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
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is wise or not wise is patient and vice versa.
Everyone who is not kind is not rich.
If john is both not rich and quiet then someone is both not funny and creative and vice versa.
Everyone who is both kind and happy is either not wise or old and vice versa.
Everyone who is not funny is both tall and not brave.
Everyone who is both calm and curious is not humble or not funny.
Everyone who is both kind and curious is not creative.
If john is both patient and not curious then someone is both not curious and not rich and vice versa.
If susan is not tall then someone is not happy or patient.
Everyone who is either tall or not kind is brave or not curious and vice versa.
If alice is generous or not creative then fred is both brave and not funny and vice versa.
If someone is both not humble and rich then someone is either patient or not patient.
Everyone who is strong is not old.
If someone is not brave or not patient then someone is either rich or creative and vice versa.
If someone is kind then paul is not quiet or not creative and vice versa.
If someone is kind or funny then lucy is both kind and not calm and vice versa.
Someone is not old or funny.
Paul is both not strong and not curious.
Alice is either quiet or old.
Someone is both calm and wise.
Mary is either not strong or happy.
John is quiet or not tall.
Susan is curious or not wise.
Someone is either quiet or brave. | Fred is quiet. | neutral | (![X]:((wise(X)|~wise(X))<=>patient(X)))&
(![X]:(~kind(X)=>~rich(X)))&
(((~rich(john)&quiet(john)))<=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((kind(X)&happy(X))<=>(~wise(X)<~>old(X))))&
(![X]:(~funny(X)=>(tall(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))=>(~humble(X)|~funny(X))))&
(![X]:((kind(X)&curious(X))=>~creative(X)))&
(((patient(john)&~curious(john)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((~tall(susan))=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>(brave(X)|~curious(X))))&
(((generous(alice)|~creative(alice)))<=>((brave(fred)&~funny(fred))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)<~>~patient(X)))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:(kind(X)))<=>((~quiet(paul)|~creative(paul))))&
((?[X]:((kind(X)|funny(X))))<=>((kind(lucy)&~calm(lucy))))&
(?[X]:((~old(X)|funny(X))))&
((~strong(paul)&~curious(paul)))&
((quiet(alice)<~>old(alice)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)<~>happy(mary)))&
((quiet(john)|~tall(john)))&
((curious(susan)|~wise(susan)))&
(?[X]:((quiet(X)<~>brave(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is not generous is either not wise or wise.
If mary is creative or happy then fred is both strong and kind.
Everyone who is either not happy or not funny is both not brave and not old and vice versa.
If paul is wise then paul is not strong or not tall.
If susan is curious or strong then someone is either calm or quiet.
Everyone who is both strong and generous is not old or not creative.
Everyone who is calm is both patient and not funny and vice versa.
If mary is either strong or creative then john is both curious and humble and vice versa.
If someone is funny or brave then mary is creative or quiet and vice versa.
Everyone who is either not funny or not wise is either funny or not kind and vice versa.
If someone is either not humble or funny then lucy is quiet or kind and vice versa.
Everyone who is not rich is not brave.
Everyone who is quiet or curious is either creative or happy.
Everyone who is not strong or not patient is wise and vice versa.
Everyone who is not brave or not humble is both rich and generous and vice versa.
If alice is creative or humble then john is not funny and vice versa.
Someone is not strong or not humble.
Someone is not calm or not old.
Alice is both not humble and not quiet.
Susan is kind.
Lucy is both not tall and generous.
Someone is either not kind or not happy.
Susan is either not funny or wise.
Mary is wise. | Susan is not old. | neutral | (![X]:(~generous(X)=>(~wise(X)<~>wise(X))))&
(((creative(mary)|happy(mary)))=>((strong(fred)&kind(fred))))&
(![X]:((~happy(X)<~>~funny(X))<=>(~brave(X)&~old(X))))&
((wise(paul))=>((~strong(paul)|~tall(paul))))&
(((curious(susan)|strong(susan)))=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((strong(X)&generous(X))=>(~old(X)|~creative(X))))&
(![X]:(calm(X)<=>(patient(X)&~funny(X))))&
(((strong(mary)<~>creative(mary)))<=>((curious(john)&humble(john))))&
((?[X]:((funny(X)|brave(X))))<=>((creative(mary)|quiet(mary))))&
(![X]:((~funny(X)<~>~wise(X))<=>(funny(X)<~>~kind(X))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((quiet(lucy)|kind(lucy))))&
(![X]:(~rich(X)=>~brave(X)))&
(![X]:((quiet(X)|curious(X))=>(creative(X)<~>happy(X))))&
(![X]:((~strong(X)|~patient(X))<=>wise(X)))&
(![X]:((~brave(X)|~humble(X))<=>(rich(X)&generous(X))))&
(((creative(alice)|humble(alice)))<=>(~funny(john)))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:((~calm(X)|~old(X))))&
((~humble(alice)&~quiet(alice)))&
(kind(susan))&
((~tall(lucy)&generous(lucy)))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~funny(susan)<~>wise(susan)))&
(wise(mary)) | ~old(susan) | [] | null | 0 |
Everyone who is either not curious or wise is either not funny or kind and vice versa. Everyone who is both not calm and creative is both not happy and not patient and vice versa. Everyone who is not tall or not calm is both not rich and strong and vice versa. Everyone who is either not old or creative is both not kind and not curious and vice versa. If john is either not quiet or not happy then fred is both not strong and not wise. Everyone who is both curious and not humble is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is both brave and humble then fred is not rich and vice versa. Someone is either not tall or not calm. Paul is old. Someone is not brave or not humble. Mary is quiet or old. Mary is creative or rich. Someone is humble. Susan is old or tall. Someone is either not calm or not tall. | Mary is calm. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~tall(X)|~calm(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:((brave(X)&humble(X))))<=>(~rich(fred)))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X)))&
((old(susan)|tall(susan)))&
(?[X]:((~calm(X)<~>~tall(X)))) | calm(mary) | [
"p1",
"p2",
"p6",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 963719519307452432135331
% SZS output start Proof for 963719519307452432135331
2. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~patient(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((~calm(X0) | ~tall(X0)) <=> (strong(X0) & ~rich(X0))) [input p2]
7. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p6]
10. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p9]
20. rich(mary) | creative(mary) [input p19]
24. ~calm(mary) [input hypothesis]
34. ! [X0] : (((creative(X0) & ~calm(X0)) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 2]
35. ! [X0] : (((creative(X0) & ~calm(X0)) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | ~creative(X0) | calm(X0))) [flattening 34]
36. ! [X0] : (((~calm(X0) | ~tall(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (calm(X0) & tall(X0)))) [nnf transformation 3]
37. ! [X0] : ((~calm(X0) | ~tall(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (calm(X0) & tall(X0)))) [flattening 36]
42. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 7]
44. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 10]
45. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0) | tall(X0))) [flattening 44]
75. ~happy(X0) | ~creative(X0) | calm(X0) [cnf transformation 35]
80. ~rich(X0) | calm(X0) [cnf transformation 37]
97. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
99. kind(X0) | kind(X0) | happy(X0) [cnf transformation 42]
109. ~rich(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 45]
129. rich(mary) | creative(mary) [cnf transformation 20]
134. ~calm(mary) [cnf transformation 24]
135. happy(X0) | ~kind(X0) [duplicate literal removal 97]
136. happy(X0) | kind(X0) [duplicate literal removal 99]
157. happy(X0) [subsumption resolution 135,136]
168. ~rich(X0) | ~calm(X0) [subsumption resolution 109,157]
169. ~rich(X0) [subsumption resolution 168,80]
209. creative(mary) [subsumption resolution 129,169]
232. ~creative(X1) | calm(X1) [resolution 75,157]
233. calm(mary) [resolution 232,209]
234. $false [subsumption resolution 233,134]
% SZS output end Proof for 963719519307452432135331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both calm and generous and vice versa.
Everyone who is not creative is not strong or not patient and vice versa.
If alice is either calm or not humble then someone is tall.
Everyone who is patient is humble and vice versa.
If fred is rich then mary is both not curious and not generous and vice versa.
If someone is either not old or patient then susan is generous and vice versa.
Everyone who is both funny and not generous is both not tall and not funny.
If lucy is not old then john is either not funny or tall and vice versa.
If john is both kind and not tall then someone is not creative.
If someone is strong then someone is not quiet or kind.
Everyone who is not happy is not creative or not wise and vice versa.
If lucy is happy or calm then lucy is either funny or not creative.
If someone is both wise and generous then someone is rich or not calm and vice versa.
Everyone who is both not humble and not patient is both happy and funny.
Everyone who is either not humble or curious is both creative and kind and vice versa.
Everyone who is not wise or not quiet is both not brave and not calm.
Someone is not brave.
John is rich or not brave.
Someone is either curious or not generous.
Alice is kind.
Someone is humble.
Someone is tall.
Paul is not humble or wise. | Mary is wise. | neutral | (![X]:(generous(X)<=>(calm(X)&generous(X))))&
(![X]:(~creative(X)<=>(~strong(X)|~patient(X))))&
(((calm(alice)<~>~humble(alice)))=>(?[X]:(tall(X))))&
(![X]:(patient(X)<=>humble(X)))&
((rich(fred))<=>((~curious(mary)&~generous(mary))))&
((?[X]:((~old(X)<~>patient(X))))<=>(generous(susan)))&
(![X]:((funny(X)&~generous(X))=>(~tall(X)&~funny(X))))&
((~old(lucy))<=>((~funny(john)<~>tall(john))))&
(((kind(john)&~tall(john)))=>(?[X]:(~creative(X))))&
((?[X]:(strong(X)))=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:(~happy(X)<=>(~creative(X)|~wise(X))))&
(((happy(lucy)|calm(lucy)))=>((funny(lucy)<~>~creative(lucy))))&
((?[X]:((wise(X)&generous(X))))<=>(?[X]:((rich(X)|~calm(X)))))&
(![X]:((~humble(X)&~patient(X))=>(happy(X)&funny(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(creative(X)&kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(~brave(X)&~calm(X))))&
(?[X]:(~brave(X)))&
((rich(john)|~brave(john)))&
(?[X]:((curious(X)<~>~generous(X))))&
(kind(alice))&
(?[X]:(humble(X)))&
(?[X]:(tall(X)))&
((~humble(paul)|wise(paul))) | wise(mary) | [] | null | 0 |
Everyone who is not humble or quiet is not quiet and vice versa.
If lucy is both not quiet and creative then someone is not brave and vice versa.
Everyone who is both not funny and not old is not tall and vice versa.
If susan is both not happy and quiet then mary is both not brave and not funny and vice versa.
Everyone who is strong is not happy or not rich.
If someone is happy then someone is either humble or not kind and vice versa.
Everyone who is either curious or not kind is not happy and vice versa.
Everyone who is both not humble and calm is not old or kind and vice versa.
Everyone who is not calm or not quiet is strong.
Everyone who is both strong and not quiet is both tall and kind and vice versa.
Everyone who is both happy and generous is not quiet.
If susan is not funny then fred is calm.
If susan is either funny or humble then john is not kind or wise and vice versa.
Everyone who is not quiet is not funny or not kind.
Lucy is calm.
John is either not wise or happy.
Lucy is tall or not strong.
Paul is both wise and not creative.
John is both not patient and not brave. | Lucy is not rich. | neutral | (![X]:((~humble(X)|quiet(X))<=>~quiet(X)))&
(((~quiet(lucy)&creative(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)&~old(X))<=>~tall(X)))&
(((~happy(susan)&quiet(susan)))<=>((~brave(mary)&~funny(mary))))&
(![X]:(strong(X)=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((curious(X)<~>~kind(X))<=>~happy(X)))&
(![X]:((~humble(X)&calm(X))<=>(~old(X)|kind(X))))&
(![X]:((~calm(X)|~quiet(X))=>strong(X)))&
(![X]:((strong(X)&~quiet(X))<=>(tall(X)&kind(X))))&
(![X]:((happy(X)&generous(X))=>~quiet(X)))&
((~funny(susan))=>(calm(fred)))&
(((funny(susan)<~>humble(susan)))<=>((~kind(john)|wise(john))))&
(![X]:(~quiet(X)=>(~funny(X)|~kind(X))))&
(calm(lucy))&
((~wise(john)<~>happy(john)))&
((tall(lucy)|~strong(lucy)))&
((wise(paul)&~creative(paul)))&
((~patient(john)&~brave(john))) | ~rich(lucy) | [] | null | 0 |
Everyone who is not curious or creative is both wise and rich. If someone is both rich and not funny then alice is not happy or not rich and vice versa. Everyone who is curious or not happy is either not rich or curious and vice versa. Everyone who is not patient is not creative or not curious. If someone is either not calm or not tall then someone is funny or not creative. If someone is calm then lucy is both patient and rich and vice versa. Everyone who is both not patient and humble is happy and vice versa. Everyone who is both patient and not strong is either not humble or funny and vice versa. Everyone who is not brave or not tall is brave or not wise and vice versa. Everyone who is either humble or calm is both strong and not generous and vice versa. If someone is either not calm or not quiet then someone is either not quiet or curious and vice versa. If someone is tall then someone is not patient and vice versa. Everyone who is humble or rich is either patient or not creative. Everyone who is not calm or rich is not patient. If mary is either wise or not creative then paul is humble or not curious and vice versa. Someone is not humble or happy. Alice is not old or not wise. Someone is not old or not wise. Lucy is either not rich or not calm. Mary is brave. Someone is not calm or calm. Someone is happy. | Lucy is not creative. | entailment | (![X]:((~curious(X)|creative(X))=>(wise(X)&rich(X))))&
((?[X]:((rich(X)&~funny(X))))<=>((~happy(alice)|~rich(alice))))&
(![X]:((curious(X)|~happy(X))<=>(~rich(X)<~>curious(X))))&
(![X]:(~patient(X)=>(~creative(X)|~curious(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:(calm(X)))<=>((patient(lucy)&rich(lucy))))&
(![X]:((~patient(X)&humble(X))<=>happy(X)))&
(![X]:((patient(X)&~strong(X))<=>(~humble(X)<~>funny(X))))&
(![X]:((~brave(X)|~tall(X))<=>(brave(X)|~wise(X))))&
(![X]:((humble(X)<~>calm(X))<=>(strong(X)&~generous(X))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:(tall(X)))<=>(?[X]:(~patient(X))))&
(![X]:((humble(X)|rich(X))=>(patient(X)<~>~creative(X))))&
(![X]:((~calm(X)|rich(X))=>~patient(X)))&
(((wise(mary)<~>~creative(mary)))<=>((humble(paul)|~curious(paul))))&
(?[X]:((~humble(X)|happy(X))))&
((~old(alice)|~wise(alice)))&
(?[X]:((~old(X)|~wise(X))))&
((~rich(lucy)<~>~calm(lucy)))&
(brave(mary))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(happy(X))) | ~creative(lucy) | [
"p0",
"p2",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3854886931345268667445178
% SZS output start Proof for 3854886931345268667445178
1. ! [X0] : ((creative(X0) | ~curious(X0)) => (rich(X0) & wise(X0))) [input p0]
3. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~rich(X0) <~> curious(X0))) [input p2]
13. ! [X0] : ((rich(X0) | humble(X0)) => (patient(X0) <~> ~creative(X0))) [input p12]
14. ! [X0] : ((rich(X0) | ~calm(X0)) => ~patient(X0)) [input p13]
23. creative(lucy) [input hypothesis]
29. ! [X0] : ((rich(X0) & wise(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 1]
33. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (~rich(X0) & ~humble(X0))) [ennf transformation 13]
34. ! [X0] : (~patient(X0) | (~rich(X0) & calm(X0))) [ennf transformation 14]
40. ! [X0] : (((~happy(X0) | curious(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (happy(X0) & ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : ((~happy(X0) | curious(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (happy(X0) & ~curious(X0)))) [flattening 40]
69. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~rich(X0) & ~humble(X0))) [nnf transformation 33]
81. rich(X0) | curious(X0) [cnf transformation 29]
90. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 41]
130. ~creative(X0) | patient(X0) | ~rich(X0) [cnf transformation 69]
134. ~patient(X0) | ~rich(X0) [cnf transformation 34]
147. creative(lucy) [cnf transformation 23]
150. ~curious(X0) | rich(X0) [duplicate literal removal 90]
177. rich(X0) [subsumption resolution 150,81]
262. ~creative(X0) | patient(X0) [subsumption resolution 130,177]
263. ~patient(X0) [subsumption resolution 134,177]
318. patient(lucy) [resolution 262,147]
319. $false [subsumption resolution 318,263]
% SZS output end Proof for 3854886931345268667445178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then someone is either not patient or generous and vice versa.
If someone is either not creative or not rich then someone is happy and vice versa.
If alice is not strong then someone is either not generous or calm and vice versa.
If someone is either not wise or not patient then someone is not calm and vice versa.
If someone is either creative or humble then mary is both kind and funny.
Everyone who is brave or not patient is both not strong and not humble.
Everyone who is not creative is both not old and humble.
Everyone who is not generous is both humble and happy.
Everyone who is both not curious and not rich is curious or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
Mary is tall.
Someone is both creative and not old.
John is either old or humble.
Paul is not brave or not funny.
Someone is either wise or generous.
John is not tall. | John is not rich. | entailment | ((?[X]:(kind(X)))<=>(?[X]:((~patient(X)<~>generous(X)))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:(happy(X))))&
((~strong(alice))<=>(?[X]:((~generous(X)<~>calm(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((creative(X)<~>humble(X))))=>((kind(mary)&funny(mary))))&
(![X]:((brave(X)|~patient(X))=>(~strong(X)&~humble(X))))&
(![X]:(~creative(X)=>(~old(X)&humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|funny(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
(tall(mary))&
(?[X]:((creative(X)&~old(X))))&
((old(john)<~>humble(john)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((wise(X)<~>generous(X))))&
(~tall(john)) | ~rich(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4052885499649280836382928
% SZS output start Proof for 4052885499649280836382928
1. ? [X0] : kind(X0) <=> ? [X0] : (~patient(X0) <~> generous(X0)) [input p0]
5. ? [X0] : (creative(X0) <~> humble(X0)) => (funny(mary) & kind(mary)) [input p4]
6. ! [X0] : ((~patient(X0) | brave(X0)) => (~humble(X0) & ~strong(X0))) [input p5]
7. ! [X0] : (~creative(X0) => (humble(X0) & ~old(X0))) [input p6]
8. ! [X0] : (~generous(X0) => (happy(X0) & humble(X0))) [input p7]
9. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) | curious(X0))) [input p8]
14. ! [X0] : ((kind(X0) <~> curious(X0)) => (curious(X0) & generous(X0))) [input p13]
15. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p14]
22. rich(john) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : (~patient(X1) <~> generous(X1)) [rectify 1]
28. (funny(mary) & kind(mary)) | ! [X0] : (creative(X0) <=> humble(X0)) [ennf transformation 5]
29. ! [X0] : ((~humble(X0) & ~strong(X0)) | (patient(X0) & ~brave(X0))) [ennf transformation 6]
30. ! [X0] : ((humble(X0) & ~old(X0)) | creative(X0)) [ennf transformation 7]
31. ! [X0] : ((happy(X0) & humble(X0)) | generous(X0)) [ennf transformation 8]
35. ! [X0] : ((curious(X0) & generous(X0)) | (kind(X0) <=> curious(X0))) [ennf transformation 14]
36. (? [X0] : kind(X0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (? [X1] : ((~generous(X1) | patient(X1)) & (generous(X1) | ~patient(X1))) | ! [X0] : ~kind(X0)) [nnf transformation 23]
37. (? [X0] : kind(X0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (? [X2] : ((~generous(X2) | patient(X2)) & (generous(X2) | ~patient(X2))) | ! [X3] : ~kind(X3)) [rectify 36]
38. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
39. ? [X2] : ((~generous(X2) | patient(X2)) & (generous(X2) | ~patient(X2))) => ((~generous(sK1) | patient(sK1)) & (generous(sK1) | ~patient(sK1))) [choice axiom]
40. (kind(sK0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (((~generous(sK1) | patient(sK1)) & (generous(sK1) | ~patient(sK1))) | ! [X3] : ~kind(X3)) [skolemisation 37,39,38]
55. (funny(mary) & kind(mary)) | ! [X0] : ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))) [nnf transformation 28]
56. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 9]
57. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 56]
62. ! [X0] : ((curious(X0) & generous(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) [nnf transformation 35]
63. ! [X0] : (((happy(X0) | ~creative(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~happy(X0) & creative(X0)))) [nnf transformation 15]
64. ! [X0] : ((happy(X0) | ~creative(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~happy(X0) & creative(X0)))) [flattening 63]
74. kind(sK0) | ~patient(X1) | ~generous(X1) [cnf transformation 40]
87. kind(mary) | humble(X0) | ~creative(X0) [cnf transformation 55]
88. kind(mary) | creative(X0) | ~humble(X0) [cnf transformation 55]
94. ~humble(X0) | patient(X0) [cnf transformation 29]
96. humble(X0) | creative(X0) [cnf transformation 30]
98. happy(X0) | generous(X0) [cnf transformation 31]
100. ~curious(X0) | ~curious(X0) [cnf transformation 57]
103. ~funny(X0) | ~rich(X0) [cnf transformation 57]
111. curious(X0) | curious(X0) | ~kind(X0) [cnf transformation 62]
114. ~happy(X0) | funny(X0) | ~patient(X0) [cnf transformation 64]
128. rich(john) [cnf transformation 22]
129. curious(X0) | ~kind(X0) [duplicate literal removal 111]
131. ~curious(X0) [duplicate literal removal 100]
133. 1 <=> ! [X1] : (~patient(X1) | ~generous(X1)) [avatar definition]
134. ~generous(X1) | ~patient(X1) <- (1) [avatar component clause 133]
136. 2 <=> kind(sK0) [avatar definition]
138. kind(sK0) <- (2) [avatar component clause 136]
139. 1 | 2 [avatar split clause 74,136,133]
145. 4 <=> ! [X3] : ~kind(X3) [avatar definition]
146. ~kind(X3) <- (4) [avatar component clause 145]
230. 24 <=> ! [X0] : (creative(X0) | ~humble(X0)) [avatar definition]
231. creative(X0) | ~humble(X0) <- (24) [avatar component clause 230]
238. 26 <=> ! [X0] : (humble(X0) | ~creative(X0)) [avatar definition]
239. humble(X0) | ~creative(X0) <- (26) [avatar component clause 238]
242. 27 <=> kind(mary) [avatar definition]
244. kind(mary) <- (27) [avatar component clause 242]
245. 24 | 27 [avatar split clause 88,242,230]
246. 26 | 27 [avatar split clause 87,242,238]
261. ~kind(X0) [subsumption resolution 129,131]
262. 4 [avatar split clause 261,145]
269. 32 <=> humble(john) [avatar definition]
270. humble(john) <- (32) [avatar component clause 269]
271. ~humble(john) <- (~32) [avatar component clause 269]
293. humble(X0) <- (26) [subsumption resolution 239,96]
297. $false <- (2, 4) [subsumption resolution 138,146]
298. ~2 | ~4 [avatar contradiction clause 297]
305. $false <- (26, ~32) [resolution 293,271]
306. ~26 | 32 [avatar contradiction clause 305]
307. creative(X0) <- (24) [subsumption resolution 231,96]
308. $false <- (4, 27) [subsumption resolution 244,146]
309. ~4 | ~27 [avatar contradiction clause 308]
310. humble(X0) <- (24, 26) [subsumption resolution 239,307]
318. patient(john) <- (32) [resolution 94,270]
319. patient(X0) <- (24, 26) [resolution 94,310]
348. funny(X0) | ~patient(X0) | generous(X0) [resolution 114,98]
350. funny(X0) | generous(X0) <- (24, 26) [subsumption resolution 348,319]
374. ~rich(X3) | generous(X3) <- (24, 26) [resolution 350,103]
388. generous(john) <- (24, 26) [resolution 374,128]
389. ~patient(john) <- (1, 24, 26) [resolution 388,134]
390. $false <- (1, 24, 26, 32) [subsumption resolution 389,318]
391. ~1 | ~24 | ~26 | ~32 [avatar contradiction clause 390]
392. $false [avatar sat refutation 139,245,246,262,298,306,309,391]
% SZS output end Proof for 4052885499649280836382928
% ------------------------------
% 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 someone is either kind or brave then someone is old or not brave. If someone is either strong or not quiet then alice is either strong or not rich and vice versa. Everyone who is not funny or not rich is both not rich and happy. Everyone who is patient is not generous or calm. Everyone who is wise or tall is both not wise and not calm. Everyone who is either old or brave is both wise and not wise. Everyone who is either generous or strong is both kind and creative. If paul is not strong then someone is not quiet or not wise. If someone is not brave or not quiet then alice is either not curious or not strong and vice versa. If mary is patient then lucy is kind. Everyone who is quiet or calm is wise or not quiet. If someone is either not calm or not humble then someone is either not funny or not patient and vice versa. Everyone who is not kind is wise or generous. If someone is either patient or not strong then someone is either not funny or calm and vice versa. Everyone who is both kind and not wise is both happy and not generous. If lucy is not curious or happy then paul is not humble or not patient and vice versa. Someone is not patient. Paul is curious. Someone is not generous or generous. Mary is not calm or not quiet. Mary is either wise or kind. Someone is not curious. Paul is either not happy or not wise. | Lucy is happy. | neutral | ((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>((strong(alice)<~>~rich(alice))))&
(![X]:((~funny(X)|~rich(X))=>(~rich(X)&happy(X))))&
(![X]:(patient(X)=>(~generous(X)|calm(X))))&
(![X]:((wise(X)|tall(X))=>(~wise(X)&~calm(X))))&
(![X]:((old(X)<~>brave(X))=>(wise(X)&~wise(X))))&
(![X]:((generous(X)<~>strong(X))=>(kind(X)&creative(X))))&
((~strong(paul))=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((~brave(X)|~quiet(X))))<=>((~curious(alice)<~>~strong(alice))))&
((patient(mary))=>(kind(lucy)))&
(![X]:((quiet(X)|calm(X))=>(wise(X)|~quiet(X))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:(~kind(X)=>(wise(X)|generous(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((kind(X)&~wise(X))=>(happy(X)&~generous(X))))&
(((~curious(lucy)|happy(lucy)))<=>((~humble(paul)|~patient(paul))))&
(?[X]:(~patient(X)))&
(curious(paul))&
(?[X]:((~generous(X)|generous(X))))&
((~calm(mary)|~quiet(mary)))&
((wise(mary)<~>kind(mary)))&
(?[X]:(~curious(X)))&
((~happy(paul)<~>~wise(paul))) | happy(lucy) | [] | null | 0 |
Everyone who is both not strong and not tall is either not patient or not creative.
Everyone who is either curious or not humble is both happy and generous and vice versa.
If mary is both not generous and old then someone is both old and tall.
Everyone who is both funny and not quiet is both not tall and wise and vice versa.
If lucy is not generous then someone is strong and vice versa.
Everyone who is not generous or not humble is either not calm or not tall and vice versa.
Everyone who is both not funny and not patient is humble and vice versa.
Everyone who is both not quiet and not rich is generous and vice versa.
Everyone who is wise is both not wise and rich.
If fred is either not wise or not creative then someone is not tall or wise and vice versa.
Everyone who is happy or not kind is either rich or not tall.
If mary is both creative and not creative then someone is either curious or not patient.
Everyone who is both tall and wise is either brave or creative and vice versa.
Everyone who is both not happy and not kind is not kind and vice versa.
If fred is both not tall and not strong then john is not brave or funny.
Everyone who is not curious or old is either wise or brave.
Alice is creative or old.
Someone is not tall or patient.
Someone is tall.
Lucy is funny.
Someone is happy or not tall.
Susan is not strong or not old.
Someone is both not happy and kind. | Lucy is not wise. | entailment | (![X]:((~strong(X)&~tall(X))=>(~patient(X)<~>~creative(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(happy(X)&generous(X))))&
(((~generous(mary)&old(mary)))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((funny(X)&~quiet(X))<=>(~tall(X)&wise(X))))&
((~generous(lucy))<=>(?[X]:(strong(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((~funny(X)&~patient(X))<=>humble(X)))&
(![X]:((~quiet(X)&~rich(X))<=>generous(X)))&
(![X]:(wise(X)=>(~wise(X)&rich(X))))&
(((~wise(fred)<~>~creative(fred)))<=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((happy(X)|~kind(X))=>(rich(X)<~>~tall(X))))&
(((creative(mary)&~creative(mary)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((tall(X)&wise(X))<=>(brave(X)<~>creative(X))))&
(![X]:((~happy(X)&~kind(X))<=>~kind(X)))&
(((~tall(fred)&~strong(fred)))=>((~brave(john)|funny(john))))&
(![X]:((~curious(X)|old(X))=>(wise(X)<~>brave(X))))&
((creative(alice)|old(alice)))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:(tall(X)))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~wise(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8780184342038948817236153
% SZS output start Proof for 8780184342038948817236153
9. ! [X0] : (wise(X0) => (rich(X0) & ~wise(X0))) [input p8]
24. wise(lucy) [input hypothesis]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | ~wise(X0)) [ennf transformation 9]
102. ~wise(X0) | ~wise(X0) [cnf transformation 29]
138. wise(lucy) [cnf transformation 24]
139. ~wise(X0) [duplicate literal removal 102]
244. $false [subsumption resolution 138,139]
% SZS output end Proof for 8780184342038948817236153
% ------------------------------
% 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 funny or not calm is humble or old and vice versa. If someone is wise or tall then someone is either not wise or not rich and vice versa. Everyone who is wise is not curious and vice versa. Everyone who is both not wise and not rich is not wise or not rich and vice versa. Everyone who is not wise or not generous is curious. Everyone who is either old or not kind is both quiet and not wise and vice versa. If someone is not happy then someone is either not creative or calm and vice versa. If someone is humble or not curious then susan is old and vice versa. Everyone who is either happy or not rich is brave. Everyone who is happy or not tall is either rich or brave and vice versa. Everyone who is either not quiet or not kind is both strong and brave. Everyone who is either quiet or old is either not happy or not calm and vice versa. If lucy is wise then someone is not old. If someone is both not humble and not calm then someone is both old and tall. If someone is quiet or generous then someone is either not calm or humble and vice versa. If someone is either calm or not old then someone is strong. Someone is either not tall or not generous. Someone is not quiet or not creative. Alice is not creative or quiet. Fred is both not humble and not wise. Someone is either brave or not kind. Someone is either generous or calm. John is tall or not rich. | Alice is quiet. | neutral | (![X]:((funny(X)|~calm(X))<=>(humble(X)|old(X))))&
((?[X]:((wise(X)|tall(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~wise(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~wise(X)|~generous(X))=>curious(X)))&
(![X]:((old(X)<~>~kind(X))<=>(quiet(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
((?[X]:((humble(X)|~curious(X))))<=>(old(susan)))&
(![X]:((happy(X)<~>~rich(X))=>brave(X)))&
(![X]:((happy(X)|~tall(X))<=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(strong(X)&brave(X))))&
(![X]:((quiet(X)<~>old(X))<=>(~happy(X)<~>~calm(X))))&
((wise(lucy))=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&~calm(X))))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:(strong(X))))&
(?[X]:((~tall(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
((~creative(alice)|quiet(alice)))&
((~humble(fred)&~wise(fred)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>calm(X))))&
((tall(john)|~rich(john))) | quiet(alice) | [] | null | 0 |
If someone is both not curious and rich then someone is not rich or generous and vice versa. If mary is not strong or not humble then someone is both not funny and not tall. Everyone who is both not creative and not humble is both not creative and creative and vice versa. Everyone who is both strong and creative is both not strong and not generous and vice versa. Everyone who is curious or not kind is not creative or not wise and vice versa. Everyone who is not curious is patient or not curious and vice versa. Everyone who is either humble or not funny is not humble and vice versa. Everyone who is either wise or quiet is tall or not brave and vice versa. If someone is either not calm or humble then lucy is funny or curious and vice versa. If susan is rich or strong then someone is either kind or not curious. Everyone who is both not tall and not strong is not wise or quiet and vice versa. Everyone who is not patient is either not funny or not brave and vice versa. If susan is either strong or kind then someone is brave and vice versa. Everyone who is both funny and not strong is old or humble. Everyone who is not tall or not kind is either strong or brave and vice versa. Mary is either not calm or creative. Someone is not kind. Someone is rich. Mary is not rich or brave. Mary is either not humble or happy. Someone is tall or not brave. Susan is not patient or not strong. John is not curious or strong. | Mary is wise. | neutral | ((?[X]:((~curious(X)&rich(X))))<=>(?[X]:((~rich(X)|generous(X)))))&
(((~strong(mary)|~humble(mary)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:((~creative(X)&~humble(X))<=>(~creative(X)&creative(X))))&
(![X]:((strong(X)&creative(X))<=>(~strong(X)&~generous(X))))&
(![X]:((curious(X)|~kind(X))<=>(~creative(X)|~wise(X))))&
(![X]:(~curious(X)<=>(patient(X)|~curious(X))))&
(![X]:((humble(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(tall(X)|~brave(X))))&
((?[X]:((~calm(X)<~>humble(X))))<=>((funny(lucy)|curious(lucy))))&
(((rich(susan)|strong(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)&~strong(X))<=>(~wise(X)|quiet(X))))&
(![X]:(~patient(X)<=>(~funny(X)<~>~brave(X))))&
(((strong(susan)<~>kind(susan)))<=>(?[X]:(brave(X))))&
(![X]:((funny(X)&~strong(X))=>(old(X)|humble(X))))&
(![X]:((~tall(X)|~kind(X))<=>(strong(X)<~>brave(X))))&
((~calm(mary)<~>creative(mary)))&
(?[X]:(~kind(X)))&
(?[X]:(rich(X)))&
((~rich(mary)|brave(mary)))&
((~humble(mary)<~>happy(mary)))&
(?[X]:((tall(X)|~brave(X))))&
((~patient(susan)|~strong(susan)))&
((~curious(john)|strong(john))) | wise(mary) | [] | null | 0 |
If someone is not strong or tall then someone is not wise or curious.
Everyone who is either not wise or patient is strong and vice versa.
If someone is not tall then alice is either creative or not old and vice versa.
If someone is not creative then susan is both not kind and rich.
If someone is not tall or not curious then someone is not kind or funny.
If someone is not generous or happy then fred is funny.
Everyone who is strong or calm is both happy and old.
Everyone who is old is strong and vice versa.
Everyone who is both not brave and not curious is both strong and happy and vice versa.
Everyone who is both not humble and tall is both not kind and not humble.
Everyone who is not strong is patient or not curious.
Everyone who is not calm or not curious is both not humble and brave.
Everyone who is old is both not rich and not tall.
Everyone who is either old or not generous is either tall or curious and vice versa.
If someone is either not happy or old then lucy is either not generous or patient.
Everyone who is wise or not brave is either patient or quiet and vice versa.
Someone is both kind and not generous.
Someone is either generous or rich.
Someone is either generous or brave.
John is either not funny or happy. | Fred is quiet. | entailment | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>strong(X)))&
((?[X]:(~tall(X)))<=>((creative(alice)<~>~old(alice))))&
((?[X]:(~creative(X)))=>((~kind(susan)&rich(susan))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((~generous(X)|happy(X))))=>(funny(fred)))&
(![X]:((strong(X)|calm(X))=>(happy(X)&old(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)&happy(X))))&
(![X]:((~humble(X)&tall(X))=>(~kind(X)&~humble(X))))&
(![X]:(~strong(X)=>(patient(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~humble(X)&brave(X))))&
(![X]:(old(X)=>(~rich(X)&~tall(X))))&
(![X]:((old(X)<~>~generous(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>old(X))))=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((wise(X)|~brave(X))<=>(patient(X)<~>quiet(X))))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((~funny(john)<~>happy(john))) | quiet(fred) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2831713165395323253104639
% SZS output start Proof for 2831713165395323253104639
2. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> strong(X0)) [input p1]
7. ! [X0] : ((calm(X0) | strong(X0)) => (old(X0) & happy(X0))) [input p6]
8. ! [X0] : (old(X0) <=> strong(X0)) [input p7]
9. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (happy(X0) & strong(X0))) [input p8]
12. ! [X0] : ((~curious(X0) | ~calm(X0)) => (brave(X0) & ~humble(X0))) [input p11]
16. ! [X0] : ((~brave(X0) | wise(X0)) <=> (patient(X0) <~> quiet(X0))) [input p15]
21. ~quiet(fred) [input hypothesis]
28. ! [X0] : ((old(X0) & happy(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 7]
33. ! [X0] : ((brave(X0) & ~humble(X0)) | (curious(X0) & calm(X0))) [ennf transformation 12]
39. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 2]
47. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 8]
48. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((~curious(X0) & ~brave(X0)) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | curious(X0) | brave(X0))) [flattening 48]
52. ! [X0] : (((~brave(X0) | wise(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 16]
53. ! [X0] : ((~brave(X0) | wise(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [flattening 52]
65. patient(X0) | strong(X0) | wise(X0) [cnf transformation 39]
66. ~patient(X0) | ~wise(X0) | strong(X0) [cnf transformation 39]
79. ~strong(X0) | happy(X0) [cnf transformation 28]
82. ~calm(X0) | old(X0) [cnf transformation 28]
83. ~old(X0) | strong(X0) [cnf transformation 47]
87. ~brave(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
88. ~curious(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
94. brave(X0) | calm(X0) [cnf transformation 33]
95. brave(X0) | curious(X0) [cnf transformation 33]
110. ~wise(X0) | patient(X0) | quiet(X0) [cnf transformation 53]
114. ~brave(X0) | wise(X0) | quiet(X0) | ~patient(X0) [cnf transformation 53]
124. ~quiet(fred) [cnf transformation 21]
198. ~curious(X0) | ~strong(X0) [subsumption resolution 88,79]
199. ~brave(X0) | ~strong(X0) [subsumption resolution 87,79]
268. ~strong(X0) | curious(X0) [resolution 199,95]
271. ~strong(X0) [subsumption resolution 268,198]
295. 28 <=> brave(fred) [avatar definition]
296. ~brave(fred) <- (~28) [avatar component clause 295]
297. brave(fred) <- (28) [avatar component clause 295]
299. 29 <=> patient(fred) [avatar definition]
300. ~patient(fred) <- (~29) [avatar component clause 299]
301. patient(fred) <- (29) [avatar component clause 299]
417. wise(fred) | quiet(fred) | ~patient(fred) <- (28) [resolution 114,297]
432. wise(fred) | ~patient(fred) <- (28) [subsumption resolution 417,124]
434. 46 <=> wise(fred) [avatar definition]
436. wise(fred) <- (46) [avatar component clause 434]
437. ~29 | 46 | ~28 [avatar split clause 432,295,434,299]
438. strong(fred) | wise(fred) <- (~29) [resolution 300,65]
439. wise(fred) <- (~29) [subsumption resolution 438,271]
440. 46 | 29 [avatar split clause 439,299,434]
466. patient(fred) | quiet(fred) <- (46) [resolution 436,110]
471. patient(fred) <- (46) [subsumption resolution 466,124]
472. 29 | ~46 [avatar split clause 471,434,299]
475. ~wise(fred) | strong(fred) <- (29) [resolution 301,66]
479. ~wise(fred) <- (29) [subsumption resolution 475,271]
480. ~46 | ~29 [avatar split clause 479,299,434]
484. calm(fred) <- (~28) [resolution 296,94]
514. old(fred) <- (~28) [resolution 484,82]
537. strong(fred) <- (~28) [resolution 514,83]
540. $false <- (~28) [subsumption resolution 537,271]
541. 28 [avatar contradiction clause 540]
542. $false [avatar sat refutation 437,440,472,480,541]
% SZS output end Proof for 2831713165395323253104639
% ------------------------------
% 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 either wise or not wise is either not rich or funny and vice versa.
Everyone who is both not old and old is not kind and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
If mary is not kind or happy then lucy is either not creative or quiet.
If someone is both not strong and not old then someone is both curious and not funny.
Everyone who is either not strong or not creative is both not tall and creative.
If mary is either not funny or not rich then someone is funny.
Everyone who is curious is either not creative or curious and vice versa.
If john is not curious or not wise then someone is either old or not funny.
If someone is both not patient and not calm then mary is curious or patient.
If someone is not strong then someone is both old and strong and vice versa.
Everyone who is either creative or kind is both creative and quiet and vice versa.
Everyone who is either not curious or wise is both happy and not funny and vice versa.
Everyone who is patient is both brave and not strong.
Everyone who is both strong and not happy is either generous or tall and vice versa.
Everyone who is happy or not calm is both brave and curious.
Someone is either not rich or calm.
Someone is kind.
Someone is not humble.
Someone is either quiet or generous.
Fred is old.
Paul is both not strong and curious. | Paul is not curious. | contradiction | (![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~old(X)&old(X))<=>~kind(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(((~kind(mary)|happy(mary)))=>((~creative(lucy)<~>quiet(lucy))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~tall(X)&creative(X))))&
(((~funny(mary)<~>~rich(mary)))=>(?[X]:(funny(X))))&
(![X]:(curious(X)<=>(~creative(X)<~>curious(X))))&
(((~curious(john)|~wise(john)))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~calm(X))))=>((curious(mary)|patient(mary))))&
((?[X]:(~strong(X)))<=>(?[X]:((old(X)&strong(X)))))&
(![X]:((creative(X)<~>kind(X))<=>(creative(X)&quiet(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(happy(X)&~funny(X))))&
(![X]:(patient(X)=>(brave(X)&~strong(X))))&
(![X]:((strong(X)&~happy(X))<=>(generous(X)<~>tall(X))))&
(![X]:((happy(X)|~calm(X))=>(brave(X)&curious(X))))&
(?[X]:((~rich(X)<~>calm(X))))&
(?[X]:(kind(X)))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)<~>generous(X))))&
(old(fred))&
((~strong(paul)&curious(paul))) | ~curious(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3951685727275501661311069
% SZS output start Proof for 3951685727275501661311069
22. curious(paul) & ~strong(paul) [input p21]
23. ~curious(paul) [input hypothesis]
141. curious(paul) [cnf transformation 22]
142. ~curious(paul) [cnf transformation 23]
250. $false [subsumption resolution 142,141]
% SZS output end Proof for 3951685727275501661311069
% ------------------------------
% 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 brave and strong is both not old and not strong and vice versa. Everyone who is not curious or generous is both rich and not generous and vice versa. Everyone who is either not curious or not calm is either not kind or not funny. If someone is both creative and not calm then fred is old. Everyone who is generous is both not kind and rich and vice versa. Everyone who is not quiet or not generous is both calm and not old. If someone is not humble or not strong then someone is not happy and vice versa. If alice is happy then someone is both not rich and not quiet. Everyone who is creative or brave is wise or not brave. If alice is not rich or not wise then someone is either not generous or not rich. If someone is either not old or generous then someone is both not old and not quiet and vice versa. If someone is not humble or strong then lucy is creative and vice versa. Everyone who is not generous is rich and vice versa. If someone is both rich and kind then fred is both quiet and not curious. If paul is not happy or kind then fred is either not quiet or not happy. Someone is creative or not calm. John is either old or patient. John is strong. Someone is creative. Someone is not quiet. | John is not humble. | neutral | (![X]:((brave(X)&strong(X))<=>(~old(X)&~strong(X))))&
(![X]:((~curious(X)|generous(X))<=>(rich(X)&~generous(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>(old(fred)))&
(![X]:(generous(X)<=>(~kind(X)&rich(X))))&
(![X]:((~quiet(X)|~generous(X))=>(calm(X)&~old(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:(~happy(X))))&
((happy(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>(wise(X)|~brave(X))))&
(((~rich(alice)|~wise(alice)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
((?[X]:((~old(X)<~>generous(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
((?[X]:((~humble(X)|strong(X))))<=>(creative(lucy)))&
(![X]:(~generous(X)<=>rich(X)))&
((?[X]:((rich(X)&kind(X))))=>((quiet(fred)&~curious(fred))))&
(((~happy(paul)|kind(paul)))=>((~quiet(fred)<~>~happy(fred))))&
(?[X]:((creative(X)|~calm(X))))&
((old(john)<~>patient(john)))&
(strong(john))&
(?[X]:(creative(X)))&
(?[X]:(~quiet(X))) | ~humble(john) | [] | null | 0 |
Everyone who is not quiet or humble is calm or not humble.
Everyone who is either not wise or not calm is both kind and not generous.
If someone is rich or brave then someone is not happy.
If someone is both calm and brave then someone is wise.
If mary is not curious or not patient then someone is not brave or funny.
If lucy is both brave and not generous then someone is creative or not curious and vice versa.
Everyone who is not patient or not quiet is either not humble or wise and vice versa.
Everyone who is patient is both generous and strong and vice versa.
If mary is both not calm and rich then fred is funny or not wise.
If john is either strong or not curious then someone is not old or brave.
Everyone who is not strong or not creative is either not creative or quiet and vice versa.
Everyone who is either tall or not old is either calm or quiet.
Everyone who is either not funny or wise is both not old and not humble and vice versa.
If someone is quiet then paul is not humble and vice versa.
If paul is both not creative and calm then someone is both not curious and not quiet and vice versa.
Everyone who is not funny or not generous is generous or happy and vice versa.
Paul is both not creative and not strong.
John is tall.
Lucy is brave or patient.
Susan is either not calm or funny.
Someone is funny.
Someone is wise.
Someone is happy or old.
Alice is either not happy or not old. | Lucy is brave. | entailment | (![X]:((~quiet(X)|humble(X))=>(calm(X)|~humble(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(kind(X)&~generous(X))))&
((?[X]:((rich(X)|brave(X))))=>(?[X]:(~happy(X))))&
((?[X]:((calm(X)&brave(X))))=>(?[X]:(wise(X))))&
(((~curious(mary)|~patient(mary)))=>(?[X]:((~brave(X)|funny(X)))))&
(((brave(lucy)&~generous(lucy)))<=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(~humble(X)<~>wise(X))))&
(![X]:(patient(X)<=>(generous(X)&strong(X))))&
(((~calm(mary)&rich(mary)))=>((funny(fred)|~wise(fred))))&
(((strong(john)<~>~curious(john)))=>(?[X]:((~old(X)|brave(X)))))&
(![X]:((~strong(X)|~creative(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~old(X))=>(calm(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(~old(X)&~humble(X))))&
((?[X]:(quiet(X)))<=>(~humble(paul)))&
(((~creative(paul)&calm(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((~funny(X)|~generous(X))<=>(generous(X)|happy(X))))&
((~creative(paul)&~strong(paul)))&
(tall(john))&
((brave(lucy)|patient(lucy)))&
((~calm(susan)<~>funny(susan)))&
(?[X]:(funny(X)))&
(?[X]:(wise(X)))&
(?[X]:((happy(X)|old(X))))&
((~happy(alice)<~>~old(alice))) | brave(lucy) | [
"p0",
"p5",
"p10",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7982548920583804729527432
% SZS output start Proof for 7982548920583804729527432
1. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~humble(X0) | calm(X0))) [input p0]
6. (~generous(lucy) & brave(lucy)) <=> ? [X0] : (~curious(X0) | creative(X0)) [input p5]
11. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (~creative(X0) <~> quiet(X0))) [input p10]
14. ? [X0] : quiet(X0) <=> ~humble(paul) [input p13]
15. (calm(paul) & ~creative(paul)) <=> ? [X0] : (~quiet(X0) & ~curious(X0)) [input p14]
17. ~strong(paul) & ~creative(paul) [input p16]
25. ~brave(lucy) [input hypothesis]
31. ! [X0] : ((~humble(X0) | calm(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 1]
32. ! [X0] : (~humble(X0) | calm(X0) | (~humble(X0) & quiet(X0))) [flattening 31]
48. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X0] : (~curious(X0) | creative(X0)) | (generous(lucy) | ~brave(lucy))) [nnf transformation 6]
49. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X0] : (~curious(X0) | creative(X0)) | generous(lucy) | ~brave(lucy)) [flattening 48]
50. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & (? [X1] : (~curious(X1) | creative(X1)) | generous(lucy) | ~brave(lucy)) [rectify 49]
51. ? [X1] : (~curious(X1) | creative(X1)) => (~curious(sK3) | creative(sK3)) [choice axiom]
52. ((~generous(lucy) & brave(lucy)) | ! [X0] : (curious(X0) & ~creative(X0))) & ((~curious(sK3) | creative(sK3)) | generous(lucy) | ~brave(lucy)) [skolemisation 50,51]
60. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 11]
61. ! [X0] : ((~creative(X0) | ~strong(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | (creative(X0) & strong(X0)))) [flattening 60]
65. (? [X0] : quiet(X0) | humble(paul)) & (~humble(paul) | ! [X0] : ~quiet(X0)) [nnf transformation 14]
66. (? [X0] : quiet(X0) | humble(paul)) & (~humble(paul) | ! [X1] : ~quiet(X1)) [rectify 65]
67. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
68. (quiet(sK5) | humble(paul)) & (~humble(paul) | ! [X1] : ~quiet(X1)) [skolemisation 66,67]
69. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X0] : (~quiet(X0) & ~curious(X0)) | (~calm(paul) | creative(paul))) [nnf transformation 15]
70. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X0] : (~quiet(X0) & ~curious(X0)) | ~calm(paul) | creative(paul)) [flattening 69]
71. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & (? [X1] : (~quiet(X1) & ~curious(X1)) | ~calm(paul) | creative(paul)) [rectify 70]
72. ? [X1] : (~quiet(X1) & ~curious(X1)) => (~quiet(sK6) & ~curious(sK6)) [choice axiom]
73. ((calm(paul) & ~creative(paul)) | ! [X0] : (quiet(X0) | curious(X0))) & ((~quiet(sK6) & ~curious(sK6)) | ~calm(paul) | creative(paul)) [skolemisation 71,72]
85. ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 32]
93. brave(lucy) | ~creative(X0) [cnf transformation 52]
94. brave(lucy) | curious(X0) [cnf transformation 52]
111. ~quiet(X0) | creative(X0) | creative(X0) [cnf transformation 61]
125. quiet(sK5) | humble(paul) [cnf transformation 68]
126. ~curious(sK6) | ~calm(paul) | creative(paul) [cnf transformation 73]
134. ~creative(paul) [cnf transformation 17]
145. ~brave(lucy) [cnf transformation 25]
148. ~quiet(X0) | creative(X0) [duplicate literal removal 111]
150. ~humble(X0) | calm(X0) [duplicate literal removal 85]
186. 9 <=> ! [X0] : curious(X0) [avatar definition]
187. curious(X0) <- (9) [avatar component clause 186]
194. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
195. ~creative(X0) <- (11) [avatar component clause 194]
198. 12 <=> brave(lucy) [avatar definition]
201. 9 | 12 [avatar split clause 94,198,186]
202. 11 | 12 [avatar split clause 93,198,194]
231. 19 <=> humble(paul) [avatar definition]
233. humble(paul) <- (19) [avatar component clause 231]
235. 20 <=> quiet(sK5) [avatar definition]
237. quiet(sK5) <- (20) [avatar component clause 235]
238. 19 | 20 [avatar split clause 125,235,231]
247. 23 <=> calm(paul) [avatar definition]
252. 24 <=> creative(paul) [avatar definition]
262. 26 <=> curious(sK6) [avatar definition]
264. ~curious(sK6) <- (~26) [avatar component clause 262]
265. 24 | ~23 | ~26 [avatar split clause 126,262,247,252]
266. ~24 [avatar split clause 134,252]
301. ~12 [avatar split clause 145,198]
307. creative(sK5) <- (20) [resolution 148,237]
308. $false <- (11, 20) [subsumption resolution 307,195]
309. ~11 | ~20 [avatar contradiction clause 308]
310. calm(paul) <- (19) [resolution 150,233]
313. 23 | ~19 [avatar split clause 310,231,247]
314. $false <- (9, ~26) [subsumption resolution 264,187]
315. ~9 | 26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 201,202,238,265,266,301,309,313,315]
% SZS output end Proof for 7982548920583804729527432
% ------------------------------
% 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 old or patient is either not creative or not tall and vice versa. Everyone who is not humble or not happy is old. Everyone who is both not kind and not humble is not creative and vice versa. If someone is either not patient or not rich then someone is not patient or not tall. Everyone who is not rich is both not creative and happy and vice versa. If mary is old then paul is not wise or not happy. Everyone who is not humble or old is both old and not rich and vice versa. Everyone who is curious or tall is either humble or not patient and vice versa. If fred is either calm or not funny then john is either not quiet or old and vice versa. If someone is not old or not quiet then mary is both not funny and not curious and vice versa. Everyone who is tall or wise is both humble and patient and vice versa. Everyone who is not funny or not wise is funny. Everyone who is both humble and funny is not happy or creative and vice versa. If someone is both wise and humble then susan is both quiet and not calm and vice versa. If mary is either funny or creative then someone is both not rich and not brave. If lucy is both not calm and brave then someone is both not brave and rich. Someone is curious or strong. Susan is either brave or not generous. Someone is either funny or patient. | Fred is curious. | entailment | (![X]:((~old(X)|patient(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~humble(X)|~happy(X))=>old(X)))&
(![X]:((~kind(X)&~humble(X))<=>~creative(X)))&
((?[X]:((~patient(X)<~>~rich(X))))=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:(~rich(X)<=>(~creative(X)&happy(X))))&
((old(mary))=>((~wise(paul)|~happy(paul))))&
(![X]:((~humble(X)|old(X))<=>(old(X)&~rich(X))))&
(![X]:((curious(X)|tall(X))<=>(humble(X)<~>~patient(X))))&
(((calm(fred)<~>~funny(fred)))<=>((~quiet(john)<~>old(john))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~funny(mary)&~curious(mary))))&
(![X]:((tall(X)|wise(X))<=>(humble(X)&patient(X))))&
(![X]:((~funny(X)|~wise(X))=>funny(X)))&
(![X]:((humble(X)&funny(X))<=>(~happy(X)|creative(X))))&
((?[X]:((wise(X)&humble(X))))<=>((quiet(susan)&~calm(susan))))&
(((funny(mary)<~>creative(mary)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((~calm(lucy)&brave(lucy)))=>(?[X]:((~brave(X)&rich(X)))))&
(?[X]:((curious(X)|strong(X))))&
((brave(susan)<~>~generous(susan)))&
(?[X]:((funny(X)<~>patient(X)))) | curious(fred) | [
"p0",
"p2",
"p7",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 903832005471396524883782
% SZS output start Proof for 903832005471396524883782
1. ! [X0] : ((patient(X0) | ~old(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p0]
3. ! [X0] : ((~humble(X0) & ~kind(X0)) <=> ~creative(X0)) [input p2]
8. ! [X0] : ((tall(X0) | curious(X0)) <=> (humble(X0) <~> ~patient(X0))) [input p7]
10. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (~curious(mary) & ~funny(mary)) [input p9]
11. ! [X0] : ((wise(X0) | tall(X0)) <=> (patient(X0) & humble(X0))) [input p10]
12. ! [X0] : ((~wise(X0) | ~funny(X0)) => funny(X0)) [input p11]
13. ! [X0] : ((funny(X0) & humble(X0)) <=> (creative(X0) | ~happy(X0))) [input p12]
20. ~curious(fred) [input hypothesis]
27. ! [X0] : (funny(X0) | (wise(X0) & funny(X0))) [ennf transformation 12]
31. ! [X0] : (((patient(X0) | ~old(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (~patient(X0) & old(X0)))) [nnf transformation 1]
32. ! [X0] : ((patient(X0) | ~old(X0) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (~patient(X0) & old(X0)))) [flattening 31]
33. ! [X0] : (((~humble(X0) & ~kind(X0)) | creative(X0)) & (~creative(X0) | (humble(X0) | kind(X0)))) [nnf transformation 3]
34. ! [X0] : (((~humble(X0) & ~kind(X0)) | creative(X0)) & (~creative(X0) | humble(X0) | kind(X0))) [flattening 33]
43. ! [X0] : (((tall(X0) | curious(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~tall(X0) & ~curious(X0)))) [nnf transformation 8]
44. ! [X0] : ((tall(X0) | curious(X0) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~tall(X0) & ~curious(X0)))) [flattening 43]
46. (? [X0] : (~quiet(X0) | ~old(X0)) | (curious(mary) | funny(mary))) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 10]
47. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 46]
48. (? [X0] : (~quiet(X0) | ~old(X0)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 47]
49. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK1) | ~old(sK1)) [choice axiom]
50. ((~quiet(sK1) | ~old(sK1)) | curious(mary) | funny(mary)) & ((~curious(mary) & ~funny(mary)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 48,49]
51. ! [X0] : (((wise(X0) | tall(X0)) | (~patient(X0) | ~humble(X0))) & ((patient(X0) & humble(X0)) | (~wise(X0) & ~tall(X0)))) [nnf transformation 11]
52. ! [X0] : ((wise(X0) | tall(X0) | ~patient(X0) | ~humble(X0)) & ((patient(X0) & humble(X0)) | (~wise(X0) & ~tall(X0)))) [flattening 51]
53. ! [X0] : (((funny(X0) & humble(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~funny(X0) | ~humble(X0)))) [nnf transformation 13]
54. ! [X0] : (((funny(X0) & humble(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~funny(X0) | ~humble(X0))) [flattening 53]
70. ~tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 32]
72. ~patient(X0) | creative(X0) | tall(X0) [cnf transformation 32]
74. ~creative(X0) | ~old(X0) | patient(X0) | tall(X0) [cnf transformation 32]
79. ~humble(X0) | creative(X0) [cnf transformation 34]
95. ~humble(X0) | curious(X0) | ~patient(X0) | tall(X0) [cnf transformation 44]
96. curious(X0) | tall(X0) | humble(X0) | patient(X0) [cnf transformation 44]
105. ~funny(mary) | old(X1) [cnf transformation 50]
110. ~tall(X0) | humble(X0) [cnf transformation 52]
112. ~tall(X0) | patient(X0) [cnf transformation 52]
115. funny(X0) | funny(X0) [cnf transformation 27]
119. ~creative(X0) | humble(X0) [cnf transformation 54]
136. ~curious(fred) [cnf transformation 20]
137. funny(X0) [duplicate literal removal 115]
192. 12 <=> funny(mary) [avatar definition]
193. ~funny(mary) <- (~12) [avatar component clause 192]
213. 17 <=> ! [X1] : old(X1) [avatar definition]
214. old(X1) <- (17) [avatar component clause 213]
217. 17 | ~12 [avatar split clause 105,192,213]
288. $false <- (~12) [subsumption resolution 193,137]
289. 12 [avatar contradiction clause 288]
323. tall(fred) | humble(fred) | patient(fred) [resolution 96,136]
329. humble(fred) | patient(fred) [subsumption resolution 323,110]
331. 32 <=> patient(fred) [avatar definition]
332. ~patient(fred) <- (~32) [avatar component clause 331]
333. patient(fred) <- (32) [avatar component clause 331]
335. 33 <=> humble(fred) [avatar definition]
337. humble(fred) <- (33) [avatar component clause 335]
338. 32 | 33 [avatar split clause 329,335,331]
350. creative(fred) | tall(fred) <- (32) [resolution 333,72]
352. 36 <=> tall(fred) [avatar definition]
353. ~tall(fred) <- (~36) [avatar component clause 352]
354. tall(fred) <- (36) [avatar component clause 352]
356. 37 <=> creative(fred) [avatar definition]
358. creative(fred) <- (37) [avatar component clause 356]
359. 36 | 37 | ~32 [avatar split clause 350,331,356,352]
380. humble(fred) <- (37) [resolution 358,119]
387. 33 | ~37 [avatar split clause 380,356,335]
389. curious(fred) | ~patient(fred) | tall(fred) <- (33) [resolution 337,95]
395. ~patient(fred) | tall(fred) <- (33) [subsumption resolution 389,136]
396. tall(fred) <- (32, 33) [subsumption resolution 395,333]
397. 36 | ~32 | ~33 [avatar split clause 396,335,331,352]
400. ~creative(fred) | ~patient(fred) <- (36) [resolution 354,70]
402. patient(fred) <- (36) [resolution 354,112]
403. humble(fred) <- (36) [resolution 354,110]
406. 33 | ~36 [avatar split clause 403,352,335]
410. creative(fred) <- (33) [resolution 337,79]
413. 37 | ~33 [avatar split clause 410,335,356]
416. ~patient(fred) <- (36, 37) [subsumption resolution 400,358]
417. ~32 | ~36 | ~37 [avatar split clause 416,356,352,331]
418. 32 | ~36 [avatar split clause 402,352,331]
420. ~old(fred) | patient(fred) | tall(fred) <- (37) [resolution 358,74]
424. patient(fred) | tall(fred) <- (17, 37) [subsumption resolution 420,214]
425. tall(fred) <- (17, ~32, 37) [subsumption resolution 424,332]
426. $false <- (17, ~32, ~36, 37) [subsumption resolution 425,353]
427. ~17 | 32 | 36 | ~37 [avatar contradiction clause 426]
428. $false [avatar sat refutation 217,289,338,359,387,397,406,413,417,418,427]
% SZS output end Proof for 903832005471396524883782
% ------------------------------
% 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 |
If someone is funny then mary is both not strong and tall and vice versa.
If mary is either not rich or not funny then someone is either not wise or not humble and vice versa.
If john is either not tall or old then mary is not wise.
Everyone who is both tall and curious is tall.
Everyone who is not rich or calm is both not quiet and not patient and vice versa.
If john is either creative or not kind then alice is both not curious and not funny.
Everyone who is not old is both not generous and wise and vice versa.
If someone is funny then someone is patient or not wise.
If someone is both calm and brave then someone is generous and vice versa.
Everyone who is either happy or kind is both generous and not creative and vice versa.
If someone is not creative then someone is both not humble and not calm and vice versa.
Everyone who is either calm or not creative is both creative and kind.
If lucy is not calm or creative then someone is both curious and kind and vice versa.
If someone is both not generous and curious then john is not generous and vice versa.
If paul is rich then john is not humble or not kind and vice versa.
If alice is either not strong or calm then mary is both strong and not kind.
Paul is old.
Alice is either quiet or strong.
Someone is either not curious or not happy.
Lucy is not strong.
Paul is both patient and humble.
Alice is both not strong and kind.
Someone is both strong and calm. | Paul is funny. | contradiction | ((?[X]:(funny(X)))<=>((~strong(mary)&tall(mary))))&
(((~rich(mary)<~>~funny(mary)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(((~tall(john)<~>old(john)))=>(~wise(mary)))&
(![X]:((tall(X)&curious(X))=>tall(X)))&
(![X]:((~rich(X)|calm(X))<=>(~quiet(X)&~patient(X))))&
(((creative(john)<~>~kind(john)))=>((~curious(alice)&~funny(alice))))&
(![X]:(~old(X)<=>(~generous(X)&wise(X))))&
((?[X]:(funny(X)))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:((calm(X)&brave(X))))<=>(?[X]:(generous(X))))&
(![X]:((happy(X)<~>kind(X))<=>(generous(X)&~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(creative(X)&kind(X))))&
(((~calm(lucy)|creative(lucy)))<=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:((~generous(X)&curious(X))))<=>(~generous(john)))&
((rich(paul))<=>((~humble(john)|~kind(john))))&
(((~strong(alice)<~>calm(alice)))=>((strong(mary)&~kind(mary))))&
(old(paul))&
((quiet(alice)<~>strong(alice)))&
(?[X]:((~curious(X)<~>~happy(X))))&
(~strong(lucy))&
((patient(paul)&humble(paul)))&
((~strong(alice)&kind(alice)))&
(?[X]:((strong(X)&calm(X)))) | funny(paul) | [
"p0",
"p4",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3572452951839677949982452
% SZS output start Proof for 3572452951839677949982452
1. ? [X0] : funny(X0) <=> (tall(mary) & ~strong(mary)) [input p0]
5. ! [X0] : ((calm(X0) | ~rich(X0)) <=> (~patient(X0) & ~quiet(X0))) [input p4]
16. (~strong(alice) <~> calm(alice)) => (~kind(mary) & strong(mary)) [input p15]
18. quiet(alice) <~> strong(alice) [input p17]
22. kind(alice) & ~strong(alice) [input p21]
24. funny(paul) [input hypothesis]
34. (~kind(mary) & strong(mary)) | (~strong(alice) <=> calm(alice)) [ennf transformation 16]
35. (? [X0] : funny(X0) | (~tall(mary) | strong(mary))) & ((tall(mary) & ~strong(mary)) | ! [X0] : ~funny(X0)) [nnf transformation 1]
36. (? [X0] : funny(X0) | ~tall(mary) | strong(mary)) & ((tall(mary) & ~strong(mary)) | ! [X0] : ~funny(X0)) [flattening 35]
37. (? [X0] : funny(X0) | ~tall(mary) | strong(mary)) & ((tall(mary) & ~strong(mary)) | ! [X1] : ~funny(X1)) [rectify 36]
38. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
39. (funny(sK0) | ~tall(mary) | strong(mary)) & ((tall(mary) & ~strong(mary)) | ! [X1] : ~funny(X1)) [skolemisation 37,38]
45. ! [X0] : (((calm(X0) | ~rich(X0)) | (patient(X0) | quiet(X0))) & ((~patient(X0) & ~quiet(X0)) | (~calm(X0) & rich(X0)))) [nnf transformation 5]
46. ! [X0] : ((calm(X0) | ~rich(X0) | patient(X0) | quiet(X0)) & ((~patient(X0) & ~quiet(X0)) | (~calm(X0) & rich(X0)))) [flattening 45]
77. (~kind(mary) & strong(mary)) | ((~strong(alice) | ~calm(alice)) & (calm(alice) | strong(alice))) [nnf transformation 34]
78. (~strong(alice) | ~quiet(alice)) & (strong(alice) | quiet(alice)) [nnf transformation 18]
84. ~strong(mary) | ~funny(X1) [cnf transformation 39]
99. ~quiet(X0) | ~calm(X0) [cnf transformation 46]
138. strong(mary) | calm(alice) | strong(alice) [cnf transformation 77]
143. strong(alice) | quiet(alice) [cnf transformation 78]
150. ~strong(alice) [cnf transformation 22]
154. funny(paul) [cnf transformation 24]
157. 1 <=> strong(mary) [avatar definition]
170. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
171. ~funny(X1) <- (4) [avatar component clause 170]
173. 4 | ~1 [avatar split clause 84,157,170]
344. 41 <=> calm(alice) [avatar definition]
348. 42 <=> strong(alice) [avatar definition]
358. 42 | 41 | 1 [avatar split clause 138,157,344,348]
360. 44 <=> quiet(alice) [avatar definition]
361. quiet(alice) <- (44) [avatar component clause 360]
364. 44 | 42 [avatar split clause 143,348,360]
375. ~42 [avatar split clause 150,348]
377. ~calm(alice) <- (44) [resolution 99,361]
380. ~41 | ~44 [avatar split clause 377,360,344]
381. $false <- (4) [resolution 171,154]
384. ~4 [avatar contradiction clause 381]
385. $false [avatar sat refutation 173,358,364,375,380,384]
% SZS output end Proof for 3572452951839677949982452
% ------------------------------
% 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is creative or brave.
If mary is strong then someone is not patient or happy.
Everyone who is not quiet or not curious is either not brave or curious and vice versa.
If someone is both curious and not generous then someone is both not humble and brave.
Everyone who is funny or not patient is either not kind or curious.
If mary is not quiet or patient then someone is either wise or not quiet and vice versa.
Everyone who is funny or humble is both not generous and not old and vice versa.
If someone is calm then someone is not patient or patient.
Everyone who is rich is not brave and vice versa.
Everyone who is not tall or humble is not rich or patient and vice versa.
If someone is not calm then susan is not creative.
Everyone who is not creative is either curious or kind and vice versa.
Everyone who is both not funny and rich is both not calm and humble.
Everyone who is rich is funny or not curious.
If someone is both brave and patient then susan is happy and vice versa.
Everyone who is both quiet and not humble is brave or curious.
Someone is not tall or kind.
Someone is not humble.
Someone is not happy.
Someone is calm.
Someone is not kind.
Someone is either happy or generous.
Someone is not curious.
Lucy is either not kind or not creative. | Susan is not old. | neutral | ((?[X]:(~generous(X)))=>(?[X]:((creative(X)|brave(X)))))&
((strong(mary))=>(?[X]:((~patient(X)|happy(X)))))&
(![X]:((~quiet(X)|~curious(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((funny(X)|~patient(X))=>(~kind(X)<~>curious(X))))&
(((~quiet(mary)|patient(mary)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((funny(X)|humble(X))<=>(~generous(X)&~old(X))))&
((?[X]:(calm(X)))=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((~tall(X)|humble(X))<=>(~rich(X)|patient(X))))&
((?[X]:(~calm(X)))=>(~creative(susan)))&
(![X]:(~creative(X)<=>(curious(X)<~>kind(X))))&
(![X]:((~funny(X)&rich(X))=>(~calm(X)&humble(X))))&
(![X]:(rich(X)=>(funny(X)|~curious(X))))&
((?[X]:((brave(X)&patient(X))))<=>(happy(susan)))&
(![X]:((quiet(X)&~humble(X))=>(brave(X)|curious(X))))&
(?[X]:((~tall(X)|kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~happy(X)))&
(?[X]:(calm(X)))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:(~curious(X)))&
((~kind(lucy)<~>~creative(lucy))) | ~old(susan) | [] | null | 0 |
If mary is not humble or not kind then paul is either not patient or curious. Everyone who is calm or wise is either quiet or brave and vice versa. Everyone who is patient or not happy is either not happy or not kind. If someone is either not strong or old then susan is both not calm and not curious. If someone is not quiet then alice is both not happy and not wise and vice versa. Everyone who is both not calm and not creative is tall. If someone is tall or not old then someone is both brave and not generous and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is both generous and not quiet is either not strong or not humble and vice versa. If fred is either not patient or not strong then susan is either strong or not quiet and vice versa. Everyone who is creative is both calm and strong and vice versa. Everyone who is both not quiet and not creative is rich or not happy and vice versa. Everyone who is both brave and not strong is either not tall or not creative and vice versa. If someone is both kind and brave then someone is not curious or not humble and vice versa. If fred is both not patient and generous then someone is curious. If someone is both not generous and not creative then someone is not patient or humble. John is both curious and not wise. John is not happy. Someone is wise or not patient. Someone is not brave. Someone is not curious or not patient. Susan is not happy. Mary is rich or not tall. | John is not tall. | contradiction | (((~humble(mary)|~kind(mary)))=>((~patient(paul)<~>curious(paul))))&
(![X]:((calm(X)|wise(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((patient(X)|~happy(X))=>(~happy(X)<~>~kind(X))))&
((?[X]:((~strong(X)<~>old(X))))=>((~calm(susan)&~curious(susan))))&
((?[X]:(~quiet(X)))<=>((~happy(alice)&~wise(alice))))&
(![X]:((~calm(X)&~creative(X))=>tall(X)))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((generous(X)&~quiet(X))<=>(~strong(X)<~>~humble(X))))&
(((~patient(fred)<~>~strong(fred)))<=>((strong(susan)<~>~quiet(susan))))&
(![X]:(creative(X)<=>(calm(X)&strong(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(rich(X)|~happy(X))))&
(![X]:((brave(X)&~strong(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:((~curious(X)|~humble(X)))))&
(((~patient(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~patient(X)|humble(X)))))&
((curious(john)&~wise(john)))&
(~happy(john))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~curious(X)|~patient(X))))&
(~happy(susan))&
((rich(mary)|~tall(mary))) | ~tall(john) | [
"p1",
"p5",
"p10",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7855820017800311913595909
% SZS output start Proof for 7855820017800311913595909
2. ! [X0] : ((wise(X0) | calm(X0)) <=> (quiet(X0) <~> brave(X0))) [input p1]
6. ! [X0] : ((~creative(X0) & ~calm(X0)) => tall(X0)) [input p5]
11. ! [X0] : (creative(X0) <=> (strong(X0) & calm(X0))) [input p10]
12. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~happy(X0) | rich(X0))) [input p11]
13. ! [X0] : ((~strong(X0) & brave(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p12]
18. ~happy(john) [input p17]
24. ~tall(john) [input hypothesis]
31. ! [X0] : (tall(X0) | (creative(X0) | calm(X0))) [ennf transformation 6]
32. ! [X0] : (tall(X0) | creative(X0) | calm(X0)) [flattening 31]
37. ! [X0] : (((wise(X0) | calm(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~wise(X0) & ~calm(X0)))) [nnf transformation 2]
38. ! [X0] : ((wise(X0) | calm(X0) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~wise(X0) & ~calm(X0)))) [flattening 37]
55. ! [X0] : ((creative(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | ~creative(X0))) [nnf transformation 11]
56. ! [X0] : ((creative(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | ~creative(X0))) [flattening 55]
57. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | creative(X0) | quiet(X0))) [flattening 57]
59. ! [X0] : (((~strong(X0) & brave(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (strong(X0) | ~brave(X0)))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & brave(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | strong(X0) | ~brave(X0))) [flattening 59]
81. ~calm(X0) | quiet(X0) | brave(X0) [cnf transformation 38]
98. tall(X0) | creative(X0) | calm(X0) [cnf transformation 32]
120. ~creative(X0) | calm(X0) [cnf transformation 56]
121. ~creative(X0) | strong(X0) [cnf transformation 56]
122. ~strong(X0) | creative(X0) | ~calm(X0) [cnf transformation 56]
125. ~quiet(X0) | happy(X0) [cnf transformation 58]
127. ~creative(X0) | happy(X0) [cnf transformation 58]
129. creative(X0) | tall(X0) | strong(X0) | ~brave(X0) [cnf transformation 60]
132. ~strong(X0) | ~creative(X0) | tall(X0) [cnf transformation 60]
133. ~tall(X0) | ~strong(X0) | creative(X0) [cnf transformation 60]
143. ~happy(john) [cnf transformation 18]
149. ~tall(john) [cnf transformation 24]
261. ~creative(X0) | tall(X0) [subsumption resolution 132,121]
262. ~brave(X0) | strong(X0) | tall(X0) [subsumption resolution 129,261]
374. creative(john) | calm(john) [resolution 98,149]
377. calm(john) [subsumption resolution 374,120]
379. quiet(john) | brave(john) [resolution 377,81]
381. 45 <=> brave(john) [avatar definition]
383. brave(john) <- (45) [avatar component clause 381]
385. 46 <=> quiet(john) [avatar definition]
387. quiet(john) <- (46) [avatar component clause 385]
388. 45 | 46 [avatar split clause 379,385,381]
472. ~strong(X0) | creative(X0) | creative(X0) | calm(X0) [resolution 133,98]
473. ~strong(X0) | creative(X0) | calm(X0) [duplicate literal removal 472]
577. ~strong(X0) | creative(X0) [subsumption resolution 473,122]
667. happy(john) <- (46) [resolution 387,125]
669. 70 <=> strong(john) [avatar definition]
671. strong(john) <- (70) [avatar component clause 669]
677. $false <- (46) [subsumption resolution 667,143]
678. ~46 [avatar contradiction clause 677]
682. strong(john) | tall(john) <- (45) [resolution 383,262]
685. strong(john) <- (45) [subsumption resolution 682,149]
686. 70 | ~45 [avatar split clause 685,381,669]
724. creative(john) <- (70) [resolution 671,577]
808. happy(john) <- (70) [resolution 724,127]
813. $false <- (70) [subsumption resolution 808,143]
814. ~70 [avatar contradiction clause 813]
815. $false [avatar sat refutation 388,678,686,814]
% SZS output end Proof for 7855820017800311913595909
% ------------------------------
% 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not generous then lucy is happy.
Everyone who is both not strong and not creative is either not creative or creative and vice versa.
If fred is either not patient or creative then lucy is quiet or generous and vice versa.
If someone is both calm and brave then john is wise or not wise and vice versa.
Everyone who is tall or not generous is strong.
If someone is not funny then paul is both creative and not brave and vice versa.
If someone is not tall or not creative then someone is either not happy or not calm.
Everyone who is either calm or not curious is generous and vice versa.
Everyone who is both creative and curious is either humble or calm and vice versa.
Everyone who is either calm or kind is not curious and vice versa.
Everyone who is not old is happy.
Everyone who is both not curious and not happy is either curious or happy.
If susan is not creative then someone is either quiet or brave.
Everyone who is not rich is not happy or curious and vice versa.
If someone is both kind and tall then paul is not happy or not strong.
Someone is both not wise and not brave.
Alice is not funny or kind.
Susan is not old.
Fred is humble or brave.
Someone is both not brave and humble.
Someone is both not wise and not tall.
Someone is either kind or not humble.
Susan is both not brave and not rich. | Fred is not patient. | entailment | ((?[X]:((quiet(X)&~generous(X))))=>(happy(lucy)))&
(![X]:((~strong(X)&~creative(X))<=>(~creative(X)<~>creative(X))))&
(((~patient(fred)<~>creative(fred)))<=>((quiet(lucy)|generous(lucy))))&
((?[X]:((calm(X)&brave(X))))<=>((wise(john)|~wise(john))))&
(![X]:((tall(X)|~generous(X))=>strong(X)))&
((?[X]:(~funny(X)))<=>((creative(paul)&~brave(paul))))&
((?[X]:((~tall(X)|~creative(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)<~>~curious(X))<=>generous(X)))&
(![X]:((creative(X)&curious(X))<=>(humble(X)<~>calm(X))))&
(![X]:((calm(X)<~>kind(X))<=>~curious(X)))&
(![X]:(~old(X)=>happy(X)))&
(![X]:((~curious(X)&~happy(X))=>(curious(X)<~>happy(X))))&
((~creative(susan))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(~rich(X)<=>(~happy(X)|curious(X))))&
((?[X]:((kind(X)&tall(X))))=>((~happy(paul)|~strong(paul))))&
(?[X]:((~wise(X)&~brave(X))))&
((~funny(alice)|kind(alice)))&
(~old(susan))&
((humble(fred)|brave(fred)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((~brave(susan)&~rich(susan))) | ~patient(fred) | [
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3703180612891660649596347
% SZS output start Proof for 3703180612891660649596347
2. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (~creative(X0) <~> creative(X0))) [input p1]
3. (~patient(fred) <~> creative(fred)) <=> (generous(lucy) | quiet(lucy)) [input p2]
5. ! [X0] : ((~generous(X0) | tall(X0)) => strong(X0)) [input p4]
24. patient(fred) [input hypothesis]
28. ! [X0] : (strong(X0) | (generous(X0) & ~tall(X0))) [ennf transformation 5]
38. ! [X0] : (((~creative(X0) & ~strong(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (creative(X0) | strong(X0)))) [nnf transformation 2]
39. ! [X0] : (((~creative(X0) & ~strong(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0) | strong(X0))) [flattening 38]
40. (((~creative(fred) | patient(fred)) & (creative(fred) | ~patient(fred))) | (~generous(lucy) & ~quiet(lucy))) & ((generous(lucy) | quiet(lucy)) | ((~patient(fred) | ~creative(fred)) & (creative(fred) | patient(fred)))) [nnf transformation 3]
41. (((~creative(fred) | patient(fred)) & (creative(fred) | ~patient(fred))) | (~generous(lucy) & ~quiet(lucy))) & (generous(lucy) | quiet(lucy) | ((~patient(fred) | ~creative(fred)) & (creative(fred) | patient(fred)))) [flattening 40]
76. ~strong(X0) | creative(X0) | creative(X0) [cnf transformation 39]
79. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 39]
83. creative(fred) | ~patient(fred) | ~generous(lucy) [cnf transformation 41]
92. strong(X0) | generous(X0) [cnf transformation 28]
134. patient(fred) [cnf transformation 24]
138. ~strong(X0) | creative(X0) [duplicate literal removal 76]
141. ~creative(X0) [duplicate literal removal 79]
150. ~strong(X0) [subsumption resolution 138,141]
151. ~patient(fred) | ~generous(lucy) [subsumption resolution 83,141]
153. 3 <=> generous(lucy) [avatar definition]
155. ~generous(lucy) <- (~3) [avatar component clause 153]
157. 4 <=> patient(fred) [avatar definition]
160. ~3 | ~4 [avatar split clause 151,157,153]
185. generous(X0) [subsumption resolution 92,150]
261. 4 [avatar split clause 134,157]
262. $false <- (~3) [subsumption resolution 155,185]
263. 3 [avatar contradiction clause 262]
264. $false [avatar sat refutation 160,261,263]
% SZS output end Proof for 3703180612891660649596347
% ------------------------------
% 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 |
If someone is generous then someone is either calm or not generous and vice versa.
If fred is both not curious and not brave then someone is both old and funny and vice versa.
Everyone who is both not generous and not happy is both not quiet and not rich.
If someone is both patient and not rich then susan is not curious or happy.
Everyone who is both not kind and not funny is both not kind and happy.
If someone is both happy and not happy then mary is not patient.
Everyone who is either calm or rich is not creative and vice versa.
Everyone who is either not creative or not humble is either not strong or creative.
If fred is not brave or patient then someone is both not generous and not curious and vice versa.
Everyone who is either quiet or not humble is not creative.
If paul is both kind and not wise then someone is both tall and not old and vice versa.
If someone is either happy or wise then john is not strong.
Everyone who is curious is curious or happy.
Everyone who is both not wise and not kind is both not brave and funny.
Everyone who is both tall and not kind is either old or not curious.
If alice is quiet or not strong then someone is both not strong and quiet and vice versa.
Susan is strong or not calm.
John is not funny or not quiet.
Susan is either not creative or not curious.
Fred is both brave and curious.
Someone is not wise or not old.
Someone is both patient and not quiet.
Someone is brave or calm.
Someone is both not brave and not tall. | John is not strong. | neutral | ((?[X]:(generous(X)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(((~curious(fred)&~brave(fred)))<=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~generous(X)&~happy(X))=>(~quiet(X)&~rich(X))))&
((?[X]:((patient(X)&~rich(X))))=>((~curious(susan)|happy(susan))))&
(![X]:((~kind(X)&~funny(X))=>(~kind(X)&happy(X))))&
((?[X]:((happy(X)&~happy(X))))=>(~patient(mary)))&
(![X]:((calm(X)<~>rich(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>~humble(X))=>(~strong(X)<~>creative(X))))&
(((~brave(fred)|patient(fred)))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((quiet(X)<~>~humble(X))=>~creative(X)))&
(((kind(paul)&~wise(paul)))<=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((happy(X)<~>wise(X))))=>(~strong(john)))&
(![X]:(curious(X)=>(curious(X)|happy(X))))&
(![X]:((~wise(X)&~kind(X))=>(~brave(X)&funny(X))))&
(![X]:((tall(X)&~kind(X))=>(old(X)<~>~curious(X))))&
(((quiet(alice)|~strong(alice)))<=>(?[X]:((~strong(X)&quiet(X)))))&
((strong(susan)|~calm(susan)))&
((~funny(john)|~quiet(john)))&
((~creative(susan)<~>~curious(susan)))&
((brave(fred)&curious(fred)))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:((patient(X)&~quiet(X))))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((~brave(X)&~tall(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is not brave is either not quiet or quiet.
Everyone who is either patient or not funny is funny and vice versa.
If someone is either rich or not quiet then paul is not humble.
If someone is either strong or curious then someone is not funny or not wise.
Everyone who is either funny or wise is patient.
Everyone who is either humble or not generous is not creative and vice versa.
Everyone who is either humble or not tall is either brave or not rich and vice versa.
Everyone who is either quiet or not old is strong.
If someone is not happy or not curious then fred is both wise and not wise.
Everyone who is both not old and wise is happy.
If someone is not kind or not curious then lucy is generous or not patient and vice versa.
If someone is either not kind or not quiet then someone is both calm and not patient and vice versa.
Everyone who is patient is either calm or not creative.
If susan is both not calm and not strong then someone is not humble and vice versa.
If john is both not happy and not brave then john is both calm and not kind and vice versa.
Everyone who is both quiet and funny is not calm and vice versa.
Lucy is both not quiet and creative.
Someone is strong or old.
Someone is rich.
Someone is not generous or tall.
Someone is either not happy or not strong.
John is either generous or not kind.
Lucy is curious or not rich. | Susan is not strong. | entailment | (![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:((patient(X)<~>~funny(X))<=>funny(X)))&
((?[X]:((rich(X)<~>~quiet(X))))=>(~humble(paul)))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((funny(X)<~>wise(X))=>patient(X)))&
(![X]:((humble(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((humble(X)<~>~tall(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>strong(X)))&
((?[X]:((~happy(X)|~curious(X))))=>((wise(fred)&~wise(fred))))&
(![X]:((~old(X)&wise(X))=>happy(X)))&
((?[X]:((~kind(X)|~curious(X))))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(?[X]:((calm(X)&~patient(X)))))&
(![X]:(patient(X)=>(calm(X)<~>~creative(X))))&
(((~calm(susan)&~strong(susan)))<=>(?[X]:(~humble(X))))&
(((~happy(john)&~brave(john)))<=>((calm(john)&~kind(john))))&
(![X]:((quiet(X)&funny(X))<=>~calm(X)))&
((~quiet(lucy)&creative(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|tall(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((generous(john)<~>~kind(john)))&
((curious(lucy)|~rich(lucy))) | ~strong(susan) | [
"p1",
"p5",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 506423019821795151157543
% SZS output start Proof for 506423019821795151157543
2. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> funny(X0)) [input p1]
6. ! [X0] : ((humble(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p5]
11. ? [X0] : (~curious(X0) | ~kind(X0)) <=> (~patient(lucy) | generous(lucy)) [input p10]
12. ? [X0] : (~kind(X0) <~> ~quiet(X0)) <=> ? [X0] : (~patient(X0) & calm(X0)) [input p11]
14. (~strong(susan) & ~calm(susan)) <=> ? [X0] : ~humble(X0) [input p13]
17. creative(lucy) & ~quiet(lucy) [input p16]
24. strong(susan) [input hypothesis]
26. ? [X0] : (~kind(X0) <~> ~quiet(X0)) <=> ? [X1] : (~patient(X1) & calm(X1)) [rectify 12]
37. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 2]
44. ! [X0] : ((((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | creative(X0)) & (~creative(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))))) [nnf transformation 6]
47. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & ((~patient(lucy) | generous(lucy)) | ! [X0] : (curious(X0) & kind(X0))) [nnf transformation 11]
48. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X0] : (curious(X0) & kind(X0))) [flattening 47]
49. (? [X0] : (~curious(X0) | ~kind(X0)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X1] : (curious(X1) & kind(X1))) [rectify 48]
50. ? [X0] : (~curious(X0) | ~kind(X0)) => (~curious(sK1) | ~kind(sK1)) [choice axiom]
51. ((~curious(sK1) | ~kind(sK1)) | (patient(lucy) & ~generous(lucy))) & (~patient(lucy) | generous(lucy) | ! [X1] : (curious(X1) & kind(X1))) [skolemisation 49,50]
52. (? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ! [X1] : (patient(X1) | ~calm(X1))) & (? [X1] : (~patient(X1) & calm(X1)) | ! [X0] : ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0)))) [nnf transformation 26]
53. (? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ! [X1] : (patient(X1) | ~calm(X1))) & (? [X2] : (~patient(X2) & calm(X2)) | ! [X3] : ((~kind(X3) | quiet(X3)) & (~quiet(X3) | kind(X3)))) [rectify 52]
54. ? [X0] : ((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) => ((quiet(sK2) | kind(sK2)) & (~quiet(sK2) | ~kind(sK2))) [choice axiom]
55. ? [X2] : (~patient(X2) & calm(X2)) => (~patient(sK3) & calm(sK3)) [choice axiom]
56. (((quiet(sK2) | kind(sK2)) & (~quiet(sK2) | ~kind(sK2))) | ! [X1] : (patient(X1) | ~calm(X1))) & ((~patient(sK3) & calm(sK3)) | ! [X3] : ((~kind(X3) | quiet(X3)) & (~quiet(X3) | kind(X3)))) [skolemisation 53,55,54]
58. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (strong(susan) | calm(susan))) [nnf transformation 14]
59. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | strong(susan) | calm(susan)) [flattening 58]
60. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | strong(susan) | calm(susan)) [rectify 59]
61. ? [X1] : ~humble(X1) => ~humble(sK4) [choice axiom]
62. ((~strong(susan) & ~calm(susan)) | ! [X0] : humble(X0)) & (~humble(sK4) | strong(susan) | calm(susan)) [skolemisation 60,61]
80. funny(X0) | patient(X0) | funny(X0) [cnf transformation 37]
81. ~funny(X0) | patient(X0) | ~funny(X0) [cnf transformation 37]
89. ~creative(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 44]
108. ~patient(lucy) | generous(lucy) | kind(X1) [cnf transformation 51]
115. ~patient(sK3) | ~kind(X3) | quiet(X3) [cnf transformation 56]
122. ~strong(susan) | humble(X0) [cnf transformation 62]
130. ~quiet(lucy) [cnf transformation 17]
131. creative(lucy) [cnf transformation 17]
140. strong(susan) [cnf transformation 24]
141. funny(X0) | patient(X0) [duplicate literal removal 80]
142. ~funny(X0) | patient(X0) [duplicate literal removal 81]
143. patient(X0) [subsumption resolution 141,142]
187. 11 <=> generous(lucy) [avatar definition]
201. generous(lucy) | kind(X1) [subsumption resolution 108,143]
203. 14 <=> ! [X1] : kind(X1) [avatar definition]
204. kind(X1) <- (14) [avatar component clause 203]
205. 14 | 11 [avatar split clause 201,187,203]
206. ~kind(X3) | quiet(X3) [subsumption resolution 115,143]
211. 15 <=> ! [X0] : humble(X0) [avatar definition]
212. humble(X0) <- (15) [avatar component clause 211]
214. 16 <=> strong(susan) [avatar definition]
217. 15 | ~16 [avatar split clause 122,214,211]
291. 16 [avatar split clause 140,214]
316. ~generous(lucy) | ~humble(lucy) [resolution 89,131]
320. ~generous(lucy) <- (15) [subsumption resolution 316,212]
321. ~11 | ~15 [avatar split clause 320,211,187]
323. quiet(X0) <- (14) [resolution 204,206]
325. $false <- (14) [resolution 323,130]
329. ~14 [avatar contradiction clause 325]
330. $false [avatar sat refutation 205,217,291,321,329]
% SZS output end Proof for 506423019821795151157543
% ------------------------------
% 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 strong and not curious then john is old or not tall.
Everyone who is not rich is either not quiet or not humble and vice versa.
If fred is both tall and not generous then someone is not calm or not kind.
Everyone who is not tall is rich or not calm.
If paul is patient or old then paul is either not creative or happy.
If mary is both not tall and not strong then lucy is both not creative and not patient and vice versa.
If mary is both funny and not patient then mary is either not wise or not patient.
If alice is kind or happy then someone is not creative.
If fred is old or not funny then paul is either not strong or not patient and vice versa.
Everyone who is both humble and curious is calm.
If mary is generous then fred is wise.
Everyone who is either wise or not patient is old and vice versa.
Everyone who is either not brave or calm is either not tall or kind and vice versa.
Everyone who is either kind or not wise is either not funny or not curious.
Everyone who is old is either generous or not generous and vice versa.
Everyone who is both not kind and old is not curious and vice versa.
Lucy is not strong or not creative.
Mary is not tall or happy.
Fred is both brave and wise.
Someone is both not strong and tall.
Alice is old or not generous.
Someone is either not generous or wise.
Someone is not tall. | Paul is patient. | neutral | ((?[X]:((~strong(X)&~curious(X))))=>((old(john)|~tall(john))))&
(![X]:(~rich(X)<=>(~quiet(X)<~>~humble(X))))&
(((tall(fred)&~generous(fred)))=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:(~tall(X)=>(rich(X)|~calm(X))))&
(((patient(paul)|old(paul)))=>((~creative(paul)<~>happy(paul))))&
(((~tall(mary)&~strong(mary)))<=>((~creative(lucy)&~patient(lucy))))&
(((funny(mary)&~patient(mary)))=>((~wise(mary)<~>~patient(mary))))&
(((kind(alice)|happy(alice)))=>(?[X]:(~creative(X))))&
(((old(fred)|~funny(fred)))<=>((~strong(paul)<~>~patient(paul))))&
(![X]:((humble(X)&curious(X))=>calm(X)))&
((generous(mary))=>(wise(fred)))&
(![X]:((wise(X)<~>~patient(X))<=>old(X)))&
(![X]:((~brave(X)<~>calm(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((kind(X)<~>~wise(X))=>(~funny(X)<~>~curious(X))))&
(![X]:(old(X)<=>(generous(X)<~>~generous(X))))&
(![X]:((~kind(X)&old(X))<=>~curious(X)))&
((~strong(lucy)|~creative(lucy)))&
((~tall(mary)|happy(mary)))&
((brave(fred)&wise(fred)))&
(?[X]:((~strong(X)&tall(X))))&
((old(alice)|~generous(alice)))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:(~tall(X))) | patient(paul) | [] | null | 0 |
Everyone who is both not funny and not calm is both not curious and not kind and vice versa. If someone is brave or not curious then someone is both not humble and patient and vice versa. If someone is both not strong and tall then someone is either not kind or quiet and vice versa. Everyone who is either happy or generous is wise. If lucy is either kind or curious then alice is not generous and vice versa. If mary is both tall and kind then fred is generous or not happy. If someone is generous then someone is both rich and funny. Everyone who is both rich and not generous is brave. If someone is quiet or brave then someone is either not strong or happy. Everyone who is either old or humble is both old and not wise. If john is both curious and patient then fred is not strong and vice versa. If mary is not kind or not humble then someone is rich or generous and vice versa. If fred is either not wise or not strong then someone is rich or brave and vice versa. If mary is either generous or not brave then lucy is curious or not humble and vice versa. If someone is funny or not strong then someone is not patient. Everyone who is not creative or not curious is either not patient or creative and vice versa. Alice is both wise and not strong. Lucy is both strong and generous. Someone is either not patient or funny. Someone is both old and not humble. John is both strong and not humble. Someone is not generous or curious. Someone is curious. | Fred is not wise. | entailment | (![X]:((~funny(X)&~calm(X))<=>(~curious(X)&~kind(X))))&
((?[X]:((brave(X)|~curious(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((~strong(X)&tall(X))))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>generous(X))=>wise(X)))&
(((kind(lucy)<~>curious(lucy)))<=>(~generous(alice)))&
(((tall(mary)&kind(mary)))=>((generous(fred)|~happy(fred))))&
((?[X]:(generous(X)))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((rich(X)&~generous(X))=>brave(X)))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((old(X)<~>humble(X))=>(old(X)&~wise(X))))&
(((curious(john)&patient(john)))<=>(~strong(fred)))&
(((~kind(mary)|~humble(mary)))<=>(?[X]:((rich(X)|generous(X)))))&
(((~wise(fred)<~>~strong(fred)))<=>(?[X]:((rich(X)|brave(X)))))&
(((generous(mary)<~>~brave(mary)))<=>((curious(lucy)|~humble(lucy))))&
((?[X]:((funny(X)|~strong(X))))=>(?[X]:(~patient(X))))&
(![X]:((~creative(X)|~curious(X))<=>(~patient(X)<~>creative(X))))&
((wise(alice)&~strong(alice)))&
((strong(lucy)&generous(lucy)))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((old(X)&~humble(X))))&
((strong(john)&~humble(john)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(curious(X))) | ~wise(fred) | [
"p6",
"p10",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6581237635233723035713565
% SZS output start Proof for 6581237635233723035713565
7. ? [X0] : generous(X0) => ? [X0] : (funny(X0) & rich(X0)) [input p6]
11. (patient(john) & curious(john)) <=> ~strong(fred) [input p10]
13. (~wise(fred) <~> ~strong(fred)) <=> ? [X0] : (brave(X0) | rich(X0)) [input p12]
16. ! [X0] : ((~curious(X0) | ~creative(X0)) <=> (~patient(X0) <~> creative(X0))) [input p15]
18. generous(lucy) & strong(lucy) [input p17]
24. wise(fred) [input hypothesis]
27. ? [X0] : generous(X0) => ? [X1] : (funny(X1) & rich(X1)) [rectify 7]
33. ? [X1] : (funny(X1) & rich(X1)) | ! [X0] : ~generous(X0) [ennf transformation 27]
53. ? [X0] : (funny(X0) & rich(X0)) | ! [X1] : ~generous(X1) [rectify 33]
54. ? [X0] : (funny(X0) & rich(X0)) => (funny(sK4) & rich(sK4)) [choice axiom]
55. (funny(sK4) & rich(sK4)) | ! [X1] : ~generous(X1) [skolemisation 53,54]
61. ((patient(john) & curious(john)) | strong(fred)) & (~strong(fred) | (~patient(john) | ~curious(john))) [nnf transformation 11]
62. ((patient(john) & curious(john)) | strong(fred)) & (~strong(fred) | ~patient(john) | ~curious(john)) [flattening 61]
68. (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X0] : (~brave(X0) & ~rich(X0))) & (? [X0] : (brave(X0) | rich(X0)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) [nnf transformation 13]
69. (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X0] : (~brave(X0) & ~rich(X0))) & (? [X1] : (brave(X1) | rich(X1)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) [rectify 68]
70. ? [X1] : (brave(X1) | rich(X1)) => (brave(sK7) | rich(sK7)) [choice axiom]
71. (((strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred))) | ! [X0] : (~brave(X0) & ~rich(X0))) & ((brave(sK7) | rich(sK7)) | ((~wise(fred) | strong(fred)) & (~strong(fred) | wise(fred)))) [skolemisation 69,70]
77. ! [X0] : (((~curious(X0) | ~creative(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (curious(X0) & creative(X0)))) [nnf transformation 16]
78. ! [X0] : ((~curious(X0) | ~creative(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (curious(X0) & creative(X0)))) [flattening 77]
110. rich(sK4) | ~generous(X1) [cnf transformation 55]
122. curious(john) | strong(fred) [cnf transformation 62]
123. patient(john) | strong(fred) [cnf transformation 62]
130. ~strong(fred) | ~wise(fred) | ~rich(X0) [cnf transformation 71]
142. creative(X0) | ~patient(X0) | creative(X0) [cnf transformation 78]
147. ~curious(X0) | ~creative(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 78]
151. generous(lucy) [cnf transformation 18]
160. wise(fred) [cnf transformation 24]
161. ~patient(X0) | creative(X0) [duplicate literal removal 142]
162. ~creative(X0) | ~curious(X0) | ~patient(X0) [duplicate literal removal 147]
259. 22 <=> ! [X1] : ~generous(X1) [avatar definition]
260. ~generous(X1) <- (22) [avatar component clause 259]
267. 24 <=> rich(sK4) [avatar definition]
269. rich(sK4) <- (24) [avatar component clause 267]
270. 22 | 24 [avatar split clause 110,267,259]
287. 28 <=> strong(fred) [avatar definition]
291. 29 <=> patient(john) [avatar definition]
293. patient(john) <- (29) [avatar component clause 291]
294. 28 | 29 [avatar split clause 123,291,287]
296. 30 <=> curious(john) [avatar definition]
298. curious(john) <- (30) [avatar component clause 296]
299. 28 | 30 [avatar split clause 122,296,287]
307. 32 <=> ! [X0] : ~rich(X0) [avatar definition]
308. ~rich(X0) <- (32) [avatar component clause 307]
321. 35 <=> wise(fred) [avatar definition]
327. 32 | ~35 | ~28 [avatar split clause 130,287,321,307]
387. 35 [avatar split clause 160,321]
392. $false <- (22) [resolution 260,151]
393. ~22 [avatar contradiction clause 392]
396. $false <- (24, 32) [subsumption resolution 269,308]
397. ~24 | ~32 [avatar contradiction clause 396]
399. creative(john) <- (29) [resolution 161,293]
511. ~curious(john) | ~patient(john) <- (29) [resolution 162,399]
513. ~patient(john) <- (29, 30) [subsumption resolution 511,298]
514. $false <- (29, 30) [subsumption resolution 513,293]
515. ~29 | ~30 [avatar contradiction clause 514]
516. $false [avatar sat refutation 270,294,299,327,387,393,397,515]
% SZS output end Proof for 6581237635233723035713565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or humble is both not happy and wise.
Everyone who is happy or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Everyone who is kind is either kind or not rich.
Everyone who is either brave or not old is both not wise and not calm.
If paul is patient or rich then someone is both not quiet and kind.
Everyone who is either humble or funny is wise and vice versa.
If someone is either not patient or creative then someone is rich or not creative.
John is both not wise and not rich.
Someone is both not brave and not rich.
Paul is not strong or patient.
Someone is creative or patient.
Alice is either not happy or creative.
Lucy is both curious and not funny.
Susan is old.
Alice is not wise. | Fred is funny. | contradiction | (![X]:((rich(X)|humble(X))=>(~happy(X)&wise(X))))&
(![X]:((happy(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
(![X]:(kind(X)=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~old(X))=>(~wise(X)&~calm(X))))&
(((patient(paul)|rich(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((~wise(john)&~rich(john)))&
(?[X]:((~brave(X)&~rich(X))))&
((~strong(paul)|patient(paul)))&
(?[X]:((creative(X)|patient(X))))&
((~happy(alice)<~>creative(alice)))&
((curious(lucy)&~funny(lucy)))&
(old(susan))&
(~wise(alice)) | funny(fred) | [
"p0",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8764384028703999012554032
% SZS output start Proof for 8764384028703999012554032
1. ! [X0] : ((humble(X0) | rich(X0)) => (wise(X0) & ~happy(X0))) [input p0]
5. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~strong(X0) & ~wise(X0))) [input p4]
15. ! [X0] : ((humble(X0) <~> funny(X0)) <=> wise(X0)) [input p14]
25. funny(fred) [input hypothesis]
32. ! [X0] : ((wise(X0) & ~happy(X0)) | (~humble(X0) & ~rich(X0))) [ennf transformation 1]
46. ! [X0] : (((brave(X0) | ~humble(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [flattening 46]
64. ! [X0] : ((((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | ~wise(X0)) & (wise(X0) | ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0))))) [nnf transformation 15]
77. ~humble(X0) | wise(X0) [cnf transformation 32]
88. ~wise(X0) | humble(X0) [cnf transformation 47]
115. wise(X0) | humble(X0) | ~funny(X0) [cnf transformation 64]
117. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 64]
132. funny(fred) [cnf transformation 25]
231. ~funny(X0) | ~wise(X0) [subsumption resolution 117,88]
232. ~funny(X0) | humble(X0) [subsumption resolution 115,231]
291. ~wise(fred) [resolution 231,132]
292. humble(fred) [resolution 232,132]
293. wise(fred) [resolution 292,77]
294. $false [subsumption resolution 293,291]
% SZS output end Proof for 8764384028703999012554032
% ------------------------------
% 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 curious and not strong is patient or not generous and vice versa.
Everyone who is not kind or patient is humble or creative and vice versa.
If lucy is not kind or not old then john is both rich and creative and vice versa.
If mary is not funny or not generous then paul is both quiet and kind and vice versa.
If someone is both not tall and wise then fred is strong and vice versa.
If susan is brave then paul is both rich and not happy and vice versa.
Everyone who is not tall or humble is not wise and vice versa.
Everyone who is curious is generous.
If someone is not curious or humble then john is not tall.
If someone is patient or not tall then susan is strong or kind and vice versa.
If someone is either strong or calm then someone is calm or not rich and vice versa.
Everyone who is either not curious or generous is brave and vice versa.
Everyone who is calm or rich is either not happy or strong and vice versa.
Everyone who is either tall or not old is happy or not funny.
If someone is both tall and not happy then lucy is not calm.
Everyone who is not happy or quiet is either patient or humble and vice versa.
Someone is either not calm or not old.
Someone is quiet.
Fred is curious.
John is either curious or tall.
Someone is both not creative and not quiet.
Lucy is either calm or happy.
John is either humble or quiet.
Alice is both patient and funny. | Alice is not curious. | entailment | (![X]:((~curious(X)&~strong(X))<=>(patient(X)|~generous(X))))&
(![X]:((~kind(X)|patient(X))<=>(humble(X)|creative(X))))&
(((~kind(lucy)|~old(lucy)))<=>((rich(john)&creative(john))))&
(((~funny(mary)|~generous(mary)))<=>((quiet(paul)&kind(paul))))&
((?[X]:((~tall(X)&wise(X))))<=>(strong(fred)))&
((brave(susan))<=>((rich(paul)&~happy(paul))))&
(![X]:((~tall(X)|humble(X))<=>~wise(X)))&
(![X]:(curious(X)=>generous(X)))&
((?[X]:((~curious(X)|humble(X))))=>(~tall(john)))&
((?[X]:((patient(X)|~tall(X))))<=>((strong(susan)|kind(susan))))&
((?[X]:((strong(X)<~>calm(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((~curious(X)<~>generous(X))<=>brave(X)))&
(![X]:((calm(X)|rich(X))<=>(~happy(X)<~>strong(X))))&
(![X]:((tall(X)<~>~old(X))=>(happy(X)|~funny(X))))&
((?[X]:((tall(X)&~happy(X))))=>(~calm(lucy)))&
(![X]:((~happy(X)|quiet(X))<=>(patient(X)<~>humble(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:(quiet(X)))&
(curious(fred))&
((curious(john)<~>tall(john)))&
(?[X]:((~creative(X)&~quiet(X))))&
((calm(lucy)<~>happy(lucy)))&
((humble(john)<~>quiet(john)))&
((patient(alice)&funny(alice))) | ~curious(alice) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1641571001774924027199319
% SZS output start Proof for 1641571001774924027199319
1. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> (~generous(X0) | patient(X0))) [input p0]
24. funny(alice) & patient(alice) [input p23]
25. curious(alice) [input hypothesis]
32. ! [X0] : (((~strong(X0) & ~curious(X0)) | (generous(X0) & ~patient(X0))) & ((~generous(X0) | patient(X0)) | (strong(X0) | curious(X0)))) [nnf transformation 1]
33. ! [X0] : (((~strong(X0) & ~curious(X0)) | (generous(X0) & ~patient(X0))) & (~generous(X0) | patient(X0) | strong(X0) | curious(X0))) [flattening 32]
75. ~patient(X0) | ~curious(X0) [cnf transformation 33]
146. patient(alice) [cnf transformation 24]
148. curious(alice) [cnf transformation 25]
343. ~curious(alice) [resolution 75,146]
344. $false [subsumption resolution 343,148]
% SZS output end Proof for 1641571001774924027199319
% ------------------------------
% 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 generous is not humble and vice versa.
If someone is not wise or curious then someone is not humble and vice versa.
If someone is wise or not creative then john is not generous and vice versa.
If fred is quiet or strong then someone is wise and vice versa.
Everyone who is both not brave and not strong is both not rich and calm and vice versa.
If lucy is either happy or not generous then lucy is either curious or quiet.
Everyone who is either not quiet or wise is both not humble and not old and vice versa.
If paul is not creative then someone is either happy or calm.
If someone is either curious or not patient then john is either not patient or quiet and vice versa.
Everyone who is both curious and not patient is either kind or not humble and vice versa.
Everyone who is quiet is both creative and not curious and vice versa.
If mary is both not calm and not wise then lucy is patient or not tall and vice versa.
Everyone who is not strong or not wise is either kind or not calm.
If someone is strong or brave then alice is generous and vice versa.
If mary is not curious then someone is not curious or humble.
If alice is either not funny or generous then someone is both not curious and not happy.
Someone is wise or quiet.
Someone is both old and not strong.
Lucy is both wise and not generous.
Someone is either not calm or wise.
Someone is either old or not calm.
Alice is old.
Fred is not tall or not creative. | John is generous. | contradiction | (![X]:(~generous(X)<=>~humble(X)))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:(~humble(X))))&
((?[X]:((wise(X)|~creative(X))))<=>(~generous(john)))&
(((quiet(fred)|strong(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~brave(X)&~strong(X))<=>(~rich(X)&calm(X))))&
(((happy(lucy)<~>~generous(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(![X]:((~quiet(X)<~>wise(X))<=>(~humble(X)&~old(X))))&
((~creative(paul))=>(?[X]:((happy(X)<~>calm(X)))))&
((?[X]:((curious(X)<~>~patient(X))))<=>((~patient(john)<~>quiet(john))))&
(![X]:((curious(X)&~patient(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(quiet(X)<=>(creative(X)&~curious(X))))&
(((~calm(mary)&~wise(mary)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((~strong(X)|~wise(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((strong(X)|brave(X))))<=>(generous(alice)))&
((~curious(mary))=>(?[X]:((~curious(X)|humble(X)))))&
(((~funny(alice)<~>generous(alice)))=>(?[X]:((~curious(X)&~happy(X)))))&
(?[X]:((wise(X)|quiet(X))))&
(?[X]:((old(X)&~strong(X))))&
((wise(lucy)&~generous(lucy)))&
(?[X]:((~calm(X)<~>wise(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(old(alice))&
((~tall(fred)|~creative(fred))) | generous(john) | [
"p2",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6110557744537706991526656
% SZS output start Proof for 6110557744537706991526656
3. ? [X0] : (~creative(X0) | wise(X0)) <=> ~generous(john) [input p2]
19. ~generous(lucy) & wise(lucy) [input p18]
24. generous(john) [input hypothesis]
37. (? [X0] : (~creative(X0) | wise(X0)) | generous(john)) & (~generous(john) | ! [X0] : (creative(X0) & ~wise(X0))) [nnf transformation 3]
38. (? [X0] : (~creative(X0) | wise(X0)) | generous(john)) & (~generous(john) | ! [X1] : (creative(X1) & ~wise(X1))) [rectify 37]
39. ? [X0] : (~creative(X0) | wise(X0)) => (~creative(sK2) | wise(sK2)) [choice axiom]
40. ((~creative(sK2) | wise(sK2)) | generous(john)) & (~generous(john) | ! [X1] : (creative(X1) & ~wise(X1))) [skolemisation 38,39]
89. ~generous(john) | ~wise(X1) [cnf transformation 40]
148. wise(lucy) [cnf transformation 19]
156. generous(john) [cnf transformation 24]
182. 7 <=> generous(john) [avatar definition]
199. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
200. ~wise(X1) <- (11) [avatar component clause 199]
201. 11 | ~7 [avatar split clause 89,182,199]
391. 7 [avatar split clause 156,182]
392. $false <- (11) [resolution 200,148]
393. ~11 [avatar contradiction clause 392]
394. $false [avatar sat refutation 201,391,393]
% SZS output end Proof for 6110557744537706991526656
% ------------------------------
% 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 tall or patient then lucy is not generous or not kind. Everyone who is not funny is both not curious and calm. If someone is both calm and not curious then someone is either not tall or brave and vice versa. If paul is brave then john is patient or not strong. If paul is generous or tall then john is both not creative and not humble. Everyone who is either not kind or not patient is not humble. If someone is not patient or kind then susan is either not calm or not wise and vice versa. Everyone who is either creative or not calm is either not brave or not tall. If someone is funny then john is not patient or not quiet and vice versa. Everyone who is not quiet is strong or not calm and vice versa. Everyone who is calm is not humble and vice versa. Everyone who is curious is not calm and vice versa. Everyone who is both not calm and humble is either calm or not old and vice versa. Everyone who is either calm or tall is either not patient or not kind and vice versa. Everyone who is funny or quiet is not kind and vice versa. If someone is not humble or not quiet then paul is either not calm or not strong and vice versa. Alice is both funny and not generous. John is not calm or patient. Paul is not calm. Mary is not calm or not curious. Paul is either old or not quiet. Someone is both rich and quiet. Someone is not tall. Lucy is not tall. | Susan is generous. | neutral | ((?[X]:((tall(X)|patient(X))))=>((~generous(lucy)|~kind(lucy))))&
(![X]:(~funny(X)=>(~curious(X)&calm(X))))&
((?[X]:((calm(X)&~curious(X))))<=>(?[X]:((~tall(X)<~>brave(X)))))&
((brave(paul))=>((patient(john)|~strong(john))))&
(((generous(paul)|tall(paul)))=>((~creative(john)&~humble(john))))&
(![X]:((~kind(X)<~>~patient(X))=>~humble(X)))&
((?[X]:((~patient(X)|kind(X))))<=>((~calm(susan)<~>~wise(susan))))&
(![X]:((creative(X)<~>~calm(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
((funny(alice)&~generous(alice)))&
((~calm(john)|patient(john)))&
(~calm(paul))&
((~calm(mary)|~curious(mary)))&
((old(paul)<~>~quiet(paul)))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:(~tall(X)))&
(~tall(lucy)) | generous(susan) | [] | null | 0 |
Everyone who is both generous and not curious is rich and vice versa.
If someone is either kind or not strong then fred is either not strong or not generous.
Everyone who is old or patient is calm or not old.
Everyone who is both happy and not calm is both not funny and not patient and vice versa.
If someone is rich or not brave then someone is both calm and strong.
If lucy is either not wise or old then someone is either patient or not strong and vice versa.
If susan is humble then someone is not brave or old and vice versa.
Everyone who is not happy is either not rich or not brave and vice versa.
Everyone who is calm or not creative is both generous and not patient and vice versa.
Everyone who is patient is either not old or brave.
Everyone who is not calm is both generous and rich and vice versa.
Everyone who is strong is not patient and vice versa.
If someone is either quiet or not quiet then fred is not humble and vice versa.
If john is either kind or funny then someone is both not generous and not strong.
Everyone who is not strong is quiet or wise.
Paul is both not strong and quiet.
Someone is not curious or not humble.
Mary is not patient or not quiet.
Someone is quiet.
Someone is not strong.
Someone is strong.
Fred is not strong or not calm. | Lucy is funny. | neutral | (![X]:((generous(X)&~curious(X))<=>rich(X)))&
((?[X]:((kind(X)<~>~strong(X))))=>((~strong(fred)<~>~generous(fred))))&
(![X]:((old(X)|patient(X))=>(calm(X)|~old(X))))&
(![X]:((happy(X)&~calm(X))<=>(~funny(X)&~patient(X))))&
((?[X]:((rich(X)|~brave(X))))=>(?[X]:((calm(X)&strong(X)))))&
(((~wise(lucy)<~>old(lucy)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
((humble(susan))<=>(?[X]:((~brave(X)|old(X)))))&
(![X]:(~happy(X)<=>(~rich(X)<~>~brave(X))))&
(![X]:((calm(X)|~creative(X))<=>(generous(X)&~patient(X))))&
(![X]:(patient(X)=>(~old(X)<~>brave(X))))&
(![X]:(~calm(X)<=>(generous(X)&rich(X))))&
(![X]:(strong(X)<=>~patient(X)))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(~humble(fred)))&
(((kind(john)<~>funny(john)))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:(~strong(X)=>(quiet(X)|wise(X))))&
((~strong(paul)&quiet(paul)))&
(?[X]:((~curious(X)|~humble(X))))&
((~patient(mary)|~quiet(mary)))&
(?[X]:(quiet(X)))&
(?[X]:(~strong(X)))&
(?[X]:(strong(X)))&
((~strong(fred)|~calm(fred))) | funny(lucy) | [] | null | 0 |
Everyone who is both funny and not old is both not strong and creative.
Everyone who is both not brave and not patient is both brave and tall.
Everyone who is either creative or tall is not old or wise and vice versa.
Everyone who is either not rich or not strong is not wise.
If paul is both kind and tall then someone is not brave and vice versa.
Everyone who is either curious or old is not rich or rich.
Everyone who is not brave is either not strong or not wise and vice versa.
Everyone who is not humble is both humble and strong and vice versa.
If mary is not strong or old then someone is funny or brave.
Everyone who is both humble and not rich is either funny or kind.
Everyone who is rich or quiet is curious or strong.
If someone is both funny and strong then someone is both not tall and not kind.
Everyone who is humble is calm and vice versa.
If mary is not quiet or not generous then alice is not kind and vice versa.
If someone is quiet then lucy is not humble or not calm.
Paul is either quiet or not tall.
Someone is either funny or not wise.
Someone is both kind and not happy.
Someone is either not tall or not curious.
Someone is not happy.
Someone is either not humble or patient.
John is not patient. | Alice is generous. | neutral | (![X]:((funny(X)&~old(X))=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))=>(brave(X)&tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~old(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~wise(X)))&
(((kind(paul)&tall(paul)))<=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>old(X))=>(~rich(X)|rich(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(humble(X)&strong(X))))&
(((~strong(mary)|old(mary)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((humble(X)&~rich(X))=>(funny(X)<~>kind(X))))&
(![X]:((rich(X)|quiet(X))=>(curious(X)|strong(X))))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(humble(X)<=>calm(X)))&
(((~quiet(mary)|~generous(mary)))<=>(~kind(alice)))&
((?[X]:(quiet(X)))=>((~humble(lucy)|~calm(lucy))))&
((quiet(paul)<~>~tall(paul)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((kind(X)&~happy(X))))&
(?[X]:((~tall(X)<~>~curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~humble(X)<~>patient(X))))&
(~patient(john)) | generous(alice) | [] | null | 0 |
If someone is either quiet or not strong then fred is tall and vice versa.
Everyone who is not kind is either kind or not brave and vice versa.
If someone is not kind or happy then someone is both quiet and wise and vice versa.
Everyone who is not rich is both not creative and rich and vice versa.
If someone is happy or tall then someone is not old.
If someone is both calm and not wise then alice is not wise or creative.
Everyone who is both not patient and not humble is either not curious or calm.
If mary is patient or wise then lucy is both not calm and quiet.
Everyone who is kind or humble is both not creative and kind.
Everyone who is either quiet or brave is either not tall or humble and vice versa.
Everyone who is either humble or kind is brave and vice versa.
Everyone who is wise or quiet is not rich or strong.
If paul is brave then someone is happy and vice versa.
Everyone who is calm is both kind and patient.
Everyone who is old or kind is either wise or funny and vice versa.
If john is either rich or not generous then someone is funny and vice versa.
Fred is either creative or not old.
Someone is either curious or creative.
Someone is both quiet and not happy.
Susan is not humble.
Someone is not humble.
Susan is either quiet or curious.
Paul is not calm or not quiet. | Lucy is not rich. | contradiction | ((?[X]:((quiet(X)<~>~strong(X))))<=>(tall(fred)))&
(![X]:(~kind(X)<=>(kind(X)<~>~brave(X))))&
((?[X]:((~kind(X)|happy(X))))<=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:(~rich(X)<=>(~creative(X)&rich(X))))&
((?[X]:((happy(X)|tall(X))))=>(?[X]:(~old(X))))&
((?[X]:((calm(X)&~wise(X))))=>((~wise(alice)|creative(alice))))&
(![X]:((~patient(X)&~humble(X))=>(~curious(X)<~>calm(X))))&
(((patient(mary)|wise(mary)))=>((~calm(lucy)&quiet(lucy))))&
(![X]:((kind(X)|humble(X))=>(~creative(X)&kind(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|kind(X))<=>(wise(X)<~>funny(X))))&
(((rich(john)<~>~generous(john)))<=>(?[X]:(funny(X))))&
((creative(fred)<~>~old(fred)))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:((quiet(X)&~happy(X))))&
(~humble(susan))&
(?[X]:(~humble(X)))&
((quiet(susan)<~>curious(susan)))&
((~calm(paul)|~quiet(paul))) | ~rich(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5336323354229767785914775
% SZS output start Proof for 5336323354229767785914775
4. ! [X0] : (~rich(X0) <=> (rich(X0) & ~creative(X0))) [input p3]
24. ~rich(lucy) [input hypothesis]
47. ! [X0] : ((~rich(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | rich(X0))) [nnf transformation 4]
48. ! [X0] : ((~rich(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | rich(X0))) [flattening 47]
88. rich(X0) | rich(X0) [cnf transformation 48]
142. ~rich(lucy) [cnf transformation 24]
143. rich(X0) [duplicate literal removal 88]
304. $false [subsumption resolution 142,143]
% SZS output end Proof for 5336323354229767785914775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is funny or not humble then someone is both not wise and creative. If paul is not patient or not creative then someone is not happy or not creative and vice versa. If someone is wise or old then someone is not curious and vice versa. Everyone who is either quiet or not rich is humble. If paul is not generous or not tall then someone is not curious. If someone is strong or not strong then fred is either calm or funny and vice versa. Everyone who is funny or not old is either not funny or not old and vice versa. If someone is either not wise or not curious then mary is either humble or not funny. If paul is either curious or not rich then paul is both not humble and not funny and vice versa. Everyone who is kind or not strong is both not rich and not creative. If susan is patient then someone is not curious or not calm and vice versa. If alice is either tall or not generous then john is either happy or not wise. If susan is either not creative or not curious then someone is funny. If someone is either creative or funny then mary is not tall or funny and vice versa. If lucy is both funny and not rich then someone is both not creative and funny and vice versa. Mary is either kind or not curious. Someone is not humble. Someone is either quiet or not wise. Someone is both tall and strong. Mary is either not kind or quiet. Someone is not rich or not humble. Someone is both tall and curious. | Alice is not curious. | neutral | (((funny(susan)|~humble(susan)))=>(?[X]:((~wise(X)&creative(X)))))&
(((~patient(paul)|~creative(paul)))<=>(?[X]:((~happy(X)|~creative(X)))))&
((?[X]:((wise(X)|old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>~rich(X))=>humble(X)))&
(((~generous(paul)|~tall(paul)))=>(?[X]:(~curious(X))))&
((?[X]:((strong(X)|~strong(X))))<=>((calm(fred)<~>funny(fred))))&
(![X]:((funny(X)|~old(X))<=>(~funny(X)<~>~old(X))))&
((?[X]:((~wise(X)<~>~curious(X))))=>((humble(mary)<~>~funny(mary))))&
(((curious(paul)<~>~rich(paul)))<=>((~humble(paul)&~funny(paul))))&
(![X]:((kind(X)|~strong(X))=>(~rich(X)&~creative(X))))&
((patient(susan))<=>(?[X]:((~curious(X)|~calm(X)))))&
(((tall(alice)<~>~generous(alice)))=>((happy(john)<~>~wise(john))))&
(((~creative(susan)<~>~curious(susan)))=>(?[X]:(funny(X))))&
((?[X]:((creative(X)<~>funny(X))))<=>((~tall(mary)|funny(mary))))&
(((funny(lucy)&~rich(lucy)))<=>(?[X]:((~creative(X)&funny(X)))))&
((kind(mary)<~>~curious(mary)))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)<~>~wise(X))))&
(?[X]:((tall(X)&strong(X))))&
((~kind(mary)<~>quiet(mary)))&
(?[X]:((~rich(X)|~humble(X))))&
(?[X]:((tall(X)&curious(X)))) | ~curious(alice) | [] | null | 0 |
If alice is not wise then paul is both wise and not kind and vice versa.
If john is both kind and not tall then susan is either calm or funny.
If someone is either curious or quiet then lucy is not patient.
Everyone who is both tall and not generous is either quiet or humble.
Everyone who is not brave or humble is brave and vice versa.
If fred is both not creative and patient then someone is either not brave or not funny and vice versa.
Everyone who is funny or patient is not curious and vice versa.
If someone is both brave and wise then someone is either not brave or strong and vice versa.
If someone is both not creative and not tall then someone is either wise or humble.
If paul is kind or happy then paul is not humble or not rich.
Everyone who is funny is brave.
Everyone who is both old and kind is not patient or not curious and vice versa.
If paul is both creative and not happy then someone is curious and vice versa.
If john is not wise then someone is both rich and not strong.
Everyone who is both not curious and happy is not quiet or patient and vice versa.
If someone is curious or not generous then someone is not generous and vice versa.
Someone is both patient and generous.
Lucy is both not happy and wise.
Someone is not creative.
Someone is curious or funny.
Susan is strong or not wise. | Fred is old. | entailment | ((~wise(alice))<=>((wise(paul)&~kind(paul))))&
(((kind(john)&~tall(john)))=>((calm(susan)<~>funny(susan))))&
((?[X]:((curious(X)<~>quiet(X))))=>(~patient(lucy)))&
(![X]:((tall(X)&~generous(X))=>(quiet(X)<~>humble(X))))&
(![X]:((~brave(X)|humble(X))<=>brave(X)))&
(((~creative(fred)&patient(fred)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:((funny(X)|patient(X))<=>~curious(X)))&
((?[X]:((brave(X)&wise(X))))<=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:((~creative(X)&~tall(X))))=>(?[X]:((wise(X)<~>humble(X)))))&
(((kind(paul)|happy(paul)))=>((~humble(paul)|~rich(paul))))&
(![X]:(funny(X)=>brave(X)))&
(![X]:((old(X)&kind(X))<=>(~patient(X)|~curious(X))))&
(((creative(paul)&~happy(paul)))<=>(?[X]:(curious(X))))&
((~wise(john))=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((~curious(X)&happy(X))<=>(~quiet(X)|patient(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:(~generous(X))))&
(?[X]:((patient(X)&generous(X))))&
((~happy(lucy)&wise(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)|funny(X))))&
((strong(susan)|~wise(susan))) | old(fred) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4611900121092093929239635
% SZS output start Proof for 4611900121092093929239635
7. ! [X0] : ((patient(X0) | funny(X0)) <=> ~curious(X0)) [input p6]
12. ! [X0] : ((kind(X0) & old(X0)) <=> (~curious(X0) | ~patient(X0))) [input p11]
22. ~old(fred) [input hypothesis]
48. ! [X0] : (((patient(X0) | funny(X0)) | curious(X0)) & (~curious(X0) | (~patient(X0) & ~funny(X0)))) [nnf transformation 7]
49. ! [X0] : ((patient(X0) | funny(X0) | curious(X0)) & (~curious(X0) | (~patient(X0) & ~funny(X0)))) [flattening 48]
59. ! [X0] : (((kind(X0) & old(X0)) | (curious(X0) & patient(X0))) & ((~curious(X0) | ~patient(X0)) | (~kind(X0) | ~old(X0)))) [nnf transformation 12]
60. ! [X0] : (((kind(X0) & old(X0)) | (curious(X0) & patient(X0))) & (~curious(X0) | ~patient(X0) | ~kind(X0) | ~old(X0))) [flattening 59]
100. ~patient(X0) | ~curious(X0) [cnf transformation 49]
114. old(X0) | patient(X0) [cnf transformation 60]
115. old(X0) | curious(X0) [cnf transformation 60]
138. ~old(fred) [cnf transformation 22]
191. 12 <=> patient(fred) [avatar definition]
193. patient(fred) <- (12) [avatar component clause 191]
332. ~curious(fred) <- (12) [resolution 100,193]
333. patient(fred) [resolution 114,138]
334. curious(fred) [resolution 115,138]
335. $false <- (12) [subsumption resolution 334,332]
336. ~12 [avatar contradiction clause 335]
337. 12 [avatar split clause 333,191]
338. $false [avatar sat refutation 336,337]
% SZS output end Proof for 4611900121092093929239635
% ------------------------------
% 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 calm or not brave is calm and vice versa.
Everyone who is brave is calm or not tall and vice versa.
Everyone who is both brave and not quiet is either quiet or not wise.
Everyone who is both happy and not funny is either not quiet or not brave.
Everyone who is both not funny and not calm is either humble or not generous.
If lucy is not brave or not creative then paul is both not curious and not humble and vice versa.
Everyone who is either not kind or generous is both calm and not strong and vice versa.
If someone is calm or not wise then someone is either curious or tall.
If lucy is tall then someone is wise or generous and vice versa.
If someone is both not wise and patient then mary is not humble.
Everyone who is humble is not kind or curious.
If someone is not calm then paul is either quiet or not happy and vice versa.
If someone is not creative or not wise then someone is either not brave or not calm.
If someone is both brave and not brave then mary is both humble and strong and vice versa.
Everyone who is both not tall and quiet is either not brave or not wise.
Lucy is both not kind and quiet.
Paul is either not strong or not tall.
Someone is not calm.
Susan is either not rich or curious.
Susan is not curious.
Alice is either not curious or not creative.
Someone is either not humble or brave.
Someone is both not strong and generous. | Paul is creative. | entailment | (![X]:((~calm(X)<~>~brave(X))<=>calm(X)))&
(![X]:(brave(X)<=>(calm(X)|~tall(X))))&
(![X]:((brave(X)&~quiet(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((happy(X)&~funny(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((~funny(X)&~calm(X))=>(humble(X)<~>~generous(X))))&
(((~brave(lucy)|~creative(lucy)))<=>((~curious(paul)&~humble(paul))))&
(![X]:((~kind(X)<~>generous(X))<=>(calm(X)&~strong(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((curious(X)<~>tall(X)))))&
((tall(lucy))<=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((~wise(X)&patient(X))))=>(~humble(mary)))&
(![X]:(humble(X)=>(~kind(X)|curious(X))))&
((?[X]:(~calm(X)))<=>((quiet(paul)<~>~happy(paul))))&
((?[X]:((~creative(X)|~wise(X))))=>(?[X]:((~brave(X)<~>~calm(X)))))&
((?[X]:((brave(X)&~brave(X))))<=>((humble(mary)&strong(mary))))&
(![X]:((~tall(X)&quiet(X))=>(~brave(X)<~>~wise(X))))&
((~kind(lucy)&quiet(lucy)))&
((~strong(paul)<~>~tall(paul)))&
(?[X]:(~calm(X)))&
((~rich(susan)<~>curious(susan)))&
(~curious(susan))&
((~curious(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((~strong(X)&generous(X)))) | creative(paul) | [
"p0",
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8783624492591133099760048
% SZS output start Proof for 8783624492591133099760048
1. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> calm(X0)) [input p0]
2. ! [X0] : (brave(X0) <=> (~tall(X0) | calm(X0))) [input p1]
13. ? [X0] : (~wise(X0) | ~creative(X0)) => ? [X0] : (~brave(X0) <~> ~calm(X0)) [input p12]
24. ~creative(paul) [input hypothesis]
26. ? [X0] : (~wise(X0) | ~creative(X0)) => ? [X1] : (~brave(X1) <~> ~calm(X1)) [rectify 13]
35. ? [X1] : (~brave(X1) <~> ~calm(X1)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 26]
38. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ~calm(X0)) & (calm(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 1]
39. ! [X0] : ((brave(X0) | (tall(X0) & ~calm(X0))) & ((~tall(X0) | calm(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (tall(X0) & ~calm(X0))) & (~tall(X0) | calm(X0) | ~brave(X0))) [flattening 39]
58. ? [X1] : ((calm(X1) | brave(X1)) & (~calm(X1) | ~brave(X1))) | ! [X0] : (wise(X0) & creative(X0)) [nnf transformation 35]
59. ? [X0] : ((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | ! [X1] : (wise(X1) & creative(X1)) [rectify 58]
60. ? [X0] : ((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) => ((calm(sK3) | brave(sK3)) & (~calm(sK3) | ~brave(sK3))) [choice axiom]
61. ((calm(sK3) | brave(sK3)) & (~calm(sK3) | ~brave(sK3))) | ! [X1] : (wise(X1) & creative(X1)) [skolemisation 59,60]
78. calm(X0) | ~brave(X0) | calm(X0) [cnf transformation 38]
80. ~brave(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 38]
83. brave(X0) | ~calm(X0) [cnf transformation 40]
112. calm(sK3) | brave(sK3) | creative(X1) [cnf transformation 61]
134. ~creative(paul) [cnf transformation 24]
136. calm(X0) | ~brave(X0) [duplicate literal removal 78]
137. ~brave(X0) | ~calm(X0) [duplicate literal removal 80]
138. ~brave(X0) [subsumption resolution 136,137]
140. ~calm(X0) [subsumption resolution 83,138]
195. brave(sK3) | creative(X1) [subsumption resolution 112,140]
196. creative(X1) [subsumption resolution 195,138]
221. $false [subsumption resolution 134,196]
% SZS output end Proof for 8783624492591133099760048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not calm is quiet or curious and vice versa.
Everyone who is either tall or not happy is not rich and vice versa.
Everyone who is not generous or brave is both generous and not kind.
Everyone who is either not creative or not brave is either not creative or strong and vice versa.
Everyone who is both patient and curious is strong or not wise and vice versa.
Everyone who is either humble or not old is either not generous or happy and vice versa.
Everyone who is either not humble or calm is happy.
If alice is both not old and not tall then someone is happy and vice versa.
If someone is either not brave or patient then mary is generous.
If john is not strong or not brave then someone is humble.
If alice is either wise or tall then john is either not creative or not humble and vice versa.
Everyone who is both generous and brave is not brave or not creative.
Everyone who is either not funny or generous is not rich or quiet and vice versa.
If someone is kind then mary is both brave and not creative and vice versa.
If someone is both not creative and not funny then mary is generous or happy.
Everyone who is both patient and not funny is not rich or rich and vice versa.
Paul is either curious or rich.
Paul is not curious or not calm.
Someone is tall or rich.
Lucy is brave.
Someone is not creative.
Paul is not humble.
Fred is either happy or tall.
John is either humble or not rich. | John is not generous. | contradiction | (![X]:((~wise(X)<~>~calm(X))<=>(quiet(X)|curious(X))))&
(![X]:((tall(X)<~>~happy(X))<=>~rich(X)))&
(![X]:((~generous(X)|brave(X))=>(generous(X)&~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~creative(X)<~>strong(X))))&
(![X]:((patient(X)&curious(X))<=>(strong(X)|~wise(X))))&
(![X]:((humble(X)<~>~old(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~humble(X)<~>calm(X))=>happy(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>(generous(mary)))&
(((~strong(john)|~brave(john)))=>(?[X]:(humble(X))))&
(((wise(alice)<~>tall(alice)))<=>((~creative(john)<~>~humble(john))))&
(![X]:((generous(X)&brave(X))=>(~brave(X)|~creative(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(~rich(X)|quiet(X))))&
((?[X]:(kind(X)))<=>((brave(mary)&~creative(mary))))&
((?[X]:((~creative(X)&~funny(X))))=>((generous(mary)|happy(mary))))&
(![X]:((patient(X)&~funny(X))<=>(~rich(X)|rich(X))))&
((curious(paul)<~>rich(paul)))&
((~curious(paul)|~calm(paul)))&
(?[X]:((tall(X)|rich(X))))&
(brave(lucy))&
(?[X]:(~creative(X)))&
(~humble(paul))&
((happy(fred)<~>tall(fred)))&
((humble(john)<~>~rich(john))) | ~generous(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3167719109133309919593485
% SZS output start Proof for 3167719109133309919593485
3. ! [X0] : ((brave(X0) | ~generous(X0)) => (~kind(X0) & generous(X0))) [input p2]
25. ~generous(john) [input hypothesis]
26. ! [X0] : ((~kind(X0) & generous(X0)) | (~brave(X0) & generous(X0))) [ennf transformation 3]
77. generous(X0) | generous(X0) [cnf transformation 26]
146. ~generous(john) [cnf transformation 25]
152. generous(X0) [duplicate literal removal 77]
276. $false [subsumption resolution 146,152]
% SZS output end Proof for 3167719109133309919593485
% ------------------------------
% 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 brave is either brave or not kind. If someone is humble or wise then someone is either tall or brave and vice versa. If fred is not calm then someone is not humble or not funny and vice versa. Everyone who is both not brave and not rich is not old and vice versa. Everyone who is either quiet or strong is not strong or not humble and vice versa. Everyone who is not wise is both funny and old and vice versa. Everyone who is either tall or not tall is not brave. Everyone who is either generous or not rich is either not strong or brave and vice versa. Everyone who is not quiet or curious is generous. If fred is both wise and not brave then paul is curious. If alice is either not wise or not calm then someone is either wise or creative. If someone is creative then alice is humble or not patient. Everyone who is generous or not creative is either not funny or not rich and vice versa. If paul is both patient and not old then mary is funny. Everyone who is either curious or not calm is not tall and vice versa. John is either not strong or not happy. Someone is not brave. Someone is either brave or not kind. John is not wise. Someone is patient. Susan is not curious or calm. Lucy is not creative. | Susan is not creative. | neutral | (![X]:(~brave(X)=>(brave(X)<~>~kind(X))))&
((?[X]:((humble(X)|wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
((~calm(fred))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~old(X)))&
(![X]:((quiet(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(![X]:(~wise(X)<=>(funny(X)&old(X))))&
(![X]:((tall(X)<~>~tall(X))=>~brave(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~quiet(X)|curious(X))=>generous(X)))&
(((wise(fred)&~brave(fred)))=>(curious(paul)))&
(((~wise(alice)<~>~calm(alice)))=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(creative(X)))=>((humble(alice)|~patient(alice))))&
(![X]:((generous(X)|~creative(X))<=>(~funny(X)<~>~rich(X))))&
(((patient(paul)&~old(paul)))=>(funny(mary)))&
(![X]:((curious(X)<~>~calm(X))<=>~tall(X)))&
((~strong(john)<~>~happy(john)))&
(?[X]:(~brave(X)))&
(?[X]:((brave(X)<~>~kind(X))))&
(~wise(john))&
(?[X]:(patient(X)))&
((~curious(susan)|calm(susan)))&
(~creative(lucy)) | ~creative(susan) | [] | null | 0 |
Everyone who is not kind is either not kind or not creative and vice versa.
If someone is both curious and not generous then john is not wise or brave and vice versa.
If fred is not patient or not rich then someone is generous.
If john is either old or quiet then someone is happy or quiet.
Everyone who is creative is either not strong or creative and vice versa.
Everyone who is not rich is tall.
If someone is humble then john is both patient and generous.
If susan is not creative or strong then paul is quiet and vice versa.
If paul is not creative then paul is either wise or not brave and vice versa.
Everyone who is both not creative and not old is both not strong and not rich and vice versa.
If john is not rich or not funny then someone is both not wise and calm.
If alice is either humble or not strong then someone is not calm or humble and vice versa.
Everyone who is either not kind or not patient is both strong and tall.
If someone is not rich or calm then alice is not strong and vice versa.
Everyone who is both not old and humble is not brave or not kind and vice versa.
If someone is both not generous and not humble then alice is either rich or not old and vice versa.
John is both old and wise.
Susan is not curious.
Susan is either brave or generous.
Someone is kind.
Someone is both kind and old.
Alice is not old or brave.
Alice is generous. | Alice is not strong. | contradiction | (![X]:(~kind(X)<=>(~kind(X)<~>~creative(X))))&
((?[X]:((curious(X)&~generous(X))))<=>((~wise(john)|brave(john))))&
(((~patient(fred)|~rich(fred)))=>(?[X]:(generous(X))))&
(((old(john)<~>quiet(john)))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:(creative(X)<=>(~strong(X)<~>creative(X))))&
(![X]:(~rich(X)=>tall(X)))&
((?[X]:(humble(X)))=>((patient(john)&generous(john))))&
(((~creative(susan)|strong(susan)))<=>(quiet(paul)))&
((~creative(paul))<=>((wise(paul)<~>~brave(paul))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)&~rich(X))))&
(((~rich(john)|~funny(john)))=>(?[X]:((~wise(X)&calm(X)))))&
(((humble(alice)<~>~strong(alice)))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~kind(X)<~>~patient(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)|calm(X))))<=>(~strong(alice)))&
(![X]:((~old(X)&humble(X))<=>(~brave(X)|~kind(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>((rich(alice)<~>~old(alice))))&
((old(john)&wise(john)))&
(~curious(susan))&
((brave(susan)<~>generous(susan)))&
(?[X]:(kind(X)))&
(?[X]:((kind(X)&old(X))))&
((~old(alice)|brave(alice)))&
(generous(alice)) | ~strong(alice) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6922648559702276904581047
% SZS output start Proof for 6922648559702276904581047
1. ! [X0] : (~kind(X0) <=> (~kind(X0) <~> ~creative(X0))) [input p0]
5. ! [X0] : (creative(X0) <=> (~strong(X0) <~> creative(X0))) [input p4]
24. ~strong(alice) [input hypothesis]
33. ! [X0] : ((~kind(X0) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0)))) & (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | kind(X0))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) & (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~creative(X0))) [nnf transformation 5]
70. creative(X0) | kind(X0) | kind(X0) [cnf transformation 33]
72. ~kind(X0) | ~kind(X0) | creative(X0) [cnf transformation 33]
81. ~creative(X0) | strong(X0) | ~creative(X0) [cnf transformation 41]
131. ~strong(alice) [cnf transformation 24]
132. ~creative(X0) | strong(X0) [duplicate literal removal 81]
134. creative(X0) | kind(X0) [duplicate literal removal 70]
135. ~kind(X0) | creative(X0) [duplicate literal removal 72]
136. creative(X0) [subsumption resolution 134,135]
175. strong(X0) [subsumption resolution 132,136]
271. $false [subsumption resolution 131,175]
% SZS output end Proof for 6922648559702276904581047
% ------------------------------
% 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 tall or funny then john is both old and funny.
Everyone who is strong or not tall is rich.
If someone is both not wise and curious then mary is either rich or not kind and vice versa.
If someone is either patient or not old then lucy is both not strong and old.
Everyone who is brave is not brave.
Everyone who is not humble is either not kind or not calm.
Everyone who is either quiet or not tall is kind or tall.
Everyone who is both not tall and funny is either happy or old and vice versa.
If lucy is either not kind or creative then someone is either patient or calm.
If someone is both calm and not happy then paul is both not funny and not kind.
If john is not funny then someone is both kind and not funny and vice versa.
Everyone who is not rich or humble is both not patient and not humble.
Everyone who is wise or not generous is both not calm and brave and vice versa.
If someone is either not calm or not creative then john is either brave or not wise.
If john is either old or not patient then fred is both not brave and not funny.
If alice is not wise or not happy then susan is either rich or not kind and vice versa.
John is either not rich or funny.
Someone is both strong and kind.
Someone is either not quiet or calm.
Susan is either curious or not kind.
Someone is not curious or not generous.
Fred is patient.
Someone is either calm or old.
Someone is either not old or kind. | Paul is generous. | entailment | (((~tall(lucy)|funny(lucy)))=>((old(john)&funny(john))))&
(![X]:((strong(X)|~tall(X))=>rich(X)))&
((?[X]:((~wise(X)&curious(X))))<=>((rich(mary)<~>~kind(mary))))&
((?[X]:((patient(X)<~>~old(X))))=>((~strong(lucy)&old(lucy))))&
(![X]:(brave(X)=>~brave(X)))&
(![X]:(~humble(X)=>(~kind(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(kind(X)|tall(X))))&
(![X]:((~tall(X)&funny(X))<=>(happy(X)<~>old(X))))&
(((~kind(lucy)<~>creative(lucy)))=>(?[X]:((patient(X)<~>calm(X)))))&
((?[X]:((calm(X)&~happy(X))))=>((~funny(paul)&~kind(paul))))&
((~funny(john))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~rich(X)|humble(X))=>(~patient(X)&~humble(X))))&
(![X]:((wise(X)|~generous(X))<=>(~calm(X)&brave(X))))&
((?[X]:((~calm(X)<~>~creative(X))))=>((brave(john)<~>~wise(john))))&
(((old(john)<~>~patient(john)))=>((~brave(fred)&~funny(fred))))&
(((~wise(alice)|~happy(alice)))<=>((rich(susan)<~>~kind(susan))))&
((~rich(john)<~>funny(john)))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
((curious(susan)<~>~kind(susan)))&
(?[X]:((~curious(X)|~generous(X))))&
(patient(fred))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((~old(X)<~>kind(X)))) | generous(paul) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5454506343709004074784122
% SZS output start Proof for 5454506343709004074784122
5. ! [X0] : (brave(X0) => ~brave(X0)) [input p4]
13. ! [X0] : ((~generous(X0) | wise(X0)) <=> (brave(X0) & ~calm(X0))) [input p12]
25. ~generous(paul) [input hypothesis]
29. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 5]
54. ! [X0] : (((~generous(X0) | wise(X0)) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 13]
55. ! [X0] : ((~generous(X0) | wise(X0) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | (generous(X0) & ~wise(X0)))) [flattening 54]
91. ~brave(X0) | ~brave(X0) [cnf transformation 29]
118. brave(X0) | generous(X0) [cnf transformation 55]
148. ~generous(paul) [cnf transformation 25]
151. ~brave(X0) [duplicate literal removal 91]
262. generous(X0) [subsumption resolution 118,151]
335. $false [subsumption resolution 148,262]
% SZS output end Proof for 5454506343709004074784122
% ------------------------------
% 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 alice is not happy or not funny then fred is wise.
If someone is not patient or humble then someone is brave and vice versa.
If someone is either rich or brave then someone is both not patient and curious.
If someone is both brave and not funny then someone is not funny or not rich.
Everyone who is creative or not quiet is either humble or not wise.
Everyone who is not happy is either not creative or patient.
Everyone who is kind or patient is creative or not brave and vice versa.
Everyone who is not wise or not curious is strong.
Everyone who is calm is both humble and not strong and vice versa.
Everyone who is creative or brave is either funny or humble.
Everyone who is tall is either not old or funny and vice versa.
If someone is both wise and not rich then fred is both brave and not creative.
If paul is patient then susan is both not kind and creative and vice versa.
Everyone who is both brave and happy is either not patient or kind.
If someone is both not calm and rich then someone is both not tall and not strong and vice versa.
If susan is funny then someone is kind.
Someone is not tall or not generous.
Someone is both not generous and rich.
Someone is quiet or strong.
Alice is not old.
Someone is happy.
Someone is kind or not generous.
Fred is either not wise or quiet.
Mary is kind. | Fred is brave. | neutral | (((~happy(alice)|~funny(alice)))=>(wise(fred)))&
((?[X]:((~patient(X)|humble(X))))<=>(?[X]:(brave(X))))&
((?[X]:((rich(X)<~>brave(X))))=>(?[X]:((~patient(X)&curious(X)))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
(![X]:((creative(X)|~quiet(X))=>(humble(X)<~>~wise(X))))&
(![X]:(~happy(X)=>(~creative(X)<~>patient(X))))&
(![X]:((kind(X)|patient(X))<=>(creative(X)|~brave(X))))&
(![X]:((~wise(X)|~curious(X))=>strong(X)))&
(![X]:(calm(X)<=>(humble(X)&~strong(X))))&
(![X]:((creative(X)|brave(X))=>(funny(X)<~>humble(X))))&
(![X]:(tall(X)<=>(~old(X)<~>funny(X))))&
((?[X]:((wise(X)&~rich(X))))=>((brave(fred)&~creative(fred))))&
((patient(paul))<=>((~kind(susan)&creative(susan))))&
(![X]:((brave(X)&happy(X))=>(~patient(X)<~>kind(X))))&
((?[X]:((~calm(X)&rich(X))))<=>(?[X]:((~tall(X)&~strong(X)))))&
((funny(susan))=>(?[X]:(kind(X))))&
(?[X]:((~tall(X)|~generous(X))))&
(?[X]:((~generous(X)&rich(X))))&
(?[X]:((quiet(X)|strong(X))))&
(~old(alice))&
(?[X]:(happy(X)))&
(?[X]:((kind(X)|~generous(X))))&
((~wise(fred)<~>quiet(fred)))&
(kind(mary)) | brave(fred) | [] | null | 0 |
Everyone who is both not curious and not brave is both calm and rich and vice versa.
Everyone who is both not happy and tall is either not rich or creative and vice versa.
Everyone who is not kind or kind is creative and vice versa.
Everyone who is both funny and humble is curious or not happy and vice versa.
If fred is calm or brave then someone is strong.
Everyone who is brave is either not calm or not old and vice versa.
If paul is funny or not tall then paul is either patient or calm.
If someone is both not brave and wise then susan is both rich and not rich and vice versa.
Everyone who is happy or not rich is patient or not calm and vice versa.
If someone is either not wise or not brave then fred is either patient or not calm.
If someone is not strong or happy then someone is brave.
Everyone who is both patient and happy is either curious or not wise.
If someone is both strong and not rich then someone is either not brave or happy and vice versa.
Everyone who is either not curious or not calm is not brave.
Everyone who is both not funny and not strong is both not creative and not generous and vice versa.
Everyone who is kind or not tall is generous.
Susan is not generous or tall.
Fred is both not happy and calm.
Lucy is creative.
Paul is both tall and strong.
Lucy is not kind.
Fred is both not patient and not generous.
Someone is wise or curious. | Fred is not rich. | contradiction | (![X]:((~curious(X)&~brave(X))<=>(calm(X)&rich(X))))&
(![X]:((~happy(X)&tall(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~kind(X)|kind(X))<=>creative(X)))&
(![X]:((funny(X)&humble(X))<=>(curious(X)|~happy(X))))&
(((calm(fred)|brave(fred)))=>(?[X]:(strong(X))))&
(![X]:(brave(X)<=>(~calm(X)<~>~old(X))))&
(((funny(paul)|~tall(paul)))=>((patient(paul)<~>calm(paul))))&
((?[X]:((~brave(X)&wise(X))))<=>((rich(susan)&~rich(susan))))&
(![X]:((happy(X)|~rich(X))<=>(patient(X)|~calm(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>((patient(fred)<~>~calm(fred))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:(brave(X))))&
(![X]:((patient(X)&happy(X))=>(curious(X)<~>~wise(X))))&
((?[X]:((strong(X)&~rich(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>~brave(X)))&
(![X]:((~funny(X)&~strong(X))<=>(~creative(X)&~generous(X))))&
(![X]:((kind(X)|~tall(X))=>generous(X)))&
((~generous(susan)|tall(susan)))&
((~happy(fred)&calm(fred)))&
(creative(lucy))&
((tall(paul)&strong(paul)))&
(~kind(lucy))&
((~patient(fred)&~generous(fred)))&
(?[X]:((wise(X)|curious(X)))) | ~rich(fred) | [
"p8",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8685959461765612941648547
% SZS output start Proof for 8685959461765612941648547
9. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~calm(X0) | patient(X0))) [input p8]
18. calm(fred) & ~happy(fred) [input p17]
22. ~generous(fred) & ~patient(fred) [input p21]
24. ~rich(fred) [input hypothesis]
52. ! [X0] : (((~rich(X0) | happy(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 9]
53. ! [X0] : ((~rich(X0) | happy(X0) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | (rich(X0) & ~happy(X0)))) [flattening 52]
102. ~calm(X0) | patient(X0) | rich(X0) [cnf transformation 53]
129. calm(fred) [cnf transformation 18]
134. ~patient(fred) [cnf transformation 22]
137. ~rich(fred) [cnf transformation 24]
149. 3 <=> calm(fred) [avatar definition]
150. calm(fred) <- (3) [avatar component clause 149]
183. 10 <=> patient(fred) [avatar definition]
185. ~patient(fred) <- (~10) [avatar component clause 183]
238. 3 [avatar split clause 129,149]
240. ~10 [avatar split clause 134,183]
386. patient(fred) | rich(fred) <- (3) [resolution 102,150]
389. rich(fred) <- (3, ~10) [subsumption resolution 386,185]
390. $false <- (3, ~10) [subsumption resolution 389,137]
391. ~3 | 10 [avatar contradiction clause 390]
402. $false [avatar sat refutation 238,240,391]
% SZS output end Proof for 8685959461765612941648547
% ------------------------------
% 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 lucy is not brave then someone is both not rich and kind. Everyone who is either brave or not humble is both rich and not funny. If susan is both not patient and not old then alice is tall or not curious. If someone is happy or generous then alice is not patient or not tall and vice versa. If lucy is generous then susan is not funny. If fred is either strong or kind then someone is not generous or not old and vice versa. Everyone who is both not brave and not old is either not old or not patient and vice versa. Everyone who is brave or happy is both not patient and generous and vice versa. Everyone who is both funny and humble is not old or wise. Everyone who is both not patient and old is happy or generous. If mary is either not brave or calm then mary is both not wise and funny. Everyone who is either calm or not calm is either creative or not funny. Everyone who is not old is both old and wise and vice versa. Everyone who is not strong or not patient is either funny or brave. Someone is not happy. Someone is both calm and quiet. Someone is both not quiet and tall. Someone is patient. Fred is funny or tall. Someone is creative or not generous. | Susan is not funny. | entailment | ((~brave(lucy))=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~humble(X))=>(rich(X)&~funny(X))))&
(((~patient(susan)&~old(susan)))=>((tall(alice)|~curious(alice))))&
((?[X]:((happy(X)|generous(X))))<=>((~patient(alice)|~tall(alice))))&
((generous(lucy))=>(~funny(susan)))&
(((strong(fred)<~>kind(fred)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)<~>~patient(X))))&
(![X]:((brave(X)|happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((funny(X)&humble(X))=>(~old(X)|wise(X))))&
(![X]:((~patient(X)&old(X))=>(happy(X)|generous(X))))&
(((~brave(mary)<~>calm(mary)))=>((~wise(mary)&funny(mary))))&
(![X]:((calm(X)<~>~calm(X))=>(creative(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(old(X)&wise(X))))&
(![X]:((~strong(X)|~patient(X))=>(funny(X)<~>brave(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:(patient(X)))&
((funny(fred)|tall(fred)))&
(?[X]:((creative(X)|~generous(X)))) | ~funny(susan) | [
"p1",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 52459964088344322124664
% SZS output start Proof for 52459964088344322124664
2. ! [X0] : ((brave(X0) <~> ~humble(X0)) => (~funny(X0) & rich(X0))) [input p1]
7. ! [X0] : ((~old(X0) & ~brave(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p6]
8. ! [X0] : ((happy(X0) | brave(X0)) <=> (generous(X0) & ~patient(X0))) [input p7]
9. ! [X0] : ((humble(X0) & funny(X0)) => (wise(X0) | ~old(X0))) [input p8]
13. ! [X0] : (~old(X0) <=> (wise(X0) & old(X0))) [input p12]
21. funny(susan) [input hypothesis]
24. ! [X0] : ((~funny(X0) & rich(X0)) | (brave(X0) <=> ~humble(X0))) [ennf transformation 2]
26. ! [X0] : ((wise(X0) | ~old(X0)) | (~humble(X0) | ~funny(X0))) [ennf transformation 9]
27. ! [X0] : (wise(X0) | ~old(X0) | ~humble(X0) | ~funny(X0)) [flattening 26]
35. ! [X0] : ((~funny(X0) & rich(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 24]
45. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (old(X0) | brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | old(X0) | brave(X0))) [flattening 45]
47. ! [X0] : (((happy(X0) | brave(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | brave(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 47]
51. ! [X0] : ((~old(X0) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | old(X0))) [nnf transformation 13]
52. ! [X0] : ((~old(X0) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | old(X0))) [flattening 51]
69. ~funny(X0) | brave(X0) | humble(X0) [cnf transformation 35]
86. ~old(X0) | ~old(X0) | patient(X0) [cnf transformation 46]
87. ~patient(X0) | ~brave(X0) [cnf transformation 48]
92. ~old(X0) | wise(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 27]
102. old(X0) | old(X0) [cnf transformation 52]
104. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 52]
117. funny(susan) [cnf transformation 21]
118. old(X0) [duplicate literal removal 102]
119. ~wise(X0) | ~old(X0) [duplicate literal removal 104]
125. ~old(X0) | patient(X0) [duplicate literal removal 86]
171. 11 <=> funny(susan) [avatar definition]
172. funny(susan) <- (11) [avatar component clause 171]
176. 12 <=> ! [X0] : old(X0) [avatar definition]
177. old(X0) <- (12) [avatar component clause 176]
226. 12 [avatar split clause 118,176]
246. 11 [avatar split clause 117,171]
252. patient(X0) <- (12) [resolution 125,177]
254. ~brave(X0) <- (12) [resolution 252,87]
269. brave(susan) | humble(susan) <- (11) [resolution 69,172]
271. humble(susan) <- (11, 12) [subsumption resolution 269,254]
284. ~funny(X0) | ~humble(X0) | wise(X0) <- (12) [resolution 92,177]
285. ~humble(susan) | wise(susan) <- (11, 12) [resolution 284,172]
287. wise(susan) <- (11, 12) [subsumption resolution 285,271]
289. ~old(susan) <- (11, 12) [resolution 287,119]
290. $false <- (11, 12) [subsumption resolution 289,177]
291. ~11 | ~12 [avatar contradiction clause 290]
292. $false [avatar sat refutation 226,246,291]
% SZS output end Proof for 52459964088344322124664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either patient or not old then paul is both not generous and old and vice versa.
Everyone who is both patient and not rich is not brave.
Everyone who is both not tall and not strong is not old and vice versa.
If someone is both calm and tall then fred is both not strong and not curious and vice versa.
Everyone who is either strong or not happy is either not funny or not wise.
If someone is both not happy and calm then someone is calm or not humble.
Everyone who is both curious and not calm is both quiet and not funny and vice versa.
If someone is tall or quiet then someone is either calm or tall and vice versa.
Everyone who is either old or strong is not old or not kind.
If someone is not brave or not strong then someone is either not patient or not generous.
Everyone who is not calm or tall is either not humble or not brave.
If someone is either humble or not calm then someone is both not kind and tall and vice versa.
Everyone who is both calm and quiet is generous or wise.
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
Mary is tall or not patient.
Someone is either curious or humble.
Alice is quiet.
Susan is not old.
Someone is both kind and not wise.
Someone is not quiet or strong.
Someone is not happy or not calm. | Susan is not funny. | neutral | (((patient(fred)<~>~old(fred)))<=>((~generous(paul)&old(paul))))&
(![X]:((patient(X)&~rich(X))=>~brave(X)))&
(![X]:((~tall(X)&~strong(X))<=>~old(X)))&
((?[X]:((calm(X)&tall(X))))<=>((~strong(fred)&~curious(fred))))&
(![X]:((strong(X)<~>~happy(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:((~happy(X)&calm(X))))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((curious(X)&~calm(X))<=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((old(X)<~>strong(X))=>(~old(X)|~kind(X))))&
((?[X]:((~brave(X)|~strong(X))))=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~calm(X)|tall(X))=>(~humble(X)<~>~brave(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((calm(X)&quiet(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((tall(mary)|~patient(mary)))&
(?[X]:((curious(X)<~>humble(X))))&
(quiet(alice))&
(~old(susan))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~happy(X)|~calm(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is either rich or tall is either not creative or creative and vice versa.
Everyone who is not kind or not humble is rich.
Everyone who is happy is both quiet and not calm and vice versa.
If someone is kind then john is both creative and not patient and vice versa.
Everyone who is not old is brave or not tall.
If john is generous then paul is not tall or not kind.
If someone is both wise and not curious then susan is not funny or funny and vice versa.
If mary is not wise or not patient then someone is funny.
Everyone who is not wise or not old is both not old and not happy and vice versa.
If someone is both not kind and old then someone is either curious or humble and vice versa.
Everyone who is not calm or not funny is both humble and old and vice versa.
Everyone who is not kind or not quiet is either not quiet or rich.
Everyone who is not creative or calm is both not rich and not humble.
If fred is generous then alice is not happy.
Everyone who is either brave or patient is both brave and rich.
Someone is either not calm or happy.
Someone is either not funny or not humble.
Someone is both generous and not patient.
Someone is quiet or generous.
Fred is not kind or patient.
Mary is humble. | Mary is not old. | contradiction | (![X]:((rich(X)<~>tall(X))<=>(~creative(X)<~>creative(X))))&
(![X]:((~kind(X)|~humble(X))=>rich(X)))&
(![X]:(happy(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(kind(X)))<=>((creative(john)&~patient(john))))&
(![X]:(~old(X)=>(brave(X)|~tall(X))))&
((generous(john))=>((~tall(paul)|~kind(paul))))&
((?[X]:((wise(X)&~curious(X))))<=>((~funny(susan)|funny(susan))))&
(((~wise(mary)|~patient(mary)))=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|~old(X))<=>(~old(X)&~happy(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~calm(X)|~funny(X))<=>(humble(X)&old(X))))&
(![X]:((~kind(X)|~quiet(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((~creative(X)|calm(X))=>(~rich(X)&~humble(X))))&
((generous(fred))=>(~happy(alice)))&
(![X]:((brave(X)<~>patient(X))=>(brave(X)&rich(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((quiet(X)|generous(X))))&
((~kind(fred)|patient(fred)))&
(humble(mary)) | ~old(mary) | [
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2632656658720919011510834
% SZS output start Proof for 2632656658720919011510834
11. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (old(X0) & humble(X0))) [input p10]
13. ! [X0] : ((calm(X0) | ~creative(X0)) => (~humble(X0) & ~rich(X0))) [input p12]
21. humble(mary) [input p20]
22. ~old(mary) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~rich(X0)) | (~calm(X0) & creative(X0))) [ennf transformation 13]
56. ! [X0] : (((~funny(X0) | ~calm(X0)) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 11]
57. ! [X0] : ((~funny(X0) | ~calm(X0) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | (funny(X0) & calm(X0)))) [flattening 56]
108. old(X0) | calm(X0) [cnf transformation 57]
118. ~calm(X0) | ~humble(X0) [cnf transformation 31]
132. humble(mary) [cnf transformation 21]
133. ~old(mary) [cnf transformation 22]
279. calm(mary) [resolution 108,133]
295. ~humble(mary) [resolution 118,279]
296. $false [subsumption resolution 295,132]
% SZS output end Proof for 2632656658720919011510834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or strong then someone is not humble and vice versa.
Everyone who is both not patient and not calm is either not happy or not funny.
Everyone who is either generous or happy is both not old and creative and vice versa.
If mary is both not brave and not rich then someone is not tall or curious.
If lucy is either not old or not funny then someone is funny and vice versa.
Everyone who is wise is either not humble or creative and vice versa.
If john is either strong or funny then someone is either not creative or not tall.
If lucy is either calm or funny then someone is not old and vice versa.
If someone is both curious and tall then someone is old and vice versa.
Everyone who is tall or creative is both calm and generous and vice versa.
Everyone who is both wise and not funny is not humble or happy and vice versa.
Everyone who is not calm or old is kind or not calm and vice versa.
If fred is not tall or not humble then someone is either not kind or old.
Everyone who is both not patient and not rich is not brave and vice versa.
Everyone who is either not old or creative is either not kind or calm.
If susan is not old then john is curious or not calm.
Someone is not kind.
Mary is both generous and calm.
Lucy is not brave.
Lucy is both not quiet and calm.
Someone is not calm or generous.
Mary is either quiet or brave.
John is both wise and kind.
Mary is both kind and generous. | Mary is not brave. | neutral | ((?[X]:((~humble(X)|strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~calm(X))=>(~happy(X)<~>~funny(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~old(X)&creative(X))))&
(((~brave(mary)&~rich(mary)))=>(?[X]:((~tall(X)|curious(X)))))&
(((~old(lucy)<~>~funny(lucy)))<=>(?[X]:(funny(X))))&
(![X]:(wise(X)<=>(~humble(X)<~>creative(X))))&
(((strong(john)<~>funny(john)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
(((calm(lucy)<~>funny(lucy)))<=>(?[X]:(~old(X))))&
((?[X]:((curious(X)&tall(X))))<=>(?[X]:(old(X))))&
(![X]:((tall(X)|creative(X))<=>(calm(X)&generous(X))))&
(![X]:((wise(X)&~funny(X))<=>(~humble(X)|happy(X))))&
(![X]:((~calm(X)|old(X))<=>(kind(X)|~calm(X))))&
(((~tall(fred)|~humble(fred)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~patient(X)&~rich(X))<=>~brave(X)))&
(![X]:((~old(X)<~>creative(X))=>(~kind(X)<~>calm(X))))&
((~old(susan))=>((curious(john)|~calm(john))))&
(?[X]:(~kind(X)))&
((generous(mary)&calm(mary)))&
(~brave(lucy))&
((~quiet(lucy)&calm(lucy)))&
(?[X]:((~calm(X)|generous(X))))&
((quiet(mary)<~>brave(mary)))&
((wise(john)&kind(john)))&
((kind(mary)&generous(mary))) | ~brave(mary) | [] | null | 0 |
Everyone who is not tall or not kind is either not tall or not calm and vice versa.
Everyone who is both patient and rich is not calm or calm.
Everyone who is either not old or not kind is both wise and not tall.
Everyone who is both not wise and not humble is both tall and not happy and vice versa.
Everyone who is not brave is curious or brave.
If someone is both not calm and not patient then someone is not funny or rich and vice versa.
Everyone who is either not curious or humble is not creative or funny.
Everyone who is not curious is both creative and old.
If someone is not creative or not calm then someone is not patient.
Everyone who is both curious and old is curious or not wise and vice versa.
Everyone who is funny or brave is both not happy and not creative and vice versa.
If someone is not patient or patient then someone is both not creative and curious and vice versa.
Everyone who is calm is not old or humble and vice versa.
Everyone who is both humble and wise is wise or tall.
If someone is not wise then susan is either curious or humble.
Everyone who is not rich is either funny or strong.
John is both not rich and not creative.
Someone is both brave and not patient.
Someone is either not patient or tall.
Susan is either old or tall. | Susan is not brave. | neutral | (![X]:((~tall(X)|~kind(X))<=>(~tall(X)<~>~calm(X))))&
(![X]:((patient(X)&rich(X))=>(~calm(X)|calm(X))))&
(![X]:((~old(X)<~>~kind(X))=>(wise(X)&~tall(X))))&
(![X]:((~wise(X)&~humble(X))<=>(tall(X)&~happy(X))))&
(![X]:(~brave(X)=>(curious(X)|brave(X))))&
((?[X]:((~calm(X)&~patient(X))))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(~creative(X)|funny(X))))&
(![X]:(~curious(X)=>(creative(X)&old(X))))&
((?[X]:((~creative(X)|~calm(X))))=>(?[X]:(~patient(X))))&
(![X]:((curious(X)&old(X))<=>(curious(X)|~wise(X))))&
(![X]:((funny(X)|brave(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((~patient(X)|patient(X))))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:(calm(X)<=>(~old(X)|humble(X))))&
(![X]:((humble(X)&wise(X))=>(wise(X)|tall(X))))&
((?[X]:(~wise(X)))=>((curious(susan)<~>humble(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>strong(X))))&
((~rich(john)&~creative(john)))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((old(susan)<~>tall(susan))) | ~brave(susan) | [] | null | 0 |
If alice is not brave then alice is both happy and rich and vice versa. If fred is not old or funny then lucy is both not generous and not curious and vice versa. Everyone who is both not kind and not creative is happy or tall. If someone is either humble or kind then someone is not humble. Everyone who is both not patient and curious is funny and vice versa. Everyone who is tall is both not rich and not quiet and vice versa. Everyone who is either not tall or wise is both not kind and strong and vice versa. If john is either generous or old then someone is both happy and wise and vice versa. If lucy is either not tall or not old then fred is both not rich and creative and vice versa. If susan is both not brave and not happy then someone is either not rich or not strong. Everyone who is not wise or rich is not happy and vice versa. Everyone who is either not calm or quiet is humble or funny and vice versa. If someone is either not tall or tall then someone is both calm and strong. If lucy is calm then susan is either not rich or not tall. Everyone who is either not brave or not humble is both happy and not humble and vice versa. If paul is quiet then someone is brave or happy and vice versa. Someone is both not calm and quiet. Lucy is either not humble or not happy. Someone is both brave and patient. Someone is both kind and curious. Someone is either not rich or generous. Someone is kind or not happy. Someone is wise or happy. Lucy is not strong. | John is not old. | neutral | ((~brave(alice))<=>((happy(alice)&rich(alice))))&
(((~old(fred)|funny(fred)))<=>((~generous(lucy)&~curious(lucy))))&
(![X]:((~kind(X)&~creative(X))=>(happy(X)|tall(X))))&
((?[X]:((humble(X)<~>kind(X))))=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&curious(X))<=>funny(X)))&
(![X]:(tall(X)<=>(~rich(X)&~quiet(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(~kind(X)&strong(X))))&
(((generous(john)<~>old(john)))<=>(?[X]:((happy(X)&wise(X)))))&
(((~tall(lucy)<~>~old(lucy)))<=>((~rich(fred)&creative(fred))))&
(((~brave(susan)&~happy(susan)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~wise(X)|rich(X))<=>~happy(X)))&
(![X]:((~calm(X)<~>quiet(X))<=>(humble(X)|funny(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>(?[X]:((calm(X)&strong(X)))))&
((calm(lucy))=>((~rich(susan)<~>~tall(susan))))&
(![X]:((~brave(X)<~>~humble(X))<=>(happy(X)&~humble(X))))&
((quiet(paul))<=>(?[X]:((brave(X)|happy(X)))))&
(?[X]:((~calm(X)&quiet(X))))&
((~humble(lucy)<~>~happy(lucy)))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:((~rich(X)<~>generous(X))))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:((wise(X)|happy(X))))&
(~strong(lucy)) | ~old(john) | [] | null | 0 |
If someone is not rich then someone is both not creative and brave and vice versa. Everyone who is kind is either not quiet or kind and vice versa. If someone is not calm then mary is not humble or rich. Everyone who is humble or not funny is both funny and not strong. If paul is either calm or rich then lucy is both wise and not tall and vice versa. If someone is generous then someone is not humble and vice versa. If mary is either not wise or humble then susan is both not old and not brave and vice versa. If lucy is not strong or not calm then fred is old or generous. Everyone who is either wise or not old is creative or brave and vice versa. Everyone who is quiet is both not strong and not tall. If mary is either humble or not calm then mary is quiet and vice versa. Everyone who is curious is both strong and not patient. Everyone who is either not old or not wise is either curious or creative. Everyone who is tall or brave is not tall and vice versa. If someone is humble then someone is either creative or quiet. Everyone who is both funny and patient is both not generous and not tall and vice versa. Fred is both not creative and funny. Lucy is either not patient or not funny. Someone is not generous. Someone is either humble or tall. Paul is brave or not happy. Susan is both not calm and not patient. | Mary is humble. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:(kind(X)<=>(~quiet(X)<~>kind(X))))&
((?[X]:(~calm(X)))=>((~humble(mary)|rich(mary))))&
(![X]:((humble(X)|~funny(X))=>(funny(X)&~strong(X))))&
(((calm(paul)<~>rich(paul)))<=>((wise(lucy)&~tall(lucy))))&
((?[X]:(generous(X)))<=>(?[X]:(~humble(X))))&
(((~wise(mary)<~>humble(mary)))<=>((~old(susan)&~brave(susan))))&
(((~strong(lucy)|~calm(lucy)))=>((old(fred)|generous(fred))))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)|brave(X))))&
(![X]:(quiet(X)=>(~strong(X)&~tall(X))))&
(((humble(mary)<~>~calm(mary)))<=>(quiet(mary)))&
(![X]:(curious(X)=>(strong(X)&~patient(X))))&
(![X]:((~old(X)<~>~wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((tall(X)|brave(X))<=>~tall(X)))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:((funny(X)&patient(X))<=>(~generous(X)&~tall(X))))&
((~creative(fred)&funny(fred)))&
((~patient(lucy)<~>~funny(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((humble(X)<~>tall(X))))&
((brave(paul)|~happy(paul)))&
((~calm(susan)&~patient(susan))) | humble(mary) | [] | null | 0 |
If someone is both not curious and brave then someone is both not calm and happy. Everyone who is funny is both rich and strong and vice versa. Everyone who is not creative or rich is not calm and vice versa. Everyone who is both not old and not calm is both patient and not funny and vice versa. Everyone who is not quiet is either wise or not funny. Everyone who is either creative or wise is not happy or not patient. If john is not calm or not rich then someone is not patient and vice versa. If someone is both patient and tall then someone is both not generous and not strong. Everyone who is either not funny or funny is both generous and not wise and vice versa. Everyone who is generous or not kind is either not wise or not funny and vice versa. If alice is happy then susan is wise or not wise. If someone is both strong and not brave then mary is not kind or old. Everyone who is not tall or not wise is strong. If mary is either humble or not funny then mary is either not patient or not rich and vice versa. If someone is quiet then alice is both old and creative and vice versa. If someone is not funny then someone is both not generous and patient. Mary is not brave. Susan is not calm. John is strong or not generous. John is not tall. | Mary is not old. | contradiction | ((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:(funny(X)<=>(rich(X)&strong(X))))&
(![X]:((~creative(X)|rich(X))<=>~calm(X)))&
(![X]:((~old(X)&~calm(X))<=>(patient(X)&~funny(X))))&
(![X]:(~quiet(X)=>(wise(X)<~>~funny(X))))&
(![X]:((creative(X)<~>wise(X))=>(~happy(X)|~patient(X))))&
(((~calm(john)|~rich(john)))<=>(?[X]:(~patient(X))))&
((?[X]:((patient(X)&tall(X))))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(generous(X)&~wise(X))))&
(![X]:((generous(X)|~kind(X))<=>(~wise(X)<~>~funny(X))))&
((happy(alice))=>((wise(susan)|~wise(susan))))&
((?[X]:((strong(X)&~brave(X))))=>((~kind(mary)|old(mary))))&
(![X]:((~tall(X)|~wise(X))=>strong(X)))&
(((humble(mary)<~>~funny(mary)))<=>((~patient(mary)<~>~rich(mary))))&
((?[X]:(quiet(X)))<=>((old(alice)&creative(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((~generous(X)&patient(X)))))&
(~brave(mary))&
(~calm(susan))&
((strong(john)|~generous(john)))&
(~tall(john)) | ~old(mary) | [
"p1",
"p2",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2623673238130999813889498
% SZS output start Proof for 2623673238130999813889498
2. ! [X0] : (funny(X0) <=> (strong(X0) & rich(X0))) [input p1]
3. ! [X0] : ((rich(X0) | ~creative(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~funny(X0) & patient(X0))) [input p3]
9. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~wise(X0) & generous(X0))) [input p8]
10. ! [X0] : ((~kind(X0) | generous(X0)) <=> (~wise(X0) <~> ~funny(X0))) [input p9]
21. ~old(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) | (~strong(X0) | ~rich(X0))) & ((strong(X0) & rich(X0)) | ~funny(X0))) [nnf transformation 2]
35. ! [X0] : ((funny(X0) | ~strong(X0) | ~rich(X0)) & ((strong(X0) & rich(X0)) | ~funny(X0))) [flattening 34]
36. ! [X0] : (((rich(X0) | ~creative(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) & creative(X0)))) [nnf transformation 3]
37. ! [X0] : ((rich(X0) | ~creative(X0) | calm(X0)) & (~calm(X0) | (~rich(X0) & creative(X0)))) [flattening 36]
38. ! [X0] : (((~calm(X0) & ~old(X0)) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | (calm(X0) | old(X0)))) [nnf transformation 4]
39. ! [X0] : (((~calm(X0) & ~old(X0)) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | calm(X0) | old(X0))) [flattening 38]
49. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [flattening 49]
51. ! [X0] : (((~kind(X0) | generous(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) & (((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~kind(X0) | generous(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) & (((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0)))) [flattening 51]
62. ~funny(X0) | rich(X0) [cnf transformation 35]
66. ~rich(X0) | ~calm(X0) [cnf transformation 37]
69. ~funny(X0) | calm(X0) | old(X0) [cnf transformation 39]
79. generous(X0) | funny(X0) | funny(X0) [cnf transformation 50]
80. generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
81. ~wise(X0) | funny(X0) | funny(X0) [cnf transformation 50]
82. ~wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
87. funny(X0) | wise(X0) | ~generous(X0) [cnf transformation 52]
111. ~old(mary) [cnf transformation 21]
112. generous(X0) | funny(X0) [duplicate literal removal 79]
113. ~funny(X0) | generous(X0) [duplicate literal removal 80]
114. ~wise(X0) | funny(X0) [duplicate literal removal 81]
115. ~wise(X0) | ~funny(X0) [duplicate literal removal 82]
143. ~wise(X0) [subsumption resolution 114,115]
144. generous(X0) [subsumption resolution 112,113]
146. funny(X0) | ~generous(X0) [subsumption resolution 87,143]
147. funny(X0) [subsumption resolution 146,144]
156. 9 <=> old(mary) [avatar definition]
157. ~old(mary) <- (~9) [avatar component clause 156]
195. ~9 [avatar split clause 111,156]
200. rich(X0) [resolution 62,147]
204. ~calm(X0) [resolution 66,200]
211. calm(X0) | old(X0) [resolution 69,147]
212. old(X0) [subsumption resolution 211,204]
215. $false <- (~9) [resolution 212,157]
216. 9 [avatar contradiction clause 215]
217. $false [avatar sat refutation 195,216]
% SZS output end Proof for 2623673238130999813889498
% ------------------------------
% 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 curious or funny is either not patient or creative.
If fred is not happy or calm then someone is either curious or generous.
If alice is either patient or not tall then susan is humble or brave.
Everyone who is not tall is patient and vice versa.
If someone is either not humble or funny then someone is not patient or not happy.
Everyone who is not calm is either not old or humble and vice versa.
Everyone who is not creative is both generous and not happy and vice versa.
Everyone who is both funny and creative is not curious and vice versa.
Everyone who is both not generous and not wise is both calm and not quiet.
Everyone who is both not kind and rich is not quiet or patient and vice versa.
Everyone who is either rich or calm is not creative.
Everyone who is patient is not funny or generous and vice versa.
If alice is both rich and not kind then someone is curious and vice versa.
If someone is both not generous and happy then paul is both not kind and creative and vice versa.
If john is not humble or humble then paul is wise.
Everyone who is not humble or not brave is both happy and not strong and vice versa.
John is creative.
Paul is both wise and not old.
Someone is either not happy or not rich.
Alice is patient.
Paul is tall or quiet.
Someone is both humble and funny.
Someone is both not wise and not quiet. | Fred is not rich. | contradiction | (![X]:((curious(X)|funny(X))=>(~patient(X)<~>creative(X))))&
(((~happy(fred)|calm(fred)))=>(?[X]:((curious(X)<~>generous(X)))))&
(((patient(alice)<~>~tall(alice)))=>((humble(susan)|brave(susan))))&
(![X]:(~tall(X)<=>patient(X)))&
((?[X]:((~humble(X)<~>funny(X))))=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:(~calm(X)<=>(~old(X)<~>humble(X))))&
(![X]:(~creative(X)<=>(generous(X)&~happy(X))))&
(![X]:((funny(X)&creative(X))<=>~curious(X)))&
(![X]:((~generous(X)&~wise(X))=>(calm(X)&~quiet(X))))&
(![X]:((~kind(X)&rich(X))<=>(~quiet(X)|patient(X))))&
(![X]:((rich(X)<~>calm(X))=>~creative(X)))&
(![X]:(patient(X)<=>(~funny(X)|generous(X))))&
(((rich(alice)&~kind(alice)))<=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)&happy(X))))<=>((~kind(paul)&creative(paul))))&
(((~humble(john)|humble(john)))=>(wise(paul)))&
(![X]:((~humble(X)|~brave(X))<=>(happy(X)&~strong(X))))&
(creative(john))&
((wise(paul)&~old(paul)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(patient(alice))&
((tall(paul)|quiet(paul)))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:((~wise(X)&~quiet(X)))) | ~rich(fred) | [
"p0",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 27883872501503872251958
% SZS output start Proof for 27883872501503872251958
1. ! [X0] : ((funny(X0) | curious(X0)) => (~patient(X0) <~> creative(X0))) [input p0]
7. ! [X0] : (~creative(X0) <=> (~happy(X0) & generous(X0))) [input p6]
8. ! [X0] : ((creative(X0) & funny(X0)) <=> ~curious(X0)) [input p7]
10. ! [X0] : ((rich(X0) & ~kind(X0)) <=> (patient(X0) | ~quiet(X0))) [input p9]
12. ! [X0] : (patient(X0) <=> (generous(X0) | ~funny(X0))) [input p11]
24. ~rich(fred) [input hypothesis]
26. ! [X0] : ((~patient(X0) <~> creative(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 1]
35. ! [X0] : (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 26]
46. ! [X0] : ((~creative(X0) | (happy(X0) | ~generous(X0))) & ((~happy(X0) & generous(X0)) | creative(X0))) [nnf transformation 7]
47. ! [X0] : ((~creative(X0) | happy(X0) | ~generous(X0)) & ((~happy(X0) & generous(X0)) | creative(X0))) [flattening 46]
48. ! [X0] : (((creative(X0) & funny(X0)) | curious(X0)) & (~curious(X0) | (~creative(X0) | ~funny(X0)))) [nnf transformation 8]
49. ! [X0] : (((creative(X0) & funny(X0)) | curious(X0)) & (~curious(X0) | ~creative(X0) | ~funny(X0))) [flattening 48]
50. ! [X0] : (((rich(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | (~rich(X0) | kind(X0)))) [nnf transformation 10]
51. ! [X0] : (((rich(X0) & ~kind(X0)) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | ~rich(X0) | kind(X0))) [flattening 50]
53. ! [X0] : ((patient(X0) | (~generous(X0) & funny(X0))) & ((generous(X0) | ~funny(X0)) | ~patient(X0))) [nnf transformation 12]
54. ! [X0] : ((patient(X0) | (~generous(X0) & funny(X0))) & (generous(X0) | ~funny(X0) | ~patient(X0))) [flattening 53]
77. ~creative(X0) | patient(X0) | ~funny(X0) [cnf transformation 35]
92. generous(X0) | creative(X0) [cnf transformation 47]
95. ~creative(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 49]
97. creative(X0) | curious(X0) [cnf transformation 49]
104. ~patient(X0) | rich(X0) [cnf transformation 51]
108. patient(X0) | funny(X0) [cnf transformation 54]
109. ~generous(X0) | patient(X0) [cnf transformation 54]
135. ~rich(fred) [cnf transformation 24]
277. creative(X0) | patient(X0) [resolution 109,92]
322. patient(X0) | ~funny(X0) | curious(X0) [resolution 77,97]
329. patient(X0) | curious(X0) [subsumption resolution 322,108]
498. patient(X0) | ~curious(X0) | ~funny(X0) [resolution 277,95]
505. patient(X0) | ~curious(X0) [subsumption resolution 498,108]
506. patient(X0) [subsumption resolution 505,329]
635. rich(X3) [resolution 506,104]
707. $false [resolution 635,135]
% SZS output end Proof for 27883872501503872251958
% ------------------------------
% 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 humble or not old is both rich and curious and vice versa. If mary is not quiet then fred is generous and vice versa. Everyone who is happy or not kind is quiet or creative. If john is both generous and not happy then someone is either strong or humble and vice versa. If mary is not happy then lucy is both not funny and patient and vice versa. Everyone who is both funny and not wise is both generous and not rich. Everyone who is wise or old is both curious and not brave. If someone is generous or strong then alice is patient or not strong and vice versa. Everyone who is both not patient and not kind is either brave or not generous and vice versa. Everyone who is not calm is both not quiet and not humble. Everyone who is both generous and not wise is not calm and vice versa. If someone is patient or brave then someone is not rich or old. Everyone who is not wise is both tall and humble. Everyone who is both tall and not rich is wise or not generous and vice versa. If someone is not strong or not quiet then someone is tall. Everyone who is not funny or not calm is not brave. John is either not creative or not calm. Alice is not tall or strong. John is not happy or not generous. Someone is both curious and not rich. Lucy is not quiet. Someone is either generous or not happy. | John is creative. | contradiction | (![X]:((humble(X)|~old(X))<=>(rich(X)&curious(X))))&
((~quiet(mary))<=>(generous(fred)))&
(![X]:((happy(X)|~kind(X))=>(quiet(X)|creative(X))))&
(((generous(john)&~happy(john)))<=>(?[X]:((strong(X)<~>humble(X)))))&
((~happy(mary))<=>((~funny(lucy)&patient(lucy))))&
(![X]:((funny(X)&~wise(X))=>(generous(X)&~rich(X))))&
(![X]:((wise(X)|old(X))=>(curious(X)&~brave(X))))&
((?[X]:((generous(X)|strong(X))))<=>((patient(alice)|~strong(alice))))&
(![X]:((~patient(X)&~kind(X))<=>(brave(X)<~>~generous(X))))&
(![X]:(~calm(X)=>(~quiet(X)&~humble(X))))&
(![X]:((generous(X)&~wise(X))<=>~calm(X)))&
((?[X]:((patient(X)|brave(X))))=>(?[X]:((~rich(X)|old(X)))))&
(![X]:(~wise(X)=>(tall(X)&humble(X))))&
(![X]:((tall(X)&~rich(X))<=>(wise(X)|~generous(X))))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:(tall(X))))&
(![X]:((~funny(X)|~calm(X))=>~brave(X)))&
((~creative(john)<~>~calm(john)))&
((~tall(alice)|strong(alice)))&
((~happy(john)|~generous(john)))&
(?[X]:((curious(X)&~rich(X))))&
(~quiet(lucy))&
(?[X]:((generous(X)<~>~happy(X)))) | creative(john) | [
"p9",
"p10",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5379676479600108852353111
% SZS output start Proof for 5379676479600108852353111
10. ! [X0] : (~calm(X0) => (~humble(X0) & ~quiet(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & generous(X0)) <=> ~calm(X0)) [input p10]
13. ! [X0] : (~wise(X0) => (humble(X0) & tall(X0))) [input p12]
17. ~creative(john) <~> ~calm(john) [input p16]
23. creative(john) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~quiet(X0)) | calm(X0)) [ennf transformation 10]
33. ! [X0] : ((humble(X0) & tall(X0)) | wise(X0)) [ennf transformation 13]
53. ! [X0] : (((~wise(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) | ~generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~wise(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | wise(X0) | ~generous(X0))) [flattening 53]
63. (calm(john) | creative(john)) & (~calm(john) | ~creative(john)) [nnf transformation 17]
104. ~humble(X0) | calm(X0) [cnf transformation 31]
107. ~wise(X0) | calm(X0) [cnf transformation 54]
111. wise(X0) | humble(X0) [cnf transformation 33]
121. ~calm(john) | ~creative(john) [cnf transformation 63]
130. creative(john) [cnf transformation 23]
228. 21 <=> creative(john) [avatar definition]
232. 22 <=> calm(john) [avatar definition]
233. ~calm(john) <- (~22) [avatar component clause 232]
236. ~21 | ~22 [avatar split clause 121,232,228]
250. 21 [avatar split clause 130,228]
257. humble(X0) | calm(X0) [resolution 111,107]
258. calm(X0) [subsumption resolution 257,104]
259. $false <- (~22) [resolution 258,233]
260. 22 [avatar contradiction clause 259]
261. $false [avatar sat refutation 236,250,260]
% SZS output end Proof for 5379676479600108852353111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not happy then john is not generous.
If john is patient then mary is not generous or happy.
Everyone who is both old and not strong is not quiet and vice versa.
If john is old then susan is both not funny and generous.
Everyone who is humble or not generous is both not happy and not funny and vice versa.
Everyone who is not wise or strong is either calm or not brave.
If lucy is either kind or not happy then someone is either not kind or funny.
If someone is not creative or happy then paul is not happy.
If someone is both not patient and wise then lucy is tall.
Everyone who is both not funny and calm is not tall or not rich and vice versa.
If someone is not funny then someone is either curious or tall and vice versa.
Everyone who is both not patient and patient is both quiet and not quiet and vice versa.
Everyone who is both not humble and not creative is both not generous and funny.
Everyone who is not brave is both brave and humble and vice versa.
If john is both patient and not creative then someone is both kind and not tall and vice versa.
If someone is both patient and not kind then susan is either quiet or not tall.
Mary is not happy or humble.
Mary is not strong or not creative.
Someone is not tall.
Someone is happy.
Someone is either not generous or funny.
Someone is either creative or old.
Someone is either not creative or old. | Mary is not creative. | contradiction | ((?[X]:((~creative(X)&~happy(X))))=>(~generous(john)))&
((patient(john))=>((~generous(mary)|happy(mary))))&
(![X]:((old(X)&~strong(X))<=>~quiet(X)))&
((old(john))=>((~funny(susan)&generous(susan))))&
(![X]:((humble(X)|~generous(X))<=>(~happy(X)&~funny(X))))&
(![X]:((~wise(X)|strong(X))=>(calm(X)<~>~brave(X))))&
(((kind(lucy)<~>~happy(lucy)))=>(?[X]:((~kind(X)<~>funny(X)))))&
((?[X]:((~creative(X)|happy(X))))=>(~happy(paul)))&
((?[X]:((~patient(X)&wise(X))))=>(tall(lucy)))&
(![X]:((~funny(X)&calm(X))<=>(~tall(X)|~rich(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~patient(X)&patient(X))<=>(quiet(X)&~quiet(X))))&
(![X]:((~humble(X)&~creative(X))=>(~generous(X)&funny(X))))&
(![X]:(~brave(X)<=>(brave(X)&humble(X))))&
(((patient(john)&~creative(john)))<=>(?[X]:((kind(X)&~tall(X)))))&
((?[X]:((patient(X)&~kind(X))))=>((quiet(susan)<~>~tall(susan))))&
((~happy(mary)|humble(mary)))&
((~strong(mary)|~creative(mary)))&
(?[X]:(~tall(X)))&
(?[X]:(happy(X)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((creative(X)<~>old(X))))&
(?[X]:((~creative(X)<~>old(X)))) | ~creative(mary) | [
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4593762954704202278657401
% SZS output start Proof for 4593762954704202278657401
5. ! [X0] : ((~generous(X0) | humble(X0)) <=> (~funny(X0) & ~happy(X0))) [input p4]
13. ! [X0] : ((~creative(X0) & ~humble(X0)) => (funny(X0) & ~generous(X0))) [input p12]
14. ! [X0] : (~brave(X0) <=> (humble(X0) & brave(X0))) [input p13]
24. ~creative(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) & ~generous(X0)) | (creative(X0) | humble(X0))) [ennf transformation 13]
35. ! [X0] : ((funny(X0) & ~generous(X0)) | creative(X0) | humble(X0)) [flattening 34]
39. ! [X0] : (((~generous(X0) | humble(X0)) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | (generous(X0) & ~humble(X0)))) [nnf transformation 5]
40. ! [X0] : ((~generous(X0) | humble(X0) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | (generous(X0) & ~humble(X0)))) [flattening 39]
54. ! [X0] : ((~brave(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | brave(X0))) [nnf transformation 14]
55. ! [X0] : ((~brave(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | brave(X0))) [flattening 54]
85. ~funny(X0) | generous(X0) [cnf transformation 40]
111. ~generous(X0) | creative(X0) | humble(X0) [cnf transformation 35]
112. humble(X0) | creative(X0) | funny(X0) [cnf transformation 35]
113. brave(X0) | brave(X0) [cnf transformation 55]
115. ~brave(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 55]
132. ~creative(mary) [cnf transformation 24]
133. brave(X0) [duplicate literal removal 113]
134. ~brave(X0) | ~humble(X0) [duplicate literal removal 115]
199. 15 <=> ! [X0] : creative(X0) [avatar definition]
200. creative(X0) <- (15) [avatar component clause 199]
274. 32 <=> creative(mary) [avatar definition]
276. ~creative(mary) <- (~32) [avatar component clause 274]
307. ~32 [avatar split clause 132,274]
331. ~humble(X1) [resolution 134,133]
360. funny(X0) | creative(X0) [resolution 112,331]
370. generous(X2) | creative(X2) [resolution 360,85]
380. creative(X1) | creative(X1) | humble(X1) [resolution 370,111]
381. creative(X1) | humble(X1) [duplicate literal removal 380]
383. creative(X1) [subsumption resolution 381,331]
384. 15 [avatar split clause 383,199]
385. $false <- (15, ~32) [resolution 200,276]
388. ~15 | 32 [avatar contradiction clause 385]
389. $false [avatar sat refutation 307,384,388]
% SZS output end Proof for 4593762954704202278657401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not generous is either rich or not patient and vice versa. Everyone who is both not wise and kind is not humble. Everyone who is happy is patient or not happy. If alice is brave or not tall then someone is quiet. If lucy is both not quiet and creative then fred is tall and vice versa. If someone is not old or not funny then paul is calm and vice versa. Everyone who is not humble is rich or not calm and vice versa. Everyone who is either not rich or not generous is not wise and vice versa. If lucy is either not calm or not patient then john is not wise. Everyone who is not patient is not wise and vice versa. Everyone who is either not creative or not quiet is both not patient and rich. If alice is not quiet then someone is either not happy or generous. Everyone who is either quiet or patient is creative or not old and vice versa. Everyone who is both tall and not rich is not creative and vice versa. If someone is both not rich and strong then paul is creative and vice versa. Everyone who is not brave or strong is not calm and vice versa. John is not happy. Mary is not strong or not quiet. Someone is not generous. Someone is not quiet or not kind. John is either happy or wise. Mary is calm. Mary is either curious or strong. | Paul is generous. | contradiction | (![X]:((~brave(X)&~generous(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))=>~humble(X)))&
(![X]:(happy(X)=>(patient(X)|~happy(X))))&
(((brave(alice)|~tall(alice)))=>(?[X]:(quiet(X))))&
(((~quiet(lucy)&creative(lucy)))<=>(tall(fred)))&
((?[X]:((~old(X)|~funny(X))))<=>(calm(paul)))&
(![X]:(~humble(X)<=>(rich(X)|~calm(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>~wise(X)))&
(((~calm(lucy)<~>~patient(lucy)))=>(~wise(john)))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~patient(X)&rich(X))))&
((~quiet(alice))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>patient(X))<=>(creative(X)|~old(X))))&
(![X]:((tall(X)&~rich(X))<=>~creative(X)))&
((?[X]:((~rich(X)&strong(X))))<=>(creative(paul)))&
(![X]:((~brave(X)|strong(X))<=>~calm(X)))&
(~happy(john))&
((~strong(mary)|~quiet(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(john)<~>wise(john)))&
(calm(mary))&
((curious(mary)<~>strong(mary))) | generous(paul) | [
"p0",
"p7",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9184693072514905204374811
% SZS output start Proof for 9184693072514905204374811
1. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (rich(X0) <~> ~patient(X0))) [input p0]
8. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p7]
10. ! [X0] : (~patient(X0) <=> ~wise(X0)) [input p9]
11. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) => (rich(X0) & ~patient(X0))) [input p10]
13. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~old(X0) | creative(X0))) [input p12]
14. ! [X0] : ((~rich(X0) & tall(X0)) <=> ~creative(X0)) [input p13]
24. generous(paul) [input hypothesis]
33. ! [X0] : ((rich(X0) & ~patient(X0)) | (~creative(X0) <=> ~quiet(X0))) [ennf transformation 11]
35. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (generous(X0) | brave(X0)))) [nnf transformation 1]
36. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | generous(X0) | brave(X0))) [flattening 35]
45. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | wise(X0)) & (~wise(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 8]
47. ! [X0] : ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))) [nnf transformation 10]
48. ! [X0] : ((rich(X0) & ~patient(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) [nnf transformation 33]
52. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 13]
53. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 52]
54. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | (rich(X0) | ~tall(X0)))) [nnf transformation 14]
55. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | rich(X0) | ~tall(X0))) [flattening 54]
71. ~generous(X0) | rich(X0) | patient(X0) [cnf transformation 36]
81. ~wise(X0) | ~generous(X0) | rich(X0) [cnf transformation 45]
83. ~rich(X0) | ~generous(X0) | wise(X0) [cnf transformation 45]
84. wise(X0) | rich(X0) | generous(X0) [cnf transformation 45]
87. ~wise(X0) | patient(X0) [cnf transformation 47]
88. ~patient(X0) | wise(X0) [cnf transformation 47]
90. ~creative(X0) | ~patient(X0) | quiet(X0) [cnf transformation 48]
99. ~patient(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 53]
103. ~rich(X0) | creative(X0) [cnf transformation 55]
118. generous(paul) [cnf transformation 24]
198. ~creative(X0) | ~patient(X0) [subsumption resolution 99,90]
203. 18 <=> creative(paul) [avatar definition]
204. creative(paul) <- (18) [avatar component clause 203]
297. rich(X2) | generous(X2) | patient(X2) [resolution 84,87]
300. patient(X2) | rich(X2) [subsumption resolution 297,71]
338. 31 <=> rich(paul) [avatar definition]
340. rich(paul) <- (31) [avatar component clause 338]
358. wise(X3) | rich(X3) [resolution 300,88]
573. rich(X1) | ~generous(X1) | rich(X1) [resolution 358,81]
575. ~generous(X1) | rich(X1) [duplicate literal removal 573]
656. rich(paul) [resolution 575,118]
658. 31 [avatar split clause 656,338]
667. ~generous(paul) | wise(paul) <- (31) [resolution 340,83]
668. creative(paul) <- (31) [resolution 340,103]
669. wise(paul) <- (31) [subsumption resolution 667,118]
672. 18 | ~31 [avatar split clause 668,338,203]
681. ~patient(paul) <- (18) [resolution 204,198]
712. patient(paul) <- (31) [resolution 669,87]
713. $false <- (18, 31) [subsumption resolution 712,681]
714. ~18 | ~31 [avatar contradiction clause 713]
715. $false [avatar sat refutation 658,672,714]
% SZS output end Proof for 9184693072514905204374811
% ------------------------------
% 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 either not brave or not generous is both not brave and not tall and vice versa.
Everyone who is not funny is either strong or not strong.
If someone is both happy and patient then someone is not kind or curious and vice versa.
Everyone who is not strong is not humble or not brave.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
Alice is not quiet or quiet.
John is curious.
Someone is either not funny or not happy.
Mary is either humble or strong.
Someone is either not happy or happy.
Someone is both not brave and rich. | Mary is not curious. | contradiction | (![X]:((~brave(X)<~>~generous(X))<=>(~brave(X)&~tall(X))))&
(![X]:(~funny(X)=>(strong(X)<~>~strong(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:(~strong(X)=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
((~quiet(alice)|quiet(alice)))&
(curious(john))&
(?[X]:((~funny(X)<~>~happy(X))))&
((humble(mary)<~>strong(mary)))&
(?[X]:((~happy(X)<~>happy(X))))&
(?[X]:((~brave(X)&rich(X)))) | ~curious(mary) | [
"p0",
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7576707195214027130594697
% SZS output start Proof for 7576707195214027130594697
1. ! [X0] : ((~brave(X0) <~> ~generous(X0)) <=> (~tall(X0) & ~brave(X0))) [input p0]
8. ! [X0] : ((funny(X0) | strong(X0)) <=> quiet(X0)) [input p7]
9. ? [X0] : ~strong(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p9]
13. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~wise(X0) & brave(X0))) [input p12]
14. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p13]
22. ~curious(mary) [input hypothesis]
24. ? [X0] : ~strong(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 9]
30. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [nnf transformation 1]
31. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [flattening 30]
50. ! [X0] : (((funny(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 8]
51. ! [X0] : ((funny(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) & ~strong(X0)))) [flattening 50]
52. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : strong(X0)) [nnf transformation 24]
53. (? [X0] : ~strong(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : strong(X3)) [rectify 52]
54. ? [X0] : ~strong(X0) => ~strong(sK4) [choice axiom]
55. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK5) & calm(sK5)) [choice axiom]
56. (~strong(sK4) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK5) & calm(sK5)) | ! [X3] : strong(X3)) [skolemisation 53,55,54]
57. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
58. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ~quiet(X0) | happy(X0))) [flattening 57]
60. ! [X0] : (((tall(X0) & ~curious(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 13]
61. ! [X0] : (((tall(X0) & ~curious(X0)) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | ~tall(X0) | curious(X0))) [flattening 60]
62. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 14]
63. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 62]
76. ~brave(X0) | ~brave(X0) | generous(X0) [cnf transformation 31]
80. generous(X0) | brave(X0) | tall(X0) | brave(X0) [cnf transformation 31]
105. ~strong(X0) | quiet(X0) [cnf transformation 51]
108. calm(sK5) | strong(X3) [cnf transformation 56]
109. ~calm(sK5) | strong(X3) [cnf transformation 56]
112. happy(X0) | ~generous(X0) | ~quiet(X0) | happy(X0) [cnf transformation 58]
113. ~happy(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 58]
126. ~wise(X0) | ~tall(X0) | curious(X0) [cnf transformation 61]
130. ~tall(X0) | wise(X0) [cnf transformation 63]
132. wise(X0) | tall(X0) [cnf transformation 63]
147. ~curious(mary) [cnf transformation 22]
148. happy(X0) | ~generous(X0) | ~quiet(X0) [duplicate literal removal 112]
149. ~happy(X0) | ~generous(X0) [duplicate literal removal 113]
150. ~brave(X0) | generous(X0) [duplicate literal removal 76]
151. tall(X0) | brave(X0) | generous(X0) [duplicate literal removal 80]
239. 20 <=> ! [X3] : strong(X3) [avatar definition]
240. strong(X3) <- (20) [avatar component clause 239]
242. 21 <=> calm(sK5) [avatar definition]
245. 20 | ~21 [avatar split clause 109,242,239]
246. 20 | 21 [avatar split clause 108,242,239]
247. ~quiet(X0) | ~generous(X0) [subsumption resolution 148,149]
269. wise(X0) [subsumption resolution 130,132]
294. quiet(X0) <- (20) [resolution 105,240]
315. ~generous(X0) <- (20) [resolution 247,294]
331. ~tall(X2) | curious(X2) [resolution 126,269]
335. brave(X0) | generous(X0) | curious(X0) [resolution 151,331]
342. curious(X0) | brave(X0) <- (20) [subsumption resolution 335,315]
343. brave(mary) <- (20) [resolution 342,147]
346. generous(mary) <- (20) [resolution 343,150]
347. $false <- (20) [subsumption resolution 346,315]
348. ~20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 245,246,348]
% SZS output end Proof for 7576707195214027130594697
% ------------------------------
% 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 old or tall is either happy or curious and vice versa. Everyone who is both funny and old is not rich and vice versa. If someone is not humble or calm then alice is not strong and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. Everyone who is either not patient or not brave is not patient or strong and vice versa. If mary is not generous or brave then alice is rich or calm. Mary is happy or not creative. Fred is strong or not generous. Someone is either humble or not curious. Someone is not kind or humble. | Alice is not rich. | contradiction | (![X]:((~old(X)|tall(X))<=>(happy(X)<~>curious(X))))&
(![X]:((funny(X)&old(X))<=>~rich(X)))&
((?[X]:((~humble(X)|calm(X))))<=>(~strong(alice)))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~patient(X)|strong(X))))&
(((~generous(mary)|brave(mary)))=>((rich(alice)|calm(alice))))&
((happy(mary)|~creative(mary)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~kind(X)|humble(X)))) | ~rich(alice) | [
"p1",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5394945102973546575147879
% SZS output start Proof for 5394945102973546575147879
2. ! [X0] : ((old(X0) & funny(X0)) <=> ~rich(X0)) [input p1]
12. ! [X0] : (funny(X0) <=> (~kind(X0) & ~strong(X0))) [input p11]
14. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p13]
21. ~rich(alice) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 14]
35. ! [X0] : (((old(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | (~old(X0) | ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : (((old(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | ~old(X0) | ~funny(X0))) [flattening 35]
58. ! [X0] : ((funny(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [nnf transformation 12]
59. ! [X0] : ((funny(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [flattening 58]
75. rich(X0) | funny(X0) [cnf transformation 36]
104. ~strong(X0) | ~funny(X0) [cnf transformation 59]
112. ~funny(X0) | strong(X0) [cnf transformation 30]
128. ~rich(alice) [cnf transformation 21]
228. ~funny(X0) [subsumption resolution 112,104]
238. 24 <=> rich(alice) [avatar definition]
239. ~rich(alice) <- (~24) [avatar component clause 238]
266. ~24 [avatar split clause 128,238]
281. funny(alice) <- (~24) [resolution 75,239]
282. $false <- (~24) [subsumption resolution 281,228]
283. 24 [avatar contradiction clause 282]
284. $false [avatar sat refutation 266,283]
% SZS output end Proof for 5394945102973546575147879
% ------------------------------
% 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 strong or generous then paul is not calm and vice versa. If susan is either happy or not wise then paul is either not humble or not rich. If fred is either kind or wise then lucy is either not brave or old and vice versa. Everyone who is either funny or not rich is both not wise and not calm. Everyone who is creative or old is both not creative and not brave. Everyone who is both patient and kind is either strong or wise. Everyone who is rich is both not rich and not brave. Everyone who is both kind and curious is tall or not wise. If mary is not generous then someone is either kind or not rich. If fred is both kind and not patient then someone is curious and vice versa. Everyone who is tall or not curious is not strong. Everyone who is both rich and creative is both wise and kind and vice versa. Everyone who is both not humble and not wise is both not curious and happy. Everyone who is either not wise or not generous is either not patient or not old and vice versa. Everyone who is either funny or not generous is both not creative and rich and vice versa. Everyone who is not rich is generous and vice versa. Someone is quiet. Someone is strong. Someone is not calm. Susan is either kind or not kind. Lucy is curious. Susan is old or generous. | Mary is old. | neutral | (((~strong(mary)<~>generous(mary)))<=>(~calm(paul)))&
(((happy(susan)<~>~wise(susan)))=>((~humble(paul)<~>~rich(paul))))&
(((kind(fred)<~>wise(fred)))<=>((~brave(lucy)<~>old(lucy))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~calm(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)<=>generous(X)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(susan)<~>~kind(susan)))&
(curious(lucy))&
((old(susan)|generous(susan))) | old(mary) | [] | null | 0 |
If someone is both brave and not calm then someone is both not funny and old.
If lucy is wise then paul is rich and vice versa.
If fred is either not humble or wise then someone is kind and vice versa.
If susan is either not patient or not strong then fred is tall.
Everyone who is not rich is both humble and not generous and vice versa.
Everyone who is either generous or strong is either humble or curious and vice versa.
Everyone who is curious or not quiet is both not wise and curious and vice versa.
If fred is either not curious or wise then someone is not funny and vice versa.
Everyone who is not humble is quiet or not calm and vice versa.
Everyone who is both tall and not generous is either curious or not patient.
Everyone who is both wise and not quiet is not kind or not patient and vice versa.
If someone is both not creative and not rich then lucy is both not tall and not creative and vice versa.
Everyone who is both not curious and calm is not humble or brave and vice versa.
Everyone who is both not happy and not brave is both not calm and not quiet and vice versa.
Everyone who is happy is not happy or not brave and vice versa.
Everyone who is either wise or funny is both brave and not old.
Someone is not quiet or curious.
Someone is either funny or not generous.
Someone is calm or creative.
Someone is either not brave or creative.
Someone is old.
Paul is either patient or curious. | Fred is humble. | contradiction | ((?[X]:((brave(X)&~calm(X))))=>(?[X]:((~funny(X)&old(X)))))&
((wise(lucy))<=>(rich(paul)))&
(((~humble(fred)<~>wise(fred)))<=>(?[X]:(kind(X))))&
(((~patient(susan)<~>~strong(susan)))=>(tall(fred)))&
(![X]:(~rich(X)<=>(humble(X)&~generous(X))))&
(![X]:((generous(X)<~>strong(X))<=>(humble(X)<~>curious(X))))&
(![X]:((curious(X)|~quiet(X))<=>(~wise(X)&curious(X))))&
(((~curious(fred)<~>wise(fred)))<=>(?[X]:(~funny(X))))&
(![X]:(~humble(X)<=>(quiet(X)|~calm(X))))&
(![X]:((tall(X)&~generous(X))=>(curious(X)<~>~patient(X))))&
(![X]:((wise(X)&~quiet(X))<=>(~kind(X)|~patient(X))))&
((?[X]:((~creative(X)&~rich(X))))<=>((~tall(lucy)&~creative(lucy))))&
(![X]:((~curious(X)&calm(X))<=>(~humble(X)|brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(~calm(X)&~quiet(X))))&
(![X]:(happy(X)<=>(~happy(X)|~brave(X))))&
(![X]:((wise(X)<~>funny(X))=>(brave(X)&~old(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
(?[X]:(old(X)))&
((patient(paul)<~>curious(paul))) | humble(fred) | [
"p2",
"p6",
"p8",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 91014727616788531969809
% SZS output start Proof for 91014727616788531969809
3. (~humble(fred) <~> wise(fred)) <=> ? [X0] : kind(X0) [input p2]
7. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (curious(X0) & ~wise(X0))) [input p6]
9. ! [X0] : (~humble(X0) <=> (~calm(X0) | quiet(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) & wise(X0)) <=> (~patient(X0) | ~kind(X0))) [input p10]
17. ? [X0] : (curious(X0) | ~quiet(X0)) [input p16]
23. humble(fred) [input hypothesis]
34. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [nnf transformation 3]
35. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [rectify 34]
36. ? [X1] : kind(X1) => kind(sK1) [choice axiom]
37. (((~wise(fred) | humble(fred)) & (wise(fred) | ~humble(fred))) | ! [X0] : ~kind(X0)) & (kind(sK1) | ((~humble(fred) | ~wise(fred)) & (wise(fred) | humble(fred)))) [skolemisation 35,36]
42. ! [X0] : (((~quiet(X0) | curious(X0)) | (~curious(X0) | wise(X0))) & ((curious(X0) & ~wise(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : ((~quiet(X0) | curious(X0) | ~curious(X0) | wise(X0)) & ((curious(X0) & ~wise(X0)) | (quiet(X0) & ~curious(X0)))) [flattening 42]
48. ! [X0] : ((~humble(X0) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | humble(X0))) [nnf transformation 9]
49. ! [X0] : ((~humble(X0) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | humble(X0))) [flattening 48]
51. ! [X0] : (((~quiet(X0) & wise(X0)) | (patient(X0) & kind(X0))) & ((~patient(X0) | ~kind(X0)) | (quiet(X0) | ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : (((~quiet(X0) & wise(X0)) | (patient(X0) & kind(X0))) & (~patient(X0) | ~kind(X0) | quiet(X0) | ~wise(X0))) [flattening 51]
65. ? [X0] : (curious(X0) | ~quiet(X0)) => (curious(sK4) | ~quiet(sK4)) [choice axiom]
66. curious(sK4) | ~quiet(sK4) [skolemisation 17,65]
84. wise(fred) | ~humble(fred) | ~kind(X0) [cnf transformation 37]
99. ~curious(X0) | ~wise(X0) [cnf transformation 43]
100. ~wise(X0) | quiet(X0) [cnf transformation 43]
102. quiet(X0) | curious(X0) [cnf transformation 43]
109. ~quiet(X0) | ~humble(X0) [cnf transformation 49]
114. kind(X0) | wise(X0) [cnf transformation 52]
138. curious(sK4) | ~quiet(sK4) [cnf transformation 66]
147. humble(fred) [cnf transformation 23]
174. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
175. ~kind(X0) <- (6) [avatar component clause 174]
177. 7 <=> humble(fred) [avatar definition]
179. humble(fred) <- (7) [avatar component clause 177]
181. 8 <=> wise(fred) [avatar definition]
182. wise(fred) <- (8) [avatar component clause 181]
185. 6 | ~7 | 8 [avatar split clause 84,181,177,174]
252. curious(sK4) [subsumption resolution 138,102]
274. 7 [avatar split clause 147,177]
275. ~wise(sK4) [resolution 99,252]
279. wise(X0) <- (6) [resolution 114,175]
283. $false <- (6) [resolution 279,275]
284. ~6 [avatar contradiction clause 283]
287. quiet(fred) <- (8) [resolution 182,100]
294. ~humble(fred) <- (8) [resolution 287,109]
295. $false <- (7, 8) [subsumption resolution 294,179]
296. ~7 | ~8 [avatar contradiction clause 295]
297. $false [avatar sat refutation 185,274,284,296]
% SZS output end Proof for 91014727616788531969809
% ------------------------------
% 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 is not old.
If mary is old then paul is wise or funny.
Everyone who is either not quiet or calm is both not curious and patient.
If someone is both not calm and funny then lucy is either not funny or not tall and vice versa.
If lucy is not generous or not patient then someone is either quiet or generous and vice versa.
Everyone who is both quiet and not curious is not strong.
If susan is happy or calm then someone is not tall and vice versa.
If someone is humble then fred is creative or not rich.
Everyone who is both old and wise is both not quiet and not strong.
If john is tall then someone is both humble and curious and vice versa.
If lucy is either patient or strong then john is both rich and not generous.
Everyone who is either not curious or not quiet is both curious and not tall.
Everyone who is both funny and not curious is either happy or wise and vice versa.
Everyone who is not brave is not rich or not tall and vice versa.
Everyone who is both not humble and happy is both not generous and wise.
If paul is not patient then someone is both not strong and old.
Fred is both rich and not patient.
Someone is not wise or tall.
Someone is both rich and not curious.
Lucy is quiet or not kind.
Someone is both not rich and not curious.
John is either tall or rich.
Fred is not funny or quiet.
Someone is curious or calm. | Lucy is not tall. | neutral | (![X]:(~humble(X)=>~old(X)))&
((old(mary))=>((wise(paul)|funny(paul))))&
(![X]:((~quiet(X)<~>calm(X))=>(~curious(X)&patient(X))))&
((?[X]:((~calm(X)&funny(X))))<=>((~funny(lucy)<~>~tall(lucy))))&
(((~generous(lucy)|~patient(lucy)))<=>(?[X]:((quiet(X)<~>generous(X)))))&
(![X]:((quiet(X)&~curious(X))=>~strong(X)))&
(((happy(susan)|calm(susan)))<=>(?[X]:(~tall(X))))&
((?[X]:(humble(X)))=>((creative(fred)|~rich(fred))))&
(![X]:((old(X)&wise(X))=>(~quiet(X)&~strong(X))))&
((tall(john))<=>(?[X]:((humble(X)&curious(X)))))&
(((patient(lucy)<~>strong(lucy)))=>((rich(john)&~generous(john))))&
(![X]:((~curious(X)<~>~quiet(X))=>(curious(X)&~tall(X))))&
(![X]:((funny(X)&~curious(X))<=>(happy(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~rich(X)|~tall(X))))&
(![X]:((~humble(X)&happy(X))=>(~generous(X)&wise(X))))&
((~patient(paul))=>(?[X]:((~strong(X)&old(X)))))&
((rich(fred)&~patient(fred)))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((rich(X)&~curious(X))))&
((quiet(lucy)|~kind(lucy)))&
(?[X]:((~rich(X)&~curious(X))))&
((tall(john)<~>rich(john)))&
((~funny(fred)|quiet(fred)))&
(?[X]:((curious(X)|calm(X)))) | ~tall(lucy) | [] | null | 0 |
If alice is not humble or not wise then paul is either not quiet or not strong and vice versa.
If someone is generous or not tall then alice is kind or brave.
If fred is either not happy or tall then someone is old and vice versa.
Everyone who is not creative is creative or tall and vice versa.
Everyone who is humble or not funny is not rich and vice versa.
Everyone who is either tall or funny is both not generous and not old and vice versa.
Everyone who is not wise is not tall and vice versa.
Everyone who is funny or happy is either not funny or brave.
Everyone who is either brave or not quiet is either patient or funny.
If someone is funny then someone is not generous or generous and vice versa.
Everyone who is either not old or strong is either patient or not wise.
If someone is either not old or not rich then someone is either strong or calm.
Everyone who is not strong or patient is either brave or not happy.
Everyone who is not tall or not curious is not tall.
If susan is not tall or not humble then someone is either quiet or not calm.
Everyone who is either happy or humble is generous and vice versa.
Lucy is both happy and brave.
John is either humble or tall.
Someone is old.
Paul is funny or not tall.
Someone is either not brave or calm.
Someone is calm.
Someone is either not curious or curious. | John is quiet. | neutral | (((~humble(alice)|~wise(alice)))<=>((~quiet(paul)<~>~strong(paul))))&
((?[X]:((generous(X)|~tall(X))))=>((kind(alice)|brave(alice))))&
(((~happy(fred)<~>tall(fred)))<=>(?[X]:(old(X))))&
(![X]:(~creative(X)<=>(creative(X)|tall(X))))&
(![X]:((humble(X)|~funny(X))<=>~rich(X)))&
(![X]:((tall(X)<~>funny(X))<=>(~generous(X)&~old(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(![X]:((funny(X)|happy(X))=>(~funny(X)<~>brave(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(patient(X)<~>funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~old(X)<~>strong(X))=>(patient(X)<~>~wise(X))))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((~strong(X)|patient(X))=>(brave(X)<~>~happy(X))))&
(![X]:((~tall(X)|~curious(X))=>~tall(X)))&
(((~tall(susan)|~humble(susan)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((happy(X)<~>humble(X))<=>generous(X)))&
((happy(lucy)&brave(lucy)))&
((humble(john)<~>tall(john)))&
(?[X]:(old(X)))&
((funny(paul)|~tall(paul)))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((~curious(X)<~>curious(X)))) | quiet(john) | [] | null | 0 |
If someone is not generous or wise then someone is both not brave and humble and vice versa. Everyone who is not creative or creative is either rich or not tall and vice versa. Everyone who is not quiet or not humble is both not calm and old and vice versa. Everyone who is rich is old and vice versa. If alice is not happy or wise then fred is not funny. Everyone who is humble or patient is both not funny and funny and vice versa. Everyone who is quiet or rich is not patient and vice versa. Everyone who is not wise or not tall is not creative. If someone is not generous or not humble then someone is not curious. Everyone who is patient is not humble. Everyone who is happy or curious is not generous and vice versa. Everyone who is both not happy and not kind is either calm or not kind and vice versa. If someone is either not wise or not humble then someone is tall. Mary is not humble. Someone is strong or not calm. Mary is either strong or not calm. Someone is either quiet or creative. | Alice is not wise. | entailment | ((?[X]:((~generous(X)|wise(X))))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~creative(X)|creative(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~calm(X)&old(X))))&
(![X]:(rich(X)<=>old(X)))&
(((~happy(alice)|wise(alice)))=>(~funny(fred)))&
(![X]:((humble(X)|patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((quiet(X)|rich(X))<=>~patient(X)))&
(![X]:((~wise(X)|~tall(X))=>~creative(X)))&
((?[X]:((~generous(X)|~humble(X))))=>(?[X]:(~curious(X))))&
(![X]:(patient(X)=>~humble(X)))&
(![X]:((happy(X)|curious(X))<=>~generous(X)))&
(![X]:((~happy(X)&~kind(X))<=>(calm(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(tall(X))))&
(~humble(mary))&
(?[X]:((strong(X)|~calm(X))))&
((strong(mary)<~>~calm(mary)))&
(?[X]:((quiet(X)<~>creative(X)))) | ~wise(alice) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 289639332404714180440495
% SZS output start Proof for 289639332404714180440495
1. ? [X0] : (wise(X0) | ~generous(X0)) <=> ? [X0] : (humble(X0) & ~brave(X0)) [input p0]
6. ! [X0] : ((patient(X0) | humble(X0)) <=> (funny(X0) & ~funny(X0))) [input p5]
18. wise(alice) [input hypothesis]
19. ? [X0] : (wise(X0) | ~generous(X0)) <=> ? [X1] : (humble(X1) & ~brave(X1)) [rectify 1]
27. (? [X0] : (wise(X0) | ~generous(X0)) | ! [X1] : (~humble(X1) | brave(X1))) & (? [X1] : (humble(X1) & ~brave(X1)) | ! [X0] : (~wise(X0) & generous(X0))) [nnf transformation 19]
28. (? [X0] : (wise(X0) | ~generous(X0)) | ! [X1] : (~humble(X1) | brave(X1))) & (? [X2] : (humble(X2) & ~brave(X2)) | ! [X3] : (~wise(X3) & generous(X3))) [rectify 27]
29. ? [X0] : (wise(X0) | ~generous(X0)) => (wise(sK0) | ~generous(sK0)) [choice axiom]
30. ? [X2] : (humble(X2) & ~brave(X2)) => (humble(sK1) & ~brave(sK1)) [choice axiom]
31. ((wise(sK0) | ~generous(sK0)) | ! [X1] : (~humble(X1) | brave(X1))) & ((humble(sK1) & ~brave(sK1)) | ! [X3] : (~wise(X3) & generous(X3))) [skolemisation 28,30,29]
37. ! [X0] : (((patient(X0) | humble(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (~patient(X0) & ~humble(X0)))) [nnf transformation 6]
38. ! [X0] : ((patient(X0) | humble(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (~patient(X0) & ~humble(X0)))) [flattening 37]
61. humble(sK1) | ~wise(X3) [cnf transformation 31]
78. ~funny(X0) | ~humble(X0) [cnf transformation 38]
80. funny(X0) | ~humble(X0) [cnf transformation 38]
108. wise(alice) [cnf transformation 18]
124. 4 <=> ! [X3] : ~wise(X3) [avatar definition]
125. ~wise(X3) <- (4) [avatar component clause 124]
127. 5 <=> humble(sK1) [avatar definition]
129. humble(sK1) <- (5) [avatar component clause 127]
130. 4 | 5 [avatar split clause 61,127,124]
144. 8 <=> wise(alice) [avatar definition]
145. wise(alice) <- (8) [avatar component clause 144]
158. ~humble(X0) [subsumption resolution 78,80]
197. 8 [avatar split clause 108,144]
198. $false <- (5) [subsumption resolution 129,158]
199. ~5 [avatar contradiction clause 198]
204. $false <- (4, 8) [resolution 145,125]
205. ~4 | ~8 [avatar contradiction clause 204]
206. $false [avatar sat refutation 130,197,199,205]
% SZS output end Proof for 289639332404714180440495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and rich then mary is old or not funny.
If fred is humble then lucy is patient.
If mary is both creative and not kind then someone is both not generous and not curious and vice versa.
Everyone who is not rich or not funny is not creative or not rich.
Everyone who is both patient and quiet is patient and vice versa.
If someone is curious then lucy is not old.
If susan is brave or creative then someone is both not funny and not tall.
Everyone who is either not calm or happy is not creative or not brave and vice versa.
Everyone who is either patient or not curious is calm and vice versa.
If someone is wise then john is both not kind and humble.
If someone is not happy then fred is both not patient and not old and vice versa.
Everyone who is either patient or not patient is either creative or old.
If john is patient then someone is both tall and creative.
If someone is either funny or curious then fred is humble or not calm and vice versa.
Everyone who is either not rich or not funny is both generous and humble.
If susan is not strong then someone is not generous or not creative.
Someone is not curious or not happy.
Someone is either rich or calm.
Susan is either not creative or rich.
Paul is not generous.
Mary is both funny and curious.
Someone is funny or not rich.
Someone is not curious or old.
Mary is either not funny or strong. | Lucy is not old. | entailment | ((?[X]:((~old(X)&rich(X))))=>((old(mary)|~funny(mary))))&
((humble(fred))=>(patient(lucy)))&
(((creative(mary)&~kind(mary)))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((~rich(X)|~funny(X))=>(~creative(X)|~rich(X))))&
(![X]:((patient(X)&quiet(X))<=>patient(X)))&
((?[X]:(curious(X)))=>(~old(lucy)))&
(((brave(susan)|creative(susan)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(~creative(X)|~brave(X))))&
(![X]:((patient(X)<~>~curious(X))<=>calm(X)))&
((?[X]:(wise(X)))=>((~kind(john)&humble(john))))&
((?[X]:(~happy(X)))<=>((~patient(fred)&~old(fred))))&
(![X]:((patient(X)<~>~patient(X))=>(creative(X)<~>old(X))))&
((patient(john))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((funny(X)<~>curious(X))))<=>((humble(fred)|~calm(fred))))&
(![X]:((~rich(X)<~>~funny(X))=>(generous(X)&humble(X))))&
((~strong(susan))=>(?[X]:((~generous(X)|~creative(X)))))&
(?[X]:((~curious(X)|~happy(X))))&
(?[X]:((rich(X)<~>calm(X))))&
((~creative(susan)<~>rich(susan)))&
(~generous(paul))&
((funny(mary)&curious(mary)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((~curious(X)|old(X))))&
((~funny(mary)<~>strong(mary))) | ~old(lucy) | [
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4237085724781915161753688
% SZS output start Proof for 4237085724781915161753688
6. ? [X0] : curious(X0) => ~old(lucy) [input p5]
21. curious(mary) & funny(mary) [input p20]
25. old(lucy) [input hypothesis]
32. ~old(lucy) | ! [X0] : ~curious(X0) [ennf transformation 6]
88. ~old(lucy) | ~curious(X0) [cnf transformation 32]
130. curious(mary) [cnf transformation 21]
135. old(lucy) [cnf transformation 25]
185. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
186. ~curious(X0) <- (11) [avatar component clause 185]
188. 12 <=> old(lucy) [avatar definition]
191. 11 | ~12 [avatar split clause 88,188,185]
333. 12 [avatar split clause 135,188]
334. $false <- (11) [resolution 186,130]
335. ~11 [avatar contradiction clause 334]
336. $false [avatar sat refutation 191,333,335]
% SZS output end Proof for 4237085724781915161753688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not happy then someone is not generous and vice versa.
If someone is not humble or happy then someone is not old or not calm and vice versa.
Everyone who is not rich is not kind.
Everyone who is not generous or not calm is both not strong and not rich and vice versa.
Everyone who is either not brave or not humble is both happy and not humble and vice versa.
If paul is quiet then someone is brave or happy and vice versa.
Everyone who is funny or not funny is both tall and curious and vice versa.
Everyone who is either brave or patient is both kind and curious.
If susan is not brave or not funny then someone is kind or not happy and vice versa.
Everyone who is either funny or happy is both funny and not calm and vice versa.
If mary is funny or wise then someone is either not quiet or not humble.
Everyone who is both not wise and calm is both old and strong and vice versa.
Everyone who is both not humble and not strong is strong or curious and vice versa.
Everyone who is both not tall and not generous is both not patient and patient.
Everyone who is rich or funny is not curious or strong and vice versa.
Everyone who is either strong or humble is both happy and not tall.
Susan is either not generous or not kind.
Fred is not calm or curious.
Someone is not happy or happy.
Paul is either not curious or not calm.
John is either calm or generous. | Paul is tall. | entailment | ((?[X]:((~rich(X)<~>~happy(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((~old(X)|~calm(X)))))&
(![X]:(~rich(X)=>~kind(X)))&
(![X]:((~generous(X)|~calm(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(happy(X)&~humble(X))))&
((quiet(paul))<=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((funny(X)|~funny(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)<~>patient(X))=>(kind(X)&curious(X))))&
(((~brave(susan)|~funny(susan)))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((funny(X)<~>happy(X))<=>(funny(X)&~calm(X))))&
(((funny(mary)|wise(mary)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:((~wise(X)&calm(X))<=>(old(X)&strong(X))))&
(![X]:((~humble(X)&~strong(X))<=>(strong(X)|curious(X))))&
(![X]:((~tall(X)&~generous(X))=>(~patient(X)&patient(X))))&
(![X]:((rich(X)|funny(X))<=>(~curious(X)|strong(X))))&
(![X]:((strong(X)<~>humble(X))=>(happy(X)&~tall(X))))&
((~generous(susan)<~>~kind(susan)))&
((~calm(fred)|curious(fred)))&
(?[X]:((~happy(X)|happy(X))))&
((~curious(paul)<~>~calm(paul)))&
((calm(john)<~>generous(john))) | tall(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9024771689489828571373396
% SZS output start Proof for 9024771689489828571373396
7. ! [X0] : ((~funny(X0) | funny(X0)) <=> (curious(X0) & tall(X0))) [input p6]
22. ~tall(paul) [input hypothesis]
49. ! [X0] : (((~funny(X0) | funny(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (funny(X0) & ~funny(X0)))) [nnf transformation 7]
50. ! [X0] : ((~funny(X0) | funny(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (funny(X0) & ~funny(X0)))) [flattening 49]
97. tall(X0) | ~funny(X0) [cnf transformation 50]
98. tall(X0) | funny(X0) [cnf transformation 50]
147. ~tall(paul) [cnf transformation 22]
230. tall(X0) [subsumption resolution 97,98]
304. $false [subsumption resolution 147,230]
% SZS output end Proof for 9024771689489828571373396
% ------------------------------
% 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 old or quiet then fred is both generous and funny and vice versa.
Everyone who is not generous or not happy is quiet.
If someone is both curious and brave then john is not wise and vice versa.
If someone is either old or curious then mary is either quiet or not rich and vice versa.
If someone is both funny and not wise then someone is both tall and not happy and vice versa.
Everyone who is either patient or creative is not creative.
If someone is funny or rich then fred is either not calm or humble and vice versa.
Everyone who is humble is not funny and vice versa.
Everyone who is both not brave and rich is both tall and not humble and vice versa.
If someone is not funny or rich then mary is tall.
If someone is both old and creative then fred is both not brave and strong.
If someone is both strong and funny then someone is happy and vice versa.
Everyone who is happy is both not curious and not kind and vice versa.
Everyone who is tall or not calm is either not happy or not strong and vice versa.
If someone is not humble then someone is both not brave and not generous and vice versa.
Everyone who is both not generous and quiet is not old or not brave and vice versa.
Someone is tall or strong.
Paul is both kind and generous.
John is quiet or not curious.
Alice is both funny and tall.
Someone is either not patient or strong.
Fred is both wise and patient.
Alice is both tall and not creative. | Paul is not calm. | neutral | ((?[X]:((old(X)|quiet(X))))<=>((generous(fred)&funny(fred))))&
(![X]:((~generous(X)|~happy(X))=>quiet(X)))&
((?[X]:((curious(X)&brave(X))))<=>(~wise(john)))&
((?[X]:((old(X)<~>curious(X))))<=>((quiet(mary)<~>~rich(mary))))&
((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((patient(X)<~>creative(X))=>~creative(X)))&
((?[X]:((funny(X)|rich(X))))<=>((~calm(fred)<~>humble(fred))))&
(![X]:(humble(X)<=>~funny(X)))&
(![X]:((~brave(X)&rich(X))<=>(tall(X)&~humble(X))))&
((?[X]:((~funny(X)|rich(X))))=>(tall(mary)))&
((?[X]:((old(X)&creative(X))))=>((~brave(fred)&strong(fred))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:(happy(X)<=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|~calm(X))<=>(~happy(X)<~>~strong(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~generous(X)&quiet(X))<=>(~old(X)|~brave(X))))&
(?[X]:((tall(X)|strong(X))))&
((kind(paul)&generous(paul)))&
((quiet(john)|~curious(john)))&
((funny(alice)&tall(alice)))&
(?[X]:((~patient(X)<~>strong(X))))&
((wise(fred)&patient(fred)))&
((tall(alice)&~creative(alice))) | ~calm(paul) | [] | null | 0 |
Everyone who is both humble and not humble is either not tall or creative.
If lucy is both not kind and happy then someone is not happy or kind and vice versa.
Everyone who is humble is generous and vice versa.
Everyone who is either not strong or generous is both tall and not kind and vice versa.
Everyone who is not happy or not rich is old or humble.
If fred is not patient or not wise then john is not generous.
If someone is both not happy and not old then someone is both not creative and not humble.
Everyone who is not kind or not calm is both not patient and wise and vice versa.
Everyone who is not humble or funny is either creative or curious and vice versa.
Everyone who is either not kind or not humble is both not brave and not calm and vice versa.
Everyone who is both calm and not humble is both brave and not calm and vice versa.
If someone is curious or strong then someone is either not tall or not strong and vice versa.
Everyone who is not rich or strong is curious or not brave and vice versa.
Everyone who is either humble or quiet is curious and vice versa.
Everyone who is either wise or not brave is not old or brave.
Someone is either patient or not curious.
Fred is curious.
Someone is both tall and generous.
Susan is not brave.
Someone is both quiet and old.
John is not strong or funny.
Someone is either brave or not strong.
Alice is either not curious or calm. | Lucy is humble. | entailment | (![X]:((humble(X)&~humble(X))=>(~tall(X)<~>creative(X))))&
(((~kind(lucy)&happy(lucy)))<=>(?[X]:((~happy(X)|kind(X)))))&
(![X]:(humble(X)<=>generous(X)))&
(![X]:((~strong(X)<~>generous(X))<=>(tall(X)&~kind(X))))&
(![X]:((~happy(X)|~rich(X))=>(old(X)|humble(X))))&
(((~patient(fred)|~wise(fred)))=>(~generous(john)))&
((?[X]:((~happy(X)&~old(X))))=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(~patient(X)&wise(X))))&
(![X]:((~humble(X)|funny(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)&~calm(X))))&
(![X]:((calm(X)&~humble(X))<=>(brave(X)&~calm(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~rich(X)|strong(X))<=>(curious(X)|~brave(X))))&
(![X]:((humble(X)<~>quiet(X))<=>curious(X)))&
(![X]:((wise(X)<~>~brave(X))=>(~old(X)|brave(X))))&
(?[X]:((patient(X)<~>~curious(X))))&
(curious(fred))&
(?[X]:((tall(X)&generous(X))))&
(~brave(susan))&
(?[X]:((quiet(X)&old(X))))&
((~strong(john)|funny(john)))&
(?[X]:((brave(X)<~>~strong(X))))&
((~curious(alice)<~>calm(alice))) | humble(lucy) | [
"p1",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2193715923051947470458875
% SZS output start Proof for 2193715923051947470458875
2. (happy(lucy) & ~kind(lucy)) <=> ? [X0] : (kind(X0) | ~happy(X0)) [input p1]
10. ! [X0] : ((~kind(X0) <~> ~humble(X0)) <=> (~calm(X0) & ~brave(X0))) [input p9]
11. ! [X0] : ((~humble(X0) & calm(X0)) <=> (~calm(X0) & brave(X0))) [input p10]
24. ~humble(lucy) [input hypothesis]
36. ((happy(lucy) & ~kind(lucy)) | ! [X0] : (~kind(X0) & happy(X0))) & (? [X0] : (kind(X0) | ~happy(X0)) | (~happy(lucy) | kind(lucy))) [nnf transformation 2]
37. ((happy(lucy) & ~kind(lucy)) | ! [X0] : (~kind(X0) & happy(X0))) & (? [X0] : (kind(X0) | ~happy(X0)) | ~happy(lucy) | kind(lucy)) [flattening 36]
38. ((happy(lucy) & ~kind(lucy)) | ! [X0] : (~kind(X0) & happy(X0))) & (? [X1] : (kind(X1) | ~happy(X1)) | ~happy(lucy) | kind(lucy)) [rectify 37]
39. ? [X1] : (kind(X1) | ~happy(X1)) => (kind(sK0) | ~happy(sK0)) [choice axiom]
40. ((happy(lucy) & ~kind(lucy)) | ! [X0] : (~kind(X0) & happy(X0))) & ((kind(sK0) | ~happy(sK0)) | ~happy(lucy) | kind(lucy)) [skolemisation 38,39]
51. ! [X0] : ((((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))))) [nnf transformation 10]
52. ! [X0] : ((((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))))) [flattening 51]
53. ! [X0] : (((~humble(X0) & calm(X0)) | (calm(X0) | ~brave(X0))) & ((~calm(X0) & brave(X0)) | (humble(X0) | ~calm(X0)))) [nnf transformation 11]
54. ! [X0] : (((~humble(X0) & calm(X0)) | calm(X0) | ~brave(X0)) & ((~calm(X0) & brave(X0)) | humble(X0) | ~calm(X0))) [flattening 53]
79. ~kind(lucy) | ~kind(X0) [cnf transformation 40]
112. brave(X0) | kind(X0) | calm(X0) | humble(X0) [cnf transformation 52]
114. ~calm(X0) | humble(X0) | ~calm(X0) [cnf transformation 54]
115. calm(X0) | calm(X0) | ~brave(X0) [cnf transformation 54]
146. ~humble(lucy) [cnf transformation 24]
148. ~calm(X0) | humble(X0) [duplicate literal removal 114]
149. ~brave(X0) | calm(X0) [duplicate literal removal 115]
151. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
152. ~kind(X0) <- (1) [avatar component clause 151]
163. 4 <=> kind(lucy) [avatar definition]
164. kind(lucy) <- (4) [avatar component clause 163]
165. ~kind(lucy) <- (~4) [avatar component clause 163]
166. 1 | ~4 [avatar split clause 79,163,151]
520. kind(X5) | calm(X5) | humble(X5) | calm(X5) [resolution 112,149]
522. kind(X5) | calm(X5) | humble(X5) [duplicate literal removal 520]
538. kind(X5) | humble(X5) [subsumption resolution 522,148]
558. humble(lucy) <- (~4) [resolution 538,165]
562. $false <- (~4) [subsumption resolution 558,146]
563. 4 [avatar contradiction clause 562]
570. $false <- (1, 4) [resolution 164,152]
573. ~1 | ~4 [avatar contradiction clause 570]
574. $false [avatar sat refutation 166,563,573]
% SZS output end Proof for 2193715923051947470458875
% ------------------------------
% 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 either old or curious then lucy is either rich or not quiet and vice versa.
Everyone who is either not generous or not calm is not tall or patient.
Everyone who is not brave is both strong and quiet and vice versa.
Everyone who is not creative is brave and vice versa.
If someone is either generous or quiet then someone is either not calm or not brave.
Everyone who is both not tall and strong is not tall.
If lucy is not brave then someone is not wise or not happy.
If someone is either humble or creative then john is not kind or not curious.
Everyone who is not creative or not curious is both not humble and not funny.
Everyone who is old or tall is not curious or generous and vice versa.
If someone is not happy then mary is not creative or not kind and vice versa.
Everyone who is not calm or strong is either not rich or patient.
Everyone who is either creative or calm is either not tall or not funny.
Everyone who is either not quiet or quiet is rich or not calm and vice versa.
Everyone who is kind or not generous is either not happy or tall.
Everyone who is either brave or funny is both calm and not wise and vice versa.
John is not rich or not tall.
Someone is quiet.
Alice is both not calm and not humble.
Someone is not humble or not patient.
Someone is patient or not kind.
Someone is not humble.
Someone is rich.
Someone is brave or curious. | Lucy is generous. | neutral | ((?[X]:((old(X)<~>curious(X))))<=>((rich(lucy)<~>~quiet(lucy))))&
(![X]:((~generous(X)<~>~calm(X))=>(~tall(X)|patient(X))))&
(![X]:(~brave(X)<=>(strong(X)&quiet(X))))&
(![X]:(~creative(X)<=>brave(X)))&
((?[X]:((generous(X)<~>quiet(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~tall(X)&strong(X))=>~tall(X)))&
((~brave(lucy))=>(?[X]:((~wise(X)|~happy(X)))))&
((?[X]:((humble(X)<~>creative(X))))=>((~kind(john)|~curious(john))))&
(![X]:((~creative(X)|~curious(X))=>(~humble(X)&~funny(X))))&
(![X]:((old(X)|tall(X))<=>(~curious(X)|generous(X))))&
((?[X]:(~happy(X)))<=>((~creative(mary)|~kind(mary))))&
(![X]:((~calm(X)|strong(X))=>(~rich(X)<~>patient(X))))&
(![X]:((creative(X)<~>calm(X))=>(~tall(X)<~>~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((kind(X)|~generous(X))=>(~happy(X)<~>tall(X))))&
(![X]:((brave(X)<~>funny(X))<=>(calm(X)&~wise(X))))&
((~rich(john)|~tall(john)))&
(?[X]:(quiet(X)))&
((~calm(alice)&~humble(alice)))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:(rich(X)))&
(?[X]:((brave(X)|curious(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is both not wise and curious is wise and vice versa. Everyone who is both not patient and curious is both quiet and humble and vice versa. Everyone who is quiet is either not generous or rich and vice versa. Everyone who is creative is both creative and not funny. Everyone who is wise is not patient or not kind and vice versa. Everyone who is wise is both not humble and not happy. Everyone who is either not strong or rich is either not tall or not patient. Everyone who is not old or not quiet is wise or curious. If someone is either tall or not curious then someone is either not happy or humble. If someone is not generous then someone is either not curious or not strong. Everyone who is both brave and not rich is both patient and rich. If someone is curious or not quiet then someone is strong or not tall. If someone is both curious and humble then alice is generous or not patient. John is both tall and brave. John is not happy or not generous. Someone is not generous or calm. Susan is both not funny and strong. | John is old. | entailment | (![X]:((~wise(X)&curious(X))<=>wise(X)))&
(![X]:((~patient(X)&curious(X))<=>(quiet(X)&humble(X))))&
(![X]:(quiet(X)<=>(~generous(X)<~>rich(X))))&
(![X]:(creative(X)=>(creative(X)&~funny(X))))&
(![X]:(wise(X)<=>(~patient(X)|~kind(X))))&
(![X]:(wise(X)=>(~humble(X)&~happy(X))))&
(![X]:((~strong(X)<~>rich(X))=>(~tall(X)<~>~patient(X))))&
(![X]:((~old(X)|~quiet(X))=>(wise(X)|curious(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((~happy(X)<~>humble(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)<~>~strong(X)))))&
(![X]:((brave(X)&~rich(X))=>(patient(X)&rich(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:((strong(X)|~tall(X)))))&
((?[X]:((curious(X)&humble(X))))=>((generous(alice)|~patient(alice))))&
((tall(john)&brave(john)))&
((~happy(john)|~generous(john)))&
(?[X]:((~generous(X)|calm(X))))&
((~funny(susan)&strong(susan))) | old(john) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7350550058768029638869980
% SZS output start Proof for 7350550058768029638869980
1. ! [X0] : ((curious(X0) & ~wise(X0)) <=> wise(X0)) [input p0]
8. ! [X0] : ((~quiet(X0) | ~old(X0)) => (curious(X0) | wise(X0))) [input p7]
18. ~old(john) [input hypothesis]
28. ! [X0] : ((curious(X0) | wise(X0)) | (quiet(X0) & old(X0))) [ennf transformation 8]
29. ! [X0] : (curious(X0) | wise(X0) | (quiet(X0) & old(X0))) [flattening 28]
37. ! [X0] : (((curious(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) | wise(X0)))) [nnf transformation 1]
38. ! [X0] : (((curious(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | ~curious(X0) | wise(X0))) [flattening 37]
56. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 38]
57. ~wise(X0) | ~wise(X0) [cnf transformation 38]
77. curious(X0) | wise(X0) | old(X0) [cnf transformation 29]
94. ~old(john) [cnf transformation 18]
96. wise(X0) | ~curious(X0) [duplicate literal removal 56]
97. ~wise(X0) [duplicate literal removal 57]
98. ~curious(X0) [subsumption resolution 96,97]
106. wise(X0) | old(X0) [subsumption resolution 77,98]
107. old(X0) [subsumption resolution 106,97]
141. $false [subsumption resolution 94,107]
% SZS output end Proof for 7350550058768029638869980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is old or not humble and vice versa.
If someone is brave or not generous then someone is both not brave and humble.
If someone is either quiet or funny then lucy is both funny and old and vice versa.
If fred is not generous then lucy is both patient and brave and vice versa.
Everyone who is not funny is happy and vice versa.
Everyone who is kind is not brave and vice versa.
If alice is both not tall and not quiet then someone is not strong or wise and vice versa.
Everyone who is brave is both not humble and not strong.
Everyone who is creative is either curious or not happy.
If mary is strong then john is both not tall and old and vice versa.
Everyone who is wise or not tall is both not rich and not quiet.
Everyone who is not strong or old is creative.
Everyone who is wise is tall and vice versa.
Everyone who is both not happy and tall is both not wise and tall.
If fred is not happy then fred is either curious or kind.
If someone is both not rich and quiet then fred is both wise and calm.
John is calm.
Someone is kind or calm.
Susan is either funny or not humble.
Lucy is either not curious or not happy.
Alice is both humble and not brave.
Someone is both not funny and tall. | Susan is funny. | contradiction | (![X]:(brave(X)<=>(old(X)|~humble(X))))&
((?[X]:((brave(X)|~generous(X))))=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:((quiet(X)<~>funny(X))))<=>((funny(lucy)&old(lucy))))&
((~generous(fred))<=>((patient(lucy)&brave(lucy))))&
(![X]:(~funny(X)<=>happy(X)))&
(![X]:(kind(X)<=>~brave(X)))&
(((~tall(alice)&~quiet(alice)))<=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:(brave(X)=>(~humble(X)&~strong(X))))&
(![X]:(creative(X)=>(curious(X)<~>~happy(X))))&
((strong(mary))<=>((~tall(john)&old(john))))&
(![X]:((wise(X)|~tall(X))=>(~rich(X)&~quiet(X))))&
(![X]:((~strong(X)|old(X))=>creative(X)))&
(![X]:(wise(X)<=>tall(X)))&
(![X]:((~happy(X)&tall(X))=>(~wise(X)&tall(X))))&
((~happy(fred))=>((curious(fred)<~>kind(fred))))&
((?[X]:((~rich(X)&quiet(X))))=>((wise(fred)&calm(fred))))&
(calm(john))&
(?[X]:((kind(X)|calm(X))))&
((funny(susan)<~>~humble(susan)))&
((~curious(lucy)<~>~happy(lucy)))&
((humble(alice)&~brave(alice)))&
(?[X]:((~funny(X)&tall(X)))) | funny(susan) | [
"p2",
"p4",
"p8",
"p10",
"p11",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6132201455801970918387594
% SZS output start Proof for 6132201455801970918387594
3. ? [X0] : (quiet(X0) <~> funny(X0)) <=> (old(lucy) & funny(lucy)) [input p2]
5. ! [X0] : (~funny(X0) <=> happy(X0)) [input p4]
9. ! [X0] : (creative(X0) => (curious(X0) <~> ~happy(X0))) [input p8]
11. ! [X0] : ((~tall(X0) | wise(X0)) => (~quiet(X0) & ~rich(X0))) [input p10]
12. ! [X0] : ((old(X0) | ~strong(X0)) => creative(X0)) [input p11]
13. ! [X0] : (wise(X0) <=> tall(X0)) [input p12]
14. ! [X0] : ((tall(X0) & ~happy(X0)) => (tall(X0) & ~wise(X0))) [input p13]
20. ~curious(lucy) <~> ~happy(lucy) [input p19]
23. funny(susan) [input hypothesis]
30. ! [X0] : ((curious(X0) <~> ~happy(X0)) | ~creative(X0)) [ennf transformation 9]
31. ! [X0] : ((~quiet(X0) & ~rich(X0)) | (tall(X0) & ~wise(X0))) [ennf transformation 11]
32. ! [X0] : (creative(X0) | (~old(X0) & strong(X0))) [ennf transformation 12]
33. ! [X0] : ((tall(X0) & ~wise(X0)) | (~tall(X0) | happy(X0))) [ennf transformation 14]
34. ! [X0] : ((tall(X0) & ~wise(X0)) | ~tall(X0) | happy(X0)) [flattening 33]
42. (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | (~old(lucy) | ~funny(lucy))) & ((old(lucy) & funny(lucy)) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) [nnf transformation 3]
43. (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ~old(lucy) | ~funny(lucy)) & ((old(lucy) & funny(lucy)) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) [flattening 42]
44. (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ~old(lucy) | ~funny(lucy)) & ((old(lucy) & funny(lucy)) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) [rectify 43]
45. ? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) => ((~funny(sK1) | ~quiet(sK1)) & (funny(sK1) | quiet(sK1))) [choice axiom]
46. (((~funny(sK1) | ~quiet(sK1)) & (funny(sK1) | quiet(sK1))) | ~old(lucy) | ~funny(lucy)) & ((old(lucy) & funny(lucy)) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) [skolemisation 44,45]
49. ! [X0] : ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))) [nnf transformation 5]
56. ! [X0] : (((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~creative(X0)) [nnf transformation 30]
59. ! [X0] : ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0))) [nnf transformation 13]
62. (happy(lucy) | curious(lucy)) & (~happy(lucy) | ~curious(lucy)) [nnf transformation 20]
73. funny(lucy) | quiet(X1) | ~funny(X1) [cnf transformation 46]
75. old(lucy) | quiet(X1) | ~funny(X1) [cnf transformation 46]
82. ~happy(X0) | ~funny(X0) [cnf transformation 49]
93. ~curious(X0) | happy(X0) | ~creative(X0) [cnf transformation 56]
100. ~quiet(X0) | tall(X0) [cnf transformation 31]
102. ~old(X0) | creative(X0) [cnf transformation 32]
104. ~tall(X0) | wise(X0) [cnf transformation 59]
105. ~wise(X0) | ~tall(X0) | happy(X0) [cnf transformation 34]
113. happy(lucy) | curious(lucy) [cnf transformation 62]
118. funny(susan) [cnf transformation 23]
138. 5 <=> funny(lucy) [avatar definition]
142. 6 <=> old(lucy) [avatar definition]
143. old(lucy) <- (6) [avatar component clause 142]
156. 9 <=> ! [X1] : (quiet(X1) | ~funny(X1)) [avatar definition]
157. ~funny(X1) | quiet(X1) <- (9) [avatar component clause 156]
158. 9 | 6 [avatar split clause 75,142,156]
163. 9 | 5 [avatar split clause 73,138,156]
222. ~tall(X0) | happy(X0) [subsumption resolution 105,104]
246. 28 <=> funny(susan) [avatar definition]
247. funny(susan) <- (28) [avatar component clause 246]
256. 30 <=> curious(lucy) [avatar definition]
258. curious(lucy) <- (30) [avatar component clause 256]
260. 31 <=> happy(lucy) [avatar definition]
261. ~happy(lucy) <- (~31) [avatar component clause 260]
262. happy(lucy) <- (31) [avatar component clause 260]
263. 30 | 31 [avatar split clause 113,260,256]
265. 28 [avatar split clause 118,246]
276. creative(lucy) <- (6) [resolution 102,143]
295. happy(lucy) | ~creative(lucy) <- (30) [resolution 93,258]
296. ~creative(lucy) <- (30, ~31) [subsumption resolution 295,261]
297. $false <- (6, 30, ~31) [subsumption resolution 296,276]
298. ~6 | ~30 | 31 [avatar contradiction clause 297]
300. ~funny(lucy) <- (31) [resolution 262,82]
303. ~5 | ~31 [avatar split clause 300,260,138]
305. quiet(susan) <- (9, 28) [resolution 157,247]
309. tall(susan) <- (9, 28) [resolution 305,100]
333. happy(susan) <- (9, 28) [resolution 309,222]
349. ~funny(susan) <- (9, 28) [resolution 333,82]
359. $false <- (9, 28) [subsumption resolution 349,247]
360. ~9 | ~28 [avatar contradiction clause 359]
361. $false [avatar sat refutation 158,163,263,265,298,303,360]
% SZS output end Proof for 6132201455801970918387594
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or creative then someone is either not rich or not humble. Everyone who is wise or humble is calm. Everyone who is not kind or not rich is either calm or not old. Everyone who is rich or happy is either not brave or not rich and vice versa. Everyone who is wise or not rich is both not old and not rich and vice versa. If someone is not old then paul is calm or tall. Everyone who is patient or funny is not strong. Everyone who is either old or patient is both not rich and not happy. If lucy is not old then mary is patient and vice versa. If lucy is funny then alice is either not generous or calm. If john is wise or not old then someone is both not humble and not generous. Everyone who is calm or generous is old and vice versa. Everyone who is patient or not rich is not humble and vice versa. If someone is happy or not patient then someone is kind or not kind and vice versa. Everyone who is calm or funny is not curious or funny and vice versa. If mary is strong or not curious then someone is not generous and vice versa. Fred is both not quiet and not patient. Someone is either not creative or wise. Lucy is old. Alice is old. Lucy is either kind or not humble. Someone is both not funny and old. Fred is either not rich or wise. Alice is calm. | Mary is humble. | contradiction | ((?[X]:((~old(X)|creative(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((wise(X)|humble(X))=>calm(X)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>~old(X))))&
(![X]:((rich(X)|happy(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((wise(X)|~rich(X))<=>(~old(X)&~rich(X))))&
((?[X]:(~old(X)))=>((calm(paul)|tall(paul))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
((~old(lucy))<=>(patient(mary)))&
((funny(lucy))=>((~generous(alice)<~>calm(alice))))&
(((wise(john)|~old(john)))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((calm(X)|generous(X))<=>old(X)))&
(![X]:((patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
((~quiet(fred)&~patient(fred)))&
(?[X]:((~creative(X)<~>wise(X))))&
(old(lucy))&
(old(alice))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~funny(X)&old(X))))&
((~rich(fred)<~>wise(fred)))&
(calm(alice)) | humble(mary) | [
"p1",
"p4",
"p7",
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6591908935095650258641188
% SZS output start Proof for 6591908935095650258641188
2. ! [X0] : ((humble(X0) | wise(X0)) => calm(X0)) [input p1]
5. ! [X0] : ((~rich(X0) | wise(X0)) <=> (~rich(X0) & ~old(X0))) [input p4]
8. ! [X0] : ((old(X0) <~> patient(X0)) => (~happy(X0) & ~rich(X0))) [input p7]
9. ~old(lucy) <=> patient(mary) [input p8]
12. ! [X0] : ((generous(X0) | calm(X0)) <=> old(X0)) [input p11]
19. old(lucy) [input p18]
25. humble(mary) [input hypothesis]
31. ! [X0] : (calm(X0) | (~humble(X0) & ~wise(X0))) [ennf transformation 2]
34. ! [X0] : ((~happy(X0) & ~rich(X0)) | (old(X0) <=> patient(X0))) [ennf transformation 8]
44. ! [X0] : (((~rich(X0) | wise(X0)) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | (rich(X0) & ~wise(X0)))) [nnf transformation 5]
45. ! [X0] : ((~rich(X0) | wise(X0) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | (rich(X0) & ~wise(X0)))) [flattening 44]
46. ! [X0] : ((~happy(X0) & ~rich(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) [nnf transformation 34]
47. (~old(lucy) | ~patient(mary)) & (patient(mary) | old(lucy)) [nnf transformation 9]
51. ! [X0] : (((generous(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (~generous(X0) & ~calm(X0)))) [nnf transformation 12]
52. ! [X0] : ((generous(X0) | calm(X0) | ~old(X0)) & (old(X0) | (~generous(X0) & ~calm(X0)))) [flattening 51]
79. ~humble(X0) | calm(X0) [cnf transformation 31]
91. ~old(X0) | rich(X0) [cnf transformation 45]
97. ~rich(X0) | patient(X0) | ~old(X0) [cnf transformation 46]
102. ~old(lucy) | ~patient(mary) [cnf transformation 47]
109. ~calm(X0) | old(X0) [cnf transformation 52]
129. old(lucy) [cnf transformation 19]
138. humble(mary) [cnf transformation 25]
159. ~old(X0) | patient(X0) [subsumption resolution 97,91]
161. 5 <=> patient(mary) [avatar definition]
163. ~patient(mary) <- (~5) [avatar component clause 161]
165. 6 <=> old(lucy) [avatar definition]
168. ~5 | ~6 [avatar split clause 102,165,161]
248. 6 [avatar split clause 129,165]
262. calm(mary) [resolution 79,138]
267. old(mary) [resolution 109,262]
271. patient(mary) [resolution 159,267]
274. $false <- (~5) [subsumption resolution 271,163]
275. 5 [avatar contradiction clause 274]
276. $false [avatar sat refutation 168,248,275]
% SZS output end Proof for 6591908935095650258641188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or not rich then someone is not creative or curious and vice versa. Everyone who is patient or calm is not wise and vice versa. Everyone who is not old or curious is not brave or creative and vice versa. If someone is both curious and brave then someone is both not funny and not kind and vice versa. Everyone who is either not quiet or kind is not funny or creative. Everyone who is not rich or not creative is not kind and vice versa. If someone is wise then someone is not happy or not patient. Everyone who is either not tall or rich is both tall and brave. If someone is not wise then john is both not humble and not patient and vice versa. If alice is both quiet and humble then mary is both generous and strong and vice versa. Everyone who is both curious and not old is both old and kind. If someone is both strong and not curious then someone is happy or rich and vice versa. If fred is either brave or humble then someone is both not curious and humble and vice versa. If someone is patient then someone is not funny and vice versa. Everyone who is not calm or quiet is not rich and vice versa. Everyone who is either calm or not tall is both tall and not strong and vice versa. Lucy is both not funny and not calm. Alice is quiet. Someone is not wise or not creative. John is not happy or not funny. Someone is either creative or not wise. Lucy is strong or not brave. Mary is both brave and not kind. Someone is old. | Fred is generous. | neutral | ((?[X]:((~calm(X)|~rich(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((patient(X)|calm(X))<=>~wise(X)))&
(![X]:((~old(X)|curious(X))<=>(~brave(X)|creative(X))))&
((?[X]:((curious(X)&brave(X))))<=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:((~quiet(X)<~>kind(X))=>(~funny(X)|creative(X))))&
(![X]:((~rich(X)|~creative(X))<=>~kind(X)))&
((?[X]:(wise(X)))=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((~tall(X)<~>rich(X))=>(tall(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((~humble(john)&~patient(john))))&
(((quiet(alice)&humble(alice)))<=>((generous(mary)&strong(mary))))&
(![X]:((curious(X)&~old(X))=>(old(X)&kind(X))))&
((?[X]:((strong(X)&~curious(X))))<=>(?[X]:((happy(X)|rich(X)))))&
(((brave(fred)<~>humble(fred)))<=>(?[X]:((~curious(X)&humble(X)))))&
((?[X]:(patient(X)))<=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)|quiet(X))<=>~rich(X)))&
(![X]:((calm(X)<~>~tall(X))<=>(tall(X)&~strong(X))))&
((~funny(lucy)&~calm(lucy)))&
(quiet(alice))&
(?[X]:((~wise(X)|~creative(X))))&
((~happy(john)|~funny(john)))&
(?[X]:((creative(X)<~>~wise(X))))&
((strong(lucy)|~brave(lucy)))&
((brave(mary)&~kind(mary)))&
(?[X]:(old(X))) | generous(fred) | [] | null | 0 |
Everyone who is not curious or generous is not wise.
If fred is either not happy or calm then fred is curious or not kind and vice versa.
If lucy is either creative or not patient then lucy is kind.
Everyone who is creative is either not funny or curious and vice versa.
If someone is both not rich and wise then someone is both tall and not kind and vice versa.
If someone is humble then someone is both strong and old and vice versa.
Everyone who is both quiet and not wise is both curious and not creative.
Everyone who is both quiet and creative is both happy and not tall.
Everyone who is both funny and generous is both not calm and generous and vice versa.
Everyone who is patient or curious is kind or tall and vice versa.
Everyone who is either not kind or not strong is humble and vice versa.
If someone is both not rich and not old then john is old.
If fred is either not patient or old then mary is not generous and vice versa.
If someone is both not strong and not quiet then someone is both not happy and calm and vice versa.
If fred is rich or not generous then someone is either not happy or not generous.
Everyone who is not patient or not funny is not old or not creative.
John is not kind.
Someone is not strong or brave.
Mary is either not humble or humble.
Someone is not creative or not rich.
Someone is not wise or patient.
Paul is either calm or patient.
Fred is patient or not funny.
John is not quiet or old. | Mary is humble. | neutral | (![X]:((~curious(X)|generous(X))=>~wise(X)))&
(((~happy(fred)<~>calm(fred)))<=>((curious(fred)|~kind(fred))))&
(((creative(lucy)<~>~patient(lucy)))=>(kind(lucy)))&
(![X]:(creative(X)<=>(~funny(X)<~>curious(X))))&
((?[X]:((~rich(X)&wise(X))))<=>(?[X]:((tall(X)&~kind(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:((quiet(X)&~wise(X))=>(curious(X)&~creative(X))))&
(![X]:((quiet(X)&creative(X))=>(happy(X)&~tall(X))))&
(![X]:((funny(X)&generous(X))<=>(~calm(X)&generous(X))))&
(![X]:((patient(X)|curious(X))<=>(kind(X)|tall(X))))&
(![X]:((~kind(X)<~>~strong(X))<=>humble(X)))&
((?[X]:((~rich(X)&~old(X))))=>(old(john)))&
(((~patient(fred)<~>old(fred)))<=>(~generous(mary)))&
((?[X]:((~strong(X)&~quiet(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
(((rich(fred)|~generous(fred)))=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((~patient(X)|~funny(X))=>(~old(X)|~creative(X))))&
(~kind(john))&
(?[X]:((~strong(X)|brave(X))))&
((~humble(mary)<~>humble(mary)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((~wise(X)|patient(X))))&
((calm(paul)<~>patient(paul)))&
((patient(fred)|~funny(fred)))&
((~quiet(john)|old(john))) | humble(mary) | [] | null | 0 |
Everyone who is kind or funny is both not strong and not quiet and vice versa.
Everyone who is patient or not brave is wise or not kind and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
Everyone who is generous or not generous is not tall.
Everyone who is not quiet is creative.
Everyone who is strong is either not kind or creative and vice versa.
If someone is both not quiet and strong then paul is not wise or calm and vice versa.
If susan is not funny or patient then susan is happy or rich and vice versa.
Everyone who is either not wise or old is not creative or creative and vice versa.
Everyone who is both patient and strong is patient and vice versa.
Everyone who is generous is not strong or rich and vice versa.
If someone is both not calm and not old then susan is not strong or not curious and vice versa.
Everyone who is both not kind and old is both creative and not calm.
If susan is either patient or curious then alice is either not humble or not strong and vice versa.
If paul is not rich then susan is both happy and not tall and vice versa.
If someone is both not calm and old then someone is either not humble or funny and vice versa.
Someone is not generous.
Someone is funny or not patient.
Mary is not creative.
Someone is rich or not quiet.
Someone is rich or not brave.
Alice is both quiet and not generous.
Someone is not happy or strong.
Lucy is not calm or old. | Susan is strong. | neutral | (![X]:((kind(X)|funny(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((patient(X)|~brave(X))<=>(wise(X)|~kind(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
(![X]:((generous(X)|~generous(X))=>~tall(X)))&
(![X]:(~quiet(X)=>creative(X)))&
(![X]:(strong(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~quiet(X)&strong(X))))<=>((~wise(paul)|calm(paul))))&
(((~funny(susan)|patient(susan)))<=>((happy(susan)|rich(susan))))&
(![X]:((~wise(X)<~>old(X))<=>(~creative(X)|creative(X))))&
(![X]:((patient(X)&strong(X))<=>patient(X)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~calm(X)&~old(X))))<=>((~strong(susan)|~curious(susan))))&
(![X]:((~kind(X)&old(X))=>(creative(X)&~calm(X))))&
(((patient(susan)<~>curious(susan)))<=>((~humble(alice)<~>~strong(alice))))&
((~rich(paul))<=>((happy(susan)&~tall(susan))))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)|~patient(X))))&
(~creative(mary))&
(?[X]:((rich(X)|~quiet(X))))&
(?[X]:((rich(X)|~brave(X))))&
((quiet(alice)&~generous(alice)))&
(?[X]:((~happy(X)|strong(X))))&
((~calm(lucy)|old(lucy))) | strong(susan) | [] | null | 0 |
Everyone who is not rich or kind is both not tall and happy and vice versa.
Everyone who is brave is both not funny and wise and vice versa.
Everyone who is both quiet and not creative is either happy or not kind.
If someone is not curious or not wise then lucy is not humble and vice versa.
If lucy is both humble and not humble then someone is either not curious or happy and vice versa.
If susan is tall then someone is not old or quiet and vice versa.
Everyone who is not funny is both not curious and not patient and vice versa.
If lucy is either curious or old then susan is happy and vice versa.
Everyone who is both quiet and strong is either not happy or patient.
Everyone who is either not tall or strong is either not patient or strong and vice versa.
If lucy is both not kind and happy then susan is generous and vice versa.
If someone is not funny then someone is funny or tall and vice versa.
Everyone who is both kind and not wise is either calm or happy and vice versa.
If alice is kind then someone is both not calm and not old.
Everyone who is not humble or tall is not rich and vice versa.
Someone is both not creative and not humble.
Paul is both not funny and old.
Someone is both curious and not calm.
Someone is both not patient and not quiet.
Lucy is either generous or not wise.
Someone is curious or not calm. | Paul is generous. | neutral | (![X]:((~rich(X)|kind(X))<=>(~tall(X)&happy(X))))&
(![X]:(brave(X)<=>(~funny(X)&wise(X))))&
(![X]:((quiet(X)&~creative(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(~humble(lucy)))&
(((humble(lucy)&~humble(lucy)))<=>(?[X]:((~curious(X)<~>happy(X)))))&
((tall(susan))<=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:(~funny(X)<=>(~curious(X)&~patient(X))))&
(((curious(lucy)<~>old(lucy)))<=>(happy(susan)))&
(![X]:((quiet(X)&strong(X))=>(~happy(X)<~>patient(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~patient(X)<~>strong(X))))&
(((~kind(lucy)&happy(lucy)))<=>(generous(susan)))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((kind(X)&~wise(X))<=>(calm(X)<~>happy(X))))&
((kind(alice))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((~humble(X)|tall(X))<=>~rich(X)))&
(?[X]:((~creative(X)&~humble(X))))&
((~funny(paul)&old(paul)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
((generous(lucy)<~>~wise(lucy)))&
(?[X]:((curious(X)|~calm(X)))) | generous(paul) | [] | null | 0 |
Everyone who is not strong is curious or not funny and vice versa.
If lucy is both quiet and strong then someone is either funny or creative and vice versa.
Everyone who is either not old or not humble is either brave or not curious.
If alice is calm or not curious then someone is not kind or patient.
If john is funny then someone is not wise or brave.
Everyone who is both not patient and not humble is brave and vice versa.
Everyone who is quiet or patient is kind or not generous.
If someone is both patient and not strong then someone is kind.
If someone is quiet or not curious then fred is both not quiet and kind.
Everyone who is tall or not strong is either curious or not funny and vice versa.
If someone is kind or calm then someone is both tall and kind.
Everyone who is creative or kind is not patient.
Everyone who is both patient and happy is humble or rich and vice versa.
Everyone who is both not wise and not happy is curious or not patient.
Everyone who is wise or not brave is both not rich and old and vice versa.
Everyone who is quiet is both tall and not curious and vice versa.
John is either generous or not curious.
Susan is either strong or not rich.
Mary is both calm and not quiet.
Someone is strong or quiet.
Someone is both not wise and not happy.
Someone is strong.
Alice is funny.
Paul is patient. | Alice is not humble. | entailment | (![X]:(~strong(X)<=>(curious(X)|~funny(X))))&
(((quiet(lucy)&strong(lucy)))<=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((~old(X)<~>~humble(X))=>(brave(X)<~>~curious(X))))&
(((calm(alice)|~curious(alice)))=>(?[X]:((~kind(X)|patient(X)))))&
((funny(john))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:((~patient(X)&~humble(X))<=>brave(X)))&
(![X]:((quiet(X)|patient(X))=>(kind(X)|~generous(X))))&
((?[X]:((patient(X)&~strong(X))))=>(?[X]:(kind(X))))&
((?[X]:((quiet(X)|~curious(X))))=>((~quiet(fred)&kind(fred))))&
(![X]:((tall(X)|~strong(X))<=>(curious(X)<~>~funny(X))))&
((?[X]:((kind(X)|calm(X))))=>(?[X]:((tall(X)&kind(X)))))&
(![X]:((creative(X)|kind(X))=>~patient(X)))&
(![X]:((patient(X)&happy(X))<=>(humble(X)|rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(curious(X)|~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~rich(X)&old(X))))&
(![X]:(quiet(X)<=>(tall(X)&~curious(X))))&
((generous(john)<~>~curious(john)))&
((strong(susan)<~>~rich(susan)))&
((calm(mary)&~quiet(mary)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((~wise(X)&~happy(X))))&
(?[X]:(strong(X)))&
(funny(alice))&
(patient(paul)) | ~humble(alice) | [
"p0",
"p1",
"p9",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8258286683630088933577288
% SZS output start Proof for 8258286683630088933577288
1. ! [X0] : (~strong(X0) <=> (~funny(X0) | curious(X0))) [input p0]
2. (strong(lucy) & quiet(lucy)) <=> ? [X0] : (funny(X0) <~> creative(X0)) [input p1]
10. ! [X0] : ((~strong(X0) | tall(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p9]
12. ! [X0] : ((kind(X0) | creative(X0)) => ~patient(X0)) [input p11]
13. ! [X0] : ((happy(X0) & patient(X0)) <=> (rich(X0) | humble(X0))) [input p12]
16. ! [X0] : (quiet(X0) <=> (~curious(X0) & tall(X0))) [input p15]
23. funny(alice) [input p22]
25. humble(alice) [input hypothesis]
36. ! [X0] : (~patient(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 12]
39. ! [X0] : ((~strong(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | strong(X0))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | strong(X0))) [flattening 39]
41. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~strong(lucy) | ~quiet(lucy))) [nnf transformation 2]
42. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X0] : ((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~strong(lucy) | ~quiet(lucy)) [flattening 41]
43. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (? [X1] : ((~creative(X1) | ~funny(X1)) & (creative(X1) | funny(X1))) | ~strong(lucy) | ~quiet(lucy)) [rectify 42]
44. ? [X1] : ((~creative(X1) | ~funny(X1)) & (creative(X1) | funny(X1))) => ((~creative(sK0) | ~funny(sK0)) & (creative(sK0) | funny(sK0))) [choice axiom]
45. ((strong(lucy) & quiet(lucy)) | ! [X0] : ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(sK0) | ~funny(sK0)) & (creative(sK0) | funny(sK0))) | ~strong(lucy) | ~quiet(lucy)) [skolemisation 43,44]
56. ! [X0] : (((~strong(X0) | tall(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (strong(X0) & ~tall(X0)))) [nnf transformation 10]
57. ! [X0] : ((~strong(X0) | tall(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (strong(X0) & ~tall(X0)))) [flattening 56]
61. ! [X0] : (((happy(X0) & patient(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (~happy(X0) | ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : (((happy(X0) & patient(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | ~happy(X0) | ~patient(X0))) [flattening 61]
65. ! [X0] : ((quiet(X0) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((quiet(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | ~quiet(X0))) [flattening 65]
77. ~strong(X0) | funny(X0) [cnf transformation 40]
80. quiet(lucy) | creative(X0) | ~funny(X0) [cnf transformation 45]
82. strong(lucy) | creative(X0) | ~funny(X0) [cnf transformation 45]
101. ~tall(X0) | curious(X0) | ~funny(X0) [cnf transformation 57]
111. ~patient(X0) | ~creative(X0) [cnf transformation 36]
114. ~humble(X0) | patient(X0) [cnf transformation 62]
124. ~quiet(X0) | tall(X0) [cnf transformation 66]
125. ~quiet(X0) | ~curious(X0) [cnf transformation 66]
137. funny(alice) [cnf transformation 23]
139. humble(alice) [cnf transformation 25]
144. 2 <=> strong(lucy) [avatar definition]
146. strong(lucy) <- (2) [avatar component clause 144]
149. 3 <=> ! [X0] : (creative(X0) | ~funny(X0)) [avatar definition]
150. ~funny(X0) | creative(X0) <- (3) [avatar component clause 149]
151. 3 | 2 [avatar split clause 82,144,149]
153. 4 <=> quiet(lucy) [avatar definition]
155. quiet(lucy) <- (4) [avatar component clause 153]
157. 3 | 4 [avatar split clause 80,153,149]
282. funny(lucy) <- (2) [resolution 77,146]
287. patient(alice) [resolution 114,139]
289. ~creative(alice) [resolution 287,111]
295. tall(lucy) <- (4) [resolution 124,155]
296. ~curious(lucy) <- (4) [resolution 125,155]
322. curious(lucy) | ~funny(lucy) <- (4) [resolution 101,295]
332. ~funny(lucy) <- (4) [subsumption resolution 322,296]
333. $false <- (2, 4) [subsumption resolution 332,282]
334. ~2 | ~4 [avatar contradiction clause 333]
336. creative(alice) <- (3) [resolution 150,137]
341. $false <- (3) [subsumption resolution 336,289]
342. ~3 [avatar contradiction clause 341]
347. $false [avatar sat refutation 151,157,334,342]
% SZS output end Proof for 8258286683630088933577288
% ------------------------------
% 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 someone is either strong or not tall then john is either happy or not kind and vice versa. If someone is not patient then someone is not happy and vice versa. Everyone who is calm or curious is either not happy or quiet. If lucy is both not generous and happy then susan is both not quiet and not calm. If someone is brave or not calm then paul is both curious and not happy and vice versa. If someone is either not wise or not curious then mary is generous or old and vice versa. Everyone who is either old or rich is not creative and vice versa. Everyone who is humble is tall or not tall. Everyone who is either not patient or not creative is rich. Everyone who is not wise or not tall is both not kind and generous and vice versa. If someone is both funny and not quiet then paul is not creative or not curious and vice versa. Everyone who is patient is not patient or not funny and vice versa. If someone is both kind and not happy then someone is either not creative or tall and vice versa. If susan is either not tall or kind then fred is both brave and not wise. If john is either not calm or quiet then someone is both not curious and not generous. Mary is either not humble or happy. Mary is happy. Mary is both not old and not curious. Someone is not wise. Paul is not kind or not humble. | Susan is funny. | contradiction | ((?[X]:((strong(X)<~>~tall(X))))<=>((happy(john)<~>~kind(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(~happy(X))))&
(![X]:((calm(X)|curious(X))=>(~happy(X)<~>quiet(X))))&
(((~generous(lucy)&happy(lucy)))=>((~quiet(susan)&~calm(susan))))&
((?[X]:((brave(X)|~calm(X))))<=>((curious(paul)&~happy(paul))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((generous(mary)|old(mary))))&
(![X]:((old(X)<~>rich(X))<=>~creative(X)))&
(![X]:(humble(X)=>(tall(X)|~tall(X))))&
(![X]:((~patient(X)<~>~creative(X))=>rich(X)))&
(![X]:((~wise(X)|~tall(X))<=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>((~creative(paul)|~curious(paul))))&
(![X]:(patient(X)<=>(~patient(X)|~funny(X))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~tall(susan)<~>kind(susan)))=>((brave(fred)&~wise(fred))))&
(((~calm(john)<~>quiet(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
((~humble(mary)<~>happy(mary)))&
(happy(mary))&
((~old(mary)&~curious(mary)))&
(?[X]:(~wise(X)))&
((~kind(paul)|~humble(paul))) | funny(susan) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 556588736854949888664362
% SZS output start Proof for 556588736854949888664362
12. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p11]
21. funny(susan) [input hypothesis]
61. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 12]
62. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 61]
119. ~funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
120. patient(X0) | patient(X0) [cnf transformation 62]
143. funny(susan) [cnf transformation 21]
144. ~funny(X0) | ~patient(X0) [duplicate literal removal 119]
145. patient(X0) [duplicate literal removal 120]
185. 9 <=> ! [X3] : patient(X3) [avatar definition]
186. patient(X3) <- (9) [avatar component clause 185]
285. 9 [avatar split clause 145,185]
394. ~patient(susan) [resolution 144,143]
397. $false <- (9) [subsumption resolution 394,186]
398. ~9 [avatar contradiction clause 397]
401. $false [avatar sat refutation 285,398]
% SZS output end Proof for 556588736854949888664362
% ------------------------------
% 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 |
If fred is kind then someone is not happy or generous.
Everyone who is not brave is either not brave or not patient.
Everyone who is not rich is not creative or not curious and vice versa.
If lucy is strong or rich then susan is both not curious and not brave.
Everyone who is either happy or kind is not tall and vice versa.
If fred is brave then alice is not generous or not brave.
Everyone who is not strong is either strong or brave and vice versa.
If someone is not happy or quiet then someone is old.
If someone is humble or not happy then alice is curious or not funny.
Everyone who is either not quiet or strong is either creative or humble.
Everyone who is wise is both not brave and wise and vice versa.
If someone is not quiet or funny then someone is strong or curious.
If lucy is not kind then someone is not generous.
If paul is not happy or not humble then mary is not rich and vice versa.
Everyone who is both humble and old is both not calm and not kind and vice versa.
If someone is not old then john is both happy and not patient and vice versa.
Someone is brave or funny.
Alice is generous or happy.
Someone is tall or not creative.
Paul is curious.
Alice is either kind or not calm.
Someone is patient or not creative.
Someone is not brave or not humble. | Mary is tall. | neutral | ((kind(fred))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:(~brave(X)=>(~brave(X)<~>~patient(X))))&
(![X]:(~rich(X)<=>(~creative(X)|~curious(X))))&
(((strong(lucy)|rich(lucy)))=>((~curious(susan)&~brave(susan))))&
(![X]:((happy(X)<~>kind(X))<=>~tall(X)))&
((brave(fred))=>((~generous(alice)|~brave(alice))))&
(![X]:(~strong(X)<=>(strong(X)<~>brave(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~happy(X))))=>((curious(alice)|~funny(alice))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~brave(X)&wise(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((strong(X)|curious(X)))))&
((~kind(lucy))=>(?[X]:(~generous(X))))&
(((~happy(paul)|~humble(paul)))<=>(~rich(mary)))&
(![X]:((humble(X)&old(X))<=>(~calm(X)&~kind(X))))&
((?[X]:(~old(X)))<=>((happy(john)&~patient(john))))&
(?[X]:((brave(X)|funny(X))))&
((generous(alice)|happy(alice)))&
(?[X]:((tall(X)|~creative(X))))&
(curious(paul))&
((kind(alice)<~>~calm(alice)))&
(?[X]:((patient(X)|~creative(X))))&
(?[X]:((~brave(X)|~humble(X)))) | tall(mary) | [] | null | 0 |
Everyone who is generous or humble is both wise and strong and vice versa.
Everyone who is either not humble or not kind is both kind and generous and vice versa.
If someone is not patient or kind then someone is either patient or not kind.
If susan is both quiet and not tall then someone is not curious and vice versa.
Everyone who is not patient or not funny is both not old and happy and vice versa.
Everyone who is not generous or not kind is both rich and generous and vice versa.
Everyone who is both not brave and not patient is kind or creative and vice versa.
If someone is not calm or not creative then paul is both kind and quiet and vice versa.
If someone is either not quiet or not happy then fred is happy and vice versa.
Everyone who is either not strong or tall is not rich or calm.
If john is curious then someone is calm.
If someone is brave then susan is either not wise or not tall.
Everyone who is either quiet or not creative is either old or humble and vice versa.
If someone is generous then mary is brave.
Everyone who is not humble or humble is both strong and calm.
If someone is either happy or not calm then mary is not curious.
Someone is curious or not happy.
John is quiet or not old.
Someone is either not wise or funny.
Alice is calm or curious.
Someone is either creative or funny.
Lucy is either happy or kind. | Alice is humble. | contradiction | (![X]:((generous(X)|humble(X))<=>(wise(X)&strong(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(kind(X)&generous(X))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
(((quiet(susan)&~tall(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~old(X)&happy(X))))&
(![X]:((~generous(X)|~kind(X))<=>(rich(X)&generous(X))))&
(![X]:((~brave(X)&~patient(X))<=>(kind(X)|creative(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>((kind(paul)&quiet(paul))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>(happy(fred)))&
(![X]:((~strong(X)<~>tall(X))=>(~rich(X)|calm(X))))&
((curious(john))=>(?[X]:(calm(X))))&
((?[X]:(brave(X)))=>((~wise(susan)<~>~tall(susan))))&
(![X]:((quiet(X)<~>~creative(X))<=>(old(X)<~>humble(X))))&
((?[X]:(generous(X)))=>(brave(mary)))&
(![X]:((~humble(X)|humble(X))=>(strong(X)&calm(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(~curious(mary)))&
(?[X]:((curious(X)|~happy(X))))&
((quiet(john)|~old(john)))&
(?[X]:((~wise(X)<~>funny(X))))&
((calm(alice)|curious(alice)))&
(?[X]:((creative(X)<~>funny(X))))&
((happy(lucy)<~>kind(lucy))) | humble(alice) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4510375809961806895785876
% SZS output start Proof for 4510375809961806895785876
2. ! [X0] : ((~humble(X0) <~> ~kind(X0)) <=> (generous(X0) & kind(X0))) [input p1]
6. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (generous(X0) & rich(X0))) [input p5]
23. humble(alice) [input hypothesis]
35. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | (~generous(X0) | ~kind(X0))) & ((generous(X0) & kind(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [nnf transformation 2]
36. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | ~generous(X0) | ~kind(X0)) & ((generous(X0) & kind(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [flattening 35]
48. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | ~generous(X0) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | (kind(X0) & generous(X0)))) [flattening 48]
82. kind(X0) | ~humble(X0) | kind(X0) [cnf transformation 36]
85. ~kind(X0) | ~humble(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 36]
101. generous(X0) | generous(X0) [cnf transformation 49]
147. humble(alice) [cnf transformation 23]
148. generous(X0) [duplicate literal removal 101]
150. ~humble(X0) | kind(X0) [duplicate literal removal 82]
151. ~kind(X0) | ~humble(X0) | ~generous(X0) [duplicate literal removal 85]
355. kind(alice) [resolution 150,147]
364. ~humble(alice) | ~generous(alice) [resolution 151,355]
366. ~generous(alice) [subsumption resolution 364,147]
367. $false [subsumption resolution 366,148]
% SZS output end Proof for 4510375809961806895785876
% ------------------------------
% 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 tall or kind is curious or tall.
Everyone who is kind or not rich is quiet or not funny.
Everyone who is either happy or not calm is either not wise or rich and vice versa.
If someone is strong or curious then someone is creative.
Everyone who is not patient or brave is either not patient or not funny and vice versa.
If lucy is either old or wise then someone is not old or strong and vice versa.
If someone is not kind or not curious then someone is not calm and vice versa.
Everyone who is not wise is not humble or not kind and vice versa.
If someone is both generous and not funny then susan is not calm.
If alice is patient or strong then alice is funny or not strong.
Everyone who is either rich or not calm is old or not creative.
Everyone who is not humble is either not quiet or wise and vice versa.
If lucy is both generous and not patient then susan is both rich and not rich and vice versa.
If fred is humble or strong then john is quiet or strong.
If someone is either not rich or wise then someone is both quiet and not creative and vice versa.
Everyone who is not wise or kind is both quiet and humble and vice versa.
Alice is not creative or not quiet.
Someone is either not tall or happy.
Mary is either brave or calm.
Someone is humble or quiet.
Someone is quiet.
Someone is not funny.
Alice is curious or not wise. | Fred is curious. | neutral | (![X]:((tall(X)|kind(X))=>(curious(X)|tall(X))))&
(![X]:((kind(X)|~rich(X))=>(quiet(X)|~funny(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((strong(X)|curious(X))))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)|brave(X))<=>(~patient(X)<~>~funny(X))))&
(((old(lucy)<~>wise(lucy)))<=>(?[X]:((~old(X)|strong(X)))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:(~calm(X))))&
(![X]:(~wise(X)<=>(~humble(X)|~kind(X))))&
((?[X]:((generous(X)&~funny(X))))=>(~calm(susan)))&
(((patient(alice)|strong(alice)))=>((funny(alice)|~strong(alice))))&
(![X]:((rich(X)<~>~calm(X))=>(old(X)|~creative(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(((generous(lucy)&~patient(lucy)))<=>((rich(susan)&~rich(susan))))&
(((humble(fred)|strong(fred)))=>((quiet(john)|strong(john))))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~wise(X)|kind(X))<=>(quiet(X)&humble(X))))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((~tall(X)<~>happy(X))))&
((brave(mary)<~>calm(mary)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~funny(X)))&
((curious(alice)|~wise(alice))) | curious(fred) | [] | null | 0 |
If someone is either not wise or not creative then someone is both happy and not wise and vice versa.
If someone is either kind or old then someone is either not patient or kind and vice versa.
Everyone who is both not patient and calm is either curious or old.
If someone is strong then someone is not strong or not tall and vice versa.
If lucy is either patient or humble then someone is either not wise or not happy and vice versa.
If paul is quiet then someone is humble and vice versa.
Everyone who is both brave and not quiet is both not curious and creative.
If alice is both not wise and not rich then someone is happy or humble.
Everyone who is not calm or old is humble or rich and vice versa.
Everyone who is either brave or not brave is both funny and not rich.
Everyone who is not humble or brave is rich.
If paul is tall or humble then lucy is both not strong and patient.
If someone is either not tall or not old then fred is calm.
Everyone who is patient or brave is both tall and not strong and vice versa.
If fred is either wise or strong then someone is both patient and not strong.
Fred is both funny and tall.
Someone is both not brave and funny.
Susan is either not patient or tall.
Mary is not brave or happy.
Someone is wise.
Someone is both generous and happy.
Someone is not tall.
Someone is not brave or not old. | Fred is old. | entailment | ((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
((?[X]:((kind(X)<~>old(X))))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((~patient(X)&calm(X))=>(curious(X)<~>old(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)|~tall(X)))))&
(((patient(lucy)<~>humble(lucy)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
((quiet(paul))<=>(?[X]:(humble(X))))&
(![X]:((brave(X)&~quiet(X))=>(~curious(X)&creative(X))))&
(((~wise(alice)&~rich(alice)))=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~calm(X)|old(X))<=>(humble(X)|rich(X))))&
(![X]:((brave(X)<~>~brave(X))=>(funny(X)&~rich(X))))&
(![X]:((~humble(X)|brave(X))=>rich(X)))&
(((tall(paul)|humble(paul)))=>((~strong(lucy)&patient(lucy))))&
((?[X]:((~tall(X)<~>~old(X))))=>(calm(fred)))&
(![X]:((patient(X)|brave(X))<=>(tall(X)&~strong(X))))&
(((wise(fred)<~>strong(fred)))=>(?[X]:((patient(X)&~strong(X)))))&
((funny(fred)&tall(fred)))&
(?[X]:((~brave(X)&funny(X))))&
((~patient(susan)<~>tall(susan)))&
((~brave(mary)|happy(mary)))&
(?[X]:(wise(X)))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)|~old(X)))) | old(fred) | [
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6221601668965588675930069
% SZS output start Proof for 6221601668965588675930069
9. ! [X0] : ((old(X0) | ~calm(X0)) <=> (rich(X0) | humble(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (~rich(X0) & funny(X0))) [input p9]
11. ! [X0] : ((brave(X0) | ~humble(X0)) => rich(X0)) [input p10]
13. ? [X0] : (~tall(X0) <~> ~old(X0)) => calm(fred) [input p12]
16. tall(fred) & funny(fred) [input p15]
24. ~old(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) <~> ~brave(X0)) => ~rich(X0)) [pure predicate removal 10]
30. tall(fred) [pure predicate removal 16]
38. ! [X0] : (~rich(X0) | (brave(X0) <=> ~brave(X0))) [ennf transformation 29]
39. ! [X0] : (rich(X0) | (~brave(X0) & humble(X0))) [ennf transformation 11]
41. calm(fred) | ! [X0] : (~tall(X0) <=> ~old(X0)) [ennf transformation 13]
69. ! [X0] : (((old(X0) | ~calm(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (~old(X0) & calm(X0)))) [nnf transformation 9]
70. ! [X0] : ((old(X0) | ~calm(X0) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | (~old(X0) & calm(X0)))) [flattening 69]
71. ! [X0] : (~rich(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 38]
72. calm(fred) | ! [X0] : ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))) [nnf transformation 41]
123. ~humble(X0) | ~calm(X0) | old(X0) [cnf transformation 70]
125. ~rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 71]
126. ~rich(X0) | brave(X0) | brave(X0) [cnf transformation 71]
127. rich(X0) | humble(X0) [cnf transformation 39]
134. calm(fred) | ~tall(X0) | old(X0) [cnf transformation 72]
144. tall(fred) [cnf transformation 30]
153. ~old(fred) [cnf transformation 24]
154. ~rich(X0) | ~brave(X0) [duplicate literal removal 125]
155. ~rich(X0) | brave(X0) [duplicate literal removal 126]
304. ~rich(X0) [subsumption resolution 154,155]
306. humble(X0) [subsumption resolution 127,304]
316. 35 <=> ! [X0] : (~tall(X0) | old(X0)) [avatar definition]
317. ~tall(X0) | old(X0) <- (35) [avatar component clause 316]
319. 36 <=> calm(fred) [avatar definition]
321. calm(fred) <- (36) [avatar component clause 319]
322. 35 | 36 [avatar split clause 134,319,316]
396. ~calm(X0) | old(X0) [resolution 123,306]
405. old(fred) <- (36) [resolution 396,321]
406. $false <- (36) [subsumption resolution 405,153]
407. ~36 [avatar contradiction clause 406]
408. old(fred) <- (35) [resolution 317,144]
410. $false <- (35) [subsumption resolution 408,153]
411. ~35 [avatar contradiction clause 410]
412. $false [avatar sat refutation 322,407,411]
% SZS output end Proof for 6221601668965588675930069
% ------------------------------
% 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 either quiet or not wise is either not quiet or not strong and vice versa.
Everyone who is either not generous or not funny is both old and generous and vice versa.
Everyone who is not strong or humble is both curious and patient and vice versa.
If someone is happy or quiet then alice is either not rich or funny.
Everyone who is not brave or not calm is not humble.
If someone is patient or not kind then someone is not humble and vice versa.
Everyone who is funny is not patient or old and vice versa.
If someone is creative or not quiet then someone is either not happy or not brave and vice versa.
Everyone who is both happy and strong is patient or not old and vice versa.
If alice is both calm and not quiet then someone is not happy.
If someone is either not brave or not generous then someone is not tall or patient and vice versa.
If someone is either not humble or not kind then alice is either not brave or not happy.
Everyone who is both not wise and humble is both tall and not wise.
If someone is not strong or not rich then alice is either not curious or tall and vice versa.
Everyone who is calm or not funny is both calm and strong.
If someone is both tall and not kind then susan is both funny and not happy.
John is kind.
Someone is either not calm or funny.
John is not quiet.
Paul is either generous or creative.
Paul is not generous.
Someone is not quiet or not funny. | Paul is not calm. | contradiction | (![X]:((quiet(X)<~>~wise(X))<=>(~quiet(X)<~>~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>(old(X)&generous(X))))&
(![X]:((~strong(X)|humble(X))<=>(curious(X)&patient(X))))&
((?[X]:((happy(X)|quiet(X))))=>((~rich(alice)<~>funny(alice))))&
(![X]:((~brave(X)|~calm(X))=>~humble(X)))&
((?[X]:((patient(X)|~kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:(funny(X)<=>(~patient(X)|old(X))))&
((?[X]:((creative(X)|~quiet(X))))<=>(?[X]:((~happy(X)<~>~brave(X)))))&
(![X]:((happy(X)&strong(X))<=>(patient(X)|~old(X))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:(~happy(X))))&
((?[X]:((~brave(X)<~>~generous(X))))<=>(?[X]:((~tall(X)|patient(X)))))&
((?[X]:((~humble(X)<~>~kind(X))))=>((~brave(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&humble(X))=>(tall(X)&~wise(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((~curious(alice)<~>tall(alice))))&
(![X]:((calm(X)|~funny(X))=>(calm(X)&strong(X))))&
((?[X]:((tall(X)&~kind(X))))=>((funny(susan)&~happy(susan))))&
(kind(john))&
(?[X]:((~calm(X)<~>funny(X))))&
(~quiet(john))&
((generous(paul)<~>creative(paul)))&
(~generous(paul))&
(?[X]:((~quiet(X)|~funny(X)))) | ~calm(paul) | [
"p1",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7232196019823048137824786
% SZS output start Proof for 7232196019823048137824786
2. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> (generous(X0) & old(X0))) [input p1]
15. ! [X0] : ((~funny(X0) | calm(X0)) => (strong(X0) & calm(X0))) [input p14]
21. ~generous(paul) [input p20]
23. ~calm(paul) [input hypothesis]
34. ! [X0] : ((strong(X0) & calm(X0)) | (funny(X0) & ~calm(X0))) [ennf transformation 15]
37. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (~generous(X0) | ~old(X0))) & ((generous(X0) & old(X0)) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 2]
38. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~generous(X0) | ~old(X0)) & ((generous(X0) & old(X0)) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [flattening 37]
84. generous(X0) | ~funny(X0) | generous(X0) [cnf transformation 38]
136. calm(X0) | funny(X0) [cnf transformation 34]
147. ~generous(paul) [cnf transformation 21]
149. ~calm(paul) [cnf transformation 23]
150. ~funny(X0) | generous(X0) [duplicate literal removal 84]
335. 40 <=> generous(paul) [avatar definition]
337. ~generous(paul) <- (~40) [avatar component clause 335]
344. ~40 [avatar split clause 147,335]
361. funny(paul) [resolution 136,149]
366. generous(paul) [resolution 361,150]
367. $false <- (~40) [subsumption resolution 366,337]
368. 40 [avatar contradiction clause 367]
369. $false [avatar sat refutation 344,368]
% SZS output end Proof for 7232196019823048137824786
% ------------------------------
% 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 |
Everyone who is both strong and not generous is curious. Everyone who is either not tall or creative is either tall or not brave and vice versa. If someone is calm or not strong then someone is not kind and vice versa. Everyone who is both calm and not happy is not calm and vice versa. If someone is generous then mary is either creative or not patient and vice versa. If someone is not rich then someone is both not creative and not quiet. Everyone who is not happy or not strong is both humble and not quiet. If someone is both humble and not kind then someone is not tall or not strong and vice versa. If alice is tall then someone is calm and vice versa. If someone is not happy or brave then lucy is happy or not generous and vice versa. If someone is both not happy and quiet then someone is both not funny and not humble. Everyone who is both old and curious is both not old and not brave. Everyone who is either not tall or wise is not humble or not calm and vice versa. If alice is either wise or not tall then lucy is both curious and old. If someone is either not patient or not humble then john is either not calm or not old and vice versa. If lucy is old then lucy is both not tall and kind and vice versa. John is either strong or old. Someone is either wise or tall. Someone is not humble or rich. Lucy is not tall or kind. Someone is wise or not rich. Someone is either wise or not calm. Alice is quiet or humble. Mary is patient or not generous. | Alice is happy. | entailment | (![X]:((strong(X)&~generous(X))=>curious(X)))&
(![X]:((~tall(X)<~>creative(X))<=>(tall(X)<~>~brave(X))))&
((?[X]:((calm(X)|~strong(X))))<=>(?[X]:(~kind(X))))&
(![X]:((calm(X)&~happy(X))<=>~calm(X)))&
((?[X]:(generous(X)))<=>((creative(mary)<~>~patient(mary))))&
((?[X]:(~rich(X)))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~happy(X)|~strong(X))=>(humble(X)&~quiet(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
((tall(alice))<=>(?[X]:(calm(X))))&
((?[X]:((~happy(X)|brave(X))))<=>((happy(lucy)|~generous(lucy))))&
((?[X]:((~happy(X)&quiet(X))))=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:((old(X)&curious(X))=>(~old(X)&~brave(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(~humble(X)|~calm(X))))&
(((wise(alice)<~>~tall(alice)))=>((curious(lucy)&old(lucy))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>((~calm(john)<~>~old(john))))&
((old(lucy))<=>((~tall(lucy)&kind(lucy))))&
((strong(john)<~>old(john)))&
(?[X]:((wise(X)<~>tall(X))))&
(?[X]:((~humble(X)|rich(X))))&
((~tall(lucy)|kind(lucy)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
((quiet(alice)|humble(alice)))&
((patient(mary)|~generous(mary))) | happy(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7244744376925357816738605
% SZS output start Proof for 7244744376925357816738605
4. ! [X0] : ((~happy(X0) & calm(X0)) <=> ~calm(X0)) [input p3]
25. ~happy(alice) [input hypothesis]
45. ! [X0] : (((~happy(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 4]
46. ! [X0] : (((~happy(X0) & calm(X0)) | calm(X0)) & (~calm(X0) | happy(X0) | ~calm(X0))) [flattening 45]
103. ~calm(X0) | happy(X0) | ~calm(X0) [cnf transformation 46]
104. calm(X0) | calm(X0) [cnf transformation 46]
162. ~happy(alice) [cnf transformation 25]
164. ~calm(X0) | happy(X0) [duplicate literal removal 103]
165. calm(X0) [duplicate literal removal 104]
196. happy(X0) [subsumption resolution 164,165]
375. $false [subsumption resolution 162,196]
% SZS output end Proof for 7244744376925357816738605
% ------------------------------
% 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 someone is old or strong then fred is either strong or kind and vice versa.
Everyone who is happy is wise or not old and vice versa.
Everyone who is both quiet and strong is either calm or not generous and vice versa.
If someone is both not curious and patient then someone is either kind or old.
Everyone who is both calm and not brave is both strong and quiet.
Everyone who is calm is not patient or humble and vice versa.
Everyone who is both quiet and not old is either old or not strong.
Everyone who is both kind and not quiet is quiet or not strong and vice versa.
Everyone who is either not wise or generous is not humble or not happy and vice versa.
Everyone who is humble is generous.
If fred is not curious or curious then susan is both not patient and not quiet.
Everyone who is either brave or not kind is calm.
If john is either not quiet or old then someone is kind.
If lucy is either rich or not strong then someone is not kind and vice versa.
Everyone who is not happy is both creative and not tall.
Everyone who is not curious or tall is not creative and vice versa.
John is both strong and not creative.
Someone is not wise or tall.
Lucy is either generous or happy.
Someone is generous or not old.
Fred is brave.
Alice is both wise and not calm.
Lucy is not generous.
Someone is brave or not funny. | Alice is patient. | entailment | ((?[X]:((old(X)|strong(X))))<=>((strong(fred)<~>kind(fred))))&
(![X]:(happy(X)<=>(wise(X)|~old(X))))&
(![X]:((quiet(X)&strong(X))<=>(calm(X)<~>~generous(X))))&
((?[X]:((~curious(X)&patient(X))))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:((calm(X)&~brave(X))=>(strong(X)&quiet(X))))&
(![X]:(calm(X)<=>(~patient(X)|humble(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)<~>~strong(X))))&
(![X]:((kind(X)&~quiet(X))<=>(quiet(X)|~strong(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~humble(X)|~happy(X))))&
(![X]:(humble(X)=>generous(X)))&
(((~curious(fred)|curious(fred)))=>((~patient(susan)&~quiet(susan))))&
(![X]:((brave(X)<~>~kind(X))=>calm(X)))&
(((~quiet(john)<~>old(john)))=>(?[X]:(kind(X))))&
(((rich(lucy)<~>~strong(lucy)))<=>(?[X]:(~kind(X))))&
(![X]:(~happy(X)=>(creative(X)&~tall(X))))&
(![X]:((~curious(X)|tall(X))<=>~creative(X)))&
((strong(john)&~creative(john)))&
(?[X]:((~wise(X)|tall(X))))&
((generous(lucy)<~>happy(lucy)))&
(?[X]:((generous(X)|~old(X))))&
(brave(fred))&
((wise(alice)&~calm(alice)))&
(~generous(lucy))&
(?[X]:((brave(X)|~funny(X)))) | patient(alice) | [
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 399563750936711559807268
% SZS output start Proof for 399563750936711559807268
6. ! [X0] : (calm(X0) <=> (humble(X0) | ~patient(X0))) [input p5]
22. ~calm(alice) & wise(alice) [input p21]
25. ~patient(alice) [input hypothesis]
50. ! [X0] : ((calm(X0) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | ~calm(X0))) [nnf transformation 6]
51. ! [X0] : ((calm(X0) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~calm(X0))) [flattening 50]
92. patient(X0) | calm(X0) [cnf transformation 51]
133. ~calm(alice) [cnf transformation 22]
135. ~patient(alice) [cnf transformation 25]
243. calm(alice) [resolution 92,135]
245. $false [subsumption resolution 243,133]
% SZS output end Proof for 399563750936711559807268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or generous then someone is not old.
If someone is not happy then someone is both not funny and humble and vice versa.
If someone is both tall and curious then someone is either not old or quiet.
Everyone who is either curious or funny is not humble or not calm and vice versa.
Everyone who is quiet is not generous or kind and vice versa.
Everyone who is either curious or not old is kind or not calm and vice versa.
If paul is not rich then alice is humble.
Everyone who is both not quiet and not kind is either brave or not wise.
Everyone who is not happy or strong is old or happy and vice versa.
Everyone who is not quiet or not humble is both humble and not strong.
If someone is either curious or not wise then susan is generous or patient and vice versa.
Everyone who is either not strong or tall is both patient and not happy and vice versa.
If lucy is both not kind and curious then mary is either old or rich.
Everyone who is brave or not strong is not humble.
Everyone who is not curious is not tall and vice versa.
If lucy is either wise or not calm then someone is either not old or not brave.
Someone is either calm or not creative.
John is not kind.
John is not tall or kind.
Someone is wise or happy.
Someone is both rich and quiet.
John is not tall.
Someone is old.
Someone is both generous and strong. | Mary is strong. | entailment | ((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:(~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
((?[X]:((tall(X)&curious(X))))=>(?[X]:((~old(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))<=>(~humble(X)|~calm(X))))&
(![X]:(quiet(X)<=>(~generous(X)|kind(X))))&
(![X]:((curious(X)<~>~old(X))<=>(kind(X)|~calm(X))))&
((~rich(paul))=>(humble(alice)))&
(![X]:((~quiet(X)&~kind(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~happy(X)|strong(X))<=>(old(X)|happy(X))))&
(![X]:((~quiet(X)|~humble(X))=>(humble(X)&~strong(X))))&
((?[X]:((curious(X)<~>~wise(X))))<=>((generous(susan)|patient(susan))))&
(![X]:((~strong(X)<~>tall(X))<=>(patient(X)&~happy(X))))&
(((~kind(lucy)&curious(lucy)))=>((old(mary)<~>rich(mary))))&
(![X]:((brave(X)|~strong(X))=>~humble(X)))&
(![X]:(~curious(X)<=>~tall(X)))&
(((wise(lucy)<~>~calm(lucy)))=>(?[X]:((~old(X)<~>~brave(X)))))&
(?[X]:((calm(X)<~>~creative(X))))&
(~kind(john))&
((~tall(john)|kind(john)))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:((rich(X)&quiet(X))))&
(~tall(john))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&strong(X)))) | strong(mary) | [
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8405154995352177773160437
% SZS output start Proof for 8405154995352177773160437
10. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (~strong(X0) & humble(X0))) [input p9]
14. ! [X0] : ((~strong(X0) | brave(X0)) => ~humble(X0)) [input p13]
25. ~strong(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) & humble(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 10]
37. ! [X0] : (~humble(X0) | (strong(X0) & ~brave(X0))) [ennf transformation 14]
114. humble(X0) | humble(X0) [cnf transformation 34]
132. ~humble(X0) | strong(X0) [cnf transformation 37]
150. ~strong(mary) [cnf transformation 25]
151. humble(X0) [duplicate literal removal 114]
259. strong(X0) [subsumption resolution 132,151]
297. $false [subsumption resolution 150,259]
% SZS output end Proof for 8405154995352177773160437
% ------------------------------
% 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 quiet or not creative then paul is either not happy or kind and vice versa. If lucy is not creative or rich then alice is both not generous and not tall. If susan is not wise or brave then lucy is both not generous and strong. Everyone who is both strong and funny is brave. Everyone who is not brave or not quiet is both tall and not rich. Everyone who is either not kind or happy is not strong or not kind. Everyone who is both not rich and not humble is either not wise or not quiet and vice versa. If someone is both not calm and creative then paul is either rich or not wise. Everyone who is either not kind or not rich is either humble or tall and vice versa. If alice is curious or not quiet then someone is both brave and not humble. If someone is either calm or humble then someone is either curious or not funny. If lucy is patient then someone is not tall or brave and vice versa. If someone is both not kind and creative then fred is creative or not funny and vice versa. Everyone who is creative is patient and vice versa. If susan is calm then someone is not happy. Everyone who is both not funny and not wise is old. Susan is not patient. John is both kind and not patient. Someone is humble. Someone is not patient. Fred is quiet. Someone is not calm or strong. | John is creative. | contradiction | ((?[X]:((quiet(X)|~creative(X))))<=>((~happy(paul)<~>kind(paul))))&
(((~creative(lucy)|rich(lucy)))=>((~generous(alice)&~tall(alice))))&
(((~wise(susan)|brave(susan)))=>((~generous(lucy)&strong(lucy))))&
(![X]:((strong(X)&funny(X))=>brave(X)))&
(![X]:((~brave(X)|~quiet(X))=>(tall(X)&~rich(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~strong(X)|~kind(X))))&
(![X]:((~rich(X)&~humble(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((~calm(X)&creative(X))))=>((rich(paul)<~>~wise(paul))))&
(![X]:((~kind(X)<~>~rich(X))<=>(humble(X)<~>tall(X))))&
(((curious(alice)|~quiet(alice)))=>(?[X]:((brave(X)&~humble(X)))))&
((?[X]:((calm(X)<~>humble(X))))=>(?[X]:((curious(X)<~>~funny(X)))))&
((patient(lucy))<=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:((~kind(X)&creative(X))))<=>((creative(fred)|~funny(fred))))&
(![X]:(creative(X)<=>patient(X)))&
((calm(susan))=>(?[X]:(~happy(X))))&
(![X]:((~funny(X)&~wise(X))=>old(X)))&
(~patient(susan))&
((kind(john)&~patient(john)))&
(?[X]:(humble(X)))&
(?[X]:(~patient(X)))&
(quiet(fred))&
(?[X]:((~calm(X)|strong(X)))) | creative(john) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 467497432330346662917559
% SZS output start Proof for 467497432330346662917559
14. ! [X0] : (creative(X0) <=> patient(X0)) [input p13]
18. ~patient(john) & kind(john) [input p17]
23. creative(john) [input hypothesis]
63. ! [X0] : ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))) [nnf transformation 14]
121. ~creative(X0) | patient(X0) [cnf transformation 63]
126. ~patient(john) [cnf transformation 18]
131. creative(john) [cnf transformation 23]
304. patient(john) [resolution 121,131]
307. $false [subsumption resolution 304,126]
% SZS output end Proof for 467497432330346662917559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not happy and calm then someone is both not calm and not funny.
Everyone who is either not kind or strong is either happy or old and vice versa.
If paul is either not patient or generous then someone is not quiet or not rich.
Everyone who is patient or brave is either not happy or not kind and vice versa.
Everyone who is not generous or kind is both kind and quiet and vice versa.
Everyone who is creative is both quiet and not tall and vice versa.
Everyone who is either not strong or humble is either brave or not patient.
Everyone who is not strong or quiet is either curious or not brave.
Everyone who is not kind or patient is tall and vice versa.
Everyone who is both not curious and not happy is either not strong or not old and vice versa.
Everyone who is both strong and not old is curious or wise.
Everyone who is either not creative or creative is either not brave or old and vice versa.
Everyone who is either strong or quiet is either not quiet or not funny.
If fred is creative or funny then alice is both quiet and kind.
If susan is both not patient and not brave then someone is not curious and vice versa.
Everyone who is not old is not happy and vice versa.
Someone is either not creative or quiet.
Lucy is patient or not wise.
Someone is not curious.
Alice is either not creative or not calm.
Someone is either kind or strong.
Someone is either funny or kind. | Paul is not tall. | contradiction | (((~happy(mary)&calm(mary)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~kind(X)<~>strong(X))<=>(happy(X)<~>old(X))))&
(((~patient(paul)<~>generous(paul)))=>(?[X]:((~quiet(X)|~rich(X)))))&
(![X]:((patient(X)|brave(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((~generous(X)|kind(X))<=>(kind(X)&quiet(X))))&
(![X]:(creative(X)<=>(quiet(X)&~tall(X))))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~strong(X)|quiet(X))=>(curious(X)<~>~brave(X))))&
(![X]:((~kind(X)|patient(X))<=>tall(X)))&
(![X]:((~curious(X)&~happy(X))<=>(~strong(X)<~>~old(X))))&
(![X]:((strong(X)&~old(X))=>(curious(X)|wise(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~brave(X)<~>old(X))))&
(![X]:((strong(X)<~>quiet(X))=>(~quiet(X)<~>~funny(X))))&
(((creative(fred)|funny(fred)))=>((quiet(alice)&kind(alice))))&
(((~patient(susan)&~brave(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(?[X]:((~creative(X)<~>quiet(X))))&
((patient(lucy)|~wise(lucy)))&
(?[X]:(~curious(X)))&
((~creative(alice)<~>~calm(alice)))&
(?[X]:((kind(X)<~>strong(X))))&
(?[X]:((funny(X)<~>kind(X)))) | ~tall(paul) | [
"p1",
"p3",
"p8",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6275511837603605316682726
% SZS output start Proof for 6275511837603605316682726
2. ! [X0] : ((~kind(X0) <~> strong(X0)) <=> (happy(X0) <~> old(X0))) [input p1]
4. ! [X0] : ((brave(X0) | patient(X0)) <=> (~happy(X0) <~> ~kind(X0))) [input p3]
9. ! [X0] : ((patient(X0) | ~kind(X0)) <=> tall(X0)) [input p8]
10. ! [X0] : ((~happy(X0) & ~curious(X0)) <=> (~strong(X0) <~> ~old(X0))) [input p9]
12. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~brave(X0) <~> old(X0))) [input p11]
16. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p15]
23. ~tall(paul) [input hypothesis]
35. ! [X0] : ((((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0))))) [nnf transformation 2]
36. ! [X0] : (((brave(X0) | patient(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~brave(X0) & ~patient(X0)))) [nnf transformation 4]
37. ! [X0] : ((brave(X0) | patient(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (~brave(X0) & ~patient(X0)))) [flattening 36]
44. ! [X0] : (((patient(X0) | ~kind(X0)) | ~tall(X0)) & (tall(X0) | (~patient(X0) & kind(X0)))) [nnf transformation 9]
45. ! [X0] : ((patient(X0) | ~kind(X0) | ~tall(X0)) & (tall(X0) | (~patient(X0) & kind(X0)))) [flattening 44]
46. ! [X0] : (((~happy(X0) & ~curious(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (happy(X0) | curious(X0)))) [nnf transformation 10]
47. ! [X0] : (((~happy(X0) & ~curious(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | happy(X0) | curious(X0))) [flattening 46]
48. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 12]
55. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 16]
73. ~old(X0) | ~happy(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 35]
82. ~kind(X0) | patient(X0) | brave(X0) | happy(X0) [cnf transformation 37]
100. tall(X0) | kind(X0) [cnf transformation 45]
101. ~patient(X0) | tall(X0) [cnf transformation 45]
107. ~old(X0) | ~happy(X0) | strong(X0) [cnf transformation 47]
110. old(X0) | ~brave(X0) | creative(X0) | creative(X0) [cnf transformation 48]
111. old(X0) | ~brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
129. ~happy(X0) | old(X0) [cnf transformation 55]
130. ~old(X0) | happy(X0) [cnf transformation 55]
141. ~tall(paul) [cnf transformation 23]
144. old(X0) | ~brave(X0) | creative(X0) [duplicate literal removal 110]
145. ~creative(X0) | ~brave(X0) | old(X0) [duplicate literal removal 111]
168. ~brave(X0) | old(X0) [subsumption resolution 144,145]
259. kind(paul) [resolution 100,141]
287. 25 <=> strong(paul) [avatar definition]
386. patient(paul) | brave(paul) | happy(paul) [resolution 82,259]
391. 35 <=> happy(paul) [avatar definition]
392. ~happy(paul) <- (~35) [avatar component clause 391]
393. happy(paul) <- (35) [avatar component clause 391]
395. 36 <=> brave(paul) [avatar definition]
397. brave(paul) <- (36) [avatar component clause 395]
399. 37 <=> patient(paul) [avatar definition]
401. patient(paul) <- (37) [avatar component clause 399]
402. 35 | 36 | 37 [avatar split clause 386,399,395,391]
465. old(paul) <- (35) [resolution 393,129]
469. ~happy(paul) | ~kind(paul) | ~strong(paul) <- (35) [resolution 465,73]
473. ~happy(paul) | strong(paul) <- (35) [resolution 465,107]
476. ~kind(paul) | ~strong(paul) <- (35) [subsumption resolution 469,393]
477. ~strong(paul) <- (35) [subsumption resolution 476,259]
478. ~25 | ~35 [avatar split clause 477,391,287]
479. strong(paul) <- (35) [subsumption resolution 473,393]
480. 25 | ~35 [avatar split clause 479,391,287]
646. old(paul) <- (36) [resolution 397,168]
724. happy(paul) <- (36) [resolution 646,130]
729. $false <- (~35, 36) [subsumption resolution 724,392]
730. 35 | ~36 [avatar contradiction clause 729]
736. tall(paul) <- (37) [resolution 401,101]
737. $false <- (37) [subsumption resolution 736,141]
738. ~37 [avatar contradiction clause 737]
739. $false [avatar sat refutation 402,478,480,730,738]
% SZS output end Proof for 6275511837603605316682726
% ------------------------------
% 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not humble is either funny or not humble.
Everyone who is both not kind and wise is both curious and strong and vice versa.
Everyone who is both humble and tall is both not generous and funny and vice versa.
If john is either old or not curious then someone is quiet and vice versa.
If someone is not calm or humble then someone is tall or happy.
Everyone who is both not strong and quiet is either not rich or not generous.
If john is not funny then someone is strong.
If alice is funny or not funny then mary is tall.
If mary is either not quiet or tall then someone is either humble or funny and vice versa.
If alice is not creative then someone is both not calm and rich and vice versa.
Everyone who is either curious or not strong is both not curious and kind.
Everyone who is not patient or calm is not kind or not funny.
If someone is curious then someone is either not strong or brave.
Everyone who is either not humble or not patient is both not calm and not quiet.
Everyone who is funny or not old is kind or rich and vice versa.
Everyone who is both not curious and tall is not brave.
John is not curious or wise.
Someone is either not patient or not kind.
Someone is rich.
Someone is either tall or curious.
John is both calm and not strong.
Alice is both not brave and not strong.
Alice is wise or quiet.
Alice is kind. | Alice is brave. | contradiction | (![X]:((~quiet(X)&~humble(X))=>(funny(X)<~>~humble(X))))&
(![X]:((~kind(X)&wise(X))<=>(curious(X)&strong(X))))&
(![X]:((humble(X)&tall(X))<=>(~generous(X)&funny(X))))&
(((old(john)<~>~curious(john)))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((~strong(X)&quiet(X))=>(~rich(X)<~>~generous(X))))&
((~funny(john))=>(?[X]:(strong(X))))&
(((funny(alice)|~funny(alice)))=>(tall(mary)))&
(((~quiet(mary)<~>tall(mary)))<=>(?[X]:((humble(X)<~>funny(X)))))&
((~creative(alice))<=>(?[X]:((~calm(X)&rich(X)))))&
(![X]:((curious(X)<~>~strong(X))=>(~curious(X)&kind(X))))&
(![X]:((~patient(X)|calm(X))=>(~kind(X)|~funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((~humble(X)<~>~patient(X))=>(~calm(X)&~quiet(X))))&
(![X]:((funny(X)|~old(X))<=>(kind(X)|rich(X))))&
(![X]:((~curious(X)&tall(X))=>~brave(X)))&
((~curious(john)|wise(john)))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(rich(X)))&
(?[X]:((tall(X)<~>curious(X))))&
((calm(john)&~strong(john)))&
((~brave(alice)&~strong(alice)))&
((wise(alice)|quiet(alice)))&
(kind(alice)) | brave(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1791871162438826529533739
% SZS output start Proof for 1791871162438826529533739
22. ~strong(alice) & ~brave(alice) [input p21]
25. brave(alice) [input hypothesis]
133. ~brave(alice) [cnf transformation 22]
137. brave(alice) [cnf transformation 25]
270. $false [subsumption resolution 137,133]
% SZS output end Proof for 1791871162438826529533739
% ------------------------------
% 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 fred is both quiet and not brave then alice is brave or strong. Everyone who is not strong is not quiet. Everyone who is not tall is either not kind or not strong and vice versa. If someone is not wise or not rich then mary is not patient or quiet and vice versa. Everyone who is tall or not generous is both not tall and not rich and vice versa. If someone is not humble or curious then someone is both creative and not rich and vice versa. If lucy is either not kind or not happy then someone is either not funny or tall. Everyone who is either not patient or calm is funny. Everyone who is both old and not kind is either not generous or not strong. Everyone who is not patient or not funny is either not patient or generous and vice versa. If susan is not patient then lucy is both not rich and old. Everyone who is not brave or creative is tall. Everyone who is not generous or tall is not old or not wise. Everyone who is either not happy or curious is both patient and not generous. Everyone who is old is either not strong or not humble and vice versa. Everyone who is either rich or funny is both not strong and strong. Someone is creative or old. Someone is not creative. Someone is both not patient and not strong. Someone is kind. | Lucy is not wise. | entailment | (((quiet(fred)&~brave(fred)))=>((brave(alice)|strong(alice))))&
(![X]:(~strong(X)=>~quiet(X)))&
(![X]:(~tall(X)<=>(~kind(X)<~>~strong(X))))&
((?[X]:((~wise(X)|~rich(X))))<=>((~patient(mary)|quiet(mary))))&
(![X]:((tall(X)|~generous(X))<=>(~tall(X)&~rich(X))))&
((?[X]:((~humble(X)|curious(X))))<=>(?[X]:((creative(X)&~rich(X)))))&
(((~kind(lucy)<~>~happy(lucy)))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((~patient(X)<~>calm(X))=>funny(X)))&
(![X]:((old(X)&~kind(X))=>(~generous(X)<~>~strong(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~patient(X)<~>generous(X))))&
((~patient(susan))=>((~rich(lucy)&old(lucy))))&
(![X]:((~brave(X)|creative(X))=>tall(X)))&
(![X]:((~generous(X)|tall(X))=>(~old(X)|~wise(X))))&
(![X]:((~happy(X)<~>curious(X))=>(patient(X)&~generous(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&strong(X))))&
(?[X]:((creative(X)|old(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~patient(X)&~strong(X))))&
(?[X]:(kind(X))) | ~wise(lucy) | [
"p4",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5398782989397323636774173
% SZS output start Proof for 5398782989397323636774173
5. ! [X0] : ((~generous(X0) | tall(X0)) <=> (~rich(X0) & ~tall(X0))) [input p4]
10. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~patient(X0) <~> generous(X0))) [input p9]
11. ~patient(susan) => (old(lucy) & ~rich(lucy)) [input p10]
13. ! [X0] : ((tall(X0) | ~generous(X0)) => (~wise(X0) | ~old(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> funny(X0)) => (strong(X0) & ~strong(X0))) [input p15]
21. wise(lucy) [input hypothesis]
30. (old(lucy) & ~rich(lucy)) | patient(susan) [ennf transformation 11]
32. ! [X0] : ((~wise(X0) | ~old(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 13]
33. ! [X0] : (~wise(X0) | ~old(X0) | (~tall(X0) & generous(X0))) [flattening 32]
35. ! [X0] : ((strong(X0) & ~strong(X0)) | (rich(X0) <=> funny(X0))) [ennf transformation 16]
42. ! [X0] : (((~generous(X0) | tall(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (generous(X0) & ~tall(X0)))) [nnf transformation 5]
43. ! [X0] : ((~generous(X0) | tall(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (generous(X0) & ~tall(X0)))) [flattening 42]
54. ! [X0] : (((~funny(X0) | ~patient(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) & (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (funny(X0) & patient(X0)))) [nnf transformation 10]
55. ! [X0] : ((~funny(X0) | ~patient(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) & (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (funny(X0) & patient(X0)))) [flattening 54]
58. ! [X0] : ((strong(X0) & ~strong(X0)) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) [nnf transformation 35]
76. ~tall(X0) | ~tall(X0) [cnf transformation 43]
79. ~rich(X0) | generous(X0) [cnf transformation 43]
80. ~generous(X0) | tall(X0) | rich(X0) | tall(X0) [cnf transformation 43]
95. ~patient(X0) | generous(X0) | funny(X0) [cnf transformation 55]
96. ~generous(X0) | patient(X0) | patient(X0) [cnf transformation 55]
99. ~funny(X0) | ~patient(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 55]
101. old(lucy) | patient(susan) [cnf transformation 30]
103. ~old(X0) | ~wise(X0) | generous(X0) [cnf transformation 33]
113. ~strong(X0) | funny(X0) | ~rich(X0) [cnf transformation 58]
114. ~strong(X0) | rich(X0) | ~funny(X0) [cnf transformation 58]
115. ~rich(X0) | funny(X0) | strong(X0) [cnf transformation 58]
116. ~funny(X0) | rich(X0) | strong(X0) [cnf transformation 58]
122. wise(lucy) [cnf transformation 21]
123. ~generous(X0) | patient(X0) [duplicate literal removal 96]
124. ~funny(X0) | ~patient(X0) | ~generous(X0) [duplicate literal removal 99]
125. ~tall(X0) [duplicate literal removal 76]
126. ~generous(X0) | tall(X0) | rich(X0) [duplicate literal removal 80]
200. 17 <=> patient(susan) [avatar definition]
202. patient(susan) <- (17) [avatar component clause 200]
204. 18 <=> old(lucy) [avatar definition]
206. old(lucy) <- (18) [avatar component clause 204]
207. 17 | 18 [avatar split clause 101,204,200]
209. 19 <=> rich(lucy) [avatar definition]
210. rich(lucy) <- (19) [avatar component clause 209]
214. ~funny(X0) | rich(X0) [subsumption resolution 114,116]
215. ~rich(X0) | funny(X0) [subsumption resolution 113,115]
228. generous(susan) | funny(susan) <- (17) [resolution 95,202]
230. 20 <=> funny(susan) [avatar definition]
231. ~funny(susan) <- (~20) [avatar component clause 230]
232. funny(susan) <- (20) [avatar component clause 230]
234. 21 <=> generous(susan) [avatar definition]
236. generous(susan) <- (21) [avatar component clause 234]
237. 20 | 21 | ~17 [avatar split clause 228,200,234,230]
255. 24 <=> funny(lucy) [avatar definition]
257. funny(lucy) <- (24) [avatar component clause 255]
265. rich(susan) <- (20) [resolution 232,214]
268. generous(susan) <- (20) [resolution 265,79]
270. 21 | ~20 [avatar split clause 268,230,234]
289. ~patient(susan) | ~generous(susan) <- (20) [resolution 124,232]
293. ~patient(susan) <- (20, 21) [subsumption resolution 289,236]
294. ~17 | ~20 | ~21 [avatar split clause 293,234,230,200]
298. ~wise(lucy) | generous(lucy) <- (18) [resolution 206,103]
300. generous(lucy) <- (18) [subsumption resolution 298,122]
314. tall(lucy) | rich(lucy) <- (18) [resolution 300,126]
318. rich(lucy) <- (18) [subsumption resolution 314,125]
328. 19 | ~18 [avatar split clause 318,204,209]
335. funny(lucy) <- (19) [resolution 210,215]
340. 24 | ~19 [avatar split clause 335,209,255]
341. tall(susan) | rich(susan) <- (21) [resolution 236,126]
345. rich(susan) <- (21) [subsumption resolution 341,125]
349. ~patient(lucy) | ~generous(lucy) <- (24) [resolution 257,124]
363. ~generous(lucy) <- (24) [subsumption resolution 349,123]
368. generous(lucy) <- (19) [resolution 210,79]
370. $false <- (19, 24) [subsumption resolution 368,363]
371. ~19 | ~24 [avatar contradiction clause 370]
373. funny(susan) <- (21) [resolution 345,215]
377. $false <- (~20, 21) [subsumption resolution 373,231]
378. 20 | ~21 [avatar contradiction clause 377]
379. $false [avatar sat refutation 207,237,270,294,328,340,371,378]
% SZS output end Proof for 5398782989397323636774173
% ------------------------------
% 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 strong is quiet. Everyone who is either not patient or calm is not patient and vice versa. If someone is not kind then paul is both funny and curious. If someone is strong or not brave then alice is not funny or not humble. Everyone who is both old and not old is not creative or not wise and vice versa. If alice is generous then paul is both strong and old and vice versa. Everyone who is not funny is not old and vice versa. Everyone who is both not strong and not patient is strong or not patient and vice versa. Everyone who is both not kind and brave is either curious or not old and vice versa. Everyone who is either not rich or not patient is either strong or not humble and vice versa. Everyone who is both strong and not kind is old or brave and vice versa. If lucy is not wise then mary is both not curious and not funny. Everyone who is not curious is humble and vice versa. If someone is not brave or calm then fred is either tall or calm and vice versa. Everyone who is either not wise or not curious is either not wise or rich. Someone is either brave or not old. Someone is not quiet or not old. | Fred is not humble. | entailment | (![X]:(~strong(X)=>quiet(X)))&
(![X]:((~patient(X)<~>calm(X))<=>~patient(X)))&
((?[X]:(~kind(X)))=>((funny(paul)&curious(paul))))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
(![X]:((old(X)&~old(X))<=>(~creative(X)|~wise(X))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(![X]:(~funny(X)<=>~old(X)))&
(![X]:((~strong(X)&~patient(X))<=>(strong(X)|~patient(X))))&
(![X]:((~kind(X)&brave(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((strong(X)&~kind(X))<=>(old(X)|brave(X))))&
((~wise(lucy))=>((~curious(mary)&~funny(mary))))&
(![X]:(~curious(X)<=>humble(X)))&
((?[X]:((~brave(X)|calm(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~wise(X)<~>~curious(X))=>(~wise(X)<~>rich(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:((~quiet(X)|~old(X)))) | ~humble(fred) | [
"p2",
"p6",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3888194093324718802727721
% SZS output start Proof for 3888194093324718802727721
3. ? [X0] : ~kind(X0) => (curious(paul) & funny(paul)) [input p2]
7. ! [X0] : (~funny(X0) <=> ~old(X0)) [input p6]
8. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> (~patient(X0) | strong(X0))) [input p7]
9. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (curious(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((~kind(X0) & strong(X0)) <=> (brave(X0) | old(X0))) [input p10]
13. ! [X0] : (~curious(X0) <=> humble(X0)) [input p12]
18. humble(fred) [input hypothesis]
20. (curious(paul) & funny(paul)) | ! [X0] : kind(X0) [ennf transformation 3]
30. ! [X0] : ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))) [nnf transformation 7]
31. ! [X0] : (((~patient(X0) & ~strong(X0)) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | (patient(X0) | strong(X0)))) [nnf transformation 8]
32. ! [X0] : (((~patient(X0) & ~strong(X0)) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | patient(X0) | strong(X0))) [flattening 31]
33. ! [X0] : (((brave(X0) & ~kind(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (~brave(X0) | kind(X0)))) [nnf transformation 9]
34. ! [X0] : (((brave(X0) & ~kind(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ~brave(X0) | kind(X0))) [flattening 33]
36. ! [X0] : (((~kind(X0) & strong(X0)) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | (kind(X0) | ~strong(X0)))) [nnf transformation 11]
37. ! [X0] : (((~kind(X0) & strong(X0)) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | kind(X0) | ~strong(X0))) [flattening 36]
38. ! [X0] : ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0))) [nnf transformation 13]
54. funny(paul) | kind(X0) [cnf transformation 20]
67. ~funny(X0) | old(X0) [cnf transformation 30]
69. ~strong(X0) | ~strong(X0) [cnf transformation 32]
76. ~kind(X0) | curious(X0) | old(X0) [cnf transformation 34]
88. ~old(X0) | strong(X0) [cnf transformation 37]
95. ~humble(X0) | ~curious(X0) [cnf transformation 38]
109. humble(fred) [cnf transformation 18]
113. ~strong(X0) [duplicate literal removal 69]
118. 1 <=> ! [X0] : kind(X0) [avatar definition]
119. kind(X0) <- (1) [avatar component clause 118]
126. 3 <=> funny(paul) [avatar definition]
128. funny(paul) <- (3) [avatar component clause 126]
129. 1 | 3 [avatar split clause 54,126,118]
143. 7 <=> ! [X0] : ~strong(X0) [avatar definition]
144. ~strong(X0) <- (7) [avatar component clause 143]
153. 9 <=> old(paul) [avatar definition]
154. old(paul) <- (9) [avatar component clause 153]
165. 7 [avatar split clause 113,143]
208. old(paul) <- (3) [resolution 67,128]
211. 9 | ~3 [avatar split clause 208,126,153]
215. strong(paul) <- (9) [resolution 88,154]
216. $false <- (7, 9) [subsumption resolution 215,144]
217. ~7 | ~9 [avatar contradiction clause 216]
219. ~curious(fred) [resolution 95,109]
221. old(X0) | curious(X0) <- (1) [resolution 76,119]
227. curious(X5) | strong(X5) <- (1) [resolution 221,88]
232. curious(X5) <- (1, 7) [subsumption resolution 227,144]
244. $false <- (1, 7) [resolution 232,219]
245. ~1 | ~7 [avatar contradiction clause 244]
246. $false [avatar sat refutation 129,165,211,217,245]
% SZS output end Proof for 3888194093324718802727721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then mary is not strong. Everyone who is either not rich or not kind is old. Everyone who is not old is not calm and vice versa. Everyone who is either not creative or brave is either tall or not strong and vice versa. Everyone who is tall is not quiet. Everyone who is either wise or not creative is kind or funny and vice versa. Everyone who is not patient or tall is both not rich and patient. If someone is either creative or not curious then susan is funny or not curious. Everyone who is not curious or not kind is not curious. Everyone who is not patient is both not brave and not curious. If someone is not strong or not funny then someone is either generous or strong. If someone is either not generous or quiet then someone is strong and vice versa. If someone is both kind and not quiet then someone is both patient and happy and vice versa. Everyone who is both funny and creative is patient and vice versa. Everyone who is not humble or calm is wise. If someone is not funny or strong then someone is strong. Alice is wise or creative. Someone is either not creative or rich. John is wise. John is either calm or not strong. Someone is either generous or rich. Susan is not curious. Lucy is not funny or happy. | John is not creative. | contradiction | ((?[X]:(~happy(X)))=>(~strong(mary)))&
(![X]:((~rich(X)<~>~kind(X))=>old(X)))&
(![X]:(~old(X)<=>~calm(X)))&
(![X]:((~creative(X)<~>brave(X))<=>(tall(X)<~>~strong(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((wise(X)<~>~creative(X))<=>(kind(X)|funny(X))))&
(![X]:((~patient(X)|tall(X))=>(~rich(X)&patient(X))))&
((?[X]:((creative(X)<~>~curious(X))))=>((funny(susan)|~curious(susan))))&
(![X]:((~curious(X)|~kind(X))=>~curious(X)))&
(![X]:(~patient(X)=>(~brave(X)&~curious(X))))&
((?[X]:((~strong(X)|~funny(X))))=>(?[X]:((generous(X)<~>strong(X)))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:((funny(X)&creative(X))<=>patient(X)))&
(![X]:((~humble(X)|calm(X))=>wise(X)))&
((?[X]:((~funny(X)|strong(X))))=>(?[X]:(strong(X))))&
((wise(alice)|creative(alice)))&
(?[X]:((~creative(X)<~>rich(X))))&
(wise(john))&
((calm(john)<~>~strong(john)))&
(?[X]:((generous(X)<~>rich(X))))&
(~curious(susan))&
((~funny(lucy)|happy(lucy))) | ~creative(john) | [
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6930542458337389076537822
% SZS output start Proof for 6930542458337389076537822
7. ! [X0] : ((tall(X0) | ~patient(X0)) => (patient(X0) & ~rich(X0))) [input p6]
14. ! [X0] : ((creative(X0) & funny(X0)) <=> patient(X0)) [input p13]
24. ~creative(john) [input hypothesis]
35. ! [X0] : ((patient(X0) & ~rich(X0)) | (~tall(X0) & patient(X0))) [ennf transformation 7]
62. ! [X0] : (((creative(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | (~creative(X0) | ~funny(X0)))) [nnf transformation 14]
63. ! [X0] : (((creative(X0) & funny(X0)) | ~patient(X0)) & (patient(X0) | ~creative(X0) | ~funny(X0))) [flattening 62]
95. patient(X0) | patient(X0) [cnf transformation 35]
117. creative(X0) | ~patient(X0) [cnf transformation 63]
131. ~creative(john) [cnf transformation 24]
132. patient(X0) [duplicate literal removal 95]
223. creative(X0) [subsumption resolution 117,132]
263. $false [subsumption resolution 131,223]
% SZS output end Proof for 6930542458337389076537822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not happy then someone is not generous or funny.
If fred is both strong and not humble then john is not funny.
Everyone who is both calm and not curious is not wise or not creative.
Everyone who is both curious and old is quiet or rich and vice versa.
Everyone who is not wise or not rich is either not generous or not funny and vice versa.
If susan is either calm or brave then someone is funny and vice versa.
Everyone who is not calm is not old or happy.
If fred is either curious or strong then someone is both not funny and not quiet.
Everyone who is not strong or generous is both calm and funny and vice versa.
Everyone who is not curious is both happy and brave.
If someone is not strong or not kind then someone is both funny and rich and vice versa.
Everyone who is not rich or not curious is not strong or not old and vice versa.
If someone is generous then alice is either quiet or rich and vice versa.
If mary is both happy and kind then susan is generous.
Everyone who is not old is tall.
Everyone who is either not brave or not quiet is not curious.
Susan is both not brave and not wise.
Someone is not funny.
Someone is both not creative and wise.
Someone is either curious or not quiet.
Someone is not patient.
Someone is generous or creative.
Lucy is both not calm and strong. | John is not funny. | neutral | ((?[X]:((curious(X)|~happy(X))))=>(?[X]:((~generous(X)|funny(X)))))&
(((strong(fred)&~humble(fred)))=>(~funny(john)))&
(![X]:((calm(X)&~curious(X))=>(~wise(X)|~creative(X))))&
(![X]:((curious(X)&old(X))<=>(quiet(X)|rich(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~generous(X)<~>~funny(X))))&
(((calm(susan)<~>brave(susan)))<=>(?[X]:(funny(X))))&
(![X]:(~calm(X)=>(~old(X)|happy(X))))&
(((curious(fred)<~>strong(fred)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)&funny(X))))&
(![X]:(~curious(X)=>(happy(X)&brave(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~strong(X)|~old(X))))&
((?[X]:(generous(X)))<=>((quiet(alice)<~>rich(alice))))&
(((happy(mary)&kind(mary)))=>(generous(susan)))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((~brave(X)<~>~quiet(X))=>~curious(X)))&
((~brave(susan)&~wise(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)|creative(X))))&
((~calm(lucy)&strong(lucy))) | ~funny(john) | [] | null | 0 |
If john is funny then lucy is either not strong or funny. Everyone who is not generous is both calm and not brave and vice versa. Everyone who is funny or strong is not generous or calm. If someone is both not funny and not creative then john is both generous and not generous. Everyone who is both kind and humble is both wise and not creative and vice versa. Everyone who is not calm is funny or not brave and vice versa. Everyone who is either happy or patient is wise or calm. If fred is funny then mary is not curious and vice versa. Everyone who is either not generous or not patient is not generous. If someone is both not calm and not kind then someone is either old or not wise and vice versa. If mary is not old then alice is either curious or humble. If paul is both calm and not kind then john is not strong or not happy. Everyone who is both not curious and not creative is either wise or not old and vice versa. If mary is both brave and not calm then someone is not wise or patient. Mary is either not happy or not strong. Alice is either not happy or not old. Susan is creative or old. Someone is not kind. Someone is either generous or curious. Someone is not wise or patient. Someone is happy or kind. | Alice is generous. | entailment | ((funny(john))=>((~strong(lucy)<~>funny(lucy))))&
(![X]:(~generous(X)<=>(calm(X)&~brave(X))))&
(![X]:((funny(X)|strong(X))=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&~creative(X))))=>((generous(john)&~generous(john))))&
(![X]:((kind(X)&humble(X))<=>(wise(X)&~creative(X))))&
(![X]:(~calm(X)<=>(funny(X)|~brave(X))))&
(![X]:((happy(X)<~>patient(X))=>(wise(X)|calm(X))))&
((funny(fred))<=>(~curious(mary)))&
(![X]:((~generous(X)<~>~patient(X))=>~generous(X)))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:((old(X)<~>~wise(X)))))&
((~old(mary))=>((curious(alice)<~>humble(alice))))&
(((calm(paul)&~kind(paul)))=>((~strong(john)|~happy(john))))&
(![X]:((~curious(X)&~creative(X))<=>(wise(X)<~>~old(X))))&
(((brave(mary)&~calm(mary)))=>(?[X]:((~wise(X)|patient(X)))))&
((~happy(mary)<~>~strong(mary)))&
((~happy(alice)<~>~old(alice)))&
((creative(susan)|old(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((~wise(X)|patient(X))))&
(?[X]:((happy(X)|kind(X)))) | generous(alice) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5463708865629199643292546
% SZS output start Proof for 5463708865629199643292546
2. ! [X0] : (~generous(X0) <=> (~brave(X0) & calm(X0))) [input p1]
6. ! [X0] : (~calm(X0) <=> (~brave(X0) | funny(X0))) [input p5]
22. ~generous(alice) [input hypothesis]
37. ! [X0] : ((~generous(X0) | (brave(X0) | ~calm(X0))) & ((~brave(X0) & calm(X0)) | generous(X0))) [nnf transformation 2]
38. ! [X0] : ((~generous(X0) | brave(X0) | ~calm(X0)) & ((~brave(X0) & calm(X0)) | generous(X0))) [flattening 37]
41. ! [X0] : ((~calm(X0) | (brave(X0) & ~funny(X0))) & ((~brave(X0) | funny(X0)) | calm(X0))) [nnf transformation 6]
42. ! [X0] : ((~calm(X0) | (brave(X0) & ~funny(X0))) & (~brave(X0) | funny(X0) | calm(X0))) [flattening 41]
69. calm(X0) | generous(X0) [cnf transformation 38]
70. ~brave(X0) | generous(X0) [cnf transformation 38]
82. ~calm(X0) | brave(X0) [cnf transformation 42]
115. ~generous(alice) [cnf transformation 22]
266. brave(X0) | generous(X0) [resolution 82,69]
267. generous(X0) [subsumption resolution 266,70]
268. $false [resolution 267,115]
% SZS output end Proof for 5463708865629199643292546
% ------------------------------
% 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 alice is happy then someone is not generous or rich and vice versa.
Everyone who is both happy and not humble is not wise and vice versa.
Everyone who is either not kind or not old is patient or calm and vice versa.
Everyone who is not funny or not calm is both not kind and not patient and vice versa.
If someone is both wise and not wise then john is kind or not calm and vice versa.
If paul is not creative then mary is quiet or wise.
Everyone who is either happy or quiet is both not creative and not brave and vice versa.
Everyone who is either not old or humble is both not calm and not brave.
If lucy is not curious or wise then someone is both not funny and wise.
If someone is either tall or brave then john is patient.
Everyone who is either not happy or not quiet is rich or not rich and vice versa.
Everyone who is both patient and not curious is rich or old.
Everyone who is both not old and funny is both rich and not strong and vice versa.
If lucy is either not brave or kind then mary is brave or not curious.
Everyone who is happy is either generous or not wise and vice versa.
Everyone who is strong is either not funny or not brave and vice versa.
Susan is strong or creative.
Someone is either calm or curious.
Someone is not rich.
Someone is both calm and tall.
Lucy is both not curious and not rich.
Someone is not wise or not funny.
Someone is curious.
Someone is either not patient or not humble. | Alice is brave. | contradiction | ((happy(alice))<=>(?[X]:((~generous(X)|rich(X)))))&
(![X]:((happy(X)&~humble(X))<=>~wise(X)))&
(![X]:((~kind(X)<~>~old(X))<=>(patient(X)|calm(X))))&
(![X]:((~funny(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
((?[X]:((wise(X)&~wise(X))))<=>((kind(john)|~calm(john))))&
((~creative(paul))=>((quiet(mary)|wise(mary))))&
(![X]:((happy(X)<~>quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~old(X)<~>humble(X))=>(~calm(X)&~brave(X))))&
(((~curious(lucy)|wise(lucy)))=>(?[X]:((~funny(X)&wise(X)))))&
((?[X]:((tall(X)<~>brave(X))))=>(patient(john)))&
(![X]:((~happy(X)<~>~quiet(X))<=>(rich(X)|~rich(X))))&
(![X]:((patient(X)&~curious(X))=>(rich(X)|old(X))))&
(![X]:((~old(X)&funny(X))<=>(rich(X)&~strong(X))))&
(((~brave(lucy)<~>kind(lucy)))=>((brave(mary)|~curious(mary))))&
(![X]:(happy(X)<=>(generous(X)<~>~wise(X))))&
(![X]:(strong(X)<=>(~funny(X)<~>~brave(X))))&
((strong(susan)|creative(susan)))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((calm(X)&tall(X))))&
((~curious(lucy)&~rich(lucy)))&
(?[X]:((~wise(X)|~funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((~patient(X)<~>~humble(X)))) | brave(alice) | [
"p0",
"p1",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4577204236519299475635908
% SZS output start Proof for 4577204236519299475635908
1. happy(alice) <=> ? [X0] : (rich(X0) | ~generous(X0)) [input p0]
2. ! [X0] : ((~humble(X0) & happy(X0)) <=> ~wise(X0)) [input p1]
7. ! [X0] : ((happy(X0) <~> quiet(X0)) <=> (~brave(X0) & ~creative(X0))) [input p6]
11. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (~rich(X0) | rich(X0))) [input p10]
15. ! [X0] : (happy(X0) <=> (generous(X0) <~> ~wise(X0))) [input p14]
25. brave(alice) [input hypothesis]
35. (happy(alice) | ! [X0] : (~rich(X0) & generous(X0))) & (? [X0] : (rich(X0) | ~generous(X0)) | ~happy(alice)) [nnf transformation 1]
36. (happy(alice) | ! [X0] : (~rich(X0) & generous(X0))) & (? [X1] : (rich(X1) | ~generous(X1)) | ~happy(alice)) [rectify 35]
37. ? [X1] : (rich(X1) | ~generous(X1)) => (rich(sK0) | ~generous(sK0)) [choice axiom]
38. (happy(alice) | ! [X0] : (~rich(X0) & generous(X0))) & ((rich(sK0) | ~generous(sK0)) | ~happy(alice)) [skolemisation 36,37]
39. ! [X0] : (((~humble(X0) & happy(X0)) | wise(X0)) & (~wise(X0) | (humble(X0) | ~happy(X0)))) [nnf transformation 2]
40. ! [X0] : (((~humble(X0) & happy(X0)) | wise(X0)) & (~wise(X0) | humble(X0) | ~happy(X0))) [flattening 39]
50. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [flattening 50]
56. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 11]
57. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [flattening 56]
61. ! [X0] : ((happy(X0) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ~happy(X0))) [nnf transformation 15]
78. happy(alice) | generous(X0) [cnf transformation 38]
81. wise(X0) | happy(X0) [cnf transformation 40]
102. ~brave(X0) | quiet(X0) | ~happy(X0) [cnf transformation 51]
103. ~brave(X0) | happy(X0) | ~quiet(X0) [cnf transformation 51]
118. ~quiet(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 57]
119. ~quiet(X0) | ~happy(X0) | rich(X0) [cnf transformation 57]
131. happy(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 61]
149. brave(alice) [cnf transformation 25]
154. 2 <=> happy(alice) [avatar definition]
155. ~happy(alice) <- (~2) [avatar component clause 154]
159. 3 <=> ! [X0] : generous(X0) [avatar definition]
160. generous(X0) <- (3) [avatar component clause 159]
161. 3 | 2 [avatar split clause 78,154,159]
233. ~quiet(X0) | ~happy(X0) [subsumption resolution 118,119]
252. ~generous(X0) | happy(X0) [subsumption resolution 131,81]
361. quiet(alice) | ~happy(alice) [resolution 102,149]
364. happy(alice) | ~quiet(alice) [resolution 103,149]
373. ~quiet(alice) [subsumption resolution 364,233]
374. ~happy(alice) [subsumption resolution 361,373]
375. ~2 [avatar split clause 374,154]
378. happy(X1) <- (3) [resolution 160,252]
392. $false <- (~2, 3) [resolution 378,155]
393. 2 | ~3 [avatar contradiction clause 392]
395. $false [avatar sat refutation 161,375,393]
% SZS output end Proof for 4577204236519299475635908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or kind is both not strong and not brave. If someone is creative or not calm then lucy is rich or calm and vice versa. If someone is strong then alice is either generous or not calm. If someone is not tall then someone is either not brave or quiet. If fred is either tall or humble then lucy is either not funny or kind. Everyone who is either old or not generous is patient. Everyone who is tall or rich is both not tall and rich and vice versa. Everyone who is not curious or rich is either funny or happy. If someone is funny or kind then someone is either not wise or humble and vice versa. Everyone who is happy is not old and vice versa. Everyone who is not happy is both generous and calm. Everyone who is old or rich is kind. Everyone who is funny is not creative or not kind. Everyone who is not humble or old is rich or not curious. If lucy is curious then fred is either strong or creative. Everyone who is both humble and generous is both kind and happy. Someone is not funny or not curious. Mary is either not brave or not happy. Someone is not tall or wise. Mary is both funny and curious. Paul is not generous or not curious. Susan is either not old or quiet. Someone is either humble or brave. Paul is not creative or not tall. | Mary is humble. | entailment | (![X]:((generous(X)|kind(X))=>(~strong(X)&~brave(X))))&
((?[X]:((creative(X)|~calm(X))))<=>((rich(lucy)|calm(lucy))))&
((?[X]:(strong(X)))=>((generous(alice)<~>~calm(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((tall(fred)<~>humble(fred)))=>((~funny(lucy)<~>kind(lucy))))&
(![X]:((old(X)<~>~generous(X))=>patient(X)))&
(![X]:((tall(X)|rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((~curious(X)|rich(X))=>(funny(X)<~>happy(X))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(?[X]:((~funny(X)|~curious(X))))&
((~brave(mary)<~>~happy(mary)))&
(?[X]:((~tall(X)|wise(X))))&
((funny(mary)&curious(mary)))&
((~generous(paul)|~curious(paul)))&
((~old(susan)<~>quiet(susan)))&
(?[X]:((humble(X)<~>brave(X))))&
((~creative(paul)|~tall(paul))) | humble(mary) | [
"p0",
"p7",
"p10",
"p13",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1015779004088602693786344
% SZS output start Proof for 1015779004088602693786344
1. ! [X0] : ((kind(X0) | generous(X0)) => (~brave(X0) & ~strong(X0))) [input p0]
8. ! [X0] : ((rich(X0) | ~curious(X0)) => (funny(X0) <~> happy(X0))) [input p7]
11. ! [X0] : (~happy(X0) => (calm(X0) & generous(X0))) [input p10]
14. ! [X0] : ((old(X0) | ~humble(X0)) => (~curious(X0) | rich(X0))) [input p13]
18. ~brave(mary) <~> ~happy(mary) [input p17]
20. curious(mary) & funny(mary) [input p19]
25. ~humble(mary) [input hypothesis]
29. ! [X0] : ((~brave(X0) & ~strong(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 1]
33. ! [X0] : ((funny(X0) <~> happy(X0)) | (~rich(X0) & curious(X0))) [ennf transformation 8]
34. ! [X0] : ((calm(X0) & generous(X0)) | happy(X0)) [ennf transformation 11]
38. ! [X0] : ((~curious(X0) | rich(X0)) | (~old(X0) & humble(X0))) [ennf transformation 14]
39. ! [X0] : (~curious(X0) | rich(X0) | (~old(X0) & humble(X0))) [flattening 38]
56. ! [X0] : (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~rich(X0) & curious(X0))) [nnf transformation 33]
66. (happy(mary) | brave(mary)) & (~happy(mary) | ~brave(mary)) [nnf transformation 18]
75. ~brave(X0) | ~generous(X0) [cnf transformation 29]
97. ~happy(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 56]
106. happy(X0) | generous(X0) [cnf transformation 34]
111. ~curious(X0) | rich(X0) | humble(X0) [cnf transformation 39]
119. happy(mary) | brave(mary) [cnf transformation 66]
121. funny(mary) [cnf transformation 20]
122. curious(mary) [cnf transformation 20]
129. ~humble(mary) [cnf transformation 25]
264. 30 <=> brave(mary) [avatar definition]
266. brave(mary) <- (30) [avatar component clause 264]
268. 31 <=> happy(mary) [avatar definition]
269. ~happy(mary) <- (~31) [avatar component clause 268]
270. happy(mary) <- (31) [avatar component clause 268]
271. 30 | 31 [avatar split clause 119,268,264]
302. ~generous(mary) <- (30) [resolution 75,266]
306. generous(mary) <- (~31) [resolution 106,269]
308. $false <- (30, ~31) [subsumption resolution 306,302]
309. ~30 | 31 [avatar contradiction clause 308]
350. ~funny(mary) | ~rich(mary) <- (31) [resolution 97,270]
352. ~rich(mary) <- (31) [subsumption resolution 350,121]
356. rich(mary) | humble(mary) [resolution 111,122]
357. humble(mary) <- (31) [subsumption resolution 356,352]
358. $false <- (31) [subsumption resolution 357,129]
359. ~31 [avatar contradiction clause 358]
360. $false [avatar sat refutation 271,309,359]
% SZS output end Proof for 1015779004088602693786344
% ------------------------------
% 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 fred is strong or not funny then someone is either not kind or quiet.
If john is either not patient or quiet then john is funny.
Everyone who is both not wise and quiet is old or not patient.
Everyone who is humble is either not creative or not rich and vice versa.
Everyone who is both rich and not patient is both not happy and wise and vice versa.
Everyone who is either not old or not humble is not wise and vice versa.
If fred is either not patient or quiet then mary is either old or not funny and vice versa.
If someone is not calm or not rich then someone is not rich or not brave.
If alice is either not curious or not patient then john is not kind and vice versa.
Everyone who is humble is funny.
Everyone who is both patient and not happy is either quiet or not creative and vice versa.
Everyone who is either not creative or not wise is funny.
If someone is quiet or tall then paul is not calm or calm.
If mary is both humble and old then paul is both not wise and not calm.
Everyone who is both not generous and wise is not generous or not tall and vice versa.
Everyone who is both not rich and not calm is either not quiet or old and vice versa.
Someone is humble.
Someone is brave or not calm.
Someone is funny or happy.
Susan is both not funny and not wise.
Lucy is either not quiet or not calm.
John is both patient and kind.
Someone is both brave and not happy. | Susan is creative. | contradiction | (((strong(fred)|~funny(fred)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
(((~patient(john)<~>quiet(john)))=>(funny(john)))&
(![X]:((~wise(X)&quiet(X))=>(old(X)|~patient(X))))&
(![X]:(humble(X)<=>(~creative(X)<~>~rich(X))))&
(![X]:((rich(X)&~patient(X))<=>(~happy(X)&wise(X))))&
(![X]:((~old(X)<~>~humble(X))<=>~wise(X)))&
(((~patient(fred)<~>quiet(fred)))<=>((old(mary)<~>~funny(mary))))&
((?[X]:((~calm(X)|~rich(X))))=>(?[X]:((~rich(X)|~brave(X)))))&
(((~curious(alice)<~>~patient(alice)))<=>(~kind(john)))&
(![X]:(humble(X)=>funny(X)))&
(![X]:((patient(X)&~happy(X))<=>(quiet(X)<~>~creative(X))))&
(![X]:((~creative(X)<~>~wise(X))=>funny(X)))&
((?[X]:((quiet(X)|tall(X))))=>((~calm(paul)|calm(paul))))&
(((humble(mary)&old(mary)))=>((~wise(paul)&~calm(paul))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)|~tall(X))))&
(![X]:((~rich(X)&~calm(X))<=>(~quiet(X)<~>old(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:((funny(X)|happy(X))))&
((~funny(susan)&~wise(susan)))&
((~quiet(lucy)<~>~calm(lucy)))&
((patient(john)&kind(john)))&
(?[X]:((brave(X)&~happy(X)))) | creative(susan) | [
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1990974034064417751829971
% SZS output start Proof for 1990974034064417751829971
12. ! [X0] : ((~creative(X0) <~> ~wise(X0)) => funny(X0)) [input p11]
20. ~wise(susan) & ~funny(susan) [input p19]
24. creative(susan) [input hypothesis]
33. ! [X0] : (funny(X0) | (~creative(X0) <=> ~wise(X0))) [ennf transformation 12]
53. ! [X0] : (funny(X0) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) [nnf transformation 33]
106. ~creative(X0) | funny(X0) | wise(X0) [cnf transformation 53]
125. ~funny(susan) [cnf transformation 20]
126. ~wise(susan) [cnf transformation 20]
133. creative(susan) [cnf transformation 24]
333. funny(susan) | wise(susan) [resolution 106,133]
336. wise(susan) [subsumption resolution 333,125]
337. $false [subsumption resolution 336,126]
% SZS output end Proof for 1990974034064417751829971
% ------------------------------
% 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 not patient or brave is quiet or rich and vice versa. Everyone who is both not patient and curious is kind. If lucy is old then lucy is both rich and not kind. Everyone who is both not rich and tall is both not generous and calm and vice versa. If someone is either strong or rich then someone is either not curious or not brave. If someone is both not wise and brave then susan is rich or patient. Everyone who is both not happy and not funny is either not tall or not wise and vice versa. If fred is old then paul is either not patient or humble and vice versa. Everyone who is either rich or not funny is both not happy and not quiet and vice versa. Everyone who is either tall or happy is not old or brave and vice versa. Everyone who is both brave and not creative is patient. Everyone who is not quiet or not brave is both humble and brave and vice versa. Everyone who is both not happy and not strong is funny. Everyone who is not creative is not happy or generous. If susan is both not quiet and generous then alice is both creative and not old. If someone is either quiet or calm then fred is tall or not tall and vice versa. Someone is kind or tall. Someone is wise or not quiet. Someone is not patient or kind. Someone is happy. Alice is both not creative and not happy. Susan is generous. Susan is not rich or strong. Alice is both strong and not creative. | Susan is not wise. | entailment | (![X]:((~patient(X)|brave(X))<=>(quiet(X)|rich(X))))&
(![X]:((~patient(X)&curious(X))=>kind(X)))&
((old(lucy))=>((rich(lucy)&~kind(lucy))))&
(![X]:((~rich(X)&tall(X))<=>(~generous(X)&calm(X))))&
((?[X]:((strong(X)<~>rich(X))))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:((~wise(X)&brave(X))))=>((rich(susan)|patient(susan))))&
(![X]:((~happy(X)&~funny(X))<=>(~tall(X)<~>~wise(X))))&
((old(fred))<=>((~patient(paul)<~>humble(paul))))&
(![X]:((rich(X)<~>~funny(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((tall(X)<~>happy(X))<=>(~old(X)|brave(X))))&
(![X]:((brave(X)&~creative(X))=>patient(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)&brave(X))))&
(![X]:((~happy(X)&~strong(X))=>funny(X)))&
(![X]:(~creative(X)=>(~happy(X)|generous(X))))&
(((~quiet(susan)&generous(susan)))=>((creative(alice)&~old(alice))))&
((?[X]:((quiet(X)<~>calm(X))))<=>((tall(fred)|~tall(fred))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((~patient(X)|kind(X))))&
(?[X]:(happy(X)))&
((~creative(alice)&~happy(alice)))&
(generous(susan))&
((~rich(susan)|strong(susan)))&
((strong(alice)&~creative(alice))) | ~wise(susan) | [
"p3",
"p6",
"p8",
"p9",
"p11",
"p14",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8607282636829236501868546
% SZS output start Proof for 8607282636829236501868546
4. ! [X0] : ((tall(X0) & ~rich(X0)) <=> (calm(X0) & ~generous(X0))) [input p3]
7. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> (~tall(X0) <~> ~wise(X0))) [input p6]
9. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (~quiet(X0) & ~happy(X0))) [input p8]
10. ! [X0] : ((tall(X0) <~> happy(X0)) <=> (brave(X0) | ~old(X0))) [input p9]
12. ! [X0] : ((~brave(X0) | ~quiet(X0)) <=> (brave(X0) & humble(X0))) [input p11]
15. (generous(susan) & ~quiet(susan)) => (~old(alice) & creative(alice)) [input p14]
22. generous(susan) [input p21]
24. ~creative(alice) & strong(alice) [input p23]
25. wise(susan) [input hypothesis]
39. (~old(alice) & creative(alice)) | (~generous(susan) | quiet(susan)) [ennf transformation 15]
40. (~old(alice) & creative(alice)) | ~generous(susan) | quiet(susan) [flattening 39]
43. ! [X0] : (((tall(X0) & ~rich(X0)) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | (~tall(X0) | rich(X0)))) [nnf transformation 4]
44. ! [X0] : (((tall(X0) & ~rich(X0)) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | ~tall(X0) | rich(X0))) [flattening 43]
49. ! [X0] : (((~funny(X0) & ~happy(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) & (((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (funny(X0) | happy(X0)))) [nnf transformation 7]
50. ! [X0] : (((~funny(X0) & ~happy(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) & (((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | funny(X0) | happy(X0))) [flattening 49]
52. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 9]
53. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [flattening 52]
54. ! [X0] : ((((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0))))) [flattening 54]
56. ! [X0] : (((~brave(X0) | ~quiet(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (brave(X0) & quiet(X0)))) [nnf transformation 12]
57. ! [X0] : ((~brave(X0) | ~quiet(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (brave(X0) & quiet(X0)))) [flattening 56]
78. ~generous(X0) | ~tall(X0) | rich(X0) [cnf transformation 44]
87. ~wise(X0) | ~tall(X0) | funny(X0) | happy(X0) [cnf transformation 50]
89. ~happy(X0) | ~wise(X0) | tall(X0) [cnf transformation 50]
91. ~funny(X0) | ~wise(X0) | tall(X0) [cnf transformation 50]
99. ~funny(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 53]
106. ~brave(X0) | tall(X0) | happy(X0) [cnf transformation 55]
108. ~happy(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 55]
113. brave(X0) | brave(X0) [cnf transformation 57]
117. creative(alice) | ~generous(susan) | quiet(susan) [cnf transformation 40]
131. generous(susan) [cnf transformation 22]
134. ~creative(alice) [cnf transformation 24]
135. wise(susan) [cnf transformation 25]
136. brave(X0) [duplicate literal removal 113]
174. 9 <=> rich(susan) [avatar definition]
176. rich(susan) <- (9) [avatar component clause 174]
199. 14 <=> quiet(susan) [avatar definition]
201. quiet(susan) <- (14) [avatar component clause 199]
203. 15 <=> generous(susan) [avatar definition]
204. generous(susan) <- (15) [avatar component clause 203]
212. 17 <=> creative(alice) [avatar definition]
215. 14 | ~15 | 17 [avatar split clause 117,212,203,199]
260. 15 [avatar split clause 131,203]
266. ~17 [avatar split clause 134,212]
281. ~tall(susan) | rich(susan) <- (15) [resolution 78,204]
333. 34 <=> funny(susan) [avatar definition]
335. funny(susan) <- (34) [avatar component clause 333]
338. 35 <=> tall(susan) [avatar definition]
341. 9 | ~35 | ~15 [avatar split clause 281,203,338,174]
368. tall(X0) | happy(X0) [resolution 106,136]
413. ~tall(susan) | funny(susan) | happy(susan) [resolution 87,135]
414. funny(susan) | happy(susan) [subsumption resolution 413,368]
416. 42 <=> happy(susan) [avatar definition]
418. happy(susan) <- (42) [avatar component clause 416]
419. 42 | 34 [avatar split clause 414,333,416]
421. ~tall(susan) | ~brave(susan) <- (42) [resolution 418,108]
425. ~wise(susan) | tall(susan) <- (42) [resolution 418,89]
426. ~tall(susan) <- (42) [subsumption resolution 421,136]
427. ~35 | ~42 [avatar split clause 426,416,338]
433. tall(susan) <- (42) [subsumption resolution 425,135]
434. 35 | ~42 [avatar split clause 433,416,338]
441. ~quiet(susan) | ~rich(susan) <- (34) [resolution 335,99]
444. ~wise(susan) | tall(susan) <- (34) [resolution 335,91]
445. ~rich(susan) <- (14, 34) [subsumption resolution 441,201]
446. $false <- (9, 14, 34) [subsumption resolution 445,176]
447. ~9 | ~14 | ~34 [avatar contradiction clause 446]
448. tall(susan) <- (34) [subsumption resolution 444,135]
449. 35 | ~34 [avatar split clause 448,333,338]
450. $false [avatar sat refutation 215,260,266,341,419,427,434,447,449]
% SZS output end Proof for 8607282636829236501868546
% ------------------------------
% 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 mary is quiet or not creative then someone is not calm and vice versa.
If someone is both not kind and calm then someone is either not patient or not brave.
If someone is either not humble or strong then susan is not brave and vice versa.
If lucy is not patient or not tall then someone is quiet or not creative.
Everyone who is both not wise and funny is either happy or not humble and vice versa.
Everyone who is either humble or brave is either rich or curious and vice versa.
Everyone who is either not generous or calm is both not brave and quiet and vice versa.
If paul is either kind or not patient then susan is either not funny or calm and vice versa.
Everyone who is either not brave or tall is not creative or not happy and vice versa.
If someone is funny then lucy is either not wise or strong.
If someone is either curious or not tall then john is not humble or not brave and vice versa.
Everyone who is tall is not curious or wise and vice versa.
Everyone who is either funny or not happy is not curious or patient and vice versa.
Everyone who is not generous is calm or tall.
Everyone who is both brave and humble is happy or not brave and vice versa.
Everyone who is rich is both happy and rich.
Lucy is not rich.
Paul is not quiet or not patient.
Susan is either tall or not generous.
Someone is quiet.
Someone is either quiet or funny.
Paul is old.
Alice is both not curious and quiet. | Lucy is tall. | entailment | (((quiet(mary)|~creative(mary)))<=>(?[X]:(~calm(X))))&
((?[X]:((~kind(X)&calm(X))))=>(?[X]:((~patient(X)<~>~brave(X)))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(~brave(susan)))&
(((~patient(lucy)|~tall(lucy)))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((~wise(X)&funny(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((humble(X)<~>brave(X))<=>(rich(X)<~>curious(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~brave(X)&quiet(X))))&
(((kind(paul)<~>~patient(paul)))<=>((~funny(susan)<~>calm(susan))))&
(![X]:((~brave(X)<~>tall(X))<=>(~creative(X)|~happy(X))))&
((?[X]:(funny(X)))=>((~wise(lucy)<~>strong(lucy))))&
((?[X]:((curious(X)<~>~tall(X))))<=>((~humble(john)|~brave(john))))&
(![X]:(tall(X)<=>(~curious(X)|wise(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~curious(X)|patient(X))))&
(![X]:(~generous(X)=>(calm(X)|tall(X))))&
(![X]:((brave(X)&humble(X))<=>(happy(X)|~brave(X))))&
(![X]:(rich(X)=>(happy(X)&rich(X))))&
(~rich(lucy))&
((~quiet(paul)|~patient(paul)))&
((tall(susan)<~>~generous(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
(old(paul))&
((~curious(alice)&quiet(alice))) | tall(lucy) | [
"p4",
"p5",
"p8",
"p10",
"p11",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 336927846959830304630028
% SZS output start Proof for 336927846959830304630028
5. ! [X0] : ((funny(X0) & ~wise(X0)) <=> (happy(X0) <~> ~humble(X0))) [input p4]
6. ! [X0] : ((humble(X0) <~> brave(X0)) <=> (rich(X0) <~> curious(X0))) [input p5]
9. ! [X0] : ((~brave(X0) <~> tall(X0)) <=> (~happy(X0) | ~creative(X0))) [input p8]
11. ? [X0] : (curious(X0) <~> ~tall(X0)) <=> (~brave(john) | ~humble(john)) [input p10]
12. ! [X0] : (tall(X0) <=> (wise(X0) | ~curious(X0))) [input p11]
13. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (patient(X0) | ~curious(X0))) [input p12]
15. ! [X0] : ((humble(X0) & brave(X0)) <=> (~brave(X0) | happy(X0))) [input p14]
17. ~rich(lucy) [input p16]
24. ~tall(lucy) [input hypothesis]
48. ! [X0] : (((funny(X0) & ~wise(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) & (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~funny(X0) | wise(X0)))) [nnf transformation 5]
49. ! [X0] : (((funny(X0) & ~wise(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) & (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ~funny(X0) | wise(X0))) [flattening 48]
50. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) & (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 6]
54. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [flattening 54]
57. (? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (brave(john) & humble(john))) & ((~brave(john) | ~humble(john)) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) [nnf transformation 11]
58. (? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (brave(john) & humble(john))) & (~brave(john) | ~humble(john) | ! [X0] : ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0)))) [flattening 57]
59. (? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (brave(john) & humble(john))) & (~brave(john) | ~humble(john) | ! [X1] : ((curious(X1) | tall(X1)) & (~tall(X1) | ~curious(X1)))) [rectify 58]
60. ? [X0] : ((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) => ((tall(sK4) | ~curious(sK4)) & (~tall(sK4) | curious(sK4))) [choice axiom]
61. (((tall(sK4) | ~curious(sK4)) & (~tall(sK4) | curious(sK4))) | (brave(john) & humble(john))) & (~brave(john) | ~humble(john) | ! [X1] : ((curious(X1) | tall(X1)) & (~tall(X1) | ~curious(X1)))) [skolemisation 59,60]
62. ! [X0] : ((tall(X0) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 12]
63. ! [X0] : ((tall(X0) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | ~tall(X0))) [flattening 62]
64. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 13]
65. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [flattening 64]
66. ! [X0] : (((humble(X0) & brave(X0)) | (brave(X0) & ~happy(X0))) & ((~brave(X0) | happy(X0)) | (~humble(X0) | ~brave(X0)))) [nnf transformation 15]
67. ! [X0] : (((humble(X0) & brave(X0)) | (brave(X0) & ~happy(X0))) & (~brave(X0) | happy(X0) | ~humble(X0) | ~brave(X0))) [flattening 66]
87. ~happy(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 49]
88. ~wise(X0) | happy(X0) | humble(X0) [cnf transformation 49]
90. happy(X0) | funny(X0) | humble(X0) [cnf transformation 49]
98. ~curious(X0) | ~humble(X0) | rich(X0) | ~brave(X0) [cnf transformation 50]
116. ~brave(X0) | tall(X0) | happy(X0) [cnf transformation 55]
121. ~brave(john) | ~humble(john) | ~tall(X1) | ~curious(X1) [cnf transformation 61]
123. ~tall(sK4) | curious(sK4) | humble(john) [cnf transformation 61]
125. tall(sK4) | ~curious(sK4) | humble(john) [cnf transformation 61]
127. ~curious(X0) | wise(X0) | ~tall(X0) [cnf transformation 63]
128. tall(X0) | curious(X0) [cnf transformation 63]
134. ~funny(X0) | happy(X0) | curious(X0) [cnf transformation 65]
137. ~brave(X0) | happy(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 67]
139. brave(X0) | brave(X0) [cnf transformation 67]
140. ~happy(X0) | humble(X0) [cnf transformation 67]
144. ~rich(lucy) [cnf transformation 17]
153. ~tall(lucy) [cnf transformation 24]
154. ~brave(X0) | happy(X0) | ~humble(X0) [duplicate literal removal 137]
155. brave(X0) [duplicate literal removal 139]
210. 13 <=> tall(lucy) [avatar definition]
211. ~tall(lucy) <- (~13) [avatar component clause 210]
265. 24 <=> brave(john) [avatar definition]
266. ~brave(john) <- (~24) [avatar component clause 265]
269. 25 <=> curious(sK4) [avatar definition]
270. curious(sK4) <- (25) [avatar component clause 269]
271. ~curious(sK4) <- (~25) [avatar component clause 269]
273. 26 <=> tall(sK4) [avatar definition]
274. ~tall(sK4) <- (~26) [avatar component clause 273]
275. tall(sK4) <- (26) [avatar component clause 273]
278. 27 <=> humble(john) [avatar definition]
281. 27 | ~25 | 26 [avatar split clause 125,273,269,278]
283. 27 | 25 | ~26 [avatar split clause 123,273,269,278]
285. 28 <=> ! [X1] : (curious(X1) | tall(X1)) [avatar definition]
286. curious(X1) | tall(X1) <- (28) [avatar component clause 285]
289. 29 <=> ! [X1] : (~tall(X1) | ~curious(X1)) [avatar definition]
290. ~curious(X1) | ~tall(X1) <- (29) [avatar component clause 289]
291. 29 | ~27 | ~24 [avatar split clause 121,265,278,289]
292. 28 [avatar split clause 128,285]
293. ~humble(X0) | happy(X0) [subsumption resolution 154,155]
319. ~13 [avatar split clause 153,210]
320. $false <- (~24) [subsumption resolution 266,155]
321. 24 [avatar contradiction clause 320]
333. tall(sK4) <- (~25, 28) [resolution 286,271]
334. $false <- (~25, ~26, 28) [subsumption resolution 333,274]
335. 25 | 26 | ~28 [avatar contradiction clause 334]
350. funny(X2) | humble(X2) | humble(X2) [resolution 90,140]
351. funny(X2) | humble(X2) [duplicate literal removal 350]
371. happy(X0) | tall(X0) [resolution 116,155]
401. wise(sK4) | ~tall(sK4) <- (25) [resolution 127,270]
402. wise(sK4) <- (25, 26) [subsumption resolution 401,275]
403. happy(sK4) | humble(sK4) <- (25, 26) [resolution 402,88]
405. happy(sK4) <- (25, 26) [subsumption resolution 403,293]
414. happy(X0) | curious(X0) | humble(X0) [resolution 134,351]
419. curious(X0) | happy(X0) [subsumption resolution 414,293]
423. ~humble(sK4) | ~wise(sK4) <- (25, 26) [resolution 405,87]
424. humble(sK4) <- (25, 26) [resolution 405,140]
436. ~humble(sK4) <- (25, 26) [subsumption resolution 423,402]
437. $false <- (25, 26) [subsumption resolution 424,436]
438. ~25 | ~26 [avatar contradiction clause 437]
507. happy(X0) | ~tall(X0) <- (29) [resolution 419,290]
509. happy(X0) <- (29) [subsumption resolution 507,371]
550. humble(X5) <- (29) [resolution 509,140]
567. ~humble(X1) | rich(X1) | ~brave(X1) | tall(X1) <- (28) [resolution 98,286]
569. rich(X1) | ~brave(X1) | tall(X1) <- (28, 29) [subsumption resolution 567,550]
570. rich(X1) | tall(X1) <- (28, 29) [subsumption resolution 569,155]
586. tall(lucy) <- (28, 29) [resolution 570,144]
590. $false <- (~13, 28, 29) [subsumption resolution 586,211]
591. 13 | ~28 | ~29 [avatar contradiction clause 590]
592. $false [avatar sat refutation 281,283,291,292,319,321,335,438,591]
% SZS output end Proof for 336927846959830304630028
% ------------------------------
% 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not humble and not happy then mary is both tall and not creative. Everyone who is not calm is not curious or tall and vice versa. Everyone who is either not brave or wise is either funny or brave. Everyone who is both not generous and rich is not calm. Everyone who is not curious is old or not quiet. If someone is not old or not quiet then paul is both not happy and not generous and vice versa. If someone is not rich then someone is funny or rich. Everyone who is both patient and generous is either generous or humble. If someone is generous then someone is either not old or not rich and vice versa. If someone is strong then someone is rich and vice versa. If susan is humble then susan is both quiet and tall and vice versa. If someone is not rich or not creative then alice is not patient or funny. Everyone who is not strong or not calm is not wise. Everyone who is either not kind or quiet is either not quiet or funny and vice versa. If john is not wise then mary is happy. Everyone who is either not strong or not generous is both brave and wise. Mary is both not strong and not patient. Someone is either not happy or not wise. Someone is both not curious and strong. Paul is not patient or generous. Someone is either not brave or calm. Susan is both not generous and humble. Paul is both strong and not quiet. Alice is not old. | Paul is generous. | contradiction | (((~humble(fred)&~happy(fred)))=>((tall(mary)&~creative(mary))))&
(![X]:(~calm(X)<=>(~curious(X)|tall(X))))&
(![X]:((~brave(X)<~>wise(X))=>(funny(X)<~>brave(X))))&
(![X]:((~generous(X)&rich(X))=>~calm(X)))&
(![X]:(~curious(X)=>(old(X)|~quiet(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~happy(paul)&~generous(paul))))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((patient(X)&generous(X))=>(generous(X)<~>humble(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
((?[X]:(strong(X)))<=>(?[X]:(rich(X))))&
((humble(susan))<=>((quiet(susan)&tall(susan))))&
((?[X]:((~rich(X)|~creative(X))))=>((~patient(alice)|funny(alice))))&
(![X]:((~strong(X)|~calm(X))=>~wise(X)))&
(![X]:((~kind(X)<~>quiet(X))<=>(~quiet(X)<~>funny(X))))&
((~wise(john))=>(happy(mary)))&
(![X]:((~strong(X)<~>~generous(X))=>(brave(X)&wise(X))))&
((~strong(mary)&~patient(mary)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((~curious(X)&strong(X))))&
((~patient(paul)|generous(paul)))&
(?[X]:((~brave(X)<~>calm(X))))&
((~generous(susan)&humble(susan)))&
((strong(paul)&~quiet(paul)))&
(~old(alice)) | generous(paul) | [
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4766896702466613818348208
% SZS output start Proof for 4766896702466613818348208
6. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (~generous(paul) & ~happy(paul)) [input p5]
23. ~quiet(paul) & strong(paul) [input p22]
25. generous(paul) [input hypothesis]
48. (? [X0] : (~quiet(X0) | ~old(X0)) | (generous(paul) | happy(paul))) & ((~generous(paul) & ~happy(paul)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 6]
49. (? [X0] : (~quiet(X0) | ~old(X0)) | generous(paul) | happy(paul)) & ((~generous(paul) & ~happy(paul)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 48]
50. (? [X0] : (~quiet(X0) | ~old(X0)) | generous(paul) | happy(paul)) & ((~generous(paul) & ~happy(paul)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 49]
51. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK0) | ~old(sK0)) [choice axiom]
52. ((~quiet(sK0) | ~old(sK0)) | generous(paul) | happy(paul)) & ((~generous(paul) & ~happy(paul)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 50,51]
91. ~generous(paul) | quiet(X1) [cnf transformation 52]
128. ~quiet(paul) [cnf transformation 23]
130. generous(paul) [cnf transformation 25]
155. 5 <=> generous(paul) [avatar definition]
168. 8 <=> ! [X1] : quiet(X1) [avatar definition]
169. quiet(X1) <- (8) [avatar component clause 168]
170. 8 | ~5 [avatar split clause 91,155,168]
278. 5 [avatar split clause 130,155]
285. $false <- (8) [resolution 169,128]
286. ~8 [avatar contradiction clause 285]
287. $false [avatar sat refutation 170,278,286]
% SZS output end Proof for 4766896702466613818348208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or brave then alice is funny or not tall.
Everyone who is either not rich or not creative is both not humble and not calm and vice versa.
Everyone who is both not tall and brave is generous or not tall and vice versa.
Everyone who is both not creative and not humble is either patient or brave and vice versa.
If john is generous then someone is either patient or rich and vice versa.
Everyone who is not strong or not tall is either not brave or not tall and vice versa.
Everyone who is both rich and not kind is generous or not generous and vice versa.
Everyone who is generous or strong is not old and vice versa.
Everyone who is either rich or not wise is humble and vice versa.
If paul is both not tall and not curious then susan is calm or not patient and vice versa.
If someone is either rich or old then someone is both not rich and wise.
If paul is both kind and old then john is both old and not generous.
Everyone who is generous or not funny is curious and vice versa.
If mary is either rich or not humble then mary is not funny and vice versa.
Everyone who is either funny or quiet is old and vice versa.
Someone is both funny and brave.
Lucy is both not humble and not quiet.
John is either quiet or not humble.
Someone is funny or patient.
Someone is old or curious.
Someone is not wise or not generous. | Susan is patient. | entailment | ((?[X]:((patient(X)<~>brave(X))))=>((funny(alice)|~tall(alice))))&
(![X]:((~rich(X)<~>~creative(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~tall(X)&brave(X))<=>(generous(X)|~tall(X))))&
(![X]:((~creative(X)&~humble(X))<=>(patient(X)<~>brave(X))))&
((generous(john))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((rich(X)&~kind(X))<=>(generous(X)|~generous(X))))&
(![X]:((generous(X)|strong(X))<=>~old(X)))&
(![X]:((rich(X)<~>~wise(X))<=>humble(X)))&
(((~tall(paul)&~curious(paul)))<=>((calm(susan)|~patient(susan))))&
((?[X]:((rich(X)<~>old(X))))=>(?[X]:((~rich(X)&wise(X)))))&
(((kind(paul)&old(paul)))=>((old(john)&~generous(john))))&
(![X]:((generous(X)|~funny(X))<=>curious(X)))&
(((rich(mary)<~>~humble(mary)))<=>(~funny(mary)))&
(![X]:((funny(X)<~>quiet(X))<=>old(X)))&
(?[X]:((funny(X)&brave(X))))&
((~humble(lucy)&~quiet(lucy)))&
((quiet(john)<~>~humble(john)))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((~wise(X)|~generous(X)))) | patient(susan) | [
"p4",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4777425574283204334517498
% SZS output start Proof for 4777425574283204334517498
5. generous(john) <=> ? [X0] : (patient(X0) <~> rich(X0)) [input p4]
7. ! [X0] : ((~kind(X0) & rich(X0)) <=> (~generous(X0) | generous(X0))) [input p6]
8. ! [X0] : ((strong(X0) | generous(X0)) <=> ~old(X0)) [input p7]
11. ? [X0] : (rich(X0) <~> old(X0)) => ? [X0] : (wise(X0) & ~rich(X0)) [input p10]
22. ~patient(susan) [input hypothesis]
23. ? [X0] : (rich(X0) <~> old(X0)) => ? [X1] : (wise(X1) & ~rich(X1)) [rectify 11]
26. ? [X1] : (wise(X1) & ~rich(X1)) | ! [X0] : (rich(X0) <=> old(X0)) [ennf transformation 23]
36. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (? [X0] : ((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | ~generous(john)) [nnf transformation 5]
37. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (? [X1] : ((~rich(X1) | ~patient(X1)) & (rich(X1) | patient(X1))) | ~generous(john)) [rectify 36]
38. ? [X1] : ((~rich(X1) | ~patient(X1)) & (rich(X1) | patient(X1))) => ((~rich(sK0) | ~patient(sK0)) & (rich(sK0) | patient(sK0))) [choice axiom]
39. (generous(john) | ! [X0] : ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) & (((~rich(sK0) | ~patient(sK0)) & (rich(sK0) | patient(sK0))) | ~generous(john)) [skolemisation 37,38]
42. ! [X0] : (((~kind(X0) & rich(X0)) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 7]
43. ! [X0] : (((~kind(X0) & rich(X0)) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | kind(X0) | ~rich(X0))) [flattening 42]
44. ! [X0] : (((strong(X0) | generous(X0)) | old(X0)) & (~old(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 8]
45. ! [X0] : ((strong(X0) | generous(X0) | old(X0)) & (~old(X0) | (~strong(X0) & ~generous(X0)))) [flattening 44]
49. ? [X1] : (wise(X1) & ~rich(X1)) | ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 26]
50. ? [X0] : (wise(X0) & ~rich(X0)) | ! [X1] : ((rich(X1) | ~old(X1)) & (old(X1) | ~rich(X1))) [rectify 49]
51. ? [X0] : (wise(X0) & ~rich(X0)) => (wise(sK1) & ~rich(sK1)) [choice axiom]
52. (wise(sK1) & ~rich(sK1)) | ! [X1] : ((rich(X1) | ~old(X1)) & (old(X1) | ~rich(X1))) [skolemisation 50,51]
88. generous(john) | patient(X0) | ~rich(X0) [cnf transformation 39]
96. rich(X0) | ~generous(X0) [cnf transformation 43]
97. generous(X0) | rich(X0) [cnf transformation 43]
100. ~old(X0) | ~generous(X0) [cnf transformation 45]
112. ~rich(sK1) | old(X1) | ~rich(X1) [cnf transformation 52]
138. ~patient(susan) [cnf transformation 22]
158. 5 <=> ! [X0] : (patient(X0) | ~rich(X0)) [avatar definition]
159. patient(X0) | ~rich(X0) <- (5) [avatar component clause 158]
161. 6 <=> generous(john) [avatar definition]
163. generous(john) <- (6) [avatar component clause 161]
164. 5 | 6 [avatar split clause 88,161,158]
181. rich(X0) [subsumption resolution 96,97]
185. 10 <=> patient(susan) [avatar definition]
186. ~patient(susan) <- (~10) [avatar component clause 185]
207. 14 <=> ! [X1] : old(X1) [avatar definition]
208. old(X1) <- (14) [avatar component clause 207]
214. old(X1) | ~rich(X1) [subsumption resolution 112,181]
215. old(X1) [subsumption resolution 214,181]
216. 14 [avatar split clause 215,207]
266. ~10 [avatar split clause 138,185]
267. patient(X0) <- (5) [subsumption resolution 159,181]
268. $false <- (5, ~10) [resolution 267,186]
269. ~5 | 10 [avatar contradiction clause 268]
279. ~generous(X0) <- (14) [resolution 100,208]
281. $false <- (6, 14) [resolution 279,163]
283. ~6 | ~14 [avatar contradiction clause 281]
284. $false [avatar sat refutation 164,216,266,269,283]
% SZS output end Proof for 4777425574283204334517498
% ------------------------------
% 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 curious or wise is both not rich and strong and vice versa. Everyone who is either not old or creative is both not kind and not curious and vice versa. If john is either not quiet or not happy then fred is both not strong and not wise. Everyone who is both curious and not humble is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. If lucy is curious or kind then mary is not brave and vice versa. Someone is happy or rich. Someone is generous. Susan is kind or not kind. Someone is either calm or not kind. Someone is both not kind and not generous. Someone is not quiet or not patient. Someone is rich or calm. Alice is both quiet and not creative. | Alice is happy. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X))))&
((quiet(alice)&~creative(alice))) | happy(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6391812373465918900532557
% SZS output start Proof for 6391812373465918900532557
5. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p4]
23. ~happy(alice) [input hypothesis]
40. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 5]
87. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
89. kind(X0) | kind(X0) | happy(X0) [cnf transformation 40]
124. ~happy(alice) [cnf transformation 23]
125. happy(X0) | ~kind(X0) [duplicate literal removal 87]
126. kind(X0) | happy(X0) [duplicate literal removal 89]
147. happy(X0) [subsumption resolution 125,126]
239. $false [subsumption resolution 124,147]
% SZS output end Proof for 6391812373465918900532557
% ------------------------------
% 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 |
Everyone who is not strong or not creative is both not humble and wise.
Everyone who is old or curious is not generous or not patient and vice versa.
If someone is not tall or rich then lucy is not brave and vice versa.
Everyone who is strong is both humble and not happy and vice versa.
If someone is generous then alice is both rich and generous and vice versa.
Everyone who is either strong or not old is both not old and not funny.
Everyone who is not tall or quiet is both not generous and not brave and vice versa.
If paul is not calm then someone is quiet.
If fred is wise or curious then someone is not kind.
If someone is not happy or not old then susan is either not creative or not generous and vice versa.
Everyone who is both not patient and not generous is curious.
If alice is not creative then paul is both not old and wise and vice versa.
If paul is either creative or brave then susan is wise or not wise.
If john is curious or not strong then someone is funny and vice versa.
Everyone who is calm or wise is not patient or generous and vice versa.
If someone is both not curious and not wise then mary is not old and vice versa.
Someone is not strong or tall.
John is either not creative or not humble.
John is not happy or humble.
Fred is either not creative or old.
Mary is tall.
Mary is either not old or creative.
Someone is either not generous or not happy. | Susan is not quiet. | neutral | (![X]:((~strong(X)|~creative(X))=>(~humble(X)&wise(X))))&
(![X]:((old(X)|curious(X))<=>(~generous(X)|~patient(X))))&
((?[X]:((~tall(X)|rich(X))))<=>(~brave(lucy)))&
(![X]:(strong(X)<=>(humble(X)&~happy(X))))&
((?[X]:(generous(X)))<=>((rich(alice)&generous(alice))))&
(![X]:((strong(X)<~>~old(X))=>(~old(X)&~funny(X))))&
(![X]:((~tall(X)|quiet(X))<=>(~generous(X)&~brave(X))))&
((~calm(paul))=>(?[X]:(quiet(X))))&
(((wise(fred)|curious(fred)))=>(?[X]:(~kind(X))))&
((?[X]:((~happy(X)|~old(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:((~patient(X)&~generous(X))=>curious(X)))&
((~creative(alice))<=>((~old(paul)&wise(paul))))&
(((creative(paul)<~>brave(paul)))=>((wise(susan)|~wise(susan))))&
(((curious(john)|~strong(john)))<=>(?[X]:(funny(X))))&
(![X]:((calm(X)|wise(X))<=>(~patient(X)|generous(X))))&
((?[X]:((~curious(X)&~wise(X))))<=>(~old(mary)))&
(?[X]:((~strong(X)|tall(X))))&
((~creative(john)<~>~humble(john)))&
((~happy(john)|humble(john)))&
((~creative(fred)<~>old(fred)))&
(tall(mary))&
((~old(mary)<~>creative(mary)))&
(?[X]:((~generous(X)<~>~happy(X)))) | ~quiet(susan) | [] | null | 0 |
If fred is either strong or not kind then someone is both funny and not happy.
If paul is not old then susan is not patient or rich and vice versa.
Everyone who is not happy is not happy or humble and vice versa.
If mary is both kind and funny then someone is funny or not creative and vice versa.
Everyone who is humble or not rich is not creative and vice versa.
Everyone who is either not rich or strong is either not brave or not tall.
If someone is either creative or not old then mary is either calm or funny and vice versa.
Everyone who is either not calm or calm is not calm and vice versa.
If alice is strong then someone is both not calm and not generous and vice versa.
If lucy is brave or kind then mary is both not kind and calm.
If someone is not strong then someone is not quiet.
If paul is strong or not wise then someone is calm or not strong and vice versa.
Everyone who is both rich and not humble is old or not calm.
Everyone who is either not kind or humble is not kind or not brave and vice versa.
If susan is strong or not tall then someone is both curious and patient and vice versa.
If someone is not happy then someone is not calm and vice versa.
Lucy is not wise.
Alice is either patient or not humble.
Lucy is not humble.
Fred is not happy or happy.
Fred is generous or wise.
Someone is strong. | Mary is quiet. | neutral | (((strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)&~happy(X)))))&
((~old(paul))<=>((~patient(susan)|rich(susan))))&
(![X]:(~happy(X)<=>(~happy(X)|humble(X))))&
(((kind(mary)&funny(mary)))<=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((humble(X)|~rich(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>strong(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:((creative(X)<~>~old(X))))<=>((calm(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>calm(X))<=>~calm(X)))&
((strong(alice))<=>(?[X]:((~calm(X)&~generous(X)))))&
(((brave(lucy)|kind(lucy)))=>((~kind(mary)&calm(mary))))&
((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
(((strong(paul)|~wise(paul)))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((rich(X)&~humble(X))=>(old(X)|~calm(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(~kind(X)|~brave(X))))&
(((strong(susan)|~tall(susan)))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~calm(X))))&
(~wise(lucy))&
((patient(alice)<~>~humble(alice)))&
(~humble(lucy))&
((~happy(fred)|happy(fred)))&
((generous(fred)|wise(fred)))&
(?[X]:(strong(X))) | quiet(mary) | [] | null | 0 |
Everyone who is not tall is either tall or creative and vice versa.
Everyone who is both kind and calm is both humble and not calm.
Everyone who is patient or not kind is creative and vice versa.
If someone is either not calm or wise then john is patient.
Everyone who is not quiet is not calm or brave.
If john is not calm then paul is not patient and vice versa.
If someone is not rich then lucy is not generous or old and vice versa.
Everyone who is either quiet or not old is generous or not old and vice versa.
Everyone who is not rich is both not rich and funny.
Everyone who is not curious or happy is either not calm or quiet and vice versa.
Everyone who is either happy or not generous is either not brave or kind and vice versa.
Everyone who is both curious and not quiet is not old and vice versa.
Everyone who is calm or not kind is both not generous and curious.
If paul is old or strong then someone is either not strong or old and vice versa.
If lucy is not curious then john is either brave or humble.
If someone is strong or quiet then someone is happy or funny.
Someone is strong.
Someone is not generous or not strong.
John is not generous or not wise.
Susan is both not funny and not quiet.
Alice is strong or not patient.
Someone is both kind and creative.
Fred is both not generous and wise. | Paul is not strong. | contradiction | (![X]:(~tall(X)<=>(tall(X)<~>creative(X))))&
(![X]:((kind(X)&calm(X))=>(humble(X)&~calm(X))))&
(![X]:((patient(X)|~kind(X))<=>creative(X)))&
((?[X]:((~calm(X)<~>wise(X))))=>(patient(john)))&
(![X]:(~quiet(X)=>(~calm(X)|brave(X))))&
((~calm(john))<=>(~patient(paul)))&
((?[X]:(~rich(X)))<=>((~generous(lucy)|old(lucy))))&
(![X]:((quiet(X)<~>~old(X))<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(~rich(X)&funny(X))))&
(![X]:((~curious(X)|happy(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((curious(X)&~quiet(X))<=>~old(X)))&
(![X]:((calm(X)|~kind(X))=>(~generous(X)&curious(X))))&
(((old(paul)|strong(paul)))<=>(?[X]:((~strong(X)<~>old(X)))))&
((~curious(lucy))=>((brave(john)<~>humble(john))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((happy(X)|funny(X)))))&
(?[X]:(strong(X)))&
(?[X]:((~generous(X)|~strong(X))))&
((~generous(john)|~wise(john)))&
((~funny(susan)&~quiet(susan)))&
((strong(alice)|~patient(alice)))&
(?[X]:((kind(X)&creative(X))))&
((~generous(fred)&wise(fred))) | ~strong(paul) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p7",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 470536125925522002798055
% SZS output start Proof for 470536125925522002798055
1. ! [X0] : (~tall(X0) <=> (tall(X0) <~> creative(X0))) [input p0]
2. ! [X0] : ((calm(X0) & kind(X0)) => (~calm(X0) & humble(X0))) [input p1]
3. ! [X0] : ((~kind(X0) | patient(X0)) <=> creative(X0)) [input p2]
5. ! [X0] : (~quiet(X0) => (brave(X0) | ~calm(X0))) [input p4]
6. ~calm(john) <=> ~patient(paul) [input p5]
8. ! [X0] : ((quiet(X0) <~> ~old(X0)) <=> (~old(X0) | generous(X0))) [input p7]
10. ! [X0] : ((happy(X0) | ~curious(X0)) <=> (~calm(X0) <~> quiet(X0))) [input p9]
11. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (~brave(X0) <~> kind(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) & curious(X0)) <=> ~old(X0)) [input p11]
13. ! [X0] : ((~kind(X0) | calm(X0)) => (curious(X0) & ~generous(X0))) [input p12]
14. (strong(paul) | old(paul)) <=> ? [X0] : (~strong(X0) <~> old(X0)) [input p13]
24. ~strong(paul) [input hypothesis]
26. ! [X0] : ((~calm(X0) & humble(X0)) | (~calm(X0) | ~kind(X0))) [ennf transformation 2]
27. ! [X0] : ((~calm(X0) & humble(X0)) | ~calm(X0) | ~kind(X0)) [flattening 26]
29. ! [X0] : ((brave(X0) | ~calm(X0)) | quiet(X0)) [ennf transformation 5]
30. ! [X0] : (brave(X0) | ~calm(X0) | quiet(X0)) [flattening 29]
32. ! [X0] : ((curious(X0) & ~generous(X0)) | (kind(X0) & ~calm(X0))) [ennf transformation 13]
35. ! [X0] : ((~tall(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | tall(X0))) [nnf transformation 1]
36. ! [X0] : (((~kind(X0) | patient(X0)) | ~creative(X0)) & (creative(X0) | (kind(X0) & ~patient(X0)))) [nnf transformation 3]
37. ! [X0] : ((~kind(X0) | patient(X0) | ~creative(X0)) & (creative(X0) | (kind(X0) & ~patient(X0)))) [flattening 36]
39. (~calm(john) | patient(paul)) & (~patient(paul) | calm(john)) [nnf transformation 6]
45. ! [X0] : ((((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))))) [nnf transformation 8]
46. ! [X0] : ((((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))))) [flattening 45]
47. ! [X0] : (((happy(X0) | ~curious(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~happy(X0) & curious(X0)))) [nnf transformation 10]
48. ! [X0] : ((happy(X0) | ~curious(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~happy(X0) & curious(X0)))) [flattening 47]
49. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) & (((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 11]
50. ! [X0] : (((~quiet(X0) & curious(X0)) | old(X0)) & (~old(X0) | (quiet(X0) | ~curious(X0)))) [nnf transformation 12]
51. ! [X0] : (((~quiet(X0) & curious(X0)) | old(X0)) & (~old(X0) | quiet(X0) | ~curious(X0))) [flattening 50]
52. ((strong(paul) | old(paul)) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (? [X0] : ((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (~strong(paul) & ~old(paul))) [nnf transformation 14]
53. (strong(paul) | old(paul) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (? [X0] : ((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (~strong(paul) & ~old(paul))) [flattening 52]
54. (strong(paul) | old(paul) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (? [X1] : ((~old(X1) | strong(X1)) & (old(X1) | ~strong(X1))) | (~strong(paul) & ~old(paul))) [rectify 53]
55. ? [X1] : ((~old(X1) | strong(X1)) & (old(X1) | ~strong(X1))) => ((~old(sK1) | strong(sK1)) & (old(sK1) | ~strong(sK1))) [choice axiom]
56. (strong(paul) | old(paul) | ! [X0] : ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(sK1) | strong(sK1)) & (old(sK1) | ~strong(sK1))) | (~strong(paul) & ~old(paul))) [skolemisation 54,55]
67. creative(X0) | tall(X0) | tall(X0) [cnf transformation 35]
69. ~tall(X0) | creative(X0) | ~tall(X0) [cnf transformation 35]
72. ~calm(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 27]
75. ~kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 37]
78. ~calm(X0) | brave(X0) | quiet(X0) [cnf transformation 30]
79. ~patient(paul) | calm(john) [cnf transformation 39]
84. ~old(X0) | generous(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 46]
89. old(X0) | ~quiet(X0) | old(X0) [cnf transformation 46]
93. ~happy(X0) | ~calm(X0) | quiet(X0) [cnf transformation 48]
96. ~curious(X0) | happy(X0) | quiet(X0) | calm(X0) [cnf transformation 48]
99. ~brave(X0) | kind(X0) | happy(X0) | generous(X0) [cnf transformation 49]
106. ~curious(X0) | quiet(X0) | ~old(X0) [cnf transformation 51]
109. ~generous(X0) | ~calm(X0) [cnf transformation 32]
110. ~generous(X0) | kind(X0) [cnf transformation 32]
111. ~calm(X0) | curious(X0) [cnf transformation 32]
112. curious(X0) | kind(X0) [cnf transformation 32]
117. strong(paul) | old(paul) | old(X0) | strong(X0) [cnf transformation 56]
133. ~strong(paul) [cnf transformation 24]
134. ~old(X0) | generous(X0) | ~quiet(X0) [duplicate literal removal 84]
135. ~quiet(X0) | old(X0) [duplicate literal removal 89]
136. ~calm(X0) | ~kind(X0) [duplicate literal removal 72]
137. creative(X0) | tall(X0) [duplicate literal removal 67]
138. ~tall(X0) | creative(X0) [duplicate literal removal 69]
139. creative(X0) [subsumption resolution 137,138]
140. ~kind(X0) | patient(X0) [subsumption resolution 75,139]
154. 4 <=> patient(paul) [avatar definition]
158. 5 <=> calm(john) [avatar definition]
159. calm(john) <- (5) [avatar component clause 158]
162. 5 | ~4 [avatar split clause 79,154,158]
181. ~quiet(X0) | generous(X0) [subsumption resolution 134,135]
186. 11 <=> old(paul) [avatar definition]
187. ~old(paul) <- (~11) [avatar component clause 186]
188. old(paul) <- (11) [avatar component clause 186]
190. 12 <=> strong(paul) [avatar definition]
191. ~strong(paul) <- (~12) [avatar component clause 190]
195. 13 <=> ! [X0] : (old(X0) | strong(X0)) [avatar definition]
196. strong(X0) | old(X0) <- (13) [avatar component clause 195]
197. 13 | 11 | 12 [avatar split clause 117,190,186,195]
215. 17 <=> brave(john) [avatar definition]
216. brave(john) <- (17) [avatar component clause 215]
250. 25 <=> generous(john) [avatar definition]
251. generous(john) <- (25) [avatar component clause 250]
267. ~12 [avatar split clause 133,190]
272. 29 <=> generous(paul) [avatar definition]
273. generous(paul) <- (29) [avatar component clause 272]
276. 30 <=> quiet(paul) [avatar definition]
278. quiet(paul) <- (30) [avatar component clause 276]
294. ~old(X0) | quiet(X0) | kind(X0) [resolution 106,112]
325. quiet(paul) | kind(paul) <- (11) [resolution 294,188]
328. 36 <=> kind(paul) [avatar definition]
330. kind(paul) <- (36) [avatar component clause 328]
331. 36 | 30 | ~11 [avatar split clause 325,186,276,328]
332. kind(john) | happy(john) | generous(john) <- (17) [resolution 99,216]
333. kind(john) | happy(john) <- (17) [subsumption resolution 332,110]
335. 37 <=> happy(john) [avatar definition]
337. happy(john) <- (37) [avatar component clause 335]
339. 38 <=> kind(john) [avatar definition]
342. 37 | 38 | ~17 [avatar split clause 333,215,339,335]
344. generous(paul) <- (30) [resolution 278,181]
349. 29 | ~30 [avatar split clause 344,276,272]
361. kind(paul) <- (29) [resolution 273,110]
363. 36 | ~29 [avatar split clause 361,272,328]
420. patient(paul) <- (36) [resolution 330,140]
433. 4 | ~36 [avatar split clause 420,328,154]
435. brave(john) | quiet(john) <- (5) [resolution 159,78]
436. ~kind(john) <- (5) [resolution 159,136]
437. curious(john) <- (5) [resolution 159,111]
439. 50 <=> curious(john) [avatar definition]
441. curious(john) <- (50) [avatar component clause 439]
443. 51 <=> quiet(john) [avatar definition]
444. ~quiet(john) <- (~51) [avatar component clause 443]
445. quiet(john) <- (51) [avatar component clause 443]
449. ~38 | ~5 [avatar split clause 436,158,339]
450. 50 | ~5 [avatar split clause 437,158,439]
452. happy(john) | quiet(john) | calm(john) <- (50) [resolution 441,96]
455. generous(john) <- (51) [resolution 445,181]
457. 25 | ~51 [avatar split clause 455,443,250]
461. ~calm(john) <- (25) [resolution 251,109]
467. $false <- (5, 25) [subsumption resolution 461,159]
468. ~5 | ~25 [avatar contradiction clause 467]
469. 51 | 17 | ~5 [avatar split clause 435,158,215,443]
481. ~calm(john) | quiet(john) <- (37) [resolution 337,93]
482. quiet(john) <- (5, 37) [subsumption resolution 481,159]
483. $false <- (5, 37, ~51) [subsumption resolution 482,444]
484. ~5 | ~37 | 51 [avatar contradiction clause 483]
485. happy(john) | calm(john) <- (50, ~51) [subsumption resolution 452,444]
486. 5 | 37 | ~50 | 51 [avatar split clause 485,443,439,335,158]
498. old(paul) <- (~12, 13) [resolution 196,191]
501. $false <- (~11, ~12, 13) [subsumption resolution 498,187]
502. 11 | 12 | ~13 [avatar contradiction clause 501]
505. $false [avatar sat refutation 162,197,267,331,342,349,363,433,449,450,457,468,469,484,486,502]
% SZS output end Proof for 470536125925522002798055
% ------------------------------
% 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 |
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