:((~strong(X)&curious(X))=>(~curious(X)&~brave(X))))&
(![X]:((generous(X)|~rich(X))=>tall(X)))&
((?[X]:((~rich(X)<~>~creative(X))))<=>(happy(alice)))&
(![X]:((wise(X)&rich(X))=>creative(X)))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)&strong(X)))))&
(((calm(mary)<~>~strong(mary)))<=>((~wise(alice)&old(alice))))&
(((tall(lucy)<~>~patient(lucy)))<=>((strong(susan)|brave(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(generous(X)=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|~generous(X))=>(curious(X)<~>strong(X))))&
((~kind(mary))<=>((generous(fred)|~wise(fred))))&
(![X]:((~brave(X)<~>calm(X))<=>~calm(X)))&
((?[X]:((patient(X)|~creative(X))))=>(creative(mary)))&
(![X]:(~creative(X)<=>(curious(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~old(susan)<~>~rich(susan))))&
(![X]:((~quiet(X)&~generous(X))<=>happy(X)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~patient(lucy)<~>curious(lucy)))&
(?[X]:((~kind(X)<~>~strong(X))))&
(?[X]:((~old(X)&~brave(X))))&
((rich(paul)<~>kind(paul))) | ~kind(paul) | [
"p0",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3813307960370833696828711
% SZS output start Proof for 3813307960370833696828711
1. ! [X0] : ((curious(X0) & ~strong(X0)) => (~brave(X0) & ~curious(X0))) [input p0]
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (curious(X0) <~> strong(X0))) [input p9]
14. ! [X0] : (~creative(X0) <=> (curious(X0) <~> creative(X0))) [input p13]
21. rich(paul) <~> kind(paul) [input p20]
22. kind(paul) [input hypothesis]
25. ! [X0] : ((~brave(X0) & ~curious(X0)) | (~curious(X0) | strong(X0))) [ennf transformation 1]
26. ! [X0] : ((~brave(X0) & ~curious(X0)) | ~curious(X0) | strong(X0)) [flattening 25]
33. ! [X0] : ((curious(X0) <~> strong(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
50. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (generous(X0) & rich(X0))) [nnf transformation 33]
54. ! [X0] : ((~creative(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | creative(X0))) [nnf transformation 14]
70. (~kind(paul) | ~rich(paul)) & (kind(paul) | rich(paul)) [nnf transformation 21]
71. ~curious(X0) | ~curious(X0) | strong(X0) [cnf transformation 26]
99. ~strong(X0) | ~curious(X0) | rich(X0) [cnf transformation 50]
110. creative(X0) | curious(X0) | creative(X0) [cnf transformation 54]
113. ~creative(X0) | curious(X0) | ~creative(X0) [cnf transformation 54]
130. ~kind(paul) | ~rich(paul) [cnf transformation 70]
131. kind(paul) [cnf transformation 22]
132. creative(X0) | curious(X0) [duplicate literal removal 110]
133. ~creative(X0) | curious(X0) [duplicate literal removal 113]
136. ~curious(X0) | strong(X0) [duplicate literal removal 71]
229. ~curious(X0) | rich(X0) [subsumption resolution 99,136]
260. curious(X0) [subsumption resolution 132,133]
303. 34 <=> rich(paul) [avatar definition]
305. ~rich(paul) <- (~34) [avatar component clause 303]
307. 35 <=> kind(paul) [avatar definition]
310. ~34 | ~35 [avatar split clause 130,307,303]
312. 35 [avatar split clause 131,307]
327. rich(X0) [resolution 229,260]
334. $false <- (~34) [resolution 327,305]
336. 34 [avatar contradiction clause 334]
338. $false [avatar sat refutation 310,312,336]
% SZS output end Proof for 3813307960370833696828711
% ------------------------------
% 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 either not quiet or curious is both not kind and not happy and vice versa.
If paul is humble then someone is not strong or not quiet.
If paul is not kind or not creative then susan is calm or not calm.
Everyone who is both curious and not funny is not kind and vice versa.
If someone is not strong then susan is either not humble or not brave and vice versa.
If someone is either happy or not strong then someone is either not tall or not funny and vice versa.
Everyone who is not generous is both old and rich and vice versa.
If lucy is both not wise and curious then fred is not humble and vice versa.
Everyone who is not strong is not quiet.
Everyone who is both rich and humble is either strong or not kind and vice versa.
Everyone who is curious or not old is either creative or not patient and vice versa.
If john is either not happy or old then someone is creative or happy and vice versa.
If someone is kind then paul is both generous and funny.
Everyone who is both not tall and not old is not patient or tall.
Everyone who is not brave or tall is both not curious and not old and vice versa.
If someone is both not tall and not old then someone is both rich and not humble and vice versa.
Alice is both patient and not rich.
Someone is both happy and not wise.
Someone is not brave or not tall.
Someone is either not generous or kind.
Alice is happy.
Fred is either not brave or generous.
Someone is both not funny and not wise.
Someone is either brave or not kind. | Alice is creative. | entailment | (![X]:((~quiet(X)<~>curious(X))<=>(~kind(X)&~happy(X))))&
((humble(paul))=>(?[X]:((~strong(X)|~quiet(X)))))&
(((~kind(paul)|~creative(paul)))=>((calm(susan)|~calm(susan))))&
(![X]:((curious(X)&~funny(X))<=>~kind(X)))&
((?[X]:(~strong(X)))<=>((~humble(susan)<~>~brave(susan))))&
((?[X]:((happy(X)<~>~strong(X))))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:(~generous(X)<=>(old(X)&rich(X))))&
(((~wise(lucy)&curious(lucy)))<=>(~humble(fred)))&
(![X]:(~strong(X)=>~quiet(X)))&
(![X]:((rich(X)&humble(X))<=>(strong(X)<~>~kind(X))))&
(![X]:((curious(X)|~old(X))<=>(creative(X)<~>~patient(X))))&
(((~happy(john)<~>old(john)))<=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:(kind(X)))=>((generous(paul)&funny(paul))))&
(![X]:((~tall(X)&~old(X))=>(~patient(X)|tall(X))))&
(![X]:((~brave(X)|tall(X))<=>(~curious(X)&~old(X))))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((rich(X)&~humble(X)))))&
((patient(alice)&~rich(alice)))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~generous(X)<~>kind(X))))&
(happy(alice))&
((~brave(fred)<~>generous(fred)))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((brave(X)<~>~kind(X)))) | creative(alice) | [
"p0",
"p3",
"p8",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3909049029618528940572126
% SZS output start Proof for 3909049029618528940572126
1. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> (~happy(X0) & ~kind(X0))) [input p0]
4. ! [X0] : ((~funny(X0) & curious(X0)) <=> ~kind(X0)) [input p3]
9. ! [X0] : (~strong(X0) => ~quiet(X0)) [input p8]
10. ! [X0] : ((humble(X0) & rich(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p9]
11. ! [X0] : ((~old(X0) | curious(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p10]
17. ~rich(alice) & patient(alice) [input p16]
25. ~creative(alice) [input hypothesis]
31. ! [X0] : (~quiet(X0) | strong(X0)) [ennf transformation 9]
35. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [flattening 35]
39. ! [X0] : (((~funny(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | (funny(X0) | ~curious(X0)))) [nnf transformation 4]
40. ! [X0] : (((~funny(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | funny(X0) | ~curious(X0))) [flattening 39]
54. ! [X0] : (((humble(X0) & rich(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | (~humble(X0) | ~rich(X0)))) [nnf transformation 10]
55. ! [X0] : (((humble(X0) & rich(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~humble(X0) | ~rich(X0))) [flattening 54]
56. ! [X0] : (((~old(X0) | curious(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 11]
57. ! [X0] : ((~old(X0) | curious(X0) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (old(X0) & ~curious(X0)))) [flattening 56]
82. ~kind(X0) | curious(X0) | quiet(X0) [cnf transformation 36]
92. kind(X0) | curious(X0) [cnf transformation 40]
112. ~quiet(X0) | strong(X0) [cnf transformation 31]
115. ~strong(X0) | ~kind(X0) | rich(X0) [cnf transformation 55]
119. ~patient(X0) | creative(X0) | ~curious(X0) [cnf transformation 57]
143. patient(alice) [cnf transformation 17]
144. ~rich(alice) [cnf transformation 17]
157. ~creative(alice) [cnf transformation 25]
393. curious(X0) | quiet(X0) | curious(X0) [resolution 82,92]
396. curious(X0) | quiet(X0) [duplicate literal removal 393]
440. 48 <=> curious(alice) [avatar definition]
442. ~curious(alice) <- (~48) [avatar component clause 440]
444. 49 <=> quiet(alice) [avatar definition]
445. quiet(alice) <- (49) [avatar component clause 444]
518. 63 <=> kind(alice) [avatar definition]
519. ~kind(alice) <- (~63) [avatar component clause 518]
520. kind(alice) <- (63) [avatar component clause 518]
522. 64 <=> strong(alice) [avatar definition]
524. strong(alice) <- (64) [avatar component clause 522]
545. creative(alice) | ~curious(alice) [resolution 119,143]
694. quiet(alice) <- (~48) [resolution 396,442]
698. 49 | 48 [avatar split clause 694,440,444]
705. strong(alice) <- (49) [resolution 445,112]
706. 64 | ~49 [avatar split clause 705,444,522]
708. ~kind(alice) | rich(alice) <- (64) [resolution 524,115]
710. rich(alice) <- (63, 64) [subsumption resolution 708,520]
711. $false <- (63, 64) [subsumption resolution 710,144]
712. ~63 | ~64 [avatar contradiction clause 711]
719. ~curious(alice) [subsumption resolution 545,157]
720. ~48 [avatar split clause 719,440]
724. curious(alice) <- (~63) [resolution 519,92]
725. $false <- (~48, ~63) [subsumption resolution 724,442]
726. 48 | 63 [avatar contradiction clause 725]
727. $false [avatar sat refutation 698,706,712,720,726]
% SZS output end Proof for 3909049029618528940572126
% ------------------------------
% 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is not rich and vice versa.
Everyone who is not generous is either not patient or not strong and vice versa.
If someone is both tall and not calm then alice is both strong and old.
If alice is both kind and not tall then john is both not rich and not generous and vice versa.
If someone is not strong or not calm then alice is rich and vice versa.
Everyone who is generous is rich or not generous.
If lucy is creative or rich then alice is either funny or wise and vice versa.
If alice is creative or not rich then someone is both rich and not old and vice versa.
Everyone who is either happy or generous is either creative or not rich and vice versa.
Everyone who is both funny and not calm is both not quiet and curious.
Everyone who is rich or not happy is brave.
If someone is wise then susan is both not generous and happy.
Everyone who is not strong is either happy or creative and vice versa.
If someone is both not funny and not wise then john is both not calm and not curious.
Everyone who is tall is either not curious or rich.
If someone is brave then someone is both tall and not funny and vice versa.
Someone is both kind and not wise.
John is both kind and rich.
Someone is tall or brave.
Mary is not brave or old.
Someone is happy or not patient.
Someone is both not quiet and creative.
Someone is not curious or not patient.
Mary is both not calm and not wise. | Susan is generous. | neutral | (![X]:(funny(X)<=>~rich(X)))&
(![X]:(~generous(X)<=>(~patient(X)<~>~strong(X))))&
((?[X]:((tall(X)&~calm(X))))=>((strong(alice)&old(alice))))&
(((kind(alice)&~tall(alice)))<=>((~rich(john)&~generous(john))))&
((?[X]:((~strong(X)|~calm(X))))<=>(rich(alice)))&
(![X]:(generous(X)=>(rich(X)|~generous(X))))&
(((creative(lucy)|rich(lucy)))<=>((funny(alice)<~>wise(alice))))&
(((creative(alice)|~rich(alice)))<=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((funny(X)&~calm(X))=>(~quiet(X)&curious(X))))&
(![X]:((rich(X)|~happy(X))=>brave(X)))&
((?[X]:(wise(X)))=>((~generous(susan)&happy(susan))))&
(![X]:(~strong(X)<=>(happy(X)<~>creative(X))))&
((?[X]:((~funny(X)&~wise(X))))=>((~calm(john)&~curious(john))))&
(![X]:(tall(X)=>(~curious(X)<~>rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)&~funny(X)))))&
(?[X]:((kind(X)&~wise(X))))&
((kind(john)&rich(john)))&
(?[X]:((tall(X)|brave(X))))&
((~brave(mary)|old(mary)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~curious(X)|~patient(X))))&
((~calm(mary)&~wise(mary))) | generous(susan) | [] | null | 0 |
If someone is patient then someone is either patient or kind and vice versa.
If someone is either not tall or kind then someone is not curious and vice versa.
Everyone who is both strong and not brave is both not happy and not patient.
If john is either not rich or creative then someone is either kind or patient.
Everyone who is not kind or not generous is humble or not quiet and vice versa.
Everyone who is either generous or creative is either not creative or not strong and vice versa.
If someone is not kind then someone is either curious or calm and vice versa.
Everyone who is both happy and not curious is either kind or not calm.
Everyone who is either not kind or not humble is either not calm or not curious and vice versa.
If someone is not strong or not kind then susan is both funny and not humble and vice versa.
If mary is not wise then lucy is tall.
Everyone who is both creative and not quiet is either rich or not strong and vice versa.
If someone is happy then paul is kind or not humble and vice versa.
Everyone who is both tall and not rich is not happy or not humble and vice versa.
Fred is not creative.
Someone is old or not rich.
Alice is not creative or not curious.
Paul is curious or tall.
Someone is not tall or not calm.
Mary is not funny or brave. | Susan is generous. | neutral | ((?[X]:(patient(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~happy(X)&~patient(X))))&
(((~rich(john)<~>creative(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:((~kind(X)|~generous(X))<=>(humble(X)|~quiet(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~creative(X)<~>~strong(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((happy(X)&~curious(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((funny(susan)&~humble(susan))))&
((~wise(mary))=>(tall(lucy)))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~strong(X))))&
((?[X]:(happy(X)))<=>((kind(paul)|~humble(paul))))&
(![X]:((tall(X)&~rich(X))<=>(~happy(X)|~humble(X))))&
(~creative(fred))&
(?[X]:((old(X)|~rich(X))))&
((~creative(alice)|~curious(alice)))&
((curious(paul)|tall(paul)))&
(?[X]:((~tall(X)|~calm(X))))&
((~funny(mary)|brave(mary))) | generous(susan) | [] | null | 0 |
Everyone who is wise or not wise is both patient and not generous. Everyone who is not quiet is not tall and vice versa. If lucy is humble then someone is both quiet and not tall and vice versa. Everyone who is both not quiet and strong is both not rich and not generous. Everyone who is creative is either not strong or generous. Everyone who is either not old or not quiet is creative or not kind. Everyone who is either kind or curious is not rich and vice versa. If someone is both not rich and funny then someone is either creative or not kind. Everyone who is both curious and not brave is not funny and vice versa. Everyone who is not old or not humble is either not creative or funny and vice versa. If john is either not quiet or not funny then mary is either patient or not strong. Everyone who is both not strong and not generous is either not humble or not curious and vice versa. Everyone who is not calm or funny is funny or tall. Everyone who is both funny and creative is not brave or not generous. Everyone who is not curious or creative is not kind and vice versa. If someone is humble or generous then john is both not patient and not strong. Someone is either generous or not old. Someone is both not quiet and not happy. Alice is not calm. | Mary is not kind. | contradiction | (![X]:((wise(X)|~wise(X))=>(patient(X)&~generous(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
((humble(lucy))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~rich(X)&~generous(X))))&
(![X]:(creative(X)=>(~strong(X)<~>generous(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(creative(X)|~kind(X))))&
(![X]:((kind(X)<~>curious(X))<=>~rich(X)))&
((?[X]:((~rich(X)&funny(X))))=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((curious(X)&~brave(X))<=>~funny(X)))&
(![X]:((~old(X)|~humble(X))<=>(~creative(X)<~>funny(X))))&
(((~quiet(john)<~>~funny(john)))=>((patient(mary)<~>~strong(mary))))&
(![X]:((~strong(X)&~generous(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~calm(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((funny(X)&creative(X))=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|creative(X))<=>~kind(X)))&
((?[X]:((humble(X)|generous(X))))=>((~patient(john)&~strong(john))))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((~quiet(X)&~happy(X))))&
(~calm(alice)) | ~kind(mary) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6756945444469112196863461
% SZS output start Proof for 6756945444469112196863461
1. ! [X0] : ((~wise(X0) | wise(X0)) => (~generous(X0) & patient(X0))) [input p0]
5. ! [X0] : (creative(X0) => (~strong(X0) <~> generous(X0))) [input p4]
7. ! [X0] : ((kind(X0) <~> curious(X0)) <=> ~rich(X0)) [input p6]
8. ? [X0] : (funny(X0) & ~rich(X0)) => ? [X0] : (creative(X0) <~> ~kind(X0)) [input p7]
9. ! [X0] : ((~brave(X0) & curious(X0)) <=> ~funny(X0)) [input p8]
10. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (~creative(X0) <~> funny(X0))) [input p9]
12. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (~humble(X0) <~> ~curious(X0))) [input p11]
15. ! [X0] : ((creative(X0) | ~curious(X0)) <=> ~kind(X0)) [input p14]
16. ? [X0] : (generous(X0) | humble(X0)) => (~strong(john) & ~patient(john)) [input p15]
20. ~kind(mary) [input hypothesis]
21. ? [X0] : (funny(X0) & ~rich(X0)) => ? [X1] : (creative(X1) <~> ~kind(X1)) [rectify 8]
23. ! [X0] : ((~generous(X0) & patient(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) <~> generous(X0)) | ~creative(X0)) [ennf transformation 5]
29. ? [X1] : (creative(X1) <~> ~kind(X1)) | ! [X0] : (~funny(X0) | rich(X0)) [ennf transformation 21]
35. (~strong(john) & ~patient(john)) | ! [X0] : (~generous(X0) & ~humble(X0)) [ennf transformation 16]
41. ! [X0] : (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~creative(X0)) [nnf transformation 26]
43. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | rich(X0)) & (~rich(X0) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 7]
44. ? [X1] : ((kind(X1) | ~creative(X1)) & (~kind(X1) | creative(X1))) | ! [X0] : (~funny(X0) | rich(X0)) [nnf transformation 29]
45. ? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | ! [X1] : (~funny(X1) | rich(X1)) [rectify 44]
46. ? [X0] : ((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) => ((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) [choice axiom]
47. ((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) | ! [X1] : (~funny(X1) | rich(X1)) [skolemisation 45,46]
48. ! [X0] : (((~brave(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | (brave(X0) | ~curious(X0)))) [nnf transformation 9]
49. ! [X0] : (((~brave(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | brave(X0) | ~curious(X0))) [flattening 48]
50. ! [X0] : (((~humble(X0) | ~old(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (humble(X0) & old(X0)))) [nnf transformation 10]
51. ! [X0] : ((~humble(X0) | ~old(X0) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (humble(X0) & old(X0)))) [flattening 50]
53. ! [X0] : (((~generous(X0) & ~strong(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (generous(X0) | strong(X0)))) [nnf transformation 12]
54. ! [X0] : (((~generous(X0) & ~strong(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | generous(X0) | strong(X0))) [flattening 53]
55. ! [X0] : (((creative(X0) | ~curious(X0)) | kind(X0)) & (~kind(X0) | (~creative(X0) & curious(X0)))) [nnf transformation 15]
56. ! [X0] : ((creative(X0) | ~curious(X0) | kind(X0)) & (~kind(X0) | (~creative(X0) & curious(X0)))) [flattening 55]
62. patient(X0) | ~wise(X0) [cnf transformation 23]
63. patient(X0) | wise(X0) [cnf transformation 23]
64. ~generous(X0) | ~wise(X0) [cnf transformation 23]
65. ~generous(X0) | wise(X0) [cnf transformation 23]
73. generous(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 41]
78. ~curious(X0) | kind(X0) | ~rich(X0) [cnf transformation 43]
81. ~kind(sK1) | creative(sK1) | ~funny(X1) | rich(X1) [cnf transformation 47]
82. kind(sK1) | ~creative(sK1) | ~funny(X1) | rich(X1) [cnf transformation 47]
84. funny(X0) | curious(X0) [cnf transformation 49]
87. ~creative(X0) | funny(X0) | humble(X0) [cnf transformation 51]
89. ~funny(X0) | creative(X0) | humble(X0) [cnf transformation 51]
97. curious(X0) | humble(X0) | generous(X0) | strong(X0) [cnf transformation 54]
98. ~curious(X0) | ~strong(X0) | humble(X0) [cnf transformation 54]
106. ~kind(X0) | ~creative(X0) [cnf transformation 56]
107. ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 56]
108. ~patient(john) | ~humble(X0) [cnf transformation 35]
116. ~kind(mary) [cnf transformation 20]
117. ~generous(X0) [subsumption resolution 64,65]
118. patient(X0) [subsumption resolution 62,63]
133. ~creative(X0) | ~strong(X0) [subsumption resolution 73,117]
135. 4 <=> ! [X1] : (~funny(X1) | rich(X1)) [avatar definition]
136. ~funny(X1) | rich(X1) <- (4) [avatar component clause 135]
138. 5 <=> creative(sK1) [avatar definition]
140. ~creative(sK1) <- (~5) [avatar component clause 138]
142. 6 <=> kind(sK1) [avatar definition]
143. ~kind(sK1) <- (~6) [avatar component clause 142]
144. kind(sK1) <- (6) [avatar component clause 142]
145. 4 | ~5 | 6 [avatar split clause 82,142,138,135]
146. 4 | 5 | ~6 [avatar split clause 81,142,138,135]
163. curious(X0) | humble(X0) | strong(X0) [subsumption resolution 97,117]
166. 10 <=> ! [X0] : ~humble(X0) [avatar definition]
167. ~humble(X0) <- (10) [avatar component clause 166]
173. ~humble(X0) [subsumption resolution 108,118]
174. 10 [avatar split clause 173,166]
196. creative(X0) | humble(X0) | curious(X0) [resolution 89,84]
197. curious(X0) | creative(X0) <- (10) [subsumption resolution 196,167]
203. creative(X0) | ~strong(X0) | humble(X0) <- (10) [resolution 197,98]
206. creative(X0) | ~strong(X0) <- (10) [subsumption resolution 203,167]
207. ~strong(X0) <- (10) [subsumption resolution 206,133]
221. creative(X0) | kind(X0) | creative(X0) <- (10) [resolution 107,197]
224. kind(X0) | creative(X0) <- (10) [duplicate literal removal 221]
229. humble(X3) | strong(X3) | kind(X3) | ~rich(X3) [resolution 163,78]
231. strong(X3) | kind(X3) | ~rich(X3) <- (10) [subsumption resolution 229,167]
232. ~rich(X3) | kind(X3) <- (10) [subsumption resolution 231,207]
278. creative(mary) <- (10) [resolution 224,116]
279. creative(sK1) <- (~6, 10) [resolution 224,143]
282. $false <- (~5, ~6, 10) [subsumption resolution 279,140]
283. 5 | 6 | ~10 [avatar contradiction clause 282]
288. ~creative(sK1) <- (6) [resolution 144,106]
297. funny(mary) | humble(mary) <- (10) [resolution 278,87]
300. funny(mary) <- (10) [subsumption resolution 297,167]
309. rich(mary) <- (4, 10) [resolution 300,136]
326. kind(mary) <- (4, 10) [resolution 309,232]
328. $false <- (4, 10) [subsumption resolution 326,116]
329. ~4 | ~10 [avatar contradiction clause 328]
330. ~5 | ~6 [avatar split clause 288,142,138]
331. $false [avatar sat refutation 145,146,174,283,329,330]
% SZS output end Proof for 6756945444469112196863461
% ------------------------------
% 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 susan is not kind then alice is kind.
Everyone who is old is either generous or not wise and vice versa.
Everyone who is kind or not humble is not generous.
Everyone who is wise or not rich is not funny or wise and vice versa.
If someone is calm then alice is patient and vice versa.
If someone is either not humble or not tall then john is funny or not kind.
If someone is either not creative or humble then someone is both curious and not rich and vice versa.
If someone is both old and quiet then mary is either not humble or not rich.
Everyone who is rich is not tall and vice versa.
Everyone who is either not happy or not strong is both wise and not generous.
If someone is curious or not wise then susan is both not brave and not funny.
Everyone who is both not creative and not kind is both happy and not funny.
If someone is either not creative or old then someone is either not curious or not calm and vice versa.
Everyone who is either old or not calm is either generous or wise and vice versa.
If susan is either not brave or not creative then someone is not calm.
If someone is either not calm or rich then susan is brave or not humble and vice versa.
Someone is happy or funny.
Someone is not brave.
Someone is not patient.
Alice is both kind and creative.
Susan is either not old or not patient.
Someone is not tall or calm.
Someone is either generous or not patient.
Fred is generous. | John is calm. | contradiction | ((~kind(susan))=>(kind(alice)))&
(![X]:(old(X)<=>(generous(X)<~>~wise(X))))&
(![X]:((kind(X)|~humble(X))=>~generous(X)))&
(![X]:((wise(X)|~rich(X))<=>(~funny(X)|wise(X))))&
((?[X]:(calm(X)))<=>(patient(alice)))&
((?[X]:((~humble(X)<~>~tall(X))))=>((funny(john)|~kind(john))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
((?[X]:((old(X)&quiet(X))))=>((~humble(mary)<~>~rich(mary))))&
(![X]:(rich(X)<=>~tall(X)))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)&~generous(X))))&
((?[X]:((curious(X)|~wise(X))))=>((~brave(susan)&~funny(susan))))&
(![X]:((~creative(X)&~kind(X))=>(happy(X)&~funny(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((old(X)<~>~calm(X))<=>(generous(X)<~>wise(X))))&
(((~brave(susan)<~>~creative(susan)))=>(?[X]:(~calm(X))))&
((?[X]:((~calm(X)<~>rich(X))))<=>((brave(susan)|~humble(susan))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~patient(X)))&
((kind(alice)&creative(alice)))&
((~old(susan)<~>~patient(susan)))&
(?[X]:((~tall(X)|calm(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
(generous(fred)) | calm(john) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4376746431065695178218487
% SZS output start Proof for 4376746431065695178218487
2. ! [X0] : (old(X0) <=> (generous(X0) <~> ~wise(X0))) [input p1]
14. ! [X0] : ((old(X0) <~> ~calm(X0)) <=> (generous(X0) <~> wise(X0))) [input p13]
25. calm(john) [input hypothesis]
38. ! [X0] : ((old(X0) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ~old(X0))) [nnf transformation 2]
58. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) & (((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [nnf transformation 14]
80. ~wise(X0) | generous(X0) | ~old(X0) [cnf transformation 38]
81. ~generous(X0) | wise(X0) | ~old(X0) [cnf transformation 38]
82. ~wise(X0) | old(X0) | ~generous(X0) [cnf transformation 38]
83. wise(X0) | generous(X0) | old(X0) [cnf transformation 38]
120. wise(X0) | generous(X0) | ~calm(X0) | ~old(X0) [cnf transformation 58]
122. ~wise(X0) | ~generous(X0) | ~calm(X0) | ~old(X0) [cnf transformation 58]
124. ~calm(X0) | old(X0) | wise(X0) | ~generous(X0) [cnf transformation 58]
125. ~calm(X0) | old(X0) | generous(X0) | ~wise(X0) [cnf transformation 58]
147. calm(john) [cnf transformation 25]
271. ~calm(X0) | generous(X0) | ~wise(X0) [subsumption resolution 125,80]
272. ~calm(X0) | old(X0) | ~generous(X0) [subsumption resolution 124,82]
273. ~generous(X0) | ~calm(X0) | ~old(X0) [subsumption resolution 122,81]
274. ~calm(X0) | ~generous(X0) [subsumption resolution 273,272]
275. ~calm(X0) | wise(X0) | ~old(X0) [subsumption resolution 120,81]
362. ~generous(john) [resolution 274,147]
413. generous(john) | ~wise(john) [resolution 271,147]
416. ~wise(john) [subsumption resolution 413,362]
423. generous(john) | old(john) [resolution 416,83]
424. old(john) [subsumption resolution 423,362]
425. wise(john) | ~old(john) [resolution 275,147]
428. ~old(john) [subsumption resolution 425,416]
429. $false [subsumption resolution 428,424]
% SZS output end Proof for 4376746431065695178218487
% ------------------------------
% 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 |
Everyone who is either not funny or strong is not humble and vice versa. If alice is either not humble or generous then someone is not creative and vice versa. If someone is rich or strong then someone is not kind or wise and vice versa. If someone is both quiet and funny then someone is not generous. Everyone who is either not curious or not tall is generous and vice versa. If someone is not wise or not strong then fred is either generous or not quiet and vice versa. If paul is both brave and not old then alice is generous or not strong. If someone is either funny or not funny then alice is not tall or not calm. Everyone who is either not kind or not old is either happy or brave. If someone is wise then paul is both brave and funny. If someone is old then paul is both curious and not wise. Everyone who is either not calm or not curious is either not calm or not generous and vice versa. If someone is either wise or quiet then someone is both not creative and not rich. If someone is both not strong and not rich then susan is both curious and not funny and vice versa. If mary is either funny or rich then john is either calm or not wise. Everyone who is quiet is either not brave or curious and vice versa. Fred is either calm or not old. Someone is either not funny or humble. Someone is either not funny or quiet. Someone is either not funny or kind. John is either wise or not happy. Someone is either old or not tall. | John is not rich. | neutral | (![X]:((~funny(X)<~>strong(X))<=>~humble(X)))&
(((~humble(alice)<~>generous(alice)))<=>(?[X]:(~creative(X))))&
((?[X]:((rich(X)|strong(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>generous(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>((generous(fred)<~>~quiet(fred))))&
(((brave(paul)&~old(paul)))=>((generous(alice)|~strong(alice))))&
((?[X]:((funny(X)<~>~funny(X))))=>((~tall(alice)|~calm(alice))))&
(![X]:((~kind(X)<~>~old(X))=>(happy(X)<~>brave(X))))&
((?[X]:(wise(X)))=>((brave(paul)&funny(paul))))&
((?[X]:(old(X)))=>((curious(paul)&~wise(paul))))&
(![X]:((~calm(X)<~>~curious(X))<=>(~calm(X)<~>~generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((~strong(X)&~rich(X))))<=>((curious(susan)&~funny(susan))))&
(((funny(mary)<~>rich(mary)))=>((calm(john)<~>~wise(john))))&
(![X]:(quiet(X)<=>(~brave(X)<~>curious(X))))&
((calm(fred)<~>~old(fred)))&
(?[X]:((~funny(X)<~>humble(X))))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:((~funny(X)<~>kind(X))))&
((wise(john)<~>~happy(john)))&
(?[X]:((old(X)<~>~tall(X)))) | ~rich(john) | [] | null | 0 |
Everyone who is either not humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | John is not strong. | contradiction | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | ~strong(john) | [
"p0",
"p1",
"p10",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 895346713866867385349719
% SZS output start Proof for 895346713866867385349719
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. ~strong(john) [input hypothesis]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
80. ~brave(X0) | strong(X0) [cnf transformation 39]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. ~strong(john) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
179. 8 <=> old(lucy) [avatar definition]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
271. strong(X1) <- (11) [resolution 194,80]
286. $false <- (11) [resolution 271,143]
289. ~11 [avatar contradiction clause 286]
290. $false [avatar sat refutation 196,250,251,265,289]
% SZS output end Proof for 895346713866867385349719
% ------------------------------
% 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 either not rich or old is both humble and curious.
Everyone who is curious or not funny is both generous and curious.
If someone is either quiet or humble then someone is either tall or strong.
Everyone who is both not happy and not patient is wise.
If someone is strong then someone is generous or not calm and vice versa.
Everyone who is not calm is creative and vice versa.
Everyone who is kind or generous is calm or not rich.
Everyone who is both not quiet and rich is both not brave and quiet.
Everyone who is happy or not strong is happy and vice versa.
Everyone who is either patient or not tall is not curious and vice versa.
If someone is either curious or not funny then alice is wise and vice versa.
If lucy is either not strong or not quiet then someone is both curious and quiet and vice versa.
If someone is wise or brave then someone is not curious or not funny.
If alice is either strong or not kind then someone is either not old or old and vice versa.
If fred is both generous and not creative then someone is both funny and not brave and vice versa.
Everyone who is either not kind or not generous is either generous or funny.
Someone is either old or not old.
Someone is creative.
Someone is both not funny and not humble.
Someone is both not old and generous.
Mary is either not generous or not rich.
Someone is either old or not kind.
Alice is both kind and not brave.
Fred is both not kind and not curious. | Alice is curious. | entailment | (![X]:((~rich(X)<~>old(X))=>(humble(X)&curious(X))))&
(![X]:((curious(X)|~funny(X))=>(generous(X)&curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((~happy(X)&~patient(X))=>wise(X)))&
((?[X]:(strong(X)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
(![X]:((kind(X)|generous(X))=>(calm(X)|~rich(X))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&quiet(X))))&
(![X]:((happy(X)|~strong(X))<=>happy(X)))&
(![X]:((patient(X)<~>~tall(X))<=>~curious(X)))&
((?[X]:((curious(X)<~>~funny(X))))<=>(wise(alice)))&
(((~strong(lucy)<~>~quiet(lucy)))<=>(?[X]:((curious(X)&quiet(X)))))&
((?[X]:((wise(X)|brave(X))))=>(?[X]:((~curious(X)|~funny(X)))))&
(((strong(alice)<~>~kind(alice)))<=>(?[X]:((~old(X)<~>old(X)))))&
(((generous(fred)&~creative(fred)))<=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~kind(X)<~>~generous(X))=>(generous(X)<~>funny(X))))&
(?[X]:((old(X)<~>~old(X))))&
(?[X]:(creative(X)))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((~old(X)&generous(X))))&
((~generous(mary)<~>~rich(mary)))&
(?[X]:((old(X)<~>~kind(X))))&
((kind(alice)&~brave(alice)))&
((~kind(fred)&~curious(fred))) | curious(alice) | [
"p1",
"p14",
"p15",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3157811911061353051404003
% SZS output start Proof for 3157811911061353051404003
2. ! [X0] : ((~funny(X0) | curious(X0)) => (curious(X0) & generous(X0))) [input p1]
15. (~creative(fred) & generous(fred)) <=> ? [X0] : (~brave(X0) & funny(X0)) [input p14]
16. ! [X0] : ((~kind(X0) <~> ~generous(X0)) => (generous(X0) <~> funny(X0))) [input p15]
23. ~brave(alice) & kind(alice) [input p22]
24. ~curious(fred) & ~kind(fred) [input p23]
25. ~curious(alice) [input hypothesis]
30. ! [X0] : ((curious(X0) & generous(X0)) | (funny(X0) & ~curious(X0))) [ennf transformation 2]
39. ! [X0] : ((generous(X0) <~> funny(X0)) | (~kind(X0) <=> ~generous(X0))) [ennf transformation 16]
69. ((~creative(fred) & generous(fred)) | ! [X0] : (brave(X0) | ~funny(X0))) & (? [X0] : (~brave(X0) & funny(X0)) | (creative(fred) | ~generous(fred))) [nnf transformation 15]
70. ((~creative(fred) & generous(fred)) | ! [X0] : (brave(X0) | ~funny(X0))) & (? [X0] : (~brave(X0) & funny(X0)) | creative(fred) | ~generous(fred)) [flattening 69]
71. ((~creative(fred) & generous(fred)) | ! [X0] : (brave(X0) | ~funny(X0))) & (? [X1] : (~brave(X1) & funny(X1)) | creative(fred) | ~generous(fred)) [rectify 70]
72. ? [X1] : (~brave(X1) & funny(X1)) => (~brave(sK7) & funny(sK7)) [choice axiom]
73. ((~creative(fred) & generous(fred)) | ! [X0] : (brave(X0) | ~funny(X0))) & ((~brave(sK7) & funny(sK7)) | creative(fred) | ~generous(fred)) [skolemisation 71,72]
74. ! [X0] : (((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) [nnf transformation 39]
95. funny(X0) | curious(X0) [cnf transformation 30]
139. generous(fred) | brave(X0) | ~funny(X0) [cnf transformation 73]
143. ~funny(X0) | ~generous(X0) | ~generous(X0) | kind(X0) [cnf transformation 74]
157. ~brave(alice) [cnf transformation 23]
158. ~kind(fred) [cnf transformation 24]
159. ~curious(fred) [cnf transformation 24]
160. ~curious(alice) [cnf transformation 25]
162. ~generous(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 143]
290. 28 <=> ! [X0] : (brave(X0) | ~funny(X0)) [avatar definition]
291. ~funny(X0) | brave(X0) <- (28) [avatar component clause 290]
298. 30 <=> generous(fred) [avatar definition]
300. generous(fred) <- (30) [avatar component clause 298]
301. 28 | 30 [avatar split clause 139,298,290]
340. brave(X0) | curious(X0) <- (28) [resolution 291,95]
511. curious(alice) <- (28) [resolution 340,157]
512. $false <- (28) [subsumption resolution 511,160]
513. ~28 [avatar contradiction clause 512]
515. ~funny(fred) | kind(fred) <- (30) [resolution 300,162]
517. ~funny(fred) <- (30) [subsumption resolution 515,158]
518. curious(fred) <- (30) [resolution 517,95]
519. $false <- (30) [subsumption resolution 518,159]
520. ~30 [avatar contradiction clause 519]
521. $false [avatar sat refutation 301,513,520]
% SZS output end Proof for 3157811911061353051404003
% ------------------------------
% 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not funny is both happy and not curious and vice versa.
If susan is not curious then someone is either not tall or kind.
If someone is tall then lucy is either not rich or curious.
If someone is both creative and not tall then someone is both not funny and curious.
Everyone who is strong is not funny or not wise and vice versa.
If someone is either funny or brave then alice is not tall or wise.
If someone is not creative then john is either not humble or not rich and vice versa.
Everyone who is either not happy or creative is both funny and not patient and vice versa.
If alice is not creative then someone is either not creative or not calm and vice versa.
Everyone who is either not humble or old is both not kind and creative.
If susan is tall or not strong then someone is not old.
Everyone who is both creative and not strong is either brave or not rich and vice versa.
Everyone who is both tall and not curious is either tall or not funny.
If susan is both curious and not happy then someone is not old and vice versa.
Everyone who is not kind is old or not patient.
Everyone who is not happy or not humble is not generous and vice versa.
Someone is brave or not patient.
Someone is either not curious or humble.
Someone is not kind.
Someone is not wise.
Someone is not generous.
Susan is funny.
Alice is not creative.
Lucy is strong or not wise. | Susan is humble. | neutral | (![X]:((~old(X)|~funny(X))<=>(happy(X)&~curious(X))))&
((~curious(susan))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(tall(X)))=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:(strong(X)<=>(~funny(X)|~wise(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((~tall(alice)|wise(alice))))&
((?[X]:(~creative(X)))<=>((~humble(john)<~>~rich(john))))&
(![X]:((~happy(X)<~>creative(X))<=>(funny(X)&~patient(X))))&
((~creative(alice))<=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>old(X))=>(~kind(X)&creative(X))))&
(((tall(susan)|~strong(susan)))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~strong(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)<~>~funny(X))))&
(((curious(susan)&~happy(susan)))<=>(?[X]:(~old(X))))&
(![X]:(~kind(X)=>(old(X)|~patient(X))))&
(![X]:((~happy(X)|~humble(X))<=>~generous(X)))&
(?[X]:((brave(X)|~patient(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:(~generous(X)))&
(funny(susan))&
(~creative(alice))&
((strong(lucy)|~wise(lucy))) | humble(susan) | [] | null | 0 |
Everyone who is old is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Alice is old. | entailment | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | old(alice) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4467320387294512788854051
% SZS output start Proof for 4467320387294512788854051
2. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p1]
3. ! [X0] : ((tall(X0) <~> ~rich(X0)) => (~wise(X0) & patient(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
9. ? [X0] : ~old(X0) <=> (~old(fred) & quiet(fred)) [input p8]
10. ! [X0] : (happy(X0) => (~wise(X0) <~> ~old(X0))) [input p9]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
13. ? [X0] : patient(X0) <=> (~rich(lucy) & wise(lucy)) [input p12]
16. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~quiet(X0) <~> tall(X0))) [input p15]
24. ~old(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 2]
26. ! [X0] : (~rich(X0) => (~happy(X0) & ~generous(X0))) [pure predicate removal 5]
28. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 25]
29. ! [X0] : ((~wise(X0) & patient(X0)) | (tall(X0) <=> ~rich(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~wise(X0) <~> ~old(X0)) | ~happy(X0)) [ennf transformation 10]
32. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
35. ! [X0] : ((~quiet(X0) <~> tall(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 16]
37. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 28]
38. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
39. patient(sK0) | ! [X1] : ~generous(X1) [skolemisation 37,38]
40. ! [X0] : ((~wise(X0) & patient(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 29]
45. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 45]
51. (? [X0] : ~old(X0) | (old(fred) | ~quiet(fred))) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [nnf transformation 9]
52. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X0] : old(X0)) [flattening 51]
53. (? [X0] : ~old(X0) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [rectify 52]
54. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
55. (~old(sK2) | old(fred) | ~quiet(fred)) & ((~old(fred) & quiet(fred)) | ! [X1] : old(X1)) [skolemisation 53,54]
56. ! [X0] : (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~happy(X0)) [nnf transformation 31]
58. (? [X0] : patient(X0) | (rich(lucy) | ~wise(lucy))) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [nnf transformation 13]
59. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X0] : ~patient(X0)) [flattening 58]
60. (? [X0] : patient(X0) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [rectify 59]
61. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
62. (patient(sK3) | rich(lucy) | ~wise(lucy)) & ((~rich(lucy) & wise(lucy)) | ! [X1] : ~patient(X1)) [skolemisation 60,61]
68. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 35]
81. patient(sK0) | ~generous(X1) [cnf transformation 39]
82. ~tall(X0) | ~rich(X0) | patient(X0) [cnf transformation 40]
90. ~generous(X0) | rich(X0) [cnf transformation 30]
91. ~happy(X0) | rich(X0) [cnf transformation 30]
92. ~kind(X0) | happy(X0) [cnf transformation 46]
104. quiet(fred) | old(X1) [cnf transformation 55]
105. ~old(fred) | old(X1) [cnf transformation 55]
108. ~happy(X0) | wise(X0) | old(X0) [cnf transformation 56]
109. kind(X0) | generous(X0) [cnf transformation 32]
110. kind(X0) | wise(X0) [cnf transformation 32]
116. ~rich(lucy) | ~patient(X1) [cnf transformation 62]
124. ~quiet(X0) | tall(X0) | ~wise(X0) | generous(X0) [cnf transformation 68]
137. ~old(alice) [cnf transformation 24]
141. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
142. ~generous(X1) <- (1) [avatar component clause 141]
144. 2 <=> patient(sK0) [avatar definition]
146. patient(sK0) <- (2) [avatar component clause 144]
147. 1 | 2 [avatar split clause 81,144,141]
192. 12 <=> quiet(fred) [avatar definition]
193. quiet(fred) <- (12) [avatar component clause 192]
196. 13 <=> old(fred) [avatar definition]
205. 15 <=> ! [X1] : old(X1) [avatar definition]
206. old(X1) <- (15) [avatar component clause 205]
207. 15 | ~13 [avatar split clause 105,196,205]
208. 15 | 12 [avatar split clause 104,192,205]
213. 17 <=> tall(fred) [avatar definition]
214. ~tall(fred) <- (~17) [avatar component clause 213]
215. tall(fred) <- (17) [avatar component clause 213]
232. 21 <=> rich(lucy) [avatar definition]
233. ~rich(lucy) <- (~21) [avatar component clause 232]
241. 23 <=> ! [X1] : ~patient(X1) [avatar definition]
242. ~patient(X1) <- (23) [avatar component clause 241]
243. 23 | ~21 [avatar split clause 116,232,241]
293. happy(X0) | generous(X0) [resolution 109,92]
294. happy(X0) | wise(X0) [resolution 110,92]
301. generous(X0) | rich(X0) [resolution 293,91]
302. rich(X0) [subsumption resolution 301,90]
303. ~rich(fred) | patient(fred) <- (17) [resolution 82,215]
305. patient(fred) <- (17) [subsumption resolution 303,302]
308. $false <- (~21) [resolution 302,233]
309. 21 [avatar contradiction clause 308]
310. $false <- (2, 23) [resolution 242,146]
312. $false <- (17, 23) [resolution 242,305]
313. ~17 | ~23 [avatar contradiction clause 312]
315. ~2 | ~23 [avatar contradiction clause 310]
371. wise(X0) | old(X0) | wise(X0) [resolution 108,294]
378. wise(X0) | old(X0) [duplicate literal removal 371]
390. tall(fred) | ~wise(fred) | generous(fred) <- (12) [resolution 124,193]
402. ~wise(fred) | generous(fred) <- (12, ~17) [subsumption resolution 390,214]
403. ~wise(fred) <- (1, 12, ~17) [subsumption resolution 402,142]
409. old(fred) <- (1, 12, ~17) [resolution 403,378]
412. 13 | ~1 | ~12 | 17 [avatar split clause 409,213,192,141,196]
414. $false <- (15) [resolution 206,137]
421. ~15 [avatar contradiction clause 414]
422. $false [avatar sat refutation 147,207,208,243,309,313,315,412,421]
% SZS output end Proof for 4467320387294512788854051
% ------------------------------
% 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 not strong or tall is both not creative and not curious and vice versa.
If someone is either tall or not brave then susan is not creative and vice versa.
Everyone who is both not old and not tall is funny and vice versa.
If mary is both not generous and not curious then someone is not happy and vice versa.
Everyone who is tall is both tall and not humble and vice versa.
Everyone who is both funny and creative is either quiet or not quiet.
If john is creative then john is either not brave or wise and vice versa.
Everyone who is either not calm or not wise is either not funny or not quiet and vice versa.
If mary is not funny then susan is not curious and vice versa.
If someone is both humble and creative then someone is kind or strong and vice versa.
If someone is rich then fred is both not rich and not wise and vice versa.
Everyone who is brave is both rich and not strong.
Everyone who is kind is wise or not wise.
If someone is either not brave or kind then someone is either patient or creative and vice versa.
Everyone who is both tall and not generous is either funny or generous.
Everyone who is either generous or kind is either not brave or not creative.
Someone is not patient.
Someone is quiet or not quiet.
Susan is either quiet or not strong.
Someone is either not rich or not creative.
Mary is brave.
Paul is not tall or not old.
Alice is not wise.
Someone is rich. | Fred is wise. | contradiction | (![X]:((~strong(X)<~>tall(X))<=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)<~>~brave(X))))<=>(~creative(susan)))&
(![X]:((~old(X)&~tall(X))<=>funny(X)))&
(((~generous(mary)&~curious(mary)))<=>(?[X]:(~happy(X))))&
(![X]:(tall(X)<=>(tall(X)&~humble(X))))&
(![X]:((funny(X)&creative(X))=>(quiet(X)<~>~quiet(X))))&
((creative(john))<=>((~brave(john)<~>wise(john))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~funny(X)<~>~quiet(X))))&
((~funny(mary))<=>(~curious(susan)))&
((?[X]:((humble(X)&creative(X))))<=>(?[X]:((kind(X)|strong(X)))))&
((?[X]:(rich(X)))<=>((~rich(fred)&~wise(fred))))&
(![X]:(brave(X)=>(rich(X)&~strong(X))))&
(![X]:(kind(X)=>(wise(X)|~wise(X))))&
((?[X]:((~brave(X)<~>kind(X))))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((tall(X)&~generous(X))=>(funny(X)<~>generous(X))))&
(![X]:((generous(X)<~>kind(X))=>(~brave(X)<~>~creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~quiet(X))))&
((quiet(susan)<~>~strong(susan)))&
(?[X]:((~rich(X)<~>~creative(X))))&
(brave(mary))&
((~tall(paul)|~old(paul)))&
(~wise(alice))&
(?[X]:(rich(X))) | wise(fred) | [
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4843325941014952930943495
% SZS output start Proof for 4843325941014952930943495
11. ? [X0] : rich(X0) <=> (~wise(fred) & ~rich(fred)) [input p10]
24. ? [X0] : rich(X0) [input p23]
25. wise(fred) [input hypothesis]
60. (? [X0] : rich(X0) | (wise(fred) | rich(fred))) & ((~wise(fred) & ~rich(fred)) | ! [X0] : ~rich(X0)) [nnf transformation 11]
61. (? [X0] : rich(X0) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X0] : ~rich(X0)) [flattening 60]
62. (? [X0] : rich(X0) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X1] : ~rich(X1)) [rectify 61]
63. ? [X0] : rich(X0) => rich(sK4) [choice axiom]
64. (rich(sK4) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X1] : ~rich(X1)) [skolemisation 62,63]
80. ? [X0] : rich(X0) => rich(sK10) [choice axiom]
81. rich(sK10) [skolemisation 24,80]
123. ~wise(fred) | ~rich(X1) [cnf transformation 64]
151. rich(sK10) [cnf transformation 81]
152. wise(fred) [cnf transformation 25]
255. 23 <=> wise(fred) [avatar definition]
264. 25 <=> ! [X1] : ~rich(X1) [avatar definition]
265. ~rich(X1) <- (25) [avatar component clause 264]
266. 25 | ~23 [avatar split clause 123,255,264]
334. 23 [avatar split clause 152,255]
335. $false <- (25) [resolution 265,151]
336. ~25 [avatar contradiction clause 335]
337. $false [avatar sat refutation 266,334,336]
% SZS output end Proof for 4843325941014952930943495
% ------------------------------
% 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 either wise or humble is not funny.
If someone is either not old or not generous then lucy is not wise or not creative and vice versa.
Everyone who is either not quiet or not strong is curious and vice versa.
Everyone who is either brave or rich is strong.
Everyone who is not patient is not calm or not kind and vice versa.
Everyone who is not quiet is either not quiet or not brave.
If paul is not kind then someone is not calm and vice versa.
Everyone who is happy or not humble is not calm and vice versa.
If someone is both old and tall then someone is not funny or brave.
Everyone who is not calm or curious is both strong and not old.
If someone is not tall or not funny then someone is funny.
If paul is both quiet and generous then alice is curious or old.
Everyone who is funny is both not rich and kind and vice versa.
If someone is patient or not brave then someone is not creative or generous.
Everyone who is either not strong or generous is both quiet and not curious and vice versa.
If alice is tall then alice is happy or calm.
Lucy is both funny and humble.
Paul is both old and not happy.
Someone is either not humble or not generous.
Mary is not rich.
Paul is either rich or old.
Mary is not quiet.
Paul is not patient.
Alice is not funny or not creative. | Alice is tall. | neutral | (![X]:((wise(X)<~>humble(X))=>~funny(X)))&
((?[X]:((~old(X)<~>~generous(X))))<=>((~wise(lucy)|~creative(lucy))))&
(![X]:((~quiet(X)<~>~strong(X))<=>curious(X)))&
(![X]:((brave(X)<~>rich(X))=>strong(X)))&
(![X]:(~patient(X)<=>(~calm(X)|~kind(X))))&
(![X]:(~quiet(X)=>(~quiet(X)<~>~brave(X))))&
((~kind(paul))<=>(?[X]:(~calm(X))))&
(![X]:((happy(X)|~humble(X))<=>~calm(X)))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~calm(X)|curious(X))=>(strong(X)&~old(X))))&
((?[X]:((~tall(X)|~funny(X))))=>(?[X]:(funny(X))))&
(((quiet(paul)&generous(paul)))=>((curious(alice)|old(alice))))&
(![X]:(funny(X)<=>(~rich(X)&kind(X))))&
((?[X]:((patient(X)|~brave(X))))=>(?[X]:((~creative(X)|generous(X)))))&
(![X]:((~strong(X)<~>generous(X))<=>(quiet(X)&~curious(X))))&
((tall(alice))=>((happy(alice)|calm(alice))))&
((funny(lucy)&humble(lucy)))&
((old(paul)&~happy(paul)))&
(?[X]:((~humble(X)<~>~generous(X))))&
(~rich(mary))&
((rich(paul)<~>old(paul)))&
(~quiet(mary))&
(~patient(paul))&
((~funny(alice)|~creative(alice))) | tall(alice) | [] | null | 0 |
Everyone who is not old is not quiet or not funny and vice versa.
Everyone who is either not creative or not quiet is creative and vice versa.
Everyone who is tall is both patient and old.
Everyone who is curious is not curious.
Everyone who is brave is either calm or not happy.
Everyone who is tall or curious is not tall.
If fred is both not patient and not quiet then someone is either curious or not patient and vice versa.
Everyone who is not funny is either not kind or old.
Everyone who is strong is not curious or not calm.
Everyone who is not humble is wise.
Everyone who is not creative is not humble or not kind and vice versa.
Everyone who is not brave is calm or not happy.
Everyone who is not funny or patient is both not strong and not generous and vice versa.
If someone is either generous or curious then fred is funny or creative.
If lucy is not tall then alice is either not kind or not patient and vice versa.
Someone is not creative or quiet.
Paul is both happy and not quiet.
Someone is humble or creative.
John is both patient and not curious.
Paul is both patient and not funny.
Someone is not generous.
Mary is not tall or not calm. | Alice is generous. | neutral | (![X]:(~old(X)<=>(~quiet(X)|~funny(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>creative(X)))&
(![X]:(tall(X)=>(patient(X)&old(X))))&
(![X]:(curious(X)=>~curious(X)))&
(![X]:(brave(X)=>(calm(X)<~>~happy(X))))&
(![X]:((tall(X)|curious(X))=>~tall(X)))&
(((~patient(fred)&~quiet(fred)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>old(X))))&
(![X]:(strong(X)=>(~curious(X)|~calm(X))))&
(![X]:(~humble(X)=>wise(X)))&
(![X]:(~creative(X)<=>(~humble(X)|~kind(X))))&
(![X]:(~brave(X)=>(calm(X)|~happy(X))))&
(![X]:((~funny(X)|patient(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((generous(X)<~>curious(X))))=>((funny(fred)|creative(fred))))&
((~tall(lucy))<=>((~kind(alice)<~>~patient(alice))))&
(?[X]:((~creative(X)|quiet(X))))&
((happy(paul)&~quiet(paul)))&
(?[X]:((humble(X)|creative(X))))&
((patient(john)&~curious(john)))&
((patient(paul)&~funny(paul)))&
(?[X]:(~generous(X)))&
((~tall(mary)|~calm(mary))) | generous(alice) | [] | null | 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Mary is not wise. | neutral | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | ~wise(mary) | [] | null | 0 |
Everyone who is either calm or not rich is either humble or not curious and vice versa. Everyone who is both not strong and not brave is both not brave and rich. If susan is rich then someone is either wise or not creative and vice versa. If susan is humble or patient then someone is both happy and not curious. If someone is not calm then mary is either curious or not patient. Everyone who is creative or not patient is either brave or creative. Everyone who is generous or humble is tall. Everyone who is not rich or not old is patient and vice versa. If someone is not tall or brave then someone is either quiet or not calm. Everyone who is not creative is either patient or not creative and vice versa. If paul is both not curious and not creative then alice is both not funny and wise. If someone is either curious or old then someone is both not kind and not generous. Everyone who is tall is not generous and vice versa. Everyone who is either patient or not strong is both not funny and creative and vice versa. If lucy is both patient and strong then someone is either creative or not strong and vice versa. Everyone who is both happy and not funny is not strong or old and vice versa. Someone is not wise. Mary is either not old or not quiet. Lucy is both not kind and calm. Alice is not funny or humble. Someone is not quiet. Someone is kind or brave. | Susan is calm. | neutral | (![X]:((calm(X)<~>~rich(X))<=>(humble(X)<~>~curious(X))))&
(![X]:((~strong(X)&~brave(X))=>(~brave(X)&rich(X))))&
((rich(susan))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((humble(susan)|patient(susan)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((curious(mary)<~>~patient(mary))))&
(![X]:((creative(X)|~patient(X))=>(brave(X)<~>creative(X))))&
(![X]:((generous(X)|humble(X))=>tall(X)))&
(![X]:((~rich(X)|~old(X))<=>patient(X)))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(patient(X)<~>~creative(X))))&
(((~curious(paul)&~creative(paul)))=>((~funny(alice)&wise(alice))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~funny(X)&creative(X))))&
(((patient(lucy)&strong(lucy)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((happy(X)&~funny(X))<=>(~strong(X)|old(X))))&
(?[X]:(~wise(X)))&
((~old(mary)<~>~quiet(mary)))&
((~kind(lucy)&calm(lucy)))&
((~funny(alice)|humble(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)|brave(X)))) | calm(susan) | [] | null | 0 |
Everyone who is either not funny or not kind is not curious or not patient.
Everyone who is both not quiet and quiet is not funny and vice versa.
Everyone who is not kind or old is humble or old and vice versa.
Everyone who is either wise or not quiet is not curious or funny and vice versa.
Everyone who is not humble or generous is either quiet or not humble and vice versa.
If susan is happy or not brave then someone is not wise or happy.
Everyone who is either not calm or not humble is not old or curious and vice versa.
If someone is both not happy and not tall then someone is either brave or not calm and vice versa.
If someone is not curious or not wise then someone is either not wise or curious and vice versa.
If susan is strong or kind then someone is humble.
If paul is either tall or not calm then someone is either not kind or not curious.
If paul is both not tall and not happy then mary is tall.
Everyone who is not humble is both not strong and not patient.
If mary is creative or brave then john is kind and vice versa.
If john is rich then someone is both wise and not generous.
If someone is not happy then someone is either not old or not rich.
Someone is strong or not funny.
Someone is either not funny or rich.
Someone is not curious or rich.
Paul is not wise.
Alice is humble.
Someone is both quiet and not happy.
Someone is both funny and creative. | Mary is tall. | neutral | (![X]:((~funny(X)<~>~kind(X))=>(~curious(X)|~patient(X))))&
(![X]:((~quiet(X)&quiet(X))<=>~funny(X)))&
(![X]:((~kind(X)|old(X))<=>(humble(X)|old(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~curious(X)|funny(X))))&
(![X]:((~humble(X)|generous(X))<=>(quiet(X)<~>~humble(X))))&
(((happy(susan)|~brave(susan)))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~old(X)|curious(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
((?[X]:((~curious(X)|~wise(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
(((strong(susan)|kind(susan)))=>(?[X]:(humble(X))))&
(((tall(paul)<~>~calm(paul)))=>(?[X]:((~kind(X)<~>~curious(X)))))&
(((~tall(paul)&~happy(paul)))=>(tall(mary)))&
(![X]:(~humble(X)=>(~strong(X)&~patient(X))))&
(((creative(mary)|brave(mary)))<=>(kind(john)))&
((rich(john))=>(?[X]:((wise(X)&~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((~old(X)<~>~rich(X)))))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((~curious(X)|rich(X))))&
(~wise(paul))&
(humble(alice))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((funny(X)&creative(X)))) | tall(mary) | [] | null | 0 |
Everyone who is both not happy and not generous is tall and vice versa.
If john is both not brave and not quiet then susan is either old or not kind.
Everyone who is not tall is both not strong and creative.
If someone is happy or not brave then someone is strong or not wise and vice versa.
If someone is wise or not happy then someone is both brave and not happy.
If mary is either kind or not strong then mary is not funny or old.
If fred is both not generous and creative then someone is either not wise or not kind.
Everyone who is not patient or not creative is both not humble and humble and vice versa.
Everyone who is either kind or humble is both not funny and generous.
Everyone who is both creative and not old is either not wise or not patient.
If someone is not tall then alice is both not wise and not happy.
Everyone who is not curious is either not generous or not happy.
Everyone who is not humble is either not creative or strong.
Everyone who is both not brave and strong is either not quiet or not wise and vice versa.
If fred is humble then alice is calm or not tall and vice versa.
If someone is both not curious and old then someone is both not calm and humble.
Lucy is either not humble or not creative.
Someone is both funny and happy.
Alice is creative.
Someone is both not old and not brave.
Someone is either not humble or not kind.
Someone is either wise or not curious.
Someone is funny or rich. | Lucy is generous. | contradiction | (![X]:((~happy(X)&~generous(X))<=>tall(X)))&
(((~brave(john)&~quiet(john)))=>((old(susan)<~>~kind(susan))))&
(![X]:(~tall(X)=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((kind(mary)<~>~strong(mary)))=>((~funny(mary)|old(mary))))&
(((~generous(fred)&creative(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(~funny(X)&generous(X))))&
(![X]:((creative(X)&~old(X))=>(~wise(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>((~wise(alice)&~happy(alice))))&
(![X]:(~curious(X)=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~brave(X)&strong(X))<=>(~quiet(X)<~>~wise(X))))&
((humble(fred))<=>((calm(alice)|~tall(alice))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((~calm(X)&humble(X)))))&
((~humble(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&happy(X))))&
(creative(alice))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((funny(X)|rich(X)))) | generous(lucy) | [
"p0",
"p2",
"p7",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7218846248152150751744642
% SZS output start Proof for 7218846248152150751744642
1. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> tall(X0)) [input p0]
3. ! [X0] : (~tall(X0) => (creative(X0) & ~strong(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (humble(X0) & ~humble(X0))) [input p7]
13. ! [X0] : (~humble(X0) => (~creative(X0) <~> strong(X0))) [input p12]
17. ~humble(lucy) <~> ~creative(lucy) [input p16]
24. generous(lucy) [input hypothesis]
31. ! [X0] : ((creative(X0) & ~strong(X0)) | tall(X0)) [ennf transformation 3]
42. ! [X0] : ((~creative(X0) <~> strong(X0)) | humble(X0)) [ennf transformation 13]
44. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) | happy(X0)))) [nnf transformation 1]
45. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | generous(X0) | happy(X0))) [flattening 44]
59. ! [X0] : (((~creative(X0) | ~patient(X0)) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
60. ! [X0] : ((~creative(X0) | ~patient(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | (creative(X0) & patient(X0)))) [flattening 59]
64. ! [X0] : (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | humble(X0)) [nnf transformation 42]
72. (creative(lucy) | humble(lucy)) & (~creative(lucy) | ~humble(lucy)) [nnf transformation 17]
85. ~tall(X0) | ~generous(X0) [cnf transformation 45]
88. ~strong(X0) | tall(X0) [cnf transformation 31]
103. ~humble(X0) | creative(X0) [cnf transformation 60]
105. humble(X0) | creative(X0) [cnf transformation 60]
117. strong(X0) | ~creative(X0) | humble(X0) [cnf transformation 64]
130. ~creative(lucy) | ~humble(lucy) [cnf transformation 72]
141. generous(lucy) [cnf transformation 24]
246. creative(X0) [subsumption resolution 103,105]
263. humble(X0) | strong(X0) [subsumption resolution 117,246]
292. ~humble(lucy) [subsumption resolution 130,246]
324. strong(lucy) [resolution 263,292]
328. tall(lucy) [resolution 324,88]
471. ~generous(lucy) [resolution 328,85]
473. $false [subsumption resolution 471,141]
% SZS output end Proof for 7218846248152150751744642
% ------------------------------
% 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 humble or not calm is either brave or kind and vice versa.
Everyone who is patient or brave is either rich or humble.
If mary is both humble and not happy then someone is generous or not happy and vice versa.
Everyone who is either calm or not happy is either not kind or not rich and vice versa.
Everyone who is both generous and not happy is happy or curious.
If someone is either generous or calm then someone is either calm or wise and vice versa.
If fred is both not creative and not brave then someone is either creative or not humble.
If mary is either not curious or not brave then someone is either not brave or happy.
Everyone who is either not patient or not calm is not calm and vice versa.
If someone is not funny or not brave then someone is both strong and happy and vice versa.
If susan is either not wise or funny then susan is not creative or generous.
If someone is not funny then someone is funny.
Everyone who is both not rich and calm is patient and vice versa.
Everyone who is both not curious and quiet is both creative and generous and vice versa.
If someone is patient or happy then someone is not quiet and vice versa.
If susan is both brave and not generous then someone is both creative and generous.
John is brave or not rich.
Lucy is wise or not happy.
Someone is either not happy or not patient.
Someone is both not rich and not brave.
Lucy is both not creative and not funny.
Someone is either creative or funny. | Lucy is not happy. | neutral | (![X]:((humble(X)|~calm(X))<=>(brave(X)<~>kind(X))))&
(![X]:((patient(X)|brave(X))=>(rich(X)<~>humble(X))))&
(((humble(mary)&~happy(mary)))<=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:((calm(X)<~>~happy(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((generous(X)&~happy(X))=>(happy(X)|curious(X))))&
((?[X]:((generous(X)<~>calm(X))))<=>(?[X]:((calm(X)<~>wise(X)))))&
(((~creative(fred)&~brave(fred)))=>(?[X]:((creative(X)<~>~humble(X)))))&
(((~curious(mary)<~>~brave(mary)))=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~patient(X)<~>~calm(X))<=>~calm(X)))&
((?[X]:((~funny(X)|~brave(X))))<=>(?[X]:((strong(X)&happy(X)))))&
(((~wise(susan)<~>funny(susan)))=>((~creative(susan)|generous(susan))))&
((?[X]:(~funny(X)))=>(?[X]:(funny(X))))&
(![X]:((~rich(X)&calm(X))<=>patient(X)))&
(![X]:((~curious(X)&quiet(X))<=>(creative(X)&generous(X))))&
((?[X]:((patient(X)|happy(X))))<=>(?[X]:(~quiet(X))))&
(((brave(susan)&~generous(susan)))=>(?[X]:((creative(X)&generous(X)))))&
((brave(john)|~rich(john)))&
((wise(lucy)|~happy(lucy)))&
(?[X]:((~happy(X)<~>~patient(X))))&
(?[X]:((~rich(X)&~brave(X))))&
((~creative(lucy)&~funny(lucy)))&
(?[X]:((creative(X)<~>funny(X)))) | ~happy(lucy) | [] | null | 0 |
If fred is either tall or generous then susan is both not generous and patient and vice versa. Everyone who is not brave or wise is curious and vice versa. Everyone who is both brave and generous is both not tall and strong and vice versa. If someone is both not rich and calm then someone is old or not quiet. If lucy is patient or not patient then someone is either creative or quiet and vice versa. If john is not strong or not wise then someone is both not generous and not old and vice versa. Everyone who is not funny is calm. Everyone who is not patient is quiet. If lucy is both not generous and not old then fred is curious and vice versa. If someone is either not tall or not funny then fred is not brave or old. Everyone who is both quiet and not brave is either not tall or patient. If someone is both not wise and not strong then someone is not calm. If someone is generous or not brave then someone is not calm or curious and vice versa. Everyone who is brave is either creative or not wise and vice versa. Everyone who is either not creative or not brave is not funny and vice versa. Everyone who is both old and patient is strong or creative and vice versa. Someone is either rich or funny. Someone is both not old and happy. Someone is both not funny and not quiet. Lucy is strong or not patient. Someone is both not humble and not kind. Someone is either not kind or not curious. Susan is calm. Someone is either not brave or brave. | Fred is brave. | neutral | (((tall(fred)<~>generous(fred)))<=>((~generous(susan)&patient(susan))))&
(![X]:((~brave(X)|wise(X))<=>curious(X)))&
(![X]:((brave(X)&generous(X))<=>(~tall(X)&strong(X))))&
((?[X]:((~rich(X)&calm(X))))=>(?[X]:((old(X)|~quiet(X)))))&
(((patient(lucy)|~patient(lucy)))<=>(?[X]:((creative(X)<~>quiet(X)))))&
(((~strong(john)|~wise(john)))<=>(?[X]:((~generous(X)&~old(X)))))&
(![X]:(~funny(X)=>calm(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(((~generous(lucy)&~old(lucy)))<=>(curious(fred)))&
((?[X]:((~tall(X)<~>~funny(X))))=>((~brave(fred)|old(fred))))&
(![X]:((quiet(X)&~brave(X))=>(~tall(X)<~>patient(X))))&
((?[X]:((~wise(X)&~strong(X))))=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)|~brave(X))))<=>(?[X]:((~calm(X)|curious(X)))))&
(![X]:(brave(X)<=>(creative(X)<~>~wise(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>~funny(X)))&
(![X]:((old(X)&patient(X))<=>(strong(X)|creative(X))))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((~old(X)&happy(X))))&
(?[X]:((~funny(X)&~quiet(X))))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:((~kind(X)<~>~curious(X))))&
(calm(susan))&
(?[X]:((~brave(X)<~>brave(X)))) | brave(fred) | [] | null | 0 |
Everyone who is both not old and not kind is both funny and not tall.
If someone is both not brave and not curious then fred is strong or not generous.
Everyone who is not patient is both wise and not rich and vice versa.
Everyone who is rich is not quiet and vice versa.
If mary is not wise then someone is not old or quiet and vice versa.
Everyone who is both not old and not generous is both not rich and not quiet and vice versa.
If someone is creative or not calm then someone is both not funny and not brave.
If susan is either not humble or not old then alice is both not creative and old.
If someone is not generous then lucy is both curious and quiet.
Everyone who is both creative and not creative is not rich.
If someone is both kind and not kind then someone is rich and vice versa.
If someone is generous then someone is curious and vice versa.
Everyone who is both happy and humble is both tall and happy and vice versa.
If someone is both not curious and not happy then mary is both old and wise.
If alice is happy then lucy is not quiet or not humble.
If someone is not curious then someone is not funny and vice versa.
Mary is either not patient or not wise.
Someone is either not rich or calm.
Someone is either rich or not strong.
Alice is either calm or rich.
Someone is brave.
Someone is not tall or not wise.
Lucy is brave.
Someone is wise. | Lucy is not quiet. | contradiction | (![X]:((~old(X)&~kind(X))=>(funny(X)&~tall(X))))&
((?[X]:((~brave(X)&~curious(X))))=>((strong(fred)|~generous(fred))))&
(![X]:(~patient(X)<=>(wise(X)&~rich(X))))&
(![X]:(rich(X)<=>~quiet(X)))&
((~wise(mary))<=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:((~old(X)&~generous(X))<=>(~rich(X)&~quiet(X))))&
((?[X]:((creative(X)|~calm(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(((~humble(susan)<~>~old(susan)))=>((~creative(alice)&old(alice))))&
((?[X]:(~generous(X)))=>((curious(lucy)&quiet(lucy))))&
(![X]:((creative(X)&~creative(X))=>~rich(X)))&
((?[X]:((kind(X)&~kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:(generous(X)))<=>(?[X]:(curious(X))))&
(![X]:((happy(X)&humble(X))<=>(tall(X)&happy(X))))&
((?[X]:((~curious(X)&~happy(X))))=>((old(mary)&wise(mary))))&
((happy(alice))=>((~quiet(lucy)|~humble(lucy))))&
((?[X]:(~curious(X)))<=>(?[X]:(~funny(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~rich(X)<~>calm(X))))&
(?[X]:((rich(X)<~>~strong(X))))&
((calm(alice)<~>rich(alice)))&
(?[X]:(brave(X)))&
(?[X]:((~tall(X)|~wise(X))))&
(brave(lucy))&
(?[X]:(wise(X))) | ~quiet(lucy) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8087033314296078265538821
% SZS output start Proof for 8087033314296078265538821
4. ! [X0] : (rich(X0) <=> ~quiet(X0)) [input p3]
11. ? [X0] : (~kind(X0) & kind(X0)) <=> ? [X0] : rich(X0) [input p10]
25. ~quiet(lucy) [input hypothesis]
27. ? [X0] : (~kind(X0) & kind(X0)) <=> ? [X1] : rich(X1) [rectify 11]
44. ! [X0] : ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))) [nnf transformation 4]
55. (? [X0] : (~kind(X0) & kind(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (kind(X0) | ~kind(X0))) [nnf transformation 27]
56. (? [X0] : (~kind(X0) & kind(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (kind(X3) | ~kind(X3))) [rectify 55]
57. ? [X0] : (~kind(X0) & kind(X0)) => (~kind(sK2) & kind(sK2)) [choice axiom]
58. ? [X2] : rich(X2) => rich(sK3) [choice axiom]
59. ((~kind(sK2) & kind(sK2)) | ! [X1] : ~rich(X1)) & (rich(sK3) | ! [X3] : (kind(X3) | ~kind(X3))) [skolemisation 56,58,57]
93. quiet(X0) | rich(X0) [cnf transformation 44]
113. kind(sK2) | ~rich(X1) [cnf transformation 59]
114. ~kind(sK2) | ~rich(X1) [cnf transformation 59]
138. ~quiet(lucy) [cnf transformation 25]
214. 18 <=> quiet(lucy) [avatar definition]
215. ~quiet(lucy) <- (~18) [avatar component clause 214]
224. 20 <=> ! [X1] : ~rich(X1) [avatar definition]
225. ~rich(X1) <- (20) [avatar component clause 224]
227. 21 <=> kind(sK2) [avatar definition]
230. 20 | ~21 [avatar split clause 114,227,224]
231. 20 | 21 [avatar split clause 113,227,224]
326. ~18 [avatar split clause 138,214]
339. rich(lucy) <- (~18) [resolution 93,215]
342. $false <- (~18, 20) [subsumption resolution 339,225]
343. 18 | ~20 [avatar contradiction clause 342]
346. $false [avatar sat refutation 230,231,326,343]
% SZS output end Proof for 8087033314296078265538821
% ------------------------------
% 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 generous and happy then fred is funny or tall.
Everyone who is humble is not generous and vice versa.
If alice is not generous then someone is either curious or not creative.
Everyone who is both not funny and not curious is either not generous or rich.
Everyone who is old or tall is wise or not calm.
If alice is old or not kind then someone is both quiet and funny and vice versa.
Everyone who is both generous and calm is funny and vice versa.
If paul is strong or rich then someone is both not old and happy.
Everyone who is both brave and not quiet is either brave or not tall and vice versa.
If fred is not quiet then someone is both rich and not quiet.
If lucy is either not curious or brave then paul is either curious or kind.
If someone is both quiet and happy then someone is both not creative and not funny and vice versa.
If someone is both calm and not rich then someone is not creative or not curious and vice versa.
Everyone who is either kind or not patient is not happy and vice versa.
Everyone who is both not calm and not rich is either old or not old and vice versa.
Everyone who is patient is both not curious and curious and vice versa.
Paul is not tall.
Someone is both quiet and old.
Someone is both not tall and not humble.
Someone is either strong or curious.
Someone is not curious or not humble.
Someone is either wise or calm.
John is both not funny and kind. | Paul is brave. | entailment | ((?[X]:((generous(X)&happy(X))))=>((funny(fred)|tall(fred))))&
(![X]:(humble(X)<=>~generous(X)))&
((~generous(alice))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~funny(X)&~curious(X))=>(~generous(X)<~>rich(X))))&
(![X]:((old(X)|tall(X))=>(wise(X)|~calm(X))))&
(((old(alice)|~kind(alice)))<=>(?[X]:((quiet(X)&funny(X)))))&
(![X]:((generous(X)&calm(X))<=>funny(X)))&
(((strong(paul)|rich(paul)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((brave(X)&~quiet(X))<=>(brave(X)<~>~tall(X))))&
((~quiet(fred))=>(?[X]:((rich(X)&~quiet(X)))))&
(((~curious(lucy)<~>brave(lucy)))=>((curious(paul)<~>kind(paul))))&
((?[X]:((quiet(X)&happy(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
((?[X]:((calm(X)&~rich(X))))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>~happy(X)))&
(![X]:((~calm(X)&~rich(X))<=>(old(X)<~>~old(X))))&
(![X]:(patient(X)<=>(~curious(X)&curious(X))))&
(~tall(paul))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((~tall(X)&~humble(X))))&
(?[X]:((strong(X)<~>curious(X))))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:((wise(X)<~>calm(X))))&
((~funny(john)&kind(john))) | brave(paul) | [
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5904337684076875165998604
% SZS output start Proof for 5904337684076875165998604
9. ! [X0] : ((~quiet(X0) & brave(X0)) <=> (brave(X0) <~> ~tall(X0))) [input p8]
17. ~tall(paul) [input p16]
24. ~brave(paul) [input hypothesis]
52. ! [X0] : (((~quiet(X0) & brave(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | (quiet(X0) | ~brave(X0)))) [nnf transformation 9]
53. ! [X0] : (((~quiet(X0) & brave(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | quiet(X0) | ~brave(X0))) [flattening 52]
107. brave(X0) | brave(X0) | tall(X0) [cnf transformation 53]
138. ~tall(paul) [cnf transformation 17]
150. ~brave(paul) [cnf transformation 24]
156. brave(X0) | tall(X0) [duplicate literal removal 107]
363. tall(paul) [resolution 156,150]
365. $false [subsumption resolution 363,138]
% SZS output end Proof for 5904337684076875165998604
% ------------------------------
% 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 patient and not brave then someone is either brave or wise.
If fred is not quiet or not rich then someone is both brave and not rich.
Everyone who is not happy or not funny is patient or wise.
Everyone who is both not brave and not wise is not calm or not strong and vice versa.
Everyone who is not wise is both creative and not funny.
Everyone who is either not kind or not quiet is both happy and brave and vice versa.
If someone is both not strong and tall then john is quiet and vice versa.
If someone is either not calm or not rich then susan is both not calm and not strong.
Everyone who is either not humble or tall is wise.
Everyone who is either generous or not kind is either not quiet or not curious.
Everyone who is not creative or humble is both curious and quiet and vice versa.
Everyone who is either not creative or rich is not happy or creative.
If john is both not rich and not curious then susan is patient or not kind and vice versa.
If someone is tall then someone is either kind or not kind and vice versa.
Everyone who is either happy or not kind is not humble.
Alice is curious.
Paul is patient or not happy.
Someone is generous or not generous.
Someone is both rich and not creative.
Paul is both not kind and not humble.
Someone is either wise or not wise.
Lucy is either funny or tall.
Susan is not calm. | John is curious. | contradiction | ((?[X]:((patient(X)&~brave(X))))=>(?[X]:((brave(X)<~>wise(X)))))&
(((~quiet(fred)|~rich(fred)))=>(?[X]:((brave(X)&~rich(X)))))&
(![X]:((~happy(X)|~funny(X))=>(patient(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(~calm(X)|~strong(X))))&
(![X]:(~wise(X)=>(creative(X)&~funny(X))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(happy(X)&brave(X))))&
((?[X]:((~strong(X)&tall(X))))<=>(quiet(john)))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~calm(susan)&~strong(susan))))&
(![X]:((~humble(X)<~>tall(X))=>wise(X)))&
(![X]:((generous(X)<~>~kind(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((~creative(X)|humble(X))<=>(curious(X)&quiet(X))))&
(![X]:((~creative(X)<~>rich(X))=>(~happy(X)|creative(X))))&
(((~rich(john)&~curious(john)))<=>((patient(susan)|~kind(susan))))&
((?[X]:(tall(X)))<=>(?[X]:((kind(X)<~>~kind(X)))))&
(![X]:((happy(X)<~>~kind(X))=>~humble(X)))&
(curious(alice))&
((patient(paul)|~happy(paul)))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((rich(X)&~creative(X))))&
((~kind(paul)&~humble(paul)))&
(?[X]:((wise(X)<~>~wise(X))))&
((funny(lucy)<~>tall(lucy)))&
(~calm(susan)) | curious(john) | [
"p2",
"p3",
"p4",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1402413772690666802885141
% SZS output start Proof for 1402413772690666802885141
3. ! [X0] : ((~funny(X0) | ~happy(X0)) => (wise(X0) | patient(X0))) [input p2]
4. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> (~strong(X0) | ~calm(X0))) [input p3]
5. ! [X0] : (~wise(X0) => (~funny(X0) & creative(X0))) [input p4]
13. (~curious(john) & ~rich(john)) <=> (~kind(susan) | patient(susan)) [input p12]
23. ~calm(susan) [input p22]
24. curious(john) [input hypothesis]
29. ! [X0] : ((wise(X0) | patient(X0)) | (funny(X0) & happy(X0))) [ennf transformation 3]
30. ! [X0] : (wise(X0) | patient(X0) | (funny(X0) & happy(X0))) [flattening 29]
31. ! [X0] : ((~funny(X0) & creative(X0)) | wise(X0)) [ennf transformation 5]
44. ! [X0] : (((~wise(X0) & ~brave(X0)) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | (wise(X0) | brave(X0)))) [nnf transformation 4]
45. ! [X0] : (((~wise(X0) & ~brave(X0)) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | wise(X0) | brave(X0))) [flattening 44]
58. ((~curious(john) & ~rich(john)) | (kind(susan) & ~patient(susan))) & ((~kind(susan) | patient(susan)) | (curious(john) | rich(john))) [nnf transformation 13]
59. ((~curious(john) & ~rich(john)) | (kind(susan) & ~patient(susan))) & (~kind(susan) | patient(susan) | curious(john) | rich(john)) [flattening 58]
81. funny(X0) | patient(X0) | wise(X0) [cnf transformation 30]
85. ~wise(X0) | calm(X0) [cnf transformation 45]
88. ~funny(X0) | wise(X0) [cnf transformation 31]
118. ~curious(john) | ~patient(susan) [cnf transformation 59]
137. ~calm(susan) [cnf transformation 23]
138. curious(john) [cnf transformation 24]
206. 15 <=> calm(susan) [avatar definition]
208. ~calm(susan) <- (~15) [avatar component clause 206]
216. 17 <=> curious(john) [avatar definition]
221. 18 <=> patient(susan) [avatar definition]
223. ~patient(susan) <- (~18) [avatar component clause 221]
224. ~18 | ~17 [avatar split clause 118,216,221]
263. ~15 [avatar split clause 137,206]
264. 17 [avatar split clause 138,216]
280. patient(X0) | wise(X0) | wise(X0) [resolution 81,88]
281. wise(X0) | patient(X0) [duplicate literal removal 280]
432. calm(X1) | patient(X1) [resolution 281,85]
489. patient(susan) <- (~15) [resolution 432,208]
492. $false <- (~15, ~18) [subsumption resolution 489,223]
493. 15 | 18 [avatar contradiction clause 492]
494. $false [avatar sat refutation 224,263,264,493]
% SZS output end Proof for 1402413772690666802885141
% ------------------------------
% 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 |
Everyone who is both generous and not patient is either not tall or not happy.
If fred is either not old or not calm then someone is not quiet or not rich and vice versa.
Everyone who is not creative or not wise is curious or generous and vice versa.
If someone is both patient and brave then alice is calm and vice versa.
Everyone who is kind is not creative and vice versa.
Everyone who is either strong or humble is not calm and vice versa.
Everyone who is both not patient and kind is both not funny and old.
If lucy is funny then someone is either not old or not calm and vice versa.
Everyone who is not quiet or not creative is both strong and humble.
If paul is humble then susan is not generous and vice versa.
Everyone who is not wise is either not wise or not kind and vice versa.
Everyone who is either wise or tall is both creative and not funny.
Everyone who is humble is either not patient or rich.
If someone is old or calm then someone is not rich or not tall.
If mary is both not happy and tall then john is either rich or not strong.
If alice is either patient or not calm then mary is both creative and funny.
John is either brave or calm.
Paul is not brave.
Alice is not calm or humble.
Susan is patient.
Someone is not curious or not calm.
Mary is not humble or calm. | John is not strong. | contradiction | (![X]:((generous(X)&~patient(X))=>(~tall(X)<~>~happy(X))))&
(((~old(fred)<~>~calm(fred)))<=>(?[X]:((~quiet(X)|~rich(X)))))&
(![X]:((~creative(X)|~wise(X))<=>(curious(X)|generous(X))))&
((?[X]:((patient(X)&brave(X))))<=>(calm(alice)))&
(![X]:(kind(X)<=>~creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~patient(X)&kind(X))=>(~funny(X)&old(X))))&
((funny(lucy))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|~creative(X))=>(strong(X)&humble(X))))&
((humble(paul))<=>(~generous(susan)))&
(![X]:(~wise(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&~funny(X))))&
(![X]:(humble(X)=>(~patient(X)<~>rich(X))))&
((?[X]:((old(X)|calm(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(((~happy(mary)&tall(mary)))=>((rich(john)<~>~strong(john))))&
(((patient(alice)<~>~calm(alice)))=>((creative(mary)&funny(mary))))&
((brave(john)<~>calm(john)))&
(~brave(paul))&
((~calm(alice)|humble(alice)))&
(patient(susan))&
(?[X]:((~curious(X)|~calm(X))))&
((~humble(mary)|calm(mary))) | ~strong(john) | [
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8117361196099385885758591
% SZS output start Proof for 8117361196099385885758591
5. ! [X0] : (kind(X0) <=> ~creative(X0)) [input p4]
9. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (humble(X0) & strong(X0))) [input p8]
11. ! [X0] : (~wise(X0) <=> (~wise(X0) <~> ~kind(X0))) [input p10]
23. ~strong(john) [input hypothesis]
29. ! [X0] : ((humble(X0) & strong(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 9]
47. ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 5]
54. ! [X0] : ((~wise(X0) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0)))) & (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | wise(X0))) [nnf transformation 11]
80. ~kind(X0) | ~creative(X0) [cnf transformation 47]
93. strong(X0) | creative(X0) [cnf transformation 29]
99. kind(X0) | wise(X0) | wise(X0) [cnf transformation 54]
101. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 54]
123. ~strong(john) [cnf transformation 23]
124. kind(X0) | wise(X0) [duplicate literal removal 99]
125. ~wise(X0) | kind(X0) [duplicate literal removal 101]
204. kind(X0) [subsumption resolution 124,125]
234. 25 <=> strong(john) [avatar definition]
235. ~strong(john) <- (~25) [avatar component clause 234]
288. ~25 [avatar split clause 123,234]
289. ~creative(X0) [resolution 80,204]
292. creative(john) <- (~25) [resolution 93,235]
293. $false <- (~25) [subsumption resolution 292,289]
294. 25 [avatar contradiction clause 293]
295. $false [avatar sat refutation 288,294]
% SZS output end Proof for 8117361196099385885758591
% ------------------------------
% 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 fred is not happy or not rich then someone is quiet and vice versa. Everyone who is both not humble and calm is kind or calm. If someone is calm or not curious then someone is wise and vice versa. Everyone who is both not humble and not funny is both tall and not funny. If someone is either not tall or old then someone is brave or humble and vice versa. If lucy is tall or brave then someone is both patient and not patient. If mary is old then john is either not old or funny and vice versa. Everyone who is both funny and old is both not curious and not calm and vice versa. If someone is rich or funny then john is creative or not calm. Everyone who is humble is both not funny and not old. Everyone who is not old is not happy and vice versa. Everyone who is quiet is both not humble and wise and vice versa. Everyone who is either old or not wise is both not curious and not generous and vice versa. Everyone who is either not kind or tall is not wise and vice versa. If paul is both not wise and not happy then someone is kind or tall and vice versa. If susan is either not rich or kind then mary is tall and vice versa. Someone is wise or funny. Someone is happy or old. Paul is either not humble or curious. Someone is old or quiet. Fred is either not funny or curious. Fred is either not patient or not kind. Someone is not curious or not calm. Susan is generous or curious. | Paul is calm. | entailment | (((~happy(fred)|~rich(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)&calm(X))=>(kind(X)|calm(X))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~funny(X))=>(tall(X)&~funny(X))))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(((tall(lucy)|brave(lucy)))=>(?[X]:((patient(X)&~patient(X)))))&
((old(mary))<=>((~old(john)<~>funny(john))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(((~wise(paul)&~happy(paul)))<=>(?[X]:((kind(X)|tall(X)))))&
(((~rich(susan)<~>kind(susan)))<=>(tall(mary)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:((happy(X)|old(X))))&
((~humble(paul)<~>curious(paul)))&
(?[X]:((old(X)|quiet(X))))&
((~funny(fred)<~>curious(fred)))&
((~patient(fred)<~>~kind(fred)))&
(?[X]:((~curious(X)|~calm(X))))&
((generous(susan)|curious(susan))) | calm(paul) | [
"p2",
"p7",
"p10",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4212515552785518859595975
% SZS output start Proof for 4212515552785518859595975
3. ? [X0] : (~curious(X0) | calm(X0)) <=> ? [X0] : wise(X0) [input p2]
8. ! [X0] : ((old(X0) & funny(X0)) <=> (~calm(X0) & ~curious(X0))) [input p7]
11. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p10]
13. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (~generous(X0) & ~curious(X0))) [input p12]
14. ! [X0] : ((~kind(X0) <~> tall(X0)) <=> ~wise(X0)) [input p13]
15. (~happy(paul) & ~wise(paul)) <=> ? [X0] : (tall(X0) | kind(X0)) [input p14]
21. ~funny(fred) <~> curious(fred) [input p20]
25. ~calm(paul) [input hypothesis]
26. ? [X0] : (~curious(X0) | calm(X0)) <=> ? [X1] : wise(X1) [rectify 3]
40. (? [X0] : (~curious(X0) | calm(X0)) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : (curious(X0) & ~calm(X0))) [nnf transformation 26]
41. (? [X0] : (~curious(X0) | calm(X0)) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : (curious(X3) & ~calm(X3))) [rectify 40]
42. ? [X0] : (~curious(X0) | calm(X0)) => (~curious(sK1) | calm(sK1)) [choice axiom]
43. ? [X2] : wise(X2) => wise(sK2) [choice axiom]
44. ((~curious(sK1) | calm(sK1)) | ! [X1] : ~wise(X1)) & (wise(sK2) | ! [X3] : (curious(X3) & ~calm(X3))) [skolemisation 41,43,42]
53. ! [X0] : (((old(X0) & funny(X0)) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | (~old(X0) | ~funny(X0)))) [nnf transformation 8]
54. ! [X0] : (((old(X0) & funny(X0)) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | ~old(X0) | ~funny(X0))) [flattening 53]
55. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 11]
58. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 13]
59. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [flattening 58]
60. ! [X0] : ((((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | wise(X0)) & (~wise(X0) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0))))) [nnf transformation 14]
61. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | (happy(paul) | wise(paul))) [nnf transformation 15]
62. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | happy(paul) | wise(paul)) [flattening 61]
63. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X1] : (tall(X1) | kind(X1)) | happy(paul) | wise(paul)) [rectify 62]
64. ? [X1] : (tall(X1) | kind(X1)) => (tall(sK6) | kind(sK6)) [choice axiom]
65. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & ((tall(sK6) | kind(sK6)) | happy(paul) | wise(paul)) [skolemisation 63,64]
74. (~curious(fred) | funny(fred)) & (curious(fred) | ~funny(fred)) [nnf transformation 21]
82. wise(sK2) | ~calm(X3) [cnf transformation 44]
83. wise(sK2) | curious(X3) [cnf transformation 44]
84. ~curious(sK1) | calm(sK1) | ~wise(X1) [cnf transformation 44]
101. ~old(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 54]
104. old(X0) | calm(X0) | curious(X0) [cnf transformation 54]
108. ~old(X0) | happy(X0) [cnf transformation 55]
113. ~curious(X0) | old(X0) | wise(X0) [cnf transformation 59]
118. ~wise(X0) | tall(X0) | kind(X0) [cnf transformation 60]
123. ~wise(paul) | ~kind(X0) [cnf transformation 65]
124. ~wise(paul) | ~tall(X0) [cnf transformation 65]
125. ~happy(paul) | ~kind(X0) [cnf transformation 65]
126. ~happy(paul) | ~tall(X0) [cnf transformation 65]
137. ~curious(fred) | funny(fred) [cnf transformation 74]
142. ~calm(paul) [cnf transformation 25]
162. 5 <=> ! [X1] : ~wise(X1) [avatar definition]
163. ~wise(X1) <- (5) [avatar component clause 162]
165. 6 <=> calm(sK1) [avatar definition]
167. calm(sK1) <- (6) [avatar component clause 165]
169. 7 <=> curious(sK1) [avatar definition]
171. ~curious(sK1) <- (~7) [avatar component clause 169]
172. 5 | 6 | ~7 [avatar split clause 84,169,165,162]
174. 8 <=> ! [X3] : curious(X3) [avatar definition]
175. curious(X3) <- (8) [avatar component clause 174]
177. 9 <=> wise(sK2) [avatar definition]
179. wise(sK2) <- (9) [avatar component clause 177]
180. 8 | 9 [avatar split clause 83,177,174]
182. 10 <=> ! [X3] : ~calm(X3) [avatar definition]
183. ~calm(X3) <- (10) [avatar component clause 182]
184. 10 | 9 [avatar split clause 82,177,182]
252. 25 <=> ! [X0] : ~tall(X0) [avatar definition]
253. ~tall(X0) <- (25) [avatar component clause 252]
255. 26 <=> happy(paul) [avatar definition]
257. ~happy(paul) <- (~26) [avatar component clause 255]
258. 25 | ~26 [avatar split clause 126,255,252]
260. 27 <=> ! [X0] : ~kind(X0) [avatar definition]
261. ~kind(X0) <- (27) [avatar component clause 260]
262. 27 | ~26 [avatar split clause 125,255,260]
264. 28 <=> wise(paul) [avatar definition]
266. ~wise(paul) <- (~28) [avatar component clause 264]
267. 25 | ~28 [avatar split clause 124,264,252]
268. 27 | ~28 [avatar split clause 123,264,260]
309. 37 <=> curious(paul) [avatar definition]
310. curious(paul) <- (37) [avatar component clause 309]
311. ~curious(paul) <- (~37) [avatar component clause 309]
324. 40 <=> funny(fred) [avatar definition]
326. funny(fred) <- (40) [avatar component clause 324]
328. 41 <=> curious(fred) [avatar definition]
329. curious(fred) <- (41) [avatar component clause 328]
330. ~curious(fred) <- (~41) [avatar component clause 328]
331. 40 | ~41 [avatar split clause 137,328,324]
434. curious(X2) | calm(X2) | happy(X2) [resolution 104,108]
559. $false <- (8, ~41) [resolution 175,330]
562. $false <- (~7, 8) [resolution 175,171]
567. 7 | ~8 [avatar contradiction clause 562]
570. ~8 | 41 [avatar contradiction clause 559]
571. tall(sK2) | kind(sK2) <- (9) [resolution 179,118]
591. old(fred) | wise(fred) <- (41) [resolution 329,113]
593. 80 <=> wise(fred) [avatar definition]
595. wise(fred) <- (80) [avatar component clause 593]
597. 81 <=> old(fred) [avatar definition]
599. old(fred) <- (81) [avatar component clause 597]
600. 80 | 81 | ~41 [avatar split clause 591,328,597,593]
698. ~curious(fred) | ~funny(fred) <- (81) [resolution 599,101]
703. ~funny(fred) <- (41, 81) [subsumption resolution 698,329]
704. $false <- (40, 41, 81) [subsumption resolution 703,326]
705. ~40 | ~41 | ~81 [avatar contradiction clause 704]
757. calm(paul) | happy(paul) <- (~37) [resolution 434,311]
764. happy(paul) <- (~37) [subsumption resolution 757,142]
769. 26 | 37 [avatar split clause 764,309,255]
793. old(paul) | wise(paul) <- (37) [resolution 310,113]
794. old(paul) <- (~28, 37) [subsumption resolution 793,266]
813. happy(paul) <- (~28, 37) [resolution 794,108]
816. $false <- (~26, ~28, 37) [subsumption resolution 813,257]
817. 26 | 28 | ~37 [avatar contradiction clause 816]
838. kind(sK2) <- (9, 25) [subsumption resolution 571,253]
839. $false <- (9, 25, 27) [subsumption resolution 838,261]
840. ~9 | ~25 | ~27 [avatar contradiction clause 839]
848. $false <- (5, 80) [resolution 163,595]
851. ~5 | ~80 [avatar contradiction clause 848]
852. $false <- (6, 10) [subsumption resolution 167,183]
853. ~6 | ~10 [avatar contradiction clause 852]
854. $false [avatar sat refutation 172,180,184,258,262,267,268,331,567,570,600,705,769,817,840,851,853]
% SZS output end Proof for 4212515552785518859595975
% ------------------------------
% 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]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both calm and not humble then lucy is both not curious and not old. If john is either curious or not patient then someone is both not rich and tall and vice versa. If someone is not curious then susan is both not rich and brave and vice versa. Everyone who is not wise or not curious is not generous and vice versa. If paul is either kind or not patient then lucy is not brave or brave and vice versa. Everyone who is rich or quiet is either not happy or not brave. Everyone who is humble is not old and vice versa. Everyone who is either not brave or generous is funny. If someone is old then paul is either tall or not generous and vice versa. Everyone who is funny is both patient and not happy. Everyone who is happy is funny. If mary is generous or patient then someone is not creative. Everyone who is not quiet or brave is either not strong or wise. Everyone who is not happy is not strong. Everyone who is kind is both not strong and not creative and vice versa. If mary is both calm and not funny then someone is both not creative and not wise. John is both tall and creative. Mary is either not kind or not funny. Mary is either happy or not generous. Fred is not brave or not funny. Lucy is either not wise or not patient. Someone is either humble or not wise. | John is not rich. | neutral | (((calm(susan)&~humble(susan)))=>((~curious(lucy)&~old(lucy))))&
(((curious(john)<~>~patient(john)))<=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:(~curious(X)))<=>((~rich(susan)&brave(susan))))&
(![X]:((~wise(X)|~curious(X))<=>~generous(X)))&
(((kind(paul)<~>~patient(paul)))<=>((~brave(lucy)|brave(lucy))))&
(![X]:((rich(X)|quiet(X))=>(~happy(X)<~>~brave(X))))&
(![X]:(humble(X)<=>~old(X)))&
(![X]:((~brave(X)<~>generous(X))=>funny(X)))&
((?[X]:(old(X)))<=>((tall(paul)<~>~generous(paul))))&
(![X]:(funny(X)=>(patient(X)&~happy(X))))&
(![X]:(happy(X)=>funny(X)))&
(((generous(mary)|patient(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)|brave(X))=>(~strong(X)<~>wise(X))))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:(kind(X)<=>(~strong(X)&~creative(X))))&
(((calm(mary)&~funny(mary)))=>(?[X]:((~creative(X)&~wise(X)))))&
((tall(john)&creative(john)))&
((~kind(mary)<~>~funny(mary)))&
((happy(mary)<~>~generous(mary)))&
((~brave(fred)|~funny(fred)))&
((~wise(lucy)<~>~patient(lucy)))&
(?[X]:((humble(X)<~>~wise(X)))) | ~rich(john) | [] | null | 0 |
Everyone who is either not generous or not kind is kind and vice versa.
If someone is both not creative and not kind then lucy is not curious or not wise and vice versa.
If someone is tall or brave then susan is both not calm and brave.
Everyone who is either not curious or not creative is either not brave or not curious and vice versa.
Everyone who is humble or brave is both tall and generous.
If someone is wise then someone is both not humble and not kind.
Everyone who is funny or not humble is either not brave or old and vice versa.
Everyone who is either not kind or funny is strong or funny and vice versa.
If alice is either not curious or not rich then lucy is not rich and vice versa.
Everyone who is not wise is calm or creative.
Everyone who is either not tall or not generous is both not calm and not humble.
If lucy is not funny then someone is either tall or not curious and vice versa.
Everyone who is either not rich or not tall is brave.
Everyone who is humble is either not patient or generous.
Everyone who is either not humble or rich is both not funny and not old and vice versa.
Someone is wise or not generous.
John is either quiet or not curious.
Alice is happy.
Someone is both not patient and kind. | Alice is not rich. | entailment | (![X]:((~generous(X)<~>~kind(X))<=>kind(X)))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((humble(X)|brave(X))=>(tall(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(strong(X)|funny(X))))&
(((~curious(alice)<~>~rich(alice)))<=>(~rich(lucy)))&
(![X]:(~wise(X)=>(calm(X)|creative(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~calm(X)&~humble(X))))&
((~funny(lucy))<=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:((~rich(X)<~>~tall(X))=>brave(X)))&
(![X]:(humble(X)=>(~patient(X)<~>generous(X))))&
(![X]:((~humble(X)<~>rich(X))<=>(~funny(X)&~old(X))))&
(?[X]:((wise(X)|~generous(X))))&
((quiet(john)<~>~curious(john)))&
(happy(alice))&
(?[X]:((~patient(X)&kind(X)))) | ~rich(alice) | [
"p0",
"p2",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4849819052708752215477738
% SZS output start Proof for 4849819052708752215477738
1. ! [X0] : ((~generous(X0) <~> ~kind(X0)) <=> kind(X0)) [input p0]
3. ? [X0] : (brave(X0) | tall(X0)) => (brave(susan) & ~calm(susan)) [input p2]
5. ! [X0] : ((brave(X0) | humble(X0)) => (generous(X0) & tall(X0))) [input p4]
13. ! [X0] : ((~rich(X0) <~> ~tall(X0)) => brave(X0)) [input p12]
20. rich(alice) [input hypothesis]
23. (brave(susan) & ~calm(susan)) | ! [X0] : (~brave(X0) & ~tall(X0)) [ennf transformation 3]
24. ! [X0] : ((generous(X0) & tall(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 5]
29. ! [X0] : (brave(X0) | (~rich(X0) <=> ~tall(X0))) [ennf transformation 13]
31. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | ~kind(X0)) & (kind(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [nnf transformation 1]
51. ! [X0] : (brave(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [nnf transformation 29]
61. kind(X0) | ~generous(X0) | kind(X0) [cnf transformation 31]
62. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 31]
71. brave(susan) | ~tall(X0) [cnf transformation 23]
82. ~brave(X0) | tall(X0) [cnf transformation 24]
84. generous(X0) | ~brave(X0) [cnf transformation 24]
113. brave(X0) | ~rich(X0) | tall(X0) [cnf transformation 51]
127. rich(alice) [cnf transformation 20]
134. kind(X0) | ~generous(X0) [duplicate literal removal 61]
135. ~kind(X0) | ~generous(X0) [duplicate literal removal 62]
136. ~generous(X0) [subsumption resolution 134,135]
162. 6 <=> ! [X0] : ~brave(X0) [avatar definition]
163. ~brave(X0) <- (6) [avatar component clause 162]
165. 7 <=> brave(susan) [avatar definition]
167. brave(susan) <- (7) [avatar component clause 165]
170. 8 <=> ! [X0] : ~tall(X0) [avatar definition]
171. ~tall(X0) <- (8) [avatar component clause 170]
172. 8 | 7 [avatar split clause 71,165,170]
181. ~brave(X0) [subsumption resolution 84,136]
182. 6 [avatar split clause 181,162]
204. 14 <=> rich(alice) [avatar definition]
206. rich(alice) <- (14) [avatar component clause 204]
234. ~rich(X0) | tall(X0) [subsumption resolution 113,82]
248. 14 [avatar split clause 127,204]
249. $false <- (6, 7) [resolution 167,163]
250. ~6 | ~7 [avatar contradiction clause 249]
252. tall(alice) <- (14) [resolution 234,206]
253. $false <- (8, 14) [subsumption resolution 252,171]
254. ~8 | ~14 [avatar contradiction clause 253]
255. $false [avatar sat refutation 172,182,248,250,254]
% SZS output end Proof for 4849819052708752215477738
% ------------------------------
% 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 either brave or kind is either not funny or generous and vice versa. If someone is not strong or not kind then fred is not generous or wise and vice versa. Everyone who is either calm or old is rich and vice versa. If someone is either calm or happy then someone is not tall and vice versa. If someone is humble or calm then mary is either patient or not tall. If alice is funny then john is both not old and not wise. Everyone who is both not generous and not brave is both curious and brave and vice versa. Everyone who is not brave is kind or not tall and vice versa. If fred is not funny or not humble then lucy is either not creative or wise and vice versa. Everyone who is both brave and not tall is creative or not wise. If paul is not brave then lucy is either brave or creative. Everyone who is both funny and not happy is either curious or wise. Everyone who is either old or curious is not calm and vice versa. Everyone who is either not wise or not brave is both not strong and not creative and vice versa. If john is humble then lucy is both not quiet and not happy. Everyone who is either not humble or not kind is not tall or old and vice versa. Susan is either brave or rich. Someone is kind. Fred is not happy. Susan is both not creative and not patient. Someone is tall or brave. Alice is both curious and funny. | Alice is not funny. | contradiction | (![X]:((brave(X)<~>kind(X))<=>(~funny(X)<~>generous(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((~generous(fred)|wise(fred))))&
(![X]:((calm(X)<~>old(X))<=>rich(X)))&
((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((humble(X)|calm(X))))=>((patient(mary)<~>~tall(mary))))&
((funny(alice))=>((~old(john)&~wise(john))))&
(![X]:((~generous(X)&~brave(X))<=>(curious(X)&brave(X))))&
(![X]:(~brave(X)<=>(kind(X)|~tall(X))))&
(((~funny(fred)|~humble(fred)))<=>((~creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)&~tall(X))=>(creative(X)|~wise(X))))&
((~brave(paul))=>((brave(lucy)<~>creative(lucy))))&
(![X]:((funny(X)&~happy(X))=>(curious(X)<~>wise(X))))&
(![X]:((old(X)<~>curious(X))<=>~calm(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(~strong(X)&~creative(X))))&
((humble(john))=>((~quiet(lucy)&~happy(lucy))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~tall(X)|old(X))))&
((brave(susan)<~>rich(susan)))&
(?[X]:(kind(X)))&
(~happy(fred))&
((~creative(susan)&~patient(susan)))&
(?[X]:((tall(X)|brave(X))))&
((curious(alice)&funny(alice))) | ~funny(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2161928349977295063251462
% SZS output start Proof for 2161928349977295063251462
22. funny(alice) & curious(alice) [input p21]
23. ~funny(alice) [input hypothesis]
134. funny(alice) [cnf transformation 22]
135. ~funny(alice) [cnf transformation 23]
208. 17 <=> funny(alice) [avatar definition]
273. 17 [avatar split clause 134,208]
274. ~17 [avatar split clause 135,208]
275. $false [avatar sat refutation 273,274]
% SZS output end Proof for 2161928349977295063251462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or calm is both humble and wise and vice versa.
Everyone who is not brave is both strong and not tall and vice versa.
If alice is both creative and not quiet then lucy is strong and vice versa.
Everyone who is both old and humble is rich or brave and vice versa.
If alice is either curious or not brave then someone is both not creative and curious.
If john is either happy or patient then someone is brave and vice versa.
If fred is funny then john is both not quiet and rich and vice versa.
If someone is both not curious and strong then someone is not quiet and vice versa.
If someone is creative then john is quiet or old.
Everyone who is not creative or strong is either not quiet or humble and vice versa.
Everyone who is not brave is creative and vice versa.
Everyone who is not funny or humble is both calm and rich.
If john is either not quiet or not generous then john is creative.
If someone is both not brave and patient then fred is both kind and not humble and vice versa.
If someone is either not funny or not rich then fred is both humble and rich.
Everyone who is not wise is not creative.
Someone is either humble or curious.
Someone is rich or not kind.
Someone is not happy or generous.
Paul is either not generous or not old.
Someone is not patient or patient.
Alice is either humble or not creative.
Mary is not wise. | Paul is humble. | neutral | (![X]:((~kind(X)<~>calm(X))<=>(humble(X)&wise(X))))&
(![X]:(~brave(X)<=>(strong(X)&~tall(X))))&
(((creative(alice)&~quiet(alice)))<=>(strong(lucy)))&
(![X]:((old(X)&humble(X))<=>(rich(X)|brave(X))))&
(((curious(alice)<~>~brave(alice)))=>(?[X]:((~creative(X)&curious(X)))))&
(((happy(john)<~>patient(john)))<=>(?[X]:(brave(X))))&
((funny(fred))<=>((~quiet(john)&rich(john))))&
((?[X]:((~curious(X)&strong(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(creative(X)))=>((quiet(john)|old(john))))&
(![X]:((~creative(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(![X]:((~funny(X)|humble(X))=>(calm(X)&rich(X))))&
(((~quiet(john)<~>~generous(john)))=>(creative(john)))&
((?[X]:((~brave(X)&patient(X))))<=>((kind(fred)&~humble(fred))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((humble(fred)&rich(fred))))&
(![X]:(~wise(X)=>~creative(X)))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~happy(X)|generous(X))))&
((~generous(paul)<~>~old(paul)))&
(?[X]:((~patient(X)|patient(X))))&
((humble(alice)<~>~creative(alice)))&
(~wise(mary)) | humble(paul) | [] | null | 0 |
If someone is not curious then someone is creative.
Everyone who is either quiet or old is either not generous or generous and vice versa.
If susan is both not calm and humble then someone is not funny.
If paul is rich then someone is both calm and old.
Everyone who is either not old or not generous is both not funny and not generous and vice versa.
Everyone who is both tall and not wise is both brave and happy and vice versa.
If fred is both wise and not brave then someone is either not rich or tall and vice versa.
Everyone who is curious or not curious is quiet or not tall.
Everyone who is rich is either tall or generous and vice versa.
Everyone who is both strong and creative is happy and vice versa.
Everyone who is both strong and generous is strong or tall and vice versa.
If someone is not patient then someone is humble or not patient.
If someone is not wise then someone is either not generous or old.
Everyone who is calm is quiet.
Everyone who is curious is either not generous or strong.
If someone is both not brave and calm then someone is both not curious and curious.
Susan is not humble or funny.
Alice is not patient.
Someone is both not creative and not wise.
Mary is not rich or strong.
Alice is kind.
Someone is curious or old.
Someone is funny or not curious. | Fred is not tall. | entailment | ((?[X]:(~curious(X)))=>(?[X]:(creative(X))))&
(![X]:((quiet(X)<~>old(X))<=>(~generous(X)<~>generous(X))))&
(((~calm(susan)&humble(susan)))=>(?[X]:(~funny(X))))&
((rich(paul))=>(?[X]:((calm(X)&old(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>(~funny(X)&~generous(X))))&
(![X]:((tall(X)&~wise(X))<=>(brave(X)&happy(X))))&
(((wise(fred)&~brave(fred)))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(![X]:((curious(X)|~curious(X))=>(quiet(X)|~tall(X))))&
(![X]:(rich(X)<=>(tall(X)<~>generous(X))))&
(![X]:((strong(X)&creative(X))<=>happy(X)))&
(![X]:((strong(X)&generous(X))<=>(strong(X)|tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:(calm(X)=>quiet(X)))&
(![X]:(curious(X)=>(~generous(X)<~>strong(X))))&
((?[X]:((~brave(X)&calm(X))))=>(?[X]:((~curious(X)&curious(X)))))&
((~humble(susan)|funny(susan)))&
(~patient(alice))&
(?[X]:((~creative(X)&~wise(X))))&
((~rich(mary)|strong(mary)))&
(kind(alice))&
(?[X]:((curious(X)|old(X))))&
(?[X]:((funny(X)|~curious(X)))) | ~tall(fred) | [
"p1",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8022505117153632281327015
% SZS output start Proof for 8022505117153632281327015
2. ! [X0] : ((quiet(X0) <~> old(X0)) <=> (~generous(X0) <~> generous(X0))) [input p1]
5. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> (~generous(X0) & ~funny(X0))) [input p4]
8. ! [X0] : ((~curious(X0) | curious(X0)) => (~tall(X0) | quiet(X0))) [input p7]
11. ! [X0] : ((generous(X0) & strong(X0)) <=> (tall(X0) | strong(X0))) [input p10]
24. tall(fred) [input hypothesis]
34. ! [X0] : ((~tall(X0) | quiet(X0)) | (curious(X0) & ~curious(X0))) [ennf transformation 8]
35. ! [X0] : (~tall(X0) | quiet(X0) | (curious(X0) & ~curious(X0))) [flattening 34]
44. ! [X0] : ((((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))))) [nnf transformation 2]
49. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (generous(X0) | funny(X0))) & ((~generous(X0) & ~funny(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 5]
50. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0) | funny(X0)) & ((~generous(X0) & ~funny(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [flattening 49]
61. ! [X0] : (((generous(X0) & strong(X0)) | (~tall(X0) & ~strong(X0))) & ((tall(X0) | strong(X0)) | (~generous(X0) | ~strong(X0)))) [nnf transformation 11]
62. ! [X0] : (((generous(X0) & strong(X0)) | (~tall(X0) & ~strong(X0))) & (tall(X0) | strong(X0) | ~generous(X0) | ~strong(X0))) [flattening 61]
87. ~old(X0) | ~quiet(X0) | generous(X0) | generous(X0) [cnf transformation 44]
88. ~old(X0) | ~quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 44]
94. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 50]
108. ~tall(X0) | quiet(X0) | ~curious(X0) [cnf transformation 35]
109. ~tall(X0) | quiet(X0) | curious(X0) [cnf transformation 35]
119. ~tall(X0) | strong(X0) [cnf transformation 62]
120. ~strong(X0) | generous(X0) [cnf transformation 62]
137. tall(fred) [cnf transformation 24]
138. ~generous(X0) | old(X0) [duplicate literal removal 94]
142. ~old(X0) | ~quiet(X0) | generous(X0) [duplicate literal removal 87]
143. ~old(X0) | ~quiet(X0) | ~generous(X0) [duplicate literal removal 88]
152. ~old(X0) | ~quiet(X0) [subsumption resolution 142,143]
209. ~tall(X0) | quiet(X0) [subsumption resolution 108,109]
275. strong(fred) [resolution 119,137]
276. generous(fred) [resolution 120,275]
278. old(fred) [resolution 138,276]
279. ~quiet(fred) [resolution 152,278]
286. quiet(fred) [resolution 209,137]
288. $false [subsumption resolution 286,279]
% SZS output end Proof for 8022505117153632281327015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not kind then mary is both humble and funny and vice versa.
If someone is creative or not funny then fred is both patient and quiet and vice versa.
Everyone who is rich or not happy is either not calm or not tall and vice versa.
If someone is funny then someone is happy or wise.
Everyone who is kind is both not brave and not creative.
Everyone who is either not brave or happy is either not brave or creative.
Everyone who is either not rich or rich is both quiet and curious.
If someone is both not old and not patient then someone is not curious or strong and vice versa.
Everyone who is both wise and quiet is either strong or humble and vice versa.
If someone is both not happy and not patient then someone is either rich or old.
If fred is funny then someone is calm or not strong and vice versa.
If someone is not generous or not strong then paul is either not curious or not humble.
Everyone who is happy or kind is either calm or not humble and vice versa.
Everyone who is either curious or not creative is both not humble and not tall and vice versa.
Everyone who is both not brave and tall is either creative or calm and vice versa.
If susan is both not strong and not humble then someone is both not generous and not humble and vice versa.
Fred is both not generous and not kind.
Susan is not wise.
Someone is either not patient or curious.
Someone is not tall or not kind.
Lucy is either humble or generous.
Paul is not rich.
Someone is calm.
Lucy is both calm and generous. | Paul is not calm. | contradiction | ((~kind(paul))<=>((humble(mary)&funny(mary))))&
((?[X]:((creative(X)|~funny(X))))<=>((patient(fred)&quiet(fred))))&
(![X]:((rich(X)|~happy(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(funny(X)))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:(kind(X)=>(~brave(X)&~creative(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>creative(X))))&
(![X]:((~rich(X)<~>rich(X))=>(quiet(X)&curious(X))))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((wise(X)&quiet(X))<=>(strong(X)<~>humble(X))))&
((?[X]:((~happy(X)&~patient(X))))=>(?[X]:((rich(X)<~>old(X)))))&
((funny(fred))<=>(?[X]:((calm(X)|~strong(X)))))&
((?[X]:((~generous(X)|~strong(X))))=>((~curious(paul)<~>~humble(paul))))&
(![X]:((happy(X)|kind(X))<=>(calm(X)<~>~humble(X))))&
(![X]:((curious(X)<~>~creative(X))<=>(~humble(X)&~tall(X))))&
(![X]:((~brave(X)&tall(X))<=>(creative(X)<~>calm(X))))&
(((~strong(susan)&~humble(susan)))<=>(?[X]:((~generous(X)&~humble(X)))))&
((~generous(fred)&~kind(fred)))&
(~wise(susan))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((~tall(X)|~kind(X))))&
((humble(lucy)<~>generous(lucy)))&
(~rich(paul))&
(?[X]:(calm(X)))&
((calm(lucy)&generous(lucy))) | ~calm(paul) | [
"p2",
"p4",
"p6",
"p11",
"p12",
"p13",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3338094321654025587555210
% SZS output start Proof for 3338094321654025587555210
3. ! [X0] : ((~happy(X0) | rich(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p2]
5. ! [X0] : (kind(X0) => (~creative(X0) & ~brave(X0))) [input p4]
7. ! [X0] : ((~rich(X0) <~> rich(X0)) => (curious(X0) & quiet(X0))) [input p6]
12. ? [X0] : (~strong(X0) | ~generous(X0)) => (~curious(paul) <~> ~humble(paul)) [input p11]
13. ! [X0] : ((kind(X0) | happy(X0)) <=> (calm(X0) <~> ~humble(X0))) [input p12]
14. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> (~tall(X0) & ~humble(X0))) [input p13]
15. ! [X0] : ((tall(X0) & ~brave(X0)) <=> (creative(X0) <~> calm(X0))) [input p14]
17. ~kind(fred) & ~generous(fred) [input p16]
22. ~rich(paul) [input p21]
25. ~calm(paul) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~brave(X0)) | ~kind(X0)) [ennf transformation 5]
32. ! [X0] : ((curious(X0) & quiet(X0)) | (~rich(X0) <=> rich(X0))) [ennf transformation 7]
34. (~curious(paul) <~> ~humble(paul)) | ! [X0] : (strong(X0) & generous(X0)) [ennf transformation 12]
42. ! [X0] : (((~happy(X0) | rich(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (happy(X0) & ~rich(X0)))) [nnf transformation 3]
43. ! [X0] : ((~happy(X0) | rich(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (happy(X0) & ~rich(X0)))) [flattening 42]
48. ! [X0] : ((curious(X0) & quiet(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 32]
64. ((humble(paul) | curious(paul)) & (~humble(paul) | ~curious(paul))) | ! [X0] : (strong(X0) & generous(X0)) [nnf transformation 34]
65. ! [X0] : (((kind(X0) | happy(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0)))) & (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~kind(X0) & ~happy(X0)))) [nnf transformation 13]
66. ! [X0] : ((kind(X0) | happy(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0)))) & (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~kind(X0) & ~happy(X0)))) [flattening 65]
67. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 14]
68. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [flattening 67]
69. ! [X0] : (((tall(X0) & ~brave(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (~tall(X0) | brave(X0)))) [nnf transformation 15]
70. ! [X0] : (((tall(X0) & ~brave(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ~tall(X0) | brave(X0))) [flattening 69]
93. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 43]
96. ~tall(X0) | rich(X0) | ~happy(X0) | calm(X0) [cnf transformation 43]
99. ~brave(X0) | ~kind(X0) [cnf transformation 30]
100. ~creative(X0) | ~kind(X0) [cnf transformation 30]
107. curious(X0) | rich(X0) | rich(X0) [cnf transformation 48]
108. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
125. ~humble(paul) | ~curious(paul) | generous(X0) [cnf transformation 64]
131. ~calm(X0) | humble(X0) | ~happy(X0) [cnf transformation 66]
134. calm(X0) | happy(X0) | kind(X0) | humble(X0) [cnf transformation 66]
137. ~tall(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 68]
140. creative(X0) | ~curious(X0) | tall(X0) | humble(X0) [cnf transformation 68]
141. calm(X0) | creative(X0) | ~tall(X0) | brave(X0) [cnf transformation 70]
145. tall(X0) | calm(X0) | ~creative(X0) [cnf transformation 70]
151. ~generous(fred) [cnf transformation 17]
159. ~rich(paul) [cnf transformation 22]
163. ~calm(paul) [cnf transformation 25]
166. curious(X0) | rich(X0) [duplicate literal removal 107]
167. ~rich(X0) | curious(X0) [duplicate literal removal 108]
179. 3 <=> kind(paul) [avatar definition]
180. kind(paul) <- (3) [avatar component clause 179]
181. ~kind(paul) <- (~3) [avatar component clause 179]
224. curious(X0) [subsumption resolution 166,167]
286. 26 <=> humble(paul) [avatar definition]
288. ~humble(paul) <- (~26) [avatar component clause 286]
290. ~humble(paul) | generous(X0) [subsumption resolution 125,224]
292. 27 <=> ! [X0] : generous(X0) [avatar definition]
293. generous(X0) <- (27) [avatar component clause 292]
294. 27 | ~26 [avatar split clause 290,286,292]
295. tall(X0) | creative(X0) | humble(X0) [subsumption resolution 140,224]
296. ~tall(X0) | ~creative(X0) [subsumption resolution 137,224]
298. ~creative(X0) | calm(X0) [subsumption resolution 145,296]
299. ~tall(X0) | calm(X0) | brave(X0) [subsumption resolution 141,298]
420. creative(X0) | humble(X0) | ~calm(X0) | happy(X0) [resolution 295,93]
423. ~calm(X0) | humble(X0) | creative(X0) [subsumption resolution 420,131]
424. calm(X0) | brave(X0) | creative(X0) | humble(X0) [resolution 299,295]
428. brave(X0) | creative(X0) | humble(X0) [subsumption resolution 424,423]
438. rich(X0) | ~happy(X0) | calm(X0) | creative(X0) | humble(X0) [resolution 96,295]
442. ~happy(X0) | rich(X0) | creative(X0) | humble(X0) [subsumption resolution 438,131]
454. happy(paul) | kind(paul) | humble(paul) [resolution 134,163]
477. creative(X2) | humble(X2) | ~kind(X2) [resolution 428,99]
480. ~kind(X2) | humble(X2) [subsumption resolution 477,100]
607. humble(paul) <- (3) [resolution 480,180]
608. $false <- (3, ~26) [subsumption resolution 607,288]
609. ~3 | 26 [avatar contradiction clause 608]
612. 56 <=> happy(paul) [avatar definition]
614. happy(paul) <- (56) [avatar component clause 612]
634. rich(paul) | creative(paul) | humble(paul) <- (56) [resolution 614,442]
636. creative(paul) | humble(paul) <- (56) [subsumption resolution 634,159]
637. creative(paul) <- (~26, 56) [subsumption resolution 636,288]
667. calm(paul) <- (~26, 56) [resolution 637,298]
670. $false <- (~26, 56) [subsumption resolution 667,163]
671. 26 | ~56 [avatar contradiction clause 670]
681. happy(paul) | humble(paul) <- (~3) [subsumption resolution 454,181]
682. 26 | 56 | 3 [avatar split clause 681,179,612,286]
728. $false <- (27) [resolution 293,151]
731. ~27 [avatar contradiction clause 728]
732. $false [avatar sat refutation 294,609,671,682,731]
% SZS output end Proof for 3338094321654025587555210
% ------------------------------
% 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and wise is both not kind and patient. If someone is quiet then someone is both creative and not funny. Everyone who is curious or funny is both curious and not creative and vice versa. If susan is tall then alice is both quiet and tall and vice versa. If someone is not patient or strong then someone is both not patient and not strong and vice versa. Everyone who is happy or not tall is quiet or not quiet. If someone is both quiet and not creative then someone is brave or not happy and vice versa. Everyone who is either brave or humble is both not calm and happy and vice versa. Everyone who is both not creative and curious is not old or happy and vice versa. Everyone who is either creative or funny is funny and vice versa. Everyone who is either not rich or creative is both not patient and not humble and vice versa. If john is not wise or generous then someone is both not funny and not kind. If someone is not old or not curious then fred is either strong or not rich. If alice is both not tall and not humble then susan is either humble or not quiet and vice versa. Everyone who is not humble is either funny or not creative. Everyone who is humble or not quiet is not strong or rich and vice versa. Someone is not patient or not kind. Someone is either strong or kind. Alice is both not creative and strong. Fred is either wise or not rich. Mary is either rich or not brave. | Susan is not rich. | neutral | (![X]:((brave(X)&wise(X))=>(~kind(X)&patient(X))))&
((?[X]:(quiet(X)))=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((curious(X)|funny(X))<=>(curious(X)&~creative(X))))&
((tall(susan))<=>((quiet(alice)&tall(alice))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:((happy(X)|~tall(X))=>(quiet(X)|~quiet(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))<=>(~old(X)|happy(X))))&
(![X]:((creative(X)<~>funny(X))<=>funny(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)&~humble(X))))&
(((~wise(john)|generous(john)))=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~old(X)|~curious(X))))=>((strong(fred)<~>~rich(fred))))&
(((~tall(alice)&~humble(alice)))<=>((humble(susan)<~>~quiet(susan))))&
(![X]:(~humble(X)=>(funny(X)<~>~creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~strong(X)|rich(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>kind(X))))&
((~creative(alice)&strong(alice)))&
((wise(fred)<~>~rich(fred)))&
((rich(mary)<~>~brave(mary))) | ~rich(susan) | [] | null | 0 |
If susan is not happy then alice is not strong or quiet. If fred is not wise or calm then lucy is happy or wise and vice versa. Everyone who is rich or humble is both curious and tall and vice versa. Everyone who is both kind and patient is both not happy and funny and vice versa. Everyone who is not brave or old is both brave and not strong and vice versa. If john is both not creative and not tall then someone is either strong or quiet. Everyone who is not humble is kind or curious. Everyone who is patient or rich is not generous and vice versa. Everyone who is not calm is both not happy and not old and vice versa. If someone is both not strong and not creative then mary is either not curious or not quiet and vice versa. Everyone who is either tall or old is not kind. Everyone who is happy or not funny is either rich or quiet and vice versa. Everyone who is humble is wise and vice versa. If someone is curious or strong then someone is either humble or not humble and vice versa. Everyone who is both strong and not generous is either tall or not patient. If susan is both old and creative then lucy is both strong and not creative and vice versa. Fred is not happy or kind. Mary is not curious. Lucy is either not brave or kind. Mary is not patient. John is wise or strong. Someone is tall or not rich. Someone is either not patient or generous. Alice is either strong or not funny. | Mary is not wise. | entailment | ((~happy(susan))=>((~strong(alice)|quiet(alice))))&
(((~wise(fred)|calm(fred)))<=>((happy(lucy)|wise(lucy))))&
(![X]:((rich(X)|humble(X))<=>(curious(X)&tall(X))))&
(![X]:((kind(X)&patient(X))<=>(~happy(X)&funny(X))))&
(![X]:((~brave(X)|old(X))<=>(brave(X)&~strong(X))))&
(((~creative(john)&~tall(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(kind(X)|curious(X))))&
(![X]:((patient(X)|rich(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~happy(X)&~old(X))))&
((?[X]:((~strong(X)&~creative(X))))<=>((~curious(mary)<~>~quiet(mary))))&
(![X]:((tall(X)<~>old(X))=>~kind(X)))&
(![X]:((happy(X)|~funny(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(humble(X)<=>wise(X)))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((strong(X)&~generous(X))=>(tall(X)<~>~patient(X))))&
(((old(susan)&creative(susan)))<=>((strong(lucy)&~creative(lucy))))&
((~happy(fred)|kind(fred)))&
(~curious(mary))&
((~brave(lucy)<~>kind(lucy)))&
(~patient(mary))&
((wise(john)|strong(john)))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((strong(alice)<~>~funny(alice))) | ~wise(mary) | [
"p2",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6912108355028756483420312
% SZS output start Proof for 6912108355028756483420312
3. ! [X0] : ((humble(X0) | rich(X0)) <=> (tall(X0) & curious(X0))) [input p2]
13. ! [X0] : (humble(X0) <=> wise(X0)) [input p12]
18. ~curious(mary) [input p17]
25. wise(mary) [input hypothesis]
38. ! [X0] : (((humble(X0) | rich(X0)) | (~tall(X0) | ~curious(X0))) & ((tall(X0) & curious(X0)) | (~humble(X0) & ~rich(X0)))) [nnf transformation 3]
39. ! [X0] : ((humble(X0) | rich(X0) | ~tall(X0) | ~curious(X0)) & ((tall(X0) & curious(X0)) | (~humble(X0) & ~rich(X0)))) [flattening 38]
58. ! [X0] : ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0))) [nnf transformation 13]
80. ~humble(X0) | curious(X0) [cnf transformation 39]
117. ~wise(X0) | humble(X0) [cnf transformation 58]
131. ~curious(mary) [cnf transformation 18]
141. wise(mary) [cnf transformation 25]
203. 13 <=> curious(mary) [avatar definition]
205. ~curious(mary) <- (~13) [avatar component clause 203]
269. ~13 [avatar split clause 131,203]
288. humble(mary) [resolution 117,141]
293. curious(mary) [resolution 288,80]
294. $false <- (~13) [subsumption resolution 293,205]
295. 13 [avatar contradiction clause 294]
296. $false [avatar sat refutation 269,295]
% SZS output end Proof for 6912108355028756483420312
% ------------------------------
% 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 patient and not brave then paul is both not patient and creative.
Everyone who is tall is either happy or not calm and vice versa.
Everyone who is tall or not funny is either kind or not funny and vice versa.
Everyone who is not generous is not tall and vice versa.
Everyone who is either tall or not quiet is both creative and calm and vice versa.
If susan is not strong or brave then mary is tall.
Everyone who is not tall or rich is kind or not quiet and vice versa.
Everyone who is either generous or not old is both creative and not calm.
If someone is both calm and tall then someone is either not calm or not strong and vice versa.
Everyone who is both tall and not old is either rich or calm and vice versa.
If alice is both not funny and curious then lucy is not curious and vice versa.
Everyone who is either strong or creative is not kind and vice versa.
Everyone who is not creative is either generous or not humble and vice versa.
Everyone who is both brave and not kind is happy or patient.
Everyone who is either creative or not quiet is calm.
Everyone who is not quiet is not creative and vice versa.
Paul is brave or creative.
Someone is calm or tall.
Lucy is either not quiet or tall.
Someone is quiet. | Paul is old. | contradiction | ((?[X]:((~patient(X)&~brave(X))))=>((~patient(paul)&creative(paul))))&
(![X]:(tall(X)<=>(happy(X)<~>~calm(X))))&
(![X]:((tall(X)|~funny(X))<=>(kind(X)<~>~funny(X))))&
(![X]:(~generous(X)<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(creative(X)&calm(X))))&
(((~strong(susan)|brave(susan)))=>(tall(mary)))&
(![X]:((~tall(X)|rich(X))<=>(kind(X)|~quiet(X))))&
(![X]:((generous(X)<~>~old(X))=>(creative(X)&~calm(X))))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((tall(X)&~old(X))<=>(rich(X)<~>calm(X))))&
(((~funny(alice)&curious(alice)))<=>(~curious(lucy)))&
(![X]:((strong(X)<~>creative(X))<=>~kind(X)))&
(![X]:(~creative(X)<=>(generous(X)<~>~humble(X))))&
(![X]:((brave(X)&~kind(X))=>(happy(X)|patient(X))))&
(![X]:((creative(X)<~>~quiet(X))=>calm(X)))&
(![X]:(~quiet(X)<=>~creative(X)))&
((brave(paul)|creative(paul)))&
(?[X]:((calm(X)|tall(X))))&
((~quiet(lucy)<~>tall(lucy)))&
(?[X]:(quiet(X))) | old(paul) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2106356021927557945919728
% SZS output start Proof for 2106356021927557945919728
3. ! [X0] : ((~funny(X0) | tall(X0)) <=> (kind(X0) <~> ~funny(X0))) [input p2]
4. ! [X0] : (~generous(X0) <=> ~tall(X0)) [input p3]
5. ! [X0] : ((tall(X0) <~> ~quiet(X0)) <=> (calm(X0) & creative(X0))) [input p4]
7. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (~quiet(X0) | kind(X0))) [input p6]
8. ! [X0] : ((generous(X0) <~> ~old(X0)) => (~calm(X0) & creative(X0))) [input p7]
16. ! [X0] : (~quiet(X0) <=> ~creative(X0)) [input p15]
21. old(paul) [input hypothesis]
25. ! [X0] : ((~calm(X0) & creative(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 8]
30. ! [X0] : (((~funny(X0) | tall(X0)) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (funny(X0) & ~tall(X0)))) [nnf transformation 3]
31. ! [X0] : ((~funny(X0) | tall(X0) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0)))) & (((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | (funny(X0) & ~tall(X0)))) [flattening 30]
32. ! [X0] : ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))) [nnf transformation 4]
33. ! [X0] : ((((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))))) [nnf transformation 5]
34. ! [X0] : ((((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))))) [flattening 33]
35. ! [X0] : (((rich(X0) | ~tall(X0)) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | (~rich(X0) & tall(X0)))) [nnf transformation 7]
36. ! [X0] : ((rich(X0) | ~tall(X0) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | (~rich(X0) & tall(X0)))) [flattening 35]
37. ! [X0] : ((~calm(X0) & creative(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 25]
50. ! [X0] : ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))) [nnf transformation 16]
65. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 31]
66. ~funny(X0) | tall(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 31]
68. ~tall(X0) | generous(X0) [cnf transformation 32]
71. quiet(X0) | tall(X0) | creative(X0) [cnf transformation 34]
72. ~quiet(X0) | calm(X0) | ~tall(X0) [cnf transformation 34]
78. ~quiet(X0) | kind(X0) | tall(X0) [cnf transformation 36]
82. ~old(X0) | creative(X0) | ~generous(X0) [cnf transformation 37]
84. ~old(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 37]
112. ~creative(X0) | quiet(X0) [cnf transformation 50]
113. ~quiet(X0) | creative(X0) [cnf transformation 50]
119. old(paul) [cnf transformation 21]
120. ~kind(X0) | funny(X0) [duplicate literal removal 65]
121. ~kind(X0) | tall(X0) | ~funny(X0) [duplicate literal removal 66]
126. 2 <=> creative(paul) [avatar definition]
127. ~creative(paul) <- (~2) [avatar component clause 126]
128. creative(paul) <- (2) [avatar component clause 126]
221. quiet(paul) <- (2) [resolution 112,128]
242. tall(X1) | creative(X1) | creative(X1) [resolution 71,113]
243. tall(X1) | creative(X1) [duplicate literal removal 242]
247. calm(paul) | ~tall(paul) <- (2) [resolution 72,221]
266. kind(paul) | tall(paul) <- (2) [resolution 78,221]
290. 24 <=> tall(paul) [avatar definition]
291. ~tall(paul) <- (~24) [avatar component clause 290]
292. tall(paul) <- (24) [avatar component clause 290]
294. 25 <=> kind(paul) [avatar definition]
296. kind(paul) <- (25) [avatar component clause 294]
297. 24 | 25 | ~2 [avatar split clause 266,126,294,290]
299. 26 <=> calm(paul) [avatar definition]
302. ~24 | 26 | ~2 [avatar split clause 247,126,299,290]
373. creative(paul) | ~generous(paul) [resolution 82,119]
377. ~calm(paul) | ~generous(paul) [resolution 84,119]
380. 35 <=> generous(paul) [avatar definition]
382. ~generous(paul) <- (~35) [avatar component clause 380]
383. ~35 | ~26 [avatar split clause 377,299,380]
487. ~35 | 2 [avatar split clause 373,126,380]
551. tall(paul) | ~funny(paul) <- (25) [resolution 296,121]
554. funny(paul) <- (25) [resolution 296,120]
555. ~funny(paul) <- (~24, 25) [subsumption resolution 551,291]
556. $false <- (~24, 25) [subsumption resolution 554,555]
557. 24 | ~25 [avatar contradiction clause 556]
580. creative(paul) <- (~24) [resolution 243,291]
584. $false <- (~2, ~24) [subsumption resolution 580,127]
585. 2 | 24 [avatar contradiction clause 584]
689. generous(paul) <- (24) [resolution 292,68]
690. $false <- (24, ~35) [subsumption resolution 689,382]
691. ~24 | 35 [avatar contradiction clause 690]
692. $false [avatar sat refutation 297,302,383,487,557,585,691]
% SZS output end Proof for 2106356021927557945919728
% ------------------------------
% 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not calm is not happy. If someone is both not wise and not happy then fred is not old and vice versa. If fred is not generous or not kind then someone is either brave or not creative and vice versa. If mary is creative then someone is either not creative or brave. If alice is both patient and calm then someone is tall or calm and vice versa. If someone is not old then someone is happy or not curious. Everyone who is either not patient or calm is not kind or calm. Everyone who is calm or not old is either not calm or humble. Everyone who is both strong and wise is not creative or quiet and vice versa. Everyone who is both tall and not strong is either funny or patient and vice versa. Everyone who is not curious is either patient or curious. If someone is either creative or wise then someone is either tall or creative. Everyone who is calm or not brave is either not quiet or old and vice versa. Everyone who is not curious or not kind is not humble or not calm. Everyone who is strong or curious is not strong and vice versa. Everyone who is not wise is both brave and not patient. Fred is either funny or tall. Someone is both not funny and curious. John is not tall. Someone is both not kind and not generous. | Mary is not strong. | entailment | (![X]:((strong(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>(~old(fred)))&
(((~generous(fred)|~kind(fred)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
((creative(mary))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((patient(alice)&calm(alice)))<=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(~kind(X)|calm(X))))&
(![X]:((calm(X)|~old(X))=>(~calm(X)<~>humble(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)|quiet(X))))&
(![X]:((tall(X)&~strong(X))<=>(funny(X)<~>patient(X))))&
(![X]:(~curious(X)=>(patient(X)<~>curious(X))))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((calm(X)|~brave(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~humble(X)|~calm(X))))&
(![X]:((strong(X)|curious(X))<=>~strong(X)))&
(![X]:(~wise(X)=>(brave(X)&~patient(X))))&
((funny(fred)<~>tall(fred)))&
(?[X]:((~funny(X)&curious(X))))&
(~tall(john))&
(?[X]:((~kind(X)&~generous(X)))) | ~strong(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4216404028475406949295501
% SZS output start Proof for 4216404028475406949295501
15. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p14]
21. strong(mary) [input hypothesis]
69. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [nnf transformation 15]
70. ! [X0] : ((curious(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [flattening 69]
126. ~strong(X0) | ~strong(X0) [cnf transformation 70]
138. strong(mary) [cnf transformation 21]
139. ~strong(X0) [duplicate literal removal 126]
277. $false [subsumption resolution 138,139]
% SZS output end Proof for 4216404028475406949295501
% ------------------------------
% 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 kind or old is both generous and not generous and vice versa.
Everyone who is kind is curious or not tall.
If fred is both not happy and funny then alice is either not funny or kind.
Everyone who is both generous and not patient is rich or happy and vice versa.
If mary is calm or not rich then fred is creative or not patient and vice versa.
Everyone who is humble is both rich and old and vice versa.
Everyone who is both not curious and not strong is both not calm and patient.
If lucy is both not wise and patient then someone is both not brave and funny and vice versa.
Everyone who is not humble or happy is either not tall or not humble and vice versa.
Everyone who is either not rich or not old is both strong and funny and vice versa.
If john is strong or creative then susan is not brave or not old and vice versa.
Everyone who is brave or calm is not kind.
Everyone who is not old is brave or not brave.
If john is not wise or not quiet then susan is both not old and rich and vice versa.
Lucy is patient or not old.
Someone is tall.
Mary is not quiet.
Paul is either not old or not patient.
Someone is curious or not humble.
John is rich. | Lucy is generous. | neutral | (![X]:((~kind(X)|old(X))<=>(generous(X)&~generous(X))))&
(![X]:(kind(X)=>(curious(X)|~tall(X))))&
(((~happy(fred)&funny(fred)))=>((~funny(alice)<~>kind(alice))))&
(![X]:((generous(X)&~patient(X))<=>(rich(X)|happy(X))))&
(((calm(mary)|~rich(mary)))<=>((creative(fred)|~patient(fred))))&
(![X]:(humble(X)<=>(rich(X)&old(X))))&
(![X]:((~curious(X)&~strong(X))=>(~calm(X)&patient(X))))&
(((~wise(lucy)&patient(lucy)))<=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(strong(X)&funny(X))))&
(((strong(john)|creative(john)))<=>((~brave(susan)|~old(susan))))&
(![X]:((brave(X)|calm(X))=>~kind(X)))&
(![X]:(~old(X)=>(brave(X)|~brave(X))))&
(((~wise(john)|~quiet(john)))<=>((~old(susan)&rich(susan))))&
((patient(lucy)|~old(lucy)))&
(?[X]:(tall(X)))&
(~quiet(mary))&
((~old(paul)<~>~patient(paul)))&
(?[X]:((curious(X)|~humble(X))))&
(rich(john)) | generous(lucy) | [] | null | 0 |
If someone is rich or not generous then someone is not strong or not calm.
Everyone who is strong or not strong is quiet and vice versa.
Everyone who is not strong is both not calm and wise.
If someone is not kind or calm then someone is not brave or tall.
Everyone who is both calm and not brave is quiet or not kind and vice versa.
If alice is either tall or not creative then paul is not brave and vice versa.
If john is humble or not quiet then someone is either not tall or brave and vice versa.
Everyone who is kind is both not humble and not old.
Everyone who is both not calm and not curious is humble.
If susan is creative or not curious then susan is either not generous or patient and vice versa.
Everyone who is strong or kind is creative or not creative and vice versa.
Everyone who is creative or tall is either not generous or tall.
Everyone who is funny or strong is either funny or rich and vice versa.
Everyone who is either calm or old is wise.
If fred is both not creative and not funny then someone is both curious and not kind.
Everyone who is either not wise or funny is happy or rich and vice versa.
Someone is both strong and quiet.
Paul is not creative or brave.
Someone is generous or funny.
Someone is either brave or funny.
Someone is funny or tall.
Susan is either not humble or brave.
Lucy is not brave or generous. | John is rich. | contradiction | ((?[X]:((rich(X)|~generous(X))))=>(?[X]:((~strong(X)|~calm(X)))))&
(![X]:((strong(X)|~strong(X))<=>quiet(X)))&
(![X]:(~strong(X)=>(~calm(X)&wise(X))))&
((?[X]:((~kind(X)|calm(X))))=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((calm(X)&~brave(X))<=>(quiet(X)|~kind(X))))&
(((tall(alice)<~>~creative(alice)))<=>(~brave(paul)))&
(((humble(john)|~quiet(john)))<=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:(kind(X)=>(~humble(X)&~old(X))))&
(![X]:((~calm(X)&~curious(X))=>humble(X)))&
(((creative(susan)|~curious(susan)))<=>((~generous(susan)<~>patient(susan))))&
(![X]:((strong(X)|kind(X))<=>(creative(X)|~creative(X))))&
(![X]:((creative(X)|tall(X))=>(~generous(X)<~>tall(X))))&
(![X]:((funny(X)|strong(X))<=>(funny(X)<~>rich(X))))&
(![X]:((calm(X)<~>old(X))=>wise(X)))&
(((~creative(fred)&~funny(fred)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~wise(X)<~>funny(X))<=>(happy(X)|rich(X))))&
(?[X]:((strong(X)&quiet(X))))&
((~creative(paul)|brave(paul)))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((funny(X)|tall(X))))&
((~humble(susan)<~>brave(susan)))&
((~brave(lucy)|generous(lucy))) | rich(john) | [
"p0",
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4703683294599869548998072
% SZS output start Proof for 4703683294599869548998072
1. ? [X0] : (~generous(X0) | rich(X0)) => ? [X0] : (~calm(X0) | ~strong(X0)) [input p0]
2. ! [X0] : ((~strong(X0) | strong(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : (~strong(X0) => (wise(X0) & ~calm(X0))) [input p2]
5. ! [X0] : ((~brave(X0) & calm(X0)) <=> (~kind(X0) | quiet(X0))) [input p4]
24. rich(john) [input hypothesis]
25. ? [X0] : (~generous(X0) | rich(X0)) => ? [X1] : (~calm(X1) | ~strong(X1)) [rectify 1]
27. ? [X1] : (~calm(X1) | ~strong(X1)) | ! [X0] : (generous(X0) & ~rich(X0)) [ennf transformation 25]
28. ! [X0] : ((wise(X0) & ~calm(X0)) | strong(X0)) [ennf transformation 3]
37. ? [X0] : (~calm(X0) | ~strong(X0)) | ! [X1] : (generous(X1) & ~rich(X1)) [rectify 27]
38. ? [X0] : (~calm(X0) | ~strong(X0)) => (~calm(sK0) | ~strong(sK0)) [choice axiom]
39. (~calm(sK0) | ~strong(sK0)) | ! [X1] : (generous(X1) & ~rich(X1)) [skolemisation 37,38]
40. ! [X0] : (((~strong(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & ~strong(X0)))) [nnf transformation 2]
41. ! [X0] : ((~strong(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & ~strong(X0)))) [flattening 40]
45. ! [X0] : (((~brave(X0) & calm(X0)) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | (brave(X0) | ~calm(X0)))) [nnf transformation 5]
46. ! [X0] : (((~brave(X0) & calm(X0)) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | brave(X0) | ~calm(X0))) [flattening 45]
75. ~calm(sK0) | ~strong(sK0) | ~rich(X1) [cnf transformation 39]
77. quiet(X0) | ~strong(X0) [cnf transformation 41]
78. quiet(X0) | strong(X0) [cnf transformation 41]
80. ~calm(X0) | strong(X0) [cnf transformation 28]
85. calm(X0) | ~quiet(X0) [cnf transformation 46]
142. rich(john) [cnf transformation 24]
150. 2 <=> strong(sK0) [avatar definition]
152. ~strong(sK0) <- (~2) [avatar component clause 150]
154. 3 <=> calm(sK0) [avatar definition]
156. ~calm(sK0) <- (~3) [avatar component clause 154]
159. 4 <=> ! [X1] : ~rich(X1) [avatar definition]
160. ~rich(X1) <- (4) [avatar component clause 159]
161. 4 | ~2 | ~3 [avatar split clause 75,154,150,159]
162. quiet(X0) [subsumption resolution 77,78]
180. calm(X0) [subsumption resolution 85,162]
276. $false <- (~3) [subsumption resolution 156,180]
277. 3 [avatar contradiction clause 276]
280. strong(X0) [resolution 80,180]
281. $false <- (~2) [resolution 280,152]
282. 2 [avatar contradiction clause 281]
285. $false <- (4) [resolution 160,142]
286. ~4 [avatar contradiction clause 285]
287. $false [avatar sat refutation 161,277,282,286]
% SZS output end Proof for 4703683294599869548998072
% ------------------------------
% 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 lucy is either not curious or not rich then someone is either tall or not quiet and vice versa.
If mary is both quiet and not brave then susan is both old and not curious.
If john is not brave then fred is not tall.
Everyone who is both creative and not generous is not humble or not patient and vice versa.
Everyone who is both curious and creative is not curious and vice versa.
Everyone who is either rich or not tall is both not strong and not quiet.
If someone is not kind or not curious then alice is both not tall and rich and vice versa.
Everyone who is happy is either not funny or not kind.
Everyone who is both not strong and kind is either rich or not calm and vice versa.
If fred is not quiet or humble then susan is both not tall and calm and vice versa.
If john is brave or kind then fred is generous and vice versa.
If someone is both tall and creative then someone is either not generous or not strong and vice versa.
Everyone who is both wise and not old is both old and not strong.
If someone is either humble or generous then fred is either quiet or old.
Everyone who is both not brave and not calm is both tall and not old.
Everyone who is not humble or brave is not generous or rich and vice versa.
Someone is not tall or not kind.
Someone is quiet or not tall.
Fred is not creative.
Someone is either not curious or rich.
Fred is both happy and kind.
John is old. | Lucy is not patient. | contradiction | (((~curious(lucy)<~>~rich(lucy)))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
(((quiet(mary)&~brave(mary)))=>((old(susan)&~curious(susan))))&
((~brave(john))=>(~tall(fred)))&
(![X]:((creative(X)&~generous(X))<=>(~humble(X)|~patient(X))))&
(![X]:((curious(X)&creative(X))<=>~curious(X)))&
(![X]:((rich(X)<~>~tall(X))=>(~strong(X)&~quiet(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>((~tall(alice)&rich(alice))))&
(![X]:(happy(X)=>(~funny(X)<~>~kind(X))))&
(![X]:((~strong(X)&kind(X))<=>(rich(X)<~>~calm(X))))&
(((~quiet(fred)|humble(fred)))<=>((~tall(susan)&calm(susan))))&
(((brave(john)|kind(john)))<=>(generous(fred)))&
((?[X]:((tall(X)&creative(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((wise(X)&~old(X))=>(old(X)&~strong(X))))&
((?[X]:((humble(X)<~>generous(X))))=>((quiet(fred)<~>old(fred))))&
(![X]:((~brave(X)&~calm(X))=>(tall(X)&~old(X))))&
(![X]:((~humble(X)|brave(X))<=>(~generous(X)|rich(X))))&
(?[X]:((~tall(X)|~kind(X))))&
(?[X]:((quiet(X)|~tall(X))))&
(~creative(fred))&
(?[X]:((~curious(X)<~>rich(X))))&
((happy(fred)&kind(fred)))&
(old(john)) | ~patient(lucy) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2726838894029327308164086
% SZS output start Proof for 2726838894029327308164086
4. ! [X0] : ((~generous(X0) & creative(X0)) <=> (~patient(X0) | ~humble(X0))) [input p3]
5. ! [X0] : ((creative(X0) & curious(X0)) <=> ~curious(X0)) [input p4]
23. ~patient(lucy) [input hypothesis]
38. ! [X0] : (((~generous(X0) & creative(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (generous(X0) | ~creative(X0)))) [nnf transformation 4]
39. ! [X0] : (((~generous(X0) & creative(X0)) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | generous(X0) | ~creative(X0))) [flattening 38]
40. ! [X0] : (((creative(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | ~curious(X0)))) [nnf transformation 5]
41. ! [X0] : (((creative(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | ~curious(X0))) [flattening 40]
83. patient(X0) | creative(X0) [cnf transformation 39]
86. ~curious(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 41]
87. curious(X0) | curious(X0) [cnf transformation 41]
138. ~patient(lucy) [cnf transformation 23]
139. ~curious(X0) | ~creative(X0) [duplicate literal removal 86]
140. curious(X0) [duplicate literal removal 87]
198. ~creative(X0) [subsumption resolution 139,140]
283. creative(lucy) [resolution 83,138]
284. $false [subsumption resolution 283,198]
% SZS output end Proof for 2726838894029327308164086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not kind then susan is either not tall or curious.
If susan is not humble then someone is either not generous or not curious.
Everyone who is both quiet and humble is either calm or strong.
Everyone who is not curious is both quiet and curious.
If someone is both not patient and not old then lucy is not creative and vice versa.
Everyone who is either curious or calm is not tall or rich.
Everyone who is both humble and not generous is both wise and curious.
Everyone who is brave is both strong and generous and vice versa.
Everyone who is not calm or old is not generous and vice versa.
If john is both not curious and not generous then someone is both curious and brave and vice versa.
Everyone who is humble is both not kind and wise.
If alice is both rich and old then someone is either not patient or rich and vice versa.
Everyone who is not old is either creative or not generous and vice versa.
Everyone who is either not strong or not humble is not kind or brave and vice versa.
If fred is both generous and rich then fred is both not tall and not rich and vice versa.
If someone is happy then someone is either not curious or funny and vice versa.
Fred is not kind.
Someone is either not humble or not creative.
John is curious or funny.
Someone is either brave or not generous.
Alice is either brave or curious.
Lucy is not calm or not kind.
Someone is not tall or not brave.
Paul is either not wise or not humble. | Lucy is not curious. | contradiction | ((~kind(mary))=>((~tall(susan)<~>curious(susan))))&
((~humble(susan))=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((quiet(X)&humble(X))=>(calm(X)<~>strong(X))))&
(![X]:(~curious(X)=>(quiet(X)&curious(X))))&
((?[X]:((~patient(X)&~old(X))))<=>(~creative(lucy)))&
(![X]:((curious(X)<~>calm(X))=>(~tall(X)|rich(X))))&
(![X]:((humble(X)&~generous(X))=>(wise(X)&curious(X))))&
(![X]:(brave(X)<=>(strong(X)&generous(X))))&
(![X]:((~calm(X)|old(X))<=>~generous(X)))&
(((~curious(john)&~generous(john)))<=>(?[X]:((curious(X)&brave(X)))))&
(![X]:(humble(X)=>(~kind(X)&wise(X))))&
(((rich(alice)&old(alice)))<=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:(~old(X)<=>(creative(X)<~>~generous(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~kind(X)|brave(X))))&
(((generous(fred)&rich(fred)))<=>((~tall(fred)&~rich(fred))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(~kind(fred))&
(?[X]:((~humble(X)<~>~creative(X))))&
((curious(john)|funny(john)))&
(?[X]:((brave(X)<~>~generous(X))))&
((brave(alice)<~>curious(alice)))&
((~calm(lucy)|~kind(lucy)))&
(?[X]:((~tall(X)|~brave(X))))&
((~wise(paul)<~>~humble(paul))) | ~curious(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8920033151610143097891384
% SZS output start Proof for 8920033151610143097891384
4. ! [X0] : (~curious(X0) => (curious(X0) & quiet(X0))) [input p3]
25. ~curious(lucy) [input hypothesis]
31. ! [X0] : ((curious(X0) & quiet(X0)) | curious(X0)) [ennf transformation 4]
88. curious(X0) | curious(X0) [cnf transformation 31]
144. ~curious(lucy) [cnf transformation 25]
147. curious(X0) [duplicate literal removal 88]
314. $false [subsumption resolution 144,147]
% SZS output end Proof for 8920033151610143097891384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not brave is both not strong and not old.
If someone is not rich then someone is not old and vice versa.
Everyone who is humble is rich or not tall and vice versa.
If mary is not strong or humble then someone is both patient and calm and vice versa.
If someone is either tall or humble then alice is humble and vice versa.
If someone is rich then someone is not funny.
If fred is not brave or not wise then alice is not humble.
Everyone who is both not calm and not generous is both not kind and not curious and vice versa.
If paul is both not tall and kind then mary is either quiet or not brave and vice versa.
Everyone who is either strong or wise is both wise and not tall.
If paul is not happy then fred is both not patient and not old and vice versa.
Everyone who is not patient or tall is either not patient or funny.
Everyone who is happy or not calm is wise or creative.
Everyone who is not patient is either not curious or old.
If someone is not strong or tall then someone is brave or not patient.
If mary is both funny and not creative then someone is not quiet.
Alice is old or not quiet.
Mary is both not generous and not quiet.
Mary is both brave and tall.
Someone is not calm.
Mary is generous or wise.
Someone is either not tall or not humble.
Mary is either not quiet or calm.
Fred is patient. | Paul is not tall. | neutral | (![X]:((patient(X)&~brave(X))=>(~strong(X)&~old(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~old(X))))&
(![X]:(humble(X)<=>(rich(X)|~tall(X))))&
(((~strong(mary)|humble(mary)))<=>(?[X]:((patient(X)&calm(X)))))&
((?[X]:((tall(X)<~>humble(X))))<=>(humble(alice)))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(((~brave(fred)|~wise(fred)))=>(~humble(alice)))&
(![X]:((~calm(X)&~generous(X))<=>(~kind(X)&~curious(X))))&
(((~tall(paul)&kind(paul)))<=>((quiet(mary)<~>~brave(mary))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)&~tall(X))))&
((~happy(paul))<=>((~patient(fred)&~old(fred))))&
(![X]:((~patient(X)|tall(X))=>(~patient(X)<~>funny(X))))&
(![X]:((happy(X)|~calm(X))=>(wise(X)|creative(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>old(X))))&
((?[X]:((~strong(X)|tall(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(((funny(mary)&~creative(mary)))=>(?[X]:(~quiet(X))))&
((old(alice)|~quiet(alice)))&
((~generous(mary)&~quiet(mary)))&
((brave(mary)&tall(mary)))&
(?[X]:(~calm(X)))&
((generous(mary)|wise(mary)))&
(?[X]:((~tall(X)<~>~humble(X))))&
((~quiet(mary)<~>calm(mary)))&
(patient(fred)) | ~tall(paul) | [] | null | 0 |
If someone is either happy or not calm then susan is not happy.
If mary is either humble or not old then someone is either not old or quiet.
If susan is both brave and not funny then paul is not patient or strong.
Everyone who is not old is both kind and generous.
Everyone who is not curious is either not funny or not strong.
Everyone who is kind or not old is creative or not generous and vice versa.
Everyone who is patient is not wise or creative and vice versa.
Everyone who is both happy and generous is not rich.
If susan is both calm and not tall then someone is not old and vice versa.
Everyone who is either not curious or creative is patient or not funny and vice versa.
Everyone who is both curious and happy is not old or rich and vice versa.
Everyone who is creative is not strong and vice versa.
If alice is either tall or not funny then someone is either not strong or patient and vice versa.
If someone is kind or not happy then someone is either not humble or not rich.
Everyone who is not funny or not calm is both brave and creative and vice versa.
If someone is calm then mary is both not quiet and brave and vice versa.
Someone is old or not creative.
Someone is not funny or humble.
Alice is calm.
Susan is not humble or not old.
Mary is not kind.
Someone is both not funny and old.
Susan is both kind and not quiet.
Someone is not old or not funny. | Mary is rich. | contradiction | ((?[X]:((happy(X)<~>~calm(X))))=>(~happy(susan)))&
(((humble(mary)<~>~old(mary)))=>(?[X]:((~old(X)<~>quiet(X)))))&
(((brave(susan)&~funny(susan)))=>((~patient(paul)|strong(paul))))&
(![X]:(~old(X)=>(kind(X)&generous(X))))&
(![X]:(~curious(X)=>(~funny(X)<~>~strong(X))))&
(![X]:((kind(X)|~old(X))<=>(creative(X)|~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)|creative(X))))&
(![X]:((happy(X)&generous(X))=>~rich(X)))&
(((calm(susan)&~tall(susan)))<=>(?[X]:(~old(X))))&
(![X]:((~curious(X)<~>creative(X))<=>(patient(X)|~funny(X))))&
(![X]:((curious(X)&happy(X))<=>(~old(X)|rich(X))))&
(![X]:(creative(X)<=>~strong(X)))&
(((tall(alice)<~>~funny(alice)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:((kind(X)|~happy(X))))=>(?[X]:((~humble(X)<~>~rich(X)))))&
(![X]:((~funny(X)|~calm(X))<=>(brave(X)&creative(X))))&
((?[X]:(calm(X)))<=>((~quiet(mary)&brave(mary))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((~funny(X)|humble(X))))&
(calm(alice))&
((~humble(susan)|~old(susan)))&
(~kind(mary))&
(?[X]:((~funny(X)&old(X))))&
((kind(susan)&~quiet(susan)))&
(?[X]:((~old(X)|~funny(X)))) | rich(mary) | [
"p3",
"p5",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3500916797828214210322868
% SZS output start Proof for 3500916797828214210322868
4. ! [X0] : (~old(X0) => (generous(X0) & kind(X0))) [input p3]
6. ! [X0] : ((~old(X0) | kind(X0)) <=> (~generous(X0) | creative(X0))) [input p5]
8. ! [X0] : ((generous(X0) & happy(X0)) => ~rich(X0)) [input p7]
11. ! [X0] : ((happy(X0) & curious(X0)) <=> (rich(X0) | ~old(X0))) [input p10]
21. ~kind(mary) [input p20]
25. rich(mary) [input hypothesis]
31. ! [X0] : ((generous(X0) & kind(X0)) | old(X0)) [ennf transformation 4]
33. ! [X0] : (~rich(X0) | (~generous(X0) | ~happy(X0))) [ennf transformation 8]
34. ! [X0] : (~rich(X0) | ~generous(X0) | ~happy(X0)) [flattening 33]
41. ! [X0] : (((~old(X0) | kind(X0)) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 6]
42. ! [X0] : ((~old(X0) | kind(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | (old(X0) & ~kind(X0)))) [flattening 41]
52. ! [X0] : (((happy(X0) & curious(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 11]
53. ! [X0] : (((happy(X0) & curious(X0)) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ~happy(X0) | ~curious(X0))) [flattening 52]
86. generous(X0) | old(X0) [cnf transformation 31]
92. ~old(X0) | kind(X0) | generous(X0) [cnf transformation 42]
96. ~rich(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 34]
110. ~rich(X0) | happy(X0) [cnf transformation 53]
137. ~kind(mary) [cnf transformation 21]
143. rich(mary) [cnf transformation 25]
193. generous(X0) | kind(X0) [subsumption resolution 92,86]
322. happy(mary) [resolution 110,143]
359. ~generous(mary) | ~happy(mary) [resolution 96,143]
360. ~generous(mary) [subsumption resolution 359,322]
361. kind(mary) [resolution 360,193]
363. $false [subsumption resolution 361,137]
% SZS output end Proof for 3500916797828214210322868
% ------------------------------
% 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 john is happy or not kind then someone is not brave.
If someone is not wise or not kind then alice is either not tall or not generous and vice versa.
Everyone who is quiet or brave is strong or wise and vice versa.
If someone is either generous or not funny then someone is either not generous or not happy.
Everyone who is not calm is not generous or rich and vice versa.
Everyone who is not rich is both strong and not brave.
Everyone who is both not happy and not kind is happy or funny.
Everyone who is rich or not generous is both patient and not curious and vice versa.
If someone is both not patient and not wise then mary is quiet or not brave and vice versa.
Everyone who is both not old and happy is not happy or wise and vice versa.
Everyone who is either generous or happy is both not calm and not happy and vice versa.
Everyone who is either rich or creative is not happy and vice versa.
Everyone who is both quiet and patient is both calm and tall.
Everyone who is generous or happy is not tall or brave.
If someone is creative then someone is either not calm or not funny.
Everyone who is either not old or not tall is not patient or wise.
Alice is curious.
Someone is creative.
Someone is not humble or not curious.
Someone is strong or not curious.
Someone is either happy or creative.
Someone is rich or strong. | John is not curious. | neutral | (((happy(john)|~kind(john)))=>(?[X]:(~brave(X))))&
((?[X]:((~wise(X)|~kind(X))))<=>((~tall(alice)<~>~generous(alice))))&
(![X]:((quiet(X)|brave(X))<=>(strong(X)|wise(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~calm(X)<=>(~generous(X)|rich(X))))&
(![X]:(~rich(X)=>(strong(X)&~brave(X))))&
(![X]:((~happy(X)&~kind(X))=>(happy(X)|funny(X))))&
(![X]:((rich(X)|~generous(X))<=>(patient(X)&~curious(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((quiet(mary)|~brave(mary))))&
(![X]:((~old(X)&happy(X))<=>(~happy(X)|wise(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)<~>creative(X))<=>~happy(X)))&
(![X]:((quiet(X)&patient(X))=>(calm(X)&tall(X))))&
(![X]:((generous(X)|happy(X))=>(~tall(X)|brave(X))))&
((?[X]:(creative(X)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((~old(X)<~>~tall(X))=>(~patient(X)|wise(X))))&
(curious(alice))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((rich(X)|strong(X)))) | ~curious(john) | [] | null | 0 |
If someone is not old then someone is not wise and vice versa.
If someone is both rich and not funny then mary is both not humble and old and vice versa.
Everyone who is strong or not old is not old or kind.
Everyone who is brave is patient.
If someone is humble or not old then someone is both rich and strong.
If someone is not calm then alice is not old.
Everyone who is both patient and curious is not brave.
If lucy is humble then mary is both old and calm and vice versa.
If someone is either not wise or not curious then someone is either not rich or not creative and vice versa.
Everyone who is either strong or humble is either not kind or humble.
Everyone who is either not wise or kind is happy or calm and vice versa.
If lucy is either patient or humble then paul is funny or patient and vice versa.
Everyone who is either not patient or not tall is either old or not patient and vice versa.
Everyone who is either kind or happy is either not old or not patient.
Everyone who is both not kind and patient is not tall.
Everyone who is either not old or strong is not strong or curious and vice versa.
Someone is rich.
Someone is either not wise or not happy.
Lucy is both not creative and old.
Paul is either not rich or not calm.
Someone is either not quiet or rich.
Someone is not wise or not quiet.
Alice is creative or tall. | Mary is old. | entailment | ((?[X]:(~old(X)))<=>(?[X]:(~wise(X))))&
((?[X]:((rich(X)&~funny(X))))<=>((~humble(mary)&old(mary))))&
(![X]:((strong(X)|~old(X))=>(~old(X)|kind(X))))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((humble(X)|~old(X))))=>(?[X]:((rich(X)&strong(X)))))&
((?[X]:(~calm(X)))=>(~old(alice)))&
(![X]:((patient(X)&curious(X))=>~brave(X)))&
((humble(lucy))<=>((old(mary)&calm(mary))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>humble(X))=>(~kind(X)<~>humble(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(happy(X)|calm(X))))&
(((patient(lucy)<~>humble(lucy)))<=>((funny(paul)|patient(paul))))&
(![X]:((~patient(X)<~>~tall(X))<=>(old(X)<~>~patient(X))))&
(![X]:((kind(X)<~>happy(X))=>(~old(X)<~>~patient(X))))&
(![X]:((~kind(X)&patient(X))=>~tall(X)))&
(![X]:((~old(X)<~>strong(X))<=>(~strong(X)|curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>~happy(X))))&
((~creative(lucy)&old(lucy)))&
((~rich(paul)<~>~calm(paul)))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
((creative(alice)|tall(alice))) | old(mary) | [
"p2",
"p7",
"p9",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 379383157302074219565196
% SZS output start Proof for 379383157302074219565196
3. ! [X0] : ((~old(X0) | strong(X0)) => (kind(X0) | ~old(X0))) [input p2]
8. humble(lucy) <=> (calm(mary) & old(mary)) [input p7]
10. ! [X0] : ((strong(X0) <~> humble(X0)) => (~kind(X0) <~> humble(X0))) [input p9]
16. ! [X0] : ((~old(X0) <~> strong(X0)) <=> (curious(X0) | ~strong(X0))) [input p15]
19. old(lucy) & ~creative(lucy) [input p18]
24. ~old(mary) [input hypothesis]
30. ! [X0] : ((kind(X0) | ~old(X0)) | (old(X0) & ~strong(X0))) [ennf transformation 3]
31. ! [X0] : (kind(X0) | ~old(X0) | (old(X0) & ~strong(X0))) [flattening 30]
34. ! [X0] : ((~kind(X0) <~> humble(X0)) | (strong(X0) <=> humble(X0))) [ennf transformation 10]
51. (humble(lucy) | (~calm(mary) | ~old(mary))) & ((calm(mary) & old(mary)) | ~humble(lucy)) [nnf transformation 8]
52. (humble(lucy) | ~calm(mary) | ~old(mary)) & ((calm(mary) & old(mary)) | ~humble(lucy)) [flattening 51]
58. ! [X0] : (((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 34]
65. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (~curious(X0) & strong(X0))) & ((curious(X0) | ~strong(X0)) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 16]
66. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (~curious(X0) & strong(X0))) & (curious(X0) | ~strong(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [flattening 65]
84. ~strong(X0) | ~old(X0) | kind(X0) [cnf transformation 31]
91. old(mary) | ~humble(lucy) [cnf transformation 52]
102. humble(X0) | ~kind(X0) | humble(X0) | ~strong(X0) [cnf transformation 58]
133. strong(X0) | ~old(X0) | strong(X0) [cnf transformation 66]
141. old(lucy) [cnf transformation 19]
148. ~old(mary) [cnf transformation 24]
150. ~old(X0) | strong(X0) [duplicate literal removal 133]
155. ~kind(X0) | humble(X0) | ~strong(X0) [duplicate literal removal 102]
178. 6 <=> old(mary) [avatar definition]
224. 16 <=> humble(lucy) [avatar definition]
225. ~humble(lucy) <- (~16) [avatar component clause 224]
229. ~16 | 6 [avatar split clause 91,178,224]
335. ~6 [avatar split clause 148,178]
338. strong(lucy) [resolution 150,141]
349. ~old(lucy) | kind(lucy) [resolution 84,338]
359. kind(lucy) [subsumption resolution 349,141]
367. humble(lucy) | ~strong(lucy) [resolution 155,359]
368. ~strong(lucy) <- (~16) [subsumption resolution 367,225]
369. $false <- (~16) [subsumption resolution 368,338]
370. 16 [avatar contradiction clause 369]
371. $false [avatar sat refutation 229,335,370]
% SZS output end Proof for 379383157302074219565196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or quiet then someone is not happy and vice versa.
If someone is both humble and not kind then someone is curious or humble and vice versa.
Everyone who is not rich or old is not curious or quiet.
Everyone who is both not kind and humble is wise or not strong and vice versa.
Everyone who is both not happy and wise is not funny or not quiet.
Everyone who is either not kind or tall is not creative or old.
If someone is either not creative or not funny then fred is either not kind or calm.
Everyone who is not funny is not calm or strong.
If someone is both strong and not calm then mary is either happy or not generous and vice versa.
Everyone who is both not happy and creative is either kind or not creative and vice versa.
Everyone who is brave or old is both not creative and patient and vice versa.
If someone is not generous then fred is generous.
Everyone who is either wise or not funny is both kind and strong.
Everyone who is not happy or not rich is happy or not curious.
Everyone who is not calm is not rich.
If lucy is quiet then susan is strong or calm and vice versa.
Susan is rich.
Someone is creative or not happy.
Someone is either not brave or not calm.
Someone is both not old and not happy.
Mary is not humble.
Someone is not kind or old.
Someone is strong. | Lucy is rich. | neutral | (((~happy(fred)|quiet(fred)))<=>(?[X]:(~happy(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((curious(X)|humble(X)))))&
(![X]:((~rich(X)|old(X))=>(~curious(X)|quiet(X))))&
(![X]:((~kind(X)&humble(X))<=>(wise(X)|~strong(X))))&
(![X]:((~happy(X)&wise(X))=>(~funny(X)|~quiet(X))))&
(![X]:((~kind(X)<~>tall(X))=>(~creative(X)|old(X))))&
((?[X]:((~creative(X)<~>~funny(X))))=>((~kind(fred)<~>calm(fred))))&
(![X]:(~funny(X)=>(~calm(X)|strong(X))))&
((?[X]:((strong(X)&~calm(X))))<=>((happy(mary)<~>~generous(mary))))&
(![X]:((~happy(X)&creative(X))<=>(kind(X)<~>~creative(X))))&
(![X]:((brave(X)|old(X))<=>(~creative(X)&patient(X))))&
((?[X]:(~generous(X)))=>(generous(fred)))&
(![X]:((wise(X)<~>~funny(X))=>(kind(X)&strong(X))))&
(![X]:((~happy(X)|~rich(X))=>(happy(X)|~curious(X))))&
(![X]:(~calm(X)=>~rich(X)))&
((quiet(lucy))<=>((strong(susan)|calm(susan))))&
(rich(susan))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((~old(X)&~happy(X))))&
(~humble(mary))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:(strong(X))) | rich(lucy) | [] | null | 0 |
If alice is both not tall and patient then fred is both tall and curious and vice versa.
Everyone who is not generous is both not happy and not calm.
If someone is both not rich and calm then fred is not patient and vice versa.
If fred is both strong and not curious then someone is not strong or creative and vice versa.
If fred is not kind or generous then fred is not kind.
Everyone who is either not humble or creative is both not creative and not rich.
If someone is either not old or humble then alice is either wise or kind and vice versa.
Everyone who is not calm is either not quiet or brave and vice versa.
If someone is not tall then someone is strong and vice versa.
Everyone who is either not quiet or not wise is either not strong or not curious and vice versa.
If someone is not quiet or not creative then someone is either not patient or not tall.
Everyone who is both humble and not humble is both creative and strong.
If paul is generous then mary is either patient or not humble and vice versa.
Everyone who is either creative or brave is both not happy and creative.
If lucy is both generous and happy then someone is not happy or not curious and vice versa.
Everyone who is both not strong and not patient is either brave or strong.
Alice is either not rich or not calm.
Fred is tall.
Fred is either not happy or not patient.
Paul is not calm or not happy.
Alice is not calm or not patient.
Someone is creative.
Fred is not happy.
Alice is not happy. | Fred is happy. | contradiction | (((~tall(alice)&patient(alice)))<=>((tall(fred)&curious(fred))))&
(![X]:(~generous(X)=>(~happy(X)&~calm(X))))&
((?[X]:((~rich(X)&calm(X))))<=>(~patient(fred)))&
(((strong(fred)&~curious(fred)))<=>(?[X]:((~strong(X)|creative(X)))))&
(((~kind(fred)|generous(fred)))=>(~kind(fred)))&
(![X]:((~humble(X)<~>creative(X))=>(~creative(X)&~rich(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>((wise(alice)<~>kind(alice))))&
(![X]:(~calm(X)<=>(~quiet(X)<~>brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~strong(X)<~>~curious(X))))&
((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((humble(X)&~humble(X))=>(creative(X)&strong(X))))&
((generous(paul))<=>((patient(mary)<~>~humble(mary))))&
(![X]:((creative(X)<~>brave(X))=>(~happy(X)&creative(X))))&
(((generous(lucy)&happy(lucy)))<=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:((~strong(X)&~patient(X))=>(brave(X)<~>strong(X))))&
((~rich(alice)<~>~calm(alice)))&
(tall(fred))&
((~happy(fred)<~>~patient(fred)))&
((~calm(paul)|~happy(paul)))&
((~calm(alice)|~patient(alice)))&
(?[X]:(creative(X)))&
(~happy(fred))&
(~happy(alice)) | happy(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1955972566684448035701062
% SZS output start Proof for 1955972566684448035701062
23. ~happy(fred) [input p22]
25. happy(fred) [input hypothesis]
147. ~happy(fred) [cnf transformation 23]
149. happy(fred) [cnf transformation 25]
343. 41 <=> happy(fred) [avatar definition]
358. ~41 [avatar split clause 147,343]
359. 41 [avatar split clause 149,343]
360. $false [avatar sat refutation 358,359]
% SZS output end Proof for 1955972566684448035701062
% ------------------------------
% 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 humble or rich is not wise and vice versa. If someone is not curious or wise then someone is strong. Everyone who is not calm is either not patient or funny. If someone is either patient or not creative then someone is both not patient and humble and vice versa. If someone is generous then someone is either not funny or not brave. Everyone who is kind is patient or not creative. Everyone who is not kind or tall is not brave or rich. If someone is both curious and patient then lucy is not quiet and vice versa. If someone is not funny then someone is both not wise and not humble and vice versa. Everyone who is not happy or humble is calm and vice versa. If lucy is rich then someone is tall and vice versa. If lucy is patient then susan is both generous and not strong and vice versa. If lucy is not tall or rich then someone is rich or not brave and vice versa. Everyone who is either not quiet or not curious is either not rich or brave and vice versa. If someone is either not happy or tall then fred is either not creative or not funny and vice versa. If someone is brave or funny then mary is wise. Someone is not strong. Fred is either not quiet or kind. Someone is not happy. Someone is either curious or humble. Paul is quiet. Mary is not brave or not calm. Mary is both curious and rich. Someone is either creative or funny. | Susan is patient. | neutral | (![X]:((~humble(X)|rich(X))<=>~wise(X)))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:(strong(X))))&
(![X]:(~calm(X)=>(~patient(X)<~>funny(X))))&
((?[X]:((patient(X)<~>~creative(X))))<=>(?[X]:((~patient(X)&humble(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:(kind(X)=>(patient(X)|~creative(X))))&
(![X]:((~kind(X)|tall(X))=>(~brave(X)|rich(X))))&
((?[X]:((curious(X)&patient(X))))<=>(~quiet(lucy)))&
((?[X]:(~funny(X)))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~happy(X)|humble(X))<=>calm(X)))&
((rich(lucy))<=>(?[X]:(tall(X))))&
((patient(lucy))<=>((generous(susan)&~strong(susan))))&
(((~tall(lucy)|rich(lucy)))<=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~rich(X)<~>brave(X))))&
((?[X]:((~happy(X)<~>tall(X))))<=>((~creative(fred)<~>~funny(fred))))&
((?[X]:((brave(X)|funny(X))))=>(wise(mary)))&
(?[X]:(~strong(X)))&
((~quiet(fred)<~>kind(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((curious(X)<~>humble(X))))&
(quiet(paul))&
((~brave(mary)|~calm(mary)))&
((curious(mary)&rich(mary)))&
(?[X]:((creative(X)<~>funny(X)))) | patient(susan) | [] | null | 0 |
Everyone who is rich is either not generous or generous.
Everyone who is not brave is both not funny and not kind.
Everyone who is both not humble and not patient is both not funny and wise and vice versa.
If someone is either strong or kind then alice is kind or not curious.
If alice is both generous and brave then someone is either curious or not generous and vice versa.
If mary is either not humble or creative then fred is not kind.
Everyone who is both not funny and not old is both not funny and old and vice versa.
If someone is either not happy or not calm then someone is both patient and not humble and vice versa.
Everyone who is not curious is both patient and not calm.
Everyone who is both humble and patient is either not calm or not rich.
Everyone who is not creative is both not curious and kind and vice versa.
If alice is both not creative and not generous then someone is either calm or happy.
Everyone who is either curious or not kind is quiet.
If someone is both not calm and happy then someone is patient or not wise and vice versa.
If fred is either funny or not happy then lucy is both not funny and not quiet.
Mary is both not wise and not old.
Lucy is happy or not kind.
John is either not rich or strong.
Susan is both rich and wise.
Susan is not kind or rich.
Someone is either happy or not brave.
Mary is curious. | John is brave. | entailment | (![X]:(rich(X)=>(~generous(X)<~>generous(X))))&
(![X]:(~brave(X)=>(~funny(X)&~kind(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~funny(X)&wise(X))))&
((?[X]:((strong(X)<~>kind(X))))=>((kind(alice)|~curious(alice))))&
(((generous(alice)&brave(alice)))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(((~humble(mary)<~>creative(mary)))=>(~kind(fred)))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&old(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:(~curious(X)=>(patient(X)&~calm(X))))&
(![X]:((humble(X)&patient(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~creative(X)<=>(~curious(X)&kind(X))))&
(((~creative(alice)&~generous(alice)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((curious(X)<~>~kind(X))=>quiet(X)))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(((funny(fred)<~>~happy(fred)))=>((~funny(lucy)&~quiet(lucy))))&
((~wise(mary)&~old(mary)))&
((happy(lucy)|~kind(lucy)))&
((~rich(john)<~>strong(john)))&
((rich(susan)&wise(susan)))&
((~kind(susan)|rich(susan)))&
(?[X]:((happy(X)<~>~brave(X))))&
(curious(mary)) | brave(john) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1814101078841684019916831
% SZS output start Proof for 1814101078841684019916831
2. ! [X0] : (~brave(X0) => (~kind(X0) & ~funny(X0))) [input p1]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (old(X0) & ~funny(X0))) [input p6]
23. ~brave(john) [input hypothesis]
27. ! [X0] : ((~kind(X0) & ~funny(X0)) | brave(X0)) [ennf transformation 2]
48. ! [X0] : (((~old(X0) & ~funny(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (old(X0) | funny(X0)))) [nnf transformation 7]
49. ! [X0] : (((~old(X0) & ~funny(X0)) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | old(X0) | funny(X0))) [flattening 48]
74. ~funny(X0) | brave(X0) [cnf transformation 27]
91. old(X0) | old(X0) | funny(X0) [cnf transformation 49]
93. ~old(X0) | ~old(X0) | funny(X0) [cnf transformation 49]
131. ~brave(john) [cnf transformation 23]
132. old(X0) | funny(X0) [duplicate literal removal 91]
133. ~old(X0) | funny(X0) [duplicate literal removal 93]
192. funny(X0) [subsumption resolution 132,133]
307. brave(X0) [resolution 74,192]
308. $false [resolution 307,131]
% SZS output end Proof for 1814101078841684019916831
% ------------------------------
% 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 |
Everyone who is not rich is either rich or strong and vice versa.
Everyone who is both not tall and not quiet is patient or not calm and vice versa.
If someone is either rich or not rich then mary is both tall and not old.
If someone is not calm or not generous then susan is not calm or rich.
Everyone who is not tall or not brave is either creative or funny and vice versa.
If someone is funny then paul is patient.
If lucy is not strong then mary is not rich and vice versa.
Everyone who is either not curious or not humble is not wise and vice versa.
If someone is either not generous or old then someone is calm or brave and vice versa.
If fred is not patient then someone is funny or curious.
Everyone who is not quiet is brave.
If someone is funny or tall then someone is both not funny and not humble.
If lucy is curious then someone is either not tall or not old and vice versa.
If paul is both not tall and not rich then lucy is either not strong or generous and vice versa.
If someone is not wise or generous then someone is not rich and vice versa.
Everyone who is either not rich or happy is curious or not patient.
Alice is old or rich.
John is not quiet.
Mary is both not kind and not old.
Alice is not old or quiet.
Paul is either not funny or not calm.
Fred is generous or not calm.
Someone is not wise.
Susan is not happy or not rich. | Fred is humble. | neutral | (![X]:(~rich(X)<=>(rich(X)<~>strong(X))))&
(![X]:((~tall(X)&~quiet(X))<=>(patient(X)|~calm(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>((tall(mary)&~old(mary))))&
((?[X]:((~calm(X)|~generous(X))))=>((~calm(susan)|rich(susan))))&
(![X]:((~tall(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((?[X]:(funny(X)))=>(patient(paul)))&
((~strong(lucy))<=>(~rich(mary)))&
(![X]:((~curious(X)<~>~humble(X))<=>~wise(X)))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((calm(X)|brave(X)))))&
((~patient(fred))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(~quiet(X)=>brave(X)))&
((?[X]:((funny(X)|tall(X))))=>(?[X]:((~funny(X)&~humble(X)))))&
((curious(lucy))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~tall(paul)&~rich(paul)))<=>((~strong(lucy)<~>generous(lucy))))&
((?[X]:((~wise(X)|generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)<~>happy(X))=>(curious(X)|~patient(X))))&
((old(alice)|rich(alice)))&
(~quiet(john))&
((~kind(mary)&~old(mary)))&
((~old(alice)|quiet(alice)))&
((~funny(paul)<~>~calm(paul)))&
((generous(fred)|~calm(fred)))&
(?[X]:(~wise(X)))&
((~happy(susan)|~rich(susan))) | humble(fred) | [] | null | 0 |
If mary is either not kind or funny then lucy is not tall or not patient and vice versa.
Everyone who is either not funny or tall is wise.
Everyone who is either kind or strong is either not curious or calm.
If mary is not old then someone is kind or rich and vice versa.
Everyone who is creative is generous and vice versa.
If someone is 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 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.
Lucy is happy.
Fred is kind or curious.
Someone is curious.
Someone is both old and humble.
Someone is not creative or not brave.
Someone is either kind or not curious.
John is kind or not strong. | Fred is generous. | neutral | (((~kind(mary)<~>funny(mary)))<=>((~tall(lucy)|~patient(lucy))))&
(![X]:((~funny(X)<~>tall(X))=>wise(X)))&
(![X]:((kind(X)<~>strong(X))=>(~curious(X)<~>calm(X))))&
((~old(mary))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:(creative(X)<=>generous(X)))&
((?[X]:(~brave(X)))<=>(?[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]:((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))))&
(happy(lucy))&
((kind(fred)|curious(fred)))&
(?[X]:(curious(X)))&
(?[X]:((old(X)&humble(X))))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((kind(X)<~>~curious(X))))&
((kind(john)|~strong(john))) | generous(fred) | [] | null | 0 |
Everyone who is not wise or brave is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Lucy is rich. | contradiction | (![X]:((~wise(X)|brave(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | rich(lucy) | [
"p1",
"p9",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5606941393868996344836935
% SZS output start Proof for 5606941393868996344836935
2. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (funny(X0) | calm(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> old(X0)) => ~humble(X0)) [input p9]
13. ! [X0] : ((humble(X0) <~> strong(X0)) => (funny(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
15. ! [X0] : (old(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
18. ~strong(lucy) | ~tall(lucy) [input p17]
23. rich(lucy) [input hypothesis]
30. ! [X0] : (~humble(X0) | (rich(X0) <=> old(X0))) [ennf transformation 10]
33. ! [X0] : ((funny(X0) & creative(X0)) | (humble(X0) <=> strong(X0))) [ennf transformation 13]
36. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 36]
55. ! [X0] : (~humble(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 30]
56. ! [X0] : ((funny(X0) & creative(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) [nnf transformation 33]
57. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
58. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 57]
59. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~old(X0))) [nnf transformation 15]
60. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~old(X0))) [flattening 59]
84. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 37]
110. ~humble(X0) | old(X0) | ~rich(X0) [cnf transformation 55]
116. ~strong(X0) | humble(X0) | funny(X0) [cnf transformation 56]
118. strong(X0) | funny(X0) [cnf transformation 58]
119. ~funny(X0) | humble(X0) [cnf transformation 58]
122. ~strong(X0) | tall(X0) | ~old(X0) [cnf transformation 60]
123. strong(X0) | old(X0) [cnf transformation 60]
132. ~strong(lucy) | ~tall(lucy) [cnf transformation 18]
141. rich(lucy) [cnf transformation 23]
234. 22 <=> tall(lucy) [avatar definition]
236. ~tall(lucy) <- (~22) [avatar component clause 234]
238. 23 <=> strong(lucy) [avatar definition]
239. strong(lucy) <- (23) [avatar component clause 238]
240. ~strong(lucy) <- (~23) [avatar component clause 238]
241. ~22 | ~23 [avatar split clause 132,238,234]
267. funny(lucy) <- (~23) [resolution 118,240]
269. old(lucy) <- (~23) [resolution 123,240]
271. ~old(lucy) | ~rich(lucy) <- (~23) [resolution 84,267]
272. ~rich(lucy) <- (~23) [subsumption resolution 271,269]
273. $false <- (~23) [subsumption resolution 272,141]
274. 23 [avatar contradiction clause 273]
348. humble(X1) | funny(X1) | funny(X1) [resolution 116,118]
352. humble(X1) | funny(X1) [duplicate literal removal 348]
354. humble(X1) [subsumption resolution 352,119]
358. tall(lucy) | ~old(lucy) <- (23) [resolution 122,239]
359. ~old(lucy) <- (~22, 23) [subsumption resolution 358,236]
406. ~rich(X3) | old(X3) [resolution 354,110]
521. old(lucy) [resolution 406,141]
523. $false <- (~22, 23) [subsumption resolution 521,359]
524. 22 | ~23 [avatar contradiction clause 523]
525. $false [avatar sat refutation 241,274,524]
% SZS output end Proof for 5606941393868996344836935
% ------------------------------
% 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 old or not generous is either not patient or kind and vice versa.
If someone is both not brave and calm then fred is humble or brave and vice versa.
If someone is generous then lucy is either not humble or happy and vice versa.
Everyone who is both not happy and not kind is either happy or calm and vice versa.
Everyone who is not tall is either not kind or tall and vice versa.
Everyone who is not happy is both old and not tall.
Everyone who is either not old or not happy is both patient and curious and vice versa.
Everyone who is either not happy or not quiet is either not curious or not generous.
Everyone who is tall is either calm or not funny.
If someone is either not happy or not rich then someone is not kind and vice versa.
Everyone who is either wise or patient is either humble or calm.
If someone is not creative or not calm then someone is both not calm and rich and vice versa.
If fred is either not calm or not creative then someone is not funny and vice versa.
If paul is both not funny and not creative then someone is either not quiet or funny.
If john is generous then someone is either funny or not kind and vice versa.
Everyone who is either tall or curious is generous or creative and vice versa.
Mary is funny or not brave.
Someone is not tall.
Paul is either not brave or kind.
Susan is either brave or rich.
Paul is generous or not rich. | Susan is funny. | entailment | (![X]:((old(X)|~generous(X))<=>(~patient(X)<~>kind(X))))&
((?[X]:((~brave(X)&calm(X))))<=>((humble(fred)|brave(fred))))&
((?[X]:(generous(X)))<=>((~humble(lucy)<~>happy(lucy))))&
(![X]:((~happy(X)&~kind(X))<=>(happy(X)<~>calm(X))))&
(![X]:(~tall(X)<=>(~kind(X)<~>tall(X))))&
(![X]:(~happy(X)=>(old(X)&~tall(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(~curious(X)<~>~generous(X))))&
(![X]:(tall(X)=>(calm(X)<~>~funny(X))))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)<~>patient(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>(?[X]:((~calm(X)&rich(X)))))&
(((~calm(fred)<~>~creative(fred)))<=>(?[X]:(~funny(X))))&
(((~funny(paul)&~creative(paul)))=>(?[X]:((~quiet(X)<~>funny(X)))))&
((generous(john))<=>(?[X]:((funny(X)<~>~kind(X)))))&
(![X]:((tall(X)<~>curious(X))<=>(generous(X)|creative(X))))&
((funny(mary)|~brave(mary)))&
(?[X]:(~tall(X)))&
((~brave(paul)<~>kind(paul)))&
((brave(susan)<~>rich(susan)))&
((generous(paul)|~rich(paul))) | funny(susan) | [
"p3",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6339447568625907850250615
% SZS output start Proof for 6339447568625907850250615
4. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (happy(X0) <~> calm(X0))) [input p3]
5. ! [X0] : (~tall(X0) <=> (~kind(X0) <~> tall(X0))) [input p4]
12. ? [X0] : (~calm(X0) | ~creative(X0)) <=> ? [X0] : (rich(X0) & ~calm(X0)) [input p11]
13. (~calm(fred) <~> ~creative(fred)) <=> ? [X0] : ~funny(X0) [input p12]
22. ~funny(susan) [input hypothesis]
24. ? [X0] : (~calm(X0) | ~creative(X0)) <=> ? [X1] : (rich(X1) & ~calm(X1)) [rectify 12]
42. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 4]
43. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | kind(X0) | happy(X0))) [flattening 42]
44. ! [X0] : ((~tall(X0) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0)))) & (((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | tall(X0))) [nnf transformation 5]
55. (? [X0] : (~calm(X0) | ~creative(X0)) | ! [X1] : (~rich(X1) | calm(X1))) & (? [X1] : (rich(X1) & ~calm(X1)) | ! [X0] : (calm(X0) & creative(X0))) [nnf transformation 24]
56. (? [X0] : (~calm(X0) | ~creative(X0)) | ! [X1] : (~rich(X1) | calm(X1))) & (? [X2] : (rich(X2) & ~calm(X2)) | ! [X3] : (calm(X3) & creative(X3))) [rectify 55]
57. ? [X0] : (~calm(X0) | ~creative(X0)) => (~calm(sK4) | ~creative(sK4)) [choice axiom]
58. ? [X2] : (rich(X2) & ~calm(X2)) => (rich(sK5) & ~calm(sK5)) [choice axiom]
59. ((~calm(sK4) | ~creative(sK4)) | ! [X1] : (~rich(X1) | calm(X1))) & ((rich(sK5) & ~calm(sK5)) | ! [X3] : (calm(X3) & creative(X3))) [skolemisation 56,58,57]
60. (((creative(fred) | calm(fred)) & (~creative(fred) | ~calm(fred))) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | ((~calm(fred) | creative(fred)) & (~creative(fred) | calm(fred)))) [nnf transformation 13]
61. (((creative(fred) | calm(fred)) & (~creative(fred) | ~calm(fred))) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | ((~calm(fred) | creative(fred)) & (~creative(fred) | calm(fred)))) [rectify 60]
62. ? [X1] : ~funny(X1) => ~funny(sK6) [choice axiom]
63. (((creative(fred) | calm(fred)) & (~creative(fred) | ~calm(fred))) | ! [X0] : funny(X0)) & (~funny(sK6) | ((~calm(fred) | creative(fred)) & (~creative(fred) | calm(fred)))) [skolemisation 61,62]
92. calm(X0) | happy(X0) | kind(X0) | happy(X0) [cnf transformation 43]
94. ~happy(X0) | calm(X0) | ~happy(X0) [cnf transformation 43]
98. tall(X0) | ~kind(X0) | tall(X0) [cnf transformation 44]
101. ~tall(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 44]
124. ~calm(sK5) | creative(X3) [cnf transformation 59]
125. ~calm(sK5) | calm(X3) [cnf transformation 59]
131. ~creative(fred) | ~calm(fred) | funny(X0) [cnf transformation 63]
152. ~funny(susan) [cnf transformation 22]
153. tall(X0) | ~kind(X0) [duplicate literal removal 98]
154. ~tall(X0) | ~kind(X0) [duplicate literal removal 101]
155. calm(X0) | happy(X0) | kind(X0) [duplicate literal removal 92]
156. ~happy(X0) | calm(X0) [duplicate literal removal 94]
200. calm(X0) | kind(X0) [subsumption resolution 155,156]
201. ~kind(X0) [subsumption resolution 153,154]
233. 15 <=> ! [X3] : calm(X3) [avatar definition]
234. calm(X3) <- (15) [avatar component clause 233]
241. 17 <=> ! [X3] : creative(X3) [avatar definition]
242. creative(X3) <- (17) [avatar component clause 241]
245. 18 <=> calm(sK5) [avatar definition]
247. ~calm(sK5) <- (~18) [avatar component clause 245]
248. 15 | ~18 [avatar split clause 125,245,233]
249. 17 | ~18 [avatar split clause 124,245,241]
251. 19 <=> ! [X0] : funny(X0) [avatar definition]
252. funny(X0) <- (19) [avatar component clause 251]
254. 20 <=> calm(fred) [avatar definition]
255. ~calm(fred) <- (~20) [avatar component clause 254]
258. 21 <=> creative(fred) [avatar definition]
259. ~creative(fred) <- (~21) [avatar component clause 258]
262. 19 | ~20 | ~21 [avatar split clause 131,258,254,251]
328. $false <- (19) [resolution 252,152]
329. ~19 [avatar contradiction clause 328]
334. kind(sK5) <- (~18) [resolution 200,247]
337. $false <- (~18) [subsumption resolution 334,201]
338. 18 [avatar contradiction clause 337]
341. $false <- (17, ~21) [resolution 242,259]
342. ~17 | 21 [avatar contradiction clause 341]
343. $false <- (15, ~20) [subsumption resolution 255,234]
344. ~15 | 20 [avatar contradiction clause 343]
345. $false [avatar sat refutation 248,249,262,329,338,342,344]
% SZS output end Proof for 6339447568625907850250615
% ------------------------------
% 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 patient is either patient or not old.
If someone is not kind then someone is either generous or not curious.
If susan is either not funny or not rich then someone is either not happy or not strong.
If someone is happy or not creative then someone is both quiet and generous and vice versa.
If mary is not creative then fred is either funny or not old and vice versa.
Everyone who is not tall or not brave is not patient and vice versa.
Everyone who is not patient is strong.
If someone is both tall and not generous then someone is not rich and vice versa.
If mary is either humble or calm then someone is both old and curious.
Everyone who is quiet is both not rich and curious.
Everyone who is tall or happy is either patient or funny.
Everyone who is strong is creative or tall.
Everyone who is not creative is either not patient or not happy and vice versa.
Everyone who is not kind or rich is happy and vice versa.
If someone is either not strong or kind then lucy is both brave and strong.
Everyone who is not old or happy is both not creative and kind and vice versa.
John is either not strong or tall.
Someone is both humble and not creative.
Susan is not old.
Someone is quiet or funny.
Someone is rich.
Someone is patient or rich.
Someone is rich or brave.
Someone is wise or not creative. | Susan is not creative. | entailment | (![X]:(patient(X)=>(patient(X)<~>~old(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((~funny(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
((?[X]:((happy(X)|~creative(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
((~creative(mary))<=>((funny(fred)<~>~old(fred))))&
(![X]:((~tall(X)|~brave(X))<=>~patient(X)))&
(![X]:(~patient(X)=>strong(X)))&
((?[X]:((tall(X)&~generous(X))))<=>(?[X]:(~rich(X))))&
(((humble(mary)<~>calm(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:(quiet(X)=>(~rich(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(patient(X)<~>funny(X))))&
(![X]:(strong(X)=>(creative(X)|tall(X))))&
(![X]:(~creative(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((~kind(X)|rich(X))<=>happy(X)))&
((?[X]:((~strong(X)<~>kind(X))))=>((brave(lucy)&strong(lucy))))&
(![X]:((~old(X)|happy(X))<=>(~creative(X)&kind(X))))&
((~strong(john)<~>tall(john)))&
(?[X]:((humble(X)&~creative(X))))&
(~old(susan))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((rich(X)|brave(X))))&
(?[X]:((wise(X)|~creative(X)))) | ~creative(susan) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7093576443345832378458668
% SZS output start Proof for 7093576443345832378458668
16. ! [X0] : ((happy(X0) | ~old(X0)) <=> (kind(X0) & ~creative(X0))) [input p15]
19. ~old(susan) [input p18]
25. creative(susan) [input hypothesis]
69. ! [X0] : (((happy(X0) | ~old(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 16]
70. ! [X0] : ((happy(X0) | ~old(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [flattening 69]
128. ~creative(X0) | old(X0) [cnf transformation 70]
137. ~old(susan) [cnf transformation 19]
142. creative(susan) [cnf transformation 25]
352. old(susan) [resolution 128,142]
354. $false [subsumption resolution 352,137]
% SZS output end Proof for 7093576443345832378458668
% ------------------------------
% 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 strong is happy or not old and vice versa.
Everyone who is both rich and not calm is both wise and tall.
Everyone who is not creative or humble is both wise and not calm.
If someone is either not funny or curious then someone is both not patient and generous and vice versa.
Everyone who is both not happy and not tall is humble and vice versa.
Everyone who is old is patient and vice versa.
If someone is either not brave or strong then someone is either patient or not kind.
If someone is quiet or humble then someone is either tall or not generous.
Everyone who is either calm or rich is quiet or brave.
Everyone who is both not generous and curious is either not old or brave.
Everyone who is either not patient or not generous is either wise or not strong and vice versa.
Everyone who is not strong or strong is both creative and not generous.
If someone is not curious or not funny then fred is both not tall and not curious.
If someone is old or rich then someone is both not humble and quiet and vice versa.
If someone is either not rich or generous then someone is happy and vice versa.
Everyone who is not old is humble or not tall and vice versa.
Mary is funny or strong.
Alice is tall.
Someone is both rich and creative.
Someone is not kind.
Lucy is both not curious and kind.
Alice is creative or not kind.
John is not old.
Someone is not tall or not curious. | Fred is not wise. | entailment | (![X]:(strong(X)<=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~calm(X))=>(wise(X)&tall(X))))&
(![X]:((~creative(X)|humble(X))=>(wise(X)&~calm(X))))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:((~happy(X)&~tall(X))<=>humble(X)))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((?[X]:((quiet(X)|humble(X))))=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>rich(X))=>(quiet(X)|brave(X))))&
(![X]:((~generous(X)&curious(X))=>(~old(X)<~>brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((~strong(X)|strong(X))=>(creative(X)&~generous(X))))&
((?[X]:((~curious(X)|~funny(X))))=>((~tall(fred)&~curious(fred))))&
((?[X]:((old(X)|rich(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(?[X]:(happy(X))))&
(![X]:(~old(X)<=>(humble(X)|~tall(X))))&
((funny(mary)|strong(mary)))&
(tall(alice))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:(~kind(X)))&
((~curious(lucy)&kind(lucy)))&
((creative(alice)|~kind(alice)))&
(~old(john))&
(?[X]:((~tall(X)|~curious(X)))) | ~wise(fred) | [
"p0",
"p5",
"p10",
"p11",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4630523851422947938303316
% SZS output start Proof for 4630523851422947938303316
1. ! [X0] : (strong(X0) <=> (~old(X0) | happy(X0))) [input p0]
6. ! [X0] : (old(X0) <=> patient(X0)) [input p5]
11. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((strong(X0) | ~strong(X0)) => (~generous(X0) & creative(X0))) [input p11]
13. ? [X0] : (~funny(X0) | ~curious(X0)) => (~curious(fred) & ~tall(fred)) [input p12]
16. ! [X0] : (~old(X0) <=> (~tall(X0) | humble(X0))) [input p15]
21. kind(lucy) & ~curious(lucy) [input p20]
25. wise(fred) [input hypothesis]
34. ! [X0] : ((strong(X0) | ~strong(X0)) => ~generous(X0)) [pure predicate removal 12]
44. ! [X0] : (~generous(X0) | (~strong(X0) & strong(X0))) [ennf transformation 34]
45. (~curious(fred) & ~tall(fred)) | ! [X0] : (funny(X0) & curious(X0)) [ennf transformation 13]
46. ! [X0] : ((strong(X0) | (old(X0) & ~happy(X0))) & ((~old(X0) | happy(X0)) | ~strong(X0))) [nnf transformation 1]
47. ! [X0] : ((strong(X0) | (old(X0) & ~happy(X0))) & (~old(X0) | happy(X0) | ~strong(X0))) [flattening 46]
55. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 6]
66. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 11]
77. ! [X0] : ((~old(X0) | (tall(X0) & ~humble(X0))) & ((~tall(X0) | humble(X0)) | old(X0))) [nnf transformation 16]
78. ! [X0] : ((~old(X0) | (tall(X0) & ~humble(X0))) & (~tall(X0) | humble(X0) | old(X0))) [flattening 77]
87. old(X0) | strong(X0) [cnf transformation 47]
101. ~old(X0) | patient(X0) [cnf transformation 55]
102. ~patient(X0) | old(X0) [cnf transformation 55]
121. ~wise(X0) | patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 66]
123. ~generous(X0) | strong(X0) [cnf transformation 44]
124. ~generous(X0) | ~strong(X0) [cnf transformation 44]
125. ~tall(fred) | curious(X0) [cnf transformation 45]
140. ~old(X0) | tall(X0) [cnf transformation 78]
145. ~curious(lucy) [cnf transformation 21]
149. wise(fred) [cnf transformation 25]
217. ~generous(X0) [subsumption resolution 123,124]
227. 18 <=> ! [X0] : curious(X0) [avatar definition]
228. curious(X0) <- (18) [avatar component clause 227]
231. 19 <=> tall(fred) [avatar definition]
235. 18 | ~19 [avatar split clause 125,231,227]
308. patient(X0) | strong(X0) [resolution 101,87]
429. patient(fred) | ~strong(fred) | generous(fred) [resolution 121,149]
431. patient(fred) | ~strong(fred) [subsumption resolution 429,217]
432. patient(fred) [subsumption resolution 431,308]
435. old(fred) [resolution 432,102]
448. tall(fred) [resolution 435,140]
453. 19 [avatar split clause 448,231]
457. $false <- (18) [resolution 228,145]
462. ~18 [avatar contradiction clause 457]
467. $false [avatar sat refutation 235,453,462]
% SZS output end Proof for 4630523851422947938303316
% ------------------------------
% 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is quiet.
Everyone who is both not kind and old is either not generous or not curious.
If someone is both not strong and funny then someone is either kind or not strong.
Everyone who is either not wise or old is not old.
If fred is either quiet or not wise then lucy is both not funny and rich and vice versa.
Everyone who is either patient or not tall is happy or not happy.
If someone is calm or kind then alice is both kind and not old.
Everyone who is not patient or humble is either not creative or not brave.
Everyone who is both not brave and not happy is not old or strong and vice versa.
Everyone who is rich or patient is both not humble and not kind.
If someone is both not kind and generous then alice is curious or calm and vice versa.
Everyone who is not strong or rich is both not creative and wise.
Everyone who is both tall and happy is old and vice versa.
Everyone who is both not generous and kind is either not happy or not rich.
If mary is either not calm or brave then fred is generous or quiet.
Alice is not old or not strong.
Someone is humble.
Someone is either funny or not funny.
Susan is calm.
Someone is not rich or patient.
Susan is patient.
Someone is not strong or strong. | Alice is creative. | entailment | (![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>quiet(X)))&
(![X]:((~kind(X)&old(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((kind(X)<~>~strong(X)))))&
(![X]:((~wise(X)<~>old(X))=>~old(X)))&
(((quiet(fred)<~>~wise(fred)))<=>((~funny(lucy)&rich(lucy))))&
(![X]:((patient(X)<~>~tall(X))=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|kind(X))))=>((kind(alice)&~old(alice))))&
(![X]:((~patient(X)|humble(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~old(X)|strong(X))))&
(![X]:((rich(X)|patient(X))=>(~humble(X)&~kind(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((curious(alice)|calm(alice))))&
(![X]:((~strong(X)|rich(X))=>(~creative(X)&wise(X))))&
(![X]:((tall(X)&happy(X))<=>old(X)))&
(![X]:((~generous(X)&kind(X))=>(~happy(X)<~>~rich(X))))&
(((~calm(mary)<~>brave(mary)))=>((generous(fred)|quiet(fred))))&
((~old(alice)|~strong(alice)))&
(?[X]:(humble(X)))&
(?[X]:((funny(X)<~>~funny(X))))&
(calm(susan))&
(?[X]:((~rich(X)|patient(X))))&
(patient(susan))&
(?[X]:((~strong(X)|strong(X)))) | creative(alice) | [
"p7",
"p8",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7360771834142346177570146
% SZS output start Proof for 7360771834142346177570146
8. ? [X0] : (kind(X0) | calm(X0)) => (~old(alice) & kind(alice)) [input p7]
9. ! [X0] : ((humble(X0) | ~patient(X0)) => (~creative(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (strong(X0) | ~old(X0))) [input p9]
11. ! [X0] : ((patient(X0) | rich(X0)) => (~kind(X0) & ~humble(X0))) [input p10]
20. calm(susan) [input p19]
24. ~creative(alice) [input hypothesis]
34. (~old(alice) & kind(alice)) | ! [X0] : (~kind(X0) & ~calm(X0)) [ennf transformation 8]
35. ! [X0] : ((~creative(X0) <~> ~brave(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 9]
36. ! [X0] : ((~kind(X0) & ~humble(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 11]
52. ! [X0] : (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | (~humble(X0) & patient(X0))) [nnf transformation 35]
53. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 10]
54. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | happy(X0) | brave(X0))) [flattening 53]
93. kind(alice) | ~calm(X0) [cnf transformation 34]
95. ~old(alice) | ~calm(X0) [cnf transformation 34]
99. brave(X0) | creative(X0) | patient(X0) [cnf transformation 52]
102. ~brave(X0) | old(X0) [cnf transformation 54]
109. ~patient(X0) | ~kind(X0) [cnf transformation 36]
130. calm(susan) [cnf transformation 20]
134. ~creative(alice) [cnf transformation 24]
177. 9 <=> old(alice) [avatar definition]
179. ~old(alice) <- (~9) [avatar component clause 177]
182. 10 <=> ! [X0] : ~calm(X0) [avatar definition]
183. ~calm(X0) <- (10) [avatar component clause 182]
184. 10 | ~9 [avatar split clause 95,177,182]
186. 11 <=> kind(alice) [avatar definition]
188. kind(alice) <- (11) [avatar component clause 186]
190. 10 | 11 [avatar split clause 93,186,182]
244. $false <- (10) [resolution 183,130]
245. ~10 [avatar contradiction clause 244]
261. creative(X3) | patient(X3) | old(X3) [resolution 99,102]
322. patient(alice) | old(alice) [resolution 261,134]
325. patient(alice) <- (~9) [subsumption resolution 322,179]
326. ~kind(alice) <- (~9) [resolution 325,109]
327. $false <- (~9, 11) [subsumption resolution 326,188]
328. 9 | ~11 [avatar contradiction clause 327]
329. $false [avatar sat refutation 184,190,245,328]
% SZS output end Proof for 7360771834142346177570146
% ------------------------------
% 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not kind then someone is not patient or not wise and vice versa. Everyone who is both humble and happy is not strong or happy and vice versa. Everyone who is not strong or humble is either tall or not humble and vice versa. If someone is patient then alice is either not patient or not old and vice versa. Everyone who is both rich and not generous is both not wise and generous and vice versa. If someone is either tall or not kind then susan is humble. Everyone who is brave or tall is happy or not rich. Everyone who is both not rich and funny is not brave or not quiet. Everyone who is quiet or not generous is calm and vice versa. Everyone who is kind or not happy is both happy and tall. If paul is curious then someone is both not strong and funny and vice versa. If someone is not wise then alice is both wise and tall. Everyone who is either not strong or not curious is both not calm and quiet. Everyone who is creative is not wise and vice versa. If susan is old or not old then someone is creative. If someone is funny or brave then paul is both wise and not happy. Someone is not strong. Lucy is either humble or not happy. Alice is old. Paul is either quiet or old. Someone is both happy and curious. Fred is both not rich and generous. | Fred is not tall. | contradiction | ((?[X]:((~happy(X)|~kind(X))))<=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((humble(X)&happy(X))<=>(~strong(X)|happy(X))))&
(![X]:((~strong(X)|humble(X))<=>(tall(X)<~>~humble(X))))&
((?[X]:(patient(X)))<=>((~patient(alice)<~>~old(alice))))&
(![X]:((rich(X)&~generous(X))<=>(~wise(X)&generous(X))))&
((?[X]:((tall(X)<~>~kind(X))))=>(humble(susan)))&
(![X]:((brave(X)|tall(X))=>(happy(X)|~rich(X))))&
(![X]:((~rich(X)&funny(X))=>(~brave(X)|~quiet(X))))&
(![X]:((quiet(X)|~generous(X))<=>calm(X)))&
(![X]:((kind(X)|~happy(X))=>(happy(X)&tall(X))))&
((curious(paul))<=>(?[X]:((~strong(X)&funny(X)))))&
((?[X]:(~wise(X)))=>((wise(alice)&tall(alice))))&
(![X]:((~strong(X)<~>~curious(X))=>(~calm(X)&quiet(X))))&
(![X]:(creative(X)<=>~wise(X)))&
(((old(susan)|~old(susan)))=>(?[X]:(creative(X))))&
((?[X]:((funny(X)|brave(X))))=>((wise(paul)&~happy(paul))))&
(?[X]:(~strong(X)))&
((humble(lucy)<~>~happy(lucy)))&
(old(alice))&
((quiet(paul)<~>old(paul)))&
(?[X]:((happy(X)&curious(X))))&
((~rich(fred)&generous(fred))) | ~tall(fred) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4359834337037698787429475
% SZS output start Proof for 4359834337037698787429475
2. ! [X0] : ((happy(X0) & humble(X0)) <=> (happy(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((humble(X0) | ~strong(X0)) <=> (tall(X0) <~> ~humble(X0))) [input p2]
23. ~tall(fred) [input hypothesis]
45. ! [X0] : (((happy(X0) & humble(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 2]
46. ! [X0] : (((happy(X0) & humble(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | ~happy(X0) | ~humble(X0))) [flattening 45]
47. ! [X0] : (((humble(X0) | ~strong(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (~humble(X0) & strong(X0)))) [nnf transformation 3]
48. ! [X0] : ((humble(X0) | ~strong(X0) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (~humble(X0) & strong(X0)))) [flattening 47]
74. humble(X0) | strong(X0) [cnf transformation 46]
79. ~humble(X0) | tall(X0) | ~humble(X0) [cnf transformation 48]
83. humble(X0) | ~strong(X0) | tall(X0) | humble(X0) [cnf transformation 48]
125. ~tall(fred) [cnf transformation 23]
129. ~humble(X0) | tall(X0) [duplicate literal removal 79]
130. humble(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 83]
163. humble(X0) | tall(X0) [subsumption resolution 130,74]
164. tall(X0) [subsumption resolution 129,163]
261. $false [subsumption resolution 125,164]
% SZS output end Proof for 4359834337037698787429475
% ------------------------------
% 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 generous or not old is either curious or not happy. If lucy is both quiet and not quiet then alice is either kind or not tall and vice versa. If someone is either not quiet or old then susan is either not happy or not curious and vice versa. Everyone who is not wise or not humble is either humble or not brave. Everyone who is both not humble and patient is both old and not brave and vice versa. If someone is not wise then someone is both humble and not creative and vice versa. Everyone who is not patient or not generous is either not old or rich and vice versa. Everyone who is generous or not rich is both not calm and strong. Everyone who is either happy or wise is not wise. Everyone who is creative is patient or not brave and vice versa. Everyone who is calm is not patient. Everyone who is not curious or not calm is not old. If john is not generous then someone is not kind. If susan is brave or not patient then someone is either strong or rich and vice versa. If someone is generous or not kind then susan is both not wise and calm. Everyone who is either not creative or brave is rich. Mary is rich. Paul is either not kind or not funny. Someone is not creative or generous. Lucy is either not quiet or not tall. Paul is both tall and not wise. Someone is either happy or not creative. Paul is not funny. John is not wise. | Susan is not generous. | entailment | (![X]:((generous(X)<~>~old(X))=>(curious(X)<~>~happy(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>((kind(alice)<~>~tall(alice))))&
((?[X]:((~quiet(X)<~>old(X))))<=>((~happy(susan)<~>~curious(susan))))&
(![X]:((~wise(X)|~humble(X))=>(humble(X)<~>~brave(X))))&
(![X]:((~humble(X)&patient(X))<=>(old(X)&~brave(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:((~patient(X)|~generous(X))<=>(~old(X)<~>rich(X))))&
(![X]:((generous(X)|~rich(X))=>(~calm(X)&strong(X))))&
(![X]:((happy(X)<~>wise(X))=>~wise(X)))&
(![X]:(creative(X)<=>(patient(X)|~brave(X))))&
(![X]:(calm(X)=>~patient(X)))&
(![X]:((~curious(X)|~calm(X))=>~old(X)))&
((~generous(john))=>(?[X]:(~kind(X))))&
(((brave(susan)|~patient(susan)))<=>(?[X]:((strong(X)<~>rich(X)))))&
((?[X]:((generous(X)|~kind(X))))=>((~wise(susan)&calm(susan))))&
(![X]:((~creative(X)<~>brave(X))=>rich(X)))&
(rich(mary))&
((~kind(paul)<~>~funny(paul)))&
(?[X]:((~creative(X)|generous(X))))&
((~quiet(lucy)<~>~tall(lucy)))&
((tall(paul)&~wise(paul)))&
(?[X]:((happy(X)<~>~creative(X))))&
(~funny(paul))&
(~wise(john)) | ~generous(susan) | [
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3404501648609580116846161
% SZS output start Proof for 3404501648609580116846161
8. ! [X0] : ((~rich(X0) | generous(X0)) => (strong(X0) & ~calm(X0))) [input p7]
13. ~generous(john) => ? [X0] : ~kind(X0) [input p12]
15. ? [X0] : (~kind(X0) | generous(X0)) => (calm(susan) & ~wise(susan)) [input p14]
25. generous(susan) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~calm(X0)) | (rich(X0) & ~generous(X0))) [ennf transformation 8]
33. ? [X0] : ~kind(X0) | generous(john) [ennf transformation 13]
34. (calm(susan) & ~wise(susan)) | ! [X0] : (kind(X0) & ~generous(X0)) [ennf transformation 15]
56. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
57. ~kind(sK3) | generous(john) [skolemisation 33,56]
106. ~calm(X0) | ~generous(X0) [cnf transformation 29]
118. ~kind(sK3) | generous(john) [cnf transformation 57]
127. calm(susan) | ~generous(X0) [cnf transformation 34]
128. calm(susan) | kind(X0) [cnf transformation 34]
143. generous(susan) [cnf transformation 25]
214. 15 <=> generous(john) [avatar definition]
216. generous(john) <- (15) [avatar component clause 214]
218. 16 <=> kind(sK3) [avatar definition]
220. ~kind(sK3) <- (~16) [avatar component clause 218]
221. 15 | ~16 [avatar split clause 118,218,214]
251. 23 <=> ! [X0] : kind(X0) [avatar definition]
252. kind(X0) <- (23) [avatar component clause 251]
254. 24 <=> calm(susan) [avatar definition]
256. calm(susan) <- (24) [avatar component clause 254]
257. 23 | 24 [avatar split clause 128,254,251]
259. 25 <=> ! [X0] : ~generous(X0) [avatar definition]
260. ~generous(X0) <- (25) [avatar component clause 259]
261. 25 | 24 [avatar split clause 127,254,259]
310. ~generous(susan) <- (24) [resolution 106,256]
311. $false <- (24) [subsumption resolution 310,143]
312. ~24 [avatar contradiction clause 311]
313. $false <- (~16, 23) [resolution 252,220]
314. 16 | ~23 [avatar contradiction clause 313]
315. $false <- (15, 25) [subsumption resolution 216,260]
316. ~15 | ~25 [avatar contradiction clause 315]
317. $false [avatar sat refutation 221,257,261,312,314,316]
% SZS output end Proof for 3404501648609580116846161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not old or curious then someone is either not curious or wise and vice versa.
Everyone who is patient is both not happy and not quiet.
Everyone who is not humble or tall is either not patient or not kind.
Everyone who is not old or not brave is not tall or not happy and vice versa.
If someone is creative or patient then someone is both not humble and creative.
Everyone who is both not quiet and not old is quiet.
Everyone who is creative or old is not generous or not curious and vice versa.
Everyone who is rich or not strong is both not rich and creative.
Everyone who is humble or not patient is not quiet and vice versa.
If someone is both patient and not strong then alice is either wise or generous and vice versa.
If alice is either curious or not strong then paul is either not happy or not generous.
Everyone who is either not wise or not rich is rich and vice versa.
If susan is not patient or not tall then someone is both not calm and not old and vice versa.
If someone is not generous then mary is both not brave and not funny and vice versa.
If john is curious or not quiet then john is both not curious and not strong.
If someone is both not tall and not curious then mary is either not strong or not calm and vice versa.
Lucy is tall or not quiet.
Someone is either curious or strong.
Lucy is not brave.
Someone is tall.
Someone is happy or not kind.
Someone is either funny or tall.
Someone is either calm or not quiet. | Lucy is not creative. | neutral | (((~old(alice)<~>curious(alice)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:(patient(X)=>(~happy(X)&~quiet(X))))&
(![X]:((~humble(X)|tall(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~old(X)|~brave(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~quiet(X)&~old(X))=>quiet(X)))&
(![X]:((creative(X)|old(X))<=>(~generous(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))=>(~rich(X)&creative(X))))&
(![X]:((humble(X)|~patient(X))<=>~quiet(X)))&
((?[X]:((patient(X)&~strong(X))))<=>((wise(alice)<~>generous(alice))))&
(((curious(alice)<~>~strong(alice)))=>((~happy(paul)<~>~generous(paul))))&
(![X]:((~wise(X)<~>~rich(X))<=>rich(X)))&
(((~patient(susan)|~tall(susan)))<=>(?[X]:((~calm(X)&~old(X)))))&
((?[X]:(~generous(X)))<=>((~brave(mary)&~funny(mary))))&
(((curious(john)|~quiet(john)))=>((~curious(john)&~strong(john))))&
((?[X]:((~tall(X)&~curious(X))))<=>((~strong(mary)<~>~calm(mary))))&
((tall(lucy)|~quiet(lucy)))&
(?[X]:((curious(X)<~>strong(X))))&
(~brave(lucy))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(?[X]:((calm(X)<~>~quiet(X)))) | ~creative(lucy) | [] | null | 0 |
If susan is either not old or quiet then susan is either not wise or brave and vice versa.
Everyone who is either happy or not rich is wise and vice versa.
If someone is creative or wise then someone is not quiet or not wise.
Everyone who is not brave is happy.
If someone is either not wise or tall then someone is both not old and creative.
Everyone who is either not tall or not brave is generous and vice versa.
If someone is not quiet then someone is both not happy and rich and vice versa.
Everyone who is patient is either not curious or not happy and vice versa.
If someone is tall then someone is old or kind and vice versa.
Everyone who is not humble or quiet is both kind and not quiet and vice versa.
Everyone who is not brave or not quiet is humble or curious and vice versa.
Everyone who is not brave or brave is not creative.
If someone is creative then susan is curious and vice versa.
Everyone who is calm is not calm or strong and vice versa.
Everyone who is both quiet and not tall is not calm.
If paul is both not happy and curious then someone is patient.
Someone is both tall and happy.
John is either not quiet or not funny.
Alice is either creative or calm.
Fred is either happy or not humble.
Someone is both old and not wise.
Someone is tall or humble.
Fred is not quiet or not happy. | Paul is brave. | neutral | (((~old(susan)<~>quiet(susan)))<=>((~wise(susan)<~>brave(susan))))&
(![X]:((happy(X)<~>~rich(X))<=>wise(X)))&
((?[X]:((creative(X)|wise(X))))=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:(~brave(X)=>happy(X)))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((~old(X)&creative(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>generous(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:(patient(X)<=>(~curious(X)<~>~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~humble(X)|quiet(X))<=>(kind(X)&~quiet(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(humble(X)|curious(X))))&
(![X]:((~brave(X)|brave(X))=>~creative(X)))&
((?[X]:(creative(X)))<=>(curious(susan)))&
(![X]:(calm(X)<=>(~calm(X)|strong(X))))&
(![X]:((quiet(X)&~tall(X))=>~calm(X)))&
(((~happy(paul)&curious(paul)))=>(?[X]:(patient(X))))&
(?[X]:((tall(X)&happy(X))))&
((~quiet(john)<~>~funny(john)))&
((creative(alice)<~>calm(alice)))&
((happy(fred)<~>~humble(fred)))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((tall(X)|humble(X))))&
((~quiet(fred)|~happy(fred))) | brave(paul) | [] | null | 0 |
If john is not quiet then alice is both not kind and not generous and vice versa.
If someone is both kind and patient then someone is not funny or wise and vice versa.
Everyone who is not strong is both not old and patient and vice versa.
Everyone who is not strong is calm and vice versa.
If alice is both not brave and not tall then someone is creative or brave.
Everyone who is either humble or generous is old.
If john is both old and not calm then mary is both not funny and not old and vice versa.
If alice is rich or not rich then alice is both humble and not quiet.
Everyone who is either brave or not strong is both calm and brave and vice versa.
Everyone who is either patient or quiet is not humble or not tall and vice versa.
Everyone who is either not creative or not happy is either quiet or not creative.
Everyone who is humble or patient is either rich or not brave.
If alice is not old then fred is not kind or tall.
If john is not patient or brave then mary is not funny and vice versa.
Everyone who is not funny is creative or not kind and vice versa.
If someone is quiet then someone is not calm or old.
Fred is both rich and not kind.
Mary is both curious and happy.
Susan is not curious.
Paul is either not quiet or not tall.
John is both quiet and kind.
Mary is curious or brave. | John is humble. | neutral | ((~quiet(john))<=>((~kind(alice)&~generous(alice))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|old(X)))))&
((rich(fred)&~kind(fred)))&
((curious(mary)&happy(mary)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((quiet(john)&kind(john)))&
((curious(mary)|brave(mary))) | humble(john) | [] | null | 0 |
Everyone who is not strong or not curious is either not curious or not quiet.
Everyone who is both not quiet and not rich is funny and vice versa.
Everyone who is quiet or generous is old or not curious and vice versa.
Everyone who is patient is either not wise or not patient and vice versa.
If susan is both strong and brave then john is funny or not quiet.
If john is quiet or not old then lucy is both not creative and not strong and vice versa.
If someone is calm or old then someone is not kind or not generous.
Everyone who is humble is not wise and vice versa.
Everyone who is creative is either not creative or happy.
Everyone who is brave is either humble or patient.
Everyone who is both wise and kind is either not rich or not tall and vice versa.
Everyone who is either not quiet or not funny is both creative and wise.
Everyone who is both not old and not humble is either calm or quiet.
Everyone who is tall or happy is quiet or not generous.
Everyone who is either quiet or not funny is patient or creative and vice versa.
Everyone who is not curious is either humble or not calm and vice versa.
Someone is both not brave and tall.
Fred is not calm or curious.
Mary is patient.
Someone is not patient.
Someone is not generous or patient.
Susan is happy or not brave.
Someone is not strong. | Fred is not old. | entailment | (![X]:((~strong(X)|~curious(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&~rich(X))<=>funny(X)))&
(![X]:((quiet(X)|generous(X))<=>(old(X)|~curious(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>~patient(X))))&
(((strong(susan)&brave(susan)))=>((funny(john)|~quiet(john))))&
(((quiet(john)|~old(john)))<=>((~creative(lucy)&~strong(lucy))))&
((?[X]:((calm(X)|old(X))))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:(creative(X)=>(~creative(X)<~>happy(X))))&
(![X]:(brave(X)=>(humble(X)<~>patient(X))))&
(![X]:((wise(X)&kind(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(creative(X)&wise(X))))&
(![X]:((~old(X)&~humble(X))=>(calm(X)<~>quiet(X))))&
(![X]:((tall(X)|happy(X))=>(quiet(X)|~generous(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(patient(X)|creative(X))))&
(![X]:(~curious(X)<=>(humble(X)<~>~calm(X))))&
(?[X]:((~brave(X)&tall(X))))&
((~calm(fred)|curious(fred)))&
(patient(mary))&
(?[X]:(~patient(X)))&
(?[X]:((~generous(X)|patient(X))))&
((happy(susan)|~brave(susan)))&
(?[X]:(~strong(X))) | ~old(fred) | [
"p1",
"p2",
"p3",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8516061980054900978206891
% SZS output start Proof for 8516061980054900978206891
2. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : ((generous(X0) | quiet(X0)) <=> (~curious(X0) | old(X0))) [input p2]
4. ! [X0] : (patient(X0) <=> (~wise(X0) <~> ~patient(X0))) [input p3]
11. ! [X0] : ((kind(X0) & wise(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) <~> ~funny(X0)) => (wise(X0) & creative(X0))) [input p11]
14. ! [X0] : ((happy(X0) | tall(X0)) => (~generous(X0) | quiet(X0))) [input p13]
24. old(fred) [input hypothesis]
33. ! [X0] : ((wise(X0) & creative(X0)) | (~quiet(X0) <=> ~funny(X0))) [ennf transformation 12]
36. ! [X0] : ((~generous(X0) | quiet(X0)) | (~happy(X0) & ~tall(X0))) [ennf transformation 14]
37. ! [X0] : (~generous(X0) | quiet(X0) | (~happy(X0) & ~tall(X0))) [flattening 36]
39. ! [X0] : (((~rich(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) | quiet(X0)))) [nnf transformation 2]
40. ! [X0] : (((~rich(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | rich(X0) | quiet(X0))) [flattening 39]
41. ! [X0] : (((generous(X0) | quiet(X0)) | (curious(X0) & ~old(X0))) & ((~curious(X0) | old(X0)) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : ((generous(X0) | quiet(X0) | (curious(X0) & ~old(X0))) & (~curious(X0) | old(X0) | (~generous(X0) & ~quiet(X0)))) [flattening 41]
43. ! [X0] : ((patient(X0) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ~patient(X0))) [nnf transformation 4]
51. ! [X0] : (((kind(X0) & wise(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~kind(X0) | ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : (((kind(X0) & wise(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ~kind(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : ((wise(X0) & creative(X0)) | ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0)))) [nnf transformation 33]
70. funny(X0) | rich(X0) | quiet(X0) [cnf transformation 40]
71. ~funny(X0) | ~quiet(X0) [cnf transformation 40]
75. ~old(X0) | quiet(X0) | generous(X0) [cnf transformation 42]
77. ~patient(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 43]
80. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 43]
95. wise(X0) | ~rich(X0) | tall(X0) [cnf transformation 52]
100. wise(X0) | ~funny(X0) | quiet(X0) [cnf transformation 53]
101. wise(X0) | ~quiet(X0) | funny(X0) [cnf transformation 53]
104. ~generous(X0) | quiet(X0) | ~tall(X0) [cnf transformation 37]
122. old(fred) [cnf transformation 24]
124. ~patient(X0) | ~wise(X0) [duplicate literal removal 77]
125. ~wise(X0) | patient(X0) [duplicate literal removal 80]
127. ~wise(X0) [subsumption resolution 124,125]
166. ~rich(X0) | tall(X0) [subsumption resolution 95,127]
168. ~quiet(X0) | funny(X0) [subsumption resolution 101,127]
169. ~quiet(X0) [subsumption resolution 168,71]
170. ~funny(X0) | quiet(X0) [subsumption resolution 100,127]
171. ~funny(X0) [subsumption resolution 170,169]
173. ~tall(X0) | ~generous(X0) [subsumption resolution 104,169]
200. rich(X2) | quiet(X2) [resolution 70,171]
201. rich(X2) [subsumption resolution 200,169]
202. tall(X0) [resolution 201,166]
204. ~generous(X0) [resolution 202,173]
206. quiet(fred) | generous(fred) [resolution 75,122]
207. generous(fred) [subsumption resolution 206,169]
208. $false [subsumption resolution 207,204]
% SZS output end Proof for 8516061980054900978206891
% ------------------------------
% 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 alice is rich or brave then fred is both wise and not generous. If someone is brave or not tall then someone is either tall or creative and vice versa. If fred is both calm and funny then susan is not creative or not kind and vice versa. Everyone who is both not rich and rich is either not creative or not tall and vice versa. Everyone who is both humble and rich is both not kind and not generous. If someone is either not tall or not happy then someone is not tall. If someone is either humble or not kind then mary is rich and vice versa. Everyone who is quiet or not generous is either not curious or quiet and vice versa. Everyone who is not happy is both calm and humble. Everyone who is not patient is either brave or not rich. If mary is either not rich or not calm then someone is old or not strong and vice versa. If someone is not patient then someone is rich and vice versa. If john is either not humble or not curious then lucy is not funny or humble. If john is both strong and humble then someone is either strong or generous. If someone is curious then someone is both not calm and curious. Everyone who is either old or quiet is either not calm or not patient. Mary is either happy or humble. Mary is calm or not rich. Someone is both not funny and happy. Someone is generous. Someone is both not quiet and humble. Someone is kind. Someone is not old. | Lucy is happy. | entailment | (((rich(alice)|brave(alice)))=>((wise(fred)&~generous(fred))))&
((?[X]:((brave(X)|~tall(X))))<=>(?[X]:((tall(X)<~>creative(X)))))&
(((calm(fred)&funny(fred)))<=>((~creative(susan)|~kind(susan))))&
(![X]:((~rich(X)&rich(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((humble(X)&rich(X))=>(~kind(X)&~generous(X))))&
((?[X]:((~tall(X)<~>~happy(X))))=>(?[X]:(~tall(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(rich(mary)))&
(![X]:((quiet(X)|~generous(X))<=>(~curious(X)<~>quiet(X))))&
(![X]:(~happy(X)=>(calm(X)&humble(X))))&
(![X]:(~patient(X)=>(brave(X)<~>~rich(X))))&
(((~rich(mary)<~>~calm(mary)))<=>(?[X]:((old(X)|~strong(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(rich(X))))&
(((~humble(john)<~>~curious(john)))=>((~funny(lucy)|humble(lucy))))&
(((strong(john)&humble(john)))=>(?[X]:((strong(X)<~>generous(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:((old(X)<~>quiet(X))=>(~calm(X)<~>~patient(X))))&
((happy(mary)<~>humble(mary)))&
((calm(mary)|~rich(mary)))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((~quiet(X)&humble(X))))&
(?[X]:(kind(X)))&
(?[X]:(~old(X))) | happy(lucy) | [
"p1",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 490133266720986769251952
% SZS output start Proof for 490133266720986769251952
2. ? [X0] : (~tall(X0) | brave(X0)) <=> ? [X0] : (tall(X0) <~> creative(X0)) [input p1]
4. ! [X0] : ((rich(X0) & ~rich(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p3]
6. ? [X0] : (~tall(X0) <~> ~happy(X0)) => ? [X0] : ~tall(X0) [input p5]
24. ~happy(lucy) [input hypothesis]
25. ? [X0] : (~tall(X0) | brave(X0)) <=> ? [X1] : (tall(X1) <~> creative(X1)) [rectify 2]
26. ? [X0] : (~tall(X0) <~> ~happy(X0)) => ? [X1] : ~tall(X1) [rectify 6]
33. ? [X1] : ~tall(X1) | ! [X0] : (~tall(X0) <=> ~happy(X0)) [ennf transformation 26]
42. (? [X0] : (~tall(X0) | brave(X0)) | ! [X1] : ((tall(X1) | ~creative(X1)) & (creative(X1) | ~tall(X1)))) & (? [X1] : ((~creative(X1) | ~tall(X1)) & (creative(X1) | tall(X1))) | ! [X0] : (tall(X0) & ~brave(X0))) [nnf transformation 25]
43. (? [X0] : (~tall(X0) | brave(X0)) | ! [X1] : ((tall(X1) | ~creative(X1)) & (creative(X1) | ~tall(X1)))) & (? [X2] : ((~creative(X2) | ~tall(X2)) & (creative(X2) | tall(X2))) | ! [X3] : (tall(X3) & ~brave(X3))) [rectify 42]
44. ? [X0] : (~tall(X0) | brave(X0)) => (~tall(sK0) | brave(sK0)) [choice axiom]
45. ? [X2] : ((~creative(X2) | ~tall(X2)) & (creative(X2) | tall(X2))) => ((~creative(sK1) | ~tall(sK1)) & (creative(sK1) | tall(sK1))) [choice axiom]
46. ((~tall(sK0) | brave(sK0)) | ! [X1] : ((tall(X1) | ~creative(X1)) & (creative(X1) | ~tall(X1)))) & (((~creative(sK1) | ~tall(sK1)) & (creative(sK1) | tall(sK1))) | ! [X3] : (tall(X3) & ~brave(X3))) [skolemisation 43,45,44]
49. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (~rich(X0) | rich(X0)))) [nnf transformation 4]
50. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | ~rich(X0) | rich(X0))) [flattening 49]
51. ? [X1] : ~tall(X1) | ! [X0] : ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0))) [nnf transformation 33]
52. ? [X0] : ~tall(X0) | ! [X1] : ((~tall(X1) | happy(X1)) & (~happy(X1) | tall(X1))) [rectify 51]
53. ? [X0] : ~tall(X0) => ~tall(sK2) [choice axiom]
54. ~tall(sK2) | ! [X1] : ((~tall(X1) | happy(X1)) & (~happy(X1) | tall(X1))) [skolemisation 52,53]
93. creative(sK1) | tall(sK1) | tall(X3) [cnf transformation 46]
95. ~creative(sK1) | ~tall(sK1) | tall(X3) [cnf transformation 46]
105. ~rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 50]
106. ~rich(X0) | ~creative(X0) | tall(X0) [cnf transformation 50]
107. rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 50]
108. rich(X0) | ~creative(X0) | tall(X0) [cnf transformation 50]
112. ~tall(sK2) | ~tall(X1) | happy(X1) [cnf transformation 54]
155. ~happy(lucy) [cnf transformation 24]
173. 4 <=> ! [X1] : (tall(X1) | ~creative(X1)) [avatar definition]
174. ~creative(X1) | tall(X1) <- (4) [avatar component clause 173]
185. 7 <=> ! [X1] : (creative(X1) | ~tall(X1)) [avatar definition]
186. ~tall(X1) | creative(X1) <- (7) [avatar component clause 185]
189. 8 <=> ! [X3] : tall(X3) [avatar definition]
190. tall(X3) <- (8) [avatar component clause 189]
192. 9 <=> tall(sK1) [avatar definition]
193. tall(sK1) <- (9) [avatar component clause 192]
194. ~tall(sK1) <- (~9) [avatar component clause 192]
196. 10 <=> creative(sK1) [avatar definition]
197. creative(sK1) <- (10) [avatar component clause 196]
198. ~creative(sK1) <- (~10) [avatar component clause 196]
199. 8 | ~9 | ~10 [avatar split clause 95,196,192,189]
204. 8 | 9 | 10 [avatar split clause 93,196,192,189]
227. ~creative(X0) | tall(X0) [subsumption resolution 106,108]
228. 4 [avatar split clause 227,173]
229. ~tall(X0) | creative(X0) [subsumption resolution 105,107]
230. 7 [avatar split clause 229,185]
232. 16 <=> ! [X1] : (~tall(X1) | happy(X1)) [avatar definition]
233. ~tall(X1) | happy(X1) <- (16) [avatar component clause 232]
235. 17 <=> tall(sK2) [avatar definition]
237. ~tall(sK2) <- (~17) [avatar component clause 235]
238. 16 | ~17 [avatar split clause 112,235,232]
369. creative(sK1) <- (7, 9) [resolution 186,193]
371. $false <- (7, 9, ~10) [subsumption resolution 369,198]
372. ~7 | ~9 | 10 [avatar contradiction clause 371]
373. $false <- (8, ~17) [resolution 190,237]
375. ~8 | 17 [avatar contradiction clause 373]
376. tall(sK1) <- (4, 10) [resolution 197,174]
377. $false <- (4, ~9, 10) [subsumption resolution 376,194]
378. ~4 | 9 | ~10 [avatar contradiction clause 377]
385. happy(X0) <- (8, 16) [resolution 233,190]
387. $false <- (8, 16) [resolution 385,155]
390. ~8 | ~16 [avatar contradiction clause 387]
391. $false [avatar sat refutation 199,204,228,230,238,372,375,378,390]
% SZS output end Proof for 490133266720986769251952
% ------------------------------
% 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 |
Everyone who is either creative or wise is not funny or tall and vice versa.
Everyone who is not calm or not kind is humble or not old and vice versa.
If someone is humble then alice is creative or not wise.
If someone is both funny and not calm then lucy is either wise or patient and vice versa.
Everyone who is either creative or not calm is either creative or not funny and vice versa.
If someone is not tall or not creative then someone is both generous and quiet and vice versa.
Everyone who is both happy and not generous is not calm or funny and vice versa.
Everyone who is either not old or not funny is not humble and vice versa.
If someone is calm then someone is not brave and vice versa.
Everyone who is either not kind or not generous is either humble or creative.
Everyone who is both wise and not curious is either not humble or not patient.
Everyone who is not funny or curious is either not strong or creative and vice versa.
If fred is old or not strong then someone is either not calm or not tall.
If someone is either not strong or not humble then alice is either old or funny and vice versa.
If paul is wise or not happy then someone is patient and vice versa.
Everyone who is either patient or not calm is not strong and vice versa.
Someone is either not quiet or not old.
John is either not wise or humble.
Alice is calm or not humble.
Alice is not funny or not quiet.
Someone is tall or strong. | John is happy. | entailment | (![X]:((creative(X)<~>wise(X))<=>(~funny(X)|tall(X))))&
(![X]:((~calm(X)|~kind(X))<=>(humble(X)|~old(X))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)|funny(X))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)<~>creative(X))))&
(![X]:((wise(X)&~curious(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((~funny(X)|curious(X))<=>(~strong(X)<~>creative(X))))&
(((old(fred)|~strong(fred)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((old(alice)<~>funny(alice))))&
(((wise(paul)|~happy(paul)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~strong(X)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~wise(john)<~>humble(john)))&
((calm(alice)|~humble(alice)))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((tall(X)|strong(X)))) | happy(john) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2364066118756519419446390
% SZS output start Proof for 2364066118756519419446390
5. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (creative(X0) <~> ~funny(X0))) [input p4]
7. ! [X0] : ((~generous(X0) & happy(X0)) <=> (funny(X0) | ~calm(X0))) [input p6]
22. ~happy(john) [input hypothesis]
39. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 5]
45. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (generous(X0) | ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | generous(X0) | ~happy(X0))) [flattening 45]
95. funny(X0) | ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 39]
98. ~calm(X0) | creative(X0) | creative(X0) | funny(X0) [cnf transformation 39]
107. happy(X0) | calm(X0) [cnf transformation 46]
108. ~funny(X0) | happy(X0) [cnf transformation 46]
155. ~happy(john) [cnf transformation 22]
157. funny(X0) | ~creative(X0) | ~calm(X0) [duplicate literal removal 95]
158. ~calm(X0) | creative(X0) | funny(X0) [duplicate literal removal 98]
197. ~calm(X0) | funny(X0) [subsumption resolution 157,158]
363. calm(john) [resolution 107,155]
370. funny(john) [resolution 197,363]
380. happy(john) [resolution 370,108]
381. $false [subsumption resolution 380,155]
% SZS output end Proof for 2364066118756519419446390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or curious is not curious or kind and vice versa. Everyone who is not patient or funny is both brave and curious and vice versa. If someone is either not kind or calm then john is not humble and vice versa. Everyone who is rich is brave. If john is both not happy and not funny then someone is not kind. If someone is not curious or not old then someone is either wise or calm and vice versa. If paul is both old and not strong then someone is either funny or kind and vice versa. Everyone who is not kind is creative or quiet. Everyone who is both curious and not calm is either humble or not happy. If susan is both rich and not patient then alice is either kind or not kind and vice versa. If susan is funny or not kind then paul is happy or not creative. Everyone who is either quiet or not quiet is either humble or funny. Everyone who is either creative or happy is funny or not strong. If mary is brave then alice is either not brave or not tall and vice versa. If alice is not kind then someone is creative or brave. If someone is not rich or happy then mary is not happy or not calm. Someone is either kind or not old. Someone is rich or not tall. Someone is rich or not wise. Someone is either not rich or not patient. Paul is not funny. Mary is old or not old. Someone is either humble or generous. | Susan is kind. | entailment | (![X]:((~old(X)|curious(X))<=>(~curious(X)|kind(X))))&
(![X]:((~patient(X)|funny(X))<=>(brave(X)&curious(X))))&
((?[X]:((~kind(X)<~>calm(X))))<=>(~humble(john)))&
(![X]:(rich(X)=>brave(X)))&
(((~happy(john)&~funny(john)))=>(?[X]:(~kind(X))))&
((?[X]:((~curious(X)|~old(X))))<=>(?[X]:((wise(X)<~>calm(X)))))&
(((old(paul)&~strong(paul)))<=>(?[X]:((funny(X)<~>kind(X)))))&
(![X]:(~kind(X)=>(creative(X)|quiet(X))))&
(![X]:((curious(X)&~calm(X))=>(humble(X)<~>~happy(X))))&
(((rich(susan)&~patient(susan)))<=>((kind(alice)<~>~kind(alice))))&
(((funny(susan)|~kind(susan)))=>((happy(paul)|~creative(paul))))&
(![X]:((quiet(X)<~>~quiet(X))=>(humble(X)<~>funny(X))))&
(![X]:((creative(X)<~>happy(X))=>(funny(X)|~strong(X))))&
((brave(mary))<=>((~brave(alice)<~>~tall(alice))))&
((~kind(alice))=>(?[X]:((creative(X)|brave(X)))))&
((?[X]:((~rich(X)|happy(X))))=>((~happy(mary)|~calm(mary))))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~rich(X)<~>~patient(X))))&
(~funny(paul))&
((old(mary)|~old(mary)))&
(?[X]:((humble(X)<~>generous(X)))) | kind(susan) | [
"p0",
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1984087087145466927550371
% SZS output start Proof for 1984087087145466927550371
1. ! [X0] : ((curious(X0) | ~old(X0)) <=> (kind(X0) | ~curious(X0))) [input p0]
2. ! [X0] : ((funny(X0) | ~patient(X0)) <=> (curious(X0) & brave(X0))) [input p1]
10. (~patient(susan) & rich(susan)) <=> (kind(alice) <~> ~kind(alice)) [input p9]
24. ~kind(susan) [input hypothesis]
41. ! [X0] : (((curious(X0) | ~old(X0)) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | (~curious(X0) & old(X0)))) [nnf transformation 1]
42. ! [X0] : ((curious(X0) | ~old(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | (~curious(X0) & old(X0)))) [flattening 41]
43. ! [X0] : (((funny(X0) | ~patient(X0)) | (~curious(X0) | ~brave(X0))) & ((curious(X0) & brave(X0)) | (~funny(X0) & patient(X0)))) [nnf transformation 2]
44. ! [X0] : ((funny(X0) | ~patient(X0) | ~curious(X0) | ~brave(X0)) & ((curious(X0) & brave(X0)) | (~funny(X0) & patient(X0)))) [flattening 43]
62. ((~patient(susan) & rich(susan)) | ((kind(alice) | kind(alice)) & (~kind(alice) | ~kind(alice)))) & (((kind(alice) | ~kind(alice)) & (~kind(alice) | kind(alice))) | (patient(susan) | ~rich(susan))) [nnf transformation 10]
63. ((~patient(susan) & rich(susan)) | ((kind(alice) | kind(alice)) & (~kind(alice) | ~kind(alice)))) & (((kind(alice) | ~kind(alice)) & (~kind(alice) | kind(alice))) | patient(susan) | ~rich(susan)) [flattening 62]
83. kind(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 42]
88. patient(X0) | curious(X0) [cnf transformation 44]
116. ~patient(susan) | ~kind(alice) | ~kind(alice) [cnf transformation 63]
117. ~patient(susan) | kind(alice) | kind(alice) [cnf transformation 63]
143. ~kind(susan) [cnf transformation 24]
150. ~patient(susan) | ~kind(alice) [duplicate literal removal 116]
151. ~patient(susan) | kind(alice) [duplicate literal removal 117]
152. ~curious(X0) | kind(X0) [duplicate literal removal 83]
250. 22 <=> kind(alice) [avatar definition]
254. 23 <=> patient(susan) [avatar definition]
256. ~patient(susan) <- (~23) [avatar component clause 254]
257. 22 | ~23 [avatar split clause 151,254,250]
258. ~22 | ~23 [avatar split clause 150,254,250]
266. 25 <=> kind(susan) [avatar definition]
267. ~kind(susan) <- (~25) [avatar component clause 266]
374. ~25 [avatar split clause 143,266]
377. curious(susan) <- (~23) [resolution 88,256]
381. kind(susan) <- (~23) [resolution 152,377]
383. $false <- (~23, ~25) [subsumption resolution 381,267]
384. 23 | 25 [avatar contradiction clause 383]
385. $false [avatar sat refutation 257,258,374,384]
% SZS output end Proof for 1984087087145466927550371
% ------------------------------
% 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then mary is either not kind or not curious.
Everyone who is tall is calm and vice versa.
Everyone who is funny is both not tall and strong and vice versa.
Everyone who is either wise or humble is both patient and creative and vice versa.
If someone is either humble or brave then mary is not patient or generous.
Everyone who is not generous or not creative is not rich.
If someone is either not rich or curious then someone is either curious or not patient and vice versa.
If someone is both not strong and curious then someone is not tall or brave.
If mary is generous then someone is both not brave and humble.
If someone is creative then someone is both brave and not brave.
Everyone who is not wise or patient is generous or not funny and vice versa.
If someone is not quiet then mary is happy.
If paul is either not happy or not humble then susan is both not generous and not calm.
If someone is old or not patient then someone is either not old or not creative.
If lucy is both calm and curious then someone is either kind or curious and vice versa.
Everyone who is not creative is quiet.
Someone is not calm or funny.
Lucy is either happy or quiet.
Susan is calm or kind.
Someone is wise or humble.
Someone is not funny or happy.
Paul is both not calm and generous. | Lucy is curious. | neutral | ((?[X]:(old(X)))=>((~kind(mary)<~>~curious(mary))))&
(![X]:(tall(X)<=>calm(X)))&
(![X]:(funny(X)<=>(~tall(X)&strong(X))))&
(![X]:((wise(X)<~>humble(X))<=>(patient(X)&creative(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((~patient(mary)|generous(mary))))&
(![X]:((~generous(X)|~creative(X))=>~rich(X)))&
((?[X]:((~rich(X)<~>curious(X))))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~tall(X)|brave(X)))))&
((generous(mary))=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:(creative(X)))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((~wise(X)|patient(X))<=>(generous(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>(happy(mary)))&
(((~happy(paul)<~>~humble(paul)))=>((~generous(susan)&~calm(susan))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:(~creative(X)=>quiet(X)))&
(?[X]:((~calm(X)|funny(X))))&
((happy(lucy)<~>quiet(lucy)))&
((calm(susan)|kind(susan)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~funny(X)|happy(X))))&
((~calm(paul)&generous(paul))) | curious(lucy) | [] | null | 0 |
Everyone who is either humble or not quiet is curious and vice versa.
If alice is either not happy or not rich then susan is both not patient and kind.
Everyone who is wise or not patient is both kind and generous.
Everyone who is either not tall or rich is both not generous and calm.
If someone is strong then someone is wise and vice versa.
Everyone who is both wise and creative is either not happy or not rich and vice versa.
Everyone who is not curious is old.
Everyone who is both wise and tall is not humble or curious and vice versa.
Everyone who is both not rich and funny is not quiet.
If alice is both not kind and quiet then alice is not rich or humble.
Everyone who is either strong or wise is either not calm or not old and vice versa.
Everyone who is not old or rich is wise or not curious and vice versa.
If susan is happy or tall then paul is generous or wise.
If fred is not quiet then susan is curious or not quiet.
Everyone who is both not patient and not old is either not tall or not generous.
Everyone who is not kind is both not quiet and not calm.
Paul is both not rich and not brave.
Someone is rich or not wise.
Someone is both rich and kind.
Fred is either not wise or tall.
Someone is kind or strong.
Alice is either funny or wise.
Alice is strong. | Susan is creative. | neutral | (![X]:((humble(X)<~>~quiet(X))<=>curious(X)))&
(((~happy(alice)<~>~rich(alice)))=>((~patient(susan)&kind(susan))))&
(![X]:((wise(X)|~patient(X))=>(kind(X)&generous(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~generous(X)&calm(X))))&
((?[X]:(strong(X)))<=>(?[X]:(wise(X))))&
(![X]:((wise(X)&creative(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(~curious(X)=>old(X)))&
(![X]:((wise(X)&tall(X))<=>(~humble(X)|curious(X))))&
(![X]:((~rich(X)&funny(X))=>~quiet(X)))&
(((~kind(alice)&quiet(alice)))=>((~rich(alice)|humble(alice))))&
(![X]:((strong(X)<~>wise(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((~old(X)|rich(X))<=>(wise(X)|~curious(X))))&
(((happy(susan)|tall(susan)))=>((generous(paul)|wise(paul))))&
((~quiet(fred))=>((curious(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~old(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~kind(X)=>(~quiet(X)&~calm(X))))&
((~rich(paul)&~brave(paul)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((rich(X)&kind(X))))&
((~wise(fred)<~>tall(fred)))&
(?[X]:((kind(X)|strong(X))))&
((funny(alice)<~>wise(alice)))&
(strong(alice)) | creative(susan) | [] | null | 0 |
If someone is wise or not tall then fred is either generous or patient. Everyone who is either patient or not generous is not humble. If lucy is either not brave or not patient then paul is tall or not happy. If alice is both not patient and not quiet then john is not tall and vice versa. Everyone who is generous is not patient or not calm. If paul is both not calm and not wise then someone is happy or generous and vice versa. Everyone who is not tall or patient is not creative or happy. Everyone who is calm or not strong is not patient or funny and vice versa. Everyone who is generous or not creative is both not humble and generous and vice versa. 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. Everyone who is not wise is happy or old and vice versa. If someone is not old then alice is old or rich. Someone is not creative. John is funny. Mary is either not strong or not rich. Fred is not tall or not patient. Someone is both not old and not patient. Someone is either not old or happy. John is either not strong or not happy. Mary is brave or not generous. | John is not rich. | neutral | ((?[X]:((wise(X)|~tall(X))))=>((generous(fred)<~>patient(fred))))&
(![X]:((patient(X)<~>~generous(X))=>~humble(X)))&
(((~brave(lucy)<~>~patient(lucy)))=>((tall(paul)|~happy(paul))))&
(((~patient(alice)&~quiet(alice)))<=>(~tall(john)))&
(![X]:(generous(X)=>(~patient(X)|~calm(X))))&
(((~calm(paul)&~wise(paul)))<=>(?[X]:((happy(X)|generous(X)))))&
(![X]:((~tall(X)|patient(X))=>(~creative(X)|happy(X))))&
(![X]:((calm(X)|~strong(X))<=>(~patient(X)|funny(X))))&
(![X]:((generous(X)|~creative(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))))&
(![X]:(~wise(X)<=>(happy(X)|old(X))))&
((?[X]:(~old(X)))=>((old(alice)|rich(alice))))&
(?[X]:(~creative(X)))&
(funny(john))&
((~strong(mary)<~>~rich(mary)))&
((~tall(fred)|~patient(fred)))&
(?[X]:((~old(X)&~patient(X))))&
(?[X]:((~old(X)<~>happy(X))))&
((~strong(john)<~>~happy(john)))&
((brave(mary)|~generous(mary))) | ~rich(john) | [] | null | 0 |
Everyone who is not wise or not happy is both not funny and old and vice versa. Everyone who is not quiet or not curious is patient or quiet and vice versa. If someone is calm or creative then someone is both not wise and wise. Everyone who is not old is both kind and curious and vice versa. If someone is quiet then mary is not tall and vice versa. Everyone who is both not brave and not rich is not kind or not happy and vice versa. Everyone who is not rich is both quiet and brave and vice versa. If lucy is both calm and not tall then fred is calm or not curious. If john is quiet then john is not creative or not patient and vice versa. If alice is old then lucy is both wise and kind and vice versa. Everyone who is either happy or humble is either not strong or not kind and vice versa. Everyone who is generous is either patient or not happy. If alice is patient then fred is either not strong or wise and vice versa. Everyone who is either not brave or not patient is funny. If mary is calm or not calm then susan is either rich or not happy. Everyone who is not funny or creative is happy. Someone is not wise. Someone is patient. Lucy is not humble or not old. Someone is either curious or strong. Lucy is either brave or rich. Paul is either funny or patient. | Paul is not happy. | contradiction | (![X]:((~wise(X)|~happy(X))<=>(~funny(X)&old(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(patient(X)|quiet(X))))&
((?[X]:((calm(X)|creative(X))))=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:(~old(X)<=>(kind(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(~tall(mary)))&
(![X]:((~brave(X)&~rich(X))<=>(~kind(X)|~happy(X))))&
(![X]:(~rich(X)<=>(quiet(X)&brave(X))))&
(((calm(lucy)&~tall(lucy)))=>((calm(fred)|~curious(fred))))&
((quiet(john))<=>((~creative(john)|~patient(john))))&
((old(alice))<=>((wise(lucy)&kind(lucy))))&
(![X]:((happy(X)<~>humble(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(generous(X)=>(patient(X)<~>~happy(X))))&
((patient(alice))<=>((~strong(fred)<~>wise(fred))))&
(![X]:((~brave(X)<~>~patient(X))=>funny(X)))&
(((calm(mary)|~calm(mary)))=>((rich(susan)<~>~happy(susan))))&
(![X]:((~funny(X)|creative(X))=>happy(X)))&
(?[X]:(~wise(X)))&
(?[X]:(patient(X)))&
((~humble(lucy)|~old(lucy)))&
(?[X]:((curious(X)<~>strong(X))))&
((brave(lucy)<~>rich(lucy)))&
((funny(paul)<~>patient(paul))) | ~happy(paul) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1707167712546193345524495
% SZS output start Proof for 1707167712546193345524495
1. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (old(X0) & ~funny(X0))) [input p0]
16. ! [X0] : ((creative(X0) | ~funny(X0)) => happy(X0)) [input p15]
23. ~happy(paul) [input hypothesis]
31. ! [X0] : (happy(X0) | (~creative(X0) & funny(X0))) [ennf transformation 16]
32. ! [X0] : (((~happy(X0) | ~wise(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 1]
33. ! [X0] : ((~happy(X0) | ~wise(X0) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | (happy(X0) & wise(X0)))) [flattening 32]
67. ~funny(X0) | happy(X0) [cnf transformation 33]
117. happy(X0) | funny(X0) [cnf transformation 31]
128. ~happy(paul) [cnf transformation 23]
234. happy(X0) [subsumption resolution 117,67]
273. $false [subsumption resolution 128,234]
% SZS output end Proof for 1707167712546193345524495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or humble is either old or not curious.
Everyone who is either tall or not strong is creative or strong.
Everyone who is generous is either patient or funny.
Everyone who is not patient or not brave is either not funny or brave.
Everyone who is either funny or not quiet is both humble and not tall and vice versa.
Everyone who is not old or kind is not quiet or brave.
Everyone who is either not old or brave is not kind.
If fred is not patient then someone is both quiet and kind and vice versa.
If someone is either not happy or not old then someone is both not calm and not quiet and vice versa.
Everyone who is generous or happy is either rich or old and vice versa.
If someone is either not tall or humble then lucy is rich and vice versa.
If someone is brave then someone is either not calm or tall.
Everyone who is creative or happy is generous or not creative and vice versa.
Everyone who is not curious or rich is both curious and not patient.
If someone is humble then someone is either not wise or not old.
Everyone who is happy is not rich.
Someone is either not old or not kind.
Someone is not calm.
Someone is rich or not wise.
Lucy is tall or happy.
Susan is either not kind or not brave.
Lucy is strong or calm.
Lucy is either not wise or happy. | Fred is rich. | contradiction | (![X]:((~generous(X)|humble(X))=>(old(X)<~>~curious(X))))&
(![X]:((tall(X)<~>~strong(X))=>(creative(X)|strong(X))))&
(![X]:(generous(X)=>(patient(X)<~>funny(X))))&
(![X]:((~patient(X)|~brave(X))=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(humble(X)&~tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)|brave(X))))&
(![X]:((~old(X)<~>brave(X))=>~kind(X)))&
((~patient(fred))<=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((generous(X)|happy(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(rich(lucy)))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((creative(X)|happy(X))<=>(generous(X)|~creative(X))))&
(![X]:((~curious(X)|rich(X))=>(curious(X)&~patient(X))))&
((?[X]:(humble(X)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:(happy(X)=>~rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)|~wise(X))))&
((tall(lucy)|happy(lucy)))&
((~kind(susan)<~>~brave(susan)))&
((strong(lucy)|calm(lucy)))&
((~wise(lucy)<~>happy(lucy))) | rich(fred) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 806575597944446116920877
% SZS output start Proof for 806575597944446116920877
1. ! [X0] : ((humble(X0) | ~generous(X0)) => (old(X0) <~> ~curious(X0))) [input p0]
4. ! [X0] : ((~brave(X0) | ~patient(X0)) => (~funny(X0) <~> brave(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> (~tall(X0) & humble(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~old(X0)) => (brave(X0) | ~quiet(X0))) [input p5]
7. ! [X0] : ((~old(X0) <~> brave(X0)) => ~kind(X0)) [input p6]
8. ~patient(fred) <=> ? [X0] : (kind(X0) & quiet(X0)) [input p7]
10. ! [X0] : ((happy(X0) | generous(X0)) <=> (rich(X0) <~> old(X0))) [input p9]
14. ! [X0] : ((rich(X0) | ~curious(X0)) => (~patient(X0) & curious(X0))) [input p13]
24. rich(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~curious(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 1]
32. ! [X0] : ((~funny(X0) <~> brave(X0)) | (brave(X0) & patient(X0))) [ennf transformation 4]
33. ! [X0] : ((brave(X0) | ~quiet(X0)) | (~kind(X0) & old(X0))) [ennf transformation 6]
34. ! [X0] : (brave(X0) | ~quiet(X0) | (~kind(X0) & old(X0))) [flattening 33]
35. ! [X0] : (~kind(X0) | (~old(X0) <=> brave(X0))) [ennf transformation 7]
37. ! [X0] : ((~patient(X0) & curious(X0)) | (~rich(X0) & curious(X0))) [ennf transformation 14]
40. ! [X0] : (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~humble(X0) & generous(X0))) [nnf transformation 28]
43. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (brave(X0) & patient(X0))) [nnf transformation 32]
44. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 5]
45. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [flattening 44]
46. ! [X0] : (~kind(X0) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0)))) [nnf transformation 35]
47. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & (? [X0] : (kind(X0) & quiet(X0)) | patient(fred)) [nnf transformation 8]
48. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & (? [X1] : (kind(X1) & quiet(X1)) | patient(fred)) [rectify 47]
49. ? [X1] : (kind(X1) & quiet(X1)) => (kind(sK0) & quiet(sK0)) [choice axiom]
50. (~patient(fred) | ! [X0] : (~kind(X0) | ~quiet(X0))) & ((kind(sK0) & quiet(sK0)) | patient(fred)) [skolemisation 48,49]
56. ! [X0] : (((happy(X0) | generous(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (~happy(X0) & ~generous(X0)))) [nnf transformation 10]
57. ! [X0] : ((happy(X0) | generous(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (~happy(X0) & ~generous(X0)))) [flattening 56]
81. ~curious(X0) | old(X0) | generous(X0) [cnf transformation 40]
82. ~curious(X0) | old(X0) | ~humble(X0) [cnf transformation 40]
91. ~brave(X0) | funny(X0) | patient(X0) [cnf transformation 43]
93. ~quiet(X0) | humble(X0) | ~funny(X0) [cnf transformation 45]
100. ~kind(X0) | ~quiet(X0) | brave(X0) [cnf transformation 34]
102. ~kind(X0) | ~old(X0) | ~brave(X0) [cnf transformation 46]
103. quiet(sK0) | patient(fred) [cnf transformation 50]
104. kind(sK0) | patient(fred) [cnf transformation 50]
112. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 57]
128. curious(X0) | curious(X0) [cnf transformation 37]
131. ~rich(X0) | ~patient(X0) [cnf transformation 37]
145. rich(fred) [cnf transformation 24]
146. curious(X0) [duplicate literal removal 128]
155. 2 <=> patient(fred) [avatar definition]
160. 3 <=> kind(sK0) [avatar definition]
162. kind(sK0) <- (3) [avatar component clause 160]
163. 2 | 3 [avatar split clause 104,160,155]
165. 4 <=> quiet(sK0) [avatar definition]
167. quiet(sK0) <- (4) [avatar component clause 165]
168. 2 | 4 [avatar split clause 103,165,155]
303. ~patient(fred) [resolution 131,145]
319. old(X0) | generous(X0) [resolution 81,146]
321. ~humble(X0) | old(X0) [resolution 82,146]
334. humble(sK0) | ~funny(sK0) <- (4) [resolution 93,167]
358. ~quiet(sK0) | brave(sK0) <- (3) [resolution 100,162]
360. brave(sK0) <- (3, 4) [subsumption resolution 358,167]
362. funny(sK0) | patient(sK0) <- (3, 4) [resolution 360,91]
400. 38 <=> patient(sK0) [avatar definition]
402. patient(sK0) <- (38) [avatar component clause 400]
404. 39 <=> funny(sK0) [avatar definition]
407. 38 | 39 | ~3 | ~4 [avatar split clause 362,165,160,404,400]
479. 55 <=> humble(sK0) [avatar definition]
481. humble(sK0) <- (55) [avatar component clause 479]
482. ~39 | 55 | ~4 [avatar split clause 334,165,479,404]
488. ~2 [avatar split clause 303,155]
490. 57 <=> old(sK0) [avatar definition]
491. ~old(sK0) <- (~57) [avatar component clause 490]
494. 58 <=> brave(sK0) [avatar definition]
496. brave(sK0) <- (58) [avatar component clause 494]
498. ~old(sK0) | ~brave(sK0) <- (3) [resolution 162,102]
500. ~quiet(sK0) | brave(sK0) <- (3) [resolution 162,100]
501. ~old(sK0) <- (3, 58) [subsumption resolution 498,496]
502. ~57 | ~3 | ~58 [avatar split clause 501,494,160,490]
605. old(sK0) <- (55) [resolution 321,481]
609. 57 | ~55 [avatar split clause 605,479,490]
610. brave(sK0) <- (3, 4) [subsumption resolution 500,167]
611. 58 | ~3 | ~4 [avatar split clause 610,165,160,494]
616. generous(sK0) <- (~57) [resolution 491,319]
656. rich(sK0) | old(sK0) <- (~57) [resolution 616,112]
658. rich(sK0) <- (~57) [subsumption resolution 656,491]
719. ~patient(sK0) <- (~57) [resolution 658,131]
721. $false <- (38, ~57) [subsumption resolution 719,402]
722. ~38 | 57 [avatar contradiction clause 721]
723. $false [avatar sat refutation 163,168,407,482,488,502,609,611,722]
% SZS output end Proof for 806575597944446116920877
% ------------------------------
% 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not happy is not old.
Everyone who is not kind or not brave is both calm and funny and vice versa.
Everyone who is both tall and old is either humble or old.
If someone is both not old and not happy then someone is rich or not wise.
Everyone who is both not curious and not generous is rich and vice versa.
Everyone who is rich or not curious is funny.
Everyone who is humble is both quiet and funny and vice versa.
If lucy is curious or patient then someone is not happy or creative and vice versa.
Everyone who is either happy or generous is either curious or creative and vice versa.
Everyone who is either not strong or not calm is patient or not curious.
Everyone who is calm is not happy.
Everyone who is both strong and not brave is either not kind or not curious.
Everyone who is rich is either generous or rich.
If paul is either curious or kind then someone is both not wise and kind.
Everyone who is old is not happy or not humble and vice versa.
Everyone who is both humble and brave is either patient or strong and vice versa.
Someone is rich.
John is either not creative or tall.
Someone is not funny.
Lucy is not rich or patient.
Paul is strong or not creative.
Someone is either humble or tall.
Someone is either not patient or humble.
Mary is rich or creative. | Paul is wise. | neutral | (![X]:((funny(X)&~happy(X))=>~old(X)))&
(![X]:((~kind(X)|~brave(X))<=>(calm(X)&funny(X))))&
(![X]:((tall(X)&old(X))=>(humble(X)<~>old(X))))&
((?[X]:((~old(X)&~happy(X))))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((~curious(X)&~generous(X))<=>rich(X)))&
(![X]:((rich(X)|~curious(X))=>funny(X)))&
(![X]:(humble(X)<=>(quiet(X)&funny(X))))&
(((curious(lucy)|patient(lucy)))<=>(?[X]:((~happy(X)|creative(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(curious(X)<~>creative(X))))&
(![X]:((~strong(X)<~>~calm(X))=>(patient(X)|~curious(X))))&
(![X]:(calm(X)=>~happy(X)))&
(![X]:((strong(X)&~brave(X))=>(~kind(X)<~>~curious(X))))&
(![X]:(rich(X)=>(generous(X)<~>rich(X))))&
(((curious(paul)<~>kind(paul)))=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:(old(X)<=>(~happy(X)|~humble(X))))&
(![X]:((humble(X)&brave(X))<=>(patient(X)<~>strong(X))))&
(?[X]:(rich(X)))&
((~creative(john)<~>tall(john)))&
(?[X]:(~funny(X)))&
((~rich(lucy)|patient(lucy)))&
((strong(paul)|~creative(paul)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((~patient(X)<~>humble(X))))&
((rich(mary)|creative(mary))) | wise(paul) | [] | null | 0 |
Everyone who is not calm is not wise and vice versa.
Everyone who is tall or not patient is curious or generous.
If john is not generous then john is both not quiet and old and vice versa.
If paul is both humble and strong then susan is not rich.
If paul is either rich or strong then lucy is creative or generous.
Everyone who is not quiet is not brave and vice versa.
Everyone who is both kind and quiet is not brave or strong and vice versa.
If someone is not kind or wise then someone is not strong.
If someone is not creative then someone is brave or humble and vice versa.
If susan is both not tall and not humble then someone is not patient and vice versa.
If mary is either not happy or humble then someone is either curious or old and vice versa.
Everyone who is creative or not wise is funny or not calm and vice versa.
If someone is both not calm and curious then fred is both kind and creative and vice versa.
Everyone who is not brave is old or patient.
Everyone who is not tall is not kind.
Everyone who is either not rich or not calm is old or not kind.
Fred is humble or funny.
Someone is funny or not happy.
Someone is both not humble and tall.
Susan is not patient or calm.
Someone is both generous and not rich.
Someone is both brave and curious.
Someone is not strong or not humble. | Paul is brave. | entailment | (![X]:(~calm(X)<=>~wise(X)))&
(![X]:((tall(X)|~patient(X))=>(curious(X)|generous(X))))&
((~generous(john))<=>((~quiet(john)&old(john))))&
(((humble(paul)&strong(paul)))=>(~rich(susan)))&
(((rich(paul)<~>strong(paul)))=>((creative(lucy)|generous(lucy))))&
(![X]:(~quiet(X)<=>~brave(X)))&
(![X]:((kind(X)&quiet(X))<=>(~brave(X)|strong(X))))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:(~strong(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((brave(X)|humble(X)))))&
(((~tall(susan)&~humble(susan)))<=>(?[X]:(~patient(X))))&
(((~happy(mary)<~>humble(mary)))<=>(?[X]:((curious(X)<~>old(X)))))&
(![X]:((creative(X)|~wise(X))<=>(funny(X)|~calm(X))))&
((?[X]:((~calm(X)&curious(X))))<=>((kind(fred)&creative(fred))))&
(![X]:(~brave(X)=>(old(X)|patient(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~rich(X)<~>~calm(X))=>(old(X)|~kind(X))))&
((humble(fred)|funny(fred)))&
(?[X]:((funny(X)|~happy(X))))&
(?[X]:((~humble(X)&tall(X))))&
((~patient(susan)|calm(susan)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~strong(X)|~humble(X)))) | brave(paul) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4986027249618152160747842
% SZS output start Proof for 4986027249618152160747842
6. ! [X0] : (~quiet(X0) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((quiet(X0) & kind(X0)) <=> (strong(X0) | ~brave(X0))) [input p6]
24. ~brave(paul) [input hypothesis]
43. ! [X0] : ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0))) [nnf transformation 6]
44. ! [X0] : (((quiet(X0) & kind(X0)) | (~strong(X0) & brave(X0))) & ((strong(X0) | ~brave(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & kind(X0)) | (~strong(X0) & brave(X0))) & (strong(X0) | ~brave(X0) | ~quiet(X0) | ~kind(X0))) [flattening 44]
92. ~quiet(X0) | brave(X0) [cnf transformation 43]
96. quiet(X0) | brave(X0) [cnf transformation 45]
136. ~brave(paul) [cnf transformation 24]
179. brave(X0) [subsumption resolution 96,92]
310. $false [subsumption resolution 136,179]
% SZS output end Proof for 4986027249618152160747842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and not old then someone is not patient or not brave and vice versa.
Everyone who is creative is patient.
If john is both quiet and not humble then john is both rich and not calm and vice versa.
If mary is both not patient and tall then mary is either not calm or not quiet and vice versa.
Everyone who is not quiet is patient.
Everyone who is not rich or funny is not old.
Everyone who is either brave or not old is either not quiet or funny.
Everyone who is not wise or not brave is both not patient and not humble and vice versa.
If someone is both not humble and not kind then fred is not quiet or old and vice versa.
If someone is rich or not calm then fred is either not humble or old and vice versa.
Everyone who is generous or humble is either not funny or patient and vice versa.
If someone is old then someone is both brave and not old.
If someone is both happy and wise then someone is both not generous and funny.
If alice is either humble or funny then alice is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Someone is not quiet or strong.
Alice is both wise and not quiet.
Someone is both rich and not patient.
Susan is both not brave and not curious.
Someone is either calm or not wise.
John is both not calm and generous.
Alice is not strong.
Alice is not rich or not old. | Paul is not rich. | neutral | (((quiet(paul)&~old(paul)))<=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:(creative(X)=>patient(X)))&
(((quiet(john)&~humble(john)))<=>((rich(john)&~calm(john))))&
(((~patient(mary)&tall(mary)))<=>((~calm(mary)<~>~quiet(mary))))&
(![X]:(~quiet(X)=>patient(X)))&
(![X]:((~rich(X)|funny(X))=>~old(X)))&
(![X]:((brave(X)<~>~old(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((rich(X)&~patient(X))))&
((~brave(susan)&~curious(susan)))&
(?[X]:((calm(X)<~>~wise(X))))&
((~calm(john)&generous(john)))&
(~strong(alice))&
((~rich(alice)|~old(alice))) | ~rich(paul) | [] | null | 0 |
Everyone who is both tall and old is calm or not generous and vice versa.
If someone is either creative or happy then someone is not funny and vice versa.
If paul is happy or tall then john is generous and vice versa.
Everyone who is both not brave and old is either strong or not humble and vice versa.
If fred is both not strong and strong then someone is either not old or not brave and vice versa.
If someone is both not tall and not quiet then fred is not strong and vice versa.
If someone is not kind then someone is not rich and vice versa.
Everyone who is either happy or patient is both not curious and humble and vice versa.
Everyone who is either not old or creative is both not creative and strong.
Everyone who is either not curious or patient is both not wise and not rich and vice versa.
Everyone who is either not funny or humble is not humble or not wise.
Everyone who is strong or happy is happy.
Everyone who is either creative or not tall is not tall or old and vice versa.
If someone is not rich or kind then mary is both funny and not kind and vice versa.
If someone is either tall or not wise then someone is either not generous or curious.
If mary is rich then john is not creative.
Susan is either old or funny.
Paul is both not wise and not brave.
Mary is not patient or not rich.
Someone is either funny or not creative.
Lucy is either humble or not quiet.
Fred is either generous or strong.
Mary is either not happy or wise.
Someone is either not generous or humble. | Paul is not calm. | entailment | (![X]:((tall(X)&old(X))<=>(calm(X)|~generous(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>(?[X]:(~funny(X))))&
(((happy(paul)|tall(paul)))<=>(generous(john)))&
(![X]:((~brave(X)&old(X))<=>(strong(X)<~>~humble(X))))&
(((~strong(fred)&strong(fred)))<=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(~strong(fred)))&
((?[X]:(~kind(X)))<=>(?[X]:(~rich(X))))&
(![X]:((happy(X)<~>patient(X))<=>(~curious(X)&humble(X))))&
(![X]:((~old(X)<~>creative(X))=>(~creative(X)&strong(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~funny(X)<~>humble(X))=>(~humble(X)|~wise(X))))&
(![X]:((strong(X)|happy(X))=>happy(X)))&
(![X]:((creative(X)<~>~tall(X))<=>(~tall(X)|old(X))))&
((?[X]:((~rich(X)|kind(X))))<=>((funny(mary)&~kind(mary))))&
((?[X]:((tall(X)<~>~wise(X))))=>(?[X]:((~generous(X)<~>curious(X)))))&
((rich(mary))=>(~creative(john)))&
((old(susan)<~>funny(susan)))&
((~wise(paul)&~brave(paul)))&
((~patient(mary)|~rich(mary)))&
(?[X]:((funny(X)<~>~creative(X))))&
((humble(lucy)<~>~quiet(lucy)))&
((generous(fred)<~>strong(fred)))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~generous(X)<~>humble(X)))) | ~calm(paul) | [
"p0",
"p4",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8775916592665011284561604
% SZS output start Proof for 8775916592665011284561604
1. ! [X0] : ((old(X0) & tall(X0)) <=> (~generous(X0) | calm(X0))) [input p0]
5. (strong(fred) & ~strong(fred)) <=> ? [X0] : (~old(X0) <~> ~brave(X0)) [input p4]
18. ~brave(paul) & ~wise(paul) [input p17]
25. calm(paul) [input hypothesis]
35. ! [X0] : (((old(X0) & tall(X0)) | (generous(X0) & ~calm(X0))) & ((~generous(X0) | calm(X0)) | (~old(X0) | ~tall(X0)))) [nnf transformation 1]
36. ! [X0] : (((old(X0) & tall(X0)) | (generous(X0) & ~calm(X0))) & (~generous(X0) | calm(X0) | ~old(X0) | ~tall(X0))) [flattening 35]
46. ((strong(fred) & ~strong(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (~strong(fred) | strong(fred))) [nnf transformation 5]
47. ((strong(fred) & ~strong(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (? [X0] : ((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | ~strong(fred) | strong(fred)) [flattening 46]
48. ((strong(fred) & ~strong(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (? [X1] : ((brave(X1) | old(X1)) & (~brave(X1) | ~old(X1))) | ~strong(fred) | strong(fred)) [rectify 47]
49. ? [X1] : ((brave(X1) | old(X1)) & (~brave(X1) | ~old(X1))) => ((brave(sK2) | old(sK2)) & (~brave(sK2) | ~old(sK2))) [choice axiom]
50. ((strong(fred) & ~strong(fred)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(sK2) | old(sK2)) & (~brave(sK2) | ~old(sK2))) | ~strong(fred) | strong(fred)) [skolemisation 48,49]
90. ~calm(X0) | old(X0) [cnf transformation 36]
108. ~strong(fred) | ~old(X0) | brave(X0) [cnf transformation 50]
110. strong(fred) | ~old(X0) | brave(X0) [cnf transformation 50]
155. ~brave(paul) [cnf transformation 18]
167. calm(paul) [cnf transformation 25]
213. 10 <=> ! [X0] : (~old(X0) | brave(X0)) [avatar definition]
214. ~old(X0) | brave(X0) <- (10) [avatar component clause 213]
216. 11 <=> strong(fred) [avatar definition]
219. 10 | 11 [avatar split clause 110,216,213]
224. 10 | ~11 [avatar split clause 108,216,213]
366. old(paul) [resolution 90,167]
371. brave(paul) <- (10) [resolution 214,366]
375. $false <- (10) [subsumption resolution 371,155]
376. ~10 [avatar contradiction clause 375]
377. $false [avatar sat refutation 219,224,376]
% SZS output end Proof for 8775916592665011284561604
% ------------------------------
% 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 someone is not humble or calm then someone is either not brave or not curious.
If someone is not wise then mary is either brave or not wise and vice versa.
Everyone who is both not curious and not humble is calm and vice versa.
Everyone who is brave is not brave.
If someone is happy then someone is not strong or not happy.
Everyone who is not kind is not wise or not calm and vice versa.
Everyone who is either old or tall is both not quiet and not funny.
If susan is both not kind and funny then someone is not humble and vice versa.
If john is either happy or not humble then susan is both curious and not wise.
If susan is both quiet and not old then alice is not kind or wise.
Everyone who is either wise or not tall is kind and vice versa.
Everyone who is both quiet and not generous is both not quiet and humble and vice versa.
Everyone who is both wise and not curious is both brave and patient.
If someone is both not creative and not brave then paul is both not quiet and not old and vice versa.
If alice is happy or tall then someone is not quiet or strong and vice versa.
If lucy is both not strong and not patient then someone is both curious and not brave and vice versa.
Susan is both not funny and humble.
Lucy is old or creative.
John is either not brave or not rich.
Someone is wise or not funny.
Fred is not tall. | Alice is brave. | contradiction | ((?[X]:((~humble(X)|calm(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:(~wise(X)))<=>((brave(mary)<~>~wise(mary))))&
(![X]:((~curious(X)&~humble(X))<=>calm(X)))&
(![X]:(brave(X)=>~brave(X)))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(~kind(X)<=>(~wise(X)|~calm(X))))&
(![X]:((old(X)<~>tall(X))=>(~quiet(X)&~funny(X))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:(~humble(X))))&
(((happy(john)<~>~humble(john)))=>((curious(susan)&~wise(susan))))&
(((quiet(susan)&~old(susan)))=>((~kind(alice)|wise(alice))))&
(![X]:((wise(X)<~>~tall(X))<=>kind(X)))&
(![X]:((quiet(X)&~generous(X))<=>(~quiet(X)&humble(X))))&
(![X]:((wise(X)&~curious(X))=>(brave(X)&patient(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>((~quiet(paul)&~old(paul))))&
(((happy(alice)|tall(alice)))<=>(?[X]:((~quiet(X)|strong(X)))))&
(((~strong(lucy)&~patient(lucy)))<=>(?[X]:((curious(X)&~brave(X)))))&
((~funny(susan)&humble(susan)))&
((old(lucy)|creative(lucy)))&
((~brave(john)<~>~rich(john)))&
(?[X]:((wise(X)|~funny(X))))&
(~tall(fred)) | brave(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 459211813099452906841273
% SZS output start Proof for 459211813099452906841273
4. ! [X0] : (brave(X0) => ~brave(X0)) [input p3]
22. brave(alice) [input hypothesis]
26. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 4]
88. ~brave(X0) | ~brave(X0) [cnf transformation 26]
134. brave(alice) [cnf transformation 22]
137. ~brave(X0) [duplicate literal removal 88]
311. $false [subsumption resolution 134,137]
% SZS output end Proof for 459211813099452906841273
% ------------------------------
% 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 funny and not funny is either not patient or not tall and vice versa. Everyone who is calm or rich is not rich and vice versa. Everyone who is creative is humble and vice versa. Everyone who is wise or old is either not wise or not kind. Everyone who is not rich or not funny is either quiet or creative and vice versa. Everyone who is happy or not wise is calm. If someone is both curious and not kind then alice is either not kind or generous and vice versa. Everyone who is calm or generous is both calm and not humble and vice versa. If paul is strong then someone is either calm or not humble and vice versa. If someone is calm or brave then alice is both wise and not kind and vice versa. Everyone who is both not calm and patient is not old or brave and vice versa. Everyone who is either not calm or rich is both not creative and curious and vice versa. If mary is both tall and not strong then someone is either not happy or not rich and vice versa. If susan is calm then fred is not generous or not curious. Someone is happy or not happy. Lucy is not funny or calm. Someone is both not tall and kind. Someone is not kind or wise. Mary is either strong or not strong. Someone is either not humble or brave. | Alice is tall. | neutral | (![X]:((funny(X)&~funny(X))<=>(~patient(X)<~>~tall(X))))&
(![X]:((calm(X)|rich(X))<=>~rich(X)))&
(![X]:(creative(X)<=>humble(X)))&
(![X]:((wise(X)|old(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((~rich(X)|~funny(X))<=>(quiet(X)<~>creative(X))))&
(![X]:((happy(X)|~wise(X))=>calm(X)))&
((?[X]:((curious(X)&~kind(X))))<=>((~kind(alice)<~>generous(alice))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~humble(X))))&
((strong(paul))<=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((calm(X)|brave(X))))<=>((wise(alice)&~kind(alice))))&
(![X]:((~calm(X)&patient(X))<=>(~old(X)|brave(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~creative(X)&curious(X))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((calm(susan))=>((~generous(fred)|~curious(fred))))&
(?[X]:((happy(X)|~happy(X))))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((~kind(X)|wise(X))))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((~humble(X)<~>brave(X)))) | tall(alice) | [] | null | 0 |
Everyone who is both not creative and rich is brave and vice versa. Everyone who is generous is not calm and vice versa. Everyone who is both not humble and strong is strong. Everyone who is not tall or creative is either not patient or humble and vice versa. Everyone who is either humble or kind is both funny and happy and vice versa. If someone is not strong then susan is either calm or rich. Everyone who is old or not funny is not tall or not wise and vice versa. If someone is not patient then someone is either not generous or not patient. If someone is not old then someone is both not patient and not kind. Everyone who is creative is both happy and not wise and vice versa. Everyone who is curious or not old is either not funny or brave and vice versa. If someone is both brave and not funny then someone is either creative or not quiet. Everyone who is both calm and kind is not brave or not patient. If john is both wise and not calm then someone is either not kind or not brave and vice versa. Everyone who is not curious or calm is both not happy and not strong. If fred is both not humble and not kind then fred is not humble or not brave and vice versa. Someone is old or not happy. Someone is not creative. Someone is both quiet and old. John is kind or not brave. Someone is both not rich and tall. Mary is creative. Mary is not humble or not kind. | Fred is happy. | neutral | (![X]:((~creative(X)&rich(X))<=>brave(X)))&
(![X]:(generous(X)<=>~calm(X)))&
(![X]:((~humble(X)&strong(X))=>strong(X)))&
(![X]:((~tall(X)|creative(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((humble(X)<~>kind(X))<=>(funny(X)&happy(X))))&
((?[X]:(~strong(X)))=>((calm(susan)<~>rich(susan))))&
(![X]:((old(X)|~funny(X))<=>(~tall(X)|~wise(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~generous(X)<~>~patient(X)))))&
((?[X]:(~old(X)))=>(?[X]:((~patient(X)&~kind(X)))))&
(![X]:(creative(X)<=>(happy(X)&~wise(X))))&
(![X]:((curious(X)|~old(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((calm(X)&kind(X))=>(~brave(X)|~patient(X))))&
(((wise(john)&~calm(john)))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((~curious(X)|calm(X))=>(~happy(X)&~strong(X))))&
(((~humble(fred)&~kind(fred)))<=>((~humble(fred)|~brave(fred))))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((quiet(X)&old(X))))&
((kind(john)|~brave(john)))&
(?[X]:((~rich(X)&tall(X))))&
(creative(mary))&
((~humble(mary)|~kind(mary))) | happy(fred) | [] | null | 0 |
Everyone who is not old is both not funny and rich.
If lucy is not happy then lucy is both rich and not strong and vice versa.
If john is either not kind or not humble then susan is both kind and strong.
If lucy is humble or funny then someone is not tall or curious and vice versa.
Everyone who is either humble or not funny is both not wise and generous.
If someone is not tall or kind then someone is either humble or not quiet and vice versa.
If someone is either not rich or not calm then susan is both creative and generous.
If someone is rich then someone is not brave or not old and vice versa.
Everyone who is both not happy and happy is either kind or generous and vice versa.
If someone is either old or humble then someone is both not strong and quiet.
Everyone who is both calm and not tall is not humble.
Everyone who is not rich or not calm is not generous or not funny.
If susan is either not generous or not patient then someone is both not happy and patient.
Everyone who is either calm or not happy is calm.
If alice is both strong and not wise then alice is either not strong or old.
If john is both old and not strong then someone is not calm.
Paul is rich or wise.
Someone is not strong.
Lucy is both not patient and creative.
Someone is either not creative or old.
John is both not brave and not generous.
Someone is both rich and not happy.
Paul is not generous.
Lucy is patient or not brave. | Paul is not kind. | entailment | (![X]:(~old(X)=>(~funny(X)&rich(X))))&
((~happy(lucy))<=>((rich(lucy)&~strong(lucy))))&
(((~kind(john)<~>~humble(john)))=>((kind(susan)&strong(susan))))&
(((humble(lucy)|funny(lucy)))<=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(~wise(X)&generous(X))))&
((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((humble(X)<~>~quiet(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((creative(susan)&generous(susan))))&
((?[X]:(rich(X)))<=>(?[X]:((~brave(X)|~old(X)))))&
(![X]:((~happy(X)&happy(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((old(X)<~>humble(X))))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((calm(X)&~tall(X))=>~humble(X)))&
(![X]:((~rich(X)|~calm(X))=>(~generous(X)|~funny(X))))&
(((~generous(susan)<~>~patient(susan)))=>(?[X]:((~happy(X)&patient(X)))))&
(![X]:((calm(X)<~>~happy(X))=>calm(X)))&
(((strong(alice)&~wise(alice)))=>((~strong(alice)<~>old(alice))))&
(((old(john)&~strong(john)))=>(?[X]:(~calm(X))))&
((rich(paul)|wise(paul)))&
(?[X]:(~strong(X)))&
((~patient(lucy)&creative(lucy)))&
(?[X]:((~creative(X)<~>old(X))))&
((~brave(john)&~generous(john)))&
(?[X]:((rich(X)&~happy(X))))&
(~generous(paul))&
((patient(lucy)|~brave(lucy))) | ~kind(paul) | [
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3282679741270381159684168
% SZS output start Proof for 3282679741270381159684168
9. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (kind(X0) <~> generous(X0))) [input p8]
23. ~generous(paul) [input p22]
25. kind(paul) [input hypothesis]
64. ! [X0] : (((happy(X0) & ~happy(X0)) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | (~happy(X0) | happy(X0)))) [nnf transformation 9]
65. ! [X0] : (((happy(X0) & ~happy(X0)) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | ~happy(X0) | happy(X0))) [flattening 64]
116. ~happy(X0) | generous(X0) | ~kind(X0) [cnf transformation 65]
118. happy(X0) | generous(X0) | ~kind(X0) [cnf transformation 65]
146. ~generous(paul) [cnf transformation 23]
148. kind(paul) [cnf transformation 25]
286. ~kind(X0) | generous(X0) [subsumption resolution 116,118]
375. generous(paul) [resolution 286,148]
376. $false [subsumption resolution 375,146]
% SZS output end Proof for 3282679741270381159684168
% ------------------------------
% 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 creative and brave is both not strong and calm.
If paul is quiet or not old then someone is both tall and calm and vice versa.
If someone is not creative then someone is either generous or tall and vice versa.
Everyone who is creative or not wise is both not kind and not brave and vice versa.
If someone is not calm or quiet then someone is either curious or brave.
Everyone who is generous is old and vice versa.
Everyone who is not creative is either not creative or not funny.
Everyone who is not brave is either not brave or not old and vice versa.
Everyone who is both quiet and creative is both humble and kind.
Everyone who is not creative or funny is both calm and not kind.
Everyone who is either not creative or tall is kind and vice versa.
If someone is both not rich and not generous then someone is not strong and vice versa.
Everyone who is funny or not brave is either brave or strong.
Everyone who is either not generous or funny is either kind or not happy.
Everyone who is funny or not brave is not quiet or curious.
Someone is either not patient or not old.
Someone is not funny.
Someone is either kind or not happy.
Lucy is brave or funny. | Lucy is funny. | entailment | (![X]:((creative(X)&brave(X))=>(~strong(X)&calm(X))))&
(((quiet(paul)|~old(paul)))<=>(?[X]:((tall(X)&calm(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((creative(X)|~wise(X))<=>(~kind(X)&~brave(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~creative(X)=>(~creative(X)<~>~funny(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~old(X))))&
(![X]:((quiet(X)&creative(X))=>(humble(X)&kind(X))))&
(![X]:((~creative(X)|funny(X))=>(calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>tall(X))<=>kind(X)))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(![X]:((~generous(X)<~>funny(X))=>(kind(X)<~>~happy(X))))&
(![X]:((funny(X)|~brave(X))=>(~quiet(X)|curious(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
((brave(lucy)|funny(lucy))) | funny(lucy) | [
"p3",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2545945697685442804355164
% SZS output start Proof for 2545945697685442804355164
4. ! [X0] : ((~wise(X0) | creative(X0)) <=> (~brave(X0) & ~kind(X0))) [input p3]
7. ! [X0] : (~creative(X0) => (~creative(X0) <~> ~funny(X0))) [input p6]
19. funny(lucy) | brave(lucy) [input p18]
20. ~funny(lucy) [input hypothesis]
28. ! [X0] : ((~creative(X0) <~> ~funny(X0)) | creative(X0)) [ennf transformation 7]
46. ! [X0] : (((~wise(X0) | creative(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 4]
47. ! [X0] : ((~wise(X0) | creative(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (wise(X0) & ~creative(X0)))) [flattening 46]
53. ! [X0] : (((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | creative(X0)) [nnf transformation 28]
84. ~brave(X0) | ~creative(X0) [cnf transformation 47]
94. funny(X0) | creative(X0) | creative(X0) [cnf transformation 53]
126. funny(lucy) | brave(lucy) [cnf transformation 19]
127. ~funny(lucy) [cnf transformation 20]
131. funny(X0) | creative(X0) [duplicate literal removal 94]
230. 21 <=> brave(lucy) [avatar definition]
232. brave(lucy) <- (21) [avatar component clause 230]
234. 22 <=> funny(lucy) [avatar definition]
235. ~funny(lucy) <- (~22) [avatar component clause 234]
237. 21 | 22 [avatar split clause 126,234,230]
238. ~22 [avatar split clause 127,234]
243. ~creative(lucy) <- (21) [resolution 84,232]
254. creative(lucy) <- (~22) [resolution 131,235]
257. $false <- (21, ~22) [subsumption resolution 254,243]
258. ~21 | 22 [avatar contradiction clause 257]
259. $false [avatar sat refutation 237,238,258]
% SZS output end Proof for 2545945697685442804355164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or old is curious.
If someone is not funny or generous then mary is either creative or not rich and vice versa.
Everyone who is humble or strong is quiet or generous.
Everyone who is either calm or not curious is both curious and not tall.
Everyone who is both not kind and not patient is both not patient and old and vice versa.
If susan is not wise then someone is either quiet or humble.
If someone is both not curious and brave then lucy is not patient.
If mary is both generous and calm then someone is both patient and not tall and vice versa.
Everyone who is old or generous is either not funny or not old and vice versa.
If fred is generous then someone is both not patient and calm.
Everyone who is both not funny and curious is not curious and vice versa.
Everyone who is not quiet is not kind or not curious.
Everyone who is happy is either curious or humble.
Everyone who is either curious or not happy is curious and vice versa.
If someone is both not kind and not curious then lucy is both not kind and not strong.
Someone is rich.
Someone is both rich and patient.
Alice is either not brave or not funny.
Someone is creative.
Someone is not kind or calm.
Susan is not old. | Susan is humble. | contradiction | (![X]:((rich(X)|old(X))=>curious(X)))&
((?[X]:((~funny(X)|generous(X))))<=>((creative(mary)<~>~rich(mary))))&
(![X]:((humble(X)|strong(X))=>(quiet(X)|generous(X))))&
(![X]:((calm(X)<~>~curious(X))=>(curious(X)&~tall(X))))&
(![X]:((~kind(X)&~patient(X))<=>(~patient(X)&old(X))))&
((~wise(susan))=>(?[X]:((quiet(X)<~>humble(X)))))&
((?[X]:((~curious(X)&brave(X))))=>(~patient(lucy)))&
(((generous(mary)&calm(mary)))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:((old(X)|generous(X))<=>(~funny(X)<~>~old(X))))&
((generous(fred))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((~funny(X)&curious(X))<=>~curious(X)))&
(![X]:(~quiet(X)=>(~kind(X)|~curious(X))))&
(![X]:(happy(X)=>(curious(X)<~>humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>curious(X)))&
((?[X]:((~kind(X)&~curious(X))))=>((~kind(lucy)&~strong(lucy))))&
(?[X]:(rich(X)))&
(?[X]:((rich(X)&patient(X))))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|calm(X))))&
(~old(susan)) | humble(susan) | [
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 170539114722903749931786
% SZS output start Proof for 170539114722903749931786
11. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~curious(X0)) [input p10]
13. ! [X0] : (happy(X0) => (curious(X0) <~> humble(X0))) [input p12]
14. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> curious(X0)) [input p13]
22. humble(susan) [input hypothesis]
31. ! [X0] : ((curious(X0) <~> humble(X0)) | ~happy(X0)) [ennf transformation 13]
49. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | funny(X0))) [flattening 49]
51. ! [X0] : (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~happy(X0)) [nnf transformation 31]
52. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 14]
93. curious(X0) | curious(X0) [cnf transformation 50]
95. ~humble(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 51]
99. happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
109. humble(susan) [cnf transformation 22]
111. happy(X0) | ~curious(X0) [duplicate literal removal 99]
113. curious(X0) [duplicate literal removal 93]
192. ~happy(X0) | ~humble(X0) [subsumption resolution 95,113]
193. happy(X0) [subsumption resolution 111,113]
222. ~humble(X0) [resolution 192,193]
225. $false [resolution 222,109]
% SZS output end Proof for 170539114722903749931786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not generous or humble then someone is not humble and vice versa.
If mary is both funny and generous then someone is wise or not strong.
If susan is not strong or not quiet then someone is not rich or curious.
Everyone who is wise is both not wise and not old and vice versa.
Everyone who is either not curious or not happy is both wise and not funny.
If someone is both creative and brave then alice is not old or brave and vice versa.
If paul is both old and not funny then lucy is either brave or tall.
Everyone who is old or patient is either not creative or humble.
Everyone who is either not rich or not strong is either generous or not tall.
Everyone who is both brave and not curious is curious and vice versa.
If someone is both patient and not wise then john is either not brave or not curious and vice versa.
If john is not old or not quiet then paul is either not curious or not calm.
Everyone who is either rich or not curious is both brave and wise and vice versa.
Everyone who is both patient and happy is not humble or not kind.
Everyone who is either not generous or not quiet is either tall or not strong and vice versa.
Everyone who is either rich or not happy is generous or creative and vice versa.
Someone is not humble.
Lucy is either creative or old.
John is not quiet or not old.
Lucy is either tall or happy.
Paul is either not old or old.
Someone is rich or not brave. | Susan is creative. | contradiction | (((~generous(mary)<~>humble(mary)))<=>(?[X]:(~humble(X))))&
(((funny(mary)&generous(mary)))=>(?[X]:((wise(X)|~strong(X)))))&
(((~strong(susan)|~quiet(susan)))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:(wise(X)<=>(~wise(X)&~old(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(wise(X)&~funny(X))))&
((?[X]:((creative(X)&brave(X))))<=>((~old(alice)|brave(alice))))&
(((old(paul)&~funny(paul)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((old(X)|patient(X))=>(~creative(X)<~>humble(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(generous(X)<~>~tall(X))))&
(![X]:((brave(X)&~curious(X))<=>curious(X)))&
((?[X]:((patient(X)&~wise(X))))<=>((~brave(john)<~>~curious(john))))&
(((~old(john)|~quiet(john)))=>((~curious(paul)<~>~calm(paul))))&
(![X]:((rich(X)<~>~curious(X))<=>(brave(X)&wise(X))))&
(![X]:((patient(X)&happy(X))=>(~humble(X)|~kind(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((rich(X)<~>~happy(X))<=>(generous(X)|creative(X))))&
(?[X]:(~humble(X)))&
((creative(lucy)<~>old(lucy)))&
((~quiet(john)|~old(john)))&
((tall(lucy)<~>happy(lucy)))&
((~old(paul)<~>old(paul)))&
(?[X]:((rich(X)|~brave(X)))) | creative(susan) | [
"p3",
"p4",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 151540675326779858320399
% SZS output start Proof for 151540675326779858320399
4. ! [X0] : (wise(X0) <=> (~old(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((~curious(X0) <~> ~happy(X0)) => (~funny(X0) & wise(X0))) [input p4]
10. ! [X0] : ((~curious(X0) & brave(X0)) <=> curious(X0)) [input p9]
13. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> (wise(X0) & brave(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> (creative(X0) | generous(X0))) [input p15]
23. creative(susan) [input hypothesis]
28. ! [X0] : ((~funny(X0) & wise(X0)) | (~curious(X0) <=> ~happy(X0))) [ennf transformation 5]
42. ! [X0] : ((wise(X0) | (old(X0) | wise(X0))) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 4]
43. ! [X0] : ((wise(X0) | old(X0) | wise(X0)) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [flattening 42]
44. ! [X0] : ((~funny(X0) & wise(X0)) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0)))) [nnf transformation 28]
53. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~brave(X0)))) [nnf transformation 10]
54. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~brave(X0))) [flattening 53]
60. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) | ~brave(X0))) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~wise(X0) | ~brave(X0)) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [flattening 60]
63. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 16]
64. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [flattening 63]
79. ~wise(X0) | ~wise(X0) [cnf transformation 43]
82. wise(X0) | ~happy(X0) | curious(X0) [cnf transformation 44]
103. ~curious(X0) | ~curious(X0) [cnf transformation 54]
117. wise(X0) | rich(X0) | curious(X0) [cnf transformation 61]
133. happy(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 64]
143. creative(susan) [cnf transformation 23]
145. ~curious(X0) [duplicate literal removal 103]
146. ~wise(X0) [duplicate literal removal 79]
199. ~happy(X0) | curious(X0) [subsumption resolution 82,146]
262. rich(X0) | curious(X0) [subsumption resolution 117,146]
263. rich(X0) [subsumption resolution 262,145]
264. ~creative(X0) | happy(X0) [subsumption resolution 133,263]
302. happy(susan) [resolution 264,143]
304. curious(susan) [resolution 302,199]
305. $false [subsumption resolution 304,145]
% SZS output end Proof for 151540675326779858320399
% ------------------------------
% 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 generous and not patient is not generous.
If someone is either not creative or not old then someone is both strong and not old and vice versa.
Everyone who is either wise or not happy is either not quiet or not kind.
If susan is creative or not kind then alice is both calm and old.
If someone is not rich then someone is both not old and brave.
Everyone who is rich is either not generous or calm and vice versa.
Everyone who is rich is either not strong or not happy.
Everyone who is not kind is kind or old.
Everyone who is either generous or humble is not humble and vice versa.
Everyone who is old is either not patient or quiet.
If someone is both not happy and happy then alice is not old and vice versa.
Everyone who is either not creative or rich is both happy and not happy.
Everyone who is tall is either happy or humble and vice versa.
If someone is wise then lucy is not creative and vice versa.
Everyone who is both humble and not patient is either quiet or not happy and vice versa.
If fred is both creative and generous then someone is not quiet.
Someone is not happy or not curious.
Lucy is rich.
Someone is not kind or rich.
Lucy is not quiet.
Someone is both not patient and not funny.
Someone is not happy. | Fred is not curious. | neutral | (![X]:((~generous(X)&~patient(X))=>~generous(X)))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((wise(X)<~>~happy(X))=>(~quiet(X)<~>~kind(X))))&
(((creative(susan)|~kind(susan)))=>((calm(alice)&old(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((~old(X)&brave(X)))))&
(![X]:(rich(X)<=>(~generous(X)<~>calm(X))))&
(![X]:(rich(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(kind(X)|old(X))))&
(![X]:((generous(X)<~>humble(X))<=>~humble(X)))&
(![X]:(old(X)=>(~patient(X)<~>quiet(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(~old(alice)))&
(![X]:((~creative(X)<~>rich(X))=>(happy(X)&~happy(X))))&
(![X]:(tall(X)<=>(happy(X)<~>humble(X))))&
((?[X]:(wise(X)))<=>(~creative(lucy)))&
(![X]:((humble(X)&~patient(X))<=>(quiet(X)<~>~happy(X))))&
(((creative(fred)&generous(fred)))=>(?[X]:(~quiet(X))))&
(?[X]:((~happy(X)|~curious(X))))&
(rich(lucy))&
(?[X]:((~kind(X)|rich(X))))&
(~quiet(lucy))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:(~happy(X))) | ~curious(fred) | [] | null | 0 |
Everyone who is kind is humble and vice versa. If someone is both quiet and patient then someone is both not generous and creative and vice versa. If someone is both not calm and rich then mary is not tall and vice versa. If susan is quiet or not calm then paul is creative and vice versa. If someone is both not tall and generous then someone is either strong or not tall and vice versa. Everyone who is both rich and generous is not funny or patient and vice versa. Everyone who is old or tall is either rich or not calm. If mary is not old then someone is either calm or brave. Everyone who is not strong is both kind and curious and vice versa. If someone is not old then mary is both not wise and not humble. If mary is not calm or wise then someone is strong. Everyone who is both not rich and not generous is either not wise or not old and vice versa. If lucy is not tall or kind then john is both kind and not quiet. If susan is not curious or not generous then someone is not funny or kind. If mary is both not tall and tall then someone is either strong or not quiet and vice versa. If someone is both not strong and not calm then paul is both rich and not wise and vice versa. Mary is not wise or quiet. Someone is funny. Someone is tall. Someone is both tall and not generous. Susan is both not brave and not wise. Susan is both not creative and not calm. Someone is not generous. Alice is not calm. | Lucy is not humble. | neutral | (![X]:(kind(X)<=>humble(X)))&
((?[X]:((quiet(X)&patient(X))))<=>(?[X]:((~generous(X)&creative(X)))))&
((?[X]:((~calm(X)&rich(X))))<=>(~tall(mary)))&
(((quiet(susan)|~calm(susan)))<=>(creative(paul)))&
((?[X]:((~tall(X)&generous(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((rich(X)&generous(X))<=>(~funny(X)|patient(X))))&
(![X]:((old(X)|tall(X))=>(rich(X)<~>~calm(X))))&
((~old(mary))=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:(~strong(X)<=>(kind(X)&curious(X))))&
((?[X]:(~old(X)))=>((~wise(mary)&~humble(mary))))&
(((~calm(mary)|wise(mary)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~wise(X)<~>~old(X))))&
(((~tall(lucy)|kind(lucy)))=>((kind(john)&~quiet(john))))&
(((~curious(susan)|~generous(susan)))=>(?[X]:((~funny(X)|kind(X)))))&
(((~tall(mary)&tall(mary)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((~strong(X)&~calm(X))))<=>((rich(paul)&~wise(paul))))&
((~wise(mary)|quiet(mary)))&
(?[X]:(funny(X)))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)&~generous(X))))&
((~brave(susan)&~wise(susan)))&
((~creative(susan)&~calm(susan)))&
(?[X]:(~generous(X)))&
(~calm(alice)) | ~humble(lucy) | [] | null | 0 |
If someone is funny or not strong then someone is both not rich and patient and vice versa.
Everyone who is either not brave or brave is not kind.
Everyone who is humble is both quiet and not humble and vice versa.
Everyone who is both quiet and humble is both calm and not curious.
Everyone who is either not rich or not calm is either not generous or not rich.
Everyone who is generous is either funny or not generous and vice versa.
If someone is not old or patient then john is not humble or not calm and vice versa.
Everyone who is either tall or generous is strong or not generous.
Everyone who is both wise and not tall is either humble or rich.
If someone is not strong or not curious then john is either brave or not creative and vice versa.
Everyone who is either not kind or strong is not rich or patient and vice versa.
If john is not generous or kind then someone is not tall and vice versa.
If someone is not creative then someone is both humble and not curious and vice versa.
If someone is both not creative and not humble then fred is quiet or strong and vice versa.
If fred is rich or quiet then fred is both patient and kind.
Fred is not curious or not generous.
Lucy is either funny or calm.
Susan is not kind or brave.
Susan is both wise and not tall.
Susan is not kind.
Someone is not creative or not rich.
Someone is wise. | John is not brave. | contradiction | ((?[X]:((funny(X)|~strong(X))))<=>(?[X]:((~rich(X)&patient(X)))))&
(![X]:((~brave(X)<~>brave(X))=>~kind(X)))&
(![X]:(humble(X)<=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)&humble(X))=>(calm(X)&~curious(X))))&
(![X]:((~rich(X)<~>~calm(X))=>(~generous(X)<~>~rich(X))))&
(![X]:(generous(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:((~old(X)|patient(X))))<=>((~humble(john)|~calm(john))))&
(![X]:((tall(X)<~>generous(X))=>(strong(X)|~generous(X))))&
(![X]:((wise(X)&~tall(X))=>(humble(X)<~>rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>((brave(john)<~>~creative(john))))&
(![X]:((~kind(X)<~>strong(X))<=>(~rich(X)|patient(X))))&
(((~generous(john)|kind(john)))<=>(?[X]:(~tall(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~creative(X)&~humble(X))))<=>((quiet(fred)|strong(fred))))&
(((rich(fred)|quiet(fred)))=>((patient(fred)&kind(fred))))&
((~curious(fred)|~generous(fred)))&
((funny(lucy)<~>calm(lucy)))&
((~kind(susan)|brave(susan)))&
((wise(susan)&~tall(susan)))&
(~kind(susan))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:(wise(X))) | ~brave(john) | [
"p2",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8129897527501565774876912
% SZS output start Proof for 8129897527501565774876912
3. ! [X0] : (humble(X0) <=> (~humble(X0) & quiet(X0))) [input p2]
10. ? [X0] : (~curious(X0) | ~strong(X0)) <=> (brave(john) <~> ~creative(john)) [input p9]
13. ? [X0] : ~creative(X0) <=> ? [X0] : (~curious(X0) & humble(X0)) [input p12]
14. ? [X0] : (~humble(X0) & ~creative(X0)) <=> (strong(fred) | quiet(fred)) [input p13]
23. ~brave(john) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : (~curious(X1) & humble(X1)) [rectify 13]
41. ! [X0] : ((humble(X0) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | ~humble(X0))) [nnf transformation 3]
42. ! [X0] : ((humble(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ~humble(X0))) [flattening 41]
52. (? [X0] : (~curious(X0) | ~strong(X0)) | ((brave(john) | creative(john)) & (~creative(john) | ~brave(john)))) & (((creative(john) | ~brave(john)) & (~creative(john) | brave(john))) | ! [X0] : (curious(X0) & strong(X0))) [nnf transformation 10]
53. (? [X0] : (~curious(X0) | ~strong(X0)) | ((brave(john) | creative(john)) & (~creative(john) | ~brave(john)))) & (((creative(john) | ~brave(john)) & (~creative(john) | brave(john))) | ! [X1] : (curious(X1) & strong(X1))) [rectify 52]
54. ? [X0] : (~curious(X0) | ~strong(X0)) => (~curious(sK3) | ~strong(sK3)) [choice axiom]
55. ((~curious(sK3) | ~strong(sK3)) | ((brave(john) | creative(john)) & (~creative(john) | ~brave(john)))) & (((creative(john) | ~brave(john)) & (~creative(john) | brave(john))) | ! [X1] : (curious(X1) & strong(X1))) [skolemisation 53,54]
63. (? [X0] : ~creative(X0) | ! [X1] : (curious(X1) | ~humble(X1))) & (? [X1] : (~curious(X1) & humble(X1)) | ! [X0] : creative(X0)) [nnf transformation 25]
64. (? [X0] : ~creative(X0) | ! [X1] : (curious(X1) | ~humble(X1))) & (? [X2] : (~curious(X2) & humble(X2)) | ! [X3] : creative(X3)) [rectify 63]
65. ? [X0] : ~creative(X0) => ~creative(sK5) [choice axiom]
66. ? [X2] : (~curious(X2) & humble(X2)) => (~curious(sK6) & humble(sK6)) [choice axiom]
67. (~creative(sK5) | ! [X1] : (curious(X1) | ~humble(X1))) & ((~curious(sK6) & humble(sK6)) | ! [X3] : creative(X3)) [skolemisation 64,66,65]
68. (? [X0] : (~humble(X0) & ~creative(X0)) | (~strong(fred) & ~quiet(fred))) & ((strong(fred) | quiet(fred)) | ! [X0] : (humble(X0) | creative(X0))) [nnf transformation 14]
69. (? [X0] : (~humble(X0) & ~creative(X0)) | (~strong(fred) & ~quiet(fred))) & (strong(fred) | quiet(fred) | ! [X0] : (humble(X0) | creative(X0))) [flattening 68]
70. (? [X0] : (~humble(X0) & ~creative(X0)) | (~strong(fred) & ~quiet(fred))) & (strong(fred) | quiet(fred) | ! [X1] : (humble(X1) | creative(X1))) [rectify 69]
71. ? [X0] : (~humble(X0) & ~creative(X0)) => (~humble(sK7) & ~creative(sK7)) [choice axiom]
72. ((~humble(sK7) & ~creative(sK7)) | (~strong(fred) & ~quiet(fred))) & (strong(fred) | quiet(fred) | ! [X1] : (humble(X1) | creative(X1))) [skolemisation 70,71]
86. ~humble(X0) | ~humble(X0) [cnf transformation 42]
106. ~creative(john) | brave(john) | strong(X1) [cnf transformation 55]
121. humble(sK6) | creative(X3) [cnf transformation 67]
126. ~creative(sK7) | ~strong(fred) [cnf transformation 72]
142. ~brave(john) [cnf transformation 23]
148. ~humble(X0) [duplicate literal removal 86]
165. 4 <=> ! [X3] : strong(X3) [avatar definition]
166. strong(X3) <- (4) [avatar component clause 165]
201. 11 <=> creative(john) [avatar definition]
202. ~creative(john) <- (~11) [avatar component clause 201]
205. 12 <=> brave(john) [avatar definition]
224. 4 | 12 | ~11 [avatar split clause 106,201,205,165]
243. 19 <=> ! [X3] : creative(X3) [avatar definition]
244. creative(X3) <- (19) [avatar component clause 243]
250. creative(X3) [subsumption resolution 121,148]
251. 19 [avatar split clause 250,243]
253. 21 <=> strong(fred) [avatar definition]
255. ~strong(fred) <- (~21) [avatar component clause 253]
257. 22 <=> creative(sK7) [avatar definition]
259. ~creative(sK7) <- (~22) [avatar component clause 257]
260. ~21 | ~22 [avatar split clause 126,257,253]
295. ~12 [avatar split clause 142,205]
296. $false <- (~11, 19) [subsumption resolution 202,244]
297. 11 | ~19 [avatar contradiction clause 296]
302. $false <- (19, ~22) [resolution 259,244]
303. ~19 | 22 [avatar contradiction clause 302]
304. $false <- (4, ~21) [subsumption resolution 255,166]
305. ~4 | 21 [avatar contradiction clause 304]
306. $false [avatar sat refutation 224,251,260,295,297,303,305]
% SZS output end Proof for 8129897527501565774876912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is either not quiet or not brave and vice versa.
Everyone who is calm is either funny or not funny and vice versa.
If lucy is tall then susan is either humble or not funny and vice versa.
If susan is both kind and rich then john is calm or kind.
Everyone who is old or kind is both old 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.
If someone is not creative or not tall then susan is not brave and vice versa.
Everyone who is creative or kind is both patient and not creative and vice versa.
Someone is not brave or not strong.
Someone is both not brave and not rich.
Someone is either not funny or not old.
Someone is either happy or humble.
Lucy is either patient or strong.
Someone is rich.
Fred is either generous or curious. | Lucy is happy. | contradiction | (![X]:(~calm(X)<=>(~quiet(X)<~>~brave(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~funny(X))))&
((tall(lucy))<=>((humble(susan)<~>~funny(susan))))&
(((kind(susan)&rich(susan)))=>((calm(john)|kind(john))))&
(![X]:((old(X)|kind(X))<=>(old(X)&creative(X))))&
(![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]:((~creative(X)|~tall(X))))<=>(~brave(susan)))&
(![X]:((creative(X)|kind(X))<=>(patient(X)&~creative(X))))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~brave(X)&~rich(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((patient(lucy)<~>strong(lucy)))&
(?[X]:(rich(X)))&
((generous(fred)<~>curious(fred))) | happy(lucy) | [
"p4",
"p8",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1505877125591215162479816
% SZS output start Proof for 1505877125591215162479816
5. ! [X0] : ((kind(X0) | old(X0)) <=> (creative(X0) & old(X0))) [input p4]
9. ! [X0] : (happy(X0) => (happy(X0) <~> strong(X0))) [input p8]
16. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) & patient(X0))) [input p15]
21. patient(lucy) <~> strong(lucy) [input p20]
24. happy(lucy) [input hypothesis]
30. ! [X0] : ((happy(X0) <~> strong(X0)) | ~happy(X0)) [ennf transformation 9]
36. ! [X0] : (((kind(X0) | old(X0)) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 5]
37. ! [X0] : ((kind(X0) | old(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | (~kind(X0) & ~old(X0)))) [flattening 36]
42. ! [X0] : (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | ~happy(X0)) [nnf transformation 30]
63. ! [X0] : (((kind(X0) | creative(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 16]
64. ! [X0] : ((kind(X0) | creative(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 63]
75. (~strong(lucy) | ~patient(lucy)) & (strong(lucy) | patient(lucy)) [nnf transformation 21]
95. ~kind(X0) | creative(X0) [cnf transformation 37]
113. ~strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 42]
145. ~creative(X0) | ~creative(X0) [cnf transformation 64]
147. kind(X0) | creative(X0) | creative(X0) | ~patient(X0) [cnf transformation 64]
155. strong(lucy) | patient(lucy) [cnf transformation 75]
160. happy(lucy) [cnf transformation 24]
161. ~creative(X0) [duplicate literal removal 145]
162. kind(X0) | creative(X0) | ~patient(X0) [duplicate literal removal 147]
163. ~happy(X0) | ~strong(X0) [duplicate literal removal 113]
189. 4 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
190. creative(X1) | ~patient(X1) <- (4) [avatar component clause 189]
285. creative(X0) | ~patient(X0) [subsumption resolution 162,95]
286. 4 [avatar split clause 285,189]
318. 32 <=> patient(lucy) [avatar definition]
319. patient(lucy) <- (32) [avatar component clause 318]
322. 33 <=> strong(lucy) [avatar definition]
323. strong(lucy) <- (33) [avatar component clause 322]
326. 32 | 33 [avatar split clause 155,322,318]
339. ~patient(X1) <- (4) [subsumption resolution 190,161]
340. $false <- (4, 32) [resolution 339,319]
341. ~4 | ~32 [avatar contradiction clause 340]
346. ~strong(lucy) [resolution 163,160]
348. $false <- (33) [subsumption resolution 346,323]
349. ~33 [avatar contradiction clause 348]
350. $false [avatar sat refutation 286,326,341,349]
% SZS output end Proof for 1505877125591215162479816
% ------------------------------
% 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 humble or not wise is not funny or quiet and vice versa. Everyone who is not strong or not humble is both not strong and not calm and vice versa. Everyone who is both humble and not strong is both not happy and humble. Everyone who is tall is either not rich or not funny and vice versa. Everyone who is both brave and not generous is humble and vice versa. If lucy is wise or not happy then fred is brave or not kind and vice versa. Everyone who is strong is both humble and not brave and vice versa. Everyone who is not generous is not wise or strong and vice versa. If mary is both brave and not quiet then john is both funny and not kind. Everyone who is wise is either humble or strong and vice versa. If lucy is both not quiet and not happy then someone is either wise or not rich and vice versa. If someone is not kind then john is either not kind or not tall. If alice is not creative or calm then someone is not rich or old. If someone is both tall and generous then lucy is quiet and vice versa. Everyone who is creative is not generous or not patient. Paul is either not patient or not curious. Alice is either creative or not creative. Someone is either not humble or brave. Someone is tall or humble. John is either not strong or quiet. Someone is patient. | John is wise. | contradiction | (![X]:((~humble(X)|~wise(X))<=>(~funny(X)|quiet(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:((humble(X)&~strong(X))=>(~happy(X)&humble(X))))&
(![X]:(tall(X)<=>(~rich(X)<~>~funny(X))))&
(![X]:((brave(X)&~generous(X))<=>humble(X)))&
(((wise(lucy)|~happy(lucy)))<=>((brave(fred)|~kind(fred))))&
(![X]:(strong(X)<=>(humble(X)&~brave(X))))&
(![X]:(~generous(X)<=>(~wise(X)|strong(X))))&
(((brave(mary)&~quiet(mary)))=>((funny(john)&~kind(john))))&
(![X]:(wise(X)<=>(humble(X)<~>strong(X))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))=>((~kind(john)<~>~tall(john))))&
(((~creative(alice)|calm(alice)))=>(?[X]:((~rich(X)|old(X)))))&
((?[X]:((tall(X)&generous(X))))<=>(quiet(lucy)))&
(![X]:(creative(X)=>(~generous(X)|~patient(X))))&
((~patient(paul)<~>~curious(paul)))&
((creative(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((tall(X)|humble(X))))&
((~strong(john)<~>quiet(john)))&
(?[X]:(patient(X))) | wise(john) | [
"p1",
"p4",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 551333409816413216365389
% SZS output start Proof for 551333409816413216365389
2. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (~calm(X0) & ~strong(X0))) [input p1]
5. ! [X0] : ((~generous(X0) & brave(X0)) <=> humble(X0)) [input p4]
7. ! [X0] : (strong(X0) <=> (~brave(X0) & humble(X0))) [input p6]
8. ! [X0] : (~generous(X0) <=> (strong(X0) | ~wise(X0))) [input p7]
10. ! [X0] : (wise(X0) <=> (humble(X0) <~> strong(X0))) [input p9]
22. wise(john) [input hypothesis]
33. ! [X0] : (((~humble(X0) | ~strong(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 2]
34. ! [X0] : ((~humble(X0) | ~strong(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (humble(X0) & strong(X0)))) [flattening 33]
36. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) | ~brave(X0)))) [nnf transformation 5]
37. ! [X0] : (((~generous(X0) & brave(X0)) | ~humble(X0)) & (humble(X0) | generous(X0) | ~brave(X0))) [flattening 36]
40. ! [X0] : ((strong(X0) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [nnf transformation 7]
41. ! [X0] : ((strong(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | ~strong(X0))) [flattening 40]
42. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | generous(X0))) [flattening 42]
44. ! [X0] : ((wise(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) & (((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | ~wise(X0))) [nnf transformation 10]
70. ~strong(X0) | humble(X0) [cnf transformation 34]
81. ~humble(X0) | brave(X0) [cnf transformation 37]
82. ~generous(X0) | ~humble(X0) [cnf transformation 37]
88. ~brave(X0) | ~strong(X0) [cnf transformation 41]
90. ~wise(X0) | strong(X0) | generous(X0) [cnf transformation 43]
95. strong(X0) | humble(X0) | ~wise(X0) [cnf transformation 44]
96. ~strong(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 44]
121. wise(john) [cnf transformation 22]
160. ~strong(X0) | ~wise(X0) [subsumption resolution 96,70]
161. ~wise(X0) | humble(X0) [subsumption resolution 95,160]
238. 25 <=> strong(john) [avatar definition]
239. ~strong(john) <- (~25) [avatar component clause 238]
250. humble(john) [resolution 161,121]
258. brave(john) [resolution 250,81]
264. ~strong(john) [resolution 258,88]
322. strong(john) | generous(john) [resolution 90,121]
324. generous(john) <- (~25) [subsumption resolution 322,239]
355. ~humble(john) <- (~25) [resolution 324,82]
356. $false <- (~25) [subsumption resolution 355,250]
357. 25 [avatar contradiction clause 356]
363. ~25 [avatar split clause 264,238]
364. $false [avatar sat refutation 357,363]
% SZS output end Proof for 551333409816413216365389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not tall is either patient or not humble and vice versa.
If lucy is either not wise or rich then someone is either calm or happy.
Everyone who is not humble is not strong.
If someone is not old then someone is both rich and not brave.
Everyone who is both patient and not rich is not tall or wise and vice versa.
Everyone who is old is both not creative and kind and vice versa.
Everyone who is funny is both not kind and not rich.
Everyone who is not happy or curious is happy or not creative and vice versa.
Everyone who is not kind is humble or not brave.
Everyone who is both strong and humble is either not brave or curious and vice versa.
If someone is both curious and not quiet then someone is either wise or not happy and vice versa.
Everyone who is either not wise or tall is both calm and tall.
Everyone who is happy or not curious is both not old and not calm and vice versa.
Everyone who is both not quiet and not patient is old and vice versa.
If someone is either not generous or not funny then mary is brave and vice versa.
Everyone who is both happy and wise is not kind or patient and vice versa.
Someone is both not wise and curious.
Lucy is creative or curious.
Someone is either not generous or not curious.
John is kind.
Paul is old.
Someone is both humble and not old.
Mary is both rich and not patient. | Mary is humble. | entailment | (![X]:((strong(X)<~>~tall(X))<=>(patient(X)<~>~humble(X))))&
(((~wise(lucy)<~>rich(lucy)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(~humble(X)=>~strong(X)))&
((?[X]:(~old(X)))=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((patient(X)&~rich(X))<=>(~tall(X)|wise(X))))&
(![X]:(old(X)<=>(~creative(X)&kind(X))))&
(![X]:(funny(X)=>(~kind(X)&~rich(X))))&
(![X]:((~happy(X)|curious(X))<=>(happy(X)|~creative(X))))&
(![X]:(~kind(X)=>(humble(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((~wise(X)<~>tall(X))=>(calm(X)&tall(X))))&
(![X]:((happy(X)|~curious(X))<=>(~old(X)&~calm(X))))&
(![X]:((~quiet(X)&~patient(X))<=>old(X)))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(brave(mary)))&
(![X]:((happy(X)&wise(X))<=>(~kind(X)|patient(X))))&
(?[X]:((~wise(X)&curious(X))))&
((creative(lucy)|curious(lucy)))&
(?[X]:((~generous(X)<~>~curious(X))))&
(kind(john))&
(old(paul))&
(?[X]:((humble(X)&~old(X))))&
((rich(mary)&~patient(mary))) | humble(mary) | [
"p0",
"p2",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 258006426510457646134917
% SZS output start Proof for 258006426510457646134917
1. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> (patient(X0) <~> ~humble(X0))) [input p0]
3. ! [X0] : (~humble(X0) => ~strong(X0)) [input p2]
5. ! [X0] : ((~rich(X0) & patient(X0)) <=> (wise(X0) | ~tall(X0))) [input p4]
23. ~patient(mary) & rich(mary) [input p22]
24. ~humble(mary) [input hypothesis]
28. ! [X0] : (~strong(X0) | humble(X0)) [ennf transformation 3]
34. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) & (((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 1]
41. ! [X0] : (((~rich(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (rich(X0) | ~patient(X0)))) [nnf transformation 5]
42. ! [X0] : (((~rich(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | rich(X0) | ~patient(X0))) [flattening 41]
77. ~tall(X0) | strong(X0) | patient(X0) | humble(X0) [cnf transformation 34]
84. ~strong(X0) | humble(X0) [cnf transformation 28]
88. patient(X0) | tall(X0) [cnf transformation 42]
145. ~patient(mary) [cnf transformation 23]
146. ~humble(mary) [cnf transformation 24]
259. tall(mary) [resolution 88,145]
557. strong(mary) | patient(mary) | humble(mary) [resolution 77,259]
571. strong(mary) | humble(mary) [subsumption resolution 557,145]
572. strong(mary) [subsumption resolution 571,146]
703. humble(mary) [resolution 572,84]
704. $false [subsumption resolution 703,146]
% SZS output end Proof for 258006426510457646134917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not creative is not calm. If alice is both funny and not happy then john is either not tall or not humble. If someone is not rich then someone is strong or not wise. Everyone who is both curious and generous is not generous or not old and vice versa. If someone is not happy or not calm then fred is both not calm and wise and vice versa. Everyone who is generous is not wise. Everyone who is not creative is either not humble or rich. If mary is not wise or curious then mary is not wise. If alice is happy or not patient then mary is either not kind or curious and vice versa. Everyone who is either happy or not humble is strong. Everyone who is not funny is not rich. Everyone who is both not patient and not quiet is both not brave and not wise and vice versa. If someone is either not funny or not humble then paul is not old or not calm and vice versa. If someone is either not curious or rich then someone is generous or not patient. If someone is strong or wise then someone is both not tall and not brave and vice versa. Everyone who is not creative or wise is wise and vice versa. Someone is either not brave or not curious. Someone is both funny and brave. Someone is either not wise or strong. Someone is both not wise and happy. Paul is not quiet or curious. Susan is either not funny or kind. | John is humble. | contradiction | (![X]:((~patient(X)<~>~creative(X))=>~calm(X)))&
(((funny(alice)&~happy(alice)))=>((~tall(john)<~>~humble(john))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((curious(X)&generous(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((~calm(fred)&wise(fred))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:(~creative(X)=>(~humble(X)<~>rich(X))))&
(((~wise(mary)|curious(mary)))=>(~wise(mary)))&
(((happy(alice)|~patient(alice)))<=>((~kind(mary)<~>curious(mary))))&
(![X]:((happy(X)<~>~humble(X))=>strong(X)))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>((~old(paul)|~calm(paul))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)|wise(X))<=>wise(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
(?[X]:((funny(X)&brave(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~quiet(paul)|curious(paul)))&
((~funny(susan)<~>kind(susan))) | humble(john) | [
"p0",
"p3",
"p4",
"p5",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7809488956474922748348178
% SZS output start Proof for 7809488956474922748348178
1. ! [X0] : ((~patient(X0) <~> ~creative(X0)) => ~calm(X0)) [input p0]
4. ! [X0] : ((generous(X0) & curious(X0)) <=> (~old(X0) | ~generous(X0))) [input p3]
5. ? [X0] : (~calm(X0) | ~happy(X0)) <=> (wise(fred) & ~calm(fred)) [input p4]
6. ! [X0] : (generous(X0) => ~wise(X0)) [input p5]
10. ! [X0] : ((happy(X0) <~> ~humble(X0)) => strong(X0)) [input p9]
12. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~wise(X0) & ~brave(X0))) [input p11]
15. ? [X0] : (wise(X0) | strong(X0)) <=> ? [X0] : (~brave(X0) & ~tall(X0)) [input p14]
16. ! [X0] : ((wise(X0) | ~creative(X0)) <=> wise(X0)) [input p15]
23. humble(john) [input hypothesis]
26. ? [X0] : (wise(X0) | strong(X0)) <=> ? [X1] : (~brave(X1) & ~tall(X1)) [rectify 15]
27. ! [X0] : (~calm(X0) | (~patient(X0) <=> ~creative(X0))) [ennf transformation 1]
31. ! [X0] : (~wise(X0) | ~generous(X0)) [ennf transformation 6]
34. ! [X0] : (strong(X0) | (happy(X0) <=> ~humble(X0))) [ennf transformation 10]
37. ! [X0] : (~calm(X0) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) [nnf transformation 27]
42. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~generous(X0) | ~curious(X0))) [flattening 42]
44. (? [X0] : (~calm(X0) | ~happy(X0)) | (~wise(fred) | calm(fred))) & ((wise(fred) & ~calm(fred)) | ! [X0] : (calm(X0) & happy(X0))) [nnf transformation 5]
45. (? [X0] : (~calm(X0) | ~happy(X0)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X0] : (calm(X0) & happy(X0))) [flattening 44]
46. (? [X0] : (~calm(X0) | ~happy(X0)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X1] : (calm(X1) & happy(X1))) [rectify 45]
47. ? [X0] : (~calm(X0) | ~happy(X0)) => (~calm(sK1) | ~happy(sK1)) [choice axiom]
48. ((~calm(sK1) | ~happy(sK1)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X1] : (calm(X1) & happy(X1))) [skolemisation 46,47]
52. ! [X0] : (strong(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 34]
53. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 12]
54. ! [X0] : (((~quiet(X0) & ~patient(X0)) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | quiet(X0) | patient(X0))) [flattening 53]
64. (? [X0] : (wise(X0) | strong(X0)) | ! [X1] : (brave(X1) | tall(X1))) & (? [X1] : (~brave(X1) & ~tall(X1)) | ! [X0] : (~wise(X0) & ~strong(X0))) [nnf transformation 26]
65. (? [X0] : (wise(X0) | strong(X0)) | ! [X1] : (brave(X1) | tall(X1))) & (? [X2] : (~brave(X2) & ~tall(X2)) | ! [X3] : (~wise(X3) & ~strong(X3))) [rectify 64]
66. ? [X0] : (wise(X0) | strong(X0)) => (wise(sK4) | strong(sK4)) [choice axiom]
67. ? [X2] : (~brave(X2) & ~tall(X2)) => (~brave(sK5) & ~tall(sK5)) [choice axiom]
68. ((wise(sK4) | strong(sK4)) | ! [X1] : (brave(X1) | tall(X1))) & ((~brave(sK5) & ~tall(sK5)) | ! [X3] : (~wise(X3) & ~strong(X3))) [skolemisation 65,67,66]
69. ! [X0] : (((wise(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (~wise(X0) & creative(X0)))) [nnf transformation 16]
70. ! [X0] : ((wise(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (~wise(X0) & creative(X0)))) [flattening 69]
82. ~calm(X0) | ~creative(X0) | patient(X0) [cnf transformation 37]
90. generous(X0) | generous(X0) [cnf transformation 43]
94. wise(fred) | happy(X1) [cnf transformation 48]
95. wise(fred) | calm(X1) [cnf transformation 48]
97. ~wise(X0) | ~generous(X0) [cnf transformation 31]
108. ~humble(X0) | strong(X0) | ~happy(X0) [cnf transformation 52]
113. ~patient(X0) | wise(X0) | brave(X0) [cnf transformation 54]
125. ~brave(sK5) | ~strong(X3) [cnf transformation 68]
128. wise(X0) | creative(X0) [cnf transformation 70]
142. humble(john) [cnf transformation 23]
144. generous(X0) [duplicate literal removal 90]
158. 4 <=> humble(john) [avatar definition]
160. humble(john) <- (4) [avatar component clause 158]
181. 9 <=> wise(fred) [avatar definition]
182. wise(fred) <- (9) [avatar component clause 181]
194. 12 <=> ! [X1] : calm(X1) [avatar definition]
195. calm(X1) <- (12) [avatar component clause 194]
196. 12 | 9 [avatar split clause 95,181,194]
198. 13 <=> ! [X1] : happy(X1) [avatar definition]
199. happy(X1) <- (13) [avatar component clause 198]
200. 13 | 9 [avatar split clause 94,181,198]
203. ~wise(X0) [subsumption resolution 97,144]
223. ~patient(X0) | brave(X0) [subsumption resolution 113,203]
262. 25 <=> ! [X3] : ~strong(X3) [avatar definition]
263. ~strong(X3) <- (25) [avatar component clause 262]
265. 26 <=> brave(sK5) [avatar definition]
267. ~brave(sK5) <- (~26) [avatar component clause 265]
268. 25 | ~26 [avatar split clause 125,265,262]
274. creative(X0) [subsumption resolution 128,203]
305. 4 [avatar split clause 142,158]
306. $false <- (9) [subsumption resolution 182,203]
307. ~9 [avatar contradiction clause 306]
329. ~creative(X0) | patient(X0) <- (12) [resolution 82,195]
330. patient(X0) <- (12) [subsumption resolution 329,274]
334. brave(X0) <- (12) [resolution 330,223]
338. $false <- (12, ~26) [resolution 334,267]
339. ~12 | 26 [avatar contradiction clause 338]
342. strong(john) | ~happy(john) <- (4) [resolution 108,160]
344. ~happy(john) <- (4, 25) [subsumption resolution 342,263]
345. $false <- (4, 13, 25) [subsumption resolution 344,199]
346. ~4 | ~13 | ~25 [avatar contradiction clause 345]
350. $false [avatar sat refutation 196,200,268,305,307,339,346]
% SZS output end Proof for 7809488956474922748348178
% ------------------------------
% 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 lucy is not old then fred is either kind or not curious and vice versa.
Everyone who is either calm or not wise is funny or not humble and vice versa.
If someone is both not quiet and strong then someone is strong.
If susan is either curious or patient then someone is humble and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
Everyone who is wise or not calm is both happy and calm.
If someone is not creative or not humble then someone is not kind and vice versa.
If someone is not wise then mary is not creative and vice versa.
Everyone who is tall is either not rich or not patient.
Everyone who is rich or humble is not patient and vice versa.
If fred is either funny or not old then john is either creative or patient and vice versa.
Everyone who is wise is both not patient and not kind and vice versa.
If lucy is not happy or old then someone is either creative or kind and vice versa.
If john is both patient and not strong then someone is not old or kind and vice versa.
If someone is either not old or not quiet then alice is both not humble and not generous.
Everyone who is happy or not funny is either not old or brave.
Paul is quiet.
Lucy is not curious.
Someone is not tall or tall.
John is curious.
Someone is either wise or humble. | Alice is not kind. | entailment | ((~old(lucy))<=>((kind(fred)<~>~curious(fred))))&
(![X]:((calm(X)<~>~wise(X))<=>(funny(X)|~humble(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:(strong(X))))&
(((curious(susan)<~>patient(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
(![X]:((wise(X)|~calm(X))=>(happy(X)&calm(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))<=>(~creative(mary)))&
(![X]:(tall(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)|humble(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>((creative(john)<~>patient(john))))&
(![X]:(wise(X)<=>(~patient(X)&~kind(X))))&
(((~happy(lucy)|old(lucy)))<=>(?[X]:((creative(X)<~>kind(X)))))&
(((patient(john)&~strong(john)))<=>(?[X]:((~old(X)|kind(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~humble(alice)&~generous(alice))))&
(![X]:((happy(X)|~funny(X))=>(~old(X)<~>brave(X))))&
(quiet(paul))&
(~curious(lucy))&
(?[X]:((~tall(X)|tall(X))))&
(curious(john))&
(?[X]:((wise(X)<~>humble(X)))) | ~kind(alice) | [
"p4",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1152446634439947377130501
% SZS output start Proof for 1152446634439947377130501
5. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p4]
10. ! [X0] : ((humble(X0) | rich(X0)) <=> ~patient(X0)) [input p9]
14. (~strong(john) & patient(john)) <=> ? [X0] : (kind(X0) | ~old(X0)) [input p13]
22. kind(alice) [input hypothesis]
41. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 5]
42. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 41]
53. ! [X0] : (((humble(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 10]
54. ! [X0] : ((humble(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [flattening 53]
63. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | (strong(john) | ~patient(john))) [nnf transformation 14]
64. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | strong(john) | ~patient(john)) [flattening 63]
65. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X1] : (kind(X1) | ~old(X1)) | strong(john) | ~patient(john)) [rectify 64]
66. ? [X1] : (kind(X1) | ~old(X1)) => (kind(sK6) | ~old(sK6)) [choice axiom]
67. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & ((kind(sK6) | ~old(sK6)) | strong(john) | ~patient(john)) [skolemisation 65,66]
91. humble(X0) | ~patient(X0) [cnf transformation 42]
107. ~patient(X0) | ~humble(X0) [cnf transformation 54]
128. patient(john) | ~kind(X0) [cnf transformation 67]
143. kind(alice) [cnf transformation 22]
228. ~patient(X0) [subsumption resolution 107,91]
275. 27 <=> ! [X0] : ~kind(X0) [avatar definition]
276. ~kind(X0) <- (27) [avatar component clause 275]
286. ~kind(X0) [subsumption resolution 128,228]
287. 27 [avatar split clause 286,275]
323. $false <- (27) [resolution 276,143]
324. ~27 [avatar contradiction clause 323]
325. $false [avatar sat refutation 287,324]
% SZS output end Proof for 1152446634439947377130501
% ------------------------------
% 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or generous then someone is not happy. Everyone who is both not wise and calm is old. If alice is both not tall and creative then fred is either not funny or not kind and vice versa. If fred is old or not strong then someone is old or kind and vice versa. Everyone who is both not creative and happy is both patient and not generous. If alice is both brave and not funny then someone is rich and vice versa. Everyone who is not happy is either not creative or quiet and vice versa. Everyone who is either funny or creative is both wise and creative. Everyone who is either quiet or generous is either not strong or not wise and vice versa. Everyone who is both not curious and old is either not kind or tall. If susan is either not brave or tall then someone is tall or curious and vice versa. Everyone who is quiet is strong or not quiet and vice versa. Everyone who is wise is not strong or curious and vice versa. If someone is both not strong and old then mary is not wise or not generous and vice versa. If someone is generous or quiet then someone is not patient or not old. Everyone who is not wise is either quiet or not patient. Lucy is both tall and not wise. Paul is both happy and old. Alice is either not wise or not strong. Someone is not wise or wise. Someone is both patient and not curious. Someone is either not calm or rich. Someone is not creative or not old. | Mary is not creative. | contradiction | (((calm(john)|generous(john)))=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&calm(X))=>old(X)))&
(((~tall(alice)&creative(alice)))<=>((~funny(fred)<~>~kind(fred))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~creative(X)&happy(X))=>(patient(X)&~generous(X))))&
(((brave(alice)&~funny(alice)))<=>(?[X]:(rich(X))))&
(![X]:(~happy(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((funny(X)<~>creative(X))=>(wise(X)&creative(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((~curious(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~brave(susan)<~>tall(susan)))<=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(quiet(X)<=>(strong(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~strong(X)|curious(X))))&
((?[X]:((~strong(X)&old(X))))<=>((~wise(mary)|~generous(mary))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(~wise(X)=>(quiet(X)<~>~patient(X))))&
((tall(lucy)&~wise(lucy)))&
((happy(paul)&old(paul)))&
((~wise(alice)<~>~strong(alice)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((~creative(X)|~old(X)))) | ~creative(mary) | [
"p4",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5490100139502423802603273
% SZS output start Proof for 5490100139502423802603273
5. ! [X0] : ((happy(X0) & ~creative(X0)) => (~generous(X0) & patient(X0))) [input p4]
7. ! [X0] : (~happy(X0) <=> (~creative(X0) <~> quiet(X0))) [input p6]
12. ! [X0] : (quiet(X0) <=> (~quiet(X0) | strong(X0))) [input p11]
14. ? [X0] : (old(X0) & ~strong(X0)) <=> (~generous(mary) | ~wise(mary)) [input p13]
24. ~creative(mary) [input hypothesis]
29. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) | creative(X0))) [ennf transformation 5]
30. ! [X0] : ((~generous(X0) & patient(X0)) | ~happy(X0) | creative(X0)) [flattening 29]
50. ! [X0] : ((~happy(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | happy(X0))) [nnf transformation 7]
58. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 12]
59. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~quiet(X0))) [flattening 58]
62. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & ((~generous(mary) | ~wise(mary)) | ! [X0] : (~old(X0) | strong(X0))) [nnf transformation 14]
63. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X0] : (~old(X0) | strong(X0))) [flattening 62]
64. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [rectify 63]
65. ? [X0] : (old(X0) & ~strong(X0)) => (old(sK4) & ~strong(sK4)) [choice axiom]
66. ((old(sK4) & ~strong(sK4)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [skolemisation 64,65]
95. ~happy(X0) | ~generous(X0) | creative(X0) [cnf transformation 30]
100. ~quiet(X0) | creative(X0) | happy(X0) [cnf transformation 50]
123. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 59]
125. quiet(X0) | quiet(X0) [cnf transformation 59]
131. ~strong(sK4) | generous(mary) [cnf transformation 66]
150. ~creative(mary) [cnf transformation 24]
151. ~quiet(X0) | strong(X0) [duplicate literal removal 123]
152. quiet(X0) [duplicate literal removal 125]
262. strong(X0) [subsumption resolution 151,152]
265. 24 <=> generous(mary) [avatar definition]
267. generous(mary) <- (24) [avatar component clause 265]
278. generous(mary) [subsumption resolution 131,262]
279. 24 [avatar split clause 278,265]
348. creative(X0) | happy(X0) [resolution 100,152]
351. happy(mary) [resolution 348,150]
362. ~generous(mary) | creative(mary) [resolution 351,95]
364. creative(mary) <- (24) [subsumption resolution 362,267]
365. $false <- (24) [subsumption resolution 364,150]
366. ~24 [avatar contradiction clause 365]
368. $false [avatar sat refutation 279,366]
% SZS output end Proof for 5490100139502423802603273
% ------------------------------
% 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 not kind and not old then lucy is either not funny or not kind and vice versa.
Everyone who is rich or not tall is both not calm and not wise.
Everyone who is brave or creative is strong or not generous and vice versa.
If susan is not creative then susan is tall or wise.
Everyone who is either rich or not old is both patient and tall and vice versa.
If susan is rich then paul is not curious.
Everyone who is not quiet is either not quiet or wise.
Everyone who is not wise or not quiet is not humble.
If alice is curious then alice is both not quiet and not brave and vice versa.
Everyone who is either not generous or not curious is either strong or not quiet.
Everyone who is not brave is curious or not strong and vice versa.
Everyone who is both kind and quiet is both rich and not quiet.
Everyone who is not tall is either calm or patient and vice versa.
If someone is both not rich and not happy then someone is creative and vice versa.
If mary is kind or creative then fred is not brave and vice versa.
Everyone who is not kind is both not generous and not old.
Someone is both not calm and not wise.
John is both tall and wise.
John is happy or kind.
Someone is both happy and rich.
Someone is patient.
Paul is both rich and not calm.
Alice is both not calm and not tall. | John is not patient. | contradiction | ((?[X]:((~kind(X)&~old(X))))<=>((~funny(lucy)<~>~kind(lucy))))&
(![X]:((rich(X)|~tall(X))=>(~calm(X)&~wise(X))))&
(![X]:((brave(X)|creative(X))<=>(strong(X)|~generous(X))))&
((~creative(susan))=>((tall(susan)|wise(susan))))&
(![X]:((rich(X)<~>~old(X))<=>(patient(X)&tall(X))))&
((rich(susan))=>(~curious(paul)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>wise(X))))&
(![X]:((~wise(X)|~quiet(X))=>~humble(X)))&
((curious(alice))<=>((~quiet(alice)&~brave(alice))))&
(![X]:((~generous(X)<~>~curious(X))=>(strong(X)<~>~quiet(X))))&
(![X]:(~brave(X)<=>(curious(X)|~strong(X))))&
(![X]:((kind(X)&quiet(X))=>(rich(X)&~quiet(X))))&
(![X]:(~tall(X)<=>(calm(X)<~>patient(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>(?[X]:(creative(X))))&
(((kind(mary)|creative(mary)))<=>(~brave(fred)))&
(![X]:(~kind(X)=>(~generous(X)&~old(X))))&
(?[X]:((~calm(X)&~wise(X))))&
((tall(john)&wise(john)))&
((happy(john)|kind(john)))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:(patient(X)))&
((rich(paul)&~calm(paul)))&
((~calm(alice)&~tall(alice))) | ~patient(john) | [
"p1",
"p4",
"p6",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4292140627186902962135102
% SZS output start Proof for 4292140627186902962135102
2. ! [X0] : ((~tall(X0) | rich(X0)) => (~wise(X0) & ~calm(X0))) [input p1]
5. ! [X0] : ((rich(X0) <~> ~old(X0)) <=> (tall(X0) & patient(X0))) [input p4]
7. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> wise(X0))) [input p6]
12. ! [X0] : ((quiet(X0) & kind(X0)) => (~quiet(X0) & rich(X0))) [input p11]
16. ! [X0] : (~kind(X0) => (~old(X0) & ~generous(X0))) [input p15]
18. wise(john) & tall(john) [input p17]
24. ~patient(john) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~calm(X0)) | (tall(X0) & ~rich(X0))) [ennf transformation 2]
31. ! [X0] : ((~quiet(X0) <~> wise(X0)) | quiet(X0)) [ennf transformation 7]
33. ! [X0] : ((~quiet(X0) & rich(X0)) | (~quiet(X0) | ~kind(X0))) [ennf transformation 12]
34. ! [X0] : ((~quiet(X0) & rich(X0)) | ~quiet(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : ((~old(X0) & ~generous(X0)) | kind(X0)) [ennf transformation 16]
42. ! [X0] : ((((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))))) [nnf transformation 5]
43. ! [X0] : ((((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))))) [flattening 42]
44. ! [X0] : (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 31]
72. ~wise(X0) | ~rich(X0) [cnf transformation 27]
80. patient(X0) | rich(X0) | old(X0) [cnf transformation 43]
87. ~wise(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
99. ~quiet(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 34]
111. ~old(X0) | kind(X0) [cnf transformation 35]
115. wise(john) [cnf transformation 18]
124. ~patient(john) [cnf transformation 24]
125. ~quiet(X0) | ~kind(X0) [duplicate literal removal 99]
126. ~wise(X0) | quiet(X0) [duplicate literal removal 87]
229. 22 <=> kind(john) [avatar definition]
230. ~kind(john) <- (~22) [avatar component clause 229]
233. ~rich(john) [resolution 72,115]
237. quiet(john) [resolution 126,115]
238. ~kind(john) [resolution 237,125]
239. ~22 [avatar split clause 238,229]
271. rich(john) | old(john) [resolution 80,124]
272. old(john) [subsumption resolution 271,233]
275. kind(john) [resolution 272,111]
276. $false <- (~22) [subsumption resolution 275,230]
277. 22 [avatar contradiction clause 276]
278. $false [avatar sat refutation 239,277]
% SZS output end Proof for 4292140627186902962135102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong or not creative then someone is calm and vice versa.
If someone is either kind or not funny then john is either not funny or not creative and vice versa.
If fred is tall or kind then paul is both calm and wise.
Everyone who is not curious or quiet is either not calm or not generous.
If someone is both not old and not strong then alice is either not tall or curious.
If someone is both not funny and tall then someone is either not quiet or wise.
Everyone who is either patient or rich is humble.
Everyone who is either kind or not humble is not patient or patient and vice versa.
Everyone who is either strong or rich is either creative or not brave.
If alice is patient or curious then someone is not old and vice versa.
If mary is not rich or not brave then mary is either not strong or not old and vice versa.
Everyone who is not wise or funny is brave.
Everyone who is both happy and rich is either not curious or generous and vice versa.
If john is both not rich and kind then someone is both not kind and happy and vice versa.
Everyone who is either not humble or not curious is both humble and not generous and vice versa.
Everyone who is old or generous is both curious and strong.
Mary is not quiet.
Someone is either generous or not quiet.
Someone is either curious or funny.
Paul is not quiet or not strong.
Someone is not old or humble. | John is not rich. | contradiction | (((~strong(mary)|~creative(mary)))<=>(?[X]:(calm(X))))&
((?[X]:((kind(X)<~>~funny(X))))<=>((~funny(john)<~>~creative(john))))&
(((tall(fred)|kind(fred)))=>((calm(paul)&wise(paul))))&
(![X]:((~curious(X)|quiet(X))=>(~calm(X)<~>~generous(X))))&
((?[X]:((~old(X)&~strong(X))))=>((~tall(alice)<~>curious(alice))))&
((?[X]:((~funny(X)&tall(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:((patient(X)<~>rich(X))=>humble(X)))&
(![X]:((kind(X)<~>~humble(X))<=>(~patient(X)|patient(X))))&
(![X]:((strong(X)<~>rich(X))=>(creative(X)<~>~brave(X))))&
(((patient(alice)|curious(alice)))<=>(?[X]:(~old(X))))&
(((~rich(mary)|~brave(mary)))<=>((~strong(mary)<~>~old(mary))))&
(![X]:((~wise(X)|funny(X))=>brave(X)))&
(![X]:((happy(X)&rich(X))<=>(~curious(X)<~>generous(X))))&
(((~rich(john)&kind(john)))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((~humble(X)<~>~curious(X))<=>(humble(X)&~generous(X))))&
(![X]:((old(X)|generous(X))=>(curious(X)&strong(X))))&
(~quiet(mary))&
(?[X]:((generous(X)<~>~quiet(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((~quiet(paul)|~strong(paul)))&
(?[X]:((~old(X)|humble(X)))) | ~rich(john) | [
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1246382283713696908905445
% SZS output start Proof for 1246382283713696908905445
13. ! [X0] : ((rich(X0) & happy(X0)) <=> (~curious(X0) <~> generous(X0))) [input p12]
15. ! [X0] : ((~humble(X0) <~> ~curious(X0)) <=> (~generous(X0) & humble(X0))) [input p14]
16. ! [X0] : ((generous(X0) | old(X0)) => (strong(X0) & curious(X0))) [input p15]
22. ~rich(john) [input hypothesis]
31. ! [X0] : ((strong(X0) & curious(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 16]
58. ! [X0] : (((rich(X0) & happy(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~rich(X0) | ~happy(X0)))) [nnf transformation 13]
59. ! [X0] : (((rich(X0) & happy(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) & (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ~rich(X0) | ~happy(X0))) [flattening 58]
65. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (generous(X0) | ~humble(X0))) & ((~generous(X0) & humble(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [nnf transformation 15]
66. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | generous(X0) | ~humble(X0)) & ((~generous(X0) & humble(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [flattening 65]
125. rich(X0) | generous(X0) | curious(X0) [cnf transformation 59]
126. ~generous(X0) | ~curious(X0) | rich(X0) [cnf transformation 59]
131. humble(X0) | ~curious(X0) | humble(X0) [cnf transformation 66]
135. ~curious(X0) | ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 66]
138. ~generous(X0) | curious(X0) [cnf transformation 31]
148. ~rich(john) [cnf transformation 22]
149. ~curious(X0) | humble(X0) [duplicate literal removal 131]
150. ~humble(X0) | ~curious(X0) | generous(X0) [duplicate literal removal 135]
288. 29 <=> rich(john) [avatar definition]
290. ~rich(john) <- (~29) [avatar component clause 288]
340. ~29 [avatar split clause 148,288]
392. generous(john) | curious(john) <- (~29) [resolution 125,290]
394. curious(john) <- (~29) [subsumption resolution 392,138]
395. humble(john) <- (~29) [resolution 394,149]
478. ~curious(john) | generous(john) <- (~29) [resolution 395,150]
482. generous(john) <- (~29) [subsumption resolution 478,394]
601. ~curious(john) | rich(john) <- (~29) [resolution 482,126]
615. rich(john) <- (~29) [subsumption resolution 601,394]
616. $false <- (~29) [subsumption resolution 615,290]
617. 29 [avatar contradiction clause 616]
618. $false [avatar sat refutation 340,617]
% SZS output end Proof for 1246382283713696908905445
% ------------------------------
% 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 rich then someone is not humble or not generous.
Everyone who is both strong and curious is either strong or quiet.
Everyone who is not generous is wise and vice versa.
If someone is curious or funny then paul is kind.
If someone is not happy or kind then susan is both kind and curious.
If someone is not brave then someone is brave or old.
Everyone who is not strong or not brave is either wise or happy.
Everyone who is not wise or old is not wise or generous and vice versa.
If mary is not humble then someone is quiet.
If susan is kind then paul is kind and vice versa.
Everyone who is both not curious and rich is both old and not old and vice versa.
Everyone who is not brave or not kind is not wise or not rich.
Everyone who is both wise and old is calm or rich and vice versa.
If someone is not kind or not tall then someone is old or brave and vice versa.
If mary is quiet then someone is both funny and wise and vice versa.
Everyone who is both not calm and kind is humble or not old.
Fred is tall.
Someone is either kind or happy.
John is not strong.
Someone is not humble or generous.
Lucy is happy or strong.
Paul is old or not strong. | Susan is tall. | neutral | ((?[X]:(rich(X)))=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((strong(X)&curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:(~generous(X)<=>wise(X)))&
((?[X]:((curious(X)|funny(X))))=>(kind(paul)))&
((?[X]:((~happy(X)|kind(X))))=>((kind(susan)&curious(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:((~strong(X)|~brave(X))=>(wise(X)<~>happy(X))))&
(![X]:((~wise(X)|old(X))<=>(~wise(X)|generous(X))))&
((~humble(mary))=>(?[X]:(quiet(X))))&
((kind(susan))<=>(kind(paul)))&
(![X]:((~curious(X)&rich(X))<=>(old(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:((wise(X)&old(X))<=>(calm(X)|rich(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((old(X)|brave(X)))))&
((quiet(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((~calm(X)&kind(X))=>(humble(X)|~old(X))))&
(tall(fred))&
(?[X]:((kind(X)<~>happy(X))))&
(~strong(john))&
(?[X]:((~humble(X)|generous(X))))&
((happy(lucy)|strong(lucy)))&
((old(paul)|~strong(paul))) | tall(susan) | [] | null | 0 |
Everyone who is both not happy and not curious is not tall and vice versa.
Everyone who is old is either humble or not wise.
If someone is not kind then john is both rich and not curious and vice versa.
If someone is calm or not calm then lucy is both creative and not generous and vice versa.
If someone is not generous or not curious then fred is not wise and vice versa.
Everyone who is either not calm or not happy is not calm and vice versa.
If someone is not curious then someone is kind or not happy.
Everyone who is either not kind or not rich is tall and vice versa.
Everyone who is not generous or not rich is curious.
If john is either humble or kind then john is either not kind or not brave.
Everyone who is not patient is old or calm.
Everyone who is not generous or not brave is both old and kind.
Everyone who is not brave is not curious and vice versa.
If lucy is not creative or happy then someone is not calm.
If someone is not funny then someone is not quiet or calm and vice versa.
If mary is rich then paul is calm and vice versa.
Susan is curious.
Someone is either old or not tall.
Mary is both creative and patient.
Someone is either not rich or funny.
Someone is not old.
Paul is curious. | Susan is kind. | entailment | (![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(![X]:(old(X)=>(humble(X)<~>~wise(X))))&
((?[X]:(~kind(X)))<=>((rich(john)&~curious(john))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(curious(susan))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(mary)&patient(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(~old(X)))&
(curious(paul)) | kind(susan) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2539665435704029806273268
% SZS output start Proof for 2539665435704029806273268
1. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> ~tall(X0)) [input p0]
3. ? [X0] : ~kind(X0) <=> (~curious(john) & rich(john)) [input p2]
6. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> ~calm(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> ~rich(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : ((~rich(X0) | ~generous(X0)) => curious(X0)) [input p8]
12. ! [X0] : ((~brave(X0) | ~generous(X0)) => (kind(X0) & old(X0))) [input p11]
13. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p12]
23. ~kind(susan) [input hypothesis]
30. ! [X0] : (curious(X0) | (rich(X0) & generous(X0))) [ennf transformation 9]
32. ! [X0] : ((kind(X0) & old(X0)) | (brave(X0) & generous(X0))) [ennf transformation 12]
34. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | happy(X0))) [flattening 34]
37. (? [X0] : ~kind(X0) | (curious(john) | ~rich(john))) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [nnf transformation 3]
38. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [flattening 37]
39. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [rectify 38]
40. ? [X0] : ~kind(X0) => ~kind(sK0) [choice axiom]
41. (~kind(sK0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [skolemisation 39,40]
51. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 6]
55. ! [X0] : ((((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~tall(X0)) & (tall(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))))) [nnf transformation 8]
57. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 13]
75. ~happy(X0) | tall(X0) [cnf transformation 35]
80. ~curious(john) | kind(X1) [cnf transformation 41]
91. ~calm(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
93. happy(X0) | calm(X0) | calm(X0) [cnf transformation 51]
97. ~rich(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 55]
100. rich(X0) | curious(X0) [cnf transformation 30]
108. brave(X0) | kind(X0) [cnf transformation 32]
110. ~brave(X0) | curious(X0) [cnf transformation 57]
126. ~kind(susan) [cnf transformation 23]
129. ~calm(X0) | happy(X0) [duplicate literal removal 91]
130. calm(X0) | happy(X0) [duplicate literal removal 93]
136. 2 <=> curious(john) [avatar definition]
137. ~curious(john) <- (~2) [avatar component clause 136]
145. 4 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (4) [avatar component clause 145]
147. 4 | ~2 [avatar split clause 80,136,145]
181. 12 <=> ! [X1] : curious(X1) [avatar definition]
182. curious(X1) <- (12) [avatar component clause 181]
188. happy(X0) [subsumption resolution 129,130]
267. $false <- (4) [resolution 146,126]
268. ~4 [avatar contradiction clause 267]
269. $false <- (~2, 12) [subsumption resolution 137,182]
270. 2 | ~12 [avatar contradiction clause 269]
273. tall(X0) [resolution 75,188]
296. kind(X0) | curious(X0) [resolution 110,108]
322. ~kind(X0) | ~tall(X0) | curious(X0) [resolution 97,100]
326. ~kind(X0) | curious(X0) [subsumption resolution 322,273]
327. curious(X0) [subsumption resolution 326,296]
328. 12 [avatar split clause 327,181]
329. $false [avatar sat refutation 147,268,270,328]
% SZS output end Proof for 2539665435704029806273268
% ------------------------------
% 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 |
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