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 both funny and not patient is not calm or not brave and vice versa.
If john is not rich then someone is both rich and curious and vice versa.
If someone is patient then someone is either humble or not funny.
If susan is not old or calm then susan is old.
Everyone who is not old or generous is not brave and vice versa.
Everyone who is rich or not strong is curious or not tall and vice versa.
If lucy is both happy and quiet then mary is either not brave or not old and vice versa.
If mary is both curious and not funny then mary is brave or not funny and vice versa.
Everyone who is either not brave or not wise is either kind or not calm and vice versa.
If someone is either not creative or not generous then someone is old.
Everyone who is both brave and not calm is not kind or not wise and vice versa.
Everyone who is either brave or not happy is not tall or generous.
Everyone who is either not old or tall is both not generous and patient and vice versa.
Everyone who is both kind and brave is not patient.
If paul is strong then alice is quiet or not wise.
Everyone who is either funny or brave is either patient or happy and vice versa.
Someone is both tall and not creative.
John is funny or not creative.
Alice is not wise or patient.
John is both calm and not tall.
Someone is not wise.
Alice is not curious or wise. | John is not happy. | contradiction | (![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((~rich(john))<=>(?[X]:((rich(X)&curious(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(((~old(susan)|calm(susan)))=>(old(susan)))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(((curious(mary)&~funny(mary)))<=>((brave(mary)|~funny(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((brave(X)&~calm(X))<=>(~kind(X)|~wise(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~tall(X)|generous(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)&patient(X))))&
(![X]:((kind(X)&brave(X))=>~patient(X)))&
((strong(paul))=>((quiet(alice)|~wise(alice))))&
(![X]:((funny(X)<~>brave(X))<=>(patient(X)<~>happy(X))))&
(?[X]:((tall(X)&~creative(X))))&
((funny(john)|~creative(john)))&
((~wise(alice)|patient(alice)))&
((calm(john)&~tall(john)))&
(?[X]:(~wise(X)))&
((~curious(alice)|wise(alice))) | ~happy(john) | [
"p0",
"p8",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1330194770555615366347782
% SZS output start Proof for 1330194770555615366347782
1. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~brave(X0) | ~calm(X0))) [input p0]
9. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p8]
11. ! [X0] : ((~calm(X0) & brave(X0)) <=> (~wise(X0) | ~kind(X0))) [input p10]
16. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (patient(X0) <~> happy(X0))) [input p15]
20. ~tall(john) & calm(john) [input p19]
23. ~happy(john) [input hypothesis]
35. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 1]
36. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | patient(X0) | ~funny(X0))) [flattening 35]
53. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 9]
58. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~calm(X0) & brave(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0))) [flattening 58]
63. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) & (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 16]
70. brave(X0) | funny(X0) [cnf transformation 36]
72. ~patient(X0) | brave(X0) [cnf transformation 36]
102. ~wise(X0) | ~brave(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 53]
108. ~wise(X0) | ~kind(X0) | calm(X0) | ~brave(X0) [cnf transformation 59]
111. ~calm(X0) | kind(X0) [cnf transformation 59]
112. ~calm(X0) | wise(X0) [cnf transformation 59]
123. happy(X0) | patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
135. calm(john) [cnf transformation 20]
139. ~happy(john) [cnf transformation 23]
227. ~kind(X0) | ~wise(X0) | ~brave(X0) [subsumption resolution 108,102]
246. happy(X0) | brave(X0) | ~funny(X0) [subsumption resolution 123,72]
247. happy(X0) | brave(X0) [subsumption resolution 246,70]
272. kind(john) [resolution 111,135]
275. wise(john) [resolution 112,135]
279. brave(john) [resolution 247,139]
348. ~wise(john) | ~brave(john) [resolution 227,272]
349. ~brave(john) [subsumption resolution 348,275]
350. $false [subsumption resolution 349,279]
% SZS output end Proof for 1330194770555615366347782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either funny or generous and vice versa.
If john is not quiet or not tall then susan is either kind or not kind.
Everyone who is not funny is not brave or funny and vice versa.
If lucy is both kind and not funny then someone is both generous and kind and vice versa.
Everyone who is not tall is not patient or funny and vice versa.
Everyone who is quiet or not strong is old.
If someone is either not curious or not calm then fred is creative.
Everyone who is both not calm and calm is tall and vice versa.
If fred is both not brave and funny then someone is old or patient and vice versa.
If paul is not curious then someone is both tall and not patient.
If someone is both kind and quiet then someone is not old or quiet.
If lucy is either generous or not happy then someone is both not calm and not creative and vice versa.
If mary is not rich then susan is quiet or not patient.
Everyone who is not curious or not creative is either not kind or tall and vice versa.
If lucy is wise then mary is kind.
Lucy is either funny or not quiet.
Someone is humble or not old.
Paul is either humble or not tall.
Someone is not kind or not humble.
Paul is not strong or kind.
John is curious.
Someone is not happy or not rich. | Lucy is not tall. | entailment | (![X]:((brave(X)&happy(X))<=>(funny(X)<~>generous(X))))&
(((~quiet(john)|~tall(john)))=>((kind(susan)<~>~kind(susan))))&
(![X]:(~funny(X)<=>(~brave(X)|funny(X))))&
(((kind(lucy)&~funny(lucy)))<=>(?[X]:((generous(X)&kind(X)))))&
(![X]:(~tall(X)<=>(~patient(X)|funny(X))))&
(![X]:((quiet(X)|~strong(X))=>old(X)))&
((?[X]:((~curious(X)<~>~calm(X))))=>(creative(fred)))&
(![X]:((~calm(X)&calm(X))<=>tall(X)))&
(((~brave(fred)&funny(fred)))<=>(?[X]:((old(X)|patient(X)))))&
((~curious(paul))=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((~old(X)|quiet(X)))))&
(((generous(lucy)<~>~happy(lucy)))<=>(?[X]:((~calm(X)&~creative(X)))))&
((~rich(mary))=>((quiet(susan)|~patient(susan))))&
(![X]:((~curious(X)|~creative(X))<=>(~kind(X)<~>tall(X))))&
((wise(lucy))=>(kind(mary)))&
((funny(lucy)<~>~quiet(lucy)))&
(?[X]:((humble(X)|~old(X))))&
((humble(paul)<~>~tall(paul)))&
(?[X]:((~kind(X)|~humble(X))))&
((~strong(paul)|kind(paul)))&
(curious(john))&
(?[X]:((~happy(X)|~rich(X)))) | ~tall(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 485904584514925569314401
% SZS output start Proof for 485904584514925569314401
8. ! [X0] : ((calm(X0) & ~calm(X0)) <=> tall(X0)) [input p7]
23. tall(lucy) [input hypothesis]
46. ! [X0] : (((calm(X0) & ~calm(X0)) | ~tall(X0)) & (tall(X0) | (~calm(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((calm(X0) & ~calm(X0)) | ~tall(X0)) & (tall(X0) | ~calm(X0) | calm(X0))) [flattening 46]
97. ~calm(X0) | ~tall(X0) [cnf transformation 47]
98. calm(X0) | ~tall(X0) [cnf transformation 47]
129. tall(lucy) [cnf transformation 23]
166. ~tall(X0) [subsumption resolution 97,98]
227. $false [subsumption resolution 129,166]
% SZS output end Proof for 485904584514925569314401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and curious then mary is both calm and not patient.
Everyone who is both brave and creative is either wise or not kind and vice versa.
If fred is not tall then mary is both not humble and curious.
If someone is wise or not rich then fred is both not calm and strong.
Everyone who is tall or not funny is both generous and not tall and vice versa.
Everyone who is rich or tall is not humble or not brave and vice versa.
Everyone who is calm or generous is either not patient or not tall.
Everyone who is patient or not old is not patient and vice versa.
Everyone who is not rich or not brave is tall.
Everyone who is either not curious or not creative is wise.
If someone is either not old or curious then someone is funny.
If someone is not happy or old then someone is both creative and not patient.
Lucy is not creative.
Someone is rich or kind.
Susan is not wise or not strong.
John is both not wise and not curious.
Susan is funny. | Susan is rich. | entailment | (((~tall(alice)&curious(alice)))=>((calm(mary)&~patient(mary))))&
(![X]:((brave(X)&creative(X))<=>(wise(X)<~>~kind(X))))&
((~tall(fred))=>((~humble(mary)&curious(mary))))&
((?[X]:((wise(X)|~rich(X))))=>((~calm(fred)&strong(fred))))&
(![X]:((tall(X)|~funny(X))<=>(generous(X)&~tall(X))))&
(![X]:((rich(X)|tall(X))<=>(~humble(X)|~brave(X))))&
(![X]:((calm(X)|generous(X))=>(~patient(X)<~>~tall(X))))&
(![X]:((patient(X)|~old(X))<=>~patient(X)))&
(![X]:((~rich(X)|~brave(X))=>tall(X)))&
(![X]:((~curious(X)<~>~creative(X))=>wise(X)))&
((?[X]:((~old(X)<~>curious(X))))=>(?[X]:(funny(X))))&
((?[X]:((~happy(X)|old(X))))=>(?[X]:((creative(X)&~patient(X)))))&
(~creative(lucy))&
(?[X]:((rich(X)|kind(X))))&
((~wise(susan)|~strong(susan)))&
((~wise(john)&~curious(john)))&
(funny(susan)) | rich(susan) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2098759574346565409416627
% SZS output start Proof for 2098759574346565409416627
5. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~tall(X0) & generous(X0))) [input p4]
9. ! [X0] : ((~brave(X0) | ~rich(X0)) => tall(X0)) [input p8]
18. ~rich(susan) [input hypothesis]
27. ! [X0] : (tall(X0) | (brave(X0) & rich(X0))) [ennf transformation 9]
33. ! [X0] : (((~funny(X0) | tall(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 5]
34. ! [X0] : ((~funny(X0) | tall(X0) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | (funny(X0) & ~tall(X0)))) [flattening 33]
66. ~tall(X0) | ~tall(X0) [cnf transformation 34]
80. tall(X0) | rich(X0) [cnf transformation 27]
94. ~rich(susan) [cnf transformation 18]
97. ~tall(X0) [duplicate literal removal 66]
132. 8 <=> ! [X0] : rich(X0) [avatar definition]
133. rich(X0) <- (8) [avatar component clause 132]
154. rich(X0) [subsumption resolution 80,97]
155. 8 [avatar split clause 154,132]
196. $false <- (8) [resolution 133,94]
197. ~8 [avatar contradiction clause 196]
198. $false [avatar sat refutation 155,197]
% SZS output end Proof for 2098759574346565409416627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both creative and generous then susan is funny or creative and vice versa.
If paul is not funny then someone is both brave and not old and vice versa.
Everyone who is not strong or patient is either not generous or old.
If someone is humble or generous then someone is either not happy or calm and vice versa.
Everyone who is either not kind or rich is not strong or not rich.
Everyone who is curious or not curious is both not rich and humble.
Everyone who is not humble or creative is patient or creative.
If someone is either not creative or not wise then mary is either not rich or wise and vice versa.
Everyone who is either kind or not generous is both not brave and wise and vice versa.
Everyone who is either not rich or kind is either creative or not patient.
Everyone who is not humble or humble is generous or not strong and vice versa.
If alice is not creative or calm then someone is either strong or humble and vice versa.
Everyone who is both funny and calm is quiet.
Everyone who is patient is not tall or not wise.
If someone is not quiet or curious then mary is tall and vice versa.
If john is both not curious and not humble then paul is both patient and old and vice versa.
Someone is not tall.
Susan is not old.
John is not wise.
Someone is patient or brave.
Fred is not generous.
Someone is both not calm and curious.
Mary is either old or not curious. | Fred is not brave. | neutral | (((creative(paul)&generous(paul)))<=>((funny(susan)|creative(susan))))&
((~funny(paul))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~strong(X)|patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(~strong(X)|~rich(X))))&
(![X]:((curious(X)|~curious(X))=>(~rich(X)&humble(X))))&
(![X]:((~humble(X)|creative(X))=>(patient(X)|creative(X))))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((~rich(mary)<~>wise(mary))))&
(![X]:((kind(X)<~>~generous(X))<=>(~brave(X)&wise(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~patient(X))))&
(![X]:((~humble(X)|humble(X))<=>(generous(X)|~strong(X))))&
(((~creative(alice)|calm(alice)))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((funny(X)&calm(X))=>quiet(X)))&
(![X]:(patient(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~quiet(X)|curious(X))))<=>(tall(mary)))&
(((~curious(john)&~humble(john)))<=>((patient(paul)&old(paul))))&
(?[X]:(~tall(X)))&
(~old(susan))&
(~wise(john))&
(?[X]:((patient(X)|brave(X))))&
(~generous(fred))&
(?[X]:((~calm(X)&curious(X))))&
((old(mary)<~>~curious(mary))) | ~brave(fred) | [] | null | 0 |
Everyone who is generous is not quiet or not kind and vice versa.
Everyone who is kind or not happy is not quiet and vice versa.
If john is both not rich and not generous then john is either not creative or curious.
Everyone who is kind is not curious and vice versa.
Everyone who is not tall or curious is both not calm and not funny.
If someone is not creative then paul is both not quiet and not strong.
If someone is both tall and rich then john is both creative and not funny and vice versa.
Everyone who is both happy and not curious is both creative and funny.
If paul is calm then someone is either calm or not old and vice versa.
If someone is either not generous or old then someone is either not brave or not rich and vice versa.
If someone is not kind then someone is not happy and vice versa.
If fred is kind or not quiet then john is not strong or not brave.
Everyone who is both generous and calm is quiet.
Everyone who is not creative or happy is both not humble and tall and vice versa.
If paul is both calm and not calm then paul is either not old or rich.
Everyone who is not creative is not humble.
Someone is both old and happy.
Lucy is both humble and funny.
Alice is either kind or patient.
Someone is rich.
Someone is not wise.
Paul is both happy and not humble.
Someone is creative or not kind. | John is calm. | contradiction | (![X]:(generous(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((kind(X)|~happy(X))<=>~quiet(X)))&
(((~rich(john)&~generous(john)))=>((~creative(john)<~>curious(john))))&
(![X]:(kind(X)<=>~curious(X)))&
(![X]:((~tall(X)|curious(X))=>(~calm(X)&~funny(X))))&
((?[X]:(~creative(X)))=>((~quiet(paul)&~strong(paul))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(john)&~funny(john))))&
(![X]:((happy(X)&~curious(X))=>(creative(X)&funny(X))))&
((calm(paul))<=>(?[X]:((calm(X)<~>~old(X)))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:(~happy(X))))&
(((kind(fred)|~quiet(fred)))=>((~strong(john)|~brave(john))))&
(![X]:((generous(X)&calm(X))=>quiet(X)))&
(![X]:((~creative(X)|happy(X))<=>(~humble(X)&tall(X))))&
(((calm(paul)&~calm(paul)))=>((~old(paul)<~>rich(paul))))&
(![X]:(~creative(X)=>~humble(X)))&
(?[X]:((old(X)&happy(X))))&
((humble(lucy)&funny(lucy)))&
((kind(alice)<~>patient(alice)))&
(?[X]:(rich(X)))&
(?[X]:(~wise(X)))&
((happy(paul)&~humble(paul)))&
(?[X]:((creative(X)|~kind(X)))) | calm(john) | [
"p0",
"p1",
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4513121946960179766857047
% SZS output start Proof for 4513121946960179766857047
1. ! [X0] : (generous(X0) <=> (~kind(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | kind(X0)) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (kind(X0) <=> ~curious(X0)) [input p3]
5. ! [X0] : ((curious(X0) | ~tall(X0)) => (~funny(X0) & ~calm(X0))) [input p4]
13. ! [X0] : ((calm(X0) & generous(X0)) => quiet(X0)) [input p12]
24. calm(john) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~calm(X0)) | (~curious(X0) & tall(X0))) [ennf transformation 5]
36. ! [X0] : (quiet(X0) | (~calm(X0) | ~generous(X0))) [ennf transformation 13]
37. ! [X0] : (quiet(X0) | ~calm(X0) | ~generous(X0)) [flattening 36]
41. ! [X0] : ((generous(X0) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ~generous(X0))) [nnf transformation 1]
42. ! [X0] : ((generous(X0) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : (((~happy(X0) | kind(X0)) | quiet(X0)) & (~quiet(X0) | (happy(X0) & ~kind(X0)))) [nnf transformation 2]
44. ! [X0] : ((~happy(X0) | kind(X0) | quiet(X0)) & (~quiet(X0) | (happy(X0) & ~kind(X0)))) [flattening 43]
46. ! [X0] : ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0))) [nnf transformation 4]
77. quiet(X0) | generous(X0) [cnf transformation 42]
79. ~kind(X0) | ~quiet(X0) [cnf transformation 44]
85. curious(X0) | kind(X0) [cnf transformation 46]
87. ~calm(X0) | ~curious(X0) [cnf transformation 32]
111. quiet(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 37]
130. calm(john) [cnf transformation 24]
144. 4 <=> curious(john) [avatar definition]
146. ~curious(john) <- (~4) [avatar component clause 144]
250. ~calm(X0) | quiet(X0) [subsumption resolution 111,77]
283. ~curious(john) [resolution 87,130]
285. ~4 [avatar split clause 283,144]
286. kind(john) <- (~4) [resolution 146,85]
292. ~quiet(john) <- (~4) [resolution 286,79]
296. quiet(john) [resolution 250,130]
298. $false <- (~4) [subsumption resolution 296,292]
299. 4 [avatar contradiction clause 298]
302. $false [avatar sat refutation 285,299]
% SZS output end Proof for 4513121946960179766857047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both wise and not kind is either not humble or creative and vice versa. Everyone who is both not kind and humble is either not rich or not quiet and vice versa. Everyone who is not tall is not wise and vice versa. If someone is both brave and not brave then lucy is both not quiet and strong and vice versa. If lucy is curious then someone is happy and vice versa. Everyone who is either rich or not happy is either brave or not funny. Everyone who is happy is funny or creative and vice versa. Everyone who is either patient or brave is both not kind and patient. Everyone who is humble or not quiet is not wise. Everyone who is not tall or not brave is both rich and old and vice versa. If someone is not funny then someone is happy and vice versa. Everyone who is either tall or curious is not old and vice versa. Everyone who is humble is both calm and not quiet. Everyone who is humble or not funny is not brave or not happy and vice versa. If someone is rich or not humble then someone is either curious or generous. If fred is both not patient and not quiet then someone is patient and vice versa. Fred is either old or strong. Fred is either strong or curious. Someone is both not wise and kind. Someone is both not patient and not calm. | Fred is not quiet. | contradiction | (![X]:((wise(X)&~kind(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~kind(X)&humble(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:(~tall(X)<=>~wise(X)))&
((?[X]:((brave(X)&~brave(X))))<=>((~quiet(lucy)&strong(lucy))))&
((curious(lucy))<=>(?[X]:(happy(X))))&
(![X]:((rich(X)<~>~happy(X))=>(brave(X)<~>~funny(X))))&
(![X]:(happy(X)<=>(funny(X)|creative(X))))&
(![X]:((patient(X)<~>brave(X))=>(~kind(X)&patient(X))))&
(![X]:((humble(X)|~quiet(X))=>~wise(X)))&
(![X]:((~tall(X)|~brave(X))<=>(rich(X)&old(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(happy(X))))&
(![X]:((tall(X)<~>curious(X))<=>~old(X)))&
(![X]:(humble(X)=>(calm(X)&~quiet(X))))&
(![X]:((humble(X)|~funny(X))<=>(~brave(X)|~happy(X))))&
((?[X]:((rich(X)|~humble(X))))=>(?[X]:((curious(X)<~>generous(X)))))&
(((~patient(fred)&~quiet(fred)))<=>(?[X]:(patient(X))))&
((old(fred)<~>strong(fred)))&
((strong(fred)<~>curious(fred)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~patient(X)&~calm(X)))) | ~quiet(fred) | [
"p2",
"p8",
"p9",
"p11",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7546547467429232124980114
% SZS output start Proof for 7546547467429232124980114
3. ! [X0] : (~tall(X0) <=> ~wise(X0)) [input p2]
9. ! [X0] : ((~quiet(X0) | humble(X0)) => ~wise(X0)) [input p8]
10. ! [X0] : ((~brave(X0) | ~tall(X0)) <=> (old(X0) & rich(X0))) [input p9]
12. ! [X0] : ((tall(X0) <~> curious(X0)) <=> ~old(X0)) [input p11]
17. old(fred) <~> strong(fred) [input p16]
18. strong(fred) <~> curious(fred) [input p17]
21. ~quiet(fred) [input hypothesis]
26. ! [X0] : (~wise(X0) | (quiet(X0) & ~humble(X0))) [ennf transformation 9]
33. ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 3]
47. ! [X0] : (((~brave(X0) | ~tall(X0)) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | (brave(X0) & tall(X0)))) [nnf transformation 10]
48. ! [X0] : ((~brave(X0) | ~tall(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | (brave(X0) & tall(X0)))) [flattening 47]
54. ! [X0] : ((((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | old(X0)) & (~old(X0) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))))) [nnf transformation 12]
66. (~strong(fred) | ~old(fred)) & (strong(fred) | old(fred)) [nnf transformation 17]
67. (~curious(fred) | ~strong(fred)) & (curious(fred) | strong(fred)) [nnf transformation 18]
85. ~tall(X0) | wise(X0) [cnf transformation 33]
104. ~wise(X0) | quiet(X0) [cnf transformation 26]
107. old(X0) | tall(X0) [cnf transformation 48]
113. ~old(X0) | tall(X0) | ~curious(X0) [cnf transformation 54]
115. ~curious(X0) | ~tall(X0) | old(X0) [cnf transformation 54]
130. ~strong(fred) | ~old(fred) [cnf transformation 66]
131. curious(fred) | strong(fred) [cnf transformation 67]
137. ~quiet(fred) [cnf transformation 21]
179. ~curious(X0) | old(X0) [subsumption resolution 115,107]
180. ~curious(X0) | tall(X0) [subsumption resolution 113,179]
203. 15 <=> quiet(fred) [avatar definition]
205. ~quiet(fred) <- (~15) [avatar component clause 203]
218. 18 <=> old(fred) [avatar definition]
220. ~old(fred) <- (~18) [avatar component clause 218]
222. 19 <=> strong(fred) [avatar definition]
225. ~18 | ~19 [avatar split clause 130,222,218]
228. 20 <=> curious(fred) [avatar definition]
229. curious(fred) <- (20) [avatar component clause 228]
232. 19 | 20 [avatar split clause 131,228,222]
233. ~15 [avatar split clause 137,203]
244. tall(fred) <- (~18) [resolution 107,220]
246. wise(fred) <- (~18) [resolution 244,85]
247. quiet(fred) <- (~18) [resolution 246,104]
249. $false <- (~15, ~18) [subsumption resolution 247,205]
250. 15 | 18 [avatar contradiction clause 249]
257. tall(fred) <- (20) [resolution 180,229]
273. wise(fred) <- (20) [resolution 257,85]
380. quiet(fred) <- (20) [resolution 273,104]
382. $false <- (~15, 20) [subsumption resolution 380,205]
383. 15 | ~20 [avatar contradiction clause 382]
384. $false [avatar sat refutation 225,232,233,250,383]
% SZS output end Proof for 7546547467429232124980114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and strong then alice is both not calm and wise.
If fred is either not patient or brave then mary is both happy and not rich.
If john is not creative then paul is creative or old and vice versa.
If susan is not patient then john is not creative.
Everyone who is both not rich and strong is not strong and vice versa.
If someone is not funny then someone is either not curious or tall.
If someone is not generous then mary is both not happy and not generous and vice versa.
Everyone who is either not generous or happy is not rich.
If fred is quiet then alice is both not tall and not generous.
Everyone who is not rich or calm is either quiet or funny and vice versa.
If alice is either rich or strong then alice is both not tall and not funny and vice versa.
Everyone who is curious or kind is wise.
Everyone who is not wise or kind is not old or not quiet and vice versa.
Someone is rich.
Someone is either not patient or creative.
Paul is not wise.
Someone is generous or not tall.
Someone is humble or not funny. | John is not tall. | neutral | ((?[X]:((~quiet(X)&strong(X))))=>((~calm(alice)&wise(alice))))&
(((~patient(fred)<~>brave(fred)))=>((happy(mary)&~rich(mary))))&
((~creative(john))<=>((creative(paul)|old(paul))))&
((~patient(susan))=>(~creative(john)))&
(![X]:((~rich(X)&strong(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:(~generous(X)))<=>((~happy(mary)&~generous(mary))))&
(![X]:((~generous(X)<~>happy(X))=>~rich(X)))&
((quiet(fred))=>((~tall(alice)&~generous(alice))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(![X]:((~wise(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
(~wise(paul))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((humble(X)|~funny(X)))) | ~tall(john) | [] | null | 0 |
Everyone who is both not rich and brave is both not funny and not old and vice versa. Everyone who is either not brave or rich is not brave. If someone is either quiet or not calm then someone is both brave and not old and vice versa. If lucy is either strong or tall then someone is strong and vice versa. Everyone who is both not creative and not happy is either tall or strong and vice versa. If mary is humble then mary is both patient and not funny and vice versa. If someone is either not humble or curious then susan is calm. If someone is generous then someone is not curious or calm. If mary is both funny and not creative then alice is old. If someone is patient or not brave then lucy is calm. Everyone who is either not humble or not funny is not brave or not rich. If someone is either not kind or not calm then alice is brave and vice versa. If alice is not funny then lucy is both old and rich. Everyone who is strong or calm is either not generous or rich and vice versa. Everyone who is happy or wise is not happy. If susan is not calm then lucy is funny. Someone is either not old or brave. Someone is either not strong or old. Someone is either tall or not wise. Lucy is both not quiet and not generous. Someone is kind. Someone is both not old and not rich. Someone is curious or not humble. | Lucy is not rich. | entailment | (![X]:((~rich(X)&brave(X))<=>(~funny(X)&~old(X))))&
(![X]:((~brave(X)<~>rich(X))=>~brave(X)))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(((strong(lucy)<~>tall(lucy)))<=>(?[X]:(strong(X))))&
(![X]:((~creative(X)&~happy(X))<=>(tall(X)<~>strong(X))))&
((humble(mary))<=>((patient(mary)&~funny(mary))))&
((?[X]:((~humble(X)<~>curious(X))))=>(calm(susan)))&
((?[X]:(generous(X)))=>(?[X]:((~curious(X)|calm(X)))))&
(((funny(mary)&~creative(mary)))=>(old(alice)))&
((?[X]:((patient(X)|~brave(X))))=>(calm(lucy)))&
(![X]:((~humble(X)<~>~funny(X))=>(~brave(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>(brave(alice)))&
((~funny(alice))=>((old(lucy)&rich(lucy))))&
(![X]:((strong(X)|calm(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((happy(X)|wise(X))=>~happy(X)))&
((~calm(susan))=>(funny(lucy)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
((~quiet(lucy)&~generous(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~old(X)&~rich(X))))&
(?[X]:((curious(X)|~humble(X)))) | ~rich(lucy) | [
"p0",
"p1",
"p9",
"p13",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3833610645856386619487916
% SZS output start Proof for 3833610645856386619487916
1. ! [X0] : ((brave(X0) & ~rich(X0)) <=> (~old(X0) & ~funny(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> rich(X0)) => ~brave(X0)) [input p1]
10. ? [X0] : (~brave(X0) | patient(X0)) => calm(lucy) [input p9]
14. ! [X0] : ((calm(X0) | strong(X0)) <=> (~generous(X0) <~> rich(X0))) [input p13]
17. ? [X0] : (~old(X0) <~> brave(X0)) [input p16]
20. ~generous(lucy) & ~quiet(lucy) [input p19]
24. rich(lucy) [input hypothesis]
27. ! [X0] : (~brave(X0) | (~brave(X0) <=> rich(X0))) [ennf transformation 2]
32. calm(lucy) | ! [X0] : (brave(X0) & ~patient(X0)) [ennf transformation 10]
38. ! [X0] : (((brave(X0) & ~rich(X0)) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | (~brave(X0) | rich(X0)))) [nnf transformation 1]
39. ! [X0] : (((brave(X0) & ~rich(X0)) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | ~brave(X0) | rich(X0))) [flattening 38]
40. ! [X0] : (~brave(X0) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) [nnf transformation 27]
63. ! [X0] : (((calm(X0) | strong(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~calm(X0) & ~strong(X0)))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | strong(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~calm(X0) & ~strong(X0)))) [flattening 63]
65. ? [X0] : ((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) [nnf transformation 17]
66. ? [X0] : ((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) => ((~brave(sK5) | old(sK5)) & (brave(sK5) | ~old(sK5))) [choice axiom]
67. (~brave(sK5) | old(sK5)) & (brave(sK5) | ~old(sK5)) [skolemisation 65,66]
81. ~old(X0) | ~brave(X0) | rich(X0) [cnf transformation 39]
85. ~brave(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 40]
110. calm(lucy) | brave(X0) [cnf transformation 32]
122. ~calm(X0) | generous(X0) | ~rich(X0) [cnf transformation 64]
129. ~brave(sK5) | old(sK5) [cnf transformation 67]
135. ~generous(lucy) [cnf transformation 20]
140. rich(lucy) [cnf transformation 24]
142. ~brave(X0) | ~rich(X0) [duplicate literal removal 85]
242. 23 <=> ! [X0] : brave(X0) [avatar definition]
243. brave(X0) <- (23) [avatar component clause 242]
245. 24 <=> calm(lucy) [avatar definition]
247. calm(lucy) <- (24) [avatar component clause 245]
248. 23 | 24 [avatar split clause 110,245,242]
280. 32 <=> rich(lucy) [avatar definition]
282. rich(lucy) <- (32) [avatar component clause 280]
295. 35 <=> old(sK5) [avatar definition]
297. old(sK5) <- (35) [avatar component clause 295]
299. 36 <=> brave(sK5) [avatar definition]
301. ~brave(sK5) <- (~36) [avatar component clause 299]
302. 35 | ~36 [avatar split clause 129,299,295]
333. 32 [avatar split clause 140,280]
400. generous(lucy) | ~rich(lucy) <- (24) [resolution 122,247]
411. ~rich(lucy) <- (24) [subsumption resolution 400,135]
412. $false <- (24, 32) [subsumption resolution 411,282]
413. ~24 | ~32 [avatar contradiction clause 412]
423. ~rich(X0) <- (23) [resolution 243,142]
425. $false <- (23, ~36) [resolution 243,301]
430. ~23 | 36 [avatar contradiction clause 425]
437. ~brave(sK5) | rich(sK5) <- (35) [resolution 297,81]
438. rich(sK5) <- (23, 35) [subsumption resolution 437,243]
439. $false <- (23, 35) [subsumption resolution 438,423]
440. ~23 | ~35 [avatar contradiction clause 439]
441. $false [avatar sat refutation 248,302,333,413,430,440]
% SZS output end Proof for 3833610645856386619487916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both tall and not happy then mary is either not tall or not patient.
If someone is not patient or not happy then mary is both not happy and not funny.
Everyone who is either quiet or not tall is either not calm or funny.
If fred is not rich then someone is funny.
Everyone who is both quiet and wise is not brave.
Everyone who is either not creative or kind is either rich or tall.
Everyone who is humble or not quiet is not kind.
Everyone who is not patient or not creative is both not patient and not kind and vice versa.
Everyone who is generous or creative is both not patient and not wise.
If someone is not strong then lucy is strong or not tall.
Everyone who is not rich or funny is both not tall and not calm.
If john is not happy or not patient then mary is generous or creative and vice versa.
If alice is either not tall or funny then someone is either not funny or not patient.
If someone is either not patient or strong then someone is old or not generous.
Everyone who is not wise or brave is not tall or humble.
Someone is not brave.
Paul is not generous or wise.
John is patient or not creative.
Someone is old or kind.
Someone is funny or tall.
John is either old or not creative.
Someone is generous or not happy. | John is not rich. | contradiction | (((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(![X]:((~patient(X)|~creative(X))<=>(~patient(X)&~kind(X))))&
(![X]:((generous(X)|creative(X))=>(~patient(X)&~wise(X))))&
((?[X]:(~strong(X)))=>((strong(lucy)|~tall(lucy))))&
(![X]:((~rich(X)|funny(X))=>(~tall(X)&~calm(X))))&
(((~happy(john)|~patient(john)))<=>((generous(mary)|creative(mary))))&
(((~tall(alice)<~>funny(alice)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~wise(X)|brave(X))=>(~tall(X)|humble(X))))&
(?[X]:(~brave(X)))&
((~generous(paul)|wise(paul)))&
((patient(john)|~creative(john)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((funny(X)|tall(X))))&
((old(john)<~>~creative(john)))&
(?[X]:((generous(X)|~happy(X)))) | ~rich(john) | [
"p5",
"p7",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2788689791419854809694287
% SZS output start Proof for 2788689791419854809694287
6. ! [X0] : ((~creative(X0) <~> kind(X0)) => (rich(X0) <~> tall(X0))) [input p5]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~kind(X0) & ~patient(X0))) [input p7]
9. ! [X0] : ((creative(X0) | generous(X0)) => (~wise(X0) & ~patient(X0))) [input p8]
11. ! [X0] : ((funny(X0) | ~rich(X0)) => (~calm(X0) & ~tall(X0))) [input p10]
18. ~creative(john) | patient(john) [input p17]
23. ~rich(john) [input hypothesis]
33. ! [X0] : ((rich(X0) <~> tall(X0)) | (~creative(X0) <=> kind(X0))) [ennf transformation 6]
35. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~creative(X0) & ~generous(X0))) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) & ~tall(X0)) | (~funny(X0) & rich(X0))) [ennf transformation 11]
47. ! [X0] : (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) [nnf transformation 33]
48. ! [X0] : (((~creative(X0) | ~patient(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
49. ! [X0] : ((~creative(X0) | ~patient(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [flattening 48]
77. kind(X0) | rich(X0) | tall(X0) | creative(X0) [cnf transformation 47]
84. ~patient(X0) | creative(X0) [cnf transformation 49]
86. ~kind(X0) | creative(X0) [cnf transformation 49]
89. ~patient(X0) | ~creative(X0) [cnf transformation 35]
93. ~tall(X0) | rich(X0) [cnf transformation 38]
109. ~creative(john) | patient(john) [cnf transformation 18]
115. ~rich(john) [cnf transformation 23]
161. ~patient(X0) [subsumption resolution 89,84]
214. ~creative(john) [subsumption resolution 109,161]
307. rich(X0) | tall(X0) | creative(X0) | creative(X0) [resolution 77,86]
310. rich(X0) | tall(X0) | creative(X0) [duplicate literal removal 307]
311. creative(X0) | rich(X0) [subsumption resolution 310,93]
320. rich(john) [resolution 311,214]
322. $false [subsumption resolution 320,115]
% SZS output end Proof for 2788689791419854809694287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not patient is both tall and quiet and vice versa.
If john is not brave then mary is either old or not kind and vice versa.
Everyone who is either not rich or funny is either not kind or old.
Everyone who is both not old and not generous is patient or not kind.
Everyone who is patient or old is both tall and not wise and vice versa.
Everyone who is both patient and not old is not old or funny and vice versa.
If lucy is either quiet or not tall then someone is either not happy or not funny.
If someone is either creative or calm then someone is either wise or not brave and vice versa.
Everyone who is not rich is rich.
If paul is not strong or generous then someone is either not funny or not strong.
If paul is not humble or creative then someone is either tall or brave and vice versa.
If someone is both not brave and not tall then someone is either not curious or funny.
Everyone who is quiet or brave is both not wise and humble and vice versa.
Everyone who is generous is either brave or not curious and vice versa.
Everyone who is both not rich and not wise is not happy or not calm and vice versa.
Everyone who is either not happy or humble is calm or not quiet and vice versa.
Someone is both not funny and creative.
Mary is not quiet or not patient.
Someone is generous.
Someone is either not curious or happy.
Someone is either old or quiet. | Mary is not rich. | contradiction | (![X]:((tall(X)<~>~patient(X))<=>(tall(X)&quiet(X))))&
((~brave(john))<=>((old(mary)<~>~kind(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>old(X))))&
(![X]:((~old(X)&~generous(X))=>(patient(X)|~kind(X))))&
(![X]:((patient(X)|old(X))<=>(tall(X)&~wise(X))))&
(![X]:((patient(X)&~old(X))<=>(~old(X)|funny(X))))&
(((quiet(lucy)<~>~tall(lucy)))=>(?[X]:((~happy(X)<~>~funny(X)))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:(~rich(X)=>rich(X)))&
(((~strong(paul)|generous(paul)))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(((~humble(paul)|creative(paul)))<=>(?[X]:((tall(X)<~>brave(X)))))&
((?[X]:((~brave(X)&~tall(X))))=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:((quiet(X)|brave(X))<=>(~wise(X)&humble(X))))&
(![X]:(generous(X)<=>(brave(X)<~>~curious(X))))&
(![X]:((~rich(X)&~wise(X))<=>(~happy(X)|~calm(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(calm(X)|~quiet(X))))&
(?[X]:((~funny(X)&creative(X))))&
((~quiet(mary)|~patient(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~curious(X)<~>happy(X))))&
(?[X]:((old(X)<~>quiet(X)))) | ~rich(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 492519984663159917132095
% SZS output start Proof for 492519984663159917132095
9. ! [X0] : (~rich(X0) => rich(X0)) [input p8]
22. ~rich(mary) [input hypothesis]
29. ! [X0] : (rich(X0) | rich(X0)) [ennf transformation 9]
114. rich(X0) | rich(X0) [cnf transformation 29]
155. ~rich(mary) [cnf transformation 22]
156. rich(X0) [duplicate literal removal 114]
295. $false [subsumption resolution 155,156]
% SZS output end Proof for 492519984663159917132095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is patient or not brave and vice versa. Everyone who is brave is either not curious or not patient and vice versa. Everyone who is either not kind or rich is not wise and vice versa. If john is both generous and not strong then someone is not funny or strong and vice versa. If john is rich or not strong then mary is either kind or quiet. If someone is either curious or not happy then someone is either humble or quiet. If someone is both quiet and not old then susan is not old. If someone is not quiet or not old then fred is either tall or curious and vice versa. Everyone who is funny or not funny is either not humble or not calm. If fred is not humble then paul is both curious and not generous. If someone is both happy and not patient then someone is not calm or not tall and vice versa. Everyone who is strong or brave is old or not funny and vice versa. Everyone who is not strong or old is not kind and vice versa. Everyone who is either not brave or wise is not quiet or not kind and vice versa. Everyone who is not old is not old or wise. Everyone who is not creative is both happy and kind. Someone is not creative or humble. Alice is either funny or not funny. John is both not kind and not wise. Someone is quiet. Someone is both old and wise. John is happy or not strong. Someone is both curious and generous. | Fred is not creative. | contradiction | (![X]:(~generous(X)<=>(patient(X)|~brave(X))))&
(![X]:(brave(X)<=>(~curious(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>rich(X))<=>~wise(X)))&
(((generous(john)&~strong(john)))<=>(?[X]:((~funny(X)|strong(X)))))&
(((rich(john)|~strong(john)))=>((kind(mary)<~>quiet(mary))))&
((?[X]:((curious(X)<~>~happy(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
((?[X]:((quiet(X)&~old(X))))=>(~old(susan)))&
((?[X]:((~quiet(X)|~old(X))))<=>((tall(fred)<~>curious(fred))))&
(![X]:((funny(X)|~funny(X))=>(~humble(X)<~>~calm(X))))&
((~humble(fred))=>((curious(paul)&~generous(paul))))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:((strong(X)|brave(X))<=>(old(X)|~funny(X))))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(~old(X)=>(~old(X)|wise(X))))&
(![X]:(~creative(X)=>(happy(X)&kind(X))))&
(?[X]:((~creative(X)|humble(X))))&
((funny(alice)<~>~funny(alice)))&
((~kind(john)&~wise(john)))&
(?[X]:(quiet(X)))&
(?[X]:((old(X)&wise(X))))&
((happy(john)|~strong(john)))&
(?[X]:((curious(X)&generous(X)))) | ~creative(fred) | [
"p0",
"p3",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7092966477929834182648575
% SZS output start Proof for 7092966477929834182648575
1. ! [X0] : (~generous(X0) <=> (~brave(X0) | patient(X0))) [input p0]
4. (~strong(john) & generous(john)) <=> ? [X0] : (strong(X0) | ~funny(X0)) [input p3]
13. ! [X0] : ((old(X0) | ~strong(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p13]
16. ! [X0] : (~creative(X0) => (kind(X0) & happy(X0))) [input p15]
19. ~wise(john) & ~kind(john) [input p18]
24. ~creative(fred) [input hypothesis]
34. ! [X0] : ((kind(X0) & happy(X0)) | creative(X0)) [ennf transformation 16]
35. ! [X0] : ((~generous(X0) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | generous(X0))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | generous(X0))) [flattening 35]
39. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X0] : (strong(X0) | ~funny(X0)) | (strong(john) | ~generous(john))) [nnf transformation 4]
40. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X0] : (strong(X0) | ~funny(X0)) | strong(john) | ~generous(john)) [flattening 39]
41. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X1] : (strong(X1) | ~funny(X1)) | strong(john) | ~generous(john)) [rectify 40]
42. ? [X1] : (strong(X1) | ~funny(X1)) => (strong(sK0) | ~funny(sK0)) [choice axiom]
43. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & ((strong(sK0) | ~funny(sK0)) | strong(john) | ~generous(john)) [skolemisation 41,42]
61. ! [X0] : (((old(X0) | ~strong(X0)) | kind(X0)) & (~kind(X0) | (~old(X0) & strong(X0)))) [nnf transformation 13]
62. ! [X0] : ((old(X0) | ~strong(X0) | kind(X0)) & (~kind(X0) | (~old(X0) & strong(X0)))) [flattening 61]
63. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 14]
64. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 63]
76. ~generous(X0) | brave(X0) [cnf transformation 36]
87. generous(john) | ~strong(X0) [cnf transformation 43]
120. ~kind(X0) | strong(X0) [cnf transformation 62]
126. ~brave(X0) | wise(X0) | kind(X0) [cnf transformation 64]
131. creative(X0) | kind(X0) [cnf transformation 34]
135. ~kind(john) [cnf transformation 19]
136. ~wise(john) [cnf transformation 19]
143. ~creative(fred) [cnf transformation 24]
145. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
146. ~strong(X0) <- (1) [avatar component clause 145]
157. 4 <=> generous(john) [avatar definition]
159. generous(john) <- (4) [avatar component clause 157]
160. 1 | 4 [avatar split clause 87,157,145]
311. kind(fred) [resolution 131,143]
315. strong(fred) [resolution 311,120]
357. $false <- (1) [resolution 315,146]
358. ~1 [avatar contradiction clause 357]
359. brave(john) <- (4) [resolution 159,76]
494. wise(john) | kind(john) <- (4) [resolution 126,359]
500. kind(john) <- (4) [subsumption resolution 494,136]
501. $false <- (4) [subsumption resolution 500,135]
502. ~4 [avatar contradiction clause 501]
503. $false [avatar sat refutation 160,358,502]
% SZS output end Proof for 7092966477929834182648575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is old or not generous and vice versa.
Everyone who is either not quiet or not old is not wise or not humble and vice versa.
If someone is either not quiet or humble then someone is not creative or patient and vice versa.
If someone is both not quiet and not humble then someone is not generous or humble.
Everyone who is not quiet or generous is either tall or old.
Everyone who is either curious or not curious is not rich or generous.
Everyone who is not creative is not happy or tall.
Everyone who is old or not humble is not old or creative and vice versa.
If someone is not calm or quiet then someone is not strong or funny and vice versa.
If alice is tall or not patient then someone is both not rich and not quiet and vice versa.
If someone is happy or not funny then susan is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
If fred is not wise or kind then someone is rich or patient.
John is not quiet or happy.
Someone is not patient.
Someone is either creative or rich.
Paul is both not wise and not brave.
Lucy is calm or not generous.
Paul is not patient or not creative.
John is either not generous or calm.
Fred is humble or not quiet. | Alice is not tall. | entailment | ((?[X]:(~strong(X)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~quiet(X)<~>~old(X))<=>(~wise(X)|~humble(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((~quiet(X)&~humble(X))))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~quiet(X)|generous(X))=>(tall(X)<~>old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~rich(X)|generous(X))))&
(![X]:(~creative(X)=>(~happy(X)|tall(X))))&
(![X]:((old(X)|~humble(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
((~quiet(john)|happy(john)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((~wise(paul)&~brave(paul)))&
((calm(lucy)|~generous(lucy)))&
((~patient(paul)|~creative(paul)))&
((~generous(john)<~>calm(john)))&
((humble(fred)|~quiet(fred))) | ~tall(alice) | [
"p1",
"p4",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8093278649362983226493188
% SZS output start Proof for 8093278649362983226493188
2. ! [X0] : ((~quiet(X0) <~> ~old(X0)) <=> (~humble(X0) | ~wise(X0))) [input p1]
5. ! [X0] : ((generous(X0) | ~quiet(X0)) => (tall(X0) <~> old(X0))) [input p4]
8. ! [X0] : ((~humble(X0) | old(X0)) <=> (creative(X0) | ~old(X0))) [input p7]
10. (~patient(alice) | tall(alice)) <=> ? [X0] : (~quiet(X0) & ~rich(X0)) [input p9]
14. ! [X0] : ((creative(X0) | humble(X0)) <=> tall(X0)) [input p13]
24. tall(alice) [input hypothesis]
32. ! [X0] : ((tall(X0) <~> old(X0)) | (~generous(X0) & quiet(X0))) [ennf transformation 5]
45. ! [X0] : ((((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0))))) [nnf transformation 2]
46. ! [X0] : ((((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0))))) [flattening 45]
55. ! [X0] : (((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | (~generous(X0) & quiet(X0))) [nnf transformation 32]
57. ! [X0] : (((~humble(X0) | old(X0)) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 8]
58. ! [X0] : ((~humble(X0) | old(X0) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | (humble(X0) & ~old(X0)))) [flattening 57]
64. ((~patient(alice) | tall(alice)) | ! [X0] : (quiet(X0) | rich(X0))) & (? [X0] : (~quiet(X0) & ~rich(X0)) | (patient(alice) & ~tall(alice))) [nnf transformation 10]
65. (~patient(alice) | tall(alice) | ! [X0] : (quiet(X0) | rich(X0))) & (? [X0] : (~quiet(X0) & ~rich(X0)) | (patient(alice) & ~tall(alice))) [flattening 64]
66. (~patient(alice) | tall(alice) | ! [X0] : (quiet(X0) | rich(X0))) & (? [X1] : (~quiet(X1) & ~rich(X1)) | (patient(alice) & ~tall(alice))) [rectify 65]
67. ? [X1] : (~quiet(X1) & ~rich(X1)) => (~quiet(sK7) & ~rich(sK7)) [choice axiom]
68. (~patient(alice) | tall(alice) | ! [X0] : (quiet(X0) | rich(X0))) & ((~quiet(sK7) & ~rich(sK7)) | (patient(alice) & ~tall(alice))) [skolemisation 66,67]
78. ! [X0] : (((creative(X0) | humble(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [nnf transformation 14]
79. ! [X0] : ((creative(X0) | humble(X0) | ~tall(X0)) & (tall(X0) | (~creative(X0) & ~humble(X0)))) [flattening 78]
96. humble(X0) | quiet(X0) | old(X0) [cnf transformation 46]
106. ~tall(X0) | ~old(X0) | quiet(X0) [cnf transformation 55]
111. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 58]
113. ~humble(X0) | old(X0) | old(X0) [cnf transformation 58]
121. ~quiet(sK7) | ~tall(alice) [cnf transformation 68]
137. ~creative(X0) | tall(X0) [cnf transformation 79]
150. tall(alice) [cnf transformation 24]
151. ~old(X0) | creative(X0) [duplicate literal removal 111]
152. ~humble(X0) | old(X0) [duplicate literal removal 113]
256. 25 <=> tall(alice) [avatar definition]
265. 27 <=> quiet(sK7) [avatar definition]
267. ~quiet(sK7) <- (~27) [avatar component clause 265]
269. ~25 | ~27 [avatar split clause 121,265,256]
392. 25 [avatar split clause 150,256]
415. quiet(X0) | old(X0) | old(X0) [resolution 96,152]
417. quiet(X0) | old(X0) [duplicate literal removal 415]
544. old(sK7) <- (~27) [resolution 417,267]
573. creative(sK7) <- (~27) [resolution 544,151]
579. 72 <=> creative(sK7) [avatar definition]
581. creative(sK7) <- (72) [avatar component clause 579]
583. 72 | 27 [avatar split clause 573,265,579]
704. tall(sK7) <- (72) [resolution 581,137]
748. ~old(sK7) | quiet(sK7) <- (72) [resolution 704,106]
749. quiet(sK7) <- (~27, 72) [subsumption resolution 748,544]
750. $false <- (~27, 72) [subsumption resolution 749,267]
751. 27 | ~72 [avatar contradiction clause 750]
752. $false [avatar sat refutation 269,392,583,751]
% SZS output end Proof for 8093278649362983226493188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not calm is either funny or strong and vice versa. Everyone who is patient is not quiet. Everyone who is not patient or happy is generous or not tall and vice versa. Everyone who is both not quiet and not tall is brave and vice versa. If someone is brave then john is humble. Everyone who is brave or generous is not generous or kind and vice versa. Everyone who is not funny or not curious is not brave or not old and vice versa. Everyone who is not curious is calm and vice versa. If susan is both brave and happy then someone is patient or generous and vice versa. If paul is not funny then mary is both not patient and not brave and vice versa. Everyone who is either wise or not funny is either creative or not calm. If susan is either humble or not humble then fred is either generous or not wise and vice versa. Everyone who is both not happy and not kind is both not humble and wise and vice versa. If someone is not strong or not happy then someone is not old. If someone is both kind and not humble then susan is both not creative and not quiet. Everyone who is not patient is either not happy or wise and vice versa. Someone is not old or creative. John is either curious or tall. Fred is either calm or not rich. Fred is not brave or quiet. Someone is either not happy or happy. Alice is not quiet. Lucy is both generous and tall. Alice is not calm. | Fred is not kind. | contradiction | (![X]:((~generous(X)<~>~calm(X))<=>(funny(X)<~>strong(X))))&
(![X]:(patient(X)=>~quiet(X)))&
(![X]:((~patient(X)|happy(X))<=>(generous(X)|~tall(X))))&
(![X]:((~quiet(X)&~tall(X))<=>brave(X)))&
((?[X]:(brave(X)))=>(humble(john)))&
(![X]:((brave(X)|generous(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|~curious(X))<=>(~brave(X)|~old(X))))&
(![X]:(~curious(X)<=>calm(X)))&
(((brave(susan)&happy(susan)))<=>(?[X]:((patient(X)|generous(X)))))&
((~funny(paul))<=>((~patient(mary)&~brave(mary))))&
(![X]:((wise(X)<~>~funny(X))=>(creative(X)<~>~calm(X))))&
(((humble(susan)<~>~humble(susan)))<=>((generous(fred)<~>~wise(fred))))&
(![X]:((~happy(X)&~kind(X))<=>(~humble(X)&wise(X))))&
((?[X]:((~strong(X)|~happy(X))))=>(?[X]:(~old(X))))&
((?[X]:((kind(X)&~humble(X))))=>((~creative(susan)&~quiet(susan))))&
(![X]:(~patient(X)<=>(~happy(X)<~>wise(X))))&
(?[X]:((~old(X)|creative(X))))&
((curious(john)<~>tall(john)))&
((calm(fred)<~>~rich(fred)))&
((~brave(fred)|quiet(fred)))&
(?[X]:((~happy(X)<~>happy(X))))&
(~quiet(alice))&
((generous(lucy)&tall(lucy)))&
(~calm(alice)) | ~kind(fred) | [
"p3",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1359419784495741057678700
% SZS output start Proof for 1359419784495741057678700
4. ! [X0] : ((~tall(X0) & ~quiet(X0)) <=> brave(X0)) [input p3]
6. ! [X0] : ((generous(X0) | brave(X0)) <=> (kind(X0) | ~generous(X0))) [input p5]
20. quiet(fred) | ~brave(fred) [input p19]
25. ~kind(fred) [input hypothesis]
35. ! [X0] : (((~tall(X0) & ~quiet(X0)) | ~brave(X0)) & (brave(X0) | (tall(X0) | quiet(X0)))) [nnf transformation 4]
36. ! [X0] : (((~tall(X0) & ~quiet(X0)) | ~brave(X0)) & (brave(X0) | tall(X0) | quiet(X0))) [flattening 35]
37. ! [X0] : (((generous(X0) | brave(X0)) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | (~generous(X0) & ~brave(X0)))) [nnf transformation 6]
38. ! [X0] : ((generous(X0) | brave(X0) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | (~generous(X0) & ~brave(X0)))) [flattening 37]
78. ~brave(X0) | ~quiet(X0) [cnf transformation 36]
82. kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
83. generous(X0) | brave(X0) | generous(X0) [cnf transformation 38]
128. quiet(fred) | ~brave(fred) [cnf transformation 20]
135. ~kind(fred) [cnf transformation 25]
140. ~generous(X0) | kind(X0) [duplicate literal removal 82]
141. brave(X0) | generous(X0) [duplicate literal removal 83]
197. 13 <=> generous(fred) [avatar definition]
198. generous(fred) <- (13) [avatar component clause 197]
262. ~brave(fred) [subsumption resolution 128,78]
273. generous(fred) [resolution 141,262]
278. 13 [avatar split clause 273,197]
279. kind(fred) <- (13) [resolution 198,140]
280. $false <- (13) [subsumption resolution 279,135]
281. ~13 [avatar contradiction clause 280]
282. $false [avatar sat refutation 278,281]
% SZS output end Proof for 1359419784495741057678700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or calm is both old and patient and vice versa.
If someone is not strong then someone is either not generous or quiet and vice versa.
Everyone who is not generous or patient is tall or not strong and vice versa.
Everyone who is quiet or not strong is not funny.
Everyone who is either brave or not brave is not strong or not calm.
If lucy is both quiet and generous then someone is not brave and vice versa.
Everyone who is either not patient or not generous is tall and vice versa.
If john is both generous and wise then john is wise or rich.
Everyone who is either not funny or not old is not patient or not generous and vice versa.
Everyone who is strong is not curious or not kind.
Everyone who is not calm is both rich and funny and vice versa.
If someone is either not creative or not wise then someone is not quiet.
If john is humble or creative then susan is not strong.
If someone is either not brave or not calm then someone is either not strong or not humble and vice versa.
If fred is either not creative or not kind then someone is not old and vice versa.
If someone is not rich or not humble then lucy is not brave and vice versa.
Someone is either strong or brave.
Susan is either creative or not calm.
Lucy is curious.
Someone is either not calm or not kind.
Alice is not kind.
Someone is curious or patient. | Fred is tall. | entailment | (![X]:((~humble(X)|calm(X))<=>(old(X)&patient(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~generous(X)<~>quiet(X)))))&
(![X]:((~generous(X)|patient(X))<=>(tall(X)|~strong(X))))&
(![X]:((quiet(X)|~strong(X))=>~funny(X)))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)|~calm(X))))&
(((quiet(lucy)&generous(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>tall(X)))&
(((generous(john)&wise(john)))=>((wise(john)|rich(john))))&
(![X]:((~funny(X)<~>~old(X))<=>(~patient(X)|~generous(X))))&
(![X]:(strong(X)=>(~curious(X)|~kind(X))))&
(![X]:(~calm(X)<=>(rich(X)&funny(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(?[X]:(~quiet(X))))&
(((humble(john)|creative(john)))=>(~strong(susan)))&
((?[X]:((~brave(X)<~>~calm(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(((~creative(fred)<~>~kind(fred)))<=>(?[X]:(~old(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(~brave(lucy)))&
(?[X]:((strong(X)<~>brave(X))))&
((creative(susan)<~>~calm(susan)))&
(curious(lucy))&
(?[X]:((~calm(X)<~>~kind(X))))&
(~kind(alice))&
(?[X]:((curious(X)|patient(X)))) | tall(fred) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7176621741002307537650839
% SZS output start Proof for 7176621741002307537650839
1. ! [X0] : ((calm(X0) | ~humble(X0)) <=> (patient(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (~strong(X0) | tall(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => ~funny(X0)) [input p3]
6. (generous(lucy) & quiet(lucy)) <=> ? [X0] : ~brave(X0) [input p5]
7. ! [X0] : ((~patient(X0) <~> ~generous(X0)) <=> tall(X0)) [input p6]
9. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (~generous(X0) | ~patient(X0))) [input p8]
11. ! [X0] : (~calm(X0) <=> (funny(X0) & rich(X0))) [input p10]
16. ? [X0] : (~humble(X0) | ~rich(X0)) <=> ~brave(lucy) [input p15]
23. ~tall(fred) [input hypothesis]
27. ! [X0] : (~funny(X0) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
36. ! [X0] : (((calm(X0) | ~humble(X0)) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | ~humble(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | (~calm(X0) & humble(X0)))) [flattening 36]
43. ! [X0] : (((patient(X0) | ~generous(X0)) | (strong(X0) & ~tall(X0))) & ((~strong(X0) | tall(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 3]
44. ! [X0] : ((patient(X0) | ~generous(X0) | (strong(X0) & ~tall(X0))) & (~strong(X0) | tall(X0) | (~patient(X0) & generous(X0)))) [flattening 43]
46. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~generous(lucy) | ~quiet(lucy))) [nnf transformation 6]
47. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~generous(lucy) | ~quiet(lucy)) [flattening 46]
48. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~generous(lucy) | ~quiet(lucy)) [rectify 47]
49. ? [X1] : ~brave(X1) => ~brave(sK2) [choice axiom]
50. ((generous(lucy) & quiet(lucy)) | ! [X0] : brave(X0)) & (~brave(sK2) | ~generous(lucy) | ~quiet(lucy)) [skolemisation 48,49]
51. ! [X0] : ((((generous(X0) | patient(X0)) & (~generous(X0) | ~patient(X0))) | ~tall(X0)) & (tall(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0))))) [nnf transformation 7]
52. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 9]
53. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [flattening 52]
54. ! [X0] : ((~calm(X0) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | calm(X0))) [nnf transformation 11]
55. ! [X0] : ((~calm(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | calm(X0))) [flattening 54]
69. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X0] : (humble(X0) & rich(X0))) [nnf transformation 16]
70. (? [X0] : (~humble(X0) | ~rich(X0)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [rectify 69]
71. ? [X0] : (~humble(X0) | ~rich(X0)) => (~humble(sK7) | ~rich(sK7)) [choice axiom]
72. ((~humble(sK7) | ~rich(sK7)) | brave(lucy)) & (~brave(lucy) | ! [X1] : (humble(X1) & rich(X1))) [skolemisation 70,71]
83. ~calm(X0) | old(X0) [cnf transformation 37]
85. ~calm(X0) | patient(X0) [cnf transformation 37]
86. ~patient(X0) | ~humble(X0) | calm(X0) | ~old(X0) [cnf transformation 37]
91. ~strong(X0) | tall(X0) | generous(X0) [cnf transformation 44]
93. ~tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 44]
95. ~funny(X0) | ~quiet(X0) [cnf transformation 27]
96. ~funny(X0) | strong(X0) [cnf transformation 27]
100. quiet(lucy) | brave(X0) [cnf transformation 50]
101. generous(lucy) | brave(X0) [cnf transformation 50]
102. tall(X0) | ~generous(X0) | patient(X0) [cnf transformation 51]
103. ~patient(X0) | tall(X0) | generous(X0) [cnf transformation 51]
104. ~generous(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 51]
105. generous(X0) | patient(X0) | ~tall(X0) [cnf transformation 51]
107. ~generous(X0) | ~patient(X0) | ~old(X0) | funny(X0) [cnf transformation 53]
108. ~generous(X0) | ~patient(X0) | ~funny(X0) | old(X0) [cnf transformation 53]
109. ~funny(X0) | ~old(X0) | patient(X0) [cnf transformation 53]
111. funny(X0) | old(X0) | patient(X0) [cnf transformation 53]
115. funny(X0) | calm(X0) [cnf transformation 55]
116. ~rich(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 55]
133. ~brave(lucy) | rich(X1) [cnf transformation 72]
134. ~brave(lucy) | humble(X1) [cnf transformation 72]
145. ~tall(fred) [cnf transformation 23]
175. 7 <=> ! [X0] : brave(X0) [avatar definition]
176. brave(X0) <- (7) [avatar component clause 175]
178. 8 <=> generous(lucy) [avatar definition]
180. generous(lucy) <- (8) [avatar component clause 178]
181. 7 | 8 [avatar split clause 101,178,175]
183. 9 <=> quiet(lucy) [avatar definition]
185. quiet(lucy) <- (9) [avatar component clause 183]
186. 7 | 9 [avatar split clause 100,183,175]
192. ~tall(X0) | patient(X0) [subsumption resolution 105,93]
193. ~tall(X0) | ~generous(X0) [subsumption resolution 104,93]
194. ~generous(X0) | patient(X0) [subsumption resolution 102,193]
195. ~funny(X0) | ~generous(X0) | old(X0) [subsumption resolution 108,194]
196. ~generous(X0) | ~old(X0) | funny(X0) [subsumption resolution 107,194]
279. 29 <=> brave(lucy) [avatar definition]
280. ~brave(lucy) <- (~29) [avatar component clause 279]
292. 32 <=> ! [X1] : humble(X1) [avatar definition]
293. humble(X1) <- (32) [avatar component clause 292]
294. 32 | ~29 [avatar split clause 134,279,292]
296. 33 <=> ! [X1] : rich(X1) [avatar definition]
297. rich(X1) <- (33) [avatar component clause 296]
298. 33 | ~29 [avatar split clause 133,279,296]
346. ~quiet(X1) | calm(X1) [resolution 115,95]
418. ~old(X0) | patient(X0) | calm(X0) [resolution 109,115]
419. ~old(X0) | patient(X0) [subsumption resolution 418,85]
433. old(X2) | patient(X2) | strong(X2) [resolution 111,96]
436. strong(X2) | patient(X2) [subsumption resolution 433,419]
477. ~generous(X2) | old(X2) | calm(X2) [resolution 195,115]
480. ~generous(X2) | old(X2) [subsumption resolution 477,83]
481. ~old(lucy) | funny(lucy) <- (8) [resolution 196,180]
484. 54 <=> funny(lucy) [avatar definition]
486. funny(lucy) <- (54) [avatar component clause 484]
488. 55 <=> old(lucy) [avatar definition]
490. ~old(lucy) <- (~55) [avatar component clause 488]
491. 54 | ~55 | ~8 [avatar split clause 481,178,488,484]
497. calm(lucy) <- (9) [resolution 346,185]
509. patient(X2) | tall(X2) | generous(X2) [resolution 436,91]
516. tall(X2) | generous(X2) [subsumption resolution 509,103]
532. $false <- (7, ~29) [resolution 176,280]
533. ~7 | 29 [avatar contradiction clause 532]
538. ~funny(X0) | ~calm(X0) <- (33) [resolution 297,116]
543. old(lucy) <- (9) [resolution 497,83]
544. $false <- (9, ~55) [subsumption resolution 543,490]
545. ~9 | 55 [avatar contradiction clause 544]
572. generous(fred) [resolution 516,145]
575. generous(X2) | patient(X2) [resolution 516,192]
576. patient(X2) [subsumption resolution 575,194]
614. old(fred) [resolution 572,480]
615. ~old(fred) | funny(fred) [resolution 572,196]
618. funny(fred) [subsumption resolution 615,614]
623. ~humble(X0) | calm(X0) | ~old(X0) [resolution 576,86]
625. ~old(X0) | calm(X0) <- (32) [subsumption resolution 623,293]
638. ~calm(fred) <- (33) [resolution 618,538]
646. calm(fred) <- (32) [resolution 625,614]
650. $false <- (32, 33) [subsumption resolution 646,638]
651. ~32 | ~33 [avatar contradiction clause 650]
666. ~quiet(lucy) <- (54) [resolution 486,95]
669. $false <- (9, 54) [subsumption resolution 666,185]
670. ~9 | ~54 [avatar contradiction clause 669]
671. $false [avatar sat refutation 181,186,294,298,491,533,545,651,670]
% SZS output end Proof for 7176621741002307537650839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If alice is strong then alice is tall and vice versa.
Everyone who is both creative and funny is either brave or kind.
If john is both not kind and old then someone is not creative or not funny and vice versa.
Everyone who is not curious is either not patient or humble.
If someone is not curious then alice is old.
Everyone who is not funny or not rich is either not strong or patient and vice versa.
If someone is humble or not brave then mary is either patient or not quiet.
Everyone who is happy or quiet is both not funny and happy.
Everyone who is either curious or humble is either quiet or not wise and vice versa.
If john is both calm and not happy then susan is either generous or calm.
Everyone who is both not wise and not calm is not rich or generous and vice versa.
Everyone who is both not old and not kind is either patient or not calm.
Everyone who is both funny and patient is not generous.
Everyone who is both not happy and kind is not old or not kind.
If someone is not patient or not creative then mary is happy.
Everyone who is either not patient or brave is brave or patient.
Someone is tall.
John is patient.
Mary is both not rich and not strong.
Susan is not old.
John is either generous or not old.
Mary is not generous or old.
Alice is not quiet or not curious.
Someone is both calm and funny. | Mary is not kind. | neutral | ((strong(alice))<=>(tall(alice)))&
(![X]:((creative(X)&funny(X))=>(brave(X)<~>kind(X))))&
(((~kind(john)&old(john)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:(~curious(X)=>(~patient(X)<~>humble(X))))&
((?[X]:(~curious(X)))=>(old(alice)))&
(![X]:((~funny(X)|~rich(X))<=>(~strong(X)<~>patient(X))))&
((?[X]:((humble(X)|~brave(X))))=>((patient(mary)<~>~quiet(mary))))&
(![X]:((happy(X)|quiet(X))=>(~funny(X)&happy(X))))&
(![X]:((curious(X)<~>humble(X))<=>(quiet(X)<~>~wise(X))))&
(((calm(john)&~happy(john)))=>((generous(susan)<~>calm(susan))))&
(![X]:((~wise(X)&~calm(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~kind(X))=>(patient(X)<~>~calm(X))))&
(![X]:((funny(X)&patient(X))=>~generous(X)))&
(![X]:((~happy(X)&kind(X))=>(~old(X)|~kind(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(happy(mary)))&
(![X]:((~patient(X)<~>brave(X))=>(brave(X)|patient(X))))&
(?[X]:(tall(X)))&
(patient(john))&
((~rich(mary)&~strong(mary)))&
(~old(susan))&
((generous(john)<~>~old(john)))&
((~generous(mary)|old(mary)))&
((~quiet(alice)|~curious(alice)))&
(?[X]:((calm(X)&funny(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is not tall or strong is either calm or not funny and vice versa.
If someone is not brave or not rich then someone is both not quiet and quiet and vice versa.
If mary is not funny or not brave then paul is strong and vice versa.
If john is either not rich or wise then someone is either old or not wise.
Everyone who is not generous or brave is not wise and vice versa.
If lucy is not brave then someone is not patient.
Everyone who is either strong or not calm is either rich or not strong and vice versa.
If john is not old or brave then someone is either old or not creative.
Everyone who is not happy is creative or not humble and vice versa.
Everyone who is either old or tall is either not funny or not creative.
If lucy is either not kind or brave then paul is both not quiet and not creative.
If someone is both wise and strong then someone is strong or not funny.
If lucy is not strong then lucy is either rich or not rich and vice versa.
Everyone who is both not creative and quiet is either curious or calm and vice versa.
If someone is quiet or brave then john is rich and vice versa.
Everyone who is both not generous and brave is curious.
Someone is either not brave or not wise.
Mary is humble or brave.
Paul is either happy or brave.
Someone is either humble or not kind.
Someone is strong or rich.
Mary is not strong or humble.
Lucy is patient or calm. | Mary is strong. | neutral | (![X]:((~tall(X)|strong(X))<=>(calm(X)<~>~funny(X))))&
((?[X]:((~brave(X)|~rich(X))))<=>(?[X]:((~quiet(X)&quiet(X)))))&
(((~funny(mary)|~brave(mary)))<=>(strong(paul)))&
(((~rich(john)<~>wise(john)))=>(?[X]:((old(X)<~>~wise(X)))))&
(![X]:((~generous(X)|brave(X))<=>~wise(X)))&
((~brave(lucy))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(rich(X)<~>~strong(X))))&
(((~old(john)|brave(john)))=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:(~happy(X)<=>(creative(X)|~humble(X))))&
(![X]:((old(X)<~>tall(X))=>(~funny(X)<~>~creative(X))))&
(((~kind(lucy)<~>brave(lucy)))=>((~quiet(paul)&~creative(paul))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((strong(X)|~funny(X)))))&
((~strong(lucy))<=>((rich(lucy)<~>~rich(lucy))))&
(![X]:((~creative(X)&quiet(X))<=>(curious(X)<~>calm(X))))&
((?[X]:((quiet(X)|brave(X))))<=>(rich(john)))&
(![X]:((~generous(X)&brave(X))=>curious(X)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((humble(mary)|brave(mary)))&
((happy(paul)<~>brave(paul)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:((strong(X)|rich(X))))&
((~strong(mary)|humble(mary)))&
((patient(lucy)|calm(lucy))) | strong(mary) | [] | null | 0 |
If john is either not funny or quiet then fred is happy.
If someone is brave or not wise then susan is both tall and not rich and vice versa.
If someone is humble then lucy is either humble or quiet.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Mary is quiet. | neutral | (((~funny(john)<~>quiet(john)))=>(happy(fred)))&
((?[X]:((brave(X)|~wise(X))))<=>((tall(susan)&~rich(susan))))&
((?[X]:(humble(X)))=>((humble(lucy)<~>quiet(lucy))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | quiet(mary) | [] | null | 0 |
If paul is kind then susan is happy and vice versa.
Everyone who is calm is both creative and old.
If fred is not kind or not tall then someone is not happy or not creative and vice versa.
Everyone who is not creative or not generous is not happy and vice versa.
Everyone who is brave or not wise is both not creative and humble.
Everyone who is not patient or not humble is curious or funny and vice versa.
If susan is both quiet and curious then lucy is humble or not rich.
Everyone who is both not funny and not old is not quiet or not wise and vice versa.
Everyone who is rich is not brave or generous and vice versa.
Everyone who is creative or brave is not humble or not brave and vice versa.
Everyone who is either happy or not quiet is both curious and not curious.
Everyone who is humble is strong or not humble and vice versa.
If someone is not tall then alice is not patient or not wise.
If susan is patient then alice is both creative and wise.
If fred is not old or old then someone is funny and vice versa.
If someone is either not creative or not calm then someone is either not patient or strong and vice versa.
Paul is not curious.
John is not old or not rich.
Someone is funny or patient.
Paul is either funny or not quiet.
Lucy is calm.
Someone is not funny or funny. | Fred is not quiet. | neutral | ((kind(paul))<=>(happy(susan)))&
(![X]:(calm(X)=>(creative(X)&old(X))))&
(((~kind(fred)|~tall(fred)))<=>(?[X]:((~happy(X)|~creative(X)))))&
(![X]:((~creative(X)|~generous(X))<=>~happy(X)))&
(![X]:((brave(X)|~wise(X))=>(~creative(X)&humble(X))))&
(![X]:((~patient(X)|~humble(X))<=>(curious(X)|funny(X))))&
(((quiet(susan)&curious(susan)))=>((humble(lucy)|~rich(lucy))))&
(![X]:((~funny(X)&~old(X))<=>(~quiet(X)|~wise(X))))&
(![X]:(rich(X)<=>(~brave(X)|generous(X))))&
(![X]:((creative(X)|brave(X))<=>(~humble(X)|~brave(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(curious(X)&~curious(X))))&
(![X]:(humble(X)<=>(strong(X)|~humble(X))))&
((?[X]:(~tall(X)))=>((~patient(alice)|~wise(alice))))&
((patient(susan))=>((creative(alice)&wise(alice))))&
(((~old(fred)|old(fred)))<=>(?[X]:(funny(X))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(~curious(paul))&
((~old(john)|~rich(john)))&
(?[X]:((funny(X)|patient(X))))&
((funny(paul)<~>~quiet(paul)))&
(calm(lucy))&
(?[X]:((~funny(X)|funny(X)))) | ~quiet(fred) | [] | null | 0 |
If paul is both not generous and not curious then lucy is either not humble or not curious and vice versa. If someone is generous then someone is either not generous or not kind. If someone is not creative or not generous then someone is not generous or not tall and vice versa. Everyone who is strong is both old and not brave. If someone is brave or humble then someone is wise or generous. Everyone who is not creative is not humble. Everyone who is not calm or not curious is either not happy or calm. If john is both humble and old then john is both not brave and creative. If alice is both not kind and generous then someone is both curious and quiet and vice versa. Everyone who is not curious or not strong is old. Everyone who is not calm or not kind is not patient. Everyone who is both funny and generous is either wise or generous and vice versa. If lucy is both kind and old then susan is either not funny or not old. Everyone who is not calm is either not humble or rich and vice versa. If alice is either not generous or not kind then lucy is either not old or not brave. Everyone who is either quiet or tall is calm or not generous and vice versa. Mary is either happy or not generous. Someone is both not quiet and not humble. Someone is happy or not old. Mary is either quiet or not curious. Mary is either calm or creative. John is wise or not humble. Alice is patient. | Alice is not kind. | contradiction | (((~generous(paul)&~curious(paul)))<=>((~humble(lucy)<~>~curious(lucy))))&
((?[X]:(generous(X)))=>(?[X]:((~generous(X)<~>~kind(X)))))&
((?[X]:((~creative(X)|~generous(X))))<=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:(strong(X)=>(old(X)&~brave(X))))&
((?[X]:((brave(X)|humble(X))))=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(~creative(X)=>~humble(X)))&
(![X]:((~calm(X)|~curious(X))=>(~happy(X)<~>calm(X))))&
(((humble(john)&old(john)))=>((~brave(john)&creative(john))))&
(((~kind(alice)&generous(alice)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~curious(X)|~strong(X))=>old(X)))&
(![X]:((~calm(X)|~kind(X))=>~patient(X)))&
(![X]:((funny(X)&generous(X))<=>(wise(X)<~>generous(X))))&
(((kind(lucy)&old(lucy)))=>((~funny(susan)<~>~old(susan))))&
(![X]:(~calm(X)<=>(~humble(X)<~>rich(X))))&
(((~generous(alice)<~>~kind(alice)))=>((~old(lucy)<~>~brave(lucy))))&
(![X]:((quiet(X)<~>tall(X))<=>(calm(X)|~generous(X))))&
((happy(mary)<~>~generous(mary)))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:((happy(X)|~old(X))))&
((quiet(mary)<~>~curious(mary)))&
((calm(mary)<~>creative(mary)))&
((wise(john)|~humble(john)))&
(patient(alice)) | ~kind(alice) | [
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2483672174164604462234167
% SZS output start Proof for 2483672174164604462234167
11. ! [X0] : ((~kind(X0) | ~calm(X0)) => ~patient(X0)) [input p10]
23. patient(alice) [input p22]
24. ~kind(alice) [input hypothesis]
36. ! [X0] : (~patient(X0) | (kind(X0) & calm(X0))) [ennf transformation 11]
104. ~patient(X0) | kind(X0) [cnf transformation 36]
137. patient(alice) [cnf transformation 23]
138. ~kind(alice) [cnf transformation 24]
244. 24 <=> kind(alice) [avatar definition]
246. ~kind(alice) <- (~24) [avatar component clause 244]
315. ~24 [avatar split clause 138,244]
318. kind(alice) [resolution 104,137]
319. $false <- (~24) [subsumption resolution 318,246]
320. 24 [avatar contradiction clause 319]
321. $false [avatar sat refutation 315,320]
% SZS output end Proof for 2483672174164604462234167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not wise is not old or not calm.
If someone is strong or happy then susan is not kind.
Everyone who is humble is both generous and not rich.
Everyone who is old or brave is both not brave and brave.
If someone is curious or not generous then lucy is quiet or generous and vice versa.
If alice is both brave and not curious then paul is old or not funny.
Everyone who is not calm is not quiet and vice versa.
If alice is either not happy or not old then someone is both not rich and not patient.
Everyone who is not rich is curious or not curious and vice versa.
Everyone who is not happy or funny is either generous or rich.
If john is tall then someone is not curious or not old and vice versa.
If someone is either not wise or patient then susan is rich and vice versa.
If susan is either not tall or calm then mary is either not curious or not funny.
If someone is calm then someone is either tall or not patient.
Everyone who is kind is either not happy or strong and vice versa.
If fred is not old or not rich then susan is both not curious and wise and vice versa.
Someone is both humble and not quiet.
Susan is tall or rich.
Someone is either not happy or not tall.
Fred is both wise and strong.
Someone is both calm and not curious.
Fred is not quiet or not old. | John is not kind. | neutral | (![X]:((strong(X)|~wise(X))=>(~old(X)|~calm(X))))&
((?[X]:((strong(X)|happy(X))))=>(~kind(susan)))&
(![X]:(humble(X)=>(generous(X)&~rich(X))))&
(![X]:((old(X)|brave(X))=>(~brave(X)&brave(X))))&
((?[X]:((curious(X)|~generous(X))))<=>((quiet(lucy)|generous(lucy))))&
(((brave(alice)&~curious(alice)))=>((old(paul)|~funny(paul))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(((~happy(alice)<~>~old(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~curious(X))))&
(![X]:((~happy(X)|funny(X))=>(generous(X)<~>rich(X))))&
((tall(john))<=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:((~wise(X)<~>patient(X))))<=>(rich(susan)))&
(((~tall(susan)<~>calm(susan)))=>((~curious(mary)<~>~funny(mary))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
(?[X]:((humble(X)&~quiet(X))))&
((tall(susan)|rich(susan)))&
(?[X]:((~happy(X)<~>~tall(X))))&
((wise(fred)&strong(fred)))&
(?[X]:((calm(X)&~curious(X))))&
((~quiet(fred)|~old(fred))) | ~kind(john) | [] | null | 0 |
Everyone who is both old and patient is not kind or old and vice versa.
If someone is not creative then someone is both creative and not brave.
Everyone who is tall or not happy is not strong.
If mary is not kind or old then susan is not generous and vice versa.
Everyone who is not generous is either not generous or wise and vice versa.
If someone is funny or brave then fred is either kind or old and vice versa.
If lucy is both wise and not calm then someone is either not brave or not calm and vice versa.
Everyone who is both not strong and not funny is either old or not creative and vice versa.
If fred is both not curious and wise then paul is either not happy or not brave.
Everyone who is not creative or not kind is both humble and creative.
If someone is either not funny or not brave then lucy is both not creative and not curious and vice versa.
If fred is either kind or creative then alice is both not wise and not calm and vice versa.
If someone is curious or not tall then alice is both wise and patient and vice versa.
Everyone who is curious is brave or rich.
Everyone who is quiet or not curious is not tall or not strong and vice versa.
Everyone who is tall is brave or not creative.
Fred is not generous.
John is quiet.
John is not old or not tall.
Lucy is not wise. | Lucy is tall. | entailment | (![X]:((old(X)&patient(X))<=>(~kind(X)|old(X))))&
((?[X]:(~creative(X)))=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((tall(X)|~happy(X))=>~strong(X)))&
(((~kind(mary)|old(mary)))<=>(~generous(susan)))&
(![X]:(~generous(X)<=>(~generous(X)<~>wise(X))))&
((?[X]:((funny(X)|brave(X))))<=>((kind(fred)<~>old(fred))))&
(((wise(lucy)&~calm(lucy)))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~strong(X)&~funny(X))<=>(old(X)<~>~creative(X))))&
(((~curious(fred)&wise(fred)))=>((~happy(paul)<~>~brave(paul))))&
(![X]:((~creative(X)|~kind(X))=>(humble(X)&creative(X))))&
((?[X]:((~funny(X)<~>~brave(X))))<=>((~creative(lucy)&~curious(lucy))))&
(((kind(fred)<~>creative(fred)))<=>((~wise(alice)&~calm(alice))))&
((?[X]:((curious(X)|~tall(X))))<=>((wise(alice)&patient(alice))))&
(![X]:(curious(X)=>(brave(X)|rich(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~tall(X)|~strong(X))))&
(![X]:(tall(X)=>(brave(X)|~creative(X))))&
(~generous(fred))&
(quiet(john))&
((~old(john)|~tall(john)))&
(~wise(lucy)) | tall(lucy) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8575071385555451340223928
% SZS output start Proof for 8575071385555451340223928
5. ! [X0] : (~generous(X0) <=> (~generous(X0) <~> wise(X0))) [input p4]
13. ? [X0] : (~tall(X0) | curious(X0)) <=> (patient(alice) & wise(alice)) [input p12]
21. ~tall(lucy) [input hypothesis]
39. ! [X0] : ((~generous(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | generous(X0))) [nnf transformation 5]
59. (? [X0] : (~tall(X0) | curious(X0)) | (~patient(alice) | ~wise(alice))) & ((patient(alice) & wise(alice)) | ! [X0] : (tall(X0) & ~curious(X0))) [nnf transformation 13]
60. (? [X0] : (~tall(X0) | curious(X0)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X0] : (tall(X0) & ~curious(X0))) [flattening 59]
61. (? [X0] : (~tall(X0) | curious(X0)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X1] : (tall(X1) & ~curious(X1))) [rectify 60]
62. ? [X0] : (~tall(X0) | curious(X0)) => (~tall(sK4) | curious(sK4)) [choice axiom]
63. ((~tall(sK4) | curious(sK4)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X1] : (tall(X1) & ~curious(X1))) [skolemisation 61,62]
79. ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 39]
81. ~generous(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 39]
117. wise(alice) | tall(X1) [cnf transformation 63]
130. ~tall(lucy) [cnf transformation 21]
132. ~wise(X0) | generous(X0) [duplicate literal removal 79]
133. ~generous(X0) | ~wise(X0) [duplicate literal removal 81]
163. ~wise(X0) [subsumption resolution 132,133]
252. 24 <=> ! [X1] : tall(X1) [avatar definition]
253. tall(X1) <- (24) [avatar component clause 252]
263. tall(X1) [subsumption resolution 117,163]
264. 24 [avatar split clause 263,252]
278. $false <- (24) [resolution 253,130]
279. ~24 [avatar contradiction clause 278]
280. $false [avatar sat refutation 264,279]
% SZS output end Proof for 8575071385555451340223928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not tall and not old then paul is happy and vice versa.
If someone is not humble then someone is not generous or not wise.
Everyone who is not strong is both not kind and tall.
If susan is either not happy or wise then lucy is either not generous or creative.
If john is humble or patient then lucy is not humble.
Everyone who is humble or not kind is both brave and not happy.
Everyone who is both not patient and not kind is both humble and creative.
If someone is old then someone is either rich or not rich.
If someone is both kind and not generous then john is either strong or humble and vice versa.
If mary is generous then alice is not patient and vice versa.
Everyone who is calm or old is not patient or wise and vice versa.
If someone is rich then someone is either not old or not generous and vice versa.
Everyone who is both not happy and not generous is not tall.
If someone is both not calm and not old then someone is both not generous and not strong.
Everyone who is both not humble and rich is not generous.
Everyone who is wise is both happy and not generous and vice versa.
Someone is generous or quiet.
Susan is either not quiet or quiet.
Someone is not happy.
Alice is either happy or strong.
Someone is both not humble and not patient.
Someone is either old or creative.
Someone is either not rich or not strong.
Someone is both not humble and strong. | Mary is not patient. | entailment | (((~tall(john)&~old(john)))<=>(happy(paul)))&
((?[X]:(~humble(X)))=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:(~strong(X)=>(~kind(X)&tall(X))))&
(((~happy(susan)<~>wise(susan)))=>((~generous(lucy)<~>creative(lucy))))&
(((humble(john)|patient(john)))=>(~humble(lucy)))&
(![X]:((humble(X)|~kind(X))=>(brave(X)&~happy(X))))&
(![X]:((~patient(X)&~kind(X))=>(humble(X)&creative(X))))&
((?[X]:(old(X)))=>(?[X]:((rich(X)<~>~rich(X)))))&
((?[X]:((kind(X)&~generous(X))))<=>((strong(john)<~>humble(john))))&
((generous(mary))<=>(~patient(alice)))&
(![X]:((calm(X)|old(X))<=>(~patient(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~generous(X))=>~tall(X)))&
((?[X]:((~calm(X)&~old(X))))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((~humble(X)&rich(X))=>~generous(X)))&
(![X]:(wise(X)<=>(happy(X)&~generous(X))))&
(?[X]:((generous(X)|quiet(X))))&
((~quiet(susan)<~>quiet(susan)))&
(?[X]:(~happy(X)))&
((happy(alice)<~>strong(alice)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((old(X)<~>creative(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
(?[X]:((~humble(X)&strong(X)))) | ~patient(mary) | [
"p2",
"p5",
"p9",
"p10",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1874110869370178508113586
% SZS output start Proof for 1874110869370178508113586
3. ! [X0] : (~strong(X0) => (tall(X0) & ~kind(X0))) [input p2]
6. ! [X0] : ((~kind(X0) | humble(X0)) => (~happy(X0) & brave(X0))) [input p5]
10. generous(mary) <=> ~patient(alice) [input p9]
11. ! [X0] : ((old(X0) | calm(X0)) <=> (wise(X0) | ~patient(X0))) [input p10]
13. ! [X0] : ((~generous(X0) & ~happy(X0)) => ~tall(X0)) [input p12]
14. ? [X0] : (~old(X0) & ~calm(X0)) => ? [X0] : (~strong(X0) & ~generous(X0)) [input p13]
16. ! [X0] : (wise(X0) <=> (~generous(X0) & happy(X0))) [input p15]
20. happy(alice) <~> strong(alice) [input p19]
25. patient(mary) [input hypothesis]
29. ? [X0] : (~old(X0) & ~calm(X0)) => ? [X1] : (~strong(X1) & ~generous(X1)) [rectify 14]
30. ! [X0] : ((~kind(X0) | humble(X0)) => ~happy(X0)) [pure predicate removal 6]
32. ! [X0] : ((tall(X0) & ~kind(X0)) | strong(X0)) [ennf transformation 3]
35. ! [X0] : (~happy(X0) | (kind(X0) & ~humble(X0))) [ennf transformation 30]
39. ! [X0] : (~tall(X0) | (generous(X0) | happy(X0))) [ennf transformation 13]
40. ! [X0] : (~tall(X0) | generous(X0) | happy(X0)) [flattening 39]
41. ? [X1] : (~strong(X1) & ~generous(X1)) | ! [X0] : (old(X0) | calm(X0)) [ennf transformation 29]
58. (generous(mary) | patient(alice)) & (~patient(alice) | ~generous(mary)) [nnf transformation 10]
59. ! [X0] : (((old(X0) | calm(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (~old(X0) & ~calm(X0)))) [nnf transformation 11]
60. ! [X0] : ((old(X0) | calm(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | (~old(X0) & ~calm(X0)))) [flattening 59]
66. ? [X0] : (~strong(X0) & ~generous(X0)) | ! [X1] : (old(X1) | calm(X1)) [rectify 41]
67. ? [X0] : (~strong(X0) & ~generous(X0)) => (~strong(sK5) & ~generous(sK5)) [choice axiom]
68. (~strong(sK5) & ~generous(sK5)) | ! [X1] : (old(X1) | calm(X1)) [skolemisation 66,67]
69. ! [X0] : ((wise(X0) | (generous(X0) | ~happy(X0))) & ((~generous(X0) & happy(X0)) | ~wise(X0))) [nnf transformation 16]
70. ! [X0] : ((wise(X0) | generous(X0) | ~happy(X0)) & ((~generous(X0) & happy(X0)) | ~wise(X0))) [flattening 69]
76. (~strong(alice) | ~happy(alice)) & (strong(alice) | happy(alice)) [nnf transformation 20]
91. ~kind(X0) | strong(X0) [cnf transformation 32]
92. strong(X0) | tall(X0) [cnf transformation 32]
100. ~happy(X0) | kind(X0) [cnf transformation 35]
112. generous(mary) | patient(alice) [cnf transformation 58]
113. ~calm(X0) | ~patient(X0) | wise(X0) [cnf transformation 60]
114. ~patient(X0) | wise(X0) | ~old(X0) [cnf transformation 60]
121. ~tall(X0) | generous(X0) | happy(X0) [cnf transformation 40]
122. ~generous(sK5) | old(X1) | calm(X1) [cnf transformation 68]
123. ~strong(sK5) | old(X1) | calm(X1) [cnf transformation 68]
125. ~wise(X0) | happy(X0) [cnf transformation 70]
126. ~wise(X0) | ~generous(X0) [cnf transformation 70]
133. ~strong(alice) | ~happy(alice) [cnf transformation 76]
142. patient(mary) [cnf transformation 25]
226. 18 <=> patient(alice) [avatar definition]
228. patient(alice) <- (18) [avatar component clause 226]
230. 19 <=> generous(mary) [avatar definition]
233. 18 | 19 [avatar split clause 112,230,226]
261. 26 <=> ! [X1] : (old(X1) | calm(X1)) [avatar definition]
262. calm(X1) | old(X1) <- (26) [avatar component clause 261]
264. 27 <=> strong(sK5) [avatar definition]
266. ~strong(sK5) <- (~27) [avatar component clause 264]
267. 26 | ~27 [avatar split clause 123,264,261]
269. 28 <=> generous(sK5) [avatar definition]
271. ~generous(sK5) <- (~28) [avatar component clause 269]
272. 26 | ~28 [avatar split clause 122,269,261]
283. 31 <=> happy(alice) [avatar definition]
284. happy(alice) <- (31) [avatar component clause 283]
285. ~happy(alice) <- (~31) [avatar component clause 283]
287. 32 <=> strong(alice) [avatar definition]
289. ~strong(alice) <- (~32) [avatar component clause 287]
290. ~31 | ~32 [avatar split clause 133,287,283]
318. tall(sK5) <- (~27) [resolution 92,266]
322. kind(alice) <- (31) [resolution 100,284]
325. strong(alice) <- (31) [resolution 322,91]
326. $false <- (31, ~32) [subsumption resolution 325,289]
327. ~31 | 32 [avatar contradiction clause 326]
345. 38 <=> wise(mary) [avatar definition]
347. wise(mary) <- (38) [avatar component clause 345]
354. 40 <=> wise(alice) [avatar definition]
356. wise(alice) <- (40) [avatar component clause 354]
360. generous(sK5) | happy(sK5) <- (~27) [resolution 121,318]
361. happy(sK5) <- (~27, ~28) [subsumption resolution 360,271]
362. kind(sK5) <- (~27, ~28) [resolution 361,100]
363. strong(sK5) <- (~27, ~28) [resolution 362,91]
364. $false <- (~27, ~28) [subsumption resolution 363,266]
365. 27 | 28 [avatar contradiction clause 364]
373. old(X0) | ~patient(X0) | wise(X0) <- (26) [resolution 262,113]
374. ~patient(X0) | wise(X0) <- (26) [subsumption resolution 373,114]
375. wise(mary) <- (26) [resolution 374,142]
376. wise(alice) <- (18, 26) [resolution 374,228]
379. 38 | ~26 [avatar split clause 375,261,345]
380. 40 | ~18 | ~26 [avatar split clause 376,261,226,354]
382. ~generous(mary) <- (38) [resolution 347,126]
386. happy(alice) <- (40) [resolution 356,125]
387. $false <- (~31, 40) [subsumption resolution 386,285]
388. 31 | ~40 [avatar contradiction clause 387]
389. ~19 | ~38 [avatar split clause 382,345,230]
390. $false [avatar sat refutation 233,267,272,290,327,365,379,380,388,389]
% SZS output end Proof for 1874110869370178508113586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not patient is not generous or not rich and vice versa.
Everyone who is either not brave or not old is either not funny or not kind and vice versa.
If someone is either not generous or not happy then someone is either not calm or not strong and vice versa.
Everyone who is humble or not quiet is both patient and tall and vice versa.
Everyone who is creative or kind is both wise and strong.
If someone is both creative and not curious then someone is both funny and not humble.
If alice is either happy or quiet then someone is not strong or patient and vice versa.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
If someone is not patient or not creative then someone is not rich or not kind.
Everyone who is quiet or not brave is either brave or patient and vice versa.
If lucy is either kind or not kind then someone is either quiet or funny.
Everyone who is either not happy or not strong is patient and vice versa.
Everyone who is happy or old is either calm or not curious and vice versa.
Someone is quiet or not creative.
Someone is creative or not brave.
Someone is both calm and not rich.
Paul is funny. | Paul is not old. | contradiction | (![X]:((creative(X)&~patient(X))<=>(~generous(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((humble(X)|~quiet(X))<=>(patient(X)&tall(X))))&
(![X]:((creative(X)|kind(X))=>(wise(X)&strong(X))))&
((?[X]:((creative(X)&~curious(X))))=>(?[X]:((funny(X)&~humble(X)))))&
(((happy(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((calm(X)&~rich(X))))&
(funny(paul)) | ~old(paul) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 617778292831176313137784
% SZS output start Proof for 617778292831176313137784
1. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~rich(X0) | ~generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (tall(X0) & patient(X0))) [input p3]
5. ! [X0] : ((kind(X0) | creative(X0)) => (strong(X0) & wise(X0))) [input p4]
7. (happy(alice) <~> quiet(alice)) <=> ? [X0] : (patient(X0) | ~strong(X0)) [input p6]
8. ! [X0] : (~old(X0) => (~strong(X0) <~> ~happy(X0))) [input p7]
10. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p9]
11. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p10]
15. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p14]
21. ~old(paul) [input hypothesis]
25. ! [X0] : ((kind(X0) | creative(X0)) => strong(X0)) [pure predicate removal 5]
26. ! [X0] : (strong(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 25]
28. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | old(X0)) [ennf transformation 8]
32. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | patient(X0) | ~creative(X0))) [flattening 32]
40. ! [X0] : (((~quiet(X0) | humble(X0)) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : ((~quiet(X0) | humble(X0) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 40]
45. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X0] : (patient(X0) | ~strong(X0)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [nnf transformation 7]
46. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X1] : (patient(X1) | ~strong(X1)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [rectify 45]
47. ? [X1] : (patient(X1) | ~strong(X1)) => (patient(sK3) | ~strong(sK3)) [choice axiom]
48. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & ((patient(sK3) | ~strong(sK3)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [skolemisation 46,47]
49. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | old(X0)) [nnf transformation 28]
51. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 51]
53. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 53]
63. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 15]
73. generous(X0) | creative(X0) [cnf transformation 33]
74. rich(X0) | creative(X0) [cnf transformation 33]
94. quiet(X0) | patient(X0) [cnf transformation 41]
98. ~creative(X0) | strong(X0) [cnf transformation 26]
105. quiet(alice) | happy(alice) | ~patient(X0) [cnf transformation 48]
106. ~quiet(alice) | ~happy(alice) | strong(X0) [cnf transformation 48]
107. ~quiet(alice) | ~happy(alice) | ~patient(X0) [cnf transformation 48]
108. ~strong(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
113. quiet(X0) | rich(X0) [cnf transformation 52]
114. ~quiet(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 52]
115. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 54]
118. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 54]
133. ~strong(X0) | patient(X0) | happy(X0) [cnf transformation 63]
135. ~strong(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 63]
148. ~old(paul) [cnf transformation 21]
155. ~happy(X0) | creative(X0) [duplicate literal removal 118]
207. 12 <=> ! [X0] : ~patient(X0) [avatar definition]
208. ~patient(X0) <- (12) [avatar component clause 207]
210. 13 <=> happy(alice) [avatar definition]
211. happy(alice) <- (13) [avatar component clause 210]
212. ~happy(alice) <- (~13) [avatar component clause 210]
214. 14 <=> quiet(alice) [avatar definition]
215. quiet(alice) <- (14) [avatar component clause 214]
216. ~quiet(alice) <- (~14) [avatar component clause 214]
217. 12 | ~13 | ~14 [avatar split clause 107,214,210,207]
219. 15 <=> ! [X0] : strong(X0) [avatar definition]
220. strong(X0) <- (15) [avatar component clause 219]
221. 15 | ~13 | ~14 [avatar split clause 106,214,210,219]
222. 12 | 13 | 14 [avatar split clause 105,214,210,207]
287. patient(alice) <- (~14) [resolution 94,216]
299. creative(alice) <- (13) [resolution 155,211]
300. strong(alice) <- (13) [resolution 299,98]
445. ~happy(alice) | ~patient(alice) <- (13) [resolution 300,135]
448. ~patient(alice) <- (13) [subsumption resolution 445,211]
449. $false <- (13, ~14) [subsumption resolution 448,287]
450. ~13 | 14 [avatar contradiction clause 449]
453. ~creative(alice) | happy(alice) <- (14) [resolution 215,115]
454. ~generous(alice) | ~rich(alice) <- (14) [resolution 215,114]
464. ~creative(alice) <- (~13, 14) [subsumption resolution 453,212]
466. 47 <=> rich(alice) [avatar definition]
468. ~rich(alice) <- (~47) [avatar component clause 466]
470. 48 <=> generous(alice) [avatar definition]
472. ~generous(alice) <- (~48) [avatar component clause 470]
473. ~47 | ~48 | ~14 [avatar split clause 454,214,470,466]
475. creative(alice) <- (~48) [resolution 472,73]
476. $false <- (~13, 14, ~48) [subsumption resolution 475,464]
477. 13 | ~14 | 48 [avatar contradiction clause 476]
484. creative(alice) <- (~47) [resolution 468,74]
485. $false <- (~13, 14, ~47) [subsumption resolution 484,464]
486. 13 | ~14 | 47 [avatar contradiction clause 485]
493. rich(alice) <- (~14) [resolution 216,113]
495. patient(alice) <- (~14) [resolution 216,94]
496. 47 | 14 [avatar split clause 493,214,466]
499. $false <- (12, ~14) [subsumption resolution 495,208]
500. ~12 | 14 [avatar contradiction clause 499]
509. patient(X1) | happy(X1) <- (15) [resolution 220,133]
510. ~happy(X2) | old(X2) <- (15) [resolution 220,108]
513. happy(X1) <- (12, 15) [subsumption resolution 509,208]
514. old(X2) <- (12, 15) [subsumption resolution 510,513]
587. $false <- (12, 15) [resolution 514,148]
589. ~12 | ~15 [avatar contradiction clause 587]
590. $false [avatar sat refutation 217,221,222,450,473,477,486,496,500,589]
% SZS output end Proof for 617778292831176313137784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not curious then fred is both happy and not happy and vice versa. Everyone who is kind or calm is both not funny and tall. Everyone who is both not brave and old is either not rich or brave and vice versa. If john is either humble or not kind then fred is both tall and curious and vice versa. Everyone who is either tall or not kind is tall or not calm and vice versa. If someone is both creative and not old then someone is patient or not old and vice versa. Everyone who is both not happy and old is old and vice versa. Everyone who is patient is both not patient and old and vice versa. Everyone who is either creative or wise is either funny or not funny. Everyone who is not old is not tall. Everyone who is either not strong or happy is both quiet and not generous and vice versa. Everyone who is both old and kind is either not calm or not rich. If someone is not tall then fred is humble or quiet and vice versa. Everyone who is calm is both not kind and strong. Everyone who is either patient or not creative is both not wise and curious and vice versa. Someone is not humble. Someone is not tall or creative. Lucy is either quiet or creative. Someone is either kind or quiet. Someone is both not quiet and not calm. | Lucy is not happy. | neutral | ((?[X]:((~creative(X)<~>~curious(X))))<=>((happy(fred)&~happy(fred))))&
(![X]:((kind(X)|calm(X))=>(~funny(X)&tall(X))))&
(![X]:((~brave(X)&old(X))<=>(~rich(X)<~>brave(X))))&
(((humble(john)<~>~kind(john)))<=>((tall(fred)&curious(fred))))&
(![X]:((tall(X)<~>~kind(X))<=>(tall(X)|~calm(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((patient(X)|~old(X)))))&
(![X]:((~happy(X)&old(X))<=>old(X)))&
(![X]:(patient(X)<=>(~patient(X)&old(X))))&
(![X]:((creative(X)<~>wise(X))=>(funny(X)<~>~funny(X))))&
(![X]:(~old(X)=>~tall(X)))&
(![X]:((~strong(X)<~>happy(X))<=>(quiet(X)&~generous(X))))&
(![X]:((old(X)&kind(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:(~tall(X)))<=>((humble(fred)|quiet(fred))))&
(![X]:(calm(X)=>(~kind(X)&strong(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~wise(X)&curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)|creative(X))))&
((quiet(lucy)<~>creative(lucy)))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((~quiet(X)&~calm(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is kind or not strong is funny or not creative and vice versa. If someone is creative or happy then someone is quiet or not creative. Everyone who is quiet is old or not happy and vice versa. Everyone who is either old or not kind is both wise and not old. If someone is not rich then paul is quiet and vice versa. If mary is either quiet or curious then mary is both not quiet and brave. If someone is not strong or not generous then someone is both humble and not humble and vice versa. Everyone who is old or quiet is patient and vice versa. If paul is not rich then fred is both wise and rich and vice versa. Everyone who is generous or not rich is either creative or wise. If alice is both brave and not happy then someone is not generous and vice versa. Everyone who is not creative or not brave is funny or patient and vice versa. If someone is creative or calm then someone is either not brave or calm and vice versa. Everyone who is either not happy or not humble is both not calm and not patient and vice versa. Everyone who is not patient or old is generous and vice versa. If paul is not rich or generous then lucy is tall or brave and vice versa. Someone is not calm. Fred is not creative or wise. Someone is either humble or not old. Mary is not rich or calm. Alice is tall or happy. Susan is both not brave and rich. Lucy is patient. Someone is not patient. | Paul is kind. | contradiction | (![X]:((kind(X)|~strong(X))<=>(funny(X)|~creative(X))))&
((?[X]:((creative(X)|happy(X))))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(quiet(X)<=>(old(X)|~happy(X))))&
(![X]:((old(X)<~>~kind(X))=>(wise(X)&~old(X))))&
((?[X]:(~rich(X)))<=>(quiet(paul)))&
(((quiet(mary)<~>curious(mary)))=>((~quiet(mary)&brave(mary))))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((old(X)|quiet(X))<=>patient(X)))&
((~rich(paul))<=>((wise(fred)&rich(fred))))&
(![X]:((generous(X)|~rich(X))=>(creative(X)<~>wise(X))))&
(((brave(alice)&~happy(alice)))<=>(?[X]:(~generous(X))))&
(![X]:((~creative(X)|~brave(X))<=>(funny(X)|patient(X))))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~calm(X)&~patient(X))))&
(![X]:((~patient(X)|old(X))<=>generous(X)))&
(((~rich(paul)|generous(paul)))<=>((tall(lucy)|brave(lucy))))&
(?[X]:(~calm(X)))&
((~creative(fred)|wise(fred)))&
(?[X]:((humble(X)<~>~old(X))))&
((~rich(mary)|calm(mary)))&
((tall(alice)|happy(alice)))&
((~brave(susan)&rich(susan)))&
(patient(lucy))&
(?[X]:(~patient(X))) | kind(paul) | [
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1062979044066078018290568
% SZS output start Proof for 1062979044066078018290568
4. ! [X0] : ((old(X0) <~> ~kind(X0)) => (~old(X0) & wise(X0))) [input p3]
5. ? [X0] : ~rich(X0) <=> quiet(paul) [input p4]
7. ? [X0] : (~generous(X0) | ~strong(X0)) <=> ? [X0] : (~humble(X0) & humble(X0)) [input p6]
8. ! [X0] : ((quiet(X0) | old(X0)) <=> patient(X0)) [input p7]
9. ~rich(paul) <=> (rich(fred) & wise(fred)) [input p8]
10. ! [X0] : ((~rich(X0) | generous(X0)) => (creative(X0) <~> wise(X0))) [input p9]
15. ! [X0] : ((old(X0) | ~patient(X0)) <=> generous(X0)) [input p14]
18. wise(fred) | ~creative(fred) [input p17]
25. kind(paul) [input hypothesis]
27. ? [X0] : (~generous(X0) | ~strong(X0)) <=> ? [X1] : (~humble(X1) & humble(X1)) [rectify 7]
30. ! [X0] : ((~old(X0) & wise(X0)) | (old(X0) <=> ~kind(X0))) [ennf transformation 4]
32. ! [X0] : ((creative(X0) <~> wise(X0)) | (rich(X0) & ~generous(X0))) [ennf transformation 10]
40. ! [X0] : ((~old(X0) & wise(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) [nnf transformation 30]
41. (? [X0] : ~rich(X0) | ~quiet(paul)) & (quiet(paul) | ! [X0] : rich(X0)) [nnf transformation 5]
42. (? [X0] : ~rich(X0) | ~quiet(paul)) & (quiet(paul) | ! [X1] : rich(X1)) [rectify 41]
43. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
44. (~rich(sK1) | ~quiet(paul)) & (quiet(paul) | ! [X1] : rich(X1)) [skolemisation 42,43]
46. (? [X0] : (~generous(X0) | ~strong(X0)) | ! [X1] : (humble(X1) | ~humble(X1))) & (? [X1] : (~humble(X1) & humble(X1)) | ! [X0] : (generous(X0) & strong(X0))) [nnf transformation 27]
47. (? [X0] : (~generous(X0) | ~strong(X0)) | ! [X1] : (humble(X1) | ~humble(X1))) & (? [X2] : (~humble(X2) & humble(X2)) | ! [X3] : (generous(X3) & strong(X3))) [rectify 46]
48. ? [X0] : (~generous(X0) | ~strong(X0)) => (~generous(sK2) | ~strong(sK2)) [choice axiom]
49. ? [X2] : (~humble(X2) & humble(X2)) => (~humble(sK3) & humble(sK3)) [choice axiom]
50. ((~generous(sK2) | ~strong(sK2)) | ! [X1] : (humble(X1) | ~humble(X1))) & ((~humble(sK3) & humble(sK3)) | ! [X3] : (generous(X3) & strong(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((quiet(X0) | old(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & ~old(X0)))) [nnf transformation 8]
52. ! [X0] : ((quiet(X0) | old(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & ~old(X0)))) [flattening 51]
53. (~rich(paul) | (~rich(fred) | ~wise(fred))) & ((rich(fred) & wise(fred)) | rich(paul)) [nnf transformation 9]
54. (~rich(paul) | ~rich(fred) | ~wise(fred)) & ((rich(fred) & wise(fred)) | rich(paul)) [flattening 53]
55. ! [X0] : (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (rich(X0) & ~generous(X0))) [nnf transformation 32]
70. ! [X0] : (((old(X0) | ~patient(X0)) | ~generous(X0)) & (generous(X0) | (~old(X0) & patient(X0)))) [nnf transformation 15]
71. ! [X0] : ((old(X0) | ~patient(X0) | ~generous(X0)) & (generous(X0) | (~old(X0) & patient(X0)))) [flattening 70]
92. ~old(X0) | ~kind(X0) | ~old(X0) [cnf transformation 40]
94. quiet(paul) | rich(X1) [cnf transformation 44]
101. humble(sK3) | generous(X3) [cnf transformation 50]
103. ~humble(sK3) | generous(X3) [cnf transformation 50]
106. ~quiet(X0) | patient(X0) [cnf transformation 52]
110. ~rich(paul) | ~rich(fred) | ~wise(fred) [cnf transformation 54]
111. ~generous(X0) | creative(X0) | wise(X0) [cnf transformation 55]
136. ~patient(X0) | old(X0) | ~generous(X0) [cnf transformation 71]
142. wise(fred) | ~creative(fred) [cnf transformation 18]
151. kind(paul) [cnf transformation 25]
153. ~old(X0) | ~kind(X0) [duplicate literal removal 92]
171. 5 <=> quiet(paul) [avatar definition]
172. quiet(paul) <- (5) [avatar component clause 171]
180. 7 <=> ! [X1] : rich(X1) [avatar definition]
181. rich(X1) <- (7) [avatar component clause 180]
182. 7 | 5 [avatar split clause 94,171,180]
199. 11 <=> ! [X3] : generous(X3) [avatar definition]
200. generous(X3) <- (11) [avatar component clause 199]
202. 12 <=> humble(sK3) [avatar definition]
205. 11 | ~12 [avatar split clause 103,202,199]
210. 11 | 12 [avatar split clause 101,202,199]
214. 14 <=> wise(fred) [avatar definition]
216. ~wise(fred) <- (~14) [avatar component clause 214]
218. 15 <=> rich(fred) [avatar definition]
220. ~rich(fred) <- (~15) [avatar component clause 218]
222. 16 <=> rich(paul) [avatar definition]
224. ~rich(paul) <- (~16) [avatar component clause 222]
225. ~14 | ~15 | ~16 [avatar split clause 110,222,218,214]
291. 30 <=> creative(fred) [avatar definition]
293. ~creative(fred) <- (~30) [avatar component clause 291]
294. ~30 | 14 [avatar split clause 142,214,291]
322. patient(paul) <- (5) [resolution 106,172]
351. 39 <=> old(paul) [avatar definition]
353. old(paul) <- (39) [avatar component clause 351]
374. wise(X0) | creative(X0) <- (11) [resolution 111,200]
482. old(paul) | ~generous(paul) <- (5) [resolution 136,322]
489. old(paul) <- (5, 11) [subsumption resolution 482,200]
490. 39 | ~5 | ~11 [avatar split clause 489,199,171,351]
494. ~kind(paul) <- (39) [resolution 353,153]
498. $false <- (39) [subsumption resolution 494,151]
499. ~39 [avatar contradiction clause 498]
506. $false <- (7, ~16) [resolution 181,224]
507. ~7 | 16 [avatar contradiction clause 506]
510. $false <- (7, ~15) [subsumption resolution 220,181]
511. ~7 | 15 [avatar contradiction clause 510]
512. creative(fred) <- (11, ~14) [resolution 216,374]
514. $false <- (11, ~14, ~30) [subsumption resolution 512,293]
515. ~11 | 14 | 30 [avatar contradiction clause 514]
516. $false [avatar sat refutation 182,205,210,225,294,490,499,507,511,515]
% SZS output end Proof for 1062979044066078018290568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not humble is either not curious or old and vice versa.
Everyone who is brave is both quiet and humble and vice versa.
If someone is calm or funny then someone is either funny or generous and vice versa.
Everyone who is not wise or creative is wise or not happy and vice versa.
Everyone who is not brave or not tall is both happy and calm and vice versa.
If someone is not strong or humble then susan is not curious or not quiet and vice versa.
If alice is either not kind or quiet then fred is both not old and not tall and vice versa.
Everyone who is tall or not funny is either not rich or not old and vice versa.
If someone is not old then someone is patient and vice versa.
Everyone who is generous or old is rich or creative and vice versa.
Everyone who is both not generous and not quiet is both quiet and not humble and vice versa.
Everyone who is not happy or tall is either not quiet or not humble.
Everyone who is not wise or not curious is not humble and vice versa.
Everyone who is not strong or not generous is either generous or funny and vice versa.
If someone is either curious or old then someone is both not kind and funny.
If someone is curious then mary is either creative or not brave and vice versa.
Someone is either not wise or patient.
Someone is strong or not creative.
Someone is not kind or brave.
Someone is both rich and creative.
Someone is old or tall. | Susan is happy. | entailment | (![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)<~>old(X))))&
(![X]:(brave(X)<=>(quiet(X)&humble(X))))&
((?[X]:((calm(X)|funny(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((~wise(X)|creative(X))<=>(wise(X)|~happy(X))))&
(![X]:((~brave(X)|~tall(X))<=>(happy(X)&calm(X))))&
((?[X]:((~strong(X)|humble(X))))<=>((~curious(susan)|~quiet(susan))))&
(((~kind(alice)<~>quiet(alice)))<=>((~old(fred)&~tall(fred))))&
(![X]:((tall(X)|~funny(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|old(X))<=>(rich(X)|creative(X))))&
(![X]:((~generous(X)&~quiet(X))<=>(quiet(X)&~humble(X))))&
(![X]:((~happy(X)|tall(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((~wise(X)|~curious(X))<=>~humble(X)))&
(![X]:((~strong(X)|~generous(X))<=>(generous(X)<~>funny(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&funny(X)))))&
((?[X]:(curious(X)))<=>((creative(mary)<~>~brave(mary))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:((old(X)|tall(X)))) | happy(susan) | [
"p1",
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1572231770095352391654107
% SZS output start Proof for 1572231770095352391654107
2. ! [X0] : (brave(X0) <=> (humble(X0) & quiet(X0))) [input p1]
5. ! [X0] : ((~tall(X0) | ~brave(X0)) <=> (calm(X0) & happy(X0))) [input p4]
6. ? [X0] : (humble(X0) | ~strong(X0)) <=> (~quiet(susan) | ~curious(susan)) [input p5]
13. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> ~humble(X0)) [input p12]
22. ~happy(susan) [input hypothesis]
29. ! [X0] : ((brave(X0) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | ~brave(X0))) [nnf transformation 2]
30. ! [X0] : ((brave(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ~brave(X0))) [flattening 29]
38. ! [X0] : (((~tall(X0) | ~brave(X0)) | (~calm(X0) | ~happy(X0))) & ((calm(X0) & happy(X0)) | (tall(X0) & brave(X0)))) [nnf transformation 5]
39. ! [X0] : ((~tall(X0) | ~brave(X0) | ~calm(X0) | ~happy(X0)) & ((calm(X0) & happy(X0)) | (tall(X0) & brave(X0)))) [flattening 38]
40. (? [X0] : (humble(X0) | ~strong(X0)) | (quiet(susan) & curious(susan))) & ((~quiet(susan) | ~curious(susan)) | ! [X0] : (~humble(X0) & strong(X0))) [nnf transformation 6]
41. (? [X0] : (humble(X0) | ~strong(X0)) | (quiet(susan) & curious(susan))) & (~quiet(susan) | ~curious(susan) | ! [X0] : (~humble(X0) & strong(X0))) [flattening 40]
42. (? [X0] : (humble(X0) | ~strong(X0)) | (quiet(susan) & curious(susan))) & (~quiet(susan) | ~curious(susan) | ! [X1] : (~humble(X1) & strong(X1))) [rectify 41]
43. ? [X0] : (humble(X0) | ~strong(X0)) => (humble(sK2) | ~strong(sK2)) [choice axiom]
44. ((humble(sK2) | ~strong(sK2)) | (quiet(susan) & curious(susan))) & (~quiet(susan) | ~curious(susan) | ! [X1] : (~humble(X1) & strong(X1))) [skolemisation 42,43]
59. ! [X0] : (((~curious(X0) | ~wise(X0)) | humble(X0)) & (~humble(X0) | (curious(X0) & wise(X0)))) [nnf transformation 13]
60. ! [X0] : ((~curious(X0) | ~wise(X0) | humble(X0)) & (~humble(X0) | (curious(X0) & wise(X0)))) [flattening 59]
90. ~brave(X0) | quiet(X0) [cnf transformation 30]
91. ~brave(X0) | humble(X0) [cnf transformation 30]
103. happy(X0) | brave(X0) [cnf transformation 39]
109. ~quiet(susan) | ~curious(susan) | ~humble(X1) [cnf transformation 44]
139. ~humble(X0) | curious(X0) [cnf transformation 60]
162. ~happy(susan) [cnf transformation 22]
204. 9 <=> quiet(susan) [avatar definition]
217. 12 <=> curious(susan) [avatar definition]
222. 13 <=> ! [X1] : ~humble(X1) [avatar definition]
223. ~humble(X1) <- (13) [avatar component clause 222]
224. 13 | ~12 | ~9 [avatar split clause 109,204,217,222]
353. brave(susan) [resolution 103,162]
355. humble(susan) [resolution 353,91]
356. quiet(susan) [resolution 353,90]
357. 9 [avatar split clause 356,204]
360. curious(susan) [resolution 139,355]
363. 12 [avatar split clause 360,217]
364. $false <- (13) [resolution 223,355]
365. ~13 [avatar contradiction clause 364]
366. $false [avatar sat refutation 224,357,363,365]
% SZS output end Proof for 1572231770095352391654107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is happy or not wise then someone is curious or not old.
If someone is both not brave and not curious then alice is both kind and tall.
If lucy is either rich or not happy then someone is kind or tall and vice versa.
Everyone who is both rich and brave is strong.
Everyone who is funny or quiet is either not curious or calm and vice versa.
If someone is brave or quiet then paul is both not happy and not strong and vice versa.
Everyone who is either not tall or not curious is not generous and vice versa.
If someone is either not wise or tall then fred is either old or not brave and vice versa.
If john is either not patient or generous then lucy is either calm or generous.
If someone is kind then someone is both creative and not brave and vice versa.
Everyone who is not calm or old is curious and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is both not old and quiet is both wise and old and vice versa.
If mary is quiet then someone is either not rich or not creative and vice versa.
Everyone who is not funny or curious is either not creative or not strong.
If someone is brave or creative then someone is generous.
Mary is not calm.
Lucy is either generous or happy.
Alice is not wise or tall.
Alice is kind.
Susan is patient or not strong.
Susan is patient or not generous. | Mary is strong. | neutral | (((happy(paul)|~wise(paul)))=>(?[X]:((curious(X)|~old(X)))))&
((?[X]:((~brave(X)&~curious(X))))=>((kind(alice)&tall(alice))))&
(((rich(lucy)<~>~happy(lucy)))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((rich(X)&brave(X))=>strong(X)))&
(![X]:((funny(X)|quiet(X))<=>(~curious(X)<~>calm(X))))&
((?[X]:((brave(X)|quiet(X))))<=>((~happy(paul)&~strong(paul))))&
(![X]:((~tall(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:((~wise(X)<~>tall(X))))<=>((old(fred)<~>~brave(fred))))&
(((~patient(john)<~>generous(john)))=>((calm(lucy)<~>generous(lucy))))&
((?[X]:(kind(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((~calm(X)|old(X))<=>curious(X)))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~old(X)&quiet(X))<=>(wise(X)&old(X))))&
((quiet(mary))<=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((~funny(X)|curious(X))=>(~creative(X)<~>~strong(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:(generous(X))))&
(~calm(mary))&
((generous(lucy)<~>happy(lucy)))&
((~wise(alice)|tall(alice)))&
(kind(alice))&
((patient(susan)|~strong(susan)))&
((patient(susan)|~generous(susan))) | strong(mary) | [] | null | 0 |
Everyone who is not calm is either not curious or not humble and vice versa.
If mary is not rich then someone is curious or not humble.
Everyone who is both not rich and old is both wise and patient.
Everyone who is not happy or old is both not calm and curious and vice versa.
Everyone who is either humble or not generous is old.
If someone is both not calm and not quiet then someone is either not wise or not funny.
If someone is old or wise then someone is both not curious and not funny and vice versa.
Everyone who is not strong is not kind or old.
If alice is tall then john is not funny or curious and vice versa.
Everyone who is not brave or patient is either not calm or tall.
Everyone who is both not happy and not curious is not kind or not funny and vice versa.
If fred is not humble then mary is both kind and not old.
Everyone who is funny or not wise is not tall and vice versa.
If someone is not humble then someone is not old and vice versa.
Everyone who is either not calm or generous is both not patient and not creative.
If someone is either patient or not quiet then someone is either not strong or creative and vice versa.
Lucy is not curious.
John is not creative or humble.
Alice is both brave and not patient.
Someone is creative.
Someone is not calm or happy.
Alice is calm. | Mary is not calm. | neutral | (![X]:(~calm(X)<=>(~curious(X)<~>~humble(X))))&
((~rich(mary))=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~rich(X)&old(X))=>(wise(X)&patient(X))))&
(![X]:((~happy(X)|old(X))<=>(~calm(X)&curious(X))))&
(![X]:((humble(X)<~>~generous(X))=>old(X)))&
((?[X]:((~calm(X)&~quiet(X))))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~strong(X)=>(~kind(X)|old(X))))&
((tall(alice))<=>((~funny(john)|curious(john))))&
(![X]:((~brave(X)|patient(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)|~funny(X))))&
((~humble(fred))=>((kind(mary)&~old(mary))))&
(![X]:((funny(X)|~wise(X))<=>~tall(X)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(~curious(lucy))&
((~creative(john)|humble(john)))&
((brave(alice)&~patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)|happy(X))))&
(calm(alice)) | ~calm(mary) | [] | null | 0 |
If someone is not brave then someone is either not brave or not wise and vice versa. Everyone who is quiet or not calm is either brave or kind and vice versa. Everyone who is not rich or brave is not creative and vice versa. Everyone who is both not patient and not curious is kind or brave. If fred is both wise and not rich then someone is both quiet and old and vice versa. Everyone who is either patient or not happy is both not creative and not kind. Everyone who is creative or not old is either not generous or not quiet and vice versa. Everyone who is generous is both not curious and not creative and vice versa. If someone is not tall or not brave then lucy is not tall or curious and vice versa. If susan is not funny or strong then lucy is either kind or not brave. Everyone who is not kind is either not happy or not strong. Everyone who is funny is happy or tall. If someone is old or not wise then lucy is humble or not funny. If paul is either patient or funny then fred is not tall. Everyone who is either patient or tall is not happy and vice versa. If someone is old or humble then alice is not happy or not funny. Fred is either not strong or not wise. John is not curious. Mary is either wise or not happy. Lucy is not humble. Susan is not creative or humble. Someone is not creative. Someone is not funny or quiet. | John is happy. | neutral | ((?[X]:(~brave(X)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((quiet(X)|~calm(X))<=>(brave(X)<~>kind(X))))&
(![X]:((~rich(X)|brave(X))<=>~creative(X)))&
(![X]:((~patient(X)&~curious(X))=>(kind(X)|brave(X))))&
(((wise(fred)&~rich(fred)))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((patient(X)<~>~happy(X))=>(~creative(X)&~kind(X))))&
(![X]:((creative(X)|~old(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(~curious(X)&~creative(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>((~tall(lucy)|curious(lucy))))&
(((~funny(susan)|strong(susan)))=>((kind(lucy)<~>~brave(lucy))))&
(![X]:(~kind(X)=>(~happy(X)<~>~strong(X))))&
(![X]:(funny(X)=>(happy(X)|tall(X))))&
((?[X]:((old(X)|~wise(X))))=>((humble(lucy)|~funny(lucy))))&
(((patient(paul)<~>funny(paul)))=>(~tall(fred)))&
(![X]:((patient(X)<~>tall(X))<=>~happy(X)))&
((?[X]:((old(X)|humble(X))))=>((~happy(alice)|~funny(alice))))&
((~strong(fred)<~>~wise(fred)))&
(~curious(john))&
((wise(mary)<~>~happy(mary)))&
(~humble(lucy))&
((~creative(susan)|humble(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)|quiet(X)))) | happy(john) | [] | null | 0 |
If someone is not kind or not creative then lucy is not rich and vice versa.
If fred is happy then someone is both not curious and kind and vice versa.
Everyone who is both not rich and not wise is not rich or humble and vice versa.
If paul is not curious then john is both wise and rich and vice versa.
If someone is not patient then someone is not quiet and vice versa.
Everyone who is creative or generous is both quiet and not calm.
Everyone who is creative is old or not patient.
Everyone who is both strong and kind is not wise.
If mary is rich then fred is wise and vice versa.
If someone is not calm or funny then susan is either generous or not quiet.
If alice is both kind and not patient then someone is not generous or not rich.
Everyone who is both not happy and brave is either not humble or rich and vice versa.
Everyone who is both not curious and not rich is curious or not generous and vice versa.
If susan is not calm then john is both not curious and wise and vice versa.
Everyone who is not tall or not happy is either patient or not generous and vice versa.
Everyone who is both not tall and not calm is not quiet or funny.
Someone is both not funny and not wise.
Alice is not patient or strong.
Someone is not generous or patient.
Susan is either quiet or not strong.
Lucy is wise.
Someone is either tall or old.
John is patient or not quiet.
Someone is not wise or quiet. | Alice is not patient. | contradiction | ((?[X]:((~kind(X)|~creative(X))))<=>(~rich(lucy)))&
((happy(fred))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((~rich(X)&~wise(X))<=>(~rich(X)|humble(X))))&
((~curious(paul))<=>((wise(john)&rich(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|generous(X))=>(quiet(X)&~calm(X))))&
(![X]:(creative(X)=>(old(X)|~patient(X))))&
(![X]:((strong(X)&kind(X))=>~wise(X)))&
((rich(mary))<=>(wise(fred)))&
((?[X]:((~calm(X)|funny(X))))=>((generous(susan)<~>~quiet(susan))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(![X]:((~tall(X)|~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~tall(X)&~calm(X))=>(~quiet(X)|funny(X))))&
(?[X]:((~funny(X)&~wise(X))))&
((~patient(alice)|strong(alice)))&
(?[X]:((~generous(X)|patient(X))))&
((quiet(susan)<~>~strong(susan)))&
(wise(lucy))&
(?[X]:((tall(X)<~>old(X))))&
((patient(john)|~quiet(john)))&
(?[X]:((~wise(X)|quiet(X)))) | ~patient(alice) | [
"p0",
"p2",
"p4",
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2759669405631705038665186
% SZS output start Proof for 2759669405631705038665186
1. ? [X0] : (~creative(X0) | ~kind(X0)) <=> ~rich(lucy) [input p0]
3. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (humble(X0) | ~rich(X0))) [input p2]
5. ? [X0] : ~patient(X0) <=> ? [X0] : ~quiet(X0) [input p4]
6. ! [X0] : ((generous(X0) | creative(X0)) => (~calm(X0) & quiet(X0))) [input p5]
21. wise(lucy) [input p20]
25. ~patient(alice) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : ~quiet(X1) [rectify 5]
27. ! [X0] : ((~calm(X0) & quiet(X0)) | (~generous(X0) & ~creative(X0))) [ennf transformation 6]
37. (? [X0] : (~creative(X0) | ~kind(X0)) | rich(lucy)) & (~rich(lucy) | ! [X0] : (creative(X0) & kind(X0))) [nnf transformation 1]
38. (? [X0] : (~creative(X0) | ~kind(X0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (creative(X1) & kind(X1))) [rectify 37]
39. ? [X0] : (~creative(X0) | ~kind(X0)) => (~creative(sK0) | ~kind(sK0)) [choice axiom]
40. ((~creative(sK0) | ~kind(sK0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (creative(X1) & kind(X1))) [skolemisation 38,39]
45. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~humble(X0) & rich(X0))) & ((humble(X0) | ~rich(X0)) | (wise(X0) | rich(X0)))) [nnf transformation 3]
46. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~humble(X0) & rich(X0))) & (humble(X0) | ~rich(X0) | wise(X0) | rich(X0))) [flattening 45]
49. (? [X0] : ~patient(X0) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : patient(X0)) [nnf transformation 26]
50. (? [X0] : ~patient(X0) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : patient(X3)) [rectify 49]
51. ? [X0] : ~patient(X0) => ~patient(sK2) [choice axiom]
52. ? [X2] : ~quiet(X2) => ~quiet(sK3) [choice axiom]
53. (~patient(sK2) | ! [X1] : quiet(X1)) & (~quiet(sK3) | ! [X3] : patient(X3)) [skolemisation 50,52,51]
77. ~rich(lucy) | creative(X1) [cnf transformation 40]
85. ~wise(X0) | rich(X0) [cnf transformation 46]
90. ~quiet(sK3) | patient(X3) [cnf transformation 53]
92. ~creative(X0) | quiet(X0) [cnf transformation 27]
132. wise(lucy) [cnf transformation 21]
137. ~patient(alice) [cnf transformation 25]
141. 1 <=> rich(lucy) [avatar definition]
154. 4 <=> ! [X1] : creative(X1) [avatar definition]
155. creative(X1) <- (4) [avatar component clause 154]
156. 4 | ~1 [avatar split clause 77,141,154]
196. 13 <=> ! [X1] : quiet(X1) [avatar definition]
197. quiet(X1) <- (13) [avatar component clause 196]
204. 15 <=> ! [X3] : patient(X3) [avatar definition]
205. patient(X3) <- (15) [avatar component clause 204]
207. 16 <=> quiet(sK3) [avatar definition]
209. ~quiet(sK3) <- (~16) [avatar component clause 207]
210. 15 | ~16 [avatar split clause 90,207,204]
242. 24 <=> patient(alice) [avatar definition]
243. ~patient(alice) <- (~24) [avatar component clause 242]
312. ~24 [avatar split clause 137,242]
314. rich(lucy) [resolution 85,132]
318. 1 [avatar split clause 314,141]
323. quiet(X0) <- (4) [resolution 92,155]
324. 13 | ~4 [avatar split clause 323,154,196]
325. $false <- (13, ~16) [resolution 197,209]
330. ~13 | 16 [avatar contradiction clause 325]
332. $false <- (15, ~24) [resolution 205,243]
333. ~15 | 24 [avatar contradiction clause 332]
335. $false [avatar sat refutation 156,210,312,318,324,330,333]
% SZS output end Proof for 2759669405631705038665186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or happy is not wise or not generous and vice versa.
If someone is either rich or not rich then mary is both funny and not quiet.
If someone is both not creative and wise then someone is either creative or patient.
If someone is both old and rich then someone is rich or humble.
If lucy is either not quiet or old then lucy is not brave or brave.
If susan is not patient or generous then someone is both not strong and not funny and vice versa.
Everyone who is both not quiet and not humble is not rich or not calm and vice versa.
Everyone who is curious or patient is either not funny or not happy.
Everyone who is either rich or not strong is either not curious or tall.
Everyone who is either not rich or strong is either not funny or not rich and vice versa.
If lucy is strong or not brave then susan is either not strong or not happy.
If paul is both not kind and not calm then someone is creative and vice versa.
Everyone who is wise or generous is rich or creative and vice versa.
Everyone who is either not creative or not strong is either calm or not calm.
Everyone who is strong or tall is curious or not curious.
Everyone who is either not creative or not funny is not happy or generous and vice versa.
Someone is both creative and humble.
Someone is both not rich and patient.
Someone is either not curious or not happy.
Someone is strong.
Someone is both quiet and not strong.
Someone is not kind or tall.
Mary is not wise or curious.
Lucy is rich or generous. | Lucy is brave. | entailment | (![X]:((~curious(X)|happy(X))<=>(~wise(X)|~generous(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>((funny(mary)&~quiet(mary))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((creative(X)<~>patient(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((rich(X)|humble(X)))))&
(((~quiet(lucy)<~>old(lucy)))=>((~brave(lucy)|brave(lucy))))&
(((~patient(susan)|generous(susan)))<=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(~rich(X)|~calm(X))))&
(![X]:((curious(X)|patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~strong(X))=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~funny(X)<~>~rich(X))))&
(((strong(lucy)|~brave(lucy)))=>((~strong(susan)<~>~happy(susan))))&
(((~kind(paul)&~calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)|generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(![X]:((strong(X)|tall(X))=>(curious(X)|~curious(X))))&
(![X]:((~creative(X)<~>~funny(X))<=>(~happy(X)|generous(X))))&
(?[X]:((creative(X)&humble(X))))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)&~strong(X))))&
(?[X]:((~kind(X)|tall(X))))&
((~wise(mary)|curious(mary)))&
((rich(lucy)|generous(lucy))) | brave(lucy) | [
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5062454434353395357212088
% SZS output start Proof for 5062454434353395357212088
6. (generous(susan) | ~patient(susan)) <=> ? [X0] : (~funny(X0) & ~strong(X0)) [input p5]
8. ! [X0] : ((patient(X0) | curious(X0)) => (~funny(X0) <~> ~happy(X0))) [input p7]
10. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (~funny(X0) <~> ~rich(X0))) [input p9]
11. (~brave(lucy) | strong(lucy)) => (~strong(susan) <~> ~happy(susan)) [input p10]
25. ~brave(lucy) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~happy(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 8]
35. (~strong(susan) <~> ~happy(susan)) | (brave(lucy) & ~strong(lucy)) [ennf transformation 11]
50. ((generous(susan) | ~patient(susan)) | ! [X0] : (funny(X0) | strong(X0))) & (? [X0] : (~funny(X0) & ~strong(X0)) | (~generous(susan) & patient(susan))) [nnf transformation 6]
51. (generous(susan) | ~patient(susan) | ! [X0] : (funny(X0) | strong(X0))) & (? [X0] : (~funny(X0) & ~strong(X0)) | (~generous(susan) & patient(susan))) [flattening 50]
52. (generous(susan) | ~patient(susan) | ! [X0] : (funny(X0) | strong(X0))) & (? [X1] : (~funny(X1) & ~strong(X1)) | (~generous(susan) & patient(susan))) [rectify 51]
53. ? [X1] : (~funny(X1) & ~strong(X1)) => (~funny(sK2) & ~strong(sK2)) [choice axiom]
54. (generous(susan) | ~patient(susan) | ! [X0] : (funny(X0) | strong(X0))) & ((~funny(sK2) & ~strong(sK2)) | (~generous(susan) & patient(susan))) [skolemisation 52,53]
57. ! [X0] : (((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~patient(X0) & ~curious(X0))) [nnf transformation 33]
59. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) & (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 10]
60. ((happy(susan) | strong(susan)) & (~happy(susan) | ~strong(susan))) | (brave(lucy) & ~strong(lucy)) [nnf transformation 35]
97. ~strong(sK2) | patient(susan) [cnf transformation 54]
99. ~funny(sK2) | patient(susan) [cnf transformation 54]
108. ~patient(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 57]
110. ~patient(X0) | funny(X0) | happy(X0) [cnf transformation 57]
116. ~rich(X0) | ~funny(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 59]
117. rich(X0) | funny(X0) | strong(X0) | rich(X0) [cnf transformation 59]
119. strong(X0) | ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 59]
122. ~strong(X0) | rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 59]
124. ~happy(susan) | ~strong(susan) | brave(lucy) [cnf transformation 60]
126. happy(susan) | strong(susan) | brave(lucy) [cnf transformation 60]
158. ~brave(lucy) [cnf transformation 25]
159. ~rich(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 116]
160. rich(X0) | funny(X0) | strong(X0) [duplicate literal removal 117]
161. strong(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 119]
162. ~strong(X0) | rich(X0) | ~funny(X0) [duplicate literal removal 122]
211. 11 <=> ! [X0] : (funny(X0) | strong(X0)) [avatar definition]
212. strong(X0) | funny(X0) <- (11) [avatar component clause 211]
214. 12 <=> patient(susan) [avatar definition]
215. patient(susan) <- (12) [avatar component clause 214]
223. 14 <=> funny(sK2) [avatar definition]
227. 12 | ~14 [avatar split clause 99,223,214]
229. 15 <=> strong(sK2) [avatar definition]
231. ~strong(sK2) <- (~15) [avatar component clause 229]
233. 12 | ~15 [avatar split clause 97,229,214]
234. funny(X0) | strong(X0) [subsumption resolution 160,161]
235. 11 [avatar split clause 234,211]
236. ~strong(X0) | ~funny(X0) [subsumption resolution 159,162]
238. 16 <=> brave(lucy) [avatar definition]
242. 17 <=> strong(susan) [avatar definition]
243. ~strong(susan) <- (~17) [avatar component clause 242]
244. strong(susan) <- (17) [avatar component clause 242]
246. 18 <=> happy(susan) [avatar definition]
247. ~happy(susan) <- (~18) [avatar component clause 246]
249. 16 | 17 | 18 [avatar split clause 126,246,242,238]
255. 16 | ~17 | ~18 [avatar split clause 124,246,242,238]
312. ~16 [avatar split clause 158,238]
321. funny(sK2) <- (11, ~15) [resolution 212,231]
324. 14 | ~11 | 15 [avatar split clause 321,229,211,223]
326. ~funny(susan) <- (17) [resolution 236,244]
362. ~funny(susan) | ~happy(susan) <- (12) [resolution 108,215]
375. funny(susan) | happy(susan) <- (12) [resolution 110,215]
378. happy(susan) <- (12, 17) [subsumption resolution 375,326]
379. $false <- (12, 17, ~18) [subsumption resolution 378,247]
380. ~12 | ~17 | 18 [avatar contradiction clause 379]
382. 39 <=> funny(susan) [avatar definition]
383. ~funny(susan) <- (~39) [avatar component clause 382]
386. ~18 | ~39 | ~12 [avatar split clause 362,214,382,246]
390. funny(susan) <- (11, ~17) [resolution 243,212]
391. $false <- (11, ~17, ~39) [subsumption resolution 390,383]
392. ~11 | 17 | 39 [avatar contradiction clause 391]
393. $false [avatar sat refutation 227,233,235,249,255,312,324,380,386,392]
% SZS output end Proof for 5062454434353395357212088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not strong is not strong or tall and vice versa.
If john is not rich then someone is quiet or old and vice versa.
If lucy is not strong or not wise then mary is either not happy or creative.
Everyone who is not tall is wise and vice versa.
Everyone who is not brave is both not rich and not patient.
If alice is not creative or tall then fred is either creative or patient and vice versa.
If mary is humble or not brave then someone is both not kind and not wise.
If susan is either happy or old then susan is either not funny or not creative and vice versa.
If paul is curious then someone is generous or not happy and vice versa.
Everyone who is not happy is not creative and vice versa.
If someone is wise then someone is not brave and vice versa.
If someone is both not kind and not funny then susan is either old or generous and vice versa.
If lucy is both not humble and not quiet then susan is both not strong and not patient.
If paul is either not wise or not tall then john is not curious and vice versa.
Everyone who is both not brave and calm is generous or not brave and vice versa.
Everyone who is not humble or not calm is either humble or not patient and vice versa.
Someone is either old or not calm.
Someone is both strong and calm.
Someone is brave or not humble.
Paul is not kind or tall.
Lucy is not strong or not humble.
Mary is both not humble and not wise.
Paul is both patient and not calm.
Someone is either curious or happy. | Paul is not humble. | contradiction | (![X]:((~calm(X)|~strong(X))<=>(~strong(X)|tall(X))))&
((~rich(john))<=>(?[X]:((quiet(X)|old(X)))))&
(((~strong(lucy)|~wise(lucy)))=>((~happy(mary)<~>creative(mary))))&
(![X]:(~tall(X)<=>wise(X)))&
(![X]:(~brave(X)=>(~rich(X)&~patient(X))))&
(((~creative(alice)|tall(alice)))<=>((creative(fred)<~>patient(fred))))&
(((humble(mary)|~brave(mary)))=>(?[X]:((~kind(X)&~wise(X)))))&
(((happy(susan)<~>old(susan)))<=>((~funny(susan)<~>~creative(susan))))&
((curious(paul))<=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~happy(X)<=>~creative(X)))&
((?[X]:(wise(X)))<=>(?[X]:(~brave(X))))&
((?[X]:((~kind(X)&~funny(X))))<=>((old(susan)<~>generous(susan))))&
(((~humble(lucy)&~quiet(lucy)))=>((~strong(susan)&~patient(susan))))&
(((~wise(paul)<~>~tall(paul)))<=>(~curious(john)))&
(![X]:((~brave(X)&calm(X))<=>(generous(X)|~brave(X))))&
(![X]:((~humble(X)|~calm(X))<=>(humble(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((brave(X)|~humble(X))))&
((~kind(paul)|tall(paul)))&
((~strong(lucy)|~humble(lucy)))&
((~humble(mary)&~wise(mary)))&
((patient(paul)&~calm(paul)))&
(?[X]:((curious(X)<~>happy(X)))) | ~humble(paul) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1294653388421436840522563
% SZS output start Proof for 1294653388421436840522563
16. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (humble(X0) <~> ~patient(X0))) [input p15]
23. ~calm(paul) & patient(paul) [input p22]
25. ~humble(paul) [input hypothesis]
62. ! [X0] : (((~calm(X0) | ~humble(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (calm(X0) & humble(X0)))) [nnf transformation 16]
63. ! [X0] : ((~calm(X0) | ~humble(X0) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (calm(X0) & humble(X0)))) [flattening 62]
131. ~patient(X0) | humble(X0) | humble(X0) [cnf transformation 63]
146. patient(paul) [cnf transformation 23]
150. ~humble(paul) [cnf transformation 25]
151. ~patient(X0) | humble(X0) [duplicate literal removal 131]
400. humble(paul) [resolution 151,146]
402. $false [subsumption resolution 400,150]
% SZS output end Proof for 1294653388421436840522563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both rich and happy and vice versa.
If someone is rich then someone is both not generous and not patient.
Everyone who is not rich or not patient is both creative and not funny and vice versa.
Everyone who is either not curious or calm is happy and vice versa.
Everyone who is not curious is not happy or not funny and vice versa.
Everyone who is not quiet or happy is either curious or not patient.
If susan is either curious or kind then alice is either not rich or quiet and vice versa.
Everyone who is not kind is not quiet or humble.
If someone is not brave or curious then john is either not creative or not calm.
If paul is either creative or not brave then someone is either not calm or not old.
If someone is either not wise or not old then someone is rich or not calm.
If paul is not strong or tall then someone is happy.
If someone is both not strong and not generous then lucy is both not quiet and not humble.
Everyone who is both not wise and creative is both wise and not old and vice versa.
If someone is creative or not humble then fred is not happy or old.
Everyone who is either not tall or not quiet is generous or not tall.
Paul is both not old and not kind.
Someone is both not generous and not calm.
Susan is not happy.
Someone is not patient or not quiet.
Fred is both calm and not humble.
Someone is either old or generous.
Mary is either not rich or not generous.
Susan is not tall or patient. | Fred is patient. | entailment | (![X]:(~humble(X)<=>(rich(X)&happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~rich(X)|~patient(X))<=>(creative(X)&~funny(X))))&
(![X]:((~curious(X)<~>calm(X))<=>happy(X)))&
(![X]:(~curious(X)<=>(~happy(X)|~funny(X))))&
(![X]:((~quiet(X)|happy(X))=>(curious(X)<~>~patient(X))))&
(((curious(susan)<~>kind(susan)))<=>((~rich(alice)<~>quiet(alice))))&
(![X]:(~kind(X)=>(~quiet(X)|humble(X))))&
((?[X]:((~brave(X)|curious(X))))=>((~creative(john)<~>~calm(john))))&
(((creative(paul)<~>~brave(paul)))=>(?[X]:((~calm(X)<~>~old(X)))))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:((rich(X)|~calm(X)))))&
(((~strong(paul)|tall(paul)))=>(?[X]:(happy(X))))&
((?[X]:((~strong(X)&~generous(X))))=>((~quiet(lucy)&~humble(lucy))))&
(![X]:((~wise(X)&creative(X))<=>(wise(X)&~old(X))))&
((?[X]:((creative(X)|~humble(X))))=>((~happy(fred)|old(fred))))&
(![X]:((~tall(X)<~>~quiet(X))=>(generous(X)|~tall(X))))&
((~old(paul)&~kind(paul)))&
(?[X]:((~generous(X)&~calm(X))))&
(~happy(susan))&
(?[X]:((~patient(X)|~quiet(X))))&
((calm(fred)&~humble(fred)))&
(?[X]:((old(X)<~>generous(X))))&
((~rich(mary)<~>~generous(mary)))&
((~tall(susan)|patient(susan))) | patient(fred) | [
"p0",
"p3",
"p4",
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7399262722734439166327068
% SZS output start Proof for 7399262722734439166327068
1. ! [X0] : (~humble(X0) <=> (happy(X0) & rich(X0))) [input p0]
4. ! [X0] : ((~curious(X0) <~> calm(X0)) <=> happy(X0)) [input p3]
5. ! [X0] : (~curious(X0) <=> (~funny(X0) | ~happy(X0))) [input p4]
6. ! [X0] : ((happy(X0) | ~quiet(X0)) => (curious(X0) <~> ~patient(X0))) [input p5]
21. ~humble(fred) & calm(fred) [input p20]
25. ~patient(fred) [input hypothesis]
31. ! [X0] : ((curious(X0) <~> ~patient(X0)) | (~happy(X0) & quiet(X0))) [ennf transformation 6]
42. ! [X0] : ((~humble(X0) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | humble(X0))) [nnf transformation 1]
43. ! [X0] : ((~humble(X0) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | humble(X0))) [flattening 42]
49. ! [X0] : ((((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ~happy(X0)) & (happy(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0))))) [nnf transformation 4]
50. ! [X0] : ((~curious(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | curious(X0))) [nnf transformation 5]
51. ! [X0] : ((~curious(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | curious(X0))) [flattening 50]
52. ! [X0] : (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (~happy(X0) & quiet(X0))) [nnf transformation 31]
76. happy(X0) | humble(X0) [cnf transformation 43]
88. ~calm(X0) | curious(X0) | ~happy(X0) [cnf transformation 49]
90. ~curious(X0) | happy(X0) [cnf transformation 51]
95. patient(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 52]
130. calm(fred) [cnf transformation 21]
131. ~humble(fred) [cnf transformation 21]
137. ~patient(fred) [cnf transformation 25]
154. ~curious(X0) | patient(X0) [subsumption resolution 95,90]
247. 23 <=> happy(fred) [avatar definition]
248. happy(fred) <- (23) [avatar component clause 247]
249. ~happy(fred) <- (~23) [avatar component clause 247]
299. humble(fred) <- (~23) [resolution 76,249]
300. $false <- (~23) [subsumption resolution 299,131]
301. 23 [avatar contradiction clause 300]
347. curious(fred) | ~happy(fred) [resolution 88,130]
350. curious(fred) <- (23) [subsumption resolution 347,248]
352. patient(fred) <- (23) [resolution 350,154]
355. $false <- (23) [subsumption resolution 352,137]
356. ~23 [avatar contradiction clause 355]
357. $false [avatar sat refutation 301,356]
% SZS output end Proof for 7399262722734439166327068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or patient is both not generous and old and vice versa.
Everyone who is not quiet or not wise is both not kind and quiet and vice versa.
Everyone who is either rich or happy is not strong and vice versa.
If mary is wise or creative then fred is both curious and not curious and vice versa.
Everyone who is not happy or kind is not creative or not happy and vice versa.
If someone is not rich or happy then john is both not old and patient and vice versa.
Everyone who is both humble and not happy is either not creative or brave and vice versa.
Everyone who is both brave and tall is either not strong or kind.
Everyone who is both curious and brave is not patient and vice versa.
If someone is both calm and not old then john is rich or not brave.
Everyone who is either curious or brave is not happy and vice versa.
Everyone who is both wise and not old is either generous or not quiet and vice versa.
Everyone who is strong is both patient and not generous.
Everyone who is happy is either not creative or not curious.
Everyone who is not calm is both old and brave.
Everyone who is either humble or calm is both happy and quiet.
John is rich or not happy.
Someone is both not calm and not funny.
Lucy is not brave.
Someone is either brave or not tall.
Someone is not wise. | John is not patient. | contradiction | (![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(![X]:((humble(X)<~>calm(X))=>(happy(X)&quiet(X))))&
((rich(john)|~happy(john)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | ~patient(john) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 660231303561047022314797
% SZS output start Proof for 660231303561047022314797
1. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p0]
6. ? [X0] : (happy(X0) | ~rich(X0)) <=> (patient(john) & ~old(john)) [input p5]
9. ! [X0] : ((brave(X0) & curious(X0)) <=> ~patient(X0)) [input p8]
11. ! [X0] : ((curious(X0) <~> brave(X0)) <=> ~happy(X0)) [input p10]
22. ~patient(john) [input hypothesis]
32. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 1]
33. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 32]
41. (? [X0] : (happy(X0) | ~rich(X0)) | (~patient(john) | old(john))) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 6]
42. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 41]
43. (? [X0] : (happy(X0) | ~rich(X0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 42]
44. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
45. ((happy(sK0) | ~rich(sK0)) | ~patient(john) | old(john)) & ((patient(john) & ~old(john)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 43,44]
49. ! [X0] : (((brave(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) | ~curious(X0)))) [nnf transformation 9]
50. ! [X0] : (((brave(X0) & curious(X0)) | patient(X0)) & (~patient(X0) | ~brave(X0) | ~curious(X0))) [flattening 49]
51. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | happy(X0)) & (~happy(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 11]
65. old(X0) | old(X0) [cnf transformation 33]
87. ~old(john) | ~happy(X1) [cnf transformation 45]
100. curious(X0) | patient(X0) [cnf transformation 50]
101. brave(X0) | patient(X0) [cnf transformation 50]
106. ~brave(X0) | ~curious(X0) | happy(X0) [cnf transformation 51]
129. ~patient(john) [cnf transformation 22]
132. old(X0) [duplicate literal removal 65]
151. 4 <=> ! [X1] : ~happy(X1) [avatar definition]
152. ~happy(X1) <- (4) [avatar component clause 151]
154. 5 <=> patient(john) [avatar definition]
155. ~patient(john) <- (~5) [avatar component clause 154]
162. ~happy(X1) [subsumption resolution 87,132]
163. 4 [avatar split clause 162,151]
187. ~5 [avatar split clause 129,154]
280. ~curious(X2) | happy(X2) | patient(X2) [resolution 106,101]
285. ~curious(X2) | patient(X2) <- (4) [subsumption resolution 280,152]
286. patient(X2) <- (4) [subsumption resolution 285,100]
297. $false <- (4, ~5) [resolution 286,155]
301. ~4 | 5 [avatar contradiction clause 297]
302. $false [avatar sat refutation 163,187,301]
% SZS output end Proof for 660231303561047022314797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or wise is not tall or rich.
Everyone who is either not wise or not funny is old and vice versa.
If mary is either not strong or not tall then someone is either not calm or not strong and vice versa.
Everyone who is strong is either not old or humble.
Everyone who is not creative or not humble is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
If someone is rich then someone is both happy and funny and vice versa.
Someone is both not calm and not strong.
Susan is not tall.
Lucy is either rich or not humble. | Mary is humble. | contradiction | (![X]:((~generous(X)<~>wise(X))=>(~tall(X)|rich(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>old(X)))&
(((~strong(mary)<~>~tall(mary)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
(?[X]:((~calm(X)&~strong(X))))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy))) | humble(mary) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 818214195496348402529870
% SZS output start Proof for 818214195496348402529870
8. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (humble(X0) <~> ~funny(X0))) [input p12]
20. humble(mary) [input hypothesis]
36. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 8]
37. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 36]
40. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 10]
41. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 40]
46. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~creative(X0) | rich(X0)))) [nnf transformation 13]
47. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~creative(X0) | rich(X0))) [flattening 46]
84. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 37]
85. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 37]
95. funny(X0) | funny(X0) [cnf transformation 41]
107. creative(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 47]
123. humble(mary) [cnf transformation 20]
125. funny(X0) [duplicate literal removal 95]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 84]
127. ~creative(X0) | strong(X0) [duplicate literal removal 85]
161. ~creative(X0) [subsumption resolution 126,127]
186. ~funny(X0) | ~humble(X0) [subsumption resolution 107,161]
187. ~humble(X0) [subsumption resolution 186,125]
202. $false [subsumption resolution 123,187]
% SZS output end Proof for 818214195496348402529870
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is not humble or not patient and vice versa. Everyone who is not brave or creative is creative and vice versa. Everyone who is quiet or not humble is wise. If mary is either kind or brave then fred is both generous and brave and vice versa. If fred is either not brave or not wise then fred is old or not quiet. If someone is calm or not curious then someone is either not humble or not wise and vice versa. If someone is either not strong or not humble then john is both calm and old and vice versa. If someone is either not creative or not tall then lucy is old. Everyone who is not quiet is either tall or patient. If someone is not happy or not rich then someone is quiet or not humble and vice versa. Everyone who is either not wise or calm is wise and vice versa. Everyone who is both generous and not patient is both wise and not tall and vice versa. If susan is happy then fred is old or kind. If someone is generous then someone is not brave and vice versa. Everyone who is humble or curious is either creative or not generous. Everyone who is curious or not creative is both not happy and tall. Someone is either rich or old. Fred is not kind. Fred is both calm and not brave. John is not patient or patient. John is creative or not brave. Fred is not creative or not old. Lucy is creative. Lucy is not strong. | Susan is not quiet. | neutral | ((?[X]:(~happy(X)))<=>(?[X]:((~humble(X)|~patient(X)))))&
(![X]:((~brave(X)|creative(X))<=>creative(X)))&
(![X]:((quiet(X)|~humble(X))=>wise(X)))&
(((kind(mary)<~>brave(mary)))<=>((generous(fred)&brave(fred))))&
(((~brave(fred)<~>~wise(fred)))=>((old(fred)|~quiet(fred))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:((~humble(X)<~>~wise(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((calm(john)&old(john))))&
((?[X]:((~creative(X)<~>~tall(X))))=>(old(lucy)))&
(![X]:(~quiet(X)=>(tall(X)<~>patient(X))))&
((?[X]:((~happy(X)|~rich(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
(![X]:((~wise(X)<~>calm(X))<=>wise(X)))&
(![X]:((generous(X)&~patient(X))<=>(wise(X)&~tall(X))))&
((happy(susan))=>((old(fred)|kind(fred))))&
((?[X]:(generous(X)))<=>(?[X]:(~brave(X))))&
(![X]:((humble(X)|curious(X))=>(creative(X)<~>~generous(X))))&
(![X]:((curious(X)|~creative(X))=>(~happy(X)&tall(X))))&
(?[X]:((rich(X)<~>old(X))))&
(~kind(fred))&
((calm(fred)&~brave(fred)))&
((~patient(john)|patient(john)))&
((creative(john)|~brave(john)))&
((~creative(fred)|~old(fred)))&
(creative(lucy))&
(~strong(lucy)) | ~quiet(susan) | [] | null | 0 |
If lucy is either rich or not quiet then someone is both funny and not old. If someone is both not creative and not rich then someone is brave or tall. If someone is kind or strong then susan is not brave and vice versa. Everyone who is both not strong and quiet is either not tall or not curious. If susan is both not happy and funny then someone is curious and vice versa. Everyone who is not old or not generous is both not creative and calm. If someone is both not quiet and not wise then someone is tall or quiet. Everyone who is both tall and not curious is not calm. Everyone who is either not tall or happy is not strong or humble. Everyone who is not happy is both rich and not curious. If someone is not strong or kind then mary is not generous. Everyone who is creative or rich is both not old and brave and vice versa. If paul is calm or not kind then someone is both creative and kind. If lucy is both not happy and wise then someone is either patient or not humble. If someone is both humble and happy then someone is not creative and vice versa. Everyone who is happy or creative is either not rich or not happy. Someone is rich or generous. Someone is both not curious and not happy. Lucy is either rich or not rich. Mary is not wise. Someone is both not rich and not wise. Paul is curious or not brave. Lucy is both not rich and not quiet. Someone is not funny or old. | Lucy is curious. | contradiction | (((rich(lucy)<~>~quiet(lucy)))=>(?[X]:((funny(X)&~old(X)))))&
((?[X]:((~creative(X)&~rich(X))))=>(?[X]:((brave(X)|tall(X)))))&
((?[X]:((kind(X)|strong(X))))<=>(~brave(susan)))&
(![X]:((~strong(X)&quiet(X))=>(~tall(X)<~>~curious(X))))&
(((~happy(susan)&funny(susan)))<=>(?[X]:(curious(X))))&
(![X]:((~old(X)|~generous(X))=>(~creative(X)&calm(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((tall(X)&~curious(X))=>~calm(X)))&
(![X]:((~tall(X)<~>happy(X))=>(~strong(X)|humble(X))))&
(![X]:(~happy(X)=>(rich(X)&~curious(X))))&
((?[X]:((~strong(X)|kind(X))))=>(~generous(mary)))&
(![X]:((creative(X)|rich(X))<=>(~old(X)&brave(X))))&
(((calm(paul)|~kind(paul)))=>(?[X]:((creative(X)&kind(X)))))&
(((~happy(lucy)&wise(lucy)))=>(?[X]:((patient(X)<~>~humble(X)))))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:((happy(X)|creative(X))=>(~rich(X)<~>~happy(X))))&
(?[X]:((rich(X)|generous(X))))&
(?[X]:((~curious(X)&~happy(X))))&
((rich(lucy)<~>~rich(lucy)))&
(~wise(mary))&
(?[X]:((~rich(X)&~wise(X))))&
((curious(paul)|~brave(paul)))&
((~rich(lucy)&~quiet(lucy)))&
(?[X]:((~funny(X)|old(X)))) | curious(lucy) | [
"p2",
"p4",
"p5",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3930464758113387558788050
% SZS output start Proof for 3930464758113387558788050
3. ? [X0] : (strong(X0) | kind(X0)) <=> ~brave(susan) [input p2]
5. (funny(susan) & ~happy(susan)) <=> ? [X0] : curious(X0) [input p4]
6. ! [X0] : ((~generous(X0) | ~old(X0)) => (calm(X0) & ~creative(X0))) [input p5]
10. ! [X0] : (~happy(X0) => (~curious(X0) & rich(X0))) [input p9]
12. ! [X0] : ((rich(X0) | creative(X0)) <=> (brave(X0) & ~old(X0))) [input p11]
13. (~kind(paul) | calm(paul)) => ? [X0] : (kind(X0) & creative(X0)) [input p12]
25. curious(lucy) [input hypothesis]
33. ! [X0] : ((calm(X0) & ~creative(X0)) | (generous(X0) & old(X0))) [ennf transformation 6]
39. ! [X0] : ((~curious(X0) & rich(X0)) | happy(X0)) [ennf transformation 10]
41. ? [X0] : (kind(X0) & creative(X0)) | (kind(paul) & ~calm(paul)) [ennf transformation 13]
51. (? [X0] : (strong(X0) | kind(X0)) | brave(susan)) & (~brave(susan) | ! [X0] : (~strong(X0) & ~kind(X0))) [nnf transformation 3]
52. (? [X0] : (strong(X0) | kind(X0)) | brave(susan)) & (~brave(susan) | ! [X1] : (~strong(X1) & ~kind(X1))) [rectify 51]
53. ? [X0] : (strong(X0) | kind(X0)) => (strong(sK2) | kind(sK2)) [choice axiom]
54. ((strong(sK2) | kind(sK2)) | brave(susan)) & (~brave(susan) | ! [X1] : (~strong(X1) & ~kind(X1))) [skolemisation 52,53]
56. ((funny(susan) & ~happy(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~funny(susan) | happy(susan))) [nnf transformation 5]
57. ((funny(susan) & ~happy(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~funny(susan) | happy(susan)) [flattening 56]
58. ((funny(susan) & ~happy(susan)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~funny(susan) | happy(susan)) [rectify 57]
59. ? [X1] : curious(X1) => curious(sK3) [choice axiom]
60. ((funny(susan) & ~happy(susan)) | ! [X0] : ~curious(X0)) & (curious(sK3) | ~funny(susan) | happy(susan)) [skolemisation 58,59]
65. ! [X0] : (((rich(X0) | creative(X0)) | (~brave(X0) | old(X0))) & ((brave(X0) & ~old(X0)) | (~rich(X0) & ~creative(X0)))) [nnf transformation 12]
66. ! [X0] : ((rich(X0) | creative(X0) | ~brave(X0) | old(X0)) & ((brave(X0) & ~old(X0)) | (~rich(X0) & ~creative(X0)))) [flattening 65]
67. ? [X0] : (kind(X0) & creative(X0)) => (kind(sK5) & creative(sK5)) [choice axiom]
68. (kind(sK5) & creative(sK5)) | (kind(paul) & ~calm(paul)) [skolemisation 41,67]
92. ~brave(susan) | ~kind(X1) [cnf transformation 54]
98. ~happy(susan) | ~curious(X0) [cnf transformation 60]
100. ~creative(X0) | old(X0) [cnf transformation 33]
108. happy(X0) | rich(X0) [cnf transformation 39]
112. ~old(X0) | ~creative(X0) [cnf transformation 66]
115. ~rich(X0) | brave(X0) [cnf transformation 66]
118. creative(sK5) | kind(paul) [cnf transformation 68]
142. curious(lucy) [cnf transformation 25]
177. 8 <=> brave(susan) [avatar definition]
194. 12 <=> ! [X1] : ~kind(X1) [avatar definition]
195. ~kind(X1) <- (12) [avatar component clause 194]
196. 12 | ~8 [avatar split clause 92,177,194]
198. 13 <=> ! [X0] : ~curious(X0) [avatar definition]
199. ~curious(X0) <- (13) [avatar component clause 198]
206. 15 <=> happy(susan) [avatar definition]
208. ~happy(susan) <- (~15) [avatar component clause 206]
209. 13 | ~15 [avatar split clause 98,206,198]
237. ~creative(X0) [subsumption resolution 112,100]
239. 22 <=> kind(paul) [avatar definition]
241. kind(paul) <- (22) [avatar component clause 239]
252. kind(paul) [subsumption resolution 118,237]
253. 22 [avatar split clause 252,239]
305. $false <- (13) [resolution 199,142]
306. ~13 [avatar contradiction clause 305]
310. rich(susan) <- (~15) [resolution 108,208]
317. brave(susan) <- (~15) [resolution 115,310]
320. 8 | 15 [avatar split clause 317,206,177]
322. $false <- (12, 22) [resolution 195,241]
323. ~12 | ~22 [avatar contradiction clause 322]
325. $false [avatar sat refutation 196,209,253,306,320,323]
% SZS output end Proof for 3930464758113387558788050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not patient is either not happy or not curious and vice versa. Everyone who is calm is not wise or not calm. If someone is both tall and generous then someone is both not creative and generous and vice versa. If mary is both not kind and not wise then john is not calm. Everyone who is either not strong or not tall is not tall and vice versa. Everyone who is quiet or not generous is patient or not kind and vice versa. If someone is not humble or not tall then someone is not funny or not happy. If susan is both patient and happy then mary is both tall and not brave and vice versa. If someone is generous or brave then lucy is either not generous or not strong. If fred is both not creative and not rich then susan is not quiet or not rich. Everyone who is not kind is happy and vice versa. Everyone who is either tall or not old is either not brave or funny. Everyone who is kind is rich or strong and vice versa. Everyone who is not humble is both generous and old and vice versa. If susan is both not brave and old then alice is kind or not strong and vice versa. If alice is both not old and not generous then someone is both not happy and not funny. Mary is either not patient or not strong. Paul is both old and not rich. Fred is both not happy and not creative. Susan is rich. Alice is calm or not kind. Someone is not generous. | Alice is wise. | contradiction | (![X]:((generous(X)<~>~patient(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:(calm(X)=>(~wise(X)|~calm(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~creative(X)&generous(X)))))&
(((~kind(mary)&~wise(mary)))=>(~calm(john)))&
(![X]:((~strong(X)<~>~tall(X))<=>~tall(X)))&
(![X]:((quiet(X)|~generous(X))<=>(patient(X)|~kind(X))))&
((?[X]:((~humble(X)|~tall(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(((patient(susan)&happy(susan)))<=>((tall(mary)&~brave(mary))))&
((?[X]:((generous(X)|brave(X))))=>((~generous(lucy)<~>~strong(lucy))))&
(((~creative(fred)&~rich(fred)))=>((~quiet(susan)|~rich(susan))))&
(![X]:(~kind(X)<=>happy(X)))&
(![X]:((tall(X)<~>~old(X))=>(~brave(X)<~>funny(X))))&
(![X]:(kind(X)<=>(rich(X)|strong(X))))&
(![X]:(~humble(X)<=>(generous(X)&old(X))))&
(((~brave(susan)&old(susan)))<=>((kind(alice)|~strong(alice))))&
(((~old(alice)&~generous(alice)))=>(?[X]:((~happy(X)&~funny(X)))))&
((~patient(mary)<~>~strong(mary)))&
((old(paul)&~rich(paul)))&
((~happy(fred)&~creative(fred)))&
(rich(susan))&
((calm(alice)|~kind(alice)))&
(?[X]:(~generous(X))) | wise(alice) | [
"p1",
"p4",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 757853943476745874225400
% SZS output start Proof for 757853943476745874225400
2. ! [X0] : (calm(X0) => (~calm(X0) | ~wise(X0))) [input p1]
5. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~tall(X0)) [input p4]
13. ! [X0] : (kind(X0) <=> (strong(X0) | rich(X0))) [input p12]
21. ~kind(alice) | calm(alice) [input p20]
23. wise(alice) [input hypothesis]
27. ! [X0] : ((~calm(X0) | ~wise(X0)) | ~calm(X0)) [ennf transformation 2]
28. ! [X0] : (~calm(X0) | ~wise(X0) | ~calm(X0)) [flattening 27]
46. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | tall(X0)) & (~tall(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 5]
57. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | ~kind(X0))) [nnf transformation 13]
58. ! [X0] : ((kind(X0) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | ~kind(X0))) [flattening 57]
74. ~calm(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 28]
80. ~tall(X0) | ~tall(X0) | strong(X0) [cnf transformation 46]
83. tall(X0) | strong(X0) | tall(X0) [cnf transformation 46]
107. kind(X0) | ~strong(X0) [cnf transformation 58]
123. ~kind(alice) | calm(alice) [cnf transformation 21]
125. wise(alice) [cnf transformation 23]
126. ~tall(X0) | strong(X0) [duplicate literal removal 80]
127. strong(X0) | tall(X0) [duplicate literal removal 83]
128. ~wise(X0) | ~calm(X0) [duplicate literal removal 74]
168. strong(X0) [subsumption resolution 126,127]
236. kind(X0) [subsumption resolution 107,168]
260. calm(alice) [subsumption resolution 123,236]
263. ~calm(alice) [resolution 128,125]
264. $false [subsumption resolution 263,260]
% SZS output end Proof for 757853943476745874225400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is tall or curious and vice versa.
Everyone who is both not patient and not brave is old or not curious and vice versa.
Everyone who is both not brave and not humble is not humble.
Everyone who is either not quiet or old is not creative and vice versa.
Everyone who is both not strong and not quiet is both not strong and creative.
If someone is either kind or not patient then someone is both not old and generous and vice versa.
If someone is either happy or generous then susan is rich and vice versa.
If lucy is either happy or not patient then someone is either old or not kind and vice versa.
If someone is both quiet and not happy then paul is not creative or not strong and vice versa.
If someone is curious or happy then susan is not generous and vice versa.
If paul is not creative then susan is both not calm and kind.
If mary is not happy or kind then lucy is both not patient and brave and vice versa.
If someone is both funny and not curious then fred is both not generous and not brave.
Everyone who is either not rich or strong is funny and vice versa.
Everyone who is either rich or not creative is generous or not calm and vice versa.
If someone is either not humble or patient then someone is either not rich or rich.
Lucy is not funny.
Someone is rich or happy.
Someone is either not creative or not old.
Someone is both wise and rich.
Someone is not kind or tall.
Someone is both not curious and happy.
Someone is either not quiet or not tall. | Paul is not quiet. | neutral | (![X]:(quiet(X)<=>(tall(X)|curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(old(X)|~curious(X))))&
(![X]:((~brave(X)&~humble(X))=>~humble(X)))&
(![X]:((~quiet(X)<~>old(X))<=>~creative(X)))&
(![X]:((~strong(X)&~quiet(X))=>(~strong(X)&creative(X))))&
((?[X]:((kind(X)<~>~patient(X))))<=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((happy(X)<~>generous(X))))<=>(rich(susan)))&
(((happy(lucy)<~>~patient(lucy)))<=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((quiet(X)&~happy(X))))<=>((~creative(paul)|~strong(paul))))&
((?[X]:((curious(X)|happy(X))))<=>(~generous(susan)))&
((~creative(paul))=>((~calm(susan)&kind(susan))))&
(((~happy(mary)|kind(mary)))<=>((~patient(lucy)&brave(lucy))))&
((?[X]:((funny(X)&~curious(X))))=>((~generous(fred)&~brave(fred))))&
(![X]:((~rich(X)<~>strong(X))<=>funny(X)))&
(![X]:((rich(X)<~>~creative(X))<=>(generous(X)|~calm(X))))&
((?[X]:((~humble(X)<~>patient(X))))=>(?[X]:((~rich(X)<~>rich(X)))))&
(~funny(lucy))&
(?[X]:((rich(X)|happy(X))))&
(?[X]:((~creative(X)<~>~old(X))))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((~quiet(X)<~>~tall(X)))) | ~quiet(paul) | [] | null | 0 |
If someone is either not humble or creative then john is curious or not creative.
Everyone who is either quiet or not calm is both tall and not patient.
Everyone who is either not wise or not humble is either strong or not wise and vice versa.
If someone is happy or creative then paul is either not strong or not generous and vice versa.
If someone is not kind or rich then someone is strong and vice versa.
If someone is either not calm or not creative then lucy is both not wise and not old and vice versa.
If susan is quiet or not kind then susan is both not happy and not kind and vice versa.
Everyone who is both brave and happy is not happy and vice versa.
Everyone who is not humble is both not rich and old and vice versa.
Everyone who is either not humble or not curious is wise.
If john is not creative or not calm then someone is not tall or not humble and vice versa.
If paul is quiet or happy then fred is not brave or old and vice versa.
Everyone who is not creative is funny.
If alice is either not brave or not creative then alice is not funny or not strong.
Everyone who is either not humble or not patient is both not quiet and not curious and vice versa.
Everyone who is both patient and not humble is either not quiet or wise.
Someone is either not patient or not kind.
Someone is not funny.
Fred is both quiet and not old.
Paul is not calm.
Someone is both tall and patient.
Lucy is both not creative and wise.
Fred is patient. | Paul is not funny. | contradiction | ((?[X]:((~humble(X)<~>creative(X))))=>((curious(john)|~creative(john))))&
(![X]:((quiet(X)<~>~calm(X))=>(tall(X)&~patient(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((happy(X)|creative(X))))<=>((~strong(paul)<~>~generous(paul))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>((~wise(lucy)&~old(lucy))))&
(((quiet(susan)|~kind(susan)))<=>((~happy(susan)&~kind(susan))))&
(![X]:((brave(X)&happy(X))<=>~happy(X)))&
(![X]:(~humble(X)<=>(~rich(X)&old(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(((~creative(john)|~calm(john)))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((quiet(paul)|happy(paul)))<=>((~brave(fred)|old(fred))))&
(![X]:(~creative(X)=>funny(X)))&
(((~brave(alice)<~>~creative(alice)))=>((~funny(alice)|~strong(alice))))&
(![X]:((~humble(X)<~>~patient(X))<=>(~quiet(X)&~curious(X))))&
(![X]:((patient(X)&~humble(X))=>(~quiet(X)<~>wise(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
((quiet(fred)&~old(fred)))&
(~calm(paul))&
(?[X]:((tall(X)&patient(X))))&
((~creative(lucy)&wise(lucy)))&
(patient(fred)) | ~funny(paul) | [
"p5",
"p12",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8985131604002699410117888
% SZS output start Proof for 8985131604002699410117888
6. ? [X0] : (~calm(X0) <~> ~creative(X0)) <=> (~old(lucy) & ~wise(lucy)) [input p5]
13. ! [X0] : (~creative(X0) => funny(X0)) [input p12]
20. ~calm(paul) [input p19]
22. wise(lucy) & ~creative(lucy) [input p21]
24. ~funny(paul) [input hypothesis]
30. ! [X0] : (funny(X0) | creative(X0)) [ennf transformation 13]
47. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (old(lucy) | wise(lucy))) & ((~old(lucy) & ~wise(lucy)) | ! [X0] : ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) [nnf transformation 6]
48. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | old(lucy) | wise(lucy)) & ((~old(lucy) & ~wise(lucy)) | ! [X0] : ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0)))) [flattening 47]
49. (? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | old(lucy) | wise(lucy)) & ((~old(lucy) & ~wise(lucy)) | ! [X1] : ((~calm(X1) | creative(X1)) & (~creative(X1) | calm(X1)))) [rectify 48]
50. ? [X0] : ((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) => ((creative(sK3) | calm(sK3)) & (~creative(sK3) | ~calm(sK3))) [choice axiom]
51. (((creative(sK3) | calm(sK3)) & (~creative(sK3) | ~calm(sK3))) | old(lucy) | wise(lucy)) & ((~old(lucy) & ~wise(lucy)) | ! [X1] : ((~calm(X1) | creative(X1)) & (~creative(X1) | calm(X1)))) [skolemisation 49,50]
100. ~wise(lucy) | ~creative(X1) | calm(X1) [cnf transformation 51]
127. funny(X0) | creative(X0) [cnf transformation 30]
143. ~calm(paul) [cnf transformation 20]
147. wise(lucy) [cnf transformation 22]
149. ~funny(paul) [cnf transformation 24]
227. 17 <=> wise(lucy) [avatar definition]
249. 22 <=> ! [X1] : (~creative(X1) | calm(X1)) [avatar definition]
250. ~creative(X1) | calm(X1) <- (22) [avatar component clause 249]
253. 22 | ~17 [avatar split clause 100,227,249]
317. 17 [avatar split clause 147,227]
322. creative(paul) [resolution 127,149]
329. calm(paul) <- (22) [resolution 250,322]
330. $false <- (22) [subsumption resolution 329,143]
331. ~22 [avatar contradiction clause 330]
332. $false [avatar sat refutation 253,317,331]
% SZS output end Proof for 8985131604002699410117888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and funny is strong or not kind. Everyone who is brave is not generous or not brave and vice versa. Everyone who is not rich is not creative and vice versa. If paul is not funny then john is rich. If paul is calm then john is both kind and not funny and vice versa. Everyone who is either strong or not kind is both curious and not calm. Everyone who is both patient and not happy is both not kind and not strong and vice versa. Everyone who is funny or not tall is either generous or tall and vice versa. Everyone who is both old and not tall is either not happy or not curious and vice versa. Everyone who is both not old and not wise is not brave or not tall. Everyone who is not brave or humble is happy or not rich. If paul is both not curious and not tall then john is both not curious and happy. Everyone who is both humble and strong is both kind and curious. Everyone who is both not calm and brave is either curious or not strong. If fred is both creative and not tall then someone is either generous or curious and vice versa. Someone is quiet or not wise. Someone is humble. Paul is humble. Susan is old. Someone is either not tall or wise. Paul is both quiet and not strong. | Paul is creative. | contradiction | (![X]:((happy(X)&funny(X))=>(strong(X)|~kind(X))))&
(![X]:(brave(X)<=>(~generous(X)|~brave(X))))&
(![X]:(~rich(X)<=>~creative(X)))&
((~funny(paul))=>(rich(john)))&
((calm(paul))<=>((kind(john)&~funny(john))))&
(![X]:((strong(X)<~>~kind(X))=>(curious(X)&~calm(X))))&
(![X]:((patient(X)&~happy(X))<=>(~kind(X)&~strong(X))))&
(![X]:((funny(X)|~tall(X))<=>(generous(X)<~>tall(X))))&
(![X]:((old(X)&~tall(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((~old(X)&~wise(X))=>(~brave(X)|~tall(X))))&
(![X]:((~brave(X)|humble(X))=>(happy(X)|~rich(X))))&
(((~curious(paul)&~tall(paul)))=>((~curious(john)&happy(john))))&
(![X]:((humble(X)&strong(X))=>(kind(X)&curious(X))))&
(![X]:((~calm(X)&brave(X))=>(curious(X)<~>~strong(X))))&
(((creative(fred)&~tall(fred)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:(humble(X)))&
(humble(paul))&
(old(susan))&
(?[X]:((~tall(X)<~>wise(X))))&
((quiet(paul)&~strong(paul))) | creative(paul) | [
"p1",
"p2",
"p7",
"p8",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1698810047755265500765591
% SZS output start Proof for 1698810047755265500765591
2. ! [X0] : (brave(X0) <=> (~brave(X0) | ~generous(X0))) [input p1]
3. ! [X0] : (~rich(X0) <=> ~creative(X0)) [input p2]
8. ! [X0] : ((~tall(X0) | funny(X0)) <=> (generous(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) & old(X0)) <=> (~happy(X0) <~> ~curious(X0))) [input p8]
11. ! [X0] : ((humble(X0) | ~brave(X0)) => (~rich(X0) | happy(X0))) [input p10]
15. (~tall(fred) & creative(fred)) <=> ? [X0] : (generous(X0) <~> curious(X0)) [input p14]
18. humble(paul) [input p17]
22. creative(paul) [input hypothesis]
31. ! [X0] : ((~rich(X0) | happy(X0)) | (~humble(X0) & brave(X0))) [ennf transformation 11]
32. ! [X0] : (~rich(X0) | happy(X0) | (~humble(X0) & brave(X0))) [flattening 31]
39. ! [X0] : ((brave(X0) | (brave(X0) & generous(X0))) & ((~brave(X0) | ~generous(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (brave(X0) & generous(X0))) & (~brave(X0) | ~generous(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0))) [nnf transformation 3]
47. ! [X0] : (((~tall(X0) | funny(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (tall(X0) & ~funny(X0)))) [nnf transformation 8]
48. ! [X0] : ((~tall(X0) | funny(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (tall(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : (((~tall(X0) & old(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (tall(X0) | ~old(X0)))) [nnf transformation 9]
50. ! [X0] : (((~tall(X0) & old(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) & (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | tall(X0) | ~old(X0))) [flattening 49]
52. ((~tall(fred) & creative(fred)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) & (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (tall(fred) | ~creative(fred))) [nnf transformation 15]
53. ((~tall(fred) & creative(fred)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) & (? [X0] : ((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | tall(fred) | ~creative(fred)) [flattening 52]
54. ((~tall(fred) & creative(fred)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) & (? [X1] : ((~curious(X1) | ~generous(X1)) & (curious(X1) | generous(X1))) | tall(fred) | ~creative(fred)) [rectify 53]
55. ? [X1] : ((~curious(X1) | ~generous(X1)) & (curious(X1) | generous(X1))) => ((~curious(sK0) | ~generous(sK0)) & (curious(sK0) | generous(sK0))) [choice axiom]
56. ((~tall(fred) & creative(fred)) | ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0)))) & (((~curious(sK0) | ~generous(sK0)) & (curious(sK0) | generous(sK0))) | tall(fred) | ~creative(fred)) [skolemisation 54,55]
63. ~brave(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 40]
65. brave(X0) | brave(X0) [cnf transformation 40]
66. ~creative(X0) | rich(X0) [cnf transformation 41]
81. tall(X0) | generous(X0) | tall(X0) [cnf transformation 48]
91. ~tall(X0) | ~happy(X0) | curious(X0) [cnf transformation 50]
94. ~humble(X0) | happy(X0) | ~rich(X0) [cnf transformation 32]
106. ~tall(fred) | generous(X0) | ~curious(X0) [cnf transformation 56]
108. humble(paul) [cnf transformation 18]
113. creative(paul) [cnf transformation 22]
114. tall(X0) | generous(X0) [duplicate literal removal 81]
116. ~brave(X0) | ~generous(X0) [duplicate literal removal 63]
117. brave(X0) [duplicate literal removal 65]
118. ~generous(X0) [subsumption resolution 116,117]
144. tall(X0) [subsumption resolution 114,118]
145. ~happy(X0) | curious(X0) [subsumption resolution 91,144]
151. generous(X0) | ~curious(X0) [subsumption resolution 106,144]
152. ~curious(X0) [subsumption resolution 151,118]
154. rich(paul) [resolution 66,113]
167. happy(paul) | ~rich(paul) [resolution 94,108]
177. happy(paul) [subsumption resolution 167,154]
185. curious(paul) [resolution 177,145]
186. $false [subsumption resolution 185,152]
% SZS output end Proof for 1698810047755265500765591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then someone is not quiet. If lucy is tall or not happy then someone is not rich. Everyone who is old is not old. If john is patient or not humble then mary is both not quiet and not wise and vice versa. Everyone who is kind or old is not calm. Everyone who is both not rich and not calm is wise or creative. If fred is both not happy and generous then susan is not funny or kind. Everyone who is either rich or not funny is either happy or calm. If someone is either not humble or not old then someone is funny and vice versa. Everyone who is not wise is not funny and vice versa. If someone is either strong or generous then paul is curious. Everyone who is either not brave or not kind is not happy and vice versa. If someone is creative or curious then someone is both happy and not curious and vice versa. Everyone who is rich or not strong is generous and vice versa. If someone is both generous and not quiet then someone is both not generous and not kind and vice versa. Everyone who is rich is both not humble and rich. Someone is not generous or happy. Someone is kind. Susan is both not quiet and creative. Someone is humble. Someone is brave. Someone is quiet or not rich. Alice is humble. Lucy is brave or not curious. | Alice is old. | contradiction | ((?[X]:(~patient(X)))=>(?[X]:(~quiet(X))))&
(((tall(lucy)|~happy(lucy)))=>(?[X]:(~rich(X))))&
(![X]:(old(X)=>~old(X)))&
(((patient(john)|~humble(john)))<=>((~quiet(mary)&~wise(mary))))&
(![X]:((kind(X)|old(X))=>~calm(X)))&
(![X]:((~rich(X)&~calm(X))=>(wise(X)|creative(X))))&
(((~happy(fred)&generous(fred)))=>((~funny(susan)|kind(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(happy(X)<~>calm(X))))&
((?[X]:((~humble(X)<~>~old(X))))<=>(?[X]:(funny(X))))&
(![X]:(~wise(X)<=>~funny(X)))&
((?[X]:((strong(X)<~>generous(X))))=>(curious(paul)))&
(![X]:((~brave(X)<~>~kind(X))<=>~happy(X)))&
((?[X]:((creative(X)|curious(X))))<=>(?[X]:((happy(X)&~curious(X)))))&
(![X]:((rich(X)|~strong(X))<=>generous(X)))&
((?[X]:((generous(X)&~quiet(X))))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:(rich(X)=>(~humble(X)&rich(X))))&
(?[X]:((~generous(X)|happy(X))))&
(?[X]:(kind(X)))&
((~quiet(susan)&creative(susan)))&
(?[X]:(humble(X)))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|~rich(X))))&
(humble(alice))&
((brave(lucy)|~curious(lucy))) | old(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4108829290975169749871063
% SZS output start Proof for 4108829290975169749871063
3. ! [X0] : (old(X0) => ~old(X0)) [input p2]
25. old(alice) [input hypothesis]
33. ! [X0] : (~old(X0) | ~old(X0)) [ennf transformation 3]
82. ~old(X0) | ~old(X0) [cnf transformation 33]
131. old(alice) [cnf transformation 25]
132. ~old(X0) [duplicate literal removal 82]
301. $false [subsumption resolution 131,132]
% SZS output end Proof for 4108829290975169749871063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either calm or generous then someone is not wise and vice versa.
If someone is either old or not strong then someone is tall and vice versa.
Everyone who is humble or quiet is both not humble and not brave and vice versa.
Everyone who is old is either not tall or not strong.
If fred is not wise or old then someone is not brave and vice versa.
Everyone who is wise or not funny is generous or not calm and vice versa.
If lucy is not rich or generous then lucy is kind and vice versa.
Everyone who is both not rich and not calm is not strong or tall.
If john is not wise or not brave then someone is creative or not happy and vice versa.
Everyone who is not brave is quiet or not wise.
Everyone who is quiet is either not brave or brave and vice versa.
Everyone who is either generous or not humble is either not tall or kind.
Everyone who is both tall and not kind is both not rich and calm.
Everyone who is either not calm or not brave is either quiet or not generous and vice versa.
Everyone who is rich is either not tall or not old and vice versa.
Everyone who is not old is funny or curious and vice versa.
Paul is curious or not tall.
Alice is wise or not patient.
Someone is not humble or rich.
Someone is not kind.
Someone is quiet.
Someone is both generous and not strong.
Someone is either humble or not patient. | Lucy is not patient. | neutral | (((calm(john)<~>generous(john)))<=>(?[X]:(~wise(X))))&
((?[X]:((old(X)<~>~strong(X))))<=>(?[X]:(tall(X))))&
(![X]:((humble(X)|quiet(X))<=>(~humble(X)&~brave(X))))&
(![X]:(old(X)=>(~tall(X)<~>~strong(X))))&
(((~wise(fred)|old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|~funny(X))<=>(generous(X)|~calm(X))))&
(((~rich(lucy)|generous(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(((~wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:(~brave(X)=>(quiet(X)|~wise(X))))&
(![X]:(quiet(X)<=>(~brave(X)<~>brave(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~tall(X)<~>kind(X))))&
(![X]:((tall(X)&~kind(X))=>(~rich(X)&calm(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(~tall(X)<~>~old(X))))&
(![X]:(~old(X)<=>(funny(X)|curious(X))))&
((curious(paul)|~tall(paul)))&
((wise(alice)|~patient(alice)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~patient(lucy) | [] | null | 0 |
Everyone who is not rich or patient is either brave or not humble.
Everyone who is either not humble or not rich is either humble or rich.
If someone is generous then lucy is not old or funny and vice versa.
Everyone who is not brave or patient is either not generous or happy and vice versa.
Everyone who is either funny or not humble is tall.
Everyone who is not funny or not tall is not patient or wise and vice versa.
Everyone who is not wise is not tall and vice versa.
Everyone who is curious is both generous and not creative and vice versa.
Everyone who is not strong or rich is either not calm or funny.
Everyone who is either quiet or strong is either not kind or old and vice versa.
If someone is either not kind or not rich then someone is either humble or not brave and vice versa.
If paul is either strong or humble then someone is both not patient and strong.
If someone is rich or creative then lucy is not kind or wise and vice versa.
If someone is both not wise and generous then someone is not kind and vice versa.
Everyone who is either not brave or not tall is either happy or not wise.
Everyone who is either rich or not funny is both creative and rich and vice versa.
Lucy is either calm or not calm.
Someone is patient.
Lucy is both not humble and not generous.
Someone is both calm and not old.
Someone is not patient or not rich.
Someone is brave.
Someone is both quiet and patient.
Someone is not curious or not patient. | Lucy is patient. | contradiction | (![X]:((~rich(X)|patient(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~rich(X))=>(humble(X)<~>rich(X))))&
((?[X]:(generous(X)))<=>((~old(lucy)|funny(lucy))))&
(![X]:((~brave(X)|patient(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((funny(X)<~>~humble(X))=>tall(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(![X]:(curious(X)<=>(generous(X)&~creative(X))))&
(![X]:((~strong(X)|rich(X))=>(~calm(X)<~>funny(X))))&
(![X]:((quiet(X)<~>strong(X))<=>(~kind(X)<~>old(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:((humble(X)<~>~brave(X)))))&
(((strong(paul)<~>humble(paul)))=>(?[X]:((~patient(X)&strong(X)))))&
((?[X]:((rich(X)|creative(X))))<=>((~kind(lucy)|wise(lucy))))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)<~>~tall(X))=>(happy(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(creative(X)&rich(X))))&
((calm(lucy)<~>~calm(lucy)))&
(?[X]:(patient(X)))&
((~humble(lucy)&~generous(lucy)))&
(?[X]:((calm(X)&~old(X))))&
(?[X]:((~patient(X)|~rich(X))))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:((~curious(X)|~patient(X)))) | patient(lucy) | [
"p0",
"p3",
"p5",
"p6",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 132278980239954197930128
% SZS output start Proof for 132278980239954197930128
1. ! [X0] : ((patient(X0) | ~rich(X0)) => (brave(X0) <~> ~humble(X0))) [input p0]
4. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (~generous(X0) <~> happy(X0))) [input p3]
6. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (wise(X0) | ~patient(X0))) [input p5]
7. ! [X0] : (~wise(X0) <=> ~tall(X0)) [input p6]
15. ! [X0] : ((~brave(X0) <~> ~tall(X0)) => (happy(X0) <~> ~wise(X0))) [input p14]
19. ~generous(lucy) & ~humble(lucy) [input p18]
25. patient(lucy) [input hypothesis]
29. ! [X0] : ((brave(X0) <~> ~humble(X0)) | (~patient(X0) & rich(X0))) [ennf transformation 1]
36. ! [X0] : ((happy(X0) <~> ~wise(X0)) | (~brave(X0) <=> ~tall(X0))) [ennf transformation 15]
37. ! [X0] : (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~patient(X0) & rich(X0))) [nnf transformation 29]
44. ! [X0] : (((patient(X0) | ~brave(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) & (((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | (~patient(X0) & brave(X0)))) [nnf transformation 4]
45. ! [X0] : ((patient(X0) | ~brave(X0) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) & (((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | (~patient(X0) & brave(X0)))) [flattening 44]
47. ! [X0] : (((~tall(X0) | ~funny(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~tall(X0) | ~funny(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | (tall(X0) & funny(X0)))) [flattening 47]
49. ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0))) [nnf transformation 7]
70. ! [X0] : (((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) [nnf transformation 36]
89. ~brave(X0) | humble(X0) | ~patient(X0) [cnf transformation 37]
100. ~happy(X0) | generous(X0) | ~patient(X0) [cnf transformation 45]
106. ~patient(X0) | wise(X0) | tall(X0) [cnf transformation 48]
109. ~tall(X0) | wise(X0) [cnf transformation 49]
110. ~wise(X0) | tall(X0) [cnf transformation 49]
143. ~wise(X0) | happy(X0) | ~tall(X0) | brave(X0) [cnf transformation 70]
156. ~humble(lucy) [cnf transformation 19]
157. ~generous(lucy) [cnf transformation 19]
165. patient(lucy) [cnf transformation 25]
247. 17 <=> wise(lucy) [avatar definition]
248. wise(lucy) <- (17) [avatar component clause 247]
294. ~wise(X0) | happy(X0) | brave(X0) [subsumption resolution 143,110]
381. wise(lucy) | tall(lucy) [resolution 106,165]
469. 53 <=> brave(lucy) [avatar definition]
471. brave(lucy) <- (53) [avatar component clause 469]
473. 54 <=> happy(lucy) [avatar definition]
475. happy(lucy) <- (54) [avatar component clause 473]
495. wise(lucy) [subsumption resolution 381,109]
496. 17 [avatar split clause 495,247]
499. happy(lucy) | brave(lucy) <- (17) [resolution 248,294]
514. humble(lucy) | ~patient(lucy) <- (53) [resolution 471,89]
516. ~patient(lucy) <- (53) [subsumption resolution 514,156]
517. $false <- (53) [subsumption resolution 516,165]
518. ~53 [avatar contradiction clause 517]
519. 53 | 54 | ~17 [avatar split clause 499,247,473,469]
526. generous(lucy) | ~patient(lucy) <- (54) [resolution 475,100]
528. ~patient(lucy) <- (54) [subsumption resolution 526,157]
529. $false <- (54) [subsumption resolution 528,165]
530. ~54 [avatar contradiction clause 529]
534. $false [avatar sat refutation 496,518,519,530]
% SZS output end Proof for 132278980239954197930128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not wise is not funny or not creative and vice versa. Everyone who is not kind is happy or not calm and vice versa. Everyone who is either funny or not patient is either humble or not quiet. Everyone who is not tall is happy or calm and vice versa. Everyone who is not funny is both tall and not humble. If someone is both not calm and not quiet then someone is either patient or strong. Everyone who is either calm or not patient is creative and vice versa. If someone is not generous then lucy is both not happy and humble. If someone is not wise or not tall then someone is strong. Everyone who is not creative or not generous is not quiet. Everyone who is humble or not patient is either not kind or not strong and vice versa. If someone is not generous then fred is both wise and tall and vice versa. Everyone who is both kind and generous is curious or not creative and vice versa. If someone is both not funny and funny then someone is brave or not strong. If paul is humble then susan is not quiet or creative and vice versa. If someone is both not strong and not happy then someone is both not happy and wise. Someone is not humble or strong. Someone is curious. Fred is either curious or rich. Lucy is both not generous and tall. Someone is either wise or brave. Lucy is either old or not humble. Paul is not brave or kind. Someone is wise or not patient. | Fred is not rich. | contradiction | (![X]:((happy(X)<~>~wise(X))<=>(~funny(X)|~creative(X))))&
(![X]:(~kind(X)<=>(happy(X)|~calm(X))))&
(![X]:((funny(X)<~>~patient(X))=>(humble(X)<~>~quiet(X))))&
(![X]:(~tall(X)<=>(happy(X)|calm(X))))&
(![X]:(~funny(X)=>(tall(X)&~humble(X))))&
((?[X]:((~calm(X)&~quiet(X))))=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:((calm(X)<~>~patient(X))<=>creative(X)))&
((?[X]:(~generous(X)))=>((~happy(lucy)&humble(lucy))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:(strong(X))))&
(![X]:((~creative(X)|~generous(X))=>~quiet(X)))&
(![X]:((humble(X)|~patient(X))<=>(~kind(X)<~>~strong(X))))&
((?[X]:(~generous(X)))<=>((wise(fred)&tall(fred))))&
(![X]:((kind(X)&generous(X))<=>(curious(X)|~creative(X))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((brave(X)|~strong(X)))))&
((humble(paul))<=>((~quiet(susan)|creative(susan))))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:((~happy(X)&wise(X)))))&
(?[X]:((~humble(X)|strong(X))))&
(?[X]:(curious(X)))&
((curious(fred)<~>rich(fred)))&
((~generous(lucy)&tall(lucy)))&
(?[X]:((wise(X)<~>brave(X))))&
((old(lucy)<~>~humble(lucy)))&
((~brave(paul)|kind(paul)))&
(?[X]:((wise(X)|~patient(X)))) | ~rich(fred) | [
"p1",
"p3",
"p11",
"p12",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4953623555814521556328593
% SZS output start Proof for 4953623555814521556328593
2. ! [X0] : (~kind(X0) <=> (~calm(X0) | happy(X0))) [input p1]
4. ! [X0] : (~tall(X0) <=> (calm(X0) | happy(X0))) [input p3]
12. ? [X0] : ~generous(X0) <=> (tall(fred) & wise(fred)) [input p11]
13. ! [X0] : ((generous(X0) & kind(X0)) <=> (~creative(X0) | curious(X0))) [input p12]
19. curious(fred) <~> rich(fred) [input p18]
20. tall(lucy) & ~generous(lucy) [input p19]
25. ~rich(fred) [input hypothesis]
40. ! [X0] : ((~kind(X0) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | kind(X0))) [nnf transformation 2]
41. ! [X0] : ((~kind(X0) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | kind(X0))) [flattening 40]
43. ! [X0] : ((~tall(X0) | (~calm(X0) & ~happy(X0))) & ((calm(X0) | happy(X0)) | tall(X0))) [nnf transformation 4]
44. ! [X0] : ((~tall(X0) | (~calm(X0) & ~happy(X0))) & (calm(X0) | happy(X0) | tall(X0))) [flattening 43]
55. (? [X0] : ~generous(X0) | (~tall(fred) | ~wise(fred))) & ((tall(fred) & wise(fred)) | ! [X0] : generous(X0)) [nnf transformation 12]
56. (? [X0] : ~generous(X0) | ~tall(fred) | ~wise(fred)) & ((tall(fred) & wise(fred)) | ! [X0] : generous(X0)) [flattening 55]
57. (? [X0] : ~generous(X0) | ~tall(fred) | ~wise(fred)) & ((tall(fred) & wise(fred)) | ! [X1] : generous(X1)) [rectify 56]
58. ? [X0] : ~generous(X0) => ~generous(sK2) [choice axiom]
59. (~generous(sK2) | ~tall(fred) | ~wise(fred)) & ((tall(fred) & wise(fred)) | ! [X1] : generous(X1)) [skolemisation 57,58]
60. ! [X0] : (((generous(X0) & kind(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 13]
61. ! [X0] : (((generous(X0) & kind(X0)) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ~generous(X0) | ~kind(X0))) [flattening 60]
74. (~rich(fred) | ~curious(fred)) & (rich(fred) | curious(fred)) [nnf transformation 19]
89. ~kind(X0) | calm(X0) [cnf transformation 41]
96. ~tall(X0) | ~calm(X0) [cnf transformation 44]
118. tall(fred) | generous(X1) [cnf transformation 59]
121. ~curious(X0) | kind(X0) [cnf transformation 61]
133. rich(fred) | curious(fred) [cnf transformation 74]
135. ~generous(lucy) [cnf transformation 20]
143. ~rich(fred) [cnf transformation 25]
158. 4 <=> ! [X0] : generous(X0) [avatar definition]
159. generous(X0) <- (4) [avatar component clause 158]
187. 11 <=> tall(fred) [avatar definition]
188. tall(fred) <- (11) [avatar component clause 187]
195. 4 | 11 [avatar split clause 118,187,158]
234. 21 <=> curious(fred) [avatar definition]
235. curious(fred) <- (21) [avatar component clause 234]
238. 22 <=> rich(fred) [avatar definition]
242. 21 | 22 [avatar split clause 133,238,234]
277. ~22 [avatar split clause 143,238]
278. $false <- (4) [resolution 159,135]
279. ~4 [avatar contradiction clause 278]
283. ~calm(fred) <- (11) [resolution 96,188]
289. kind(fred) <- (21) [resolution 121,235]
296. calm(fred) <- (21) [resolution 289,89]
298. $false <- (11, 21) [subsumption resolution 296,283]
299. ~11 | ~21 [avatar contradiction clause 298]
300. $false [avatar sat refutation 195,242,277,279,299]
% SZS output end Proof for 4953623555814521556328593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is not strong is either not calm or not patient.
If someone is either not patient or not happy then alice is not curious.
Everyone who is rich is both rich and brave and vice versa.
If someone is not calm or old then susan is either not creative or not calm and vice versa.
If alice is both not tall and wise then john is either not humble or not strong.
If someone is kind then mary is either happy or strong.
If susan is not tall then someone is strong or not patient and vice versa.
If someone is curious or old then lucy is both not old and rich and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Everyone who is either not strong or strong is creative or calm.
Everyone who is both not quiet and funny is not brave or generous.
Everyone who is not tall or not generous is strong or not rich and vice versa.
If someone is not calm then someone is rich or kind.
If alice is either not humble or patient then someone is calm or not happy.
Paul is not kind or not tall.
Someone is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall.
Lucy is funny.
Someone is happy or not tall.
Susan is not strong or not old. | Lucy is generous. | entailment | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(~strong(X)=>(~calm(X)<~>~patient(X))))&
((?[X]:((~patient(X)<~>~happy(X))))=>(~curious(alice)))&
(![X]:(rich(X)<=>(rich(X)&brave(X))))&
((?[X]:((~calm(X)|old(X))))<=>((~creative(susan)<~>~calm(susan))))&
(((~tall(alice)&wise(alice)))=>((~humble(john)<~>~strong(john))))&
((?[X]:(kind(X)))=>((happy(mary)<~>strong(mary))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
((~kind(paul)|~tall(paul)))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan))) | generous(lucy) | [
"p3",
"p8",
"p9",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7665339435780450627526270
% SZS output start Proof for 7665339435780450627526270
4. ! [X0] : (rich(X0) <=> (brave(X0) & rich(X0))) [input p3]
9. ? [X0] : (old(X0) | curious(X0)) <=> (rich(lucy) & ~old(lucy)) [input p8]
10. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> funny(X0)) [input p9]
11. ? [X0] : ~generous(X0) <=> (~happy(mary) & curious(mary)) [input p10]
21. funny(lucy) [input p20]
24. ~generous(lucy) [input hypothesis]
39. ! [X0] : ((rich(X0) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ~rich(X0))) [nnf transformation 4]
40. ! [X0] : ((rich(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~rich(X0))) [flattening 39]
50. (? [X0] : (old(X0) | curious(X0)) | (~rich(lucy) | old(lucy))) & ((rich(lucy) & ~old(lucy)) | ! [X0] : (~old(X0) & ~curious(X0))) [nnf transformation 9]
51. (? [X0] : (old(X0) | curious(X0)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X0] : (~old(X0) & ~curious(X0))) [flattening 50]
52. (? [X0] : (old(X0) | curious(X0)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X1] : (~old(X1) & ~curious(X1))) [rectify 51]
53. ? [X0] : (old(X0) | curious(X0)) => (old(sK2) | curious(sK2)) [choice axiom]
54. ((old(sK2) | curious(sK2)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X1] : (~old(X1) & ~curious(X1))) [skolemisation 52,53]
55. ! [X0] : (((~brave(X0) | ~rich(X0)) | ~funny(X0)) & (funny(X0) | (brave(X0) & rich(X0)))) [nnf transformation 10]
56. ! [X0] : ((~brave(X0) | ~rich(X0) | ~funny(X0)) & (funny(X0) | (brave(X0) & rich(X0)))) [flattening 55]
57. (? [X0] : ~generous(X0) | (happy(mary) | ~curious(mary))) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [nnf transformation 11]
58. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [flattening 57]
59. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [rectify 58]
60. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
61. (~generous(sK3) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [skolemisation 59,60]
86. ~rich(X0) | brave(X0) [cnf transformation 40]
101. rich(lucy) | ~curious(X1) [cnf transformation 54]
106. ~brave(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 56]
107. curious(mary) | generous(X1) [cnf transformation 61]
124. funny(lucy) [cnf transformation 21]
127. ~generous(lucy) [cnf transformation 24]
209. 19 <=> rich(lucy) [avatar definition]
223. 22 <=> ! [X1] : ~curious(X1) [avatar definition]
224. ~curious(X1) <- (22) [avatar component clause 223]
225. 22 | 19 [avatar split clause 101,209,223]
228. ~funny(X0) | ~rich(X0) [subsumption resolution 106,86]
230. 23 <=> curious(mary) [avatar definition]
231. curious(mary) <- (23) [avatar component clause 230]
239. 25 <=> ! [X1] : generous(X1) [avatar definition]
240. generous(X1) <- (25) [avatar component clause 239]
242. 25 | 23 [avatar split clause 107,230,239]
329. ~rich(lucy) [resolution 228,124]
335. ~19 [avatar split clause 329,209]
339. $false <- (22, 23) [resolution 224,231]
340. ~22 | ~23 [avatar contradiction clause 339]
342. $false <- (25) [resolution 240,127]
345. ~25 [avatar contradiction clause 342]
346. $false [avatar sat refutation 225,242,335,340,345]
% SZS output end Proof for 7665339435780450627526270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is tall is not tall.
If john is either humble or not strong then fred is either patient or calm and vice versa.
Everyone who is either not kind or not humble is not kind.
If mary is both rich and funny then someone is not quiet or funny.
If someone is kind then someone is both not wise and happy.
If someone is either wise or happy then john is both quiet and not humble.
Everyone who is both not humble and strong is not curious.
Everyone who is not tall is both rich and quiet and vice versa.
If someone is both not generous and not wise then someone is either not kind or not quiet and vice versa.
If someone is both not patient and not tall then alice is both quiet and not brave and vice versa.
If lucy is either not humble or not funny then someone is strong and vice versa.
If john is both not tall and not generous then someone is strong or not rich.
If someone is not calm then someone is rich or kind.
Paul is funny.
Someone is both not happy and not old.
Paul is not patient.
Paul is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall. | Mary is old. | neutral | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(tall(X)=>~tall(X)))&
(((humble(john)<~>~strong(john)))<=>((patient(fred)<~>calm(fred))))&
(![X]:((~kind(X)<~>~humble(X))=>~kind(X)))&
(((rich(mary)&funny(mary)))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((wise(X)<~>happy(X))))=>((quiet(john)&~humble(john))))&
(![X]:((~humble(X)&strong(X))=>~curious(X)))&
(![X]:(~tall(X)<=>(rich(X)&quiet(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)&~brave(alice))))&
(((~humble(lucy)<~>~funny(lucy)))<=>(?[X]:(strong(X))))&
(((~tall(john)&~generous(john)))=>(?[X]:((strong(X)|~rich(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(funny(paul))&
(?[X]:((~happy(X)&~old(X))))&
(~patient(paul))&
((old(paul)|~humble(paul)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X)))) | old(mary) | [] | null | 0 |
Everyone who is happy is both not curious and curious.
If paul is both not quiet and happy then someone is either rich or not creative and vice versa.
Everyone who is either not rich or not strong is strong and vice versa.
If susan is both not brave and not quiet then someone is either brave or not strong.
If someone is not humble then someone is both funny and not brave.
Everyone who is both not tall and generous is either strong or kind.
Everyone who is either patient or old is kind or not creative and vice versa.
Everyone who is not tall is both not funny and not calm.
If lucy is not funny then paul is not curious.
Everyone who is both curious and strong is brave and vice versa.
Everyone who is either rich or tall is happy and vice versa.
Everyone who is humble or not generous is old and vice versa.
Everyone who is either not curious or generous is either old or not quiet and vice versa.
Everyone who is either humble or not wise is either happy or not rich.
If lucy is both wise and not wise then fred is both not strong and not generous.
Everyone who is not creative is strong and vice versa.
Someone is both curious and not kind.
Someone is either not curious or quiet.
Lucy is either not happy or calm.
Someone is not generous.
Fred is either not quiet or not rich. | Lucy is quiet. | neutral | (![X]:(happy(X)=>(~curious(X)&curious(X))))&
(((~quiet(paul)&happy(paul)))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>~strong(X))<=>strong(X)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~tall(X)&generous(X))=>(strong(X)<~>kind(X))))&
(![X]:((patient(X)<~>old(X))<=>(kind(X)|~creative(X))))&
(![X]:(~tall(X)=>(~funny(X)&~calm(X))))&
((~funny(lucy))=>(~curious(paul)))&
(![X]:((curious(X)&strong(X))<=>brave(X)))&
(![X]:((rich(X)<~>tall(X))<=>happy(X)))&
(![X]:((humble(X)|~generous(X))<=>old(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((humble(X)<~>~wise(X))=>(happy(X)<~>~rich(X))))&
(((wise(lucy)&~wise(lucy)))=>((~strong(fred)&~generous(fred))))&
(![X]:(~creative(X)<=>strong(X)))&
(?[X]:((curious(X)&~kind(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((~happy(lucy)<~>calm(lucy)))&
(?[X]:(~generous(X)))&
((~quiet(fred)<~>~rich(fred))) | quiet(lucy) | [] | null | 0 |
Everyone who is calm or old is happy and vice versa.
Everyone who is humble is both humble and kind and vice versa.
If someone is both not calm and not quiet then someone is both creative and not happy and vice versa.
Everyone who is not creative or not tall is wise or quiet.
If fred is not generous or not happy then alice is either curious or not curious and vice versa.
If john is calm or not rich then someone is both not quiet and not creative.
Everyone who is either curious or strong is curious.
Everyone who is not wise is old or happy and vice versa.
Everyone who is kind or not brave is not creative and vice versa.
If someone is both old and not funny then someone is both happy and not strong and vice versa.
If someone is either rich or kind then someone is not rich.
Everyone who is not happy is quiet and vice versa.
Everyone who is either calm or not kind is not kind or funny.
Everyone who is either generous or quiet is not old and vice versa.
If someone is not tall or strong then someone is strong or calm and vice versa.
Everyone who is either curious or patient is quiet or patient.
Fred is funny or tall.
Someone is creative.
Susan is either not generous or not quiet.
Someone is not strong.
Someone is quiet or generous.
Susan is either old or quiet.
Someone is not funny. | Alice is brave. | neutral | (![X]:((calm(X)|old(X))<=>happy(X)))&
(![X]:(humble(X)<=>(humble(X)&kind(X))))&
((?[X]:((~calm(X)&~quiet(X))))<=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~creative(X)|~tall(X))=>(wise(X)|quiet(X))))&
(((~generous(fred)|~happy(fred)))<=>((curious(alice)<~>~curious(alice))))&
(((calm(john)|~rich(john)))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((curious(X)<~>strong(X))=>curious(X)))&
(![X]:(~wise(X)<=>(old(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:((happy(X)&~strong(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:(~rich(X))))&
(![X]:(~happy(X)<=>quiet(X)))&
(![X]:((calm(X)<~>~kind(X))=>(~kind(X)|funny(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~old(X)))&
((?[X]:((~tall(X)|strong(X))))<=>(?[X]:((strong(X)|calm(X)))))&
(![X]:((curious(X)<~>patient(X))=>(quiet(X)|patient(X))))&
((funny(fred)|tall(fred)))&
(?[X]:(creative(X)))&
((~generous(susan)<~>~quiet(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((quiet(X)|generous(X))))&
((old(susan)<~>quiet(susan)))&
(?[X]:(~funny(X))) | brave(alice) | [] | null | 0 |
If john is either tall or curious then someone is not generous and vice versa.
Everyone who is humble or tall is either not creative or curious and vice versa.
If lucy is either tall or generous then someone is quiet.
Everyone who is either generous or not old is not humble or not quiet and vice versa.
Everyone who is both not wise and not generous is not old or not rich.
Everyone who is not rich is generous.
If someone is both brave and old then someone is not generous and vice versa.
If john is both brave and kind then someone is humble or not brave and vice versa.
If mary is not tall or not calm then paul is both not kind and wise.
Everyone who is either not tall or generous is either not funny or creative and vice versa.
Everyone who is both not quiet and not calm is not generous and vice versa.
If someone is old or not happy then someone is wise and vice versa.
If someone is both tall and not kind then someone is both not wise and not humble.
If someone is both not calm and humble then fred is not quiet or not generous.
Everyone who is both kind and brave is kind or not generous.
Everyone who is curious or not curious is either not creative or not old.
John is generous or not curious.
Someone is humble.
Someone is not tall.
Susan is either not patient or humble.
Mary is wise.
Paul is both quiet and not rich.
Fred is creative or old. | John is not curious. | neutral | (((tall(john)<~>curious(john)))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)|tall(X))<=>(~creative(X)<~>curious(X))))&
(((tall(lucy)<~>generous(lucy)))=>(?[X]:(quiet(X))))&
(![X]:((generous(X)<~>~old(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~wise(X)&~generous(X))=>(~old(X)|~rich(X))))&
(![X]:(~rich(X)=>generous(X)))&
((?[X]:((brave(X)&old(X))))<=>(?[X]:(~generous(X))))&
(((brave(john)&kind(john)))<=>(?[X]:((humble(X)|~brave(X)))))&
(((~tall(mary)|~calm(mary)))=>((~kind(paul)&wise(paul))))&
(![X]:((~tall(X)<~>generous(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~quiet(X)&~calm(X))<=>~generous(X)))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:(wise(X))))&
((?[X]:((tall(X)&~kind(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((~calm(X)&humble(X))))=>((~quiet(fred)|~generous(fred))))&
(![X]:((kind(X)&brave(X))=>(kind(X)|~generous(X))))&
(![X]:((curious(X)|~curious(X))=>(~creative(X)<~>~old(X))))&
((generous(john)|~curious(john)))&
(?[X]:(humble(X)))&
(?[X]:(~tall(X)))&
((~patient(susan)<~>humble(susan)))&
(wise(mary))&
((quiet(paul)&~rich(paul)))&
((creative(fred)|old(fred))) | ~curious(john) | [] | null | 0 |
If someone is both not calm and happy then lucy is both not quiet and generous and vice versa.
Everyone who is not humble is either not tall or old and vice versa.
Everyone who is either generous or humble is both humble and not calm and vice versa.
Everyone who is brave is both not rich and not tall and vice versa.
Everyone who is both patient and old is tall or rich.
Everyone who is not wise or not tall is curious or humble.
If mary is kind then paul is not quiet and vice versa.
If someone is either generous or not curious then fred is not humble and vice versa.
Everyone who is wise or strong is either not old or not tall.
If someone is curious then someone is not humble and vice versa.
If alice is not quiet then alice is not old or rich and vice versa.
Everyone who is rich is not creative or not tall and vice versa.
Everyone who is both not creative and not tall is rich and vice versa.
If someone is either funny or not humble then susan is creative or not wise.
Everyone who is both brave and creative is either brave or tall and vice versa.
If fred is kind then someone is either calm or not humble.
John is both calm and old.
Someone is both rich and not creative.
Someone is both not kind and wise.
Susan is not quiet or generous.
Susan is either not funny or brave.
Someone is either not wise or tall.
Someone is funny.
John is either calm or not old. | John is creative. | contradiction | ((?[X]:((~calm(X)&happy(X))))<=>((~quiet(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>(~tall(X)<~>old(X))))&
(![X]:((generous(X)<~>humble(X))<=>(humble(X)&~calm(X))))&
(![X]:(brave(X)<=>(~rich(X)&~tall(X))))&
(![X]:((patient(X)&old(X))=>(tall(X)|rich(X))))&
(![X]:((~wise(X)|~tall(X))=>(curious(X)|humble(X))))&
((kind(mary))<=>(~quiet(paul)))&
((?[X]:((generous(X)<~>~curious(X))))<=>(~humble(fred)))&
(![X]:((wise(X)|strong(X))=>(~old(X)<~>~tall(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>((~old(alice)|rich(alice))))&
(![X]:(rich(X)<=>(~creative(X)|~tall(X))))&
(![X]:((~creative(X)&~tall(X))<=>rich(X)))&
((?[X]:((funny(X)<~>~humble(X))))=>((creative(susan)|~wise(susan))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>tall(X))))&
((kind(fred))=>(?[X]:((calm(X)<~>~humble(X)))))&
((calm(john)&old(john)))&
(?[X]:((rich(X)&~creative(X))))&
(?[X]:((~kind(X)&wise(X))))&
((~quiet(susan)|generous(susan)))&
((~funny(susan)<~>brave(susan)))&
(?[X]:((~wise(X)<~>tall(X))))&
(?[X]:(funny(X)))&
((calm(john)<~>~old(john))) | creative(john) | [
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 898557549694534779743478
% SZS output start Proof for 898557549694534779743478
4. ! [X0] : (brave(X0) <=> (~tall(X0) & ~rich(X0))) [input p3]
12. ! [X0] : (rich(X0) <=> (~tall(X0) | ~creative(X0))) [input p11]
13. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((creative(X0) & brave(X0)) <=> (brave(X0) <~> tall(X0))) [input p14]
25. creative(john) [input hypothesis]
43. ! [X0] : ((brave(X0) | (tall(X0) | rich(X0))) & ((~tall(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 4]
44. ! [X0] : ((brave(X0) | tall(X0) | rich(X0)) & ((~tall(X0) & ~rich(X0)) | ~brave(X0))) [flattening 43]
58. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~rich(X0))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~rich(X0))) [flattening 58]
60. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) | creative(X0)))) [nnf transformation 13]
61. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~rich(X0)) & (rich(X0) | tall(X0) | creative(X0))) [flattening 60]
63. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~creative(X0) | ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : (((creative(X0) & brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) & (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | ~creative(X0) | ~brave(X0))) [flattening 63]
94. ~brave(X0) | ~tall(X0) [cnf transformation 44]
113. rich(X0) | tall(X0) [cnf transformation 59]
115. ~creative(X0) | ~rich(X0) [cnf transformation 61]
122. brave(X0) | brave(X0) | ~tall(X0) [cnf transformation 64]
141. creative(john) [cnf transformation 25]
143. brave(X0) | ~tall(X0) [duplicate literal removal 122]
250. ~tall(X0) [subsumption resolution 143,94]
293. ~rich(john) [resolution 115,141]
295. tall(john) [resolution 293,113]
296. $false [subsumption resolution 295,250]
% SZS output end Proof for 898557549694534779743478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not old then mary is calm and vice versa.
Everyone who is wise or tall is happy or not generous.
Everyone who is both humble and creative is calm and vice versa.
Everyone who is either wise or not curious is strong.
If fred is both not kind and happy then someone is either not old or not kind and vice versa.
Everyone who is not rich is both not tall and not creative and vice versa.
Everyone who is not happy is both not funny and not curious and vice versa.
If someone is not wise or not quiet then someone is not old.
If someone is not funny then someone is wise.
If lucy is both rich and not generous then mary is calm.
If someone is either not creative or calm then someone is creative or calm and vice versa.
If someone is either not rich or not strong then someone is humble or not strong.
If someone is either not patient or brave then alice is not rich or not generous and vice versa.
Everyone who is not curious or generous is either not old or tall and vice versa.
Everyone who is patient is both not humble and humble.
Everyone who is both calm and funny is both quiet and strong and vice versa.
Someone is creative.
Lucy is not generous.
John is tall or not strong.
John is either kind or not strong.
John is quiet or creative.
Someone is both wise and not old.
Fred is calm. | Mary is generous. | neutral | ((?[X]:((~curious(X)|~old(X))))<=>(calm(mary)))&
(![X]:((wise(X)|tall(X))=>(happy(X)|~generous(X))))&
(![X]:((humble(X)&creative(X))<=>calm(X)))&
(![X]:((wise(X)<~>~curious(X))=>strong(X)))&
(((~kind(fred)&happy(fred)))<=>(?[X]:((~old(X)<~>~kind(X)))))&
(![X]:(~rich(X)<=>(~tall(X)&~creative(X))))&
(![X]:(~happy(X)<=>(~funny(X)&~curious(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:(~old(X))))&
((?[X]:(~funny(X)))=>(?[X]:(wise(X))))&
(((rich(lucy)&~generous(lucy)))=>(calm(mary)))&
((?[X]:((~creative(X)<~>calm(X))))<=>(?[X]:((creative(X)|calm(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>brave(X))))<=>((~rich(alice)|~generous(alice))))&
(![X]:((~curious(X)|generous(X))<=>(~old(X)<~>tall(X))))&
(![X]:(patient(X)=>(~humble(X)&humble(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)&strong(X))))&
(?[X]:(creative(X)))&
(~generous(lucy))&
((tall(john)|~strong(john)))&
((kind(john)<~>~strong(john)))&
((quiet(john)|creative(john)))&
(?[X]:((wise(X)&~old(X))))&
(calm(fred)) | generous(mary) | [] | null | 0 |
Everyone who is not quiet or not strong is rich or funny and vice versa.
If someone is old or happy then paul is wise or brave.
Everyone who is either not old or not tall is generous or old and vice versa.
Everyone who is old is both not curious and quiet.
If someone is either quiet or not happy then someone is wise and vice versa.
Everyone who is both not humble and not tall is either not rich or tall.
Everyone who is rich or not quiet is both calm and happy.
Everyone who is calm is quiet and vice versa.
Everyone who is not strong is not funny and vice versa.
If someone is not strong then paul is humble.
Everyone who is either rich or not brave is either not old or creative and vice versa.
Everyone who is kind is both curious and not kind and vice versa.
If someone is either tall or quiet then someone is old.
Everyone who is either creative or not patient is both old and kind and vice versa.
Someone is not kind.
Someone is patient or funny.
Fred is not calm or patient.
Someone is either not curious or not creative.
Fred is not funny or generous. | Fred is not strong. | entailment | (![X]:((~quiet(X)|~strong(X))<=>(rich(X)|funny(X))))&
((?[X]:((old(X)|happy(X))))=>((wise(paul)|brave(paul))))&
(![X]:((~old(X)<~>~tall(X))<=>(generous(X)|old(X))))&
(![X]:(old(X)=>(~curious(X)&quiet(X))))&
((?[X]:((quiet(X)<~>~happy(X))))<=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~tall(X))=>(~rich(X)<~>tall(X))))&
(![X]:((rich(X)|~quiet(X))=>(calm(X)&happy(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
((?[X]:(~strong(X)))=>(humble(paul)))&
(![X]:((rich(X)<~>~brave(X))<=>(~old(X)<~>creative(X))))&
(![X]:(kind(X)<=>(curious(X)&~kind(X))))&
((?[X]:((tall(X)<~>quiet(X))))=>(?[X]:(old(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(old(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)|funny(X))))&
((~calm(fred)|patient(fred)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~funny(fred)|generous(fred))) | ~strong(fred) | [
"p0",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6946122517145641538359
% SZS output start Proof for 6946122517145641538359
1. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> (funny(X0) | rich(X0))) [input p0]
7. ! [X0] : ((~quiet(X0) | rich(X0)) => (happy(X0) & calm(X0))) [input p6]
8. ! [X0] : (calm(X0) <=> quiet(X0)) [input p7]
9. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p8]
20. strong(fred) [input hypothesis]
28. ! [X0] : ((happy(X0) & calm(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 7]
30. ! [X0] : (((~strong(X0) | ~quiet(X0)) | (~funny(X0) & ~rich(X0))) & ((funny(X0) | rich(X0)) | (strong(X0) & quiet(X0)))) [nnf transformation 1]
31. ! [X0] : ((~strong(X0) | ~quiet(X0) | (~funny(X0) & ~rich(X0))) & (funny(X0) | rich(X0) | (strong(X0) & quiet(X0)))) [flattening 30]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 8]
40. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 9]
60. ~funny(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 31]
76. calm(X0) | quiet(X0) [cnf transformation 28]
79. quiet(X0) | ~calm(X0) [cnf transformation 39]
80. calm(X0) | ~quiet(X0) [cnf transformation 39]
82. ~strong(X0) | funny(X0) [cnf transformation 40]
108. strong(fred) [cnf transformation 20]
156. calm(X0) [subsumption resolution 80,76]
157. quiet(X0) [subsumption resolution 79,156]
190. 17 <=> funny(fred) [avatar definition]
191. funny(fred) <- (17) [avatar component clause 190]
205. funny(fred) [resolution 82,108]
208. 17 [avatar split clause 205,190]
225. ~quiet(fred) | ~strong(fred) <- (17) [resolution 60,191]
228. ~strong(fred) <- (17) [subsumption resolution 225,157]
229. $false <- (17) [subsumption resolution 228,108]
230. ~17 [avatar contradiction clause 229]
231. $false [avatar sat refutation 208,230]
% SZS output end Proof for 6946122517145641538359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not quiet or calm.
Everyone who is not creative or brave is either happy or not happy and vice versa.
If someone is not brave or rich then fred is strong and vice versa.
Everyone who is kind or not quiet is either rich or curious and vice versa.
If fred is either tall or strong then someone is both rich and humble.
Everyone who is both patient and not rich is generous or not calm and vice versa.
If susan is creative then someone is both old and humble.
If someone is quiet then lucy is not rich or not strong.
Everyone who is both not patient and not old is either not curious or curious and vice versa.
If someone is both wise and not happy then someone is both rich and not kind.
If mary is both funny and creative then alice is not funny.
If someone is curious or patient then john is either humble or not rich.
Everyone who is either creative or not quiet is either not creative or not humble.
Everyone who is not creative or rich is not funny.
Everyone who is brave or quiet is both not creative and quiet.
If someone is brave or creative then someone is either not happy or not old and vice versa.
John is not happy.
Fred is not tall.
Lucy is tall or not rich.
Lucy is not calm or not kind.
Lucy is patient or not wise.
Someone is not generous. | Fred is not patient. | entailment | (![X]:(~quiet(X)=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)|brave(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((~brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((kind(X)|~quiet(X))<=>(rich(X)<~>curious(X))))&
(((tall(fred)<~>strong(fred)))=>(?[X]:((rich(X)&humble(X)))))&
(![X]:((patient(X)&~rich(X))<=>(generous(X)|~calm(X))))&
((creative(susan))=>(?[X]:((old(X)&humble(X)))))&
((?[X]:(quiet(X)))=>((~rich(lucy)|~strong(lucy))))&
(![X]:((~patient(X)&~old(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((wise(X)&~happy(X))))=>(?[X]:((rich(X)&~kind(X)))))&
(((funny(mary)&creative(mary)))=>(~funny(alice)))&
((?[X]:((curious(X)|patient(X))))=>((humble(john)<~>~rich(john))))&
(![X]:((creative(X)<~>~quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((~creative(X)|rich(X))=>~funny(X)))&
(![X]:((brave(X)|quiet(X))=>(~creative(X)&quiet(X))))&
((?[X]:((brave(X)|creative(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(~happy(john))&
(~tall(fred))&
((tall(lucy)|~rich(lucy)))&
((~calm(lucy)|~kind(lucy)))&
((patient(lucy)|~wise(lucy)))&
(?[X]:(~generous(X))) | ~patient(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 962009753365663649195352
% SZS output start Proof for 962009753365663649195352
9. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~curious(X0) <~> curious(X0))) [input p8]
23. patient(fred) [input hypothesis]
54. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (old(X0) | patient(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | old(X0) | patient(X0))) [flattening 54]
96. ~patient(X0) | curious(X0) | curious(X0) [cnf transformation 55]
97. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
123. patient(fred) [cnf transformation 23]
126. ~patient(X0) | curious(X0) [duplicate literal removal 96]
127. ~patient(X0) | ~curious(X0) [duplicate literal removal 97]
198. ~patient(X0) [subsumption resolution 126,127]
247. $false [subsumption resolution 123,198]
% SZS output end Proof for 962009753365663649195352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not creative and not old is both rich and humble and vice versa. If lucy is rich or curious then someone is not funny and vice versa. If someone is either not brave or not old then paul is not creative or not calm and vice versa. Everyone who is either not creative or tall is not patient and vice versa. If john is not funny then john is not generous. Everyone who is either not old or not generous is either calm or wise. If someone is not wise or tall then someone is wise or not quiet. If someone is either not wise or strong then someone is not funny or not quiet and vice versa. Everyone who is strong is either quiet or wise and vice versa. If susan is calm then someone is not tall or kind and vice versa. If susan is generous then fred is either not old or quiet. Everyone who is both tall and funny is calm and vice versa. Everyone who is either curious or not brave is not patient or not curious. If someone is old or not brave then someone is not wise or brave and vice versa. If mary is not curious or not kind then mary is not quiet and vice versa. Everyone who is either not patient or tall is calm and vice versa. Paul is not funny. Someone is either not strong or not kind. Someone is not wise or brave. Alice is both curious and quiet. Someone is both not generous and humble. Someone is kind or not funny. Fred is both funny and generous. Someone is either strong or happy. | Paul is not creative. | contradiction | (![X]:((~creative(X)&~old(X))<=>(rich(X)&humble(X))))&
(((rich(lucy)|curious(lucy)))<=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>~old(X))))<=>((~creative(paul)|~calm(paul))))&
(![X]:((~creative(X)<~>tall(X))<=>~patient(X)))&
((~funny(john))=>(~generous(john)))&
(![X]:((~old(X)<~>~generous(X))=>(calm(X)<~>wise(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:((~funny(X)|~quiet(X)))))&
(![X]:(strong(X)<=>(quiet(X)<~>wise(X))))&
((calm(susan))<=>(?[X]:((~tall(X)|kind(X)))))&
((generous(susan))=>((~old(fred)<~>quiet(fred))))&
(![X]:((tall(X)&funny(X))<=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))=>(~patient(X)|~curious(X))))&
((?[X]:((old(X)|~brave(X))))<=>(?[X]:((~wise(X)|brave(X)))))&
(((~curious(mary)|~kind(mary)))<=>(~quiet(mary)))&
(![X]:((~patient(X)<~>tall(X))<=>calm(X)))&
(~funny(paul))&
(?[X]:((~strong(X)<~>~kind(X))))&
(?[X]:((~wise(X)|brave(X))))&
((curious(alice)&quiet(alice)))&
(?[X]:((~generous(X)&humble(X))))&
(?[X]:((kind(X)|~funny(X))))&
((funny(fred)&generous(fred)))&
(?[X]:((strong(X)<~>happy(X)))) | ~creative(paul) | [
"p3",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6259803739544937534404578
% SZS output start Proof for 6259803739544937534404578
4. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> ~patient(X0)) [input p3]
12. ! [X0] : ((funny(X0) & tall(X0)) <=> calm(X0)) [input p11]
16. ! [X0] : ((~patient(X0) <~> tall(X0)) <=> calm(X0)) [input p15]
17. ~funny(paul) [input p16]
25. ~creative(paul) [input hypothesis]
47. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | patient(X0)) & (~patient(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 4]
63. ! [X0] : (((funny(X0) & tall(X0)) | ~calm(X0)) & (calm(X0) | (~funny(X0) | ~tall(X0)))) [nnf transformation 12]
64. ! [X0] : (((funny(X0) & tall(X0)) | ~calm(X0)) & (calm(X0) | ~funny(X0) | ~tall(X0))) [flattening 63]
73. ! [X0] : ((((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ~calm(X0)) & (calm(X0) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0))))) [nnf transformation 16]
99. ~patient(X0) | tall(X0) | creative(X0) [cnf transformation 47]
102. ~tall(X0) | creative(X0) | patient(X0) [cnf transformation 47]
126. ~calm(X0) | tall(X0) [cnf transformation 64]
127. ~calm(X0) | funny(X0) [cnf transformation 64]
137. calm(X0) | tall(X0) | patient(X0) [cnf transformation 73]
138. ~patient(X0) | calm(X0) | ~tall(X0) [cnf transformation 73]
140. ~tall(X0) | patient(X0) | ~calm(X0) [cnf transformation 73]
141. ~funny(paul) [cnf transformation 17]
154. ~creative(paul) [cnf transformation 25]
188. 8 <=> creative(paul) [avatar definition]
189. ~creative(paul) <- (~8) [avatar component clause 188]
337. ~calm(X0) | patient(X0) [subsumption resolution 140,126]
338. patient(X0) | tall(X0) [subsumption resolution 137,337]
377. ~8 [avatar split clause 154,188]
402. tall(X0) | creative(X0) | tall(X0) [resolution 99,338]
404. tall(X0) | creative(X0) [duplicate literal removal 402]
410. creative(X0) | creative(X0) | patient(X0) [resolution 404,102]
411. patient(X0) | creative(X0) [duplicate literal removal 410]
452. calm(X0) | ~tall(X0) | creative(X0) [resolution 138,411]
455. calm(X0) | creative(X0) [subsumption resolution 452,404]
480. funny(X1) | creative(X1) [resolution 455,127]
482. creative(paul) [resolution 480,141]
486. $false <- (~8) [subsumption resolution 482,189]
487. 8 [avatar contradiction clause 486]
488. $false [avatar sat refutation 377,487]
% SZS output end Proof for 6259803739544937534404578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not wise and not curious then someone is either not strong or not generous.
Everyone who is funny or not curious is wise and vice versa.
Everyone who is rich is not wise or not patient.
Everyone who is humble is either not rich or not old.
Everyone who is either not creative or old is humble or funny and vice versa.
Everyone who is both not humble and not curious is both tall and not strong and vice versa.
If lucy is not quiet then someone is wise and vice versa.
Everyone who is either strong or not funny is not calm and vice versa.
If someone is either not humble or brave then someone is not creative or quiet.
If fred is patient then lucy is calm or not creative and vice versa.
Everyone who is either not generous or not old is both kind and curious.
Everyone who is not rich or old is either not tall or creative.
If susan is both not tall and funny then someone is both not curious and kind and vice versa.
Everyone who is either rich or not brave is either happy or not curious and vice versa.
Everyone who is not tall or humble is tall or calm and vice versa.
Everyone who is rich or not rich is either tall or patient and vice versa.
Susan is not funny or brave.
Fred is funny or humble.
Fred is either not creative or not patient.
Someone is quiet or brave.
Mary is either not kind or not strong.
Susan is both kind and old.
Someone is strong.
Someone is both not curious and rich. | Susan is curious. | entailment | (((~wise(mary)&~curious(mary)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((funny(X)|~curious(X))<=>wise(X)))&
(![X]:(rich(X)=>(~wise(X)|~patient(X))))&
(![X]:(humble(X)=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>old(X))<=>(humble(X)|funny(X))))&
(![X]:((~humble(X)&~curious(X))<=>(tall(X)&~strong(X))))&
((~quiet(lucy))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((patient(fred))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~generous(X)<~>~old(X))=>(kind(X)&curious(X))))&
(![X]:((~rich(X)|old(X))=>(~tall(X)<~>creative(X))))&
(((~tall(susan)&funny(susan)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((~tall(X)|humble(X))<=>(tall(X)|calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((~funny(susan)|brave(susan)))&
((funny(fred)|humble(fred)))&
((~creative(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)|brave(X))))&
((~kind(mary)<~>~strong(mary)))&
((kind(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&rich(X)))) | curious(susan) | [
"p1",
"p2",
"p4",
"p5",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2186585520504782089343102
% SZS output start Proof for 2186585520504782089343102
2. ! [X0] : ((~curious(X0) | funny(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : (rich(X0) => (~patient(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((~creative(X0) <~> old(X0)) <=> (funny(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (~strong(X0) & tall(X0))) [input p5]
12. ! [X0] : ((old(X0) | ~rich(X0)) => (~tall(X0) <~> creative(X0))) [input p11]
13. (funny(susan) & ~tall(susan)) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p12]
15. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p14]
16. ! [X0] : ((~rich(X0) | rich(X0)) <=> (tall(X0) <~> patient(X0))) [input p15]
22. old(susan) & kind(susan) [input p21]
25. ~curious(susan) [input hypothesis]
29. ! [X0] : ((~patient(X0) | ~wise(X0)) | ~rich(X0)) [ennf transformation 3]
30. ! [X0] : (~patient(X0) | ~wise(X0) | ~rich(X0)) [flattening 29]
34. ! [X0] : ((~tall(X0) <~> creative(X0)) | (~old(X0) & rich(X0))) [ennf transformation 12]
38. ! [X0] : (((~curious(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((~curious(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [flattening 38]
41. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & ((funny(X0) | humble(X0)) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & (funny(X0) | humble(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [flattening 41]
43. ! [X0] : (((~curious(X0) & ~humble(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (curious(X0) | humble(X0)))) [nnf transformation 6]
44. ! [X0] : (((~curious(X0) & ~humble(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | curious(X0) | humble(X0))) [flattening 43]
57. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~old(X0) & rich(X0))) [nnf transformation 34]
58. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | (~funny(susan) | tall(susan))) [nnf transformation 13]
59. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | ~funny(susan) | tall(susan)) [flattening 58]
60. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X1] : (kind(X1) & ~curious(X1)) | ~funny(susan) | tall(susan)) [rectify 59]
61. ? [X1] : (kind(X1) & ~curious(X1)) => (kind(sK3) & ~curious(sK3)) [choice axiom]
62. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & ((kind(sK3) & ~curious(sK3)) | ~funny(susan) | tall(susan)) [skolemisation 60,61]
64. ! [X0] : (((humble(X0) | ~tall(X0)) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | (~humble(X0) & tall(X0)))) [nnf transformation 15]
65. ! [X0] : ((humble(X0) | ~tall(X0) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | (~humble(X0) & tall(X0)))) [flattening 64]
66. ! [X0] : (((~rich(X0) | rich(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [nnf transformation 16]
67. ! [X0] : ((~rich(X0) | rich(X0) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [flattening 66]
79. curious(X0) | wise(X0) [cnf transformation 39]
81. ~patient(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 30]
88. ~old(X0) | creative(X0) | ~humble(X0) [cnf transformation 42]
90. tall(X0) | curious(X0) | humble(X0) [cnf transformation 44]
111. ~creative(X0) | tall(X0) | rich(X0) [cnf transformation 57]
115. ~tall(susan) | ~kind(X0) | curious(X0) [cnf transformation 62]
127. humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
129. patient(X0) | tall(X0) | ~rich(X0) [cnf transformation 67]
130. patient(X0) | tall(X0) | rich(X0) [cnf transformation 67]
131. ~patient(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 67]
132. ~patient(X0) | ~tall(X0) | rich(X0) [cnf transformation 67]
142. kind(susan) [cnf transformation 22]
143. old(susan) [cnf transformation 22]
147. ~curious(susan) [cnf transformation 25]
149. ~tall(X0) | humble(X0) [duplicate literal removal 127]
213. 15 <=> ! [X0] : (~kind(X0) | curious(X0)) [avatar definition]
214. ~kind(X0) | curious(X0) <- (15) [avatar component clause 213]
221. 17 <=> tall(susan) [avatar definition]
223. ~tall(susan) <- (~17) [avatar component clause 221]
224. 15 | ~17 [avatar split clause 115,221,213]
235. ~tall(X0) | ~patient(X0) [subsumption resolution 131,132]
236. tall(X0) | patient(X0) [subsumption resolution 129,130]
280. wise(susan) [resolution 79,147]
281. curious(susan) <- (15) [resolution 214,142]
283. $false <- (15) [subsumption resolution 281,147]
284. ~15 [avatar contradiction clause 283]
288. humble(X1) | patient(X1) [resolution 236,149]
289. patient(susan) <- (~17) [resolution 236,223]
298. ~wise(susan) | ~rich(susan) <- (~17) [resolution 81,289]
300. ~rich(susan) <- (~17) [subsumption resolution 298,280]
303. creative(susan) | ~humble(susan) [resolution 88,143]
305. 29 <=> humble(susan) [avatar definition]
307. ~humble(susan) <- (~29) [avatar component clause 305]
309. 30 <=> creative(susan) [avatar definition]
311. creative(susan) <- (30) [avatar component clause 309]
312. ~29 | 30 [avatar split clause 303,309,305]
319. curious(X0) | humble(X0) | ~patient(X0) [resolution 90,235]
323. humble(X0) | curious(X0) [subsumption resolution 319,288]
325. curious(susan) <- (~29) [resolution 323,307]
326. $false <- (~29) [subsumption resolution 325,147]
327. 29 [avatar contradiction clause 326]
421. tall(susan) | rich(susan) <- (30) [resolution 111,311]
422. rich(susan) <- (~17, 30) [subsumption resolution 421,223]
423. $false <- (~17, 30) [subsumption resolution 422,300]
424. 17 | ~30 [avatar contradiction clause 423]
425. $false [avatar sat refutation 224,284,312,327,424]
% SZS output end Proof for 2186585520504782089343102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and tall then someone is either brave or humble and vice versa. If alice is both funny and not brave then fred is not strong or not rich. Everyone who is either calm or quiet is not generous or quiet and vice versa. Everyone who is not wise or not quiet is both not brave and wise and vice versa. Everyone who is kind or quiet is not quiet or tall. Everyone who is quiet is both not creative and not calm and vice versa. If alice is not kind then alice is both not kind and calm and vice versa. Everyone who is both not happy and not patient is either not kind or not humble and vice versa. Everyone who is generous or kind is creative and vice versa. Everyone who is either not funny or not generous is not wise or funny. If paul is either strong or brave then someone is both brave and quiet and vice versa. If someone is both rich and not calm then someone is either curious or funny and vice versa. Everyone who is either humble or patient is either not funny or curious. If someone is both humble and not happy then susan is both humble and curious. Everyone who is not calm is both not quiet and not generous. If someone is quiet then someone is not calm or not rich. Someone is calm. Lucy is not funny or not old. Fred is either quiet or old. Someone is not happy. Someone is either quiet or calm. Someone is not creative or generous. Paul is both not generous and not happy. | Susan is humble. | neutral | ((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(alice)&~brave(alice)))=>((~strong(fred)|~rich(fred))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((humble(X)&~happy(X))))=>((humble(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(?[X]:(calm(X)))&
((~funny(lucy)|~old(lucy)))&
((quiet(fred)<~>old(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)<~>calm(X))))&
(?[X]:((~creative(X)|generous(X))))&
((~generous(paul)&~happy(paul))) | humble(susan) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If someone is both not humble and creative then someone is either curious or creative.
Everyone who is creative is rich or not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Fred is both quiet and funny.
Lucy is both not brave and creative.
Someone is not kind or not tall.
Lucy is either not humble or funny. | Fred is old. | entailment | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((curious(X)<~>creative(X)))))&
(![X]:(creative(X)<=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
((quiet(fred)&funny(fred)))&
((~brave(lucy)&creative(lucy)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(lucy)<~>funny(lucy))) | old(fred) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5894321059148517678984706
% SZS output start Proof for 5894321059148517678984706
4. ? [X0] : (~patient(X0) | ~brave(X0)) <=> old(fred) [input p3]
16. creative(lucy) & ~brave(lucy) [input p15]
19. ~old(fred) [input hypothesis]
37. (? [X0] : (~patient(X0) | ~brave(X0)) | ~old(fred)) & (old(fred) | ! [X0] : (patient(X0) & brave(X0))) [nnf transformation 4]
38. (? [X0] : (~patient(X0) | ~brave(X0)) | ~old(fred)) & (old(fred) | ! [X1] : (patient(X1) & brave(X1))) [rectify 37]
39. ? [X0] : (~patient(X0) | ~brave(X0)) => (~patient(sK1) | ~brave(sK1)) [choice axiom]
40. ((~patient(sK1) | ~brave(sK1)) | ~old(fred)) & (old(fred) | ! [X1] : (patient(X1) & brave(X1))) [skolemisation 38,39]
65. old(fred) | brave(X1) [cnf transformation 40]
104. ~brave(lucy) [cnf transformation 16]
109. ~old(fred) [cnf transformation 19]
126. 4 <=> old(fred) [avatar definition]
143. 8 <=> ! [X1] : brave(X1) [avatar definition]
144. brave(X1) <- (8) [avatar component clause 143]
145. 8 | 4 [avatar split clause 65,126,143]
203. ~4 [avatar split clause 109,126]
204. $false <- (8) [resolution 144,104]
205. ~8 [avatar contradiction clause 204]
206. $false [avatar sat refutation 145,203,205]
% SZS output end Proof for 5894321059148517678984706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not curious then someone is either not patient or calm and vice versa.
Everyone who is not creative or not funny is either not tall or not curious.
Everyone who is humble or tall is both wise and not brave and vice versa.
If lucy is rich then alice is either not kind or quiet and vice versa.
If john is funny then fred is curious and vice versa.
If someone is both not wise and generous then someone is both generous and not humble.
Everyone who is not quiet or curious is both not calm and old.
Everyone who is either not kind or not calm is both humble and old and vice versa.
If paul is not humble or funny then someone is funny or not happy and vice versa.
Everyone who is rich or not tall is calm or humble.
Everyone who is calm or happy is both calm and not funny and vice versa.
Everyone who is old or not tall is not happy.
Everyone who is both not curious and not funny is not rich.
Everyone who is brave is tall or strong.
If alice is happy then fred is either tall or not curious and vice versa.
Paul is not generous or calm.
John is not old or not calm.
Someone is both happy and not patient.
John is curious.
John is not humble.
Alice is both generous and not brave. | Paul is not calm. | neutral | ((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:((~creative(X)|~funny(X))=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)|tall(X))<=>(wise(X)&~brave(X))))&
((rich(lucy))<=>((~kind(alice)<~>quiet(alice))))&
((funny(john))<=>(curious(fred)))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~quiet(X)|curious(X))=>(~calm(X)&old(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(humble(X)&old(X))))&
(((~humble(paul)|funny(paul)))<=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:((rich(X)|~tall(X))=>(calm(X)|humble(X))))&
(![X]:((calm(X)|happy(X))<=>(calm(X)&~funny(X))))&
(![X]:((old(X)|~tall(X))=>~happy(X)))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:(brave(X)=>(tall(X)|strong(X))))&
((happy(alice))<=>((tall(fred)<~>~curious(fred))))&
((~generous(paul)|calm(paul)))&
((~old(john)|~calm(john)))&
(?[X]:((happy(X)&~patient(X))))&
(curious(john))&
(~humble(john))&
((generous(alice)&~brave(alice))) | ~calm(paul) | [] | null | 0 |
If someone is either humble or quiet then someone is old and vice versa. Everyone who is not creative is kind or calm. If susan is not old then alice is not happy or kind and vice versa. If alice is happy then alice is creative and vice versa. Everyone who is generous or not creative is either generous or not funny. If paul is either not wise or humble then alice is either not brave or not patient and vice versa. Everyone who is patient or curious is both not wise and patient and vice versa. If someone is either not happy or not calm then someone is both not strong and not humble. Everyone who is either not humble or wise is not tall. Everyone who is both old and creative is either generous or not calm and vice versa. Everyone who is both not kind and not generous is not happy or strong. Everyone who is both not kind and happy is patient or not strong. If mary is wise or not old then someone is both old and kind and vice versa. Everyone who is patient is kind or not creative. If fred is tall or not curious then paul is not quiet and vice versa. If mary is not patient then someone is not funny or funny and vice versa. Someone is both not curious and happy. Someone is either calm or brave. Fred is calm. Susan is either not strong or creative. Paul is not humble. Lucy is either wise or kind. Paul is both calm and happy. Someone is either not rich or rich. | Alice is creative. | neutral | ((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:(old(X))))&
(![X]:(~creative(X)=>(kind(X)|calm(X))))&
((~old(susan))<=>((~happy(alice)|kind(alice))))&
((happy(alice))<=>(creative(alice)))&
(![X]:((generous(X)|~creative(X))=>(generous(X)<~>~funny(X))))&
(((~wise(paul)<~>humble(paul)))<=>((~brave(alice)<~>~patient(alice))))&
(![X]:((patient(X)|curious(X))<=>(~wise(X)&patient(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:((~humble(X)<~>wise(X))=>~tall(X)))&
(![X]:((old(X)&creative(X))<=>(generous(X)<~>~calm(X))))&
(![X]:((~kind(X)&~generous(X))=>(~happy(X)|strong(X))))&
(![X]:((~kind(X)&happy(X))=>(patient(X)|~strong(X))))&
(((wise(mary)|~old(mary)))<=>(?[X]:((old(X)&kind(X)))))&
(![X]:(patient(X)=>(kind(X)|~creative(X))))&
(((tall(fred)|~curious(fred)))<=>(~quiet(paul)))&
((~patient(mary))<=>(?[X]:((~funny(X)|funny(X)))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((calm(X)<~>brave(X))))&
(calm(fred))&
((~strong(susan)<~>creative(susan)))&
(~humble(paul))&
((wise(lucy)<~>kind(lucy)))&
((calm(paul)&happy(paul)))&
(?[X]:((~rich(X)<~>rich(X)))) | creative(alice) | [] | null | 0 |
If someone is both not tall and not humble then john is either strong or not curious and vice versa.
Everyone who is not kind is tall or not curious.
Everyone who is creative or not patient is not kind and vice versa.
If someone is not funny then susan is both not wise and patient and vice versa.
If someone is either curious or tall then someone is either not happy or not generous and vice versa.
Everyone who is creative or not humble is curious.
If john is both not creative and not curious then mary is both not curious and not humble.
Everyone who is humble is both creative and not curious and vice versa.
Everyone who is both old and not creative is both calm and not strong and vice versa.
Everyone who is both not quiet and brave is not creative or old and vice versa.
Everyone who is not quiet is happy or tall.
If someone is calm or funny then someone is both humble and strong.
If someone is both not creative and generous then someone is not generous or happy.
If mary is not funny then john is both generous and creative and vice versa.
Everyone who is both not calm and not wise is not creative.
Paul is not tall or not strong.
Someone is brave or not tall.
Someone is not old.
Fred is not humble or old.
Fred is strong.
Someone is both curious and not calm.
Someone is not curious or not generous. | John is not curious. | contradiction | ((?[X]:((~tall(X)&~humble(X))))<=>((strong(john)<~>~curious(john))))&
(![X]:(~kind(X)=>(tall(X)|~curious(X))))&
(![X]:((creative(X)|~patient(X))<=>~kind(X)))&
((?[X]:(~funny(X)))<=>((~wise(susan)&patient(susan))))&
((?[X]:((curious(X)<~>tall(X))))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((creative(X)|~humble(X))=>curious(X)))&
(((~creative(john)&~curious(john)))=>((~curious(mary)&~humble(mary))))&
(![X]:(humble(X)<=>(creative(X)&~curious(X))))&
(![X]:((old(X)&~creative(X))<=>(calm(X)&~strong(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~creative(X)|old(X))))&
(![X]:(~quiet(X)=>(happy(X)|tall(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:((humble(X)&strong(X)))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((~generous(X)|happy(X)))))&
((~funny(mary))<=>((generous(john)&creative(john))))&
(![X]:((~calm(X)&~wise(X))=>~creative(X)))&
((~tall(paul)|~strong(paul)))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:(~old(X)))&
((~humble(fred)|old(fred)))&
(strong(fred))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~curious(X)|~generous(X)))) | ~curious(john) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9164667214576090256213094
% SZS output start Proof for 9164667214576090256213094
6. ! [X0] : ((~humble(X0) | creative(X0)) => curious(X0)) [input p5]
7. (~curious(john) & ~creative(john)) => (~humble(mary) & ~curious(mary)) [input p6]
23. ~curious(john) [input hypothesis]
31. ! [X0] : (curious(X0) | (humble(X0) & ~creative(X0))) [ennf transformation 6]
32. (~humble(mary) & ~curious(mary)) | (curious(john) | creative(john)) [ennf transformation 7]
33. (~humble(mary) & ~curious(mary)) | curious(john) | creative(john) [flattening 32]
96. ~creative(X0) | curious(X0) [cnf transformation 31]
97. curious(X0) | humble(X0) [cnf transformation 31]
98. ~curious(mary) | curious(john) | creative(john) [cnf transformation 33]
99. ~humble(mary) | curious(john) | creative(john) [cnf transformation 33]
130. ~curious(john) [cnf transformation 23]
132. 1 <=> curious(john) [avatar definition]
210. ~humble(mary) | curious(john) [subsumption resolution 99,96]
212. 18 <=> humble(mary) [avatar definition]
214. ~humble(mary) <- (~18) [avatar component clause 212]
215. 1 | ~18 [avatar split clause 210,212,132]
216. ~curious(mary) | curious(john) [subsumption resolution 98,96]
218. 19 <=> curious(mary) [avatar definition]
220. ~curious(mary) <- (~19) [avatar component clause 218]
221. 1 | ~19 [avatar split clause 216,218,132]
303. ~1 [avatar split clause 130,132]
311. humble(mary) <- (~19) [resolution 97,220]
312. $false <- (~18, ~19) [subsumption resolution 311,214]
313. 18 | 19 [avatar contradiction clause 312]
314. $false [avatar sat refutation 215,221,303,313]
% SZS output end Proof for 9164667214576090256213094
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or generous is either quiet or patient.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
If someone is old then lucy is happy or rich.
Everyone who is both happy and curious is strong.
If someone is rich then someone is both not brave and not kind.
Everyone who is not funny or not rich is not tall.
If lucy is not kind or strong then alice is old or not happy and vice versa.
Someone is curious or not brave.
Someone is humble or generous.
Fred is both not happy and rich.
Someone is kind or wise.
Someone is not calm or not generous. | Alice is creative. | neutral | (![X]:((~funny(X)<~>generous(X))=>(quiet(X)<~>patient(X))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~funny(X)|~rich(X))=>~tall(X)))&
(((~kind(lucy)|strong(lucy)))<=>((old(alice)|~happy(alice))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((humble(X)|generous(X))))&
((~happy(fred)&rich(fred)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~calm(X)|~generous(X)))) | creative(alice) | [] | null | 0 |
If someone is curious or not strong then someone is either calm or kind and vice versa. Everyone who is not humble is both not brave and not wise and vice versa. Everyone who is tall is both not wise and quiet and vice versa. If paul is either humble or strong then someone is kind or not funny and vice versa. Everyone who is both not humble and brave is either not generous or not rich. Everyone who is either not brave or not strong is tall or calm. Everyone who is either rich or not humble is not kind and vice versa. Everyone who is either calm or not calm is both not tall and not humble and vice versa. Everyone who is either not happy or not generous is old. If mary is either not happy or not calm then susan is not tall. Everyone who is curious or not curious is generous. If someone is strong or humble then someone is both kind and generous and vice versa. Everyone who is not curious or not generous is both patient and not funny. If someone is funny then someone is not creative or not calm and vice versa. Everyone who is either not tall or not generous is not creative or creative and vice versa. If fred is both not creative and not funny then someone is both not wise and kind and vice versa. Susan is not wise. Someone is both not quiet and not rich. Lucy is either creative or funny. Mary is creative. Mary is both calm and kind. Someone is both not funny and curious. Someone is old. | Mary is not creative. | contradiction | ((?[X]:((curious(X)|~strong(X))))<=>(?[X]:((calm(X)<~>kind(X)))))&
(![X]:(~humble(X)<=>(~brave(X)&~wise(X))))&
(![X]:(tall(X)<=>(~wise(X)&quiet(X))))&
(((humble(paul)<~>strong(paul)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~humble(X)&brave(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>~strong(X))=>(tall(X)|calm(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~kind(X)))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
(~wise(susan))&
(?[X]:((~quiet(X)&~rich(X))))&
((creative(lucy)<~>funny(lucy)))&
(creative(mary))&
((calm(mary)&kind(mary)))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:(old(X))) | ~creative(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7956329506056860417269810
% SZS output start Proof for 7956329506056860417269810
20. creative(mary) [input p19]
24. ~creative(mary) [input hypothesis]
140. creative(mary) [cnf transformation 20]
145. ~creative(mary) [cnf transformation 24]
287. $false [subsumption resolution 145,140]
% SZS output end Proof for 7956329506056860417269810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not curious is either not generous or strong and vice versa. If alice is both patient and not happy then someone is either kind or happy. If lucy is not generous then someone is either tall or brave. If paul is not strong then someone is not tall or not calm and vice versa. If alice is both calm and brave then mary is happy. Everyone who is either quiet or not wise is both not funny and not wise and vice versa. Everyone who is both quiet and kind is either creative or not wise. Everyone who is either creative or curious is either generous or not creative. Everyone who is either quiet or not wise is both rich and calm. Everyone who is both happy and not funny is both brave and patient and vice versa. If someone is not happy or kind then susan is funny or not curious. Everyone who is both not quiet and not happy is either not tall or funny. Everyone who is not strong or not creative is not wise or not generous and vice versa. Everyone who is both not kind and happy is kind. If lucy is not curious then someone is either old or not funny and vice versa. Everyone who is not quiet or not brave is both calm and not wise. Someone is both not calm and brave. Fred is wise or funny. Lucy is not tall or not happy. Lucy is either curious or not happy. Mary is both happy and not quiet. Someone is both curious and happy. | Mary is happy. | entailment | (![X]:((~patient(X)|~curious(X))<=>(~generous(X)<~>strong(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((kind(X)<~>happy(X)))))&
((~generous(lucy))=>(?[X]:((tall(X)<~>brave(X)))))&
((~strong(paul))<=>(?[X]:((~tall(X)|~calm(X)))))&
(((calm(alice)&brave(alice)))=>(happy(mary)))&
(![X]:((quiet(X)<~>~wise(X))<=>(~funny(X)&~wise(X))))&
(![X]:((quiet(X)&kind(X))=>(creative(X)<~>~wise(X))))&
(![X]:((creative(X)<~>curious(X))=>(generous(X)<~>~creative(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(rich(X)&calm(X))))&
(![X]:((happy(X)&~funny(X))<=>(brave(X)&patient(X))))&
((?[X]:((~happy(X)|kind(X))))=>((funny(susan)|~curious(susan))))&
(![X]:((~quiet(X)&~happy(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~strong(X)|~creative(X))<=>(~wise(X)|~generous(X))))&
(![X]:((~kind(X)&happy(X))=>kind(X)))&
((~curious(lucy))<=>(?[X]:((old(X)<~>~funny(X)))))&
(![X]:((~quiet(X)|~brave(X))=>(calm(X)&~wise(X))))&
(?[X]:((~calm(X)&brave(X))))&
((wise(fred)|funny(fred)))&
((~tall(lucy)|~happy(lucy)))&
((curious(lucy)<~>~happy(lucy)))&
((happy(mary)&~quiet(mary)))&
(?[X]:((curious(X)&happy(X)))) | happy(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7881919287215349429404085
% SZS output start Proof for 7881919287215349429404085
21. ~quiet(mary) & happy(mary) [input p20]
23. ~happy(mary) [input hypothesis]
127. happy(mary) [cnf transformation 21]
131. ~happy(mary) [cnf transformation 23]
199. 15 <=> happy(mary) [avatar definition]
255. 15 [avatar split clause 127,199]
256. ~15 [avatar split clause 131,199]
257. $false [avatar sat refutation 255,256]
% SZS output end Proof for 7881919287215349429404085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not wise is both generous and not funny and vice versa.
Everyone who is both quiet and not quiet is not brave or not old.
Everyone who is both humble and not kind is creative or wise.
If someone is not happy then mary is not kind or calm.
Everyone who is both not strong and not calm is both not wise and not brave and vice versa.
If someone is funny then someone is either not humble or curious.
Everyone who is funny or quiet is either not generous or not happy.
Everyone who is not patient is wise or not rich.
Everyone who is wise is not kind.
Everyone who is not humble or not brave is not quiet or wise.
If lucy is both patient and rich then john is not funny or not brave.
Everyone who is both happy and rich is creative.
Everyone who is both happy and not strong is either not patient or not happy and vice versa.
If lucy is either humble or old then someone is happy or not brave and vice versa.
Everyone who is either curious or humble is both not curious and not kind.
Everyone who is not strong or not kind is either strong or tall.
Paul is quiet.
Paul is both not generous and not brave.
Fred is both not wise and not creative.
Someone is both quiet and patient.
Someone is both wise and old.
Someone is both rich and curious.
Someone is not kind or not humble.
Someone is either not kind or not tall. | Fred is not rich. | entailment | (![X]:((kind(X)|~wise(X))<=>(generous(X)&~funny(X))))&
(![X]:((quiet(X)&~quiet(X))=>(~brave(X)|~old(X))))&
(![X]:((humble(X)&~kind(X))=>(creative(X)|wise(X))))&
((?[X]:(~happy(X)))=>((~kind(mary)|calm(mary))))&
(![X]:((~strong(X)&~calm(X))<=>(~wise(X)&~brave(X))))&
((?[X]:(funny(X)))=>(?[X]:((~humble(X)<~>curious(X)))))&
(![X]:((funny(X)|quiet(X))=>(~generous(X)<~>~happy(X))))&
(![X]:(~patient(X)=>(wise(X)|~rich(X))))&
(![X]:(wise(X)=>~kind(X)))&
(![X]:((~humble(X)|~brave(X))=>(~quiet(X)|wise(X))))&
(((patient(lucy)&rich(lucy)))=>((~funny(john)|~brave(john))))&
(![X]:((happy(X)&rich(X))=>creative(X)))&
(![X]:((happy(X)&~strong(X))<=>(~patient(X)<~>~happy(X))))&
(((humble(lucy)<~>old(lucy)))<=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>humble(X))=>(~curious(X)&~kind(X))))&
(![X]:((~strong(X)|~kind(X))=>(strong(X)<~>tall(X))))&
(quiet(paul))&
((~generous(paul)&~brave(paul)))&
((~wise(fred)&~creative(fred)))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((~kind(X)<~>~tall(X)))) | ~rich(fred) | [
"p7",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1250491490348524417519698
% SZS output start Proof for 1250491490348524417519698
8. ! [X0] : (~patient(X0) => (~rich(X0) | wise(X0))) [input p7]
12. ! [X0] : ((rich(X0) & happy(X0)) => creative(X0)) [input p11]
13. ! [X0] : ((~strong(X0) & happy(X0)) <=> (~patient(X0) <~> ~happy(X0))) [input p12]
19. ~creative(fred) & ~wise(fred) [input p18]
25. rich(fred) [input hypothesis]
35. ! [X0] : ((~rich(X0) | wise(X0)) | patient(X0)) [ennf transformation 8]
36. ! [X0] : (~rich(X0) | wise(X0) | patient(X0)) [flattening 35]
42. ! [X0] : (creative(X0) | (~rich(X0) | ~happy(X0))) [ennf transformation 12]
43. ! [X0] : (creative(X0) | ~rich(X0) | ~happy(X0)) [flattening 42]
55. ! [X0] : (((~strong(X0) & happy(X0)) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (strong(X0) | ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : (((~strong(X0) & happy(X0)) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | strong(X0) | ~happy(X0))) [flattening 55]
92. ~rich(X0) | wise(X0) | patient(X0) [cnf transformation 36]
97. ~rich(X0) | creative(X0) | ~happy(X0) [cnf transformation 43]
101. happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 56]
121. ~wise(fred) [cnf transformation 19]
122. ~creative(fred) [cnf transformation 19]
132. rich(fred) [cnf transformation 25]
136. ~patient(X0) | happy(X0) [duplicate literal removal 101]
299. wise(fred) | patient(fred) [resolution 92,132]
309. patient(fred) [subsumption resolution 299,121]
315. happy(fred) [resolution 309,136]
325. creative(fred) | ~happy(fred) [resolution 97,132]
327. ~happy(fred) [subsumption resolution 325,122]
328. $false [subsumption resolution 327,315]
% SZS output end Proof for 1250491490348524417519698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and humble is tall or brave. Everyone who is wise or not curious is either curious or wise and vice versa. If john is patient then someone is both not happy and generous. Everyone who is old is either not wise or not tall and vice versa. If john is both wise and generous then someone is not rich and vice versa. If someone is not brave or not strong then someone is either not happy or not funny and vice versa. If susan is not patient then alice is strong or curious and vice versa. Everyone who is not rich or not creative is rich or not calm. Everyone who is happy is not brave and vice versa. Everyone who is both not humble and rich is either not quiet or not creative and vice versa. Everyone who is either not calm or happy is either curious or happy. If susan is both creative and happy then someone is either not brave or humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. John is not generous or generous. Lucy is either wise or generous. Someone is either not wise or not rich. Someone is funny. Paul is both patient and rich. Someone is not tall. Lucy is not strong or creative. | Alice is generous. | entailment | (![X]:((patient(X)&humble(X))=>(tall(X)|brave(X))))&
(![X]:((wise(X)|~curious(X))<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(((wise(john)&generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~patient(susan))<=>((strong(alice)|curious(alice))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
((~generous(john)|generous(john)))&
((wise(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
((patient(paul)&rich(paul)))&
(?[X]:(~tall(X)))&
((~strong(lucy)|creative(lucy))) | generous(alice) | [
"p1",
"p3",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3369852844509976727502064
% SZS output start Proof for 3369852844509976727502064
2. ! [X0] : ((~curious(X0) | wise(X0)) <=> (curious(X0) <~> wise(X0))) [input p1]
4. ! [X0] : (old(X0) <=> (~wise(X0) <~> ~tall(X0))) [input p3]
13. (curious(alice) <~> generous(alice)) <=> ? [X0] : (happy(X0) | old(X0)) [input p12]
22. ? [X0] : ~tall(X0) [input p21]
24. ~generous(alice) [input hypothesis]
37. ! [X0] : (((~curious(X0) | wise(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & ~wise(X0)))) [nnf transformation 2]
38. ! [X0] : ((~curious(X0) | wise(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (curious(X0) & ~wise(X0)))) [flattening 37]
41. ! [X0] : ((old(X0) | ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | ~old(X0))) [nnf transformation 4]
61. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & (? [X0] : (happy(X0) | old(X0)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [nnf transformation 13]
62. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & (? [X1] : (happy(X1) | old(X1)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [rectify 61]
63. ? [X1] : (happy(X1) | old(X1)) => (happy(sK5) | old(sK5)) [choice axiom]
64. (((~generous(alice) | ~curious(alice)) & (generous(alice) | curious(alice))) | ! [X0] : (~happy(X0) & ~old(X0))) & ((happy(sK5) | old(sK5)) | ((curious(alice) | ~generous(alice)) & (generous(alice) | ~curious(alice)))) [skolemisation 62,63]
74. ? [X0] : ~tall(X0) => ~tall(sK8) [choice axiom]
75. ~tall(sK8) [skolemisation 22,74]
78. wise(X0) | curious(X0) | curious(X0) [cnf transformation 38]
79. ~wise(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 38]
81. ~curious(X0) | wise(X0) | wise(X0) | ~curious(X0) [cnf transformation 38]
88. old(X0) | ~wise(X0) | tall(X0) [cnf transformation 41]
119. generous(alice) | curious(alice) | ~old(X0) [cnf transformation 64]
140. ~tall(sK8) [cnf transformation 75]
142. ~generous(alice) [cnf transformation 24]
147. wise(X0) | curious(X0) [duplicate literal removal 78]
148. ~wise(X0) | ~curious(X0) [duplicate literal removal 79]
149. ~curious(X0) | wise(X0) [duplicate literal removal 81]
150. ~curious(X0) [subsumption resolution 148,149]
151. wise(X0) [subsumption resolution 147,150]
166. old(X0) | tall(X0) [subsumption resolution 88,151]
251. 22 <=> generous(alice) [avatar definition]
255. generous(alice) | ~old(X0) [subsumption resolution 119,150]
257. 23 <=> ! [X0] : ~old(X0) [avatar definition]
258. ~old(X0) <- (23) [avatar component clause 257]
259. 23 | 22 [avatar split clause 255,251,257]
283. ~22 [avatar split clause 142,251]
293. tall(X0) <- (23) [resolution 166,258]
295. $false <- (23) [resolution 293,140]
297. ~23 [avatar contradiction clause 295]
300. $false [avatar sat refutation 259,283,297]
% SZS output end Proof for 3369852844509976727502064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not patient is strong or not generous. If susan is not calm or quiet then someone is rich or not strong. Everyone who is patient or not curious is either kind or not generous and vice versa. Everyone who is tall or not rich is either calm or strong and vice versa. If someone is either rich or happy then someone is both generous and not creative and vice versa. If paul is generous or rich then mary is both not curious and funny. If someone is both not humble and not funny then paul is not curious. If susan is either not generous or not wise then john is humble or not wise and vice versa. Everyone who is both not rich and creative is both not wise and not old and vice versa. Everyone who is not funny is curious or patient and vice versa. If lucy is not funny then someone is curious or rich. Everyone who is strong or not creative is both old and not generous and vice versa. If someone is brave then someone is either not happy or humble. Everyone who is creative is not strong and vice versa. Everyone who is either curious or not rich is either curious or quiet and vice versa. Everyone who is both generous and calm is old or not old. Susan is either curious or wise. Someone is both not wise and tall. Someone is happy. Paul is not generous or not quiet. Someone is either kind or curious. Someone is not patient or not wise. Mary is funny. Someone is either rich or quiet. | Mary is wise. | neutral | (![X]:((old(X)<~>~patient(X))=>(strong(X)|~generous(X))))&
(((~calm(susan)|quiet(susan)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:((patient(X)|~curious(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((tall(X)|~rich(X))<=>(calm(X)<~>strong(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((generous(X)&~creative(X)))))&
(((generous(paul)|rich(paul)))=>((~curious(mary)&funny(mary))))&
((?[X]:((~humble(X)&~funny(X))))=>(~curious(paul)))&
(((~generous(susan)<~>~wise(susan)))<=>((humble(john)|~wise(john))))&
(![X]:((~rich(X)&creative(X))<=>(~wise(X)&~old(X))))&
(![X]:(~funny(X)<=>(curious(X)|patient(X))))&
((~funny(lucy))=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((strong(X)|~creative(X))<=>(old(X)&~generous(X))))&
((?[X]:(brave(X)))=>(?[X]:((~happy(X)<~>humble(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(curious(X)<~>quiet(X))))&
(![X]:((generous(X)&calm(X))=>(old(X)|~old(X))))&
((curious(susan)<~>wise(susan)))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:(happy(X)))&
((~generous(paul)|~quiet(paul)))&
(?[X]:((kind(X)<~>curious(X))))&
(?[X]:((~patient(X)|~wise(X))))&
(funny(mary))&
(?[X]:((rich(X)<~>quiet(X)))) | wise(mary) | [] | null | 0 |
Everyone who is kind is old. If someone is humble then lucy is not quiet or not old and vice versa. If someone is not tall then lucy is both wise and not tall. If lucy is either not old or not strong then paul is not happy. If susan is wise then someone is happy or wise. Everyone who is both not old and old is kind or wise and vice versa. Everyone who is either not curious or strong is either patient or not generous and vice versa. Everyone who is either calm or generous is not calm or kind and vice versa. If someone is happy or not tall then someone is wise or not generous. Everyone who is not tall or not strong is not rich or not calm and vice versa. Everyone who is either not quiet or not tall is either funny or not brave. If lucy is patient or rich then paul is not patient. If someone is not patient or patient then john is both not funny and not wise. Everyone who is either not generous or not funny is not rich and vice versa. If someone is strong then someone is both not tall and happy and vice versa. Fred is calm or not generous. Someone is funny. Alice is humble or quiet. Someone is either funny or not quiet. Someone is either brave or funny. John is curious. Someone is either quiet or creative. | John is not strong. | entailment | (![X]:(kind(X)=>old(X)))&
((?[X]:(humble(X)))<=>((~quiet(lucy)|~old(lucy))))&
((?[X]:(~tall(X)))=>((wise(lucy)&~tall(lucy))))&
(((~old(lucy)<~>~strong(lucy)))=>(~happy(paul)))&
((wise(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~old(X)&old(X))<=>(kind(X)|wise(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)|kind(X))))&
((?[X]:((happy(X)|~tall(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(funny(X)<~>~brave(X))))&
(((patient(lucy)|rich(lucy)))=>(~patient(paul)))&
((?[X]:((~patient(X)|patient(X))))=>((~funny(john)&~wise(john))))&
(![X]:((~generous(X)<~>~funny(X))<=>~rich(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
((calm(fred)|~generous(fred)))&
(?[X]:(funny(X)))&
((humble(alice)|quiet(alice)))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(curious(john))&
(?[X]:((quiet(X)<~>creative(X)))) | ~strong(john) | [
"p0",
"p5",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 42279417361053599639260
% SZS output start Proof for 42279417361053599639260
1. ! [X0] : (kind(X0) => old(X0)) [input p0]
6. ! [X0] : ((old(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p5]
8. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (kind(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~tall(X0) | happy(X0)) => ? [X0] : (~generous(X0) | wise(X0)) [input p8]
15. ? [X0] : strong(X0) <=> ? [X0] : (happy(X0) & ~tall(X0)) [input p14]
23. strong(john) [input hypothesis]
24. ? [X0] : (~tall(X0) | happy(X0)) => ? [X1] : (~generous(X1) | wise(X1)) [rectify 9]
25. ? [X0] : strong(X0) <=> ? [X1] : (happy(X1) & ~tall(X1)) [rectify 15]
26. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 1]
30. ? [X1] : (~generous(X1) | wise(X1)) | ! [X0] : (tall(X0) & ~happy(X0)) [ennf transformation 24]
42. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | old(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | old(X0))) [flattening 42]
45. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [flattening 45]
47. ? [X0] : (~generous(X0) | wise(X0)) | ! [X1] : (tall(X1) & ~happy(X1)) [rectify 30]
48. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK2) | wise(sK2)) [choice axiom]
49. (~generous(sK2) | wise(sK2)) | ! [X1] : (tall(X1) & ~happy(X1)) [skolemisation 47,48]
54. (? [X0] : strong(X0) | ! [X1] : (~happy(X1) | tall(X1))) & (? [X1] : (happy(X1) & ~tall(X1)) | ! [X0] : ~strong(X0)) [nnf transformation 25]
55. (? [X0] : strong(X0) | ! [X1] : (~happy(X1) | tall(X1))) & (? [X2] : (happy(X2) & ~tall(X2)) | ! [X3] : ~strong(X3)) [rectify 54]
56. ? [X0] : strong(X0) => strong(sK3) [choice axiom]
57. ? [X2] : (happy(X2) & ~tall(X2)) => (happy(sK4) & ~tall(sK4)) [choice axiom]
58. (strong(sK3) | ! [X1] : (~happy(X1) | tall(X1))) & ((happy(sK4) & ~tall(sK4)) | ! [X3] : ~strong(X3)) [skolemisation 55,57,56]
70. old(X0) | ~kind(X0) [cnf transformation 26]
80. ~old(X0) | ~kind(X0) [cnf transformation 43]
81. ~old(X0) | ~wise(X0) [cnf transformation 43]
83. old(X0) | ~wise(X0) [cnf transformation 43]
92. kind(X0) | ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 46]
94. generous(X0) | calm(X0) | calm(X0) [cnf transformation 46]
98. ~generous(sK2) | wise(sK2) | ~happy(X1) [cnf transformation 49]
119. happy(sK4) | ~strong(X3) [cnf transformation 58]
131. strong(john) [cnf transformation 23]
132. kind(X0) | ~calm(X0) | generous(X0) [duplicate literal removal 92]
133. generous(X0) | calm(X0) [duplicate literal removal 94]
188. ~wise(X0) [subsumption resolution 81,83]
189. ~kind(X0) [subsumption resolution 80,70]
190. ~calm(X0) | generous(X0) [subsumption resolution 132,189]
191. generous(X0) [subsumption resolution 190,133]
195. wise(sK2) | ~happy(X1) [subsumption resolution 98,191]
196. ~happy(X1) [subsumption resolution 195,188]
225. ~strong(X3) [subsumption resolution 119,196]
266. $false [subsumption resolution 131,225]
% SZS output end Proof for 42279417361053599639260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not curious or generous.
Everyone who is either not funny or old is brave.
If fred is not wise then lucy is either not generous or old and vice versa.
Everyone who is funny is not funny or calm and vice versa.
Everyone who is both not kind and not patient is either not old or wise and vice versa.
Everyone who is strong or not generous is not tall and vice versa.
Everyone who is not old is not wise or happy.
If someone is either not brave or not humble then someone is both not generous and not quiet.
Everyone who is not humble is creative or strong.
If someone is both not strong and not generous then john is not wise or not curious.
Everyone who is not tall is both not happy and not kind and vice versa.
If paul is both rich and not old then someone is calm.
Everyone who is not generous or quiet is both tall and not tall.
Everyone who is not wise is either not humble or calm.
If someone is either not old or not creative then paul is not funny.
If mary is not strong or not happy then susan is both not patient and not curious.
Someone is both not curious and happy.
Fred is either not rich or happy.
Someone is both old and happy.
Someone is either not brave or not quiet.
Alice is either not tall or happy. | Fred is not happy. | neutral | (![X]:(~strong(X)=>(~curious(X)|generous(X))))&
(![X]:((~funny(X)<~>old(X))=>brave(X)))&
((~wise(fred))<=>((~generous(lucy)<~>old(lucy))))&
(![X]:(funny(X)<=>(~funny(X)|calm(X))))&
(![X]:((~kind(X)&~patient(X))<=>(~old(X)<~>wise(X))))&
(![X]:((strong(X)|~generous(X))<=>~tall(X)))&
(![X]:(~old(X)=>(~wise(X)|happy(X))))&
((?[X]:((~brave(X)<~>~humble(X))))=>(?[X]:((~generous(X)&~quiet(X)))))&
(![X]:(~humble(X)=>(creative(X)|strong(X))))&
((?[X]:((~strong(X)&~generous(X))))=>((~wise(john)|~curious(john))))&
(![X]:(~tall(X)<=>(~happy(X)&~kind(X))))&
(((rich(paul)&~old(paul)))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)|quiet(X))=>(tall(X)&~tall(X))))&
(![X]:(~wise(X)=>(~humble(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~creative(X))))=>(~funny(paul)))&
(((~strong(mary)|~happy(mary)))=>((~patient(susan)&~curious(susan))))&
(?[X]:((~curious(X)&happy(X))))&
((~rich(fred)<~>happy(fred)))&
(?[X]:((old(X)&happy(X))))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((~tall(alice)<~>happy(alice))) | ~happy(fred) | [] | null | 0 |
Everyone who is both calm and not old is either quiet or not generous.
If fred is not old then someone is either old or kind.
If mary is happy or not funny then lucy is brave or not generous.
If paul is either not humble or curious then someone is not strong or not generous.
If lucy is either not humble or humble then paul is creative.
If lucy is either calm or humble then someone is both happy and not happy.
If someone is either not funny or not creative then alice is humble or not kind and vice versa.
If someone is brave then someone is both patient and not strong and vice versa.
Everyone who is humble is calm.
Everyone who is not tall or old is either brave or patient.
Everyone who is both patient and wise is not calm.
Everyone who is either not old or not quiet is quiet and vice versa.
If someone is either not old or not happy then alice is wise or not brave.
Everyone who is generous is tall or creative and vice versa.
Everyone who is not calm or rich is both humble and funny and vice versa.
Someone is both not tall and quiet.
Someone is not kind.
Someone is not rich.
Someone is not tall or not humble.
Susan is not humble or not funny.
Alice is either rich or strong. | Lucy is not generous. | neutral | (![X]:((calm(X)&~old(X))=>(quiet(X)<~>~generous(X))))&
((~old(fred))=>(?[X]:((old(X)<~>kind(X)))))&
(((happy(mary)|~funny(mary)))=>((brave(lucy)|~generous(lucy))))&
(((~humble(paul)<~>curious(paul)))=>(?[X]:((~strong(X)|~generous(X)))))&
(((~humble(lucy)<~>humble(lucy)))=>(creative(paul)))&
(((calm(lucy)<~>humble(lucy)))=>(?[X]:((happy(X)&~happy(X)))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((humble(alice)|~kind(alice))))&
((?[X]:(brave(X)))<=>(?[X]:((patient(X)&~strong(X)))))&
(![X]:(humble(X)=>calm(X)))&
(![X]:((~tall(X)|old(X))=>(brave(X)<~>patient(X))))&
(![X]:((patient(X)&wise(X))=>~calm(X)))&
(![X]:((~old(X)<~>~quiet(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~happy(X))))=>((wise(alice)|~brave(alice))))&
(![X]:(generous(X)<=>(tall(X)|creative(X))))&
(![X]:((~calm(X)|rich(X))<=>(humble(X)&funny(X))))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~rich(X)))&
(?[X]:((~tall(X)|~humble(X))))&
((~humble(susan)|~funny(susan)))&
((rich(alice)<~>strong(alice))) | ~generous(lucy) | [] | null | 0 |
Everyone who is both humble and not happy is not generous or patient.
Everyone who is either creative or patient is tall or patient and vice versa.
If someone is wise then susan is either curious or quiet.
If fred is not patient or not generous then fred is both happy and creative and vice versa.
Everyone who is either not calm or not humble is either humble or happy and vice versa.
If someone is either not humble or kind then someone is not wise.
Everyone who is not strong or not quiet is creative and vice versa.
Everyone who is both not creative and not patient is not patient or not humble and vice versa.
Everyone who is not generous or not tall is not kind and vice versa.
If paul is rich then someone is both not strong and not generous and vice versa.
If someone is strong then paul is creative or quiet and vice versa.
If someone is brave or kind then someone is not kind or brave and vice versa.
If someone is not happy or quiet then susan is calm.
If someone is either not rich or wise then someone is old or brave and vice versa.
Someone is old.
Susan is not generous.
Someone is not generous.
Lucy is humble.
Someone is not rich or funny.
Someone is not creative.
Someone is either not tall or not kind. | Fred is not generous. | contradiction | (![X]:((humble(X)&~happy(X))=>(~generous(X)|patient(X))))&
(![X]:((creative(X)<~>patient(X))<=>(tall(X)|patient(X))))&
((?[X]:(wise(X)))=>((curious(susan)<~>quiet(susan))))&
(((~patient(fred)|~generous(fred)))<=>((happy(fred)&creative(fred))))&
(![X]:((~calm(X)<~>~humble(X))<=>(humble(X)<~>happy(X))))&
((?[X]:((~humble(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)|~quiet(X))<=>creative(X)))&
(![X]:((~creative(X)&~patient(X))<=>(~patient(X)|~humble(X))))&
(![X]:((~generous(X)|~tall(X))<=>~kind(X)))&
((rich(paul))<=>(?[X]:((~strong(X)&~generous(X)))))&
((?[X]:(strong(X)))<=>((creative(paul)|quiet(paul))))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~kind(X)|brave(X)))))&
((?[X]:((~happy(X)|quiet(X))))=>(calm(susan)))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:((old(X)|brave(X)))))&
(?[X]:(old(X)))&
(~generous(susan))&
(?[X]:(~generous(X)))&
(humble(lucy))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)<~>~kind(X)))) | ~generous(fred) | [
"p1",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5697751469533620495210763
% SZS output start Proof for 5697751469533620495210763
2. ! [X0] : ((creative(X0) <~> patient(X0)) <=> (patient(X0) | tall(X0))) [input p1]
4. (~generous(fred) | ~patient(fred)) <=> (creative(fred) & happy(fred)) [input p3]
8. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (~humble(X0) | ~patient(X0))) [input p7]
22. ~generous(fred) [input hypothesis]
32. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (~patient(X0) & ~tall(X0))) & ((patient(X0) | tall(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [nnf transformation 2]
33. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (~patient(X0) & ~tall(X0))) & (patient(X0) | tall(X0) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [flattening 32]
35. ((~generous(fred) | ~patient(fred)) | (~creative(fred) | ~happy(fred))) & ((creative(fred) & happy(fred)) | (generous(fred) & patient(fred))) [nnf transformation 4]
36. (~generous(fred) | ~patient(fred) | ~creative(fred) | ~happy(fred)) & ((creative(fred) & happy(fred)) | (generous(fred) & patient(fred))) [flattening 35]
44. ! [X0] : (((~patient(X0) & ~creative(X0)) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 8]
45. ! [X0] : (((~patient(X0) & ~creative(X0)) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | patient(X0) | creative(X0))) [flattening 44]
82. ~patient(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 33]
88. creative(fred) | generous(fred) [cnf transformation 36]
104. ~creative(X0) | patient(X0) [cnf transformation 45]
136. ~generous(fred) [cnf transformation 22]
142. ~patient(X0) | ~creative(X0) [duplicate literal removal 82]
158. 4 <=> generous(fred) [avatar definition]
162. 5 <=> creative(fred) [avatar definition]
164. creative(fred) <- (5) [avatar component clause 162]
165. 4 | 5 [avatar split clause 88,162,158]
191. ~creative(X0) [subsumption resolution 104,142]
293. ~4 [avatar split clause 136,158]
294. $false <- (5) [subsumption resolution 164,191]
295. ~5 [avatar contradiction clause 294]
296. $false [avatar sat refutation 165,293,295]
% SZS output end Proof for 5697751469533620495210763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is either kind or not wise then someone is both quiet and happy. If someone is not wise or not brave then someone is not creative or not funny and vice versa. If someone is tall then fred is creative or tall and vice versa. Everyone who is not rich is rich or not creative and vice versa. Everyone who is not patient is old and vice versa. Everyone who is both not strong and not quiet is not happy or creative. Everyone who is not brave is calm. If fred is not old then fred is either funny or creative. If someone is humble or not generous then lucy is strong and vice versa. Everyone who is curious is not happy. If someone is curious then lucy is either not brave or generous. If susan is both happy and quiet then mary is funny or not happy. If lucy is funny then john is either not calm or not tall and vice versa. If alice is not patient then mary is old or creative and vice versa. Everyone who is not creative is both old and tall. Everyone who is funny or not calm is kind or not generous. Alice is either quiet or humble. Someone is not old or wise. Someone is either creative or strong. Susan is not brave or brave. Someone is calm or not creative. Someone is brave. | Mary is rich. | contradiction | (((kind(john)<~>~wise(john)))=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((~creative(X)|~funny(X)))))&
((?[X]:(tall(X)))<=>((creative(fred)|tall(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~creative(X))))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~strong(X)&~quiet(X))=>(~happy(X)|creative(X))))&
(![X]:(~brave(X)=>calm(X)))&
((~old(fred))=>((funny(fred)<~>creative(fred))))&
((?[X]:((humble(X)|~generous(X))))<=>(strong(lucy)))&
(![X]:(curious(X)=>~happy(X)))&
((?[X]:(curious(X)))=>((~brave(lucy)<~>generous(lucy))))&
(((happy(susan)&quiet(susan)))=>((funny(mary)|~happy(mary))))&
((funny(lucy))<=>((~calm(john)<~>~tall(john))))&
((~patient(alice))<=>((old(mary)|creative(mary))))&
(![X]:(~creative(X)=>(old(X)&tall(X))))&
(![X]:((funny(X)|~calm(X))=>(kind(X)|~generous(X))))&
((quiet(alice)<~>humble(alice)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((creative(X)<~>strong(X))))&
((~brave(susan)|brave(susan)))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:(brave(X))) | rich(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5629615091976878897696731
% SZS output start Proof for 5629615091976878897696731
4. ! [X0] : (~rich(X0) <=> (~creative(X0) | rich(X0))) [input p3]
23. rich(mary) [input hypothesis]
50. ! [X0] : ((~rich(X0) | (creative(X0) & ~rich(X0))) & ((~creative(X0) | rich(X0)) | rich(X0))) [nnf transformation 4]
51. ! [X0] : ((~rich(X0) | (creative(X0) & ~rich(X0))) & (~creative(X0) | rich(X0) | rich(X0))) [flattening 50]
83. ~rich(X0) | ~rich(X0) [cnf transformation 51]
114. rich(mary) [cnf transformation 23]
116. ~rich(X0) [duplicate literal removal 83]
278. $false [subsumption resolution 114,116]
% SZS output end Proof for 5629615091976878897696731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not tall or not happy then someone is not funny and vice versa. If someone is happy or not curious then john is either not calm or brave and vice versa. If someone is not creative or humble then susan is not old. Everyone who is either not patient or strong is patient and vice versa. If john is wise then someone is old or funny and vice versa. If someone is both old and not happy then someone is either not funny or not curious. If lucy is not rich or wise then someone is not funny or not calm. Everyone who is both not funny and not kind is both curious and not curious and vice versa. If someone is both not rich and old then someone is both not kind and not brave and vice versa. Everyone who is either not strong or wise is not happy and vice versa. If someone is not quiet or not curious then paul is not patient or not kind. If paul is both not humble and not happy then someone is not patient and vice versa. Everyone who is not wise or rich is not humble and vice versa. Everyone who is both quiet and tall is both not old and old. Everyone who is patient or old is either not calm or brave. Everyone who is curious is either not tall or not patient and vice versa. Mary is brave or not wise. Someone is both not kind and tall. Fred is both not wise and not generous. Susan is both not humble and not generous. Someone is either not happy or not old. Mary is either not patient or not kind. Alice is not generous or creative. Someone is either not funny or not wise. | Fred is not happy. | contradiction | ((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((happy(X)|~curious(X))))<=>((~calm(john)<~>brave(john))))&
((?[X]:((~creative(X)|humble(X))))=>(~old(susan)))&
(![X]:((~patient(X)<~>strong(X))<=>patient(X)))&
((wise(john))<=>(?[X]:((old(X)|funny(X)))))&
((?[X]:((old(X)&~happy(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~rich(lucy)|wise(lucy)))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)&~curious(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>~happy(X)))&
((?[X]:((~quiet(X)|~curious(X))))=>((~patient(paul)|~kind(paul))))&
(((~humble(paul)&~happy(paul)))<=>(?[X]:(~patient(X))))&
(![X]:((~wise(X)|rich(X))<=>~humble(X)))&
(![X]:((quiet(X)&tall(X))=>(~old(X)&old(X))))&
(![X]:((patient(X)|old(X))=>(~calm(X)<~>brave(X))))&
(![X]:(curious(X)<=>(~tall(X)<~>~patient(X))))&
((brave(mary)|~wise(mary)))&
(?[X]:((~kind(X)&tall(X))))&
((~wise(fred)&~generous(fred)))&
((~humble(susan)&~generous(susan)))&
(?[X]:((~happy(X)<~>~old(X))))&
((~patient(mary)<~>~kind(mary)))&
((~generous(alice)|creative(alice)))&
(?[X]:((~funny(X)<~>~wise(X)))) | ~happy(fred) | [
"p3",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6897436002797846129217677
% SZS output start Proof for 6897436002797846129217677
4. ! [X0] : ((~patient(X0) <~> strong(X0)) <=> patient(X0)) [input p3]
10. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> ~happy(X0)) [input p9]
19. ~generous(fred) & ~wise(fred) [input p18]
25. ~happy(fred) [input hypothesis]
29. ~wise(fred) [pure predicate removal 19]
50. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [nnf transformation 4]
68. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | happy(X0)) & (~happy(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 10]
98. patient(X0) | strong(X0) | patient(X0) [cnf transformation 50]
100. strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 50]
119. wise(X0) | ~strong(X0) | happy(X0) [cnf transformation 68]
142. ~wise(fred) [cnf transformation 29]
150. ~happy(fred) [cnf transformation 25]
151. patient(X0) | strong(X0) [duplicate literal removal 98]
152. ~patient(X0) | strong(X0) [duplicate literal removal 100]
214. strong(X0) [subsumption resolution 151,152]
294. wise(X0) | happy(X0) [subsumption resolution 119,214]
383. happy(fred) [resolution 294,142]
386. $false [subsumption resolution 383,150]
% SZS output end Proof for 6897436002797846129217677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either strong or not generous and vice versa. Everyone who is funny is not kind or not calm. If paul is either patient or not curious then someone is creative or strong. If someone is both patient and not strong then someone is quiet and vice versa. If lucy is not strong then fred is both humble and not funny. If lucy is either rich or not patient then someone is kind and vice versa. Everyone who is either not quiet or not curious is either not tall or not creative. If someone is not tall then alice is not rich. If someone is not patient or tall then someone is both not wise and not brave and vice versa. Everyone who is not brave or not rich is both not curious and rich. If mary is not curious then mary is not quiet and vice versa. If someone is not brave then someone is both happy and rich. Everyone who is both not humble and not funny is humble. Everyone who is kind is not strong or rich. If john is both not funny and not kind then john is both not humble and curious and vice versa. Someone is old. Paul is rich or not generous. Mary is not funny. Lucy is both not patient and not generous. Someone is not humble or patient. | Lucy is not calm. | neutral | (![X]:(~humble(X)<=>(strong(X)<~>~generous(X))))&
(![X]:(funny(X)=>(~kind(X)|~calm(X))))&
(((patient(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((~curious(mary))<=>(~quiet(mary)))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((~humble(X)&~funny(X))=>humble(X)))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(((~funny(john)&~kind(john)))<=>((~humble(john)&curious(john))))&
(?[X]:(old(X)))&
((rich(paul)|~generous(paul)))&
(~funny(mary))&
((~patient(lucy)&~generous(lucy)))&
(?[X]:((~humble(X)|patient(X)))) | ~calm(lucy) | [] | null | 0 |
If paul is both strong and quiet then susan is not kind or not generous and vice versa. If someone is not old or quiet then someone is both old and not calm and vice versa. If lucy is not rich or funny then lucy is not calm and vice versa. If someone is tall or brave then someone is old and vice versa. If paul is either not old or patient then someone is either not curious or kind. Everyone who is both not patient and generous is not generous. If someone is not calm or not wise then someone is both not patient and patient and vice versa. Everyone who is creative or brave is either not kind or not generous. If someone is quiet or not kind then someone is not rich or strong and vice versa. If someone is not wise then fred is happy and vice versa. If someone is both not old and calm then someone is either happy or patient. Everyone who is both not funny and not quiet is not generous or kind and vice versa. Everyone who is either not brave or tall is both creative and not brave and vice versa. If someone is either generous or strong then someone is not calm or patient and vice versa. If paul is not creative then someone is both calm and kind and vice versa. Someone is not brave. Someone is curious or patient. Someone is not creative or rich. Fred is both curious and not humble. Lucy is either not creative or not brave. Paul is wise. Someone is either not generous or not kind. Someone is both calm and kind. | Susan is not tall. | contradiction | (((strong(paul)&quiet(paul)))<=>((~kind(susan)|~generous(susan))))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:((old(X)&~calm(X)))))&
(((~rich(lucy)|funny(lucy)))<=>(~calm(lucy)))&
((?[X]:((tall(X)|brave(X))))<=>(?[X]:(old(X))))&
(((~old(paul)<~>patient(paul)))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~patient(X)&generous(X))=>~generous(X)))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((creative(X)|brave(X))=>(~kind(X)<~>~generous(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~rich(X)|strong(X)))))&
((?[X]:(~wise(X)))<=>(happy(fred)))&
((?[X]:((~old(X)&calm(X))))=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~calm(X)|patient(X)))))&
((~creative(paul))<=>(?[X]:((calm(X)&kind(X)))))&
(?[X]:(~brave(X)))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((~creative(X)|rich(X))))&
((curious(fred)&~humble(fred)))&
((~creative(lucy)<~>~brave(lucy)))&
(wise(paul))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:((calm(X)&kind(X)))) | ~tall(susan) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7456773483890491622879800
% SZS output start Proof for 7456773483890491622879800
1. (quiet(paul) & strong(paul)) <=> (~generous(susan) | ~kind(susan)) [input p0]
2. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X0] : (~calm(X0) & old(X0)) [input p1]
7. ? [X0] : (~wise(X0) | ~calm(X0)) <=> ? [X0] : (patient(X0) & ~patient(X0)) [input p6]
8. ! [X0] : ((brave(X0) | creative(X0)) => (~kind(X0) <~> ~generous(X0))) [input p7]
13. ! [X0] : ((~brave(X0) <~> tall(X0)) <=> (~brave(X0) & creative(X0))) [input p12]
24. ~tall(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X1] : (~calm(X1) & old(X1)) [rectify 2]
27. ? [X0] : (~wise(X0) | ~calm(X0)) <=> ? [X1] : (patient(X1) & ~patient(X1)) [rectify 7]
35. ! [X0] : ((~kind(X0) <~> ~generous(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 8]
37. ((quiet(paul) & strong(paul)) | (generous(susan) & kind(susan))) & ((~generous(susan) | ~kind(susan)) | (~quiet(paul) | ~strong(paul))) [nnf transformation 1]
38. ((quiet(paul) & strong(paul)) | (generous(susan) & kind(susan))) & (~generous(susan) | ~kind(susan) | ~quiet(paul) | ~strong(paul)) [flattening 37]
39. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : (calm(X1) | ~old(X1))) & (? [X1] : (~calm(X1) & old(X1)) | ! [X0] : (~quiet(X0) & old(X0))) [nnf transformation 25]
40. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : (calm(X1) | ~old(X1))) & (? [X2] : (~calm(X2) & old(X2)) | ! [X3] : (~quiet(X3) & old(X3))) [rectify 39]
41. ? [X0] : (quiet(X0) | ~old(X0)) => (quiet(sK0) | ~old(sK0)) [choice axiom]
42. ? [X2] : (~calm(X2) & old(X2)) => (~calm(sK1) & old(sK1)) [choice axiom]
43. ((quiet(sK0) | ~old(sK0)) | ! [X1] : (calm(X1) | ~old(X1))) & ((~calm(sK1) & old(sK1)) | ! [X3] : (~quiet(X3) & old(X3))) [skolemisation 40,42,41]
54. (? [X0] : (~wise(X0) | ~calm(X0)) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X1] : (patient(X1) & ~patient(X1)) | ! [X0] : (wise(X0) & calm(X0))) [nnf transformation 27]
55. (? [X0] : (~wise(X0) | ~calm(X0)) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X2] : (patient(X2) & ~patient(X2)) | ! [X3] : (wise(X3) & calm(X3))) [rectify 54]
56. ? [X0] : (~wise(X0) | ~calm(X0)) => (~wise(sK5) | ~calm(sK5)) [choice axiom]
57. ? [X2] : (patient(X2) & ~patient(X2)) => (patient(sK6) & ~patient(sK6)) [choice axiom]
58. ((~wise(sK5) | ~calm(sK5)) | ! [X1] : (~patient(X1) | patient(X1))) & ((patient(sK6) & ~patient(sK6)) | ! [X3] : (wise(X3) & calm(X3))) [skolemisation 55,57,56]
59. ! [X0] : (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | (~brave(X0) & ~creative(X0))) [nnf transformation 35]
75. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | (brave(X0) | ~creative(X0))) & ((~brave(X0) & creative(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [nnf transformation 13]
76. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | brave(X0) | ~creative(X0)) & ((~brave(X0) & creative(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [flattening 75]
101. quiet(paul) | kind(susan) [cnf transformation 38]
102. quiet(paul) | generous(susan) [cnf transformation 38]
106. ~calm(sK1) | ~quiet(X3) [cnf transformation 43]
119. ~patient(sK6) | calm(X3) [cnf transformation 58]
121. patient(sK6) | calm(X3) [cnf transformation 58]
124. ~creative(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 59]
125. ~brave(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 59]
141. creative(X0) | tall(X0) | brave(X0) [cnf transformation 76]
167. ~tall(susan) [cnf transformation 24]
172. 1 <=> generous(susan) [avatar definition]
174. generous(susan) <- (1) [avatar component clause 172]
176. 2 <=> quiet(paul) [avatar definition]
178. quiet(paul) <- (2) [avatar component clause 176]
179. 1 | 2 [avatar split clause 102,176,172]
181. 3 <=> kind(susan) [avatar definition]
183. kind(susan) <- (3) [avatar component clause 181]
184. 3 | 2 [avatar split clause 101,176,181]
205. 8 <=> ! [X3] : ~quiet(X3) [avatar definition]
206. ~quiet(X3) <- (8) [avatar component clause 205]
208. 9 <=> calm(sK1) [avatar definition]
210. ~calm(sK1) <- (~9) [avatar component clause 208]
211. 8 | ~9 [avatar split clause 106,208,205]
285. 26 <=> patient(sK6) [avatar definition]
290. 27 <=> ! [X3] : calm(X3) [avatar definition]
291. calm(X3) <- (27) [avatar component clause 290]
292. 27 | 26 [avatar split clause 121,285,290]
294. 27 | ~26 [avatar split clause 119,285,290]
438. $false <- (2, 8) [subsumption resolution 178,206]
439. ~2 | ~8 [avatar contradiction clause 438]
442. $false <- (~9, 27) [subsumption resolution 210,291]
443. 9 | ~27 [avatar contradiction clause 442]
484. tall(X1) | brave(X1) | ~kind(X1) | ~generous(X1) [resolution 141,124]
488. ~generous(X1) | ~kind(X1) | tall(X1) [subsumption resolution 484,125]
573. ~kind(susan) | tall(susan) <- (1) [resolution 488,174]
576. tall(susan) <- (1, 3) [subsumption resolution 573,183]
577. $false <- (1, 3) [subsumption resolution 576,167]
578. ~1 | ~3 [avatar contradiction clause 577]
580. $false [avatar sat refutation 179,184,211,292,294,439,443,578]
% SZS output end Proof for 7456773483890491622879800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not rich and creative then john is either curious or not happy and vice versa. Everyone who is not curious is both not rich and kind and vice versa. If someone is not calm then someone is not patient or not tall and vice versa. If someone is both not old and kind then mary is not creative or not happy. Everyone who is both funny and old is not strong and vice versa. Everyone who is kind is either strong or not quiet. If fred is calm or patient then someone is either not strong or rich. Everyone who is both not curious and quiet is either not calm or happy. Everyone who is funny or not kind is either strong or humble. If lucy is not creative then someone is not humble or not brave and vice versa. If lucy is wise then someone is rich or patient and vice versa. Everyone who is kind is both strong and tall. Everyone who is strong or not humble is not quiet or not generous and vice versa. If susan is both happy and not generous then someone is not humble or patient and vice versa. Everyone who is not tall is both happy and not wise. If lucy is quiet then alice is not happy. Someone is either humble or old. Someone is not rich or kind. Someone is both not tall and not funny. Someone is both not happy and calm. Fred is either funny or not tall. John is humble. Lucy is both generous and not happy. Someone is generous or wise. | Lucy is creative. | contradiction | (((~rich(fred)&creative(fred)))<=>((curious(john)<~>~happy(john))))&
(![X]:(~curious(X)<=>(~rich(X)&kind(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~patient(X)|~tall(X)))))&
((?[X]:((~old(X)&kind(X))))=>((~creative(mary)|~happy(mary))))&
(![X]:((funny(X)&old(X))<=>~strong(X)))&
(![X]:(kind(X)=>(strong(X)<~>~quiet(X))))&
(((calm(fred)|patient(fred)))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((~curious(X)&quiet(X))=>(~calm(X)<~>happy(X))))&
(![X]:((funny(X)|~kind(X))=>(strong(X)<~>humble(X))))&
((~creative(lucy))<=>(?[X]:((~humble(X)|~brave(X)))))&
((wise(lucy))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(kind(X)=>(strong(X)&tall(X))))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~generous(susan)))<=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
((quiet(lucy))=>(~happy(alice)))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((~tall(X)&~funny(X))))&
(?[X]:((~happy(X)&calm(X))))&
((funny(fred)<~>~tall(fred)))&
(humble(john))&
((generous(lucy)&~happy(lucy)))&
(?[X]:((generous(X)|wise(X)))) | creative(lucy) | [
"p4",
"p8",
"p9",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1258249113537027979560165
% SZS output start Proof for 1258249113537027979560165
5. ! [X0] : ((old(X0) & funny(X0)) <=> ~strong(X0)) [input p4]
9. ! [X0] : ((~kind(X0) | funny(X0)) => (strong(X0) <~> humble(X0))) [input p8]
10. ~creative(lucy) <=> ? [X0] : (~brave(X0) | ~humble(X0)) [input p9]
12. ! [X0] : (kind(X0) => (tall(X0) & strong(X0))) [input p11]
19. ? [X0] : (~funny(X0) & ~tall(X0)) [input p18]
25. creative(lucy) [input hypothesis]
33. ! [X0] : ((strong(X0) <~> humble(X0)) | (kind(X0) & ~funny(X0))) [ennf transformation 9]
34. ! [X0] : ((tall(X0) & strong(X0)) | ~kind(X0)) [ennf transformation 12]
46. ! [X0] : (((old(X0) & funny(X0)) | strong(X0)) & (~strong(X0) | (~old(X0) | ~funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((old(X0) & funny(X0)) | strong(X0)) & (~strong(X0) | ~old(X0) | ~funny(X0))) [flattening 46]
53. ! [X0] : (((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | (kind(X0) & ~funny(X0))) [nnf transformation 33]
54. (~creative(lucy) | ! [X0] : (brave(X0) & humble(X0))) & (? [X0] : (~brave(X0) | ~humble(X0)) | creative(lucy)) [nnf transformation 10]
55. (~creative(lucy) | ! [X0] : (brave(X0) & humble(X0))) & (? [X1] : (~brave(X1) | ~humble(X1)) | creative(lucy)) [rectify 54]
56. ? [X1] : (~brave(X1) | ~humble(X1)) => (~brave(sK3) | ~humble(sK3)) [choice axiom]
57. (~creative(lucy) | ! [X0] : (brave(X0) & humble(X0))) & ((~brave(sK3) | ~humble(sK3)) | creative(lucy)) [skolemisation 55,56]
74. ? [X0] : (~funny(X0) & ~tall(X0)) => (~funny(sK8) & ~tall(sK8)) [choice axiom]
75. ~funny(sK8) & ~tall(sK8) [skolemisation 19,74]
95. strong(X0) | funny(X0) [cnf transformation 47]
108. ~humble(X0) | ~strong(X0) | kind(X0) [cnf transformation 53]
110. ~creative(lucy) | humble(X0) [cnf transformation 57]
116. ~kind(X0) | tall(X0) [cnf transformation 34]
132. ~tall(sK8) [cnf transformation 75]
133. ~funny(sK8) [cnf transformation 75]
142. creative(lucy) [cnf transformation 25]
226. 19 <=> creative(lucy) [avatar definition]
231. 20 <=> ! [X0] : humble(X0) [avatar definition]
232. humble(X0) <- (20) [avatar component clause 231]
233. 20 | ~19 [avatar split clause 110,226,231]
334. 19 [avatar split clause 142,226]
372. ~strong(X2) | kind(X2) <- (20) [resolution 108,232]
436. funny(X2) | kind(X2) <- (20) [resolution 372,95]
509. kind(sK8) <- (20) [resolution 436,133]
531. tall(sK8) <- (20) [resolution 509,116]
537. $false <- (20) [subsumption resolution 531,132]
538. ~20 [avatar contradiction clause 537]
539. $false [avatar sat refutation 233,334,538]
% SZS output end Proof for 1258249113537027979560165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not brave is both not kind and kind and vice versa.
If someone is either calm or tall then someone is funny and vice versa.
Everyone who is not calm or quiet is both not wise and not generous.
If susan is not calm then someone is both not humble and not rich.
Everyone who is both not patient and not humble is not old or curious.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Someone is not rich or not funny.
Mary is not quiet.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Mary is creative. | neutral | (![X]:((kind(X)&~brave(X))<=>(~kind(X)&kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|quiet(X))=>(~wise(X)&~generous(X))))&
((~calm(susan))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((~patient(X)&~humble(X))=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(?[X]:((~rich(X)|~funny(X))))&
(~quiet(mary))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | creative(mary) | [] | null | 0 |
If someone is either not kind or humble then john is curious.
Everyone who is not creative is either not calm or old.
Everyone who is generous is both happy and not kind and vice versa.
If someone is creative or not calm then someone is either not rich or not strong.
Everyone who is both not kind and tall is both not funny and not kind.
If john is not strong then fred is both not patient and curious.
Everyone who is either not old or not calm is either creative or not humble and vice versa.
If someone is wise or not quiet then paul is not quiet.
Everyone who is humble or not rich is not patient and vice versa.
Everyone who is calm is humble and vice versa.
If lucy is either not happy or calm then fred is kind or creative.
Everyone who is creative or quiet is either rich or not calm and vice versa.
Everyone who is not wise is both not kind and old and vice versa.
Everyone who is not tall is not rich and vice versa.
Everyone who is not rich or generous is not generous or tall and vice versa.
If someone is old then someone is patient and vice versa.
Someone is not tall or not curious.
Someone is either brave or strong.
Lucy is both curious and not patient.
Someone is old or kind.
Someone is not calm or quiet.
Paul is either not curious or not old.
Lucy is both not old and not kind. | Paul is patient. | contradiction | ((?[X]:((~kind(X)<~>humble(X))))=>(curious(john)))&
(![X]:(~creative(X)=>(~calm(X)<~>old(X))))&
(![X]:(generous(X)<=>(happy(X)&~kind(X))))&
((?[X]:((creative(X)|~calm(X))))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~kind(X)&tall(X))=>(~funny(X)&~kind(X))))&
((~strong(john))=>((~patient(fred)&curious(fred))))&
(![X]:((~old(X)<~>~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|~quiet(X))))=>(~quiet(paul)))&
(![X]:((humble(X)|~rich(X))<=>~patient(X)))&
(![X]:(calm(X)<=>humble(X)))&
(((~happy(lucy)<~>calm(lucy)))=>((kind(fred)|creative(fred))))&
(![X]:((creative(X)|quiet(X))<=>(rich(X)<~>~calm(X))))&
(![X]:(~wise(X)<=>(~kind(X)&old(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:((~rich(X)|generous(X))<=>(~generous(X)|tall(X))))&
((?[X]:(old(X)))<=>(?[X]:(patient(X))))&
(?[X]:((~tall(X)|~curious(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((curious(lucy)&~patient(lucy)))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((~calm(X)|quiet(X))))&
((~curious(paul)<~>~old(paul)))&
((~old(lucy)&~kind(lucy))) | patient(paul) | [
"p1",
"p6",
"p8",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7280923264583674261292600
% SZS output start Proof for 7280923264583674261292600
2. ! [X0] : (~creative(X0) => (~calm(X0) <~> old(X0))) [input p1]
7. ! [X0] : ((~old(X0) <~> ~calm(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p6]
9. ! [X0] : ((~rich(X0) | humble(X0)) <=> ~patient(X0)) [input p8]
10. ! [X0] : (calm(X0) <=> humble(X0)) [input p9]
12. ! [X0] : ((quiet(X0) | creative(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p11]
16. ? [X0] : old(X0) <=> ? [X0] : patient(X0) [input p15]
24. patient(paul) [input hypothesis]
26. ? [X0] : old(X0) <=> ? [X1] : patient(X1) [rectify 16]
30. ! [X0] : ((~calm(X0) <~> old(X0)) | creative(X0)) [ennf transformation 2]
40. ! [X0] : (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | creative(X0)) [nnf transformation 30]
47. ! [X0] : ((((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0))))) [nnf transformation 7]
48. ! [X0] : (((~rich(X0) | humble(X0)) | patient(X0)) & (~patient(X0) | (rich(X0) & ~humble(X0)))) [nnf transformation 9]
49. ! [X0] : ((~rich(X0) | humble(X0) | patient(X0)) & (~patient(X0) | (rich(X0) & ~humble(X0)))) [flattening 48]
50. ! [X0] : ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))) [nnf transformation 10]
52. ! [X0] : (((quiet(X0) | creative(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~quiet(X0) & ~creative(X0)))) [nnf transformation 12]
53. ! [X0] : ((quiet(X0) | creative(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~quiet(X0) & ~creative(X0)))) [flattening 52]
57. (? [X0] : old(X0) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : ~old(X0)) [nnf transformation 26]
58. (? [X0] : old(X0) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : ~old(X3)) [rectify 57]
59. ? [X0] : old(X0) => old(sK1) [choice axiom]
60. ? [X2] : patient(X2) => patient(sK2) [choice axiom]
61. (old(sK1) | ! [X1] : ~patient(X1)) & (patient(sK2) | ! [X3] : ~old(X3)) [skolemisation 58,60,59]
74. ~calm(X0) | old(X0) | creative(X0) [cnf transformation 40]
75. ~old(X0) | calm(X0) | creative(X0) [cnf transformation 40]
91. ~calm(X0) | ~old(X0) | creative(X0) | humble(X0) [cnf transformation 47]
93. calm(X0) | old(X0) | creative(X0) | humble(X0) [cnf transformation 47]
96. ~patient(X0) | ~humble(X0) [cnf transformation 49]
97. ~patient(X0) | rich(X0) [cnf transformation 49]
99. ~calm(X0) | humble(X0) [cnf transformation 50]
105. ~rich(X0) | calm(X0) | ~creative(X0) [cnf transformation 53]
117. patient(sK2) | ~old(X3) [cnf transformation 61]
118. old(sK1) | ~patient(X1) [cnf transformation 61]
130. patient(paul) [cnf transformation 24]
177. old(X0) | creative(X0) | humble(X0) [subsumption resolution 93,74]
178. ~old(X0) | creative(X0) | humble(X0) [subsumption resolution 91,75]
179. creative(X0) | humble(X0) [subsumption resolution 178,177]
214. 18 <=> ! [X1] : ~patient(X1) [avatar definition]
215. ~patient(X1) <- (18) [avatar component clause 214]
217. 19 <=> old(sK1) [avatar definition]
219. old(sK1) <- (19) [avatar component clause 217]
220. 18 | 19 [avatar split clause 118,217,214]
222. 20 <=> ! [X3] : ~old(X3) [avatar definition]
223. ~old(X3) <- (20) [avatar component clause 222]
225. 21 <=> patient(sK2) [avatar definition]
227. patient(sK2) <- (21) [avatar component clause 225]
228. 20 | 21 [avatar split clause 117,225,222]
276. $false <- (18) [resolution 215,130]
277. ~18 [avatar contradiction clause 276]
278. $false <- (19, 20) [subsumption resolution 219,223]
279. ~19 | ~20 [avatar contradiction clause 278]
281. ~humble(sK2) <- (21) [resolution 96,227]
283. rich(sK2) <- (21) [resolution 97,227]
354. calm(sK2) | ~creative(sK2) <- (21) [resolution 105,283]
357. 38 <=> creative(sK2) [avatar definition]
359. ~creative(sK2) <- (~38) [avatar component clause 357]
361. 39 <=> calm(sK2) [avatar definition]
363. calm(sK2) <- (39) [avatar component clause 361]
364. ~38 | 39 | ~21 [avatar split clause 354,225,361,357]
377. humble(sK2) <- (~38) [resolution 359,179]
378. $false <- (21, ~38) [subsumption resolution 377,281]
379. ~21 | 38 [avatar contradiction clause 378]
398. humble(sK2) <- (39) [resolution 363,99]
400. $false <- (21, 39) [subsumption resolution 398,281]
401. ~21 | ~39 [avatar contradiction clause 400]
402. $false [avatar sat refutation 220,228,277,279,364,379,401]
% SZS output end Proof for 7280923264583674261292600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not old is not tall or not patient.
If someone is both wise and brave then mary is either happy or generous.
Everyone who is either kind or not kind is happy.
If someone is tall then someone is both tall and not patient and vice versa.
If someone is both not rich and not wise then john is both patient and strong.
If someone is both quiet and not calm then someone is either brave or not quiet and vice versa.
Everyone who is happy or quiet is curious or generous.
If fred is either not wise or not rich then someone is both humble and not patient.
Everyone who is either patient or quiet is happy or wise and vice versa.
Everyone who is not quiet is both wise and not funny.
Everyone who is not patient is not generous.
If susan is creative then lucy is not kind and vice versa.
If someone is not wise then alice is not old and vice versa.
If mary is not old or not generous then someone is both creative and not humble and vice versa.
Everyone who is both kind and rich is not quiet or not calm.
Everyone who is not curious is both not strong and funny and vice versa.
Lucy is brave or not quiet.
Someone is not rich.
Someone is happy.
Someone is either wise or not old.
Someone is not old.
Paul is not curious or humble.
Someone is either wise or not brave. | Alice is not curious. | contradiction | (![X]:((patient(X)&~old(X))=>(~tall(X)|~patient(X))))&
((?[X]:((wise(X)&brave(X))))=>((happy(mary)<~>generous(mary))))&
(![X]:((kind(X)<~>~kind(X))=>happy(X)))&
((?[X]:(tall(X)))<=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((~rich(X)&~wise(X))))=>((patient(john)&strong(john))))&
((?[X]:((quiet(X)&~calm(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((happy(X)|quiet(X))=>(curious(X)|generous(X))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((humble(X)&~patient(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(happy(X)|wise(X))))&
(![X]:(~quiet(X)=>(wise(X)&~funny(X))))&
(![X]:(~patient(X)=>~generous(X)))&
((creative(susan))<=>(~kind(lucy)))&
((?[X]:(~wise(X)))<=>(~old(alice)))&
(((~old(mary)|~generous(mary)))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((kind(X)&rich(X))=>(~quiet(X)|~calm(X))))&
(![X]:(~curious(X)<=>(~strong(X)&funny(X))))&
((brave(lucy)|~quiet(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:(~old(X)))&
((~curious(paul)|humble(paul)))&
(?[X]:((wise(X)<~>~brave(X)))) | ~curious(alice) | [
"p2",
"p6",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2069933649845262839423027
% SZS output start Proof for 2069933649845262839423027
3. ! [X0] : ((kind(X0) <~> ~kind(X0)) => happy(X0)) [input p2]
7. ! [X0] : ((quiet(X0) | happy(X0)) => (generous(X0) | curious(X0))) [input p6]
9. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (wise(X0) | happy(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~funny(X0) & wise(X0))) [input p9]
11. ! [X0] : (~patient(X0) => ~generous(X0)) [input p10]
16. ! [X0] : (~curious(X0) <=> (funny(X0) & ~strong(X0))) [input p15]
24. ~curious(alice) [input hypothesis]
30. ! [X0] : (happy(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 3]
32. ! [X0] : ((generous(X0) | curious(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 7]
33. ! [X0] : (generous(X0) | curious(X0) | (~quiet(X0) & ~happy(X0))) [flattening 32]
35. ! [X0] : ((~funny(X0) & wise(X0)) | quiet(X0)) [ennf transformation 10]
36. ! [X0] : (~generous(X0) | patient(X0)) [ennf transformation 11]
40. ! [X0] : (happy(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
54. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 54]
66. ! [X0] : ((~curious(X0) | (~funny(X0) | strong(X0))) & ((funny(X0) & ~strong(X0)) | curious(X0))) [nnf transformation 16]
67. ! [X0] : ((~curious(X0) | ~funny(X0) | strong(X0)) & ((funny(X0) & ~strong(X0)) | curious(X0))) [flattening 66]
83. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
84. happy(X0) | kind(X0) | kind(X0) [cnf transformation 40]
96. generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 33]
106. ~quiet(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 55]
109. ~funny(X0) | quiet(X0) [cnf transformation 35]
110. ~generous(X0) | patient(X0) [cnf transformation 36]
122. funny(X0) | curious(X0) [cnf transformation 67]
133. ~curious(alice) [cnf transformation 24]
134. happy(X0) | ~kind(X0) [duplicate literal removal 83]
135. kind(X0) | happy(X0) [duplicate literal removal 84]
150. happy(X0) [subsumption resolution 134,135]
216. curious(X0) | generous(X0) [subsumption resolution 96,150]
237. ~quiet(X0) | ~patient(X0) [subsumption resolution 106,150]
324. curious(X0) | quiet(X0) [resolution 122,109]
337. generous(alice) [resolution 216,133]
341. patient(alice) [resolution 337,110]
359. quiet(alice) [resolution 324,133]
363. ~patient(alice) [resolution 359,237]
366. $false [subsumption resolution 363,341]
% SZS output end Proof for 2069933649845262839423027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not calm then lucy is either calm or not funny and vice versa. If susan is not kind or not patient then someone is creative or not quiet. If someone is not calm then fred is either not curious or quiet and vice versa. If john is humble then someone is both happy and brave and vice versa. Everyone who is both not humble and not funny is either not humble or tall. Everyone who is not patient is either patient or not humble and vice versa. Everyone who is not calm or not happy is not wise or calm and vice versa. Everyone who is either not funny or wise is both creative and not old and vice versa. Everyone who is rich is both not brave and not tall. If someone is either not brave or quiet then john is both rich and not creative and vice versa. Everyone who is either not calm or not tall is not patient or not generous and vice versa. Everyone who is both not creative and not old is not strong or not curious. Everyone who is curious or tall is both rich and not generous. If fred is quiet or not happy then susan is creative or kind. Everyone who is not tall or rich is old or funny. Everyone who is both rich and not calm is not strong. Susan is old. John is both not wise and not patient. Someone is not wise. Susan is patient or happy. Susan is both kind and strong. Susan is curious. John is not funny or quiet. | John is quiet. | entailment | ((~calm(mary))<=>((calm(lucy)<~>~funny(lucy))))&
(((~kind(susan)|~patient(susan)))=>(?[X]:((creative(X)|~quiet(X)))))&
((?[X]:(~calm(X)))<=>((~curious(fred)<~>quiet(fred))))&
((humble(john))<=>(?[X]:((happy(X)&brave(X)))))&
(![X]:((~humble(X)&~funny(X))=>(~humble(X)<~>tall(X))))&
(![X]:(~patient(X)<=>(patient(X)<~>~humble(X))))&
(![X]:((~calm(X)|~happy(X))<=>(~wise(X)|calm(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(creative(X)&~old(X))))&
(![X]:(rich(X)=>(~brave(X)&~tall(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((rich(john)&~creative(john))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~patient(X)|~generous(X))))&
(![X]:((~creative(X)&~old(X))=>(~strong(X)|~curious(X))))&
(![X]:((curious(X)|tall(X))=>(rich(X)&~generous(X))))&
(((quiet(fred)|~happy(fred)))=>((creative(susan)|kind(susan))))&
(![X]:((~tall(X)|rich(X))=>(old(X)|funny(X))))&
(![X]:((rich(X)&~calm(X))=>~strong(X)))&
(old(susan))&
((~wise(john)&~patient(john)))&
(?[X]:(~wise(X)))&
((patient(susan)|happy(susan)))&
((kind(susan)&strong(susan)))&
(curious(susan))&
((~funny(john)|quiet(john))) | quiet(john) | [
"p7",
"p8",
"p12",
"p14",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1052567245832210744864023
% SZS output start Proof for 1052567245832210744864023
8. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> (~old(X0) & creative(X0))) [input p7]
9. ! [X0] : (rich(X0) => (~tall(X0) & ~brave(X0))) [input p8]
13. ! [X0] : ((tall(X0) | curious(X0)) => (~generous(X0) & rich(X0))) [input p12]
15. ! [X0] : ((rich(X0) | ~tall(X0)) => (funny(X0) | old(X0))) [input p14]
18. ~patient(john) & ~wise(john) [input p17]
23. quiet(john) | ~funny(john) [input p22]
24. ~quiet(john) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~brave(X0)) | ~rich(X0)) [ennf transformation 9]
34. ! [X0] : ((~generous(X0) & rich(X0)) | (~tall(X0) & ~curious(X0))) [ennf transformation 13]
35. ! [X0] : ((funny(X0) | old(X0)) | (~rich(X0) & tall(X0))) [ennf transformation 15]
36. ! [X0] : (funny(X0) | old(X0) | (~rich(X0) & tall(X0))) [flattening 35]
54. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 8]
55. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [flattening 54]
89. ~old(X0) | wise(X0) | funny(X0) [cnf transformation 55]
94. ~rich(X0) | ~tall(X0) [cnf transformation 31]
109. rich(X0) | ~tall(X0) [cnf transformation 34]
112. funny(X0) | old(X0) | tall(X0) [cnf transformation 36]
116. ~wise(john) [cnf transformation 18]
122. quiet(john) | ~funny(john) [cnf transformation 23]
123. ~quiet(john) [cnf transformation 24]
224. ~tall(X0) [subsumption resolution 109,94]
225. old(X0) | funny(X0) [subsumption resolution 112,224]
232. 22 <=> funny(john) [avatar definition]
234. ~funny(john) <- (~22) [avatar component clause 232]
236. 23 <=> quiet(john) [avatar definition]
239. ~22 | 23 [avatar split clause 122,236,232]
240. ~23 [avatar split clause 123,236]
278. wise(X0) | funny(X0) | funny(X0) [resolution 89,225]
279. wise(X0) | funny(X0) [duplicate literal removal 278]
298. funny(john) [resolution 279,116]
300. $false <- (~22) [subsumption resolution 298,234]
301. 22 [avatar contradiction clause 300]
302. $false [avatar sat refutation 239,240,301]
% SZS output end Proof for 1052567245832210744864023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or brave then someone is both not creative and wise and vice versa.
Everyone who is either not humble or not old is funny or not funny and vice versa.
Everyone who is either not brave or humble is not happy or not quiet.
If fred is both patient and creative then paul is either old or brave.
Everyone who is generous is not quiet and vice versa.
Everyone who is not wise or generous is not old and vice versa.
If susan is either not old or happy then someone is both not strong and not brave and vice versa.
If someone is old then fred is not calm.
Everyone who is not kind or rich is calm or not brave and vice versa.
If alice is both not strong and funny then susan is either brave or tall and vice versa.
If someone is both humble and not wise then john is both brave and not funny and vice versa.
If fred is both not happy and quiet then paul is either not creative or generous and vice versa.
Everyone who is happy or not rich is not wise.
If lucy is funny or not wise then paul is both not quiet and brave and vice versa.
Everyone who is either not funny or tall is strong or not patient.
Everyone who is both happy and not tall is not brave or tall and vice versa.
Lucy is not wise.
Someone is either not humble or quiet.
Someone is not humble or tall.
Someone is both not patient and not quiet. | Lucy is not funny. | neutral | ((?[X]:((~curious(X)<~>brave(X))))<=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((~humble(X)<~>~old(X))<=>(funny(X)|~funny(X))))&
(![X]:((~brave(X)<~>humble(X))=>(~happy(X)|~quiet(X))))&
(((patient(fred)&creative(fred)))=>((old(paul)<~>brave(paul))))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:((~wise(X)|generous(X))<=>~old(X)))&
(((~old(susan)<~>happy(susan)))<=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:(old(X)))=>(~calm(fred)))&
(![X]:((~kind(X)|rich(X))<=>(calm(X)|~brave(X))))&
(((~strong(alice)&funny(alice)))<=>((brave(susan)<~>tall(susan))))&
((?[X]:((humble(X)&~wise(X))))<=>((brave(john)&~funny(john))))&
(((~happy(fred)&quiet(fred)))<=>((~creative(paul)<~>generous(paul))))&
(![X]:((happy(X)|~rich(X))=>~wise(X)))&
(((funny(lucy)|~wise(lucy)))<=>((~quiet(paul)&brave(paul))))&
(![X]:((~funny(X)<~>tall(X))=>(strong(X)|~patient(X))))&
(![X]:((happy(X)&~tall(X))<=>(~brave(X)|tall(X))))&
(~wise(lucy))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((~patient(X)&~quiet(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is brave or not generous is not tall or not generous and vice versa.
Everyone who is quiet or not funny is not tall and vice versa.
If someone is both calm and brave then mary is strong or quiet and vice versa.
If fred is brave then someone is not generous or calm.
Everyone who is not humble is either kind or quiet and vice versa.
Everyone who is not funny is both kind and not old and vice versa.
Everyone who is both not quiet and generous is both not happy and not creative.
Everyone who is not rich is both not old and not kind and vice versa.
Everyone who is either not quiet or funny is not quiet.
If someone is not generous then someone is both not funny and generous and vice versa.
Everyone who is humble or not calm is either calm or not funny and vice versa.
If alice is both curious and creative then alice is both not humble and not happy and vice versa.
Everyone who is old is either not kind or creative and vice versa.
If someone is both not wise and not brave then someone is either rich or kind.
If susan is both not strong and not wise then susan is both funny and not calm and vice versa.
If someone is humble or curious then paul is old or not tall.
Fred is kind.
Someone is wise or humble.
Susan is either not humble or quiet.
Alice is not wise.
Susan is happy or brave.
Someone is brave or not calm.
Someone is not curious or brave.
Susan is both not quiet and not tall. | Fred is brave. | neutral | (![X]:((brave(X)|~generous(X))<=>(~tall(X)|~generous(X))))&
(![X]:((quiet(X)|~funny(X))<=>~tall(X)))&
((?[X]:((calm(X)&brave(X))))<=>((strong(mary)|quiet(mary))))&
((brave(fred))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:(~humble(X)<=>(kind(X)<~>quiet(X))))&
(![X]:(~funny(X)<=>(kind(X)&~old(X))))&
(![X]:((~quiet(X)&generous(X))=>(~happy(X)&~creative(X))))&
(![X]:(~rich(X)<=>(~old(X)&~kind(X))))&
(![X]:((~quiet(X)<~>funny(X))=>~quiet(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((humble(X)|~calm(X))<=>(calm(X)<~>~funny(X))))&
(((curious(alice)&creative(alice)))<=>((~humble(alice)&~happy(alice))))&
(![X]:(old(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((rich(X)<~>kind(X)))))&
(((~strong(susan)&~wise(susan)))<=>((funny(susan)&~calm(susan))))&
((?[X]:((humble(X)|curious(X))))=>((old(paul)|~tall(paul))))&
(kind(fred))&
(?[X]:((wise(X)|humble(X))))&
((~humble(susan)<~>quiet(susan)))&
(~wise(alice))&
((happy(susan)|brave(susan)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:((~curious(X)|brave(X))))&
((~quiet(susan)&~tall(susan))) | brave(fred) | [] | null | 0 |
Everyone who is curious or funny is not tall and vice versa. If fred is either not generous or kind then susan is either not patient or calm. If someone is either not wise or not quiet then someone is either not old or old and vice versa. Everyone who is either not calm or not rich is not rich. If alice is not kind then susan is not happy or not old and vice versa. If paul is funny or not curious then mary is either not tall or quiet and vice versa. Everyone who is not brave or not wise is either old or not tall and vice versa. Everyone who is wise or patient is not brave or old. If lucy is not patient then paul is either patient or not curious. If someone is kind or rich then someone is both not kind and creative and vice versa. Everyone who is both not tall and not kind is either humble or not strong. If someone is quiet then someone is both not quiet and wise and vice versa. Everyone who is brave is tall. Everyone who is strong or tall is both generous and not old and vice versa. Everyone who is either not generous or tall is not happy. Everyone who is both not old and happy is not calm and vice versa. Someone is quiet or wise. Someone is not generous or strong. Alice is creative. Alice is both generous and strong. Someone is both not quiet and wise. Fred is creative. Someone is either not tall or wise. | Susan is not patient. | neutral | (![X]:((curious(X)|funny(X))<=>~tall(X)))&
(((~generous(fred)<~>kind(fred)))=>((~patient(susan)<~>calm(susan))))&
((?[X]:((~wise(X)<~>~quiet(X))))<=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((~calm(X)<~>~rich(X))=>~rich(X)))&
((~kind(alice))<=>((~happy(susan)|~old(susan))))&
(((funny(paul)|~curious(paul)))<=>((~tall(mary)<~>quiet(mary))))&
(![X]:((~brave(X)|~wise(X))<=>(old(X)<~>~tall(X))))&
(![X]:((wise(X)|patient(X))=>(~brave(X)|old(X))))&
((~patient(lucy))=>((patient(paul)<~>~curious(paul))))&
((?[X]:((kind(X)|rich(X))))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~tall(X)&~kind(X))=>(humble(X)<~>~strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:(brave(X)=>tall(X)))&
(![X]:((strong(X)|tall(X))<=>(generous(X)&~old(X))))&
(![X]:((~generous(X)<~>tall(X))=>~happy(X)))&
(![X]:((~old(X)&happy(X))<=>~calm(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:((~generous(X)|strong(X))))&
(creative(alice))&
((generous(alice)&strong(alice)))&
(?[X]:((~quiet(X)&wise(X))))&
(creative(fred))&
(?[X]:((~tall(X)<~>wise(X)))) | ~patient(susan) | [] | null | 0 |
Everyone who is curious or not generous is rich or not curious and vice versa.
If john is either rich or calm then alice is either patient or not calm.
If someone is either brave or not calm then lucy is either happy or not patient.
Everyone who is both quiet and rich is not tall or strong.
Everyone who is both not curious and brave is curious.
Everyone who is both tall and happy is both not kind and old and vice versa.
Everyone who is either not generous or not creative is brave.
If someone is not wise or not rich then alice is kind and vice versa.
If someone is tall then someone is not humble or not brave and vice versa.
If someone is both patient and not happy then paul is either not calm or patient.
Everyone who is either not happy or not curious is either calm or not curious and vice versa.
Everyone who is either not funny or not generous is both not patient and humble and vice versa.
Everyone who is kind is either not rich or not kind and vice versa.
If alice is either quiet or old then mary is either not wise or patient and vice versa.
If fred is either generous or not wise then fred is both calm and funny.
Everyone who is both not brave and not humble is either generous or not strong and vice versa.
Alice is not creative or curious.
Someone is either not tall or not funny.
Someone is not quiet or curious.
Someone is not curious.
Susan is both not tall and happy.
Fred is old.
Alice is calm. | Mary is creative. | contradiction | (![X]:((curious(X)|~generous(X))<=>(rich(X)|~curious(X))))&
(((rich(john)<~>calm(john)))=>((patient(alice)<~>~calm(alice))))&
((?[X]:((brave(X)<~>~calm(X))))=>((happy(lucy)<~>~patient(lucy))))&
(![X]:((quiet(X)&rich(X))=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)&brave(X))=>curious(X)))&
(![X]:((tall(X)&happy(X))<=>(~kind(X)&old(X))))&
(![X]:((~generous(X)<~>~creative(X))=>brave(X)))&
((?[X]:((~wise(X)|~rich(X))))<=>(kind(alice)))&
((?[X]:(tall(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((patient(X)&~happy(X))))=>((~calm(paul)<~>patient(paul))))&
(![X]:((~happy(X)<~>~curious(X))<=>(calm(X)<~>~curious(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~patient(X)&humble(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>~kind(X))))&
(((quiet(alice)<~>old(alice)))<=>((~wise(mary)<~>patient(mary))))&
(((generous(fred)<~>~wise(fred)))=>((calm(fred)&funny(fred))))&
(![X]:((~brave(X)&~humble(X))<=>(generous(X)<~>~strong(X))))&
((~creative(alice)|curious(alice)))&
(?[X]:((~tall(X)<~>~funny(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:(~curious(X)))&
((~tall(susan)&happy(susan)))&
(old(fred))&
(calm(alice)) | creative(mary) | [
"p0",
"p4",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4005682598829685464367309
% SZS output start Proof for 4005682598829685464367309
1. ! [X0] : ((~generous(X0) | curious(X0)) <=> (~curious(X0) | rich(X0))) [input p0]
5. ! [X0] : ((brave(X0) & ~curious(X0)) => curious(X0)) [input p4]
7. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => brave(X0)) [input p6]
13. ! [X0] : (kind(X0) <=> (~rich(X0) <~> ~kind(X0))) [input p12]
24. creative(mary) [input hypothesis]
30. ! [X0] : (curious(X0) | (~brave(X0) | curious(X0))) [ennf transformation 5]
31. ! [X0] : (curious(X0) | ~brave(X0) | curious(X0)) [flattening 30]
32. ! [X0] : (brave(X0) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 7]
35. ! [X0] : (((~generous(X0) | curious(X0)) | (curious(X0) & ~rich(X0))) & ((~curious(X0) | rich(X0)) | (generous(X0) & ~curious(X0)))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | curious(X0) | (curious(X0) & ~rich(X0))) & (~curious(X0) | rich(X0) | (generous(X0) & ~curious(X0)))) [flattening 35]
41. ! [X0] : (brave(X0) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 32]
55. ! [X0] : ((kind(X0) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | ~kind(X0))) [nnf transformation 13]
67. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 36]
70. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 36]
80. curious(X0) | ~brave(X0) | curious(X0) [cnf transformation 31]
85. ~creative(X0) | brave(X0) | generous(X0) [cnf transformation 41]
109. ~kind(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 55]
112. kind(X0) | ~rich(X0) | kind(X0) [cnf transformation 55]
140. creative(mary) [cnf transformation 24]
141. ~kind(X0) | ~rich(X0) [duplicate literal removal 109]
142. ~rich(X0) | kind(X0) [duplicate literal removal 112]
147. ~brave(X0) | curious(X0) [duplicate literal removal 80]
148. ~curious(X0) | rich(X0) [duplicate literal removal 67]
149. ~generous(X0) | curious(X0) [duplicate literal removal 70]
248. ~rich(X0) [subsumption resolution 141,142]
368. brave(mary) | generous(mary) [resolution 85,140]
370. 45 <=> generous(mary) [avatar definition]
372. generous(mary) <- (45) [avatar component clause 370]
374. 46 <=> brave(mary) [avatar definition]
376. brave(mary) <- (46) [avatar component clause 374]
377. 45 | 46 [avatar split clause 368,374,370]
387. curious(mary) <- (45) [resolution 372,149]
392. rich(mary) <- (45) [resolution 387,148]
393. $false <- (45) [subsumption resolution 392,248]
394. ~45 [avatar contradiction clause 393]
401. curious(mary) <- (46) [resolution 376,147]
404. rich(mary) <- (46) [resolution 401,148]
408. $false <- (46) [subsumption resolution 404,248]
409. ~46 [avatar contradiction clause 408]
410. $false [avatar sat refutation 377,394,409]
% SZS output end Proof for 4005682598829685464367309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and tall then someone is not calm or not creative.
Everyone who is rich is both wise and curious.
If mary is either kind or patient then alice is both not quiet and not strong and vice versa.
Everyone who is wise is either not calm or patient.
Everyone who is either happy or brave is both not humble and funny and vice versa.
If someone is not creative then mary is both old and not creative and vice versa.
If someone is not calm then someone is generous and vice versa.
Everyone who is tall is either creative or brave and vice versa.
Everyone who is either funny or not generous is both wise and not brave.
Everyone who is both kind and humble is both not strong and brave.
Everyone who is both not generous and tall is old or patient.
Everyone who is either rich or not curious is either not quiet or not curious and vice versa.
If susan is both not calm and not wise then someone is not creative or humble and vice versa.
If fred is either not funny or curious then someone is calm or wise and vice versa.
Everyone who is both calm and funny is not quiet or not calm and vice versa.
If someone is either not brave or not wise then someone is either tall or not brave and vice versa.
Someone is calm.
Someone is both brave and not kind.
Someone is both strong and rich.
Fred is not generous or not brave.
Someone is either kind or brave.
Alice is either funny or not patient.
Someone is either happy or rich. | Susan is quiet. | contradiction | ((?[X]:((~curious(X)&tall(X))))=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:(rich(X)=>(wise(X)&curious(X))))&
(((kind(mary)<~>patient(mary)))<=>((~quiet(alice)&~strong(alice))))&
(![X]:(wise(X)=>(~calm(X)<~>patient(X))))&
(![X]:((happy(X)<~>brave(X))<=>(~humble(X)&funny(X))))&
((?[X]:(~creative(X)))<=>((old(mary)&~creative(mary))))&
((?[X]:(~calm(X)))<=>(?[X]:(generous(X))))&
(![X]:(tall(X)<=>(creative(X)<~>brave(X))))&
(![X]:((funny(X)<~>~generous(X))=>(wise(X)&~brave(X))))&
(![X]:((kind(X)&humble(X))=>(~strong(X)&brave(X))))&
(![X]:((~generous(X)&tall(X))=>(old(X)|patient(X))))&
(![X]:((rich(X)<~>~curious(X))<=>(~quiet(X)<~>~curious(X))))&
(((~calm(susan)&~wise(susan)))<=>(?[X]:((~creative(X)|humble(X)))))&
(((~funny(fred)<~>curious(fred)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((calm(X)&funny(X))<=>(~quiet(X)|~calm(X))))&
((?[X]:((~brave(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((strong(X)&rich(X))))&
((~generous(fred)|~brave(fred)))&
(?[X]:((kind(X)<~>brave(X))))&
((funny(alice)<~>~patient(alice)))&
(?[X]:((happy(X)<~>rich(X)))) | quiet(susan) | [
"p1",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 546840728877029541361447
% SZS output start Proof for 546840728877029541361447
2. ! [X0] : (rich(X0) => (curious(X0) & wise(X0))) [input p1]
5. ! [X0] : ((happy(X0) <~> brave(X0)) <=> (funny(X0) & ~humble(X0))) [input p4]
7. ? [X0] : ~calm(X0) <=> ? [X0] : generous(X0) [input p6]
8. ! [X0] : (tall(X0) <=> (creative(X0) <~> brave(X0))) [input p7]
9. ! [X0] : ((funny(X0) <~> ~generous(X0)) => (~brave(X0) & wise(X0))) [input p8]
12. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> (~quiet(X0) <~> ~curious(X0))) [input p11]
13. (~wise(susan) & ~calm(susan)) <=> ? [X0] : (humble(X0) | ~creative(X0)) [input p12]
15. ! [X0] : ((funny(X0) & calm(X0)) <=> (~calm(X0) | ~quiet(X0))) [input p14]
16. ? [X0] : (~brave(X0) <~> ~wise(X0)) <=> ? [X0] : (tall(X0) <~> ~brave(X0)) [input p15]
24. quiet(susan) [input hypothesis]
26. ? [X0] : ~calm(X0) <=> ? [X1] : generous(X1) [rectify 7]
27. ? [X0] : (~brave(X0) <~> ~wise(X0)) <=> ? [X1] : (tall(X1) <~> ~brave(X1)) [rectify 16]
29. ! [X0] : ((curious(X0) & wise(X0)) | ~rich(X0)) [ennf transformation 2]
31. ! [X0] : ((~brave(X0) & wise(X0)) | (funny(X0) <=> ~generous(X0))) [ennf transformation 9]
42. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0))))) [flattening 42]
49. (? [X0] : ~calm(X0) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : calm(X0)) [nnf transformation 26]
50. (? [X0] : ~calm(X0) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : calm(X3)) [rectify 49]
51. ? [X0] : ~calm(X0) => ~calm(sK2) [choice axiom]
52. ? [X2] : generous(X2) => generous(sK3) [choice axiom]
53. (~calm(sK2) | ! [X1] : ~generous(X1)) & (generous(sK3) | ! [X3] : calm(X3)) [skolemisation 50,52,51]
54. ! [X0] : ((tall(X0) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0)))) & (((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | ~tall(X0))) [nnf transformation 8]
55. ! [X0] : ((~brave(X0) & wise(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0)))) [nnf transformation 31]
56. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) & (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 12]
57. ((~wise(susan) & ~calm(susan)) | ! [X0] : (~humble(X0) & creative(X0))) & (? [X0] : (humble(X0) | ~creative(X0)) | (wise(susan) | calm(susan))) [nnf transformation 13]
58. ((~wise(susan) & ~calm(susan)) | ! [X0] : (~humble(X0) & creative(X0))) & (? [X0] : (humble(X0) | ~creative(X0)) | wise(susan) | calm(susan)) [flattening 57]
59. ((~wise(susan) & ~calm(susan)) | ! [X0] : (~humble(X0) & creative(X0))) & (? [X1] : (humble(X1) | ~creative(X1)) | wise(susan) | calm(susan)) [rectify 58]
60. ? [X1] : (humble(X1) | ~creative(X1)) => (humble(sK4) | ~creative(sK4)) [choice axiom]
61. ((~wise(susan) & ~calm(susan)) | ! [X0] : (~humble(X0) & creative(X0))) & ((humble(sK4) | ~creative(sK4)) | wise(susan) | calm(susan)) [skolemisation 59,60]
66. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 15]
67. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | ~funny(X0) | ~calm(X0))) [flattening 66]
68. (? [X0] : ((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | ! [X1] : ((tall(X1) | brave(X1)) & (~brave(X1) | ~tall(X1)))) & (? [X1] : ((brave(X1) | ~tall(X1)) & (~brave(X1) | tall(X1))) | ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) [nnf transformation 27]
69. (? [X0] : ((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | ! [X1] : ((tall(X1) | brave(X1)) & (~brave(X1) | ~tall(X1)))) & (? [X2] : ((brave(X2) | ~tall(X2)) & (~brave(X2) | tall(X2))) | ! [X3] : ((~brave(X3) | wise(X3)) & (~wise(X3) | brave(X3)))) [rectify 68]
70. ? [X0] : ((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) => ((wise(sK6) | brave(sK6)) & (~wise(sK6) | ~brave(sK6))) [choice axiom]
71. ? [X2] : ((brave(X2) | ~tall(X2)) & (~brave(X2) | tall(X2))) => ((brave(sK7) | ~tall(sK7)) & (~brave(sK7) | tall(sK7))) [choice axiom]
72. (((wise(sK6) | brave(sK6)) & (~wise(sK6) | ~brave(sK6))) | ! [X1] : ((tall(X1) | brave(X1)) & (~brave(X1) | ~tall(X1)))) & (((brave(sK7) | ~tall(sK7)) & (~brave(sK7) | tall(sK7))) | ! [X3] : ((~brave(X3) | wise(X3)) & (~wise(X3) | brave(X3)))) [skolemisation 69,71,70]
87. ~rich(X0) | wise(X0) [cnf transformation 29]
101. ~funny(X0) | happy(X0) | brave(X0) | humble(X0) [cnf transformation 43]
102. ~funny(X0) | ~happy(X0) | ~brave(X0) | humble(X0) [cnf transformation 43]
107. ~calm(sK2) | ~generous(X1) [cnf transformation 53]
109. ~brave(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 54]
110. ~creative(X0) | brave(X0) | tall(X0) [cnf transformation 54]
113. generous(X0) | funny(X0) | wise(X0) [cnf transformation 55]
115. ~brave(X0) | funny(X0) | generous(X0) [cnf transformation 55]
122. curious(X0) | quiet(X0) | rich(X0) | curious(X0) [cnf transformation 56]
123. ~curious(X0) | rich(X0) | ~curious(X0) | quiet(X0) [cnf transformation 56]
128. ~calm(susan) | creative(X0) [cnf transformation 61]
129. ~calm(susan) | ~humble(X0) [cnf transformation 61]
138. ~calm(X0) | ~quiet(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 67]
140. calm(X0) | calm(X0) [cnf transformation 67]
143. ~brave(sK7) | tall(sK7) | ~wise(X3) | brave(X3) [cnf transformation 72]
145. brave(sK7) | ~tall(sK7) | ~wise(X3) | brave(X3) [cnf transformation 72]
147. ~wise(sK6) | ~brave(sK6) | ~brave(X1) | ~tall(X1) [cnf transformation 72]
163. quiet(susan) [cnf transformation 24]
164. ~funny(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 138]
165. calm(X0) [duplicate literal removal 140]
167. curious(X0) | quiet(X0) | rich(X0) [duplicate literal removal 122]
168. ~curious(X0) | rich(X0) | quiet(X0) [duplicate literal removal 123]
218. 11 <=> ! [X1] : creative(X1) [avatar definition]
219. creative(X1) <- (11) [avatar component clause 218]
223. 12 <=> ! [X1] : ~generous(X1) [avatar definition]
224. ~generous(X1) <- (12) [avatar component clause 223]
226. 13 <=> calm(sK2) [avatar definition]
228. ~calm(sK2) <- (~13) [avatar component clause 226]
229. 12 | ~13 [avatar split clause 107,226,223]
231. 14 <=> ! [X3] : calm(X3) [avatar definition]
232. calm(X3) <- (14) [avatar component clause 231]
238. quiet(X0) | rich(X0) [subsumption resolution 167,168]
241. 16 <=> ! [X0] : ~humble(X0) [avatar definition]
242. ~humble(X0) <- (16) [avatar component clause 241]
250. 18 <=> calm(susan) [avatar definition]
252. ~calm(susan) <- (~18) [avatar component clause 250]
253. 16 | ~18 [avatar split clause 129,250,241]
254. 11 | ~18 [avatar split clause 128,250,218]
292. 14 [avatar split clause 165,231]
294. 27 <=> ! [X1] : (tall(X1) | brave(X1)) [avatar definition]
295. brave(X1) | tall(X1) <- (27) [avatar component clause 294]
297. 28 <=> brave(sK6) [avatar definition]
298. ~brave(sK6) <- (~28) [avatar component clause 297]
301. 29 <=> wise(sK6) [avatar definition]
302. ~wise(sK6) <- (~29) [avatar component clause 301]
303. wise(sK6) <- (29) [avatar component clause 301]
306. 30 <=> ! [X1] : (~brave(X1) | ~tall(X1)) [avatar definition]
307. ~brave(X1) | ~tall(X1) <- (30) [avatar component clause 306]
310. 30 | ~28 | ~29 [avatar split clause 147,301,297,306]
315. 32 <=> tall(sK7) [avatar definition]
316. tall(sK7) <- (32) [avatar component clause 315]
317. ~tall(sK7) <- (~32) [avatar component clause 315]
319. 33 <=> brave(sK7) [avatar definition]
320. ~brave(sK7) <- (~33) [avatar component clause 319]
321. brave(sK7) <- (33) [avatar component clause 319]
324. 34 <=> ! [X3] : (~wise(X3) | brave(X3)) [avatar definition]
325. ~wise(X3) | brave(X3) <- (34) [avatar component clause 324]
326. 34 | ~32 | 33 [avatar split clause 145,319,315,324]
328. 34 | 32 | ~33 [avatar split clause 143,319,315,324]
374. $false <- (14, ~18) [subsumption resolution 252,232]
375. ~14 | 18 [avatar contradiction clause 374]
380. $false <- (~13, 14) [resolution 232,228]
381. 13 | ~14 [avatar contradiction clause 380]
440. brave(X0) | tall(X0) <- (11) [resolution 110,219]
441. 27 | ~11 [avatar split clause 440,218,294]
442. tall(sK7) <- (27, ~33) [resolution 295,320]
446. $false <- (27, ~32, ~33) [subsumption resolution 442,317]
447. ~27 | 32 | 33 [avatar contradiction clause 446]
450. ~creative(sK7) | ~tall(sK7) <- (33) [resolution 321,109]
452. ~tall(sK7) <- (11, 33) [subsumption resolution 450,219]
453. $false <- (11, 32, 33) [subsumption resolution 452,316]
454. ~11 | ~32 | ~33 [avatar contradiction clause 453]
477. brave(sK6) <- (29, 34) [resolution 325,303]
478. $false <- (~28, 29, 34) [subsumption resolution 477,298]
479. 28 | ~29 | ~34 [avatar contradiction clause 478]
493. funny(X1) | wise(X1) <- (12) [resolution 113,224]
513. funny(X0) | generous(X0) | tall(X0) <- (27) [resolution 115,295]
517. funny(X0) | tall(X0) <- (12, 27) [subsumption resolution 513,224]
611. wise(X1) | happy(X1) | brave(X1) | humble(X1) <- (12) [resolution 493,101]
612. wise(X2) | ~quiet(X2) | ~calm(X2) <- (12) [resolution 493,164]
613. wise(X1) | happy(X1) | brave(X1) <- (12, 16) [subsumption resolution 611,242]
614. brave(X1) | happy(X1) <- (12, 16, 34) [subsumption resolution 613,325]
615. ~quiet(X2) | wise(X2) <- (12, 14) [subsumption resolution 612,232]
618. tall(X0) | ~happy(X0) | ~brave(X0) | humble(X0) <- (12, 27) [resolution 517,102]
620. tall(X2) | ~quiet(X2) | ~calm(X2) <- (12, 27) [resolution 517,164]
621. tall(X0) | ~happy(X0) | ~brave(X0) <- (12, 16, 27) [subsumption resolution 618,242]
622. ~brave(X0) | ~happy(X0) <- (12, 16, 27, 30) [subsumption resolution 621,307]
623. ~quiet(X2) | tall(X2) <- (12, 14, 27) [subsumption resolution 620,232]
771. happy(X1) | ~creative(X1) | ~tall(X1) <- (12, 16, 34) [resolution 614,109]
781. ~tall(X1) | happy(X1) <- (11, 12, 16, 34) [subsumption resolution 771,219]
815. wise(X0) | rich(X0) <- (12, 14) [resolution 615,238]
819. wise(X0) <- (12, 14) [subsumption resolution 815,87]
835. tall(susan) <- (12, 14, 27) [resolution 623,163]
898. brave(X0) <- (12, 14, 34) [resolution 819,325]
900. $false <- (12, 14, ~29) [resolution 819,302]
901. ~12 | ~14 | 29 [avatar contradiction clause 900]
922. happy(susan) <- (11, 12, 14, 16, 27, 34) [resolution 781,835]
943. ~happy(X7) <- (12, 14, 16, 27, 30, 34) [resolution 898,622]
969. $false <- (11, 12, 14, 16, 27, 30, 34) [resolution 943,922]
972. ~11 | ~12 | ~14 | ~16 | ~27 | ~30 | ~34 [avatar contradiction clause 969]
973. $false [avatar sat refutation 229,253,254,292,310,326,328,375,381,441,447,454,479,901,972]
% SZS output end Proof for 546840728877029541361447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If alice is generous or not patient then someone is not strong or happy and vice versa.
If john is both not wise and tall then someone is not kind or patient and vice versa.
Everyone who is brave is not wise.
Everyone who is brave is both not generous and not happy.
If someone is not patient then someone is humble or curious.
Everyone who is not quiet is tall.
If paul is either not strong or quiet then someone is both not wise and not tall and vice versa.
If someone is not rich then susan is both curious and strong.
If alice is both not rich and not wise then lucy is creative and vice versa.
If paul is not wise then susan is not patient or brave.
Everyone who is generous or not humble is funny or not patient.
Everyone who is not tall is not funny and vice versa.
If fred is quiet or not strong then someone is strong or not funny and vice versa.
Everyone who is not old or tall is not funny or generous.
If someone is generous then someone is either not wise or calm.
Everyone who is not calm is not rich.
Lucy is not calm.
Someone is both not quiet and tall.
Paul is not generous or not curious.
Someone is creative.
Mary is either not patient or not tall.
Someone is patient.
John is not kind or not rich.
John is not humble or not generous. | John is not tall. | contradiction | (((generous(alice)|~patient(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(((~wise(john)&tall(john)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:(brave(X)=>(~generous(X)&~happy(X))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:(~quiet(X)=>tall(X)))&
(((~strong(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))=>((curious(susan)&strong(susan))))&
(((~rich(alice)&~wise(alice)))<=>(creative(lucy)))&
((~wise(paul))=>((~patient(susan)|brave(susan))))&
(![X]:((generous(X)|~humble(X))=>(funny(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((quiet(fred)|~strong(fred)))<=>(?[X]:((strong(X)|~funny(X)))))&
(![X]:((~old(X)|tall(X))=>(~funny(X)|generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(~calm(X)=>~rich(X)))&
(~calm(lucy))&
(?[X]:((~quiet(X)&tall(X))))&
((~generous(paul)|~curious(paul)))&
(?[X]:(creative(X)))&
((~patient(mary)<~>~tall(mary)))&
(?[X]:(patient(X)))&
((~kind(john)|~rich(john)))&
((~humble(john)|~generous(john))) | ~tall(john) | [
"p1",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9197586509356837344238468
% SZS output start Proof for 9197586509356837344238468
2. (tall(john) & ~wise(john)) <=> ? [X0] : (patient(X0) | ~kind(X0)) [input p1]
22. ? [X0] : patient(X0) [input p21]
25. ~tall(john) [input hypothesis]
47. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | (~tall(john) | wise(john))) [nnf transformation 2]
48. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | ~tall(john) | wise(john)) [flattening 47]
49. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X1] : (patient(X1) | ~kind(X1)) | ~tall(john) | wise(john)) [rectify 48]
50. ? [X1] : (patient(X1) | ~kind(X1)) => (patient(sK1) | ~kind(sK1)) [choice axiom]
51. ((tall(john) & ~wise(john)) | ! [X0] : (~patient(X0) & kind(X0))) & ((patient(sK1) | ~kind(sK1)) | ~tall(john) | wise(john)) [skolemisation 49,50]
76. ? [X0] : patient(X0) => patient(sK8) [choice axiom]
77. patient(sK8) [skolemisation 22,76]
86. tall(john) | ~patient(X0) [cnf transformation 51]
123. patient(sK8) [cnf transformation 77]
126. ~tall(john) [cnf transformation 25]
154. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
155. ~patient(X0) <- (7) [avatar component clause 154]
157. 8 <=> tall(john) [avatar definition]
160. 7 | 8 [avatar split clause 86,157,154]
335. ~8 [avatar split clause 126,157]
340. $false <- (7) [resolution 155,123]
341. ~7 [avatar contradiction clause 340]
342. $false [avatar sat refutation 160,335,341]
% SZS output end Proof for 9197586509356837344238468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or old is not wise and vice versa. If lucy is not generous then fred is generous or tall. Everyone who is either creative or old is either calm or old and vice versa. Everyone who is not kind or not brave is tall and vice versa. Everyone who is either not strong or not rich is both not humble and creative. Everyone who is both strong and not wise is generous or calm. If susan is either rich or not wise then someone is either quiet or rich and vice versa. Everyone who is both wise and happy is either not quiet or not brave. Everyone who is kind is either not kind or funny and vice versa. Everyone who is either calm or not creative is both funny and not wise and vice versa. If someone is both not patient and tall then someone is either kind or tall. If someone is not calm then john is not quiet or not old. Everyone who is either not wise or funny is not humble and vice versa. Everyone who is both curious and not funny is humble. If alice is either old or strong then someone is not old or patient and vice versa. If someone is not strong then lucy is either not happy or not brave and vice versa. Someone is both not brave and kind. Fred is both not tall and not quiet. Mary is humble or not patient. Someone is not brave or not funny. Someone is wise or generous. Someone is funny. | Lucy is curious. | neutral | (![X]:((creative(X)|old(X))<=>~wise(X)))&
((~generous(lucy))=>((generous(fred)|tall(fred))))&
(![X]:((creative(X)<~>old(X))<=>(calm(X)<~>old(X))))&
(![X]:((~kind(X)|~brave(X))<=>tall(X)))&
(![X]:((~strong(X)<~>~rich(X))=>(~humble(X)&creative(X))))&
(![X]:((strong(X)&~wise(X))=>(generous(X)|calm(X))))&
(((rich(susan)<~>~wise(susan)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((wise(X)&happy(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:(kind(X)<=>(~kind(X)<~>funny(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~patient(X)&tall(X))))=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:(~calm(X)))=>((~quiet(john)|~old(john))))&
(![X]:((~wise(X)<~>funny(X))<=>~humble(X)))&
(![X]:((curious(X)&~funny(X))=>humble(X)))&
(((old(alice)<~>strong(alice)))<=>(?[X]:((~old(X)|patient(X)))))&
((?[X]:(~strong(X)))<=>((~happy(lucy)<~>~brave(lucy))))&
(?[X]:((~brave(X)&kind(X))))&
((~tall(fred)&~quiet(fred)))&
((humble(mary)|~patient(mary)))&
(?[X]:((~brave(X)|~funny(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:(funny(X))) | curious(lucy) | [] | null | 0 |
If lucy is both not calm and brave then someone is both not brave and rich.
Everyone who is both happy and patient is not funny and vice versa.
Everyone who is either not humble or not patient is not creative.
If someone is both generous and not brave then someone is either humble or not generous.
If mary is generous then someone is brave.
Everyone who is not wise is patient or wise and vice versa.
If john is both tall and not generous then paul is brave or not strong and vice versa.
Everyone who is either wise or kind is either calm or funny and vice versa.
If fred is both funny and generous then someone is curious.
If paul is wise then mary is either not quiet or not brave.
If fred is tall then lucy is not happy.
If someone is calm or humble then mary is either not old or happy.
If alice is creative or happy then someone is not happy or not strong.
Everyone who is patient or not wise is funny and vice versa.
Everyone who is both not quiet and funny is both not tall and wise and vice versa.
If someone is not kind or humble then alice is not calm and vice versa.
Fred is both not kind and brave.
Mary is either not kind or tall.
Lucy is not humble or brave.
Mary is not brave or kind.
Paul is tall or not patient.
Someone is not generous or kind.
Paul is humble. | Paul is not funny. | contradiction | (((~calm(lucy)&brave(lucy)))=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((happy(X)&patient(X))<=>~funny(X)))&
(![X]:((~humble(X)<~>~patient(X))=>~creative(X)))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((humble(X)<~>~generous(X)))))&
((generous(mary))=>(?[X]:(brave(X))))&
(![X]:(~wise(X)<=>(patient(X)|wise(X))))&
(((tall(john)&~generous(john)))<=>((brave(paul)|~strong(paul))))&
(![X]:((wise(X)<~>kind(X))<=>(calm(X)<~>funny(X))))&
(((funny(fred)&generous(fred)))=>(?[X]:(curious(X))))&
((wise(paul))=>((~quiet(mary)<~>~brave(mary))))&
((tall(fred))=>(~happy(lucy)))&
((?[X]:((calm(X)|humble(X))))=>((~old(mary)<~>happy(mary))))&
(((creative(alice)|happy(alice)))=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:((patient(X)|~wise(X))<=>funny(X)))&
(![X]:((~quiet(X)&funny(X))<=>(~tall(X)&wise(X))))&
((?[X]:((~kind(X)|humble(X))))<=>(~calm(alice)))&
((~kind(fred)&brave(fred)))&
((~kind(mary)<~>tall(mary)))&
((~humble(lucy)|brave(lucy)))&
((~brave(mary)|kind(mary)))&
((tall(paul)|~patient(paul)))&
(?[X]:((~generous(X)|kind(X))))&
(humble(paul)) | ~funny(paul) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 352910608691226189801548
% SZS output start Proof for 352910608691226189801548
6. ! [X0] : (~wise(X0) <=> (wise(X0) | patient(X0))) [input p5]
14. ! [X0] : ((~wise(X0) | patient(X0)) <=> funny(X0)) [input p13]
24. ~funny(paul) [input hypothesis]
48. ! [X0] : ((~wise(X0) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | wise(X0))) [nnf transformation 6]
49. ! [X0] : ((~wise(X0) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | wise(X0))) [flattening 48]
57. ! [X0] : (((~wise(X0) | patient(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) & ~patient(X0)))) [nnf transformation 14]
58. ! [X0] : ((~wise(X0) | patient(X0) | ~funny(X0)) & (funny(X0) | (wise(X0) & ~patient(X0)))) [flattening 57]
77. ~wise(X0) | ~wise(X0) [cnf transformation 49]
100. funny(X0) | wise(X0) [cnf transformation 58]
118. ~funny(paul) [cnf transformation 24]
120. ~wise(X0) [duplicate literal removal 77]
222. funny(X0) [subsumption resolution 100,120]
273. $false [subsumption resolution 118,222]
% SZS output end Proof for 352910608691226189801548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not tall is both generous and not happy. Everyone who is curious is humble and vice versa. Everyone who is happy is not curious and vice versa. If alice is both curious and not wise then lucy is either not old or curious and vice versa. If john is not calm or not humble then alice is both not humble and humble and vice versa. Everyone who is both patient and rich is both generous and quiet. If someone is either not happy or not quiet then lucy is either patient or not quiet and vice versa. Everyone who is either kind or not tall is either strong or not old and vice versa. If mary is both tall and curious then someone is patient and vice versa. If someone is not wise then alice is either not funny or rich. Everyone who is happy or not brave is either quiet or old and vice versa. Everyone who is wise or not curious is not strong and vice versa. Everyone who is not patient is patient. If susan is brave then someone is tall. If someone is either funny or kind then someone is strong. Susan is happy. Someone is either not kind or wise. Lucy is either kind or tall. John is either not kind or not old. Someone is not strong. Someone is not happy. | John is calm. | entailment | (![X]:((~kind(X)&~tall(X))=>(generous(X)&~happy(X))))&
(![X]:(curious(X)<=>humble(X)))&
(![X]:(happy(X)<=>~curious(X)))&
(((curious(alice)&~wise(alice)))<=>((~old(lucy)<~>curious(lucy))))&
(((~calm(john)|~humble(john)))<=>((~humble(alice)&humble(alice))))&
(![X]:((patient(X)&rich(X))=>(generous(X)&quiet(X))))&
((?[X]:((~happy(X)<~>~quiet(X))))<=>((patient(lucy)<~>~quiet(lucy))))&
(![X]:((kind(X)<~>~tall(X))<=>(strong(X)<~>~old(X))))&
(((tall(mary)&curious(mary)))<=>(?[X]:(patient(X))))&
((?[X]:(~wise(X)))=>((~funny(alice)<~>rich(alice))))&
(![X]:((happy(X)|~brave(X))<=>(quiet(X)<~>old(X))))&
(![X]:((wise(X)|~curious(X))<=>~strong(X)))&
(![X]:(~patient(X)=>patient(X)))&
((brave(susan))=>(?[X]:(tall(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:(strong(X))))&
(happy(susan))&
(?[X]:((~kind(X)<~>wise(X))))&
((kind(lucy)<~>tall(lucy)))&
((~kind(john)<~>~old(john)))&
(?[X]:(~strong(X)))&
(?[X]:(~happy(X))) | calm(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5876693043784566068938844
% SZS output start Proof for 5876693043784566068938844
5. (~humble(john) | ~calm(john)) <=> (humble(alice) & ~humble(alice)) [input p4]
22. ~calm(john) [input hypothesis]
38. ((~humble(john) | ~calm(john)) | (~humble(alice) | humble(alice))) & ((humble(alice) & ~humble(alice)) | (humble(john) & calm(john))) [nnf transformation 5]
39. (~humble(john) | ~calm(john) | ~humble(alice) | humble(alice)) & ((humble(alice) & ~humble(alice)) | (humble(john) & calm(john))) [flattening 38]
81. ~humble(alice) | calm(john) [cnf transformation 39]
83. humble(alice) | calm(john) [cnf transformation 39]
130. ~calm(john) [cnf transformation 22]
159. 6 <=> humble(alice) [avatar definition]
164. 7 <=> calm(john) [avatar definition]
167. 7 | 6 [avatar split clause 83,159,164]
169. 7 | ~6 [avatar split clause 81,159,164]
282. ~7 [avatar split clause 130,164]
283. $false [avatar sat refutation 167,169,282]
% SZS output end Proof for 5876693043784566068938844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and generous is rich or kind and vice versa.
Everyone who is both not strong and happy is patient or rich.
If lucy is not curious or not happy then susan is either patient or not kind.
If someone is either not tall or wise then alice is not happy or wise.
If someone is both not tall and creative then someone is both patient and wise and vice versa.
Everyone who is not humble or not rich is creative or strong and vice versa.
Everyone who is not rich is tall or not calm and vice versa.
Everyone who is not happy or not strong is both not funny and strong.
Everyone who is not curious is strong or quiet and vice versa.
Everyone who is not patient is either kind or creative and vice versa.
If paul is not generous or not tall then paul is not wise or humble and vice versa.
Everyone who is both kind and not wise is not wise or generous and vice versa.
Everyone who is both not rich and not calm is both not creative and humble.
If someone is old then someone is either not quiet or not tall.
If mary is either not rich or funny then someone is either generous or strong.
Everyone who is brave is not patient.
Lucy is not old.
Someone is strong or not happy.
Lucy is not generous.
Someone is humble.
Someone is not old.
Someone is strong or tall.
Alice is both not funny and happy. | Mary is funny. | neutral | (![X]:((creative(X)&generous(X))<=>(rich(X)|kind(X))))&
(![X]:((~strong(X)&happy(X))=>(patient(X)|rich(X))))&
(((~curious(lucy)|~happy(lucy)))=>((patient(susan)<~>~kind(susan))))&
((?[X]:((~tall(X)<~>wise(X))))=>((~happy(alice)|wise(alice))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((patient(X)&wise(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(creative(X)|strong(X))))&
(![X]:(~rich(X)<=>(tall(X)|~calm(X))))&
(![X]:((~happy(X)|~strong(X))=>(~funny(X)&strong(X))))&
(![X]:(~curious(X)<=>(strong(X)|quiet(X))))&
(![X]:(~patient(X)<=>(kind(X)<~>creative(X))))&
(((~generous(paul)|~tall(paul)))<=>((~wise(paul)|humble(paul))))&
(![X]:((kind(X)&~wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((~rich(X)&~calm(X))=>(~creative(X)&humble(X))))&
((?[X]:(old(X)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(((~rich(mary)<~>funny(mary)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(brave(X)=>~patient(X)))&
(~old(lucy))&
(?[X]:((strong(X)|~happy(X))))&
(~generous(lucy))&
(?[X]:(humble(X)))&
(?[X]:(~old(X)))&
(?[X]:((strong(X)|tall(X))))&
((~funny(alice)&happy(alice))) | funny(mary) | [] | null | 0 |
Everyone who is not humble or curious is happy.
Everyone who is both patient and not patient is not old or wise and vice versa.
Everyone who is either not happy or patient is old.
Everyone who is kind is both funny and not funny.
If fred is not patient then someone is either generous or creative and vice versa.
If alice is not brave then paul is either not creative or wise and vice versa.
Everyone who is not creative or not rich is both funny and not curious and vice versa.
If john is both rich and creative then paul is old or strong and vice versa.
If someone is not patient then susan is calm and vice versa.
Everyone who is not curious or tall is tall or calm and vice versa.
Everyone who is both not humble and patient is both calm and patient.
If someone is not kind then someone is both not creative and not brave.
Everyone who is both rich and not happy is not funny.
If someone is either tall or not tall then susan is either patient or not old.
If someone is either old or not strong then fred is both brave and rich.
Everyone who is not old is both quiet and not generous and vice versa.
Someone is not tall or rich.
Paul is not humble or kind.
Someone is both not calm and not tall.
Someone is either wise or not brave.
Someone is both not wise and not happy.
Susan is both not quiet and not wise.
John is both not generous and not quiet. | John is not kind. | entailment | (![X]:((~humble(X)|curious(X))=>happy(X)))&
(![X]:((patient(X)&~patient(X))<=>(~old(X)|wise(X))))&
(![X]:((~happy(X)<~>patient(X))=>old(X)))&
(![X]:(kind(X)=>(funny(X)&~funny(X))))&
((~patient(fred))<=>(?[X]:((generous(X)<~>creative(X)))))&
((~brave(alice))<=>((~creative(paul)<~>wise(paul))))&
(![X]:((~creative(X)|~rich(X))<=>(funny(X)&~curious(X))))&
(((rich(john)&creative(john)))<=>((old(paul)|strong(paul))))&
((?[X]:(~patient(X)))<=>(calm(susan)))&
(![X]:((~curious(X)|tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&patient(X))=>(calm(X)&patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((rich(X)&~happy(X))=>~funny(X)))&
((?[X]:((tall(X)<~>~tall(X))))=>((patient(susan)<~>~old(susan))))&
((?[X]:((old(X)<~>~strong(X))))=>((brave(fred)&rich(fred))))&
(![X]:(~old(X)<=>(quiet(X)&~generous(X))))&
(?[X]:((~tall(X)|rich(X))))&
((~humble(paul)|kind(paul)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~quiet(susan)&~wise(susan)))&
((~generous(john)&~quiet(john))) | ~kind(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7553182343526390432284274
% SZS output start Proof for 7553182343526390432284274
4. ! [X0] : (kind(X0) => (~funny(X0) & funny(X0))) [input p3]
24. kind(john) [input hypothesis]
28. ! [X0] : ((~funny(X0) & funny(X0)) | ~kind(X0)) [ennf transformation 4]
79. funny(X0) | ~kind(X0) [cnf transformation 28]
80. ~funny(X0) | ~kind(X0) [cnf transformation 28]
133. kind(john) [cnf transformation 24]
140. ~kind(X0) [subsumption resolution 79,80]
249. $false [subsumption resolution 133,140]
% SZS output end Proof for 7553182343526390432284274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is either not funny or patient and vice versa.
Everyone who is not patient or not generous is either calm or not happy.
Everyone who is not tall or not happy is both not calm and old.
If someone is both tall and not strong then john is both wise and not humble and vice versa.
If someone is brave then paul is both quiet and rich.
Everyone who is either happy or rich is not calm or not creative and vice versa.
If someone is kind then fred is rich and vice versa.
If someone is creative or brave then someone is both wise and kind and vice versa.
If alice is not generous or not tall then paul is not quiet and vice versa.
Everyone who is both calm and not curious is kind or patient and vice versa.
Everyone who is either not funny or not generous is either not curious or tall.
Everyone who is humble is not tall.
If paul is humble or not brave then alice is generous.
Everyone who is calm is both not creative and not strong.
If someone is not quiet or generous then alice is old.
Someone is either not tall or creative.
Mary is not old or not rich.
Someone is both not calm and tall.
Lucy is kind or humble.
Someone is not brave or not old.
Someone is humble or brave.
Someone is both curious and generous. | John is not wise. | contradiction | ((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~patient(X)|~generous(X))=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~happy(X))=>(~calm(X)&old(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((wise(john)&~humble(john))))&
((?[X]:(brave(X)))=>((quiet(paul)&rich(paul))))&
(![X]:((happy(X)<~>rich(X))<=>(~calm(X)|~creative(X))))&
((?[X]:(kind(X)))<=>(rich(fred)))&
((?[X]:((creative(X)|brave(X))))<=>(?[X]:((wise(X)&kind(X)))))&
(((~generous(alice)|~tall(alice)))<=>(~quiet(paul)))&
(![X]:((calm(X)&~curious(X))<=>(kind(X)|patient(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(~curious(X)<~>tall(X))))&
(![X]:(humble(X)=>~tall(X)))&
(((humble(paul)|~brave(paul)))=>(generous(alice)))&
(![X]:(calm(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~quiet(X)|generous(X))))=>(old(alice)))&
(?[X]:((~tall(X)<~>creative(X))))&
((~old(mary)|~rich(mary)))&
(?[X]:((~calm(X)&tall(X))))&
((kind(lucy)|humble(lucy)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((curious(X)&generous(X)))) | ~wise(john) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4387191137832180140908512
% SZS output start Proof for 4387191137832180140908512
2. ! [X0] : ((~generous(X0) | ~patient(X0)) => (calm(X0) <~> ~happy(X0))) [input p1]
3. ! [X0] : ((~happy(X0) | ~tall(X0)) => (old(X0) & ~calm(X0))) [input p2]
4. ? [X0] : (~strong(X0) & tall(X0)) <=> (~humble(john) & wise(john)) [input p3]
6. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (~creative(X0) | ~calm(X0))) [input p5]
7. ? [X0] : kind(X0) <=> rich(fred) [input p6]
10. ! [X0] : ((~curious(X0) & calm(X0)) <=> (patient(X0) | kind(X0))) [input p9]
14. ! [X0] : (calm(X0) => (~strong(X0) & ~creative(X0))) [input p13]
23. ~wise(john) [input hypothesis]
26. ! [X0] : ((calm(X0) <~> ~happy(X0)) | (generous(X0) & patient(X0))) [ennf transformation 2]
27. ! [X0] : ((old(X0) & ~calm(X0)) | (happy(X0) & tall(X0))) [ennf transformation 3]
32. ! [X0] : ((~strong(X0) & ~creative(X0)) | ~calm(X0)) [ennf transformation 14]
39. ! [X0] : (((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | (generous(X0) & patient(X0))) [nnf transformation 26]
40. (? [X0] : (~strong(X0) & tall(X0)) | (humble(john) | ~wise(john))) & ((~humble(john) & wise(john)) | ! [X0] : (strong(X0) | ~tall(X0))) [nnf transformation 4]
41. (? [X0] : (~strong(X0) & tall(X0)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X0] : (strong(X0) | ~tall(X0))) [flattening 40]
42. (? [X0] : (~strong(X0) & tall(X0)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X1] : (strong(X1) | ~tall(X1))) [rectify 41]
43. ? [X0] : (~strong(X0) & tall(X0)) => (~strong(sK2) & tall(sK2)) [choice axiom]
44. ((~strong(sK2) & tall(sK2)) | humble(john) | ~wise(john)) & ((~humble(john) & wise(john)) | ! [X1] : (strong(X1) | ~tall(X1))) [skolemisation 42,43]
45. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & ((~creative(X0) | ~calm(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & (~creative(X0) | ~calm(X0) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 45]
47. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X0] : ~kind(X0)) [nnf transformation 7]
48. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [rectify 47]
49. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
50. (kind(sK3) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [skolemisation 48,49]
58. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 10]
59. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | curious(X0) | ~calm(X0))) [flattening 58]
76. ~happy(X0) | calm(X0) | patient(X0) [cnf transformation 39]
80. ~calm(X0) | tall(X0) [cnf transformation 27]
81. ~calm(X0) | happy(X0) [cnf transformation 27]
84. wise(john) | strong(X1) | ~tall(X1) [cnf transformation 44]
92. rich(X0) | happy(X0) | calm(X0) [cnf transformation 46]
97. kind(sK3) | ~rich(fred) [cnf transformation 50]
107. ~kind(X0) | calm(X0) [cnf transformation 59]
108. ~patient(X0) | calm(X0) [cnf transformation 59]
119. ~strong(X0) | ~calm(X0) [cnf transformation 32]
132. ~wise(john) [cnf transformation 23]
159. 7 <=> wise(john) [avatar definition]
177. 11 <=> ! [X1] : (strong(X1) | ~tall(X1)) [avatar definition]
178. ~tall(X1) | strong(X1) <- (11) [avatar component clause 177]
180. 11 | 7 [avatar split clause 84,159,177]
194. rich(X0) | happy(X0) [subsumption resolution 92,81]
197. 15 <=> rich(fred) [avatar definition]
199. ~rich(fred) <- (~15) [avatar component clause 197]
201. 16 <=> kind(sK3) [avatar definition]
203. kind(sK3) <- (16) [avatar component clause 201]
204. ~15 | 16 [avatar split clause 97,201,197]
315. ~7 [avatar split clause 132,159]
316. calm(sK3) <- (16) [resolution 107,203]
319. tall(sK3) <- (16) [resolution 316,80]
335. strong(sK3) <- (11, 16) [resolution 319,178]
353. 41 <=> calm(fred) [avatar definition]
355. calm(fred) <- (41) [avatar component clause 353]
357. 42 <=> happy(fred) [avatar definition]
358. happy(fred) <- (42) [avatar component clause 357]
363. ~calm(sK3) <- (11, 16) [resolution 335,119]
364. $false <- (11, 16) [subsumption resolution 363,316]
365. ~11 | ~16 [avatar contradiction clause 364]
366. happy(fred) <- (~15) [resolution 199,194]
369. 42 | 15 [avatar split clause 366,197,357]
374. calm(fred) | patient(fred) <- (42) [resolution 358,76]
380. calm(fred) <- (42) [subsumption resolution 374,108]
381. 41 | ~42 [avatar split clause 380,357,353]
387. tall(fred) <- (41) [resolution 355,80]
473. strong(fred) <- (11, 41) [resolution 387,178]
504. ~calm(fred) <- (11, 41) [resolution 473,119]
505. $false <- (11, 41) [subsumption resolution 504,355]
506. ~11 | ~41 [avatar contradiction clause 505]
507. $false [avatar sat refutation 180,204,315,365,369,381,506]
% SZS output end Proof for 4387191137832180140908512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not brave is either not rich or not quiet and vice versa.
Everyone who is either quiet or kind is not strong or not creative and vice versa.
If lucy is not patient or not funny then someone is both tall and not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
Susan is not old.
Someone is quiet.
Someone is both not strong and not patient.
Someone is both not generous and tall.
Someone is both strong and happy.
Paul is both tall and not kind.
Someone is both not brave and not funny. | Alice is kind. | contradiction | (![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(~strong(X)|~creative(X))))&
(((~patient(lucy)|~funny(lucy)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
(~old(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((strong(X)&happy(X))))&
((tall(paul)&~kind(paul)))&
(?[X]:((~brave(X)&~funny(X)))) | kind(alice) | [
"p3",
"p4",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7859709397438543645140844
% SZS output start Proof for 7859709397438543645140844
4. ! [X0] : ((~patient(X0) | ~calm(X0)) => (wise(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (tall(X0) | ~wise(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (old(X0) | happy(X0))) [input p5]
9. ! [X0] : ((wise(X0) | curious(X0)) => (calm(X0) <~> humble(X0))) [input p8]
11. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p10]
24. kind(alice) [input hypothesis]
26. ! [X0] : ((wise(X0) | ~kind(X0)) | (patient(X0) & calm(X0))) [ennf transformation 4]
27. ! [X0] : (wise(X0) | ~kind(X0) | (patient(X0) & calm(X0))) [flattening 26]
30. ! [X0] : ((calm(X0) <~> humble(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 9]
40. ! [X0] : (((humble(X0) | ~wise(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 5]
41. ! [X0] : ((humble(X0) | ~wise(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | (~humble(X0) & wise(X0)))) [flattening 40]
42. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | kind(X0))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | kind(X0))) [flattening 42]
50. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 30]
56. ! [X0] : (((creative(X0) | ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 11]
57. ! [X0] : ((creative(X0) | ~old(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [flattening 56]
91. ~kind(X0) | wise(X0) | calm(X0) [cnf transformation 27]
94. ~humble(X0) | ~wise(X0) | tall(X0) [cnf transformation 41]
99. ~old(X0) | ~kind(X0) [cnf transformation 43]
109. ~wise(X0) | calm(X0) | humble(X0) [cnf transformation 50]
116. ~calm(X0) | old(X0) [cnf transformation 57]
118. ~tall(X0) | old(X0) [cnf transformation 57]
151. kind(alice) [cnf transformation 24]
195. 9 <=> old(alice) [avatar definition]
196. ~old(alice) <- (~9) [avatar component clause 195]
197. old(alice) <- (9) [avatar component clause 195]
260. ~kind(alice) <- (9) [resolution 99,197]
261. $false <- (9) [subsumption resolution 260,151]
262. ~9 [avatar contradiction clause 261]
351. wise(alice) | calm(alice) [resolution 91,151]
354. 31 <=> calm(alice) [avatar definition]
355. ~calm(alice) <- (~31) [avatar component clause 354]
356. calm(alice) <- (31) [avatar component clause 354]
358. 32 <=> wise(alice) [avatar definition]
360. wise(alice) <- (32) [avatar component clause 358]
361. 31 | 32 [avatar split clause 351,358,354]
394. 36 <=> humble(alice) [avatar definition]
396. humble(alice) <- (36) [avatar component clause 394]
403. calm(alice) | humble(alice) <- (32) [resolution 360,109]
426. 37 <=> tall(alice) [avatar definition]
427. tall(alice) <- (37) [avatar component clause 426]
430. humble(alice) <- (~31, 32) [subsumption resolution 403,355]
431. 36 | 31 | ~32 [avatar split clause 430,358,354,394]
476. ~wise(alice) | tall(alice) <- (36) [resolution 396,94]
781. old(alice) <- (37) [resolution 427,118]
784. $false <- (~9, 37) [subsumption resolution 781,196]
785. 9 | ~37 [avatar contradiction clause 784]
787. 37 | ~32 | ~36 [avatar split clause 476,394,358,426]
789. old(alice) <- (31) [resolution 356,116]
792. $false <- (~9, 31) [subsumption resolution 789,196]
793. 9 | ~31 [avatar contradiction clause 792]
794. $false [avatar sat refutation 262,361,431,785,787,793]
% SZS output end Proof for 7859709397438543645140844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or creative is creative and vice versa. Everyone who is strong or curious is both brave and not patient. Everyone who is wise or patient is both patient and not brave and vice versa. If mary is either not creative or not generous then someone is both kind and patient. Everyone who is funny or not old is both not rich and patient. Everyone who is funny or not curious is patient or quiet and vice versa. Everyone who is either not patient or happy is old and vice versa. If someone is both not kind and not brave then someone is both not strong and not old. If lucy is either not kind or not calm then someone is old or rich and vice versa. Everyone who is either happy or generous is both calm and not happy. If someone is both funny and not calm then someone is not calm and vice versa. Everyone who is creative or humble is both brave and not old and vice versa. Everyone who is either not funny or tall is either not tall or not humble and vice versa. If someone is not kind then mary is either not kind or not generous and vice versa. If lucy is kind then alice is wise or patient and vice versa. Everyone who is not old is both not strong and not creative. Someone is either strong or calm. John is either kind or not quiet. Lucy is not curious. Lucy is funny or not happy. John is not kind or funny. Someone is not quiet. | Mary is kind. | neutral | (![X]:((old(X)<~>creative(X))<=>creative(X)))&
(![X]:((strong(X)|curious(X))=>(brave(X)&~patient(X))))&
(![X]:((wise(X)|patient(X))<=>(patient(X)&~brave(X))))&
(((~creative(mary)<~>~generous(mary)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((funny(X)|~old(X))=>(~rich(X)&patient(X))))&
(![X]:((funny(X)|~curious(X))<=>(patient(X)|quiet(X))))&
(![X]:((~patient(X)<~>happy(X))<=>old(X)))&
((?[X]:((~kind(X)&~brave(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(((~kind(lucy)<~>~calm(lucy)))<=>(?[X]:((old(X)|rich(X)))))&
(![X]:((happy(X)<~>generous(X))=>(calm(X)&~happy(X))))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|humble(X))<=>(brave(X)&~old(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(~tall(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>((~kind(mary)<~>~generous(mary))))&
((kind(lucy))<=>((wise(alice)|patient(alice))))&
(![X]:(~old(X)=>(~strong(X)&~creative(X))))&
(?[X]:((strong(X)<~>calm(X))))&
((kind(john)<~>~quiet(john)))&
(~curious(lucy))&
((funny(lucy)|~happy(lucy)))&
((~kind(john)|funny(john)))&
(?[X]:(~quiet(X))) | kind(mary) | [] | null | 0 |
Everyone who is either happy or not wise is not tall.
If someone is patient or not curious then someone is either curious or strong.
Everyone who is humble or wise is either tall or not rich.
Everyone who is either humble or not humble is either not funny or calm.
Everyone who is both old and not tall is not strong or calm and vice versa.
Everyone who is not calm is not funny and vice versa.
If susan is tall or not calm then someone is strong or not strong.
Everyone who is either not funny or patient is both not curious and strong.
If someone is not brave or not creative then mary is either not kind or generous.
Everyone who is both kind and funny is not brave or creative and vice versa.
Everyone who is not tall or not happy is funny or creative.
If someone is not strong then someone is either strong or not calm and vice versa.
If fred is both kind and calm then susan is funny and vice versa.
Everyone who is either not curious or generous is not calm.
If mary is old or not rich then someone is either not wise or humble and vice versa.
If mary is either generous or not calm then fred is humble or not generous and vice versa.
Someone is not tall or not strong.
Someone is both not humble and not generous.
Someone is not strong.
Someone is creative.
Lucy is brave or funny.
Paul is both humble and not rich.
Susan is calm or not funny.
Susan is not wise or brave. | Susan is tall. | neutral | (![X]:((happy(X)<~>~wise(X))=>~tall(X)))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:((curious(X)<~>strong(X)))))&
(![X]:((humble(X)|wise(X))=>(tall(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~humble(X))=>(~funny(X)<~>calm(X))))&
(![X]:((old(X)&~tall(X))<=>(~strong(X)|calm(X))))&
(![X]:(~calm(X)<=>~funny(X)))&
(((tall(susan)|~calm(susan)))=>(?[X]:((strong(X)|~strong(X)))))&
(![X]:((~funny(X)<~>patient(X))=>(~curious(X)&strong(X))))&
((?[X]:((~brave(X)|~creative(X))))=>((~kind(mary)<~>generous(mary))))&
(![X]:((kind(X)&funny(X))<=>(~brave(X)|creative(X))))&
(![X]:((~tall(X)|~happy(X))=>(funny(X)|creative(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(((kind(fred)&calm(fred)))<=>(funny(susan)))&
(![X]:((~curious(X)<~>generous(X))=>~calm(X)))&
(((old(mary)|~rich(mary)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(((generous(mary)<~>~calm(mary)))<=>((humble(fred)|~generous(fred))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:(~strong(X)))&
(?[X]:(creative(X)))&
((brave(lucy)|funny(lucy)))&
((humble(paul)&~rich(paul)))&
((calm(susan)|~funny(susan)))&
((~wise(susan)|brave(susan))) | tall(susan) | [] | null | 0 |
Everyone who is brave or not patient is not generous. Everyone who is both brave and tall is calm or generous and vice versa. If someone is not quiet then fred is either not quiet or not calm. Everyone who is not curious or calm is not generous or old and vice versa. If lucy is either not old or not brave then someone is not humble or not strong. If susan is either not rich or happy then someone is either wise or patient and vice versa. If john is either brave or not humble then someone is either quiet or creative. Everyone who is not humble or old is either strong or kind. Everyone who is either funny or not calm is generous. Everyone who is both curious and strong is creative or not kind. If someone is both not tall and not creative then mary is both happy and not humble and vice versa. If someone is either not strong or not brave then someone is either creative or curious. If lucy is tall then alice is both not strong and not generous and vice versa. If someone is not brave or not curious then lucy is both funny and calm and vice versa. If someone is either not patient or not curious then someone is either funny or not strong and vice versa. Mary is creative or patient. Someone is either not wise or creative. Mary is rich or brave. Someone is tall or not quiet. John is either old or happy. John is both patient and not funny. Someone is not happy or not calm. | Mary is not funny. | entailment | (![X]:((brave(X)|~patient(X))=>~generous(X)))&
(![X]:((brave(X)&tall(X))<=>(calm(X)|generous(X))))&
((?[X]:(~quiet(X)))=>((~quiet(fred)<~>~calm(fred))))&
(![X]:((~curious(X)|calm(X))<=>(~generous(X)|old(X))))&
(((~old(lucy)<~>~brave(lucy)))=>(?[X]:((~humble(X)|~strong(X)))))&
(((~rich(susan)<~>happy(susan)))<=>(?[X]:((wise(X)<~>patient(X)))))&
(((brave(john)<~>~humble(john)))=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~humble(X)|old(X))=>(strong(X)<~>kind(X))))&
(![X]:((funny(X)<~>~calm(X))=>generous(X)))&
(![X]:((curious(X)&strong(X))=>(creative(X)|~kind(X))))&
((?[X]:((~tall(X)&~creative(X))))<=>((happy(mary)&~humble(mary))))&
((?[X]:((~strong(X)<~>~brave(X))))=>(?[X]:((creative(X)<~>curious(X)))))&
((tall(lucy))<=>((~strong(alice)&~generous(alice))))&
((?[X]:((~brave(X)|~curious(X))))<=>((funny(lucy)&calm(lucy))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((creative(mary)|patient(mary)))&
(?[X]:((~wise(X)<~>creative(X))))&
((rich(mary)|brave(mary)))&
(?[X]:((tall(X)|~quiet(X))))&
((old(john)<~>happy(john)))&
((patient(john)&~funny(john)))&
(?[X]:((~happy(X)|~calm(X)))) | ~funny(mary) | [
"p0",
"p1",
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 704711134836396388815507
% SZS output start Proof for 704711134836396388815507
1. ! [X0] : ((~patient(X0) | brave(X0)) => ~generous(X0)) [input p0]
2. ! [X0] : ((tall(X0) & brave(X0)) <=> (generous(X0) | calm(X0))) [input p1]
4. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (old(X0) | ~generous(X0))) [input p3]
9. ! [X0] : ((funny(X0) <~> ~calm(X0)) => generous(X0)) [input p8]
14. ? [X0] : (~curious(X0) | ~brave(X0)) <=> (calm(lucy) & funny(lucy)) [input p13]
23. funny(mary) [input hypothesis]
26. ! [X0] : (~generous(X0) | (patient(X0) & ~brave(X0))) [ennf transformation 1]
31. ! [X0] : (generous(X0) | (funny(X0) <=> ~calm(X0))) [ennf transformation 9]
35. ! [X0] : (((tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~tall(X0) | ~brave(X0)))) [nnf transformation 2]
36. ! [X0] : (((tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | ~tall(X0) | ~brave(X0))) [flattening 35]
38. ! [X0] : (((calm(X0) | ~curious(X0)) | (~old(X0) & generous(X0))) & ((old(X0) | ~generous(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 4]
39. ! [X0] : ((calm(X0) | ~curious(X0) | (~old(X0) & generous(X0))) & (old(X0) | ~generous(X0) | (~calm(X0) & curious(X0)))) [flattening 38]
51. ! [X0] : (generous(X0) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) [nnf transformation 31]
63. (? [X0] : (~curious(X0) | ~brave(X0)) | (~calm(lucy) | ~funny(lucy))) & ((calm(lucy) & funny(lucy)) | ! [X0] : (curious(X0) & brave(X0))) [nnf transformation 14]
64. (? [X0] : (~curious(X0) | ~brave(X0)) | ~calm(lucy) | ~funny(lucy)) & ((calm(lucy) & funny(lucy)) | ! [X0] : (curious(X0) & brave(X0))) [flattening 63]
65. (? [X0] : (~curious(X0) | ~brave(X0)) | ~calm(lucy) | ~funny(lucy)) & ((calm(lucy) & funny(lucy)) | ! [X1] : (curious(X1) & brave(X1))) [rectify 64]
66. ? [X0] : (~curious(X0) | ~brave(X0)) => (~curious(sK5) | ~brave(sK5)) [choice axiom]
67. ((~curious(sK5) | ~brave(sK5)) | ~calm(lucy) | ~funny(lucy)) & ((calm(lucy) & funny(lucy)) | ! [X1] : (curious(X1) & brave(X1))) [skolemisation 65,66]
81. ~generous(X0) | ~brave(X0) [cnf transformation 26]
85. brave(X0) | ~generous(X0) [cnf transformation 36]
92. calm(X0) | ~curious(X0) | generous(X0) [cnf transformation 39]
112. generous(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 51]
127. funny(lucy) | curious(X1) [cnf transformation 67]
129. calm(lucy) | curious(X1) [cnf transformation 67]
149. funny(mary) [cnf transformation 23]
150. ~generous(X0) [subsumption resolution 85,81]
165. ~curious(X0) | calm(X0) [subsumption resolution 92,150]
235. ~funny(X0) | ~calm(X0) [subsumption resolution 112,150]
289. 29 <=> ! [X1] : curious(X1) [avatar definition]
290. curious(X1) <- (29) [avatar component clause 289]
292. 30 <=> calm(lucy) [avatar definition]
294. calm(lucy) <- (30) [avatar component clause 292]
295. 29 | 30 [avatar split clause 129,292,289]
301. 32 <=> funny(lucy) [avatar definition]
303. funny(lucy) <- (32) [avatar component clause 301]
304. 29 | 32 [avatar split clause 127,301,289]
406. calm(X0) <- (29) [resolution 165,290]
419. ~calm(mary) [resolution 235,149]
421. $false <- (29) [subsumption resolution 419,406]
422. ~29 [avatar contradiction clause 421]
426. ~calm(lucy) <- (32) [resolution 303,235]
427. $false <- (30, 32) [subsumption resolution 426,294]
428. ~30 | ~32 [avatar contradiction clause 427]
429. $false [avatar sat refutation 295,304,422,428]
% SZS output end Proof for 704711134836396388815507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not quiet and wise and vice versa.
Everyone who is both not curious and not tall is both tall and not kind and vice versa.
Everyone who is both not rich and not humble is both calm and not generous.
If someone is either kind or not calm then mary is either not brave or not wise.
If someone is either not creative or not generous then someone is kind or patient and vice versa.
If someone is either tall or humble then susan is both wise and curious.
If alice is either happy or wise then alice is tall or funny and vice versa.
If fred is both not happy and not patient then lucy is creative and vice versa.
Everyone who is either not happy or not rich is either strong or not strong.
Everyone who is both not funny and calm is not quiet.
If paul is either strong or not patient then alice is both kind and not calm.
If lucy is either patient or not humble then someone is both not quiet and not strong and vice versa.
Everyone who is tall is brave or not generous and vice versa.
Everyone who is either curious or rich is not wise or not tall and vice versa.
If john is both not tall and funny then someone is not tall and vice versa.
Everyone who is either not patient or happy is not calm or patient and vice versa.
Someone is brave.
Fred is both kind and rich.
Susan is not humble.
Someone is either not wise or not creative.
Someone is quiet or not quiet.
Someone is either not calm or humble.
Someone is not strong or brave.
Fred is both not strong and humble. | Lucy is quiet. | entailment | (![X]:(~wise(X)<=>(~quiet(X)&wise(X))))&
(![X]:((~curious(X)&~tall(X))<=>(tall(X)&~kind(X))))&
(![X]:((~rich(X)&~humble(X))=>(calm(X)&~generous(X))))&
((?[X]:((kind(X)<~>~calm(X))))=>((~brave(mary)<~>~wise(mary))))&
((?[X]:((~creative(X)<~>~generous(X))))<=>(?[X]:((kind(X)|patient(X)))))&
((?[X]:((tall(X)<~>humble(X))))=>((wise(susan)&curious(susan))))&
(((happy(alice)<~>wise(alice)))<=>((tall(alice)|funny(alice))))&
(((~happy(fred)&~patient(fred)))<=>(creative(lucy)))&
(![X]:((~happy(X)<~>~rich(X))=>(strong(X)<~>~strong(X))))&
(![X]:((~funny(X)&calm(X))=>~quiet(X)))&
(((strong(paul)<~>~patient(paul)))=>((kind(alice)&~calm(alice))))&
(((patient(lucy)<~>~humble(lucy)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:(tall(X)<=>(brave(X)|~generous(X))))&
(![X]:((curious(X)<~>rich(X))<=>(~wise(X)|~tall(X))))&
(((~tall(john)&funny(john)))<=>(?[X]:(~tall(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~calm(X)|patient(X))))&
(?[X]:(brave(X)))&
((kind(fred)&rich(fred)))&
(~humble(susan))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~strong(X)|brave(X))))&
((~strong(fred)&humble(fred))) | quiet(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 498218408385098675391960
% SZS output start Proof for 498218408385098675391960
1. ! [X0] : (~wise(X0) <=> (wise(X0) & ~quiet(X0))) [input p0]
25. ~quiet(lucy) [input hypothesis]
35. ! [X0] : ((~wise(X0) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 1]
36. ! [X0] : ((~wise(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | wise(X0))) [flattening 35]
80. wise(X0) | wise(X0) [cnf transformation 36]
81. ~wise(X0) | ~wise(X0) | quiet(X0) [cnf transformation 36]
156. ~quiet(lucy) [cnf transformation 25]
161. wise(X0) [duplicate literal removal 80]
162. ~wise(X0) | quiet(X0) [duplicate literal removal 81]
354. quiet(X0) [resolution 162,161]
356. $false [resolution 354,156]
% SZS output end Proof for 498218408385098675391960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
If mary is either not happy or not calm then susan is not tall.
Everyone who is curious or not curious is generous.
If someone is strong or humble then someone is both kind and generous and vice versa.
Everyone who is not curious or not generous is both patient and not funny.
If someone is funny then someone is not creative or not calm and vice versa.
Everyone who is either not tall or not generous is not creative or creative and vice versa.
If fred is both not creative and not funny then someone is both not wise and kind and vice versa.
If someone is humble or wise then fred is not rich and vice versa.
If someone is not happy or funny then mary is creative.
Everyone who is both not happy and patient is either not patient or not calm.
Everyone who is old or not happy is either generous or not tall and vice versa.
Everyone who is not kind or not strong is calm or not quiet and vice versa.
Lucy is calm or rich.
Someone is both not kind and not brave.
Someone is creative or humble.
Someone is rich or curious.
John is brave or not humble.
Someone is creative or not kind.
Someone is wise or not wise. | Mary is old. | contradiction | (![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((humble(X)|wise(X))))<=>(~rich(fred)))&
((?[X]:((~happy(X)|funny(X))))=>(creative(mary)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((old(X)|~happy(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~kind(X)|~strong(X))<=>(calm(X)|~quiet(X))))&
((calm(lucy)|rich(lucy)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((rich(X)|curious(X))))&
((brave(john)|~humble(john)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((wise(X)|~wise(X)))) | old(mary) | [
"p4",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2669922905806069895215895
% SZS output start Proof for 2669922905806069895215895
5. ! [X0] : ((~curious(X0) | curious(X0)) => generous(X0)) [input p4]
9. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (creative(X0) | ~creative(X0))) [input p8]
14. ! [X0] : ((~happy(X0) | old(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p13]
23. old(mary) [input hypothesis]
28. ! [X0] : (generous(X0) | (curious(X0) & ~curious(X0))) [ennf transformation 5]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 9]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
61. ! [X0] : (((~happy(X0) | old(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [nnf transformation 14]
62. ! [X0] : ((~happy(X0) | old(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [flattening 61]
88. generous(X0) | ~curious(X0) [cnf transformation 28]
89. generous(X0) | curious(X0) [cnf transformation 28]
104. ~generous(X0) | ~tall(X0) | creative(X0) [cnf transformation 50]
105. ~generous(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 50]
121. tall(X0) | ~generous(X0) | ~old(X0) [cnf transformation 62]
137. old(mary) [cnf transformation 23]
155. generous(X0) [subsumption resolution 88,89]
205. ~tall(X0) | ~creative(X0) [subsumption resolution 105,155]
206. ~tall(X0) | creative(X0) [subsumption resolution 104,155]
207. ~tall(X0) [subsumption resolution 206,205]
246. ~generous(X0) | ~old(X0) [subsumption resolution 121,207]
247. ~old(X0) [subsumption resolution 246,155]
276. $false [subsumption resolution 137,247]
% SZS output end Proof for 2669922905806069895215895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is humble then someone is either not kind or not quiet. If susan is not creative then mary is not patient or strong and vice versa. If someone is strong or calm then john is strong or rich. If someone is both wise and tall then someone is not calm. If john is kind or not strong then someone is either not wise or brave and vice versa. Everyone who is either curious or generous is either not humble or not creative. If susan is either kind or quiet then someone is both not quiet and curious. Everyone who is generous or not quiet is rich or curious and vice versa. Everyone who is both calm and kind is curious or old. If someone is both not wise and not generous then someone is kind or old and vice versa. Everyone who is calm or not rich is either happy or not brave. Everyone who is either not wise or humble is both not rich and generous and vice versa. If fred is not wise or not curious then lucy is either not calm or not curious. Everyone who is not brave or old is both not patient and patient and vice versa. Everyone who is both not brave and tall is either brave or wise and vice versa. If alice is quiet then susan is old. Someone is calm or rich. John is happy. Paul is either humble or not funny. Someone is curious. Paul is either not wise or not rich. Someone is either not happy or not old. | Susan is generous. | neutral | ((humble(susan))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((~creative(susan))<=>((~patient(mary)|strong(mary))))&
((?[X]:((strong(X)|calm(X))))=>((strong(john)|rich(john))))&
((?[X]:((wise(X)&tall(X))))=>(?[X]:(~calm(X))))&
(((kind(john)|~strong(john)))<=>(?[X]:((~wise(X)<~>brave(X)))))&
(![X]:((curious(X)<~>generous(X))=>(~humble(X)<~>~creative(X))))&
(((kind(susan)<~>quiet(susan)))=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(rich(X)|curious(X))))&
(![X]:((calm(X)&kind(X))=>(curious(X)|old(X))))&
((?[X]:((~wise(X)&~generous(X))))<=>(?[X]:((kind(X)|old(X)))))&
(![X]:((calm(X)|~rich(X))=>(happy(X)<~>~brave(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(~rich(X)&generous(X))))&
(((~wise(fred)|~curious(fred)))=>((~calm(lucy)<~>~curious(lucy))))&
(![X]:((~brave(X)|old(X))<=>(~patient(X)&patient(X))))&
(![X]:((~brave(X)&tall(X))<=>(brave(X)<~>wise(X))))&
((quiet(alice))=>(old(susan)))&
(?[X]:((calm(X)|rich(X))))&
(happy(john))&
((humble(paul)<~>~funny(paul)))&
(?[X]:(curious(X)))&
((~wise(paul)<~>~rich(paul)))&
(?[X]:((~happy(X)<~>~old(X)))) | generous(susan) | [] | null | 0 |
Everyone who is both not wise and strong is curious or not kind and vice versa.
If someone is not tall or kind then someone is generous or not happy and vice versa.
Everyone who is not funny is creative.
Everyone who is both creative and happy is calm or not humble and vice versa.
Everyone who is either quiet or generous is creative or not curious and vice versa.
If someone is not generous then mary is not generous.
Everyone who is not happy is both not tall and not happy.
Everyone who is both not brave and not curious is brave or not calm.
Everyone who is both not kind and creative is both not calm and tall.
If mary is both strong and curious then someone is either quiet or not creative and vice versa.
Everyone who is quiet is both tall and not creative.
Everyone who is either not old or calm is both generous and old and vice versa.
If someone is funny or not calm then someone is not happy or funny and vice versa.
Everyone who is either kind or not curious is both humble and calm and vice versa.
If alice is kind or not funny then susan is either curious or not wise.
If susan is tall then someone is not humble or not strong and vice versa.
Susan is not strong or not tall.
Alice is either not brave or not creative.
Paul is both not humble and happy.
Lucy is either not old or brave.
Alice is happy.
Someone is either kind or rich.
Someone is not strong.
Lucy is both not old and not tall. | Alice is funny. | neutral | (![X]:((~wise(X)&strong(X))<=>(curious(X)|~kind(X))))&
((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~funny(X)=>creative(X)))&
(![X]:((creative(X)&happy(X))<=>(calm(X)|~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(creative(X)|~curious(X))))&
((?[X]:(~generous(X)))=>(~generous(mary)))&
(![X]:(~happy(X)=>(~tall(X)&~happy(X))))&
(![X]:((~brave(X)&~curious(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)&creative(X))=>(~calm(X)&tall(X))))&
(((strong(mary)&curious(mary)))<=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:(quiet(X)=>(tall(X)&~creative(X))))&
(![X]:((~old(X)<~>calm(X))<=>(generous(X)&old(X))))&
((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((kind(X)<~>~curious(X))<=>(humble(X)&calm(X))))&
(((kind(alice)|~funny(alice)))=>((curious(susan)<~>~wise(susan))))&
((tall(susan))<=>(?[X]:((~humble(X)|~strong(X)))))&
((~strong(susan)|~tall(susan)))&
((~brave(alice)<~>~creative(alice)))&
((~humble(paul)&happy(paul)))&
((~old(lucy)<~>brave(lucy)))&
(happy(alice))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:(~strong(X)))&
((~old(lucy)&~tall(lucy))) | funny(alice) | [] | null | 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.