premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either not curious or quiet is not kind and vice versa.
Everyone who is either kind or tall is either wise or not humble and vice versa.
If susan is not strong then someone is either tall or not rich and vice versa.
Everyone who is both not strong and not patient is patient and vice versa.
Everyone who is either not brave or old is not happy or not strong.
If someone is not humble or humble then someone is both not happy and not calm.
Everyone who is both strong and not creative is either quiet or patient and vice versa.
Everyone who is not rich or not happy is curious and vice versa.
Everyone who is not strong is not tall or strong.
Everyone who is not curious or happy is not humble or old.
Everyone who is not tall is both not rich and kind and vice versa.
Everyone who is not strong is either wise or strong.
If someone is either quiet or old then someone is not kind or not curious.
If mary is either wise or not kind then someone is tall and vice versa.
If paul is not humble then lucy is not wise.
Everyone who is rich or not tall is both not strong and not rich and vice versa.
Fred is not happy or not rich.
Someone is not quiet or not happy.
Susan is either not patient or generous.
Susan is not humble or not strong.
Someone is either brave or not calm.
Someone is funny. | Fred is tall. | entailment | (![X]:((~curious(X)<~>quiet(X))<=>~kind(X)))&
(![X]:((kind(X)<~>tall(X))<=>(wise(X)<~>~humble(X))))&
((~strong(susan))<=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((~strong(X)&~patient(X))<=>patient(X)))&
(![X]:((~brave(X)<~>old(X))=>(~happy(X)|~strong(X))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((strong(X)&~creative(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~rich(X)|~happy(X))<=>curious(X)))&
(![X]:(~strong(X)=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)|happy(X))=>(~humble(X)|old(X))))&
(![X]:(~tall(X)<=>(~rich(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>strong(X))))&
((?[X]:((quiet(X)<~>old(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(((wise(mary)<~>~kind(mary)))<=>(?[X]:(tall(X))))&
((~humble(paul))=>(~wise(lucy)))&
(![X]:((rich(X)|~tall(X))<=>(~strong(X)&~rich(X))))&
((~happy(fred)|~rich(fred)))&
(?[X]:((~quiet(X)|~happy(X))))&
((~patient(susan)<~>generous(susan)))&
((~humble(susan)|~strong(susan)))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:(funny(X))) | tall(fred) | [
"p3",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4052882816099250489604983
% SZS output start Proof for 4052882816099250489604983
4. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> patient(X0)) [input p3]
16. ! [X0] : ((~tall(X0) | rich(X0)) <=> (~rich(X0) & ~strong(X0))) [input p15]
23. ~tall(fred) [input hypothesis]
43. ! [X0] : (((~patient(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | strong(X0)))) [nnf transformation 4]
44. ! [X0] : (((~patient(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | strong(X0))) [flattening 43]
64. ! [X0] : (((~tall(X0) | rich(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [nnf transformation 16]
65. ! [X0] : ((~tall(X0) | rich(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (tall(X0) & ~rich(X0)))) [flattening 64]
88. patient(X0) | patient(X0) | strong(X0) [cnf transformation 44]
90. ~patient(X0) | ~patient(X0) [cnf transformation 44]
122. ~strong(X0) | tall(X0) [cnf transformation 65]
133. ~tall(fred) [cnf transformation 23]
138. patient(X0) | strong(X0) [duplicate literal removal 88]
139. ~patient(X0) [duplicate literal removal 90]
162. strong(X0) [subsumption resolution 138,139]
230. tall(X0) [subsumption resolution 122,162]
252. $false [subsumption resolution 133,230]
% SZS output end Proof for 4052882816099250489604983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong is both humble and wise.
Everyone who is either brave or quiet is either not brave or not calm.
Everyone who is not creative or humble is rich or strong and vice versa.
Everyone who is both not humble and curious is either not funny or old.
If mary is generous or not generous then mary is not curious or not creative.
If mary is either humble or quiet then someone is kind and vice versa.
Everyone who is not old is both old and patient and vice versa.
Everyone who is both creative and not happy is quiet or not humble and vice versa.
If lucy is either kind or strong then someone is kind or not funny and vice versa.
Everyone who is quiet is not rich or funny and vice versa.
If fred is both not generous and not happy then someone is both wise and funny.
Everyone who is calm or strong is either old or tall and vice versa.
Everyone who is either not rich or rich is either funny or not curious and vice versa.
Everyone who is not calm or quiet is old.
If someone is either not wise or calm then someone is not generous or old.
Everyone who is both calm and not patient is both not quiet and strong.
Someone is either not humble or brave.
Someone is old.
John is either not happy or not generous.
Lucy is either funny or not strong.
John is both not wise and rich.
John is brave or not brave. | Fred is strong. | neutral | (![X]:((~rich(X)|~strong(X))=>(humble(X)&wise(X))))&
(![X]:((brave(X)<~>quiet(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~creative(X)|humble(X))<=>(rich(X)|strong(X))))&
(![X]:((~humble(X)&curious(X))=>(~funny(X)<~>old(X))))&
(((generous(mary)|~generous(mary)))=>((~curious(mary)|~creative(mary))))&
(((humble(mary)<~>quiet(mary)))<=>(?[X]:(kind(X))))&
(![X]:(~old(X)<=>(old(X)&patient(X))))&
(![X]:((creative(X)&~happy(X))<=>(quiet(X)|~humble(X))))&
(((kind(lucy)<~>strong(lucy)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:(quiet(X)<=>(~rich(X)|funny(X))))&
(((~generous(fred)&~happy(fred)))=>(?[X]:((wise(X)&funny(X)))))&
(![X]:((calm(X)|strong(X))<=>(old(X)<~>tall(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(funny(X)<~>~curious(X))))&
(![X]:((~calm(X)|quiet(X))=>old(X)))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((~generous(X)|old(X)))))&
(![X]:((calm(X)&~patient(X))=>(~quiet(X)&strong(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:(old(X)))&
((~happy(john)<~>~generous(john)))&
((funny(lucy)<~>~strong(lucy)))&
((~wise(john)&rich(john)))&
((brave(john)|~brave(john))) | strong(fred) | []
| null | 0 |
If someone is both kind and generous then someone is both not calm and not tall and vice versa. Everyone who is quiet or wise is either not humble or rich and vice versa. If susan is not generous or not wise then someone is not kind or creative and vice versa. Everyone who is not tall or strong is both tall and humble and vice versa. Everyone who is both creative and not tall is not wise or funny and vice versa. If fred is either not generous or wise then someone is both not wise and not curious and vice versa. Everyone who is brave or humble is either not quiet or humble and vice versa. If someone is either not humble or rich then john is wise. If someone is both rich and not tall then alice is not quiet. If fred is creative or funny then fred is not old or not tall. Everyone who is brave or quiet is either not tall or not kind. If fred is patient then mary is both humble and not kind. Everyone who is patient 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. Someone is both happy and humble. John is either not old or calm. Paul is not funny or creative. Someone is either not tall or strong. Lucy is either not rich or wise. Mary is not rich or not brave. John is not kind. | Alice is tall. | entailment | ((?[X]:((kind(X)&generous(X))))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)&humble(X))))&
(![X]:((creative(X)&~tall(X))<=>(~wise(X)|funny(X))))&
(((~generous(fred)<~>wise(fred)))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|humble(X))<=>(~quiet(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(wise(john)))&
((?[X]:((rich(X)&~tall(X))))=>(~quiet(alice)))&
(((creative(fred)|funny(fred)))=>((~old(fred)|~tall(fred))))&
(![X]:((brave(X)|quiet(X))=>(~tall(X)<~>~kind(X))))&
((patient(fred))=>((humble(mary)&~kind(mary))))&
(![X]:(patient(X)<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(?[X]:((happy(X)&humble(X))))&
((~old(john)<~>calm(john)))&
((~funny(paul)|creative(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~rich(lucy)<~>wise(lucy)))&
((~rich(mary)|~brave(mary)))&
(~kind(john)) | tall(alice) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 3054457107453719308888349
% SZS output start Proof for 3054457107453719308888349
4. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (humble(X0) & tall(X0))) [input p3]
23. ~tall(alice) [input hypothesis]
46. ! [X0] : (((strong(X0) | ~tall(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 4]
47. ! [X0] : ((strong(X0) | ~tall(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | (~strong(X0) & tall(X0)))) [flattening 46]
83. tall(X0) | tall(X0) [cnf transformation 47]
135. ~tall(alice) [cnf transformation 23]
138. tall(X0) [duplicate literal removal 83]
262. $false [subsumption resolution 135,138]
% SZS output end Proof for 3054457107453719308888349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not quiet is either curious or humble.
If someone is funny then susan is either old or not quiet.
Everyone who is both not calm and not wise is not humble.
If someone is both not curious and kind then someone is not strong and vice versa.
Everyone who is both not brave and generous is humble.
If someone is brave then paul is either not rich or not old.
Everyone who is not tall is either curious or tall and vice versa.
If someone is either not rich or not strong then someone is not tall or not generous.
If lucy is both not quiet and not tall then someone is either not wise or generous.
If susan is happy then someone is both not old and not humble.
Everyone who is either wise or funny is brave and vice versa.
If someone is not rich then alice is not brave and vice versa.
Everyone who is either not creative or quiet is humble or not patient.
Everyone who is either patient or tall is both curious and not rich and vice versa.
Everyone who is both calm and patient is either not calm or patient.
Susan is both calm and rich.
Someone is both old and not patient.
Susan is humble or not kind.
Someone is happy.
Paul is not kind.
Someone is strong or curious.
Fred is tall. | Alice is not strong. | contradiction | (![X]:((rich(X)|~quiet(X))=>(curious(X)<~>humble(X))))&
((?[X]:(funny(X)))=>((old(susan)<~>~quiet(susan))))&
(![X]:((~calm(X)&~wise(X))=>~humble(X)))&
((?[X]:((~curious(X)&kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)&generous(X))=>humble(X)))&
((?[X]:(brave(X)))=>((~rich(paul)<~>~old(paul))))&
(![X]:(~tall(X)<=>(curious(X)<~>tall(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~quiet(lucy)&~tall(lucy)))=>(?[X]:((~wise(X)<~>generous(X)))))&
((happy(susan))=>(?[X]:((~old(X)&~humble(X)))))&
(![X]:((wise(X)<~>funny(X))<=>brave(X)))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
((calm(susan)&rich(susan)))&
(?[X]:((old(X)&~patient(X))))&
((humble(susan)|~kind(susan)))&
(?[X]:(happy(X)))&
(~kind(paul))&
(?[X]:((strong(X)|curious(X))))&
(tall(fred)) | ~strong(alice) | [
"p3",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 8064341650570875601905537
% SZS output start Proof for 8064341650570875601905537
4. ? [X0] : (kind(X0) & ~curious(X0)) <=> ? [X0] : ~strong(X0) [input p3]
7. ! [X0] : (~tall(X0) <=> (curious(X0) <~> tall(X0))) [input p6]
23. ~strong(alice) [input hypothesis]
24. ? [X0] : (kind(X0) & ~curious(X0)) <=> ? [X1] : ~strong(X1) [rectify 4]
43. (? [X0] : (kind(X0) & ~curious(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (~kind(X0) | curious(X0))) [nnf transformation 24]
44. (? [X0] : (kind(X0) & ~curious(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (~kind(X3) | curious(X3))) [rectify 43]
45. ? [X0] : (kind(X0) & ~curious(X0)) => (kind(sK0) & ~curious(sK0)) [choice axiom]
46. ? [X2] : ~strong(X2) => ~strong(sK1) [choice axiom]
47. ((kind(sK0) & ~curious(sK0)) | ! [X1] : strong(X1)) & (~strong(sK1) | ! [X3] : (~kind(X3) | curious(X3))) [skolemisation 44,46,45]
49. ! [X0] : ((~tall(X0) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) & (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | tall(X0))) [nnf transformation 7]
82. ~curious(sK0) | strong(X1) [cnf transformation 47]
87. tall(X0) | curious(X0) | tall(X0) [cnf transformation 49]
90. ~tall(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
122. ~strong(alice) [cnf transformation 23]
125. tall(X0) | curious(X0) [duplicate literal removal 87]
126. ~tall(X0) | curious(X0) [duplicate literal removal 90]
141. 4 <=> ! [X1] : strong(X1) [avatar definition]
142. strong(X1) <- (4) [avatar component clause 141]
149. 6 <=> curious(sK0) [avatar definition]
151. ~curious(sK0) <- (~6) [avatar component clause 149]
152. 4 | ~6 [avatar split clause 82,149,141]
174. curious(X0) [subsumption resolution 125,126]
247. $false <- (4) [resolution 142,122]
248. ~4 [avatar contradiction clause 247]
249. $false <- (~6) [subsumption resolution 151,174]
250. 6 [avatar contradiction clause 249]
251. $false [avatar sat refutation 152,248,250]
% SZS output end Proof for 8064341650570875601905537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is brave then susan is both not tall and not happy and vice versa. Everyone who is not tall is both wise and generous. If alice is curious then someone is curious or not tall and vice versa. If susan is both not funny and not calm then someone is either not curious or not strong and vice versa. If someone is either not creative or generous then paul is tall or patient. Everyone who is rich is humble. Everyone who is both rich and generous is not old or not quiet. Everyone who is wise is both not wise and old and vice versa. Everyone who is both not happy and not funny is not funny or patient and vice versa. Everyone who is not creative is not curious or not old and vice versa. If susan is both not strong and not quiet then someone is either funny or not happy and vice versa. If someone is funny or calm then alice is either creative or not brave and vice versa. Everyone who is not old is kind. Everyone who is not generous is tall or not strong and vice versa. If someone is old or not brave then susan is not patient or not kind and vice versa. Someone is either not generous or brave. Someone is funny. Susan is funny. Alice is either calm or not strong. Paul is both not funny and not curious. Someone is either not curious or not humble. Lucy is both happy and kind. Lucy is either humble or not calm. | Susan is not funny. | contradiction | ((brave(alice))<=>((~tall(susan)&~happy(susan))))&
(![X]:(~tall(X)=>(wise(X)&generous(X))))&
((curious(alice))<=>(?[X]:((curious(X)|~tall(X)))))&
(((~funny(susan)&~calm(susan)))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:((~creative(X)<~>generous(X))))=>((tall(paul)|patient(paul))))&
(![X]:(rich(X)=>humble(X)))&
(![X]:((rich(X)&generous(X))=>(~old(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~wise(X)&old(X))))&
(![X]:((~happy(X)&~funny(X))<=>(~funny(X)|patient(X))))&
(![X]:(~creative(X)<=>(~curious(X)|~old(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((creative(alice)<~>~brave(alice))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~generous(X)<=>(tall(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))<=>((~patient(susan)|~kind(susan))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:(funny(X)))&
(funny(susan))&
((calm(alice)<~>~strong(alice)))&
((~funny(paul)&~curious(paul)))&
(?[X]:((~curious(X)<~>~humble(X))))&
((happy(lucy)&kind(lucy)))&
((humble(lucy)<~>~calm(lucy))) | ~funny(susan) | [
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 686464590145875607703688
% SZS output start Proof for 686464590145875607703688
18. funny(susan) [input p17]
24. ~funny(susan) [input hypothesis]
125. funny(susan) [cnf transformation 18]
136. ~funny(susan) [cnf transformation 24]
188. 12 <=> funny(susan) [avatar definition]
310. 12 [avatar split clause 125,188]
341. ~12 [avatar split clause 136,188]
342. $false [avatar sat refutation 310,341]
% SZS output end Proof for 686464590145875607703688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Susan is not patient. | entailment | (![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))) | ~patient(susan) | [
"p1",
"p5",
"p6",
"p7",
"p8",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5681281491631730499339487
% SZS output start Proof for 5681281491631730499339487
2. ! [X0] : (brave(X0) <=> (~brave(X0) | ~generous(X0))) [input p1]
6. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (~calm(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & patient(X0)) <=> (~strong(X0) & ~kind(X0))) [input p6]
8. ! [X0] : ((~tall(X0) | funny(X0)) <=> (generous(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) & old(X0)) <=> (~happy(X0) <~> ~curious(X0))) [input p8]
15. (~tall(fred) & creative(fred)) <=> ? [X0] : (generous(X0) <~> curious(X0)) [input p14]
22. patient(susan) [input hypothesis]
28. ! [X0] : ((~calm(X0) & curious(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 6]
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]
44. ! [X0] : ((~calm(X0) & curious(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 28]
45. ! [X0] : (((~happy(X0) & patient(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (happy(X0) | ~patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((~happy(X0) & patient(X0)) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | happy(X0) | ~patient(X0))) [flattening 45]
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]
73. curious(X0) | strong(X0) | kind(X0) [cnf transformation 44]
76. ~patient(X0) | happy(X0) | ~kind(X0) [cnf transformation 46]
77. ~patient(X0) | happy(X0) | ~strong(X0) [cnf transformation 46]
79. ~happy(X0) | strong(X0) | kind(X0) [cnf transformation 46]
81. tall(X0) | generous(X0) | tall(X0) [cnf transformation 48]
90. ~tall(X0) | ~curious(X0) | happy(X0) [cnf transformation 50]
91. ~tall(X0) | ~happy(X0) | curious(X0) [cnf transformation 50]
106. ~tall(fred) | generous(X0) | ~curious(X0) [cnf transformation 56]
113. patient(susan) [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]
146. ~curious(X0) | happy(X0) [subsumption resolution 90,144]
151. generous(X0) | ~curious(X0) [subsumption resolution 106,144]
152. ~curious(X0) [subsumption resolution 151,118]
157. strong(X0) | kind(X0) | happy(X0) [resolution 73,146]
159. kind(X0) | strong(X0) [subsumption resolution 157,79]
162. happy(susan) | ~kind(susan) [resolution 76,113]
164. 6 <=> kind(susan) [avatar definition]
166. ~kind(susan) <- (~6) [avatar component clause 164]
168. 7 <=> happy(susan) [avatar definition]
170. happy(susan) <- (7) [avatar component clause 168]
171. ~6 | 7 [avatar split clause 162,168,164]
172. strong(susan) <- (~6) [resolution 166,159]
173. happy(susan) | ~strong(susan) [resolution 77,113]
174. happy(susan) <- (~6) [subsumption resolution 173,172]
175. 7 | 6 [avatar split clause 174,164,168]
176. curious(susan) <- (7) [resolution 170,145]
177. $false <- (7) [subsumption resolution 176,152]
178. ~7 [avatar contradiction clause 177]
179. $false [avatar sat refutation 171,175,178]
% SZS output end Proof for 5681281491631730499339487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or creative is not tall and vice versa. If lucy is either not wise or not quiet then someone is both not old and strong. Everyone who is curious is both funny and not brave. Everyone who is rich or strong is both creative and not quiet. Everyone who is both not wise and curious is kind or curious and vice versa. Everyone who is not brave or not wise is either not kind or funny and vice versa. If fred is both quiet and wise then someone is either kind or not kind. Everyone who is either kind or patient is both not rich and not funny. Everyone who is either kind or quiet is not happy or not strong and vice versa. Everyone who is either not curious or not creative is either wise or generous. Everyone who is not curious is both not kind and not calm. If someone is either not strong or rich then john is not happy or not rich. If someone is not quiet then mary is both not tall and creative. Everyone who is either wise or not kind is both humble and rich. If someone is either not strong or creative then paul is either kind or patient. If someone is both not funny and quiet then susan is not kind or humble. Susan is not patient. Someone is both kind and humble. Lucy is either not happy or creative. Someone is patient. Someone is not creative. John is both old and curious. Someone is not quiet. John is not tall. | Susan is not calm. | entailment | (![X]:((~old(X)|creative(X))<=>~tall(X)))&
(((~wise(lucy)<~>~quiet(lucy)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(curious(X)=>(funny(X)&~brave(X))))&
(![X]:((rich(X)|strong(X))=>(creative(X)&~quiet(X))))&
(![X]:((~wise(X)&curious(X))<=>(kind(X)|curious(X))))&
(![X]:((~brave(X)|~wise(X))<=>(~kind(X)<~>funny(X))))&
(((quiet(fred)&wise(fred)))=>(?[X]:((kind(X)<~>~kind(X)))))&
(![X]:((kind(X)<~>patient(X))=>(~rich(X)&~funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(~happy(X)|~strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(wise(X)<~>generous(X))))&
(![X]:(~curious(X)=>(~kind(X)&~calm(X))))&
((?[X]:((~strong(X)<~>rich(X))))=>((~happy(john)|~rich(john))))&
((?[X]:(~quiet(X)))=>((~tall(mary)&creative(mary))))&
(![X]:((wise(X)<~>~kind(X))=>(humble(X)&rich(X))))&
((?[X]:((~strong(X)<~>creative(X))))=>((kind(paul)<~>patient(paul))))&
((?[X]:((~funny(X)&quiet(X))))=>((~kind(susan)|humble(susan))))&
(~patient(susan))&
(?[X]:((kind(X)&humble(X))))&
((~happy(lucy)<~>creative(lucy)))&
(?[X]:(patient(X)))&
(?[X]:(~creative(X)))&
((old(john)&curious(john)))&
(?[X]:(~quiet(X)))&
(~tall(john)) | ~calm(susan) | [
"p2",
"p4",
"p5",
"p7",
"p10",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6885300588370305944565517
% SZS output start Proof for 6885300588370305944565517
3. ! [X0] : (curious(X0) => (~brave(X0) & funny(X0))) [input p2]
5. ! [X0] : ((curious(X0) & ~wise(X0)) <=> (curious(X0) | kind(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | ~brave(X0)) <=> (~kind(X0) <~> funny(X0))) [input p5]
8. ! [X0] : ((kind(X0) <~> patient(X0)) => (~funny(X0) & ~rich(X0))) [input p7]
11. ! [X0] : (~curious(X0) => (~calm(X0) & ~kind(X0))) [input p10]
17. ~patient(susan) [input p16]
25. calm(susan) [input hypothesis]
33. ! [X0] : ((~brave(X0) & funny(X0)) | ~curious(X0)) [ennf transformation 3]
37. ! [X0] : ((~funny(X0) & ~rich(X0)) | (kind(X0) <=> patient(X0))) [ennf transformation 8]
39. ! [X0] : ((~calm(X0) & ~kind(X0)) | curious(X0)) [ennf transformation 11]
48. ! [X0] : (((curious(X0) & ~wise(X0)) | (~curious(X0) & ~kind(X0))) & ((curious(X0) | kind(X0)) | (~curious(X0) | wise(X0)))) [nnf transformation 5]
49. ! [X0] : (((curious(X0) & ~wise(X0)) | (~curious(X0) & ~kind(X0))) & (curious(X0) | kind(X0) | ~curious(X0) | wise(X0))) [flattening 48]
50. ! [X0] : (((~wise(X0) | ~brave(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (wise(X0) & brave(X0)))) [nnf transformation 6]
51. ! [X0] : ((~wise(X0) | ~brave(X0) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (wise(X0) & brave(X0)))) [flattening 50]
55. ! [X0] : ((~funny(X0) & ~rich(X0)) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0)))) [nnf transformation 37]
76. ~curious(X0) | funny(X0) [cnf transformation 33]
83. ~kind(X0) | ~wise(X0) [cnf transformation 49]
84. ~curious(X0) | ~wise(X0) [cnf transformation 49]
88. funny(X0) | ~kind(X0) | wise(X0) [cnf transformation 51]
90. ~funny(X0) | kind(X0) | wise(X0) [cnf transformation 51]
97. ~funny(X0) | patient(X0) | ~kind(X0) [cnf transformation 55]
110. ~calm(X0) | curious(X0) [cnf transformation 39]
121. ~patient(susan) [cnf transformation 17]
131. calm(susan) [cnf transformation 25]
153. ~kind(X0) | funny(X0) [subsumption resolution 88,83]
154. ~kind(X0) | patient(X0) [subsumption resolution 97,153]
234. curious(susan) [resolution 110,131]
235. ~wise(susan) [resolution 234,84]
236. funny(susan) [resolution 234,76]
257. kind(susan) | wise(susan) [resolution 236,90]
259. kind(susan) [subsumption resolution 257,235]
482. patient(susan) [resolution 259,154]
486. $false [subsumption resolution 482,121]
% SZS output end Proof for 6885300588370305944565517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not creative or patient is strong or creative and vice versa.
If paul is calm or rich then john is either kind or not patient and vice versa.
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Fred is wise.
Alice is either kind or patient.
Fred is creative or not creative.
Paul is both wise and strong.
Fred is funny or not quiet.
Mary is calm or not calm.
Someone is either brave or funny. | Paul is not generous. | neutral | (![X]:((~creative(X)|patient(X))<=>(strong(X)|creative(X))))&
(((calm(paul)|rich(paul)))<=>((kind(john)<~>~patient(john))))&
(![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(wise(fred))&
((kind(alice)<~>patient(alice)))&
((creative(fred)|~creative(fred)))&
((wise(paul)&strong(paul)))&
((funny(fred)|~quiet(fred)))&
((calm(mary)|~calm(mary)))&
(?[X]:((brave(X)<~>funny(X)))) | ~generous(paul) | []
| null | 0 |
Everyone who is either not humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | Paul is strong. | entailment | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | strong(paul) | [
"p0",
"p1",
"p10",
"p11",
"p21",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4348041320909620726299080
% SZS output start Proof for 4348041320909620726299080
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. ~strong(paul) [input hypothesis]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
80. ~brave(X0) | strong(X0) [cnf transformation 39]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. ~strong(paul) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
179. 8 <=> old(lucy) [avatar definition]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
271. strong(X1) <- (11) [resolution 194,80]
286. $false <- (11) [resolution 271,143]
289. ~11 [avatar contradiction clause 286]
290. $false [avatar sat refutation 196,250,251,265,289]
% SZS output end Proof for 4348041320909620726299080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not brave is both not humble and funny.
If john is patient then someone is not calm or happy.
Everyone who is either not quiet or wise is not old or creative and vice versa.
Everyone who is not quiet or not humble is either not kind or old.
Everyone who is either curious or generous is both not quiet and generous.
If paul is either quiet or old then someone is not tall.
If someone is not funny or curious then mary is both not rich and strong and vice versa.
Everyone who is not rich is both generous and not brave.
If lucy is either curious or rich then mary is calm or not happy and vice versa.
If alice is either not calm or not tall then lucy is either not calm or not funny and vice versa.
Everyone who is both kind and brave is either tall or old.
If someone is funny then someone is either calm or not patient and vice versa.
Everyone who is not wise is tall.
Everyone who is not curious or not happy is not old.
If paul is not patient or not quiet then mary is quiet or not tall and vice versa.
Everyone who is both funny and not calm is both old and kind.
Someone is not brave.
Fred is generous.
Someone is not old or calm.
Someone is humble.
Someone is not brave or tall.
John is both generous and not wise.
Someone is funny. | Mary is not rich. | neutral | (![X]:((creative(X)|~brave(X))=>(~humble(X)&funny(X))))&
((patient(john))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~quiet(X)<~>wise(X))<=>(~old(X)|creative(X))))&
(![X]:((~quiet(X)|~humble(X))=>(~kind(X)<~>old(X))))&
(![X]:((curious(X)<~>generous(X))=>(~quiet(X)&generous(X))))&
(((quiet(paul)<~>old(paul)))=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)|curious(X))))<=>((~rich(mary)&strong(mary))))&
(![X]:(~rich(X)=>(generous(X)&~brave(X))))&
(((curious(lucy)<~>rich(lucy)))<=>((calm(mary)|~happy(mary))))&
(((~calm(alice)<~>~tall(alice)))<=>((~calm(lucy)<~>~funny(lucy))))&
(![X]:((kind(X)&brave(X))=>(tall(X)<~>old(X))))&
((?[X]:(funny(X)))<=>(?[X]:((calm(X)<~>~patient(X)))))&
(![X]:(~wise(X)=>tall(X)))&
(![X]:((~curious(X)|~happy(X))=>~old(X)))&
(((~patient(paul)|~quiet(paul)))<=>((quiet(mary)|~tall(mary))))&
(![X]:((funny(X)&~calm(X))=>(old(X)&kind(X))))&
(?[X]:(~brave(X)))&
(generous(fred))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)|tall(X))))&
((generous(john)&~wise(john)))&
(?[X]:(funny(X))) | ~rich(mary) | []
| null | 0 |
Everyone who is either brave or kind is either not strong or not rich and vice versa. Everyone who is either not patient or not humble is curious and vice versa. If paul is both funny and generous then someone is either curious or not quiet and vice versa. Everyone who is both not happy and strong is generous and vice versa. If someone is kind then john is both strong and creative and vice versa. If someone is strong or rich then paul is happy or not wise. Everyone who is not rich or not strong is either not rich or happy. Everyone who is wise or kind is either not generous or not rich. Everyone who is both not happy and not rich is curious. If susan is both quiet and not kind then fred is either not quiet or curious. If someone is not creative or old then paul is both generous and old. Everyone who is humble or not generous is not tall and vice versa. If someone is not generous then someone is not calm and vice versa. Everyone who is calm is both funny and not happy. Everyone who is not creative is not funny or tall. Everyone who is creative or old is both not creative and not tall. Fred is not old or quiet. Someone is brave or generous. Lucy is not quiet. Someone is kind or not old. Someone is patient or calm. Someone is both tall and quiet. | Paul is calm. | contradiction | (![X]:((brave(X)<~>kind(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>curious(X)))&
(((funny(paul)&generous(paul)))<=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:((~happy(X)&strong(X))<=>generous(X)))&
((?[X]:(kind(X)))<=>((strong(john)&creative(john))))&
((?[X]:((strong(X)|rich(X))))=>((happy(paul)|~wise(paul))))&
(![X]:((~rich(X)|~strong(X))=>(~rich(X)<~>happy(X))))&
(![X]:((wise(X)|kind(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((~happy(X)&~rich(X))=>curious(X)))&
(((quiet(susan)&~kind(susan)))=>((~quiet(fred)<~>curious(fred))))&
((?[X]:((~creative(X)|old(X))))=>((generous(paul)&old(paul))))&
(![X]:((humble(X)|~generous(X))<=>~tall(X)))&
((?[X]:(~generous(X)))<=>(?[X]:(~calm(X))))&
(![X]:(calm(X)=>(funny(X)&~happy(X))))&
(![X]:(~creative(X)=>(~funny(X)|tall(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~tall(X))))&
((~old(fred)|quiet(fred)))&
(?[X]:((brave(X)|generous(X))))&
(~quiet(lucy))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:((tall(X)&quiet(X)))) | calm(paul) | [
"p10",
"p13",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3233914910879648642464686
% SZS output start Proof for 3233914910879648642464686
11. ? [X0] : (old(X0) | ~creative(X0)) => (old(paul) & generous(paul)) [input p10]
14. ! [X0] : (calm(X0) => (~happy(X0) & funny(X0))) [input p13]
15. ! [X0] : (~creative(X0) => (tall(X0) | ~funny(X0))) [input p14]
16. ! [X0] : ((old(X0) | creative(X0)) => (~tall(X0) & ~creative(X0))) [input p15]
23. calm(paul) [input hypothesis]
33. (old(paul) & generous(paul)) | ! [X0] : (~old(X0) & creative(X0)) [ennf transformation 11]
34. ! [X0] : ((~happy(X0) & funny(X0)) | ~calm(X0)) [ennf transformation 14]
35. ! [X0] : ((tall(X0) | ~funny(X0)) | creative(X0)) [ennf transformation 15]
36. ! [X0] : (tall(X0) | ~funny(X0) | creative(X0)) [flattening 35]
37. ! [X0] : ((~tall(X0) & ~creative(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 16]
105. old(paul) | creative(X0) [cnf transformation 33]
112. ~calm(X0) | funny(X0) [cnf transformation 34]
114. ~funny(X0) | tall(X0) | creative(X0) [cnf transformation 36]
115. ~creative(X0) | ~creative(X0) [cnf transformation 37]
118. ~tall(X0) | ~old(X0) [cnf transformation 37]
126. calm(paul) [cnf transformation 23]
127. ~creative(X0) [duplicate literal removal 115]
142. 4 <=> funny(paul) [avatar definition]
144. funny(paul) <- (4) [avatar component clause 142]
198. 16 <=> old(paul) [avatar definition]
200. old(paul) <- (16) [avatar component clause 198]
203. 17 <=> ! [X0] : creative(X0) [avatar definition]
204. creative(X0) <- (17) [avatar component clause 203]
205. 17 | 16 [avatar split clause 105,198,203]
264. funny(paul) [resolution 112,126]
335. 38 <=> tall(paul) [avatar definition]
336. ~tall(paul) <- (~38) [avatar component clause 335]
337. tall(paul) <- (38) [avatar component clause 335]
343. ~old(paul) <- (38) [resolution 337,118]
347. $false <- (16, 38) [subsumption resolution 343,200]
348. ~16 | ~38 [avatar contradiction clause 347]
350. tall(paul) | creative(paul) <- (4) [resolution 114,144]
352. creative(paul) <- (4, ~38) [subsumption resolution 350,336]
353. $false <- (4, ~38) [subsumption resolution 352,127]
354. ~4 | 38 [avatar contradiction clause 353]
356. 4 [avatar split clause 264,142]
357. $false <- (17) [subsumption resolution 204,127]
358. ~17 [avatar contradiction clause 357]
359. $false [avatar sat refutation 205,348,354,356,358]
% SZS output end Proof for 3233914910879648642464686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or creative then fred is generous.
If someone is not generous or generous then john is either happy or not tall and vice versa.
If someone is humble or not rich then someone is rich and vice versa.
Everyone who is wise is both kind and rich and vice versa.
Everyone who is not curious or happy is either curious or patient and vice versa.
Everyone who is not funny is either brave or not strong.
If alice is both calm and not happy then alice is curious or funny and vice versa.
Everyone who is quiet is either not rich or not curious.
Everyone who is happy is calm or old.
Everyone who is wise or not funny is both patient and not old.
Everyone who is either not quiet or not funny is both not old and strong.
Everyone who is not generous or happy is both strong and quiet.
Everyone who is not tall or not creative is either happy or not creative.
Everyone who is both old and creative is either strong or not happy and vice versa.
If paul is not tall then someone is both not curious and not happy.
Everyone who is both kind and not funny is wise.
Someone is both not creative and brave.
Susan is creative.
Fred is both tall and not curious.
Fred is not curious or not brave.
Alice is not generous.
Lucy is patient.
Alice is not tall.
John is both funny and not brave. | Alice is strong. | entailment | ((?[X]:((~brave(X)|creative(X))))=>(generous(fred)))&
((?[X]:((~generous(X)|generous(X))))<=>((happy(john)<~>~tall(john))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:(rich(X))))&
(![X]:(wise(X)<=>(kind(X)&rich(X))))&
(![X]:((~curious(X)|happy(X))<=>(curious(X)<~>patient(X))))&
(![X]:(~funny(X)=>(brave(X)<~>~strong(X))))&
(((calm(alice)&~happy(alice)))<=>((curious(alice)|funny(alice))))&
(![X]:(quiet(X)=>(~rich(X)<~>~curious(X))))&
(![X]:(happy(X)=>(calm(X)|old(X))))&
(![X]:((wise(X)|~funny(X))=>(patient(X)&~old(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~old(X)&strong(X))))&
(![X]:((~generous(X)|happy(X))=>(strong(X)&quiet(X))))&
(![X]:((~tall(X)|~creative(X))=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&creative(X))<=>(strong(X)<~>~happy(X))))&
((~tall(paul))=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((kind(X)&~funny(X))=>wise(X)))&
(?[X]:((~creative(X)&brave(X))))&
(creative(susan))&
((tall(fred)&~curious(fred)))&
((~curious(fred)|~brave(fred)))&
(~generous(alice))&
(patient(lucy))&
(~tall(alice))&
((funny(john)&~brave(john))) | strong(alice) | [
"p11",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 2344188469871135633197659
% SZS output start Proof for 2344188469871135633197659
12. ! [X0] : ((happy(X0) | ~generous(X0)) => (quiet(X0) & strong(X0))) [input p11]
21. ~generous(alice) [input p20]
25. ~strong(alice) [input hypothesis]
34. ! [X0] : ((quiet(X0) & strong(X0)) | (~happy(X0) & generous(X0))) [ennf transformation 12]
102. strong(X0) | generous(X0) [cnf transformation 34]
125. ~generous(alice) [cnf transformation 21]
130. ~strong(alice) [cnf transformation 25]
228. generous(alice) [resolution 102,130]
229. $false [subsumption resolution 228,125]
% SZS output end Proof for 2344188469871135633197659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not wise is happy and vice versa.
If someone is either not old or patient then someone is both funny and curious and vice versa.
Everyone who is not old is funny or calm and vice versa.
Everyone who is funny is not happy or happy and vice versa.
If fred is not brave or not patient then fred is both not old and brave.
If someone is both not strong and not rich then mary is both not patient and not wise and vice versa.
If someone is not rich then mary is generous or brave.
Everyone who is not kind is calm and vice versa.
Everyone who is not creative is not rich or calm.
Everyone who is either not kind or quiet is both not creative and not happy and vice versa.
Everyone who is both calm and kind is either old or not tall and vice versa.
If someone is quiet or wise then susan is both wise and not old.
If paul is not patient or quiet then john is either not quiet or not happy.
If fred is either wise or brave then susan is both brave and calm and vice versa.
Everyone who is old or quiet is not creative or kind.
Everyone who is rich or not funny is both humble and calm and vice versa.
John is either happy or creative.
Someone is not rich.
Someone is both not brave and humble.
Someone is either not humble or not brave.
Mary is not tall or not happy.
John is kind or brave.
Fred is not generous or happy. | Fred is rich. | neutral | (![X]:((~brave(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~old(X)<=>(funny(X)|calm(X))))&
(![X]:(funny(X)<=>(~happy(X)|happy(X))))&
(((~brave(fred)|~patient(fred)))=>((~old(fred)&brave(fred))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:(~rich(X)))=>((generous(mary)|brave(mary))))&
(![X]:(~kind(X)<=>calm(X)))&
(![X]:(~creative(X)=>(~rich(X)|calm(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((quiet(X)|wise(X))))=>((wise(susan)&~old(susan))))&
(((~patient(paul)|quiet(paul)))=>((~quiet(john)<~>~happy(john))))&
(((wise(fred)<~>brave(fred)))<=>((brave(susan)&calm(susan))))&
(![X]:((old(X)|quiet(X))=>(~creative(X)|kind(X))))&
(![X]:((rich(X)|~funny(X))<=>(humble(X)&calm(X))))&
((happy(john)<~>creative(john)))&
(?[X]:(~rich(X)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((~humble(X)<~>~brave(X))))&
((~tall(mary)|~happy(mary)))&
((kind(john)|brave(john)))&
((~generous(fred)|happy(fred))) | rich(fred) | []
| null | 0 |
If mary is both not creative and not tall then someone is wise or strong and vice versa.
Everyone who is not wise or creative is both not patient and curious and vice versa.
If paul is both brave and old then alice is both not old and not patient and vice versa.
Everyone who is not strong or not happy is either creative or quiet and vice versa.
Everyone who is either quiet or brave is both rich and patient.
If john is either not humble or not calm then someone is either not generous or rich.
Everyone who is humble is creative and vice versa.
If lucy is either humble or strong then john is not curious or not generous and vice versa.
If lucy is strong or patient then susan is calm and vice versa.
If fred is not rich or quiet then someone is either not generous or wise.
If someone is both not old and not patient then someone is both not generous and generous and vice versa.
If mary is wise then someone is either quiet or rich and vice versa.
Everyone who is not kind or not humble is either patient or brave.
Everyone who is both humble and rich is not kind or not brave and vice versa.
If someone is not quiet or quiet then someone is both quiet and happy.
If someone is not funny then susan is funny or tall.
Someone is curious or humble.
Alice is calm or not humble.
Someone is not creative.
Susan is either not brave or rich.
Mary is either not patient or not funny.
Someone is brave. | Mary is tall. | contradiction | (((~creative(mary)&~tall(mary)))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:((~wise(X)|creative(X))<=>(~patient(X)&curious(X))))&
(((brave(paul)&old(paul)))<=>((~old(alice)&~patient(alice))))&
(![X]:((~strong(X)|~happy(X))<=>(creative(X)<~>quiet(X))))&
(![X]:((quiet(X)<~>brave(X))=>(rich(X)&patient(X))))&
(((~humble(john)<~>~calm(john)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:(humble(X)<=>creative(X)))&
(((humble(lucy)<~>strong(lucy)))<=>((~curious(john)|~generous(john))))&
(((strong(lucy)|patient(lucy)))<=>(calm(susan)))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~generous(X)<~>wise(X)))))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~generous(X)&generous(X)))))&
((wise(mary))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((~kind(X)|~humble(X))=>(patient(X)<~>brave(X))))&
(![X]:((humble(X)&rich(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:(~funny(X)))=>((funny(susan)|tall(susan))))&
(?[X]:((curious(X)|humble(X))))&
((calm(alice)|~humble(alice)))&
(?[X]:(~creative(X)))&
((~brave(susan)<~>rich(susan)))&
((~patient(mary)<~>~funny(mary)))&
(?[X]:(brave(X))) | tall(mary) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 2953491070317163485606289
% SZS output start Proof for 2953491070317163485606289
1. (~tall(mary) & ~creative(mary)) <=> ? [X0] : (strong(X0) | wise(X0)) [input p0]
2. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (curious(X0) & ~patient(X0))) [input p1]
3. (old(paul) & brave(paul)) <=> (~patient(alice) & ~old(alice)) [input p2]
5. ! [X0] : ((quiet(X0) <~> brave(X0)) => (patient(X0) & rich(X0))) [input p4]
7. ! [X0] : (humble(X0) <=> creative(X0)) [input p6]
11. ? [X0] : (~patient(X0) & ~old(X0)) <=> ? [X0] : (generous(X0) & ~generous(X0)) [input p10]
12. wise(mary) <=> ? [X0] : (quiet(X0) <~> rich(X0)) [input p11]
13. ! [X0] : ((~humble(X0) | ~kind(X0)) => (patient(X0) <~> brave(X0))) [input p12]
14. ! [X0] : ((rich(X0) & humble(X0)) <=> (~brave(X0) | ~kind(X0))) [input p13]
23. tall(mary) [input hypothesis]
24. ? [X0] : (~patient(X0) & ~old(X0)) <=> ? [X1] : (generous(X1) & ~generous(X1)) [rectify 11]
26. ! [X0] : ((patient(X0) & rich(X0)) | (quiet(X0) <=> brave(X0))) [ennf transformation 5]
29. ! [X0] : ((patient(X0) <~> brave(X0)) | (humble(X0) & kind(X0))) [ennf transformation 13]
33. ((~tall(mary) & ~creative(mary)) | ! [X0] : (~strong(X0) & ~wise(X0))) & (? [X0] : (strong(X0) | wise(X0)) | (tall(mary) | creative(mary))) [nnf transformation 1]
34. ((~tall(mary) & ~creative(mary)) | ! [X0] : (~strong(X0) & ~wise(X0))) & (? [X0] : (strong(X0) | wise(X0)) | tall(mary) | creative(mary)) [flattening 33]
35. ((~tall(mary) & ~creative(mary)) | ! [X0] : (~strong(X0) & ~wise(X0))) & (? [X1] : (strong(X1) | wise(X1)) | tall(mary) | creative(mary)) [rectify 34]
36. ? [X1] : (strong(X1) | wise(X1)) => (strong(sK0) | wise(sK0)) [choice axiom]
37. ((~tall(mary) & ~creative(mary)) | ! [X0] : (~strong(X0) & ~wise(X0))) & ((strong(sK0) | wise(sK0)) | tall(mary) | creative(mary)) [skolemisation 35,36]
38. ! [X0] : (((creative(X0) | ~wise(X0)) | (~curious(X0) | patient(X0))) & ((curious(X0) & ~patient(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 2]
39. ! [X0] : ((creative(X0) | ~wise(X0) | ~curious(X0) | patient(X0)) & ((curious(X0) & ~patient(X0)) | (~creative(X0) & wise(X0)))) [flattening 38]
40. ((old(paul) & brave(paul)) | (patient(alice) | old(alice))) & ((~patient(alice) & ~old(alice)) | (~old(paul) | ~brave(paul))) [nnf transformation 3]
41. ((old(paul) & brave(paul)) | patient(alice) | old(alice)) & ((~patient(alice) & ~old(alice)) | ~old(paul) | ~brave(paul)) [flattening 40]
44. ! [X0] : ((patient(X0) & rich(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) [nnf transformation 26]
48. ! [X0] : ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))) [nnf transformation 7]
56. (? [X0] : (~patient(X0) & ~old(X0)) | ! [X1] : (~generous(X1) | generous(X1))) & (? [X1] : (generous(X1) & ~generous(X1)) | ! [X0] : (patient(X0) | old(X0))) [nnf transformation 24]
57. (? [X0] : (~patient(X0) & ~old(X0)) | ! [X1] : (~generous(X1) | generous(X1))) & (? [X2] : (generous(X2) & ~generous(X2)) | ! [X3] : (patient(X3) | old(X3))) [rectify 56]
58. ? [X0] : (~patient(X0) & ~old(X0)) => (~patient(sK3) & ~old(sK3)) [choice axiom]
59. ? [X2] : (generous(X2) & ~generous(X2)) => (generous(sK4) & ~generous(sK4)) [choice axiom]
60. ((~patient(sK3) & ~old(sK3)) | ! [X1] : (~generous(X1) | generous(X1))) & ((generous(sK4) & ~generous(sK4)) | ! [X3] : (patient(X3) | old(X3))) [skolemisation 57,59,58]
61. (wise(mary) | ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (? [X0] : ((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~wise(mary)) [nnf transformation 12]
62. (wise(mary) | ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (? [X1] : ((~rich(X1) | ~quiet(X1)) & (rich(X1) | quiet(X1))) | ~wise(mary)) [rectify 61]
63. ? [X1] : ((~rich(X1) | ~quiet(X1)) & (rich(X1) | quiet(X1))) => ((~rich(sK5) | ~quiet(sK5)) & (rich(sK5) | quiet(sK5))) [choice axiom]
64. (wise(mary) | ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(sK5) | ~quiet(sK5)) & (rich(sK5) | quiet(sK5))) | ~wise(mary)) [skolemisation 62,63]
65. ! [X0] : (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (humble(X0) & kind(X0))) [nnf transformation 29]
66. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 14]
67. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~rich(X0) | ~humble(X0))) [flattening 66]
82. ~tall(mary) | ~wise(X0) [cnf transformation 37]
84. ~patient(X0) | wise(X0) [cnf transformation 39]
85. ~patient(X0) | ~creative(X0) [cnf transformation 39]
89. ~old(alice) | ~old(paul) | ~brave(paul) [cnf transformation 41]
101. ~quiet(X0) | brave(X0) | patient(X0) [cnf transformation 44]
107. ~humble(X0) | creative(X0) [cnf transformation 48]
122. ~generous(sK4) | patient(X3) | old(X3) [cnf transformation 60]
123. generous(sK4) | patient(X3) | old(X3) [cnf transformation 60]
129. wise(mary) | quiet(X0) | ~rich(X0) [cnf transformation 64]
133. ~brave(X0) | ~patient(X0) | humble(X0) [cnf transformation 65]
136. humble(X0) | brave(X0) [cnf transformation 67]
138. rich(X0) | brave(X0) [cnf transformation 67]
152. tall(mary) [cnf transformation 23]
157. 2 <=> tall(mary) [avatar definition]
162. 3 <=> ! [X0] : ~wise(X0) [avatar definition]
163. ~wise(X0) <- (3) [avatar component clause 162]
164. 3 | ~2 [avatar split clause 82,157,162]
181. 7 <=> old(alice) [avatar definition]
182. ~old(alice) <- (~7) [avatar component clause 181]
185. 8 <=> patient(alice) [avatar definition]
187. patient(alice) <- (8) [avatar component clause 185]
189. 9 <=> old(paul) [avatar definition]
190. ~old(paul) <- (~9) [avatar component clause 189]
194. 10 <=> brave(paul) [avatar definition]
195. ~brave(paul) <- (~10) [avatar component clause 194]
199. ~10 | ~9 | ~7 [avatar split clause 89,181,189,194]
274. 25 <=> ! [X3] : (patient(X3) | old(X3)) [avatar definition]
275. old(X3) | patient(X3) <- (25) [avatar component clause 274]
277. 26 <=> generous(sK4) [avatar definition]
280. 25 | 26 [avatar split clause 123,277,274]
281. 25 | ~26 [avatar split clause 122,277,274]
283. 27 <=> ! [X0] : (quiet(X0) | ~rich(X0)) [avatar definition]
284. ~rich(X0) | quiet(X0) <- (27) [avatar component clause 283]
286. 28 <=> wise(mary) [avatar definition]
288. wise(mary) <- (28) [avatar component clause 286]
289. 27 | 28 [avatar split clause 129,286,283]
364. 2 [avatar split clause 152,157]
379. $false <- (3, 28) [subsumption resolution 288,163]
380. ~3 | ~28 [avatar contradiction clause 379]
386. brave(X0) | creative(X0) [resolution 136,107]
402. patient(paul) <- (~9, 25) [resolution 190,275]
409. wise(paul) <- (~9, 25) [resolution 402,84]
410. $false <- (3, ~9, 25) [subsumption resolution 409,163]
411. ~3 | 9 | ~25 [avatar contradiction clause 410]
412. patient(alice) <- (~7, 25) [resolution 182,275]
415. 8 | 7 | ~25 [avatar split clause 412,274,181,185]
417. wise(alice) <- (8) [resolution 187,84]
418. $false <- (3, 8) [subsumption resolution 417,163]
419. ~3 | ~8 [avatar contradiction clause 418]
437. quiet(X0) | brave(X0) <- (27) [resolution 284,138]
590. ~patient(X0) | humble(X0) | creative(X0) [resolution 133,386]
595. ~patient(X0) | creative(X0) [subsumption resolution 590,107]
596. ~patient(X0) [subsumption resolution 595,85]
668. brave(X1) | brave(X1) | patient(X1) <- (27) [resolution 437,101]
674. brave(X1) | patient(X1) <- (27) [duplicate literal removal 668]
675. brave(X1) <- (27) [subsumption resolution 674,596]
718. $false <- (~10, 27) [resolution 675,195]
723. 10 | ~27 [avatar contradiction clause 718]
727. $false [avatar sat refutation 164,199,280,281,289,364,380,411,415,419,723]
% SZS output end Proof for 2953491070317163485606289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not creative is tall and vice versa.
Everyone who is either rich or not humble is humble.
If lucy is not strong then paul is either not curious or not kind.
If lucy is either not curious or not quiet then lucy is not kind or funny and vice versa.
If someone is not curious then someone is both not creative and old and vice versa.
Everyone who is not funny or not creative is quiet or generous and vice versa.
Everyone who is both patient and wise is humble.
Everyone who is either not funny or not old is both not quiet and not creative and vice versa.
If someone is patient or not quiet then paul is either calm or not curious.
If someone is either rich or not generous then someone is not funny or funny.
Everyone who is either humble or not generous is either strong or not funny and vice versa.
Everyone who is both patient and calm is not brave or not humble.
If john is happy or not creative then someone is not generous.
If susan is both not creative and tall then susan is not tall or not old and vice versa.
Everyone who is either not old or not tall is generous or not old.
Everyone who is not tall or brave is both not quiet and not generous and vice versa.
Lucy is old or brave.
Paul is either old or brave.
Someone is not patient or not strong.
Lucy is not generous or humble.
Someone is tall or not calm.
John is either tall or calm.
Someone is funny.
Someone is creative or not creative. | Paul is kind. | neutral | (![X]:((brave(X)<~>~creative(X))<=>tall(X)))&
(![X]:((rich(X)<~>~humble(X))=>humble(X)))&
((~strong(lucy))=>((~curious(paul)<~>~kind(paul))))&
(((~curious(lucy)<~>~quiet(lucy)))<=>((~kind(lucy)|funny(lucy))))&
((?[X]:(~curious(X)))<=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~funny(X)|~creative(X))<=>(quiet(X)|generous(X))))&
(![X]:((patient(X)&wise(X))=>humble(X)))&
(![X]:((~funny(X)<~>~old(X))<=>(~quiet(X)&~creative(X))))&
((?[X]:((patient(X)|~quiet(X))))=>((calm(paul)<~>~curious(paul))))&
((?[X]:((rich(X)<~>~generous(X))))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((humble(X)<~>~generous(X))<=>(strong(X)<~>~funny(X))))&
(![X]:((patient(X)&calm(X))=>(~brave(X)|~humble(X))))&
(((happy(john)|~creative(john)))=>(?[X]:(~generous(X))))&
(((~creative(susan)&tall(susan)))<=>((~tall(susan)|~old(susan))))&
(![X]:((~old(X)<~>~tall(X))=>(generous(X)|~old(X))))&
(![X]:((~tall(X)|brave(X))<=>(~quiet(X)&~generous(X))))&
((old(lucy)|brave(lucy)))&
((old(paul)<~>brave(paul)))&
(?[X]:((~patient(X)|~strong(X))))&
((~generous(lucy)|humble(lucy)))&
(?[X]:((tall(X)|~calm(X))))&
((tall(john)<~>calm(john)))&
(?[X]:(funny(X)))&
(?[X]:((creative(X)|~creative(X)))) | kind(paul) | []
| null | 0 |
If fred is either not strong or brave then someone is either not calm or not funny.
Everyone who is either strong or not tall is both strong and not kind and vice versa.
Everyone who is both not creative and not generous is calm and vice versa.
Everyone who is either not funny or not strong is either tall or not wise and vice versa.
Everyone who is not humble or not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
If paul is not happy or brave then alice is either creative or brave.
If paul is strong or not strong then john is old and vice versa.
Alice is strong or wise.
Someone is wise.
Someone is either creative or not humble.
Someone is either happy or not creative.
Someone is quiet or not patient.
Fred is not patient or rich. | John is not patient. | entailment | (((~strong(fred)<~>brave(fred)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((strong(X)<~>~tall(X))<=>(strong(X)&~kind(X))))&
(![X]:((~creative(X)&~generous(X))<=>calm(X)))&
(![X]:((~funny(X)<~>~strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
(((~happy(paul)|brave(paul)))=>((creative(alice)<~>brave(alice))))&
(((strong(paul)|~strong(paul)))<=>(old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((quiet(X)|~patient(X))))&
((~patient(fred)|rich(fred))) | ~patient(john) | [
"p1",
"p7",
"p9",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 98061396169382568551008
% SZS output start Proof for 98061396169382568551008
2. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> (~kind(X0) & strong(X0))) [input p1]
8. ! [X0] : ((~old(X0) & ~wise(X0)) <=> strong(X0)) [input p7]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (~tall(X0) & creative(X0))) [input p9]
16. (~strong(paul) | strong(paul)) <=> old(john) [input p15]
23. patient(john) [input hypothesis]
42. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | (kind(X0) | ~strong(X0))) & ((~kind(X0) & strong(X0)) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 2]
43. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | kind(X0) | ~strong(X0)) & ((~kind(X0) & strong(X0)) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [flattening 42]
51. ! [X0] : (((~old(X0) & ~wise(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) | wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((~old(X0) & ~wise(X0)) | ~strong(X0)) & (strong(X0) | old(X0) | wise(X0))) [flattening 51]
54. ! [X0] : (((calm(X0) | patient(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
55. ! [X0] : ((calm(X0) | patient(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [flattening 54]
61. ((~strong(paul) | strong(paul)) | ~old(john)) & (old(john) | (strong(paul) & ~strong(paul))) [nnf transformation 16]
62. (~strong(paul) | strong(paul) | ~old(john)) & (old(john) | (strong(paul) & ~strong(paul))) [flattening 61]
78. strong(X0) | strong(X0) | tall(X0) [cnf transformation 43]
101. ~old(X0) | ~strong(X0) [cnf transformation 52]
112. ~patient(X0) | ~tall(X0) [cnf transformation 55]
125. old(john) | ~strong(paul) [cnf transformation 62]
126. old(john) | strong(paul) [cnf transformation 62]
135. patient(john) [cnf transformation 23]
140. tall(X0) | strong(X0) [duplicate literal removal 78]
207. 13 <=> strong(paul) [avatar definition]
211. 14 <=> old(john) [avatar definition]
213. old(john) <- (14) [avatar component clause 211]
214. 13 | 14 [avatar split clause 126,211,207]
215. ~13 | 14 [avatar split clause 125,211,207]
249. ~strong(john) <- (14) [resolution 101,213]
258. ~tall(john) [resolution 112,135]
259. strong(john) [resolution 140,258]
261. $false <- (14) [subsumption resolution 259,249]
262. ~14 [avatar contradiction clause 261]
263. $false [avatar sat refutation 214,215,262]
% SZS output end Proof for 98061396169382568551008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not brave or rich then someone is both not wise and tall.
If someone is either wise or strong then susan is brave.
If paul is either not quiet or not tall then fred is not humble or not calm.
Everyone who is both not strong and not curious is either curious or humble.
Everyone who is not generous is not strong or generous and vice versa.
If someone is either not funny or not strong then susan is either not tall or not happy and vice versa.
Everyone who is not rich is not kind.
Everyone who is both not funny and wise is not happy or not old and vice versa.
If mary is either quiet or not kind then someone is either creative or not quiet.
Everyone who is both tall and rich is curious or not funny and vice versa.
Everyone who is both not kind and not generous is both patient and not funny and vice versa.
Everyone who is tall or quiet is either not calm or not generous and vice versa.
If paul is not happy or not rich then mary is not quiet or funny.
Everyone who is tall is either not funny or curious.
If someone is funny or humble then paul is either not creative or not wise.
If mary is either wise or not old then someone is either calm or not tall.
Someone is brave or curious.
Someone is not curious or generous.
Someone is not wise or not strong.
Someone is not generous or not funny.
Someone is old or not kind.
Someone is both not quiet and kind. | Mary is not happy. | neutral | (((~brave(mary)<~>rich(mary)))=>(?[X]:((~wise(X)&tall(X)))))&
((?[X]:((wise(X)<~>strong(X))))=>(brave(susan)))&
(((~quiet(paul)<~>~tall(paul)))=>((~humble(fred)|~calm(fred))))&
(![X]:((~strong(X)&~curious(X))=>(curious(X)<~>humble(X))))&
(![X]:(~generous(X)<=>(~strong(X)|generous(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>((~tall(susan)<~>~happy(susan))))&
(![X]:(~rich(X)=>~kind(X)))&
(![X]:((~funny(X)&wise(X))<=>(~happy(X)|~old(X))))&
(((quiet(mary)<~>~kind(mary)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)&rich(X))<=>(curious(X)|~funny(X))))&
(![X]:((~kind(X)&~generous(X))<=>(patient(X)&~funny(X))))&
(![X]:((tall(X)|quiet(X))<=>(~calm(X)<~>~generous(X))))&
(((~happy(paul)|~rich(paul)))=>((~quiet(mary)|funny(mary))))&
(![X]:(tall(X)=>(~funny(X)<~>curious(X))))&
((?[X]:((funny(X)|humble(X))))=>((~creative(paul)<~>~wise(paul))))&
(((wise(mary)<~>~old(mary)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:((~quiet(X)&kind(X)))) | ~happy(mary) | []
| null | 0 |
Everyone who is calm or not quiet is generous or not funny and vice versa.
If susan is both not curious and humble then mary is either not curious or happy.
Everyone who is wise or not generous is both brave and not wise and vice versa.
Everyone who is either rich or not strong is both not generous and not wise and vice versa.
Everyone who is both funny and kind is not calm and vice versa.
Everyone who is strong is either calm or generous and vice versa.
If someone is curious then john is patient.
If alice is not happy or not tall then paul is tall or strong and vice versa.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Fred is not strong or not creative.
Someone is generous or not kind. | Paul is not humble. | contradiction | (![X]:((calm(X)|~quiet(X))<=>(generous(X)|~funny(X))))&
(((~curious(susan)&humble(susan)))=>((~curious(mary)<~>happy(mary))))&
(![X]:((wise(X)|~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((funny(X)&kind(X))<=>~calm(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
((?[X]:(curious(X)))=>(patient(john)))&
(((~happy(alice)|~tall(alice)))<=>((tall(paul)|strong(paul))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~humble(paul) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 3199821574351291096788388
% SZS output start Proof for 3199821574351291096788388
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~wise(X0) & brave(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (~wise(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((kind(X0) & funny(X0)) <=> ~calm(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p5]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p10]
22. ~humble(paul) [input hypothesis]
26. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
33. ! [X0] : (((~generous(X0) | wise(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
34. ! [X0] : ((~generous(X0) | wise(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [flattening 33]
35. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 4]
36. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [flattening 35]
37. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 5]
38. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 6]
42. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
43. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 11]
45. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 44]
66. ~wise(X0) | ~wise(X0) [cnf transformation 34]
70. ~generous(X0) | rich(X0) | strong(X0) [cnf transformation 36]
73. ~strong(X0) | rich(X0) | wise(X0) | generous(X0) [cnf transformation 36]
76. funny(X0) | calm(X0) [cnf transformation 38]
79. ~strong(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 39]
80. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 39]
87. ~rich(X0) | quiet(X0) [cnf transformation 26]
89. ~funny(X0) | ~rich(X0) [cnf transformation 43]
90. ~funny(X0) | rich(X0) [cnf transformation 43]
92. ~quiet(X0) | humble(X0) [cnf transformation 45]
114. ~humble(paul) [cnf transformation 22]
115. ~wise(X0) [duplicate literal removal 66]
136. ~strong(X0) | rich(X0) | generous(X0) [subsumption resolution 73,115]
146. 7 <=> strong(paul) [avatar definition]
147. strong(paul) <- (7) [avatar component clause 146]
148. ~strong(paul) <- (~7) [avatar component clause 146]
165. ~funny(X0) [subsumption resolution 89,90]
214. calm(X0) [resolution 76,165]
233. ~calm(paul) | ~generous(paul) <- (7) [resolution 79,147]
234. ~generous(paul) <- (7) [subsumption resolution 233,214]
235. strong(X0) | generous(X0) [resolution 80,214]
262. rich(paul) | generous(paul) <- (7) [resolution 136,147]
265. rich(paul) <- (7) [subsumption resolution 262,234]
268. quiet(paul) <- (7) [resolution 265,87]
272. humble(paul) <- (7) [resolution 268,92]
275. $false <- (7) [subsumption resolution 272,114]
276. ~7 [avatar contradiction clause 275]
277. generous(paul) <- (~7) [resolution 148,235]
279. rich(paul) | strong(paul) <- (~7) [resolution 277,70]
281. rich(paul) <- (~7) [subsumption resolution 279,148]
289. quiet(paul) <- (~7) [resolution 281,87]
299. humble(paul) <- (~7) [resolution 289,92]
300. $false <- (~7) [subsumption resolution 299,114]
301. 7 [avatar contradiction clause 300]
302. $false [avatar sat refutation 276,301]
% SZS output end Proof for 3199821574351291096788388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not curious or not generous and vice versa.
If lucy is brave then someone is tall or generous.
Everyone who is both happy and strong is not tall or curious.
Everyone who is not curious is not humble or kind.
Everyone who is not old is not funny and vice versa.
Everyone who is either strong or not strong is funny and vice versa.
Everyone who is not generous or tall is strong.
If someone is both rich and calm then someone is either funny or generous and vice versa.
If someone is either old or curious then mary is either wise or rich.
Everyone who is humble is both kind and strong and vice versa.
Everyone who is both not curious and not kind is either calm or not generous and vice versa.
Everyone who is both generous and strong is not calm.
If someone is either humble or not happy then someone is not creative or not tall and vice versa.
If mary is strong or not curious then someone is not rich and vice versa.
Everyone who is brave is old and vice versa.
If someone is not wise or not strong then paul is both humble and creative and vice versa.
Paul is calm.
Fred is either not generous or not curious.
Paul is both curious and not humble.
John is not humble or humble.
Someone is not humble.
John is both not curious and not happy.
Someone is funny.
Lucy is either not wise or not generous. | John is strong. | entailment | (![X]:(~quiet(X)<=>(~curious(X)|~generous(X))))&
((brave(lucy))=>(?[X]:((tall(X)|generous(X)))))&
(![X]:((happy(X)&strong(X))=>(~tall(X)|curious(X))))&
(![X]:(~curious(X)=>(~humble(X)|kind(X))))&
(![X]:(~old(X)<=>~funny(X)))&
(![X]:((strong(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~generous(X)|tall(X))=>strong(X)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
((?[X]:((old(X)<~>curious(X))))=>((wise(mary)<~>rich(mary))))&
(![X]:(humble(X)<=>(kind(X)&strong(X))))&
(![X]:((~curious(X)&~kind(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)&strong(X))=>~calm(X)))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:((~creative(X)|~tall(X)))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(brave(X)<=>old(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>((humble(paul)&creative(paul))))&
(calm(paul))&
((~generous(fred)<~>~curious(fred)))&
((curious(paul)&~humble(paul)))&
((~humble(john)|humble(john)))&
(?[X]:(~humble(X)))&
((~curious(john)&~happy(john)))&
(?[X]:(funny(X)))&
((~wise(lucy)<~>~generous(lucy))) | strong(john) | [
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6763078745252158411556058
% SZS output start Proof for 6763078745252158411556058
16. ? [X0] : (~strong(X0) | ~wise(X0)) <=> (creative(paul) & humble(paul)) [input p15]
19. ~humble(paul) & curious(paul) [input p18]
25. ~strong(john) [input hypothesis]
63. (? [X0] : (~strong(X0) | ~wise(X0)) | (~creative(paul) | ~humble(paul))) & ((creative(paul) & humble(paul)) | ! [X0] : (strong(X0) & wise(X0))) [nnf transformation 16]
64. (? [X0] : (~strong(X0) | ~wise(X0)) | ~creative(paul) | ~humble(paul)) & ((creative(paul) & humble(paul)) | ! [X0] : (strong(X0) & wise(X0))) [flattening 63]
65. (? [X0] : (~strong(X0) | ~wise(X0)) | ~creative(paul) | ~humble(paul)) & ((creative(paul) & humble(paul)) | ! [X1] : (strong(X1) & wise(X1))) [rectify 64]
66. ? [X0] : (~strong(X0) | ~wise(X0)) => (~strong(sK6) | ~wise(sK6)) [choice axiom]
67. ((~strong(sK6) | ~wise(sK6)) | ~creative(paul) | ~humble(paul)) & ((creative(paul) & humble(paul)) | ! [X1] : (strong(X1) & wise(X1))) [skolemisation 65,66]
116. humble(paul) | strong(X1) [cnf transformation 67]
124. ~humble(paul) [cnf transformation 19]
132. ~strong(john) [cnf transformation 25]
244. 25 <=> humble(paul) [avatar definition]
261. 29 <=> ! [X1] : strong(X1) [avatar definition]
262. strong(X1) <- (29) [avatar component clause 261]
268. 29 | 25 [avatar split clause 116,244,261]
280. ~25 [avatar split clause 124,244]
293. $false <- (29) [resolution 262,132]
294. ~29 [avatar contradiction clause 293]
295. $false [avatar sat refutation 268,280,294]
% SZS output end Proof for 6763078745252158411556058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both tall and not funny and vice versa. Everyone who is either not funny or happy is creative or rich and vice versa. Everyone who is both kind and strong is either curious or not patient. Everyone who is not creative or not funny is either calm or wise and vice versa. If someone is both not kind and not humble then fred is both brave and not rich. If fred is both kind and creative then fred is not brave and vice versa. If lucy is not humble then someone is not rich or quiet. Everyone who is not brave is not curious and vice versa. Everyone who is not creative or not calm is not humble or quiet. If susan is either not calm or creative then someone is not humble or quiet and vice versa. Everyone who is both not quiet and not strong is not funny and vice versa. Everyone who is both not generous and not curious is brave and vice versa. Everyone who is both not tall and not quiet is both not quiet and not calm. If alice is not rich or creative then someone is not humble or not funny and vice versa. If paul is both not creative and wise then fred is not calm. If someone is creative then fred is either generous or not creative and vice versa. Fred is either not wise or not generous. Someone is either not wise or not humble. Someone is happy or wise. Someone is either humble or not quiet. Someone is not rich. Someone is either not brave or not creative. | Fred is not humble. | neutral | (![X]:(patient(X)<=>(tall(X)&~funny(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(creative(X)|rich(X))))&
(![X]:((kind(X)&strong(X))=>(curious(X)<~>~patient(X))))&
(![X]:((~creative(X)|~funny(X))<=>(calm(X)<~>wise(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((brave(fred)&~rich(fred))))&
(((kind(fred)&creative(fred)))<=>(~brave(fred)))&
((~humble(lucy))=>(?[X]:((~rich(X)|quiet(X)))))&
(![X]:(~brave(X)<=>~curious(X)))&
(![X]:((~creative(X)|~calm(X))=>(~humble(X)|quiet(X))))&
(((~calm(susan)<~>creative(susan)))<=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((~quiet(X)&~strong(X))<=>~funny(X)))&
(![X]:((~generous(X)&~curious(X))<=>brave(X)))&
(![X]:((~tall(X)&~quiet(X))=>(~quiet(X)&~calm(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((~humble(X)|~funny(X)))))&
(((~creative(paul)&wise(paul)))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>((generous(fred)<~>~creative(fred))))&
((~wise(fred)<~>~generous(fred)))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~humble(fred) | []
| null | 0 |
If lucy is wise or happy then paul is both patient and humble.
Everyone who is both not creative and brave is quiet or wise.
Everyone who is either old or not kind is both patient and humble and vice versa.
Everyone who is not calm or strong is not quiet and vice versa.
If someone is old then alice is either wise or not calm and vice versa.
Everyone who is patient is both brave and not generous and vice versa.
Everyone who is either old or funny is funny or not wise.
If paul is either brave or not funny then john is both strong and not strong.
If lucy is both patient and not strong then someone is either not rich or not humble and vice versa.
Everyone who is not patient or patient is both humble and patient.
Everyone who is both not curious and not strong is kind or not funny.
Everyone who is both not curious and not wise is brave or not happy and vice versa.
Everyone who is not quiet is either curious or generous.
If someone is not creative then paul is either not quiet or not tall and vice versa.
Everyone who is funny or not strong is both patient and brave.
If mary is not old then someone is kind or quiet and vice versa.
Someone is either not tall or not quiet.
Someone is either not generous or not rich.
Mary is old or happy.
Someone is quiet.
Someone is not quiet or not rich. | Lucy is calm. | entailment | (((wise(lucy)|happy(lucy)))=>((patient(paul)&humble(paul))))&
(![X]:((~creative(X)&brave(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)|strong(X))<=>~quiet(X)))&
((?[X]:(old(X)))<=>((wise(alice)<~>~calm(alice))))&
(![X]:(patient(X)<=>(brave(X)&~generous(X))))&
(![X]:((old(X)<~>funny(X))=>(funny(X)|~wise(X))))&
(((brave(paul)<~>~funny(paul)))=>((strong(john)&~strong(john))))&
(((patient(lucy)&~strong(lucy)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~patient(X)|patient(X))=>(humble(X)&patient(X))))&
(![X]:((~curious(X)&~strong(X))=>(kind(X)|~funny(X))))&
(![X]:((~curious(X)&~wise(X))<=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~generous(X)<~>~rich(X))))&
((old(mary)|happy(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)|~rich(X)))) | calm(lucy) | [
"p3",
"p5",
"p9",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 4741824288562845352726444
% SZS output start Proof for 4741824288562845352726444
4. ! [X0] : ((strong(X0) | ~calm(X0)) <=> ~quiet(X0)) [input p3]
6. ! [X0] : (patient(X0) <=> (~generous(X0) & brave(X0))) [input p5]
10. ! [X0] : ((patient(X0) | ~patient(X0)) => (patient(X0) & humble(X0))) [input p9]
12. ! [X0] : ((~wise(X0) & ~curious(X0)) <=> (~happy(X0) | brave(X0))) [input p11]
13. ! [X0] : (~quiet(X0) => (curious(X0) <~> generous(X0))) [input p12]
22. ~calm(lucy) [input hypothesis]
29. ! [X0] : ((patient(X0) & humble(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 10]
32. ! [X0] : ((curious(X0) <~> generous(X0)) | quiet(X0)) [ennf transformation 13]
36. ! [X0] : (((strong(X0) | ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & calm(X0)))) [nnf transformation 4]
37. ! [X0] : ((strong(X0) | ~calm(X0) | quiet(X0)) & (~quiet(X0) | (~strong(X0) & calm(X0)))) [flattening 36]
42. ! [X0] : ((patient(X0) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | ~patient(X0))) [nnf transformation 6]
43. ! [X0] : ((patient(X0) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | ~patient(X0))) [flattening 42]
51. ! [X0] : (((~wise(X0) & ~curious(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (wise(X0) | curious(X0)))) [nnf transformation 12]
52. ! [X0] : (((~wise(X0) & ~curious(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | wise(X0) | curious(X0))) [flattening 51]
53. ! [X0] : (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | quiet(X0)) [nnf transformation 32]
83. ~quiet(X0) | calm(X0) [cnf transformation 37]
90. ~patient(X0) | brave(X0) [cnf transformation 43]
91. ~generous(X0) | ~patient(X0) [cnf transformation 43]
107. patient(X0) | patient(X0) [cnf transformation 29]
111. ~curious(X0) | ~brave(X0) [cnf transformation 52]
115. curious(X0) | generous(X0) | quiet(X0) [cnf transformation 53]
135. ~calm(lucy) [cnf transformation 22]
136. patient(X0) [duplicate literal removal 107]
306. brave(X0) [resolution 90,136]
327. generous(X1) | quiet(X1) | ~brave(X1) [resolution 115,111]
328. generous(X1) | quiet(X1) [subsumption resolution 327,306]
331. quiet(X0) | ~patient(X0) [resolution 328,91]
333. quiet(X0) [subsumption resolution 331,136]
335. calm(X0) [resolution 333,83]
342. $false [resolution 335,135]
% SZS output end Proof for 4741824288562845352726444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is happy or not strong then someone is either not tall or not old and vice versa. Everyone who is creative is either not old or wise and vice versa. Everyone who is rich or humble is not quiet or rich and vice versa. If mary is generous then alice is brave and vice versa. Everyone who is brave or rich is either not tall or not curious and vice versa. Everyone who is either humble or not tall is funny and vice versa. Everyone who is funny or not funny is brave and vice versa. Everyone who is both creative and not calm is not brave or not strong. If lucy is both brave and humble then lucy is strong or patient. Everyone who is brave or not funny is both strong and not funny. If susan is both not old and curious then someone is kind or not wise and vice versa. Everyone who is tall or strong is curious or not rich and vice versa. Everyone who is not humble or rich is either wise or not creative. If fred is not kind or creative then someone is not curious or curious and vice versa. If mary is curious then john is either not generous or not humble and vice versa. John is not rich or tall. Someone is either kind or not happy. Someone is both humble and not patient. Someone is tall or curious. Someone is both not old and not wise. | Mary is brave. | entailment | (((happy(susan)|~strong(susan)))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:(creative(X)<=>(~old(X)<~>wise(X))))&
(![X]:((rich(X)|humble(X))<=>(~quiet(X)|rich(X))))&
((generous(mary))<=>(brave(alice)))&
(![X]:((brave(X)|rich(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)<~>~tall(X))<=>funny(X)))&
(![X]:((funny(X)|~funny(X))<=>brave(X)))&
(![X]:((creative(X)&~calm(X))=>(~brave(X)|~strong(X))))&
(((brave(lucy)&humble(lucy)))=>((strong(lucy)|patient(lucy))))&
(![X]:((brave(X)|~funny(X))=>(strong(X)&~funny(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((tall(X)|strong(X))<=>(curious(X)|~rich(X))))&
(![X]:((~humble(X)|rich(X))=>(wise(X)<~>~creative(X))))&
(((~kind(fred)|creative(fred)))<=>(?[X]:((~curious(X)|curious(X)))))&
((curious(mary))<=>((~generous(john)<~>~humble(john))))&
((~rich(john)|tall(john)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((~old(X)&~wise(X)))) | brave(mary) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 2618877639493624897439615
% SZS output start Proof for 2618877639493624897439615
7. ! [X0] : ((~funny(X0) | funny(X0)) <=> brave(X0)) [input p6]
21. ~brave(mary) [input hypothesis]
39. ! [X0] : (((~funny(X0) | funny(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~funny(X0)))) [nnf transformation 7]
40. ! [X0] : ((~funny(X0) | funny(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~funny(X0)))) [flattening 39]
90. brave(X0) | ~funny(X0) [cnf transformation 40]
91. brave(X0) | funny(X0) [cnf transformation 40]
127. ~brave(mary) [cnf transformation 21]
166. brave(X0) [subsumption resolution 90,91]
271. $false [subsumption resolution 127,166]
% SZS output end Proof for 2618877639493624897439615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not humble then mary is either calm or funny.
Everyone who is funny or not happy is not humble and vice versa.
Everyone who is not happy or creative is both funny and happy and vice versa.
If john is creative then paul is not patient and vice versa.
If someone is both not curious and not wise then someone is either not tall or not generous and vice versa.
Everyone who is not brave or not humble is either not strong or old and vice versa.
Everyone who is both not calm and not old is not curious or rich and vice versa.
If john is curious then someone is either patient or happy and vice versa.
Everyone who is either not curious or not kind is not humble or kind and vice versa.
If someone is humble or not old then john is either not rich or happy and vice versa.
Everyone who is quiet or not happy is both not patient and happy and vice versa.
If someone is not humble or tall then someone is not rich or brave and vice versa.
Everyone who is either not kind or generous is not tall and vice versa.
Everyone who is not curious or not generous is either humble or not calm.
Everyone who is both not tall and patient is patient or not rich and vice versa.
Everyone who is calm is either quiet or happy and vice versa.
Someone is not old or calm.
Someone is curious.
Someone is both not curious and quiet.
Someone is both not brave and not curious.
Mary is rich.
Fred is quiet.
Paul is both not curious and wise. | Fred is rich. | entailment | ((?[X]:((humble(X)&~humble(X))))=>((calm(mary)<~>funny(mary))))&
(![X]:((funny(X)|~happy(X))<=>~humble(X)))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)&happy(X))))&
((creative(john))<=>(~patient(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(~strong(X)<~>old(X))))&
(![X]:((~calm(X)&~old(X))<=>(~curious(X)|rich(X))))&
((curious(john))<=>(?[X]:((patient(X)<~>happy(X)))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~humble(X)|kind(X))))&
((?[X]:((humble(X)|~old(X))))<=>((~rich(john)<~>happy(john))))&
(![X]:((quiet(X)|~happy(X))<=>(~patient(X)&happy(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~kind(X)<~>generous(X))<=>~tall(X)))&
(![X]:((~curious(X)|~generous(X))=>(humble(X)<~>~calm(X))))&
(![X]:((~tall(X)&patient(X))<=>(patient(X)|~rich(X))))&
(![X]:(calm(X)<=>(quiet(X)<~>happy(X))))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(rich(mary))&
(quiet(fred))&
((~curious(paul)&wise(paul))) | rich(fred) | [
"p10",
"p14",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4025966343676395426719143
% SZS output start Proof for 4025966343676395426719143
11. ! [X0] : ((~happy(X0) | quiet(X0)) <=> (happy(X0) & ~patient(X0))) [input p10]
15. ! [X0] : ((patient(X0) & ~tall(X0)) <=> (~rich(X0) | patient(X0))) [input p14]
22. quiet(fred) [input p21]
24. ~rich(fred) [input hypothesis]
54. ! [X0] : (((~happy(X0) | quiet(X0)) | (~happy(X0) | patient(X0))) & ((happy(X0) & ~patient(X0)) | (happy(X0) & ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : ((~happy(X0) | quiet(X0) | ~happy(X0) | patient(X0)) & ((happy(X0) & ~patient(X0)) | (happy(X0) & ~quiet(X0)))) [flattening 54]
63. ! [X0] : (((patient(X0) & ~tall(X0)) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | (~patient(X0) | tall(X0)))) [nnf transformation 15]
64. ! [X0] : (((patient(X0) & ~tall(X0)) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | ~patient(X0) | tall(X0))) [flattening 63]
119. ~quiet(X0) | ~patient(X0) [cnf transformation 55]
140. rich(X0) | patient(X0) [cnf transformation 64]
152. quiet(fred) [cnf transformation 22]
155. ~rich(fred) [cnf transformation 24]
300. ~patient(fred) [resolution 119,152]
301. patient(fred) [resolution 140,155]
305. $false [subsumption resolution 301,300]
% SZS output end Proof for 4025966343676395426719143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not generous is rich or not kind and vice versa.
If alice is both not creative and calm then paul is either strong or not curious and vice versa.
If someone is wise then john is funny and vice versa.
Everyone who is not patient or old is generous or not quiet.
If someone is either not rich or humble then someone is both not calm and not funny and vice versa.
Everyone who is not curious or funny is old.
Everyone who is strong is either curious or not wise.
Everyone who is not brave is either tall or not funny and vice versa.
If fred is both not humble and not happy then someone is not creative or humble and vice versa.
If someone is strong then someone is both brave and creative.
Everyone who is generous or not quiet is either curious or not curious.
If someone is old or wise then fred is either not wise or not creative and vice versa.
If susan is happy or not wise then someone is both generous and curious and vice versa.
If mary is either old or not brave then someone is either humble or not curious and vice versa.
Everyone who is kind or not wise is generous and vice versa.
If someone is not calm or wise then mary is wise and vice versa.
Mary is either not old or funny.
Someone is both quiet and not humble.
Someone is either kind or old.
Alice is either not brave or generous.
Paul is either old or not kind.
Susan is both curious and creative.
Alice is either rich or not rich.
Someone is both old and strong. | Susan is kind. | entailment | (![X]:((~creative(X)&~generous(X))<=>(rich(X)|~kind(X))))&
(((~creative(alice)&calm(alice)))<=>((strong(paul)<~>~curious(paul))))&
((?[X]:(wise(X)))<=>(funny(john)))&
(![X]:((~patient(X)|old(X))=>(generous(X)|~quiet(X))))&
((?[X]:((~rich(X)<~>humble(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~curious(X)|funny(X))=>old(X)))&
(![X]:(strong(X)=>(curious(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~funny(X))))&
(((~humble(fred)&~happy(fred)))<=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:(strong(X)))=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((generous(X)|~quiet(X))=>(curious(X)<~>~curious(X))))&
((?[X]:((old(X)|wise(X))))<=>((~wise(fred)<~>~creative(fred))))&
(((happy(susan)|~wise(susan)))<=>(?[X]:((generous(X)&curious(X)))))&
(((old(mary)<~>~brave(mary)))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((kind(X)|~wise(X))<=>generous(X)))&
((?[X]:((~calm(X)|wise(X))))<=>(wise(mary)))&
((~old(mary)<~>funny(mary)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((kind(X)<~>old(X))))&
((~brave(alice)<~>generous(alice)))&
((old(paul)<~>~kind(paul)))&
((curious(susan)&creative(susan)))&
((rich(alice)<~>~rich(alice)))&
(?[X]:((old(X)&strong(X)))) | kind(susan) | [
"p0",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 2518528813809978363741123
% SZS output start Proof for 2518528813809978363741123
1. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (~kind(X0) | rich(X0))) [input p0]
22. creative(susan) & curious(susan) [input p21]
25. ~kind(susan) [input hypothesis]
35. ! [X0] : (((~generous(X0) & ~creative(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 1]
36. ! [X0] : (((~generous(X0) & ~creative(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | generous(X0) | creative(X0))) [flattening 35]
91. ~creative(X0) | kind(X0) [cnf transformation 36]
164. creative(susan) [cnf transformation 22]
169. ~kind(susan) [cnf transformation 25]
412. kind(susan) [resolution 91,164]
415. $false [subsumption resolution 412,169]
% SZS output end Proof for 2518528813809978363741123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not calm or happy.
Everyone who is strong is both rich and tall and vice versa.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
If lucy is both rich and not strong then paul is not curious or curious.
If someone is tall or humble then alice is either not humble or patient.
Lucy is not generous.
Susan is not patient.
Alice is either happy or not old.
Susan is either curious or creative.
Mary is not calm or not curious. | Paul is not wise. | neutral | (![X]:(~brave(X)=>(~calm(X)<~>happy(X))))&
(![X]:(strong(X)<=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(((rich(lucy)&~strong(lucy)))=>((~curious(paul)|curious(paul))))&
((?[X]:((tall(X)|humble(X))))=>((~humble(alice)<~>patient(alice))))&
(~generous(lucy))&
(~patient(susan))&
((happy(alice)<~>~old(alice)))&
((curious(susan)<~>creative(susan)))&
((~calm(mary)|~curious(mary))) | ~wise(paul) | []
| null | 0 |
Everyone who is not rich or not curious is both not calm and not funny and vice versa.
If paul is both not funny and not creative then someone is not quiet and vice versa.
If someone is both strong and wise then mary is both strong and old.
If someone is generous or happy then fred is generous or not humble.
Everyone who is either not calm or brave is not funny or curious and vice versa.
Everyone who is either creative or wise is not rich or strong.
If someone is quiet then someone is generous or not curious and vice versa.
Everyone who is either brave or not old is either not strong or not funny and vice versa.
If john is not old or brave then someone is either quiet or not quiet.
Everyone who is not kind is not curious or not quiet and vice versa.
If someone is tall then someone is both not old and kind.
If fred is both not strong and not funny then someone is both not patient and old.
Everyone who is either kind or not strong is either tall or strong and vice versa.
Everyone who is either not strong or brave is not tall.
Everyone who is not generous is both not brave and generous and vice versa.
If someone is not calm then susan is either not curious or not creative and vice versa.
Someone is wise or rich.
Paul is either calm or not tall.
Someone is not creative or patient.
Mary is kind.
John is not happy or not tall. | Fred is not strong. | neutral | (![X]:((~rich(X)|~curious(X))<=>(~calm(X)&~funny(X))))&
(((~funny(paul)&~creative(paul)))<=>(?[X]:(~quiet(X))))&
((?[X]:((strong(X)&wise(X))))=>((strong(mary)&old(mary))))&
((?[X]:((generous(X)|happy(X))))=>((generous(fred)|~humble(fred))))&
(![X]:((~calm(X)<~>brave(X))<=>(~funny(X)|curious(X))))&
(![X]:((creative(X)<~>wise(X))=>(~rich(X)|strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(~strong(X)<~>~funny(X))))&
(((~old(john)|brave(john)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(?[X]:((wise(X)|rich(X))))&
((calm(paul)<~>~tall(paul)))&
(?[X]:((~creative(X)|patient(X))))&
(kind(mary))&
((~happy(john)|~tall(john))) | ~strong(fred) | []
| null | 0 |
If susan is curious or not humble then someone is not calm or generous and vice versa. Everyone who is not strong or not patient is both rich and not old and vice versa. Everyone who is strong or calm is both creative and not curious. Everyone who is both wise and creative is not funny and vice versa. If mary is either not tall or not creative then someone is either not creative or quiet and vice versa. Everyone who is not humble or not quiet is not kind. If someone is not quiet or not rich then someone is both not happy and strong and vice versa. Everyone who is both humble and wise is brave or not brave. Everyone who is either not tall or not happy is either tall or creative. If susan is not brave then fred is wise. If john is generous or not rich then someone is rich or kind. If someone is tall then lucy is humble. Everyone who is not quiet is tall or calm. If fred is either not generous or curious then fred is both not generous and not tall and vice versa. Everyone who is both not patient and not generous is kind or generous. If susan is either rich or tall then someone is generous or humble and vice versa. Alice is not tall or not calm. Someone is not calm. Someone is both not happy and not wise. Someone is creative or rich. Someone is either curious or calm. Fred is curious. Paul is both not old and strong. Someone is either patient or wise. | Fred is calm. | contradiction | (((curious(susan)|~humble(susan)))<=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:((~strong(X)|~patient(X))<=>(rich(X)&~old(X))))&
(![X]:((strong(X)|calm(X))=>(creative(X)&~curious(X))))&
(![X]:((wise(X)&creative(X))<=>~funny(X)))&
(((~tall(mary)<~>~creative(mary)))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:((~humble(X)|~quiet(X))=>~kind(X)))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:((humble(X)&wise(X))=>(brave(X)|~brave(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(tall(X)<~>creative(X))))&
((~brave(susan))=>(wise(fred)))&
(((generous(john)|~rich(john)))=>(?[X]:((rich(X)|kind(X)))))&
((?[X]:(tall(X)))=>(humble(lucy)))&
(![X]:(~quiet(X)=>(tall(X)|calm(X))))&
(((~generous(fred)<~>curious(fred)))<=>((~generous(fred)&~tall(fred))))&
(![X]:((~patient(X)&~generous(X))=>(kind(X)|generous(X))))&
(((rich(susan)<~>tall(susan)))<=>(?[X]:((generous(X)|humble(X)))))&
((~tall(alice)|~calm(alice)))&
(?[X]:(~calm(X)))&
(?[X]:((~happy(X)&~wise(X))))&
(?[X]:((creative(X)|rich(X))))&
(?[X]:((curious(X)<~>calm(X))))&
(curious(fred))&
((~old(paul)&strong(paul)))&
(?[X]:((patient(X)<~>wise(X)))) | calm(fred) | [
"p2",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5446484366465465884475704
% SZS output start Proof for 5446484366465465884475704
3. ! [X0] : ((calm(X0) | strong(X0)) => (~curious(X0) & creative(X0))) [input p2]
22. curious(fred) [input p21]
25. calm(fred) [input hypothesis]
27. ! [X0] : ((~curious(X0) & creative(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 3]
88. ~calm(X0) | ~curious(X0) [cnf transformation 27]
134. curious(fred) [cnf transformation 22]
139. calm(fred) [cnf transformation 25]
275. 30 <=> curious(fred) [avatar definition]
276. curious(fred) <- (30) [avatar component clause 275]
334. 30 [avatar split clause 134,275]
352. ~curious(fred) [resolution 88,139]
353. $false <- (30) [subsumption resolution 352,276]
354. ~30 [avatar contradiction clause 353]
355. $false [avatar sat refutation 334,354]
% SZS output end Proof for 5446484366465465884475704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not creative or wise and vice versa.
If someone is both generous and creative then fred is either not brave or wise.
Everyone who is either happy or not wise is either happy or rich and vice versa.
If someone is both not old and funny then someone is old and vice versa.
If john is both not patient and not strong then someone is quiet or not happy.
Everyone who is brave or rich is both generous and not wise.
Everyone who is not strong is either not calm or not tall and vice versa.
Everyone who is both not happy and not strong is calm and vice versa.
If someone is creative then someone is both wise and patient and vice versa.
Everyone who is either happy or not rich is either curious or not humble.
If susan is either funny or not happy then someone is either not old or kind and vice versa.
If alice is funny then lucy is kind or generous.
If someone is not rich or creative then susan is either not tall or happy.
Someone is either not generous or not old.
Someone is tall or not brave.
Someone is not strong.
Someone is either not happy or old.
Someone is both happy and not tall.
Paul is rich. | Lucy is rich. | entailment | (![X]:(~wise(X)<=>(~creative(X)|wise(X))))&
((?[X]:((generous(X)&creative(X))))=>((~brave(fred)<~>wise(fred))))&
(![X]:((happy(X)<~>~wise(X))<=>(happy(X)<~>rich(X))))&
((?[X]:((~old(X)&funny(X))))<=>(?[X]:(old(X))))&
(((~patient(john)&~strong(john)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((brave(X)|rich(X))=>(generous(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~calm(X)<~>~tall(X))))&
(![X]:((~happy(X)&~strong(X))<=>calm(X)))&
((?[X]:(creative(X)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((happy(X)<~>~rich(X))=>(curious(X)<~>~humble(X))))&
(((funny(susan)<~>~happy(susan)))<=>(?[X]:((~old(X)<~>kind(X)))))&
((funny(alice))=>((kind(lucy)|generous(lucy))))&
((?[X]:((~rich(X)|creative(X))))=>((~tall(susan)<~>happy(susan))))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((happy(X)&~tall(X))))&
(rich(paul)) | rich(lucy) | [
"p0",
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 9127217900491591579224909
% SZS output start Proof for 9127217900491591579224909
1. ! [X0] : (~wise(X0) <=> (wise(X0) | ~creative(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~wise(X0)) <=> (happy(X0) <~> rich(X0))) [input p2]
20. ~rich(lucy) [input hypothesis]
30. ! [X0] : ((~wise(X0) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | wise(X0))) [nnf transformation 1]
31. ! [X0] : ((~wise(X0) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | wise(X0))) [flattening 30]
33. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0)))) & (((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [nnf transformation 3]
67. ~wise(X0) | ~wise(X0) [cnf transformation 31]
71. rich(X0) | happy(X0) | happy(X0) | wise(X0) [cnf transformation 33]
76. wise(X0) | ~happy(X0) | rich(X0) | ~happy(X0) [cnf transformation 33]
121. ~rich(lucy) [cnf transformation 20]
122. rich(X0) | happy(X0) | wise(X0) [duplicate literal removal 71]
125. wise(X0) | ~happy(X0) | rich(X0) [duplicate literal removal 76]
127. ~wise(X0) [duplicate literal removal 67]
129. ~happy(X0) | rich(X0) [subsumption resolution 125,127]
130. rich(X0) | happy(X0) [subsumption resolution 122,127]
131. rich(X0) [subsumption resolution 130,129]
206. $false [subsumption resolution 121,131]
% SZS output end Proof for 9127217900491591579224909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is either curious or not generous and vice versa.
Everyone who is both tall and not generous is creative or not happy and vice versa.
Everyone who is not curious or wise is not generous and vice versa.
Everyone who is not generous or not funny is funny.
Everyone who is old is not creative and vice versa.
If someone is either not creative or creative then alice is either rich or kind and vice versa.
Everyone who is both not rich and not happy is strong.
If fred is kind or patient then susan is both wise and not generous.
Everyone who is tall is both not rich and not humble.
Everyone who is both not humble and strong is not wise or creative.
If lucy is both kind and not tall then john is curious and vice versa.
If fred is quiet then someone is either curious or wise.
Everyone who is both not brave and not happy is creative or quiet.
If someone is both not tall and not wise then someone is not humble or creative and vice versa.
Everyone who is both kind and not curious is not old or rich and vice versa.
Everyone who is both strong and not tall is not calm.
John is either creative or old.
Someone is not old or brave.
Fred is kind or not creative.
Someone is both wise and strong.
Lucy is either not wise or calm.
Someone is either tall or not patient. | Lucy is not wise. | contradiction | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:((~curious(X)|wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:(old(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
((creative(john)<~>old(john)))&
(?[X]:((~old(X)|brave(X))))&
((kind(fred)|~creative(fred)))&
(?[X]:((wise(X)&strong(X))))&
((~wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)<~>~patient(X)))) | ~wise(lucy) | [
"p0",
"p2",
"p3",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8853056961570519857568446
% SZS output start Proof for 8853056961570519857568446
1. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p0]
3. ! [X0] : ((wise(X0) | ~curious(X0)) <=> ~generous(X0)) [input p2]
4. ! [X0] : ((~funny(X0) | ~generous(X0)) => funny(X0)) [input p3]
9. ! [X0] : (tall(X0) => (~humble(X0) & ~rich(X0))) [input p8]
14. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X0] : (creative(X0) | ~humble(X0)) [input p13]
23. ~wise(lucy) [input hypothesis]
24. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X1] : (creative(X1) | ~humble(X1)) [rectify 14]
27. ! [X0] : (funny(X0) | (funny(X0) & generous(X0))) [ennf transformation 4]
31. ! [X0] : ((~humble(X0) & ~rich(X0)) | ~tall(X0)) [ennf transformation 9]
37. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (funny(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | funny(X0) | ~quiet(X0))) [flattening 37]
41. ! [X0] : (((wise(X0) | ~curious(X0)) | generous(X0)) & (~generous(X0) | (~wise(X0) & curious(X0)))) [nnf transformation 3]
42. ! [X0] : ((wise(X0) | ~curious(X0) | generous(X0)) & (~generous(X0) | (~wise(X0) & curious(X0)))) [flattening 41]
53. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (~creative(X1) & humble(X1))) & (? [X1] : (creative(X1) | ~humble(X1)) | ! [X0] : (wise(X0) | tall(X0))) [nnf transformation 24]
54. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (~creative(X1) & humble(X1))) & (? [X2] : (creative(X2) | ~humble(X2)) | ! [X3] : (wise(X3) | tall(X3))) [rectify 53]
55. ? [X0] : (~wise(X0) & ~tall(X0)) => (~wise(sK2) & ~tall(sK2)) [choice axiom]
56. ? [X2] : (creative(X2) | ~humble(X2)) => (creative(sK3) | ~humble(sK3)) [choice axiom]
57. ((~wise(sK2) & ~tall(sK2)) | ! [X1] : (~creative(X1) & humble(X1))) & ((creative(sK3) | ~humble(sK3)) | ! [X3] : (wise(X3) | tall(X3))) [skolemisation 54,56,55]
71. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 38]
72. ~funny(X0) | curious(X0) | generous(X0) [cnf transformation 38]
78. ~generous(X0) | curious(X0) [cnf transformation 42]
80. ~curious(X0) | wise(X0) | generous(X0) [cnf transformation 42]
82. funny(X0) | funny(X0) [cnf transformation 27]
99. ~humble(X0) | ~tall(X0) [cnf transformation 31]
106. creative(sK3) | ~humble(sK3) | wise(X3) | tall(X3) [cnf transformation 57]
109. ~wise(sK2) | humble(X1) [cnf transformation 57]
110. ~wise(sK2) | ~creative(X1) [cnf transformation 57]
126. ~wise(lucy) [cnf transformation 23]
131. funny(X0) [duplicate literal removal 82]
133. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
134. ~creative(X1) <- (1) [avatar component clause 133]
200. 15 <=> wise(sK2) [avatar definition]
202. ~wise(sK2) <- (~15) [avatar component clause 200]
203. 1 | ~15 [avatar split clause 110,200,133]
205. 16 <=> ! [X1] : humble(X1) [avatar definition]
206. humble(X1) <- (16) [avatar component clause 205]
207. 16 | ~15 [avatar split clause 109,200,205]
215. 18 <=> ! [X3] : (wise(X3) | tall(X3)) [avatar definition]
216. wise(X3) | tall(X3) <- (18) [avatar component clause 215]
218. 19 <=> humble(sK3) [avatar definition]
220. ~humble(sK3) <- (~19) [avatar component clause 218]
222. 20 <=> creative(sK3) [avatar definition]
224. creative(sK3) <- (20) [avatar component clause 222]
225. 18 | ~19 | 20 [avatar split clause 106,222,218,215]
232. 22 <=> wise(lucy) [avatar definition]
233. ~wise(lucy) <- (~22) [avatar component clause 232]
251. ~22 [avatar split clause 126,232]
284. curious(X0) | generous(X0) [resolution 72,131]
285. curious(X0) [subsumption resolution 284,78]
289. wise(X0) | generous(X0) [resolution 80,285]
293. generous(sK2) <- (~15) [resolution 289,202]
299. ~funny(sK2) | ~curious(sK2) <- (~15) [resolution 293,71]
303. ~curious(sK2) <- (~15) [subsumption resolution 299,131]
304. $false <- (~15) [subsumption resolution 303,285]
305. 15 [avatar contradiction clause 304]
308. $false <- (16, ~19) [resolution 206,220]
309. ~tall(X0) <- (16) [resolution 206,99]
310. ~16 | 19 [avatar contradiction clause 308]
311. wise(X3) <- (16, 18) [subsumption resolution 216,309]
313. $false <- (16, 18, ~22) [resolution 311,233]
314. ~16 | ~18 | 22 [avatar contradiction clause 313]
315. $false <- (1, 20) [subsumption resolution 224,134]
316. ~1 | ~20 [avatar contradiction clause 315]
317. $false [avatar sat refutation 203,207,225,251,305,310,314,316]
% SZS output end Proof for 8853056961570519857568446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then alice is both not curious and calm.
If someone is either not generous or happy then someone is both not strong and not funny and vice versa.
If john is either not old or generous then fred is not curious.
Everyone who is either not tall or not kind is not brave and vice versa.
If someone is happy then someone is kind or rich and vice versa.
Everyone who is both brave and curious is both brave and not old and vice versa.
Everyone who is not brave or brave is both not old and strong.
Everyone who is strong is both not creative and not brave and vice versa.
If lucy is either rich or calm then paul is not brave.
Everyone who is not old is either wise or creative.
Everyone who is both patient and humble is both humble and old.
Everyone who is either tall or not patient is either not kind or wise and vice versa.
Everyone who is creative is not curious or calm and vice versa.
If fred is generous or not curious then susan is not humble and vice versa.
If someone is both wise and not curious then someone is both not rich and not old.
Paul is both not old and not creative.
Mary is brave or not funny.
Susan is either quiet or not humble.
Susan is calm or not creative.
Paul is both tall and not old. | John is not strong. | contradiction | ((?[X]:(~generous(X)))=>((~curious(alice)&calm(alice))))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((~strong(X)&~funny(X)))))&
(((~old(john)<~>generous(john)))=>(~curious(fred)))&
(![X]:((~tall(X)<~>~kind(X))<=>~brave(X)))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(![X]:(creative(X)<=>(~curious(X)|calm(X))))&
(((generous(fred)|~curious(fred)))<=>(~humble(susan)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~rich(X)&~old(X)))))&
((~old(paul)&~creative(paul)))&
((brave(mary)|~funny(mary)))&
((quiet(susan)<~>~humble(susan)))&
((calm(susan)|~creative(susan)))&
((tall(paul)&~old(paul))) | ~strong(john) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 6968290590635119096734876
% SZS output start Proof for 6968290590635119096734876
7. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p6]
21. ~strong(john) [input hypothesis]
27. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 7]
83. strong(X0) | brave(X0) [cnf transformation 27]
84. strong(X0) | ~brave(X0) [cnf transformation 27]
118. ~strong(john) [cnf transformation 21]
201. strong(X0) [subsumption resolution 83,84]
232. $false [subsumption resolution 118,201]
% SZS output end Proof for 6968290590635119096734876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not brave or wise then someone is not humble and vice versa.
If someone is not calm or strong then someone is generous or curious and vice versa.
If paul is rich then someone is either funny or not old and vice versa.
If lucy is both humble and not humble then someone is not curious and vice versa.
Everyone who is calm is either strong or quiet.
If john is not creative or old then someone is both not old and patient and vice versa.
Everyone who is not creative is either not tall or not happy.
Everyone who is either not generous or old is either old or humble and vice versa.
Everyone who is not quiet is happy.
Everyone who is either not generous or humble is not quiet and vice versa.
Everyone who is either happy or not kind is either tall or not brave and vice versa.
If mary is happy or strong then someone is both funny and wise and vice versa.
If lucy is not happy or kind then paul is creative or not funny.
If john is not funny then someone is not patient or not creative.
Everyone who is funny or generous is either not rich or creative.
If susan is wise then someone is both creative and not patient.
Fred is either creative or kind.
Alice is not creative or not kind.
Alice is either not curious or not happy.
Someone is either not strong or happy.
Someone is not brave or not patient.
Someone is both not happy and not brave.
Lucy is both not patient and not creative.
Someone is old or tall. | Susan is not quiet. | contradiction | (((~brave(lucy)<~>wise(lucy)))<=>(?[X]:(~humble(X))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((generous(X)|curious(X)))))&
((rich(paul))<=>(?[X]:((funny(X)<~>~old(X)))))&
(((humble(lucy)&~humble(lucy)))<=>(?[X]:(~curious(X))))&
(![X]:(calm(X)=>(strong(X)<~>quiet(X))))&
(((~creative(john)|old(john)))<=>(?[X]:((~old(X)&patient(X)))))&
(![X]:(~creative(X)=>(~tall(X)<~>~happy(X))))&
(![X]:((~generous(X)<~>old(X))<=>(old(X)<~>humble(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:((~generous(X)<~>humble(X))<=>~quiet(X)))&
(![X]:((happy(X)<~>~kind(X))<=>(tall(X)<~>~brave(X))))&
(((happy(mary)|strong(mary)))<=>(?[X]:((funny(X)&wise(X)))))&
(((~happy(lucy)|kind(lucy)))=>((creative(paul)|~funny(paul))))&
((~funny(john))=>(?[X]:((~patient(X)|~creative(X)))))&
(![X]:((funny(X)|generous(X))=>(~rich(X)<~>creative(X))))&
((wise(susan))=>(?[X]:((creative(X)&~patient(X)))))&
((creative(fred)<~>kind(fred)))&
((~creative(alice)|~kind(alice)))&
((~curious(alice)<~>~happy(alice)))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:((~happy(X)&~brave(X))))&
((~patient(lucy)&~creative(lucy)))&
(?[X]:((old(X)|tall(X)))) | ~quiet(susan) | [
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 8652571788966255532560513
% SZS output start Proof for 8652571788966255532560513
8. ! [X0] : ((~generous(X0) <~> old(X0)) <=> (old(X0) <~> humble(X0))) [input p7]
10. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> ~quiet(X0)) [input p9]
25. ~quiet(susan) [input hypothesis]
60. ! [X0] : ((((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))))) [nnf transformation 8]
61. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 10]
108. humble(X0) | old(X0) | old(X0) | generous(X0) [cnf transformation 60]
111. ~humble(X0) | ~old(X0) | ~generous(X0) | ~old(X0) [cnf transformation 60]
113. old(X0) | ~generous(X0) | old(X0) | ~humble(X0) [cnf transformation 60]
114. ~old(X0) | generous(X0) | humble(X0) | ~old(X0) [cnf transformation 60]
119. humble(X0) | ~generous(X0) | quiet(X0) [cnf transformation 61]
120. ~humble(X0) | generous(X0) | quiet(X0) [cnf transformation 61]
156. ~quiet(susan) [cnf transformation 25]
157. humble(X0) | old(X0) | generous(X0) [duplicate literal removal 108]
158. ~humble(X0) | ~old(X0) | ~generous(X0) [duplicate literal removal 111]
159. old(X0) | ~generous(X0) | ~humble(X0) [duplicate literal removal 113]
160. ~old(X0) | generous(X0) | humble(X0) [duplicate literal removal 114]
267. ~generous(X0) | ~humble(X0) [subsumption resolution 158,159]
268. generous(X0) | humble(X0) [subsumption resolution 157,160]
269. quiet(X0) | generous(X0) [subsumption resolution 120,268]
270. quiet(X0) | humble(X0) [subsumption resolution 119,269]
403. generous(susan) [resolution 269,156]
404. humble(susan) [resolution 270,156]
405. ~humble(susan) [resolution 403,267]
406. $false [subsumption resolution 405,404]
% SZS output end Proof for 8652571788966255532560513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not rich then lucy is funny or not wise.
If someone is funny or not funny then someone is not tall or not brave.
Everyone who is not tall or generous is both not humble and kind and vice versa.
Everyone who is either happy or tall is not generous.
Everyone who is either not creative or creative is either kind or wise.
If fred is either not kind or not patient then fred is both not generous and not old.
If someone is patient then paul is either curious or not generous.
Everyone who is either brave or not strong is kind or brave and vice versa.
Everyone who is calm or rich is both not creative and not strong and vice versa.
Everyone who is not old or not generous is both happy and wise.
Everyone who is either not patient or not funny is either creative or calm and vice versa.
If alice is either not wise or patient then john is not generous or not calm and vice versa.
Everyone who is either not patient or creative is both kind and strong and vice versa.
Everyone who is either not happy or not generous is patient or humble and vice versa.
Everyone who is not quiet or kind is not kind or quiet.
Lucy is not calm.
Alice is patient or not creative.
Susan is both not rich and quiet.
Lucy is either not creative or curious.
John is both curious and not quiet.
Someone is not kind. | John is funny. | entailment | ((?[X]:((kind(X)|~rich(X))))=>((funny(lucy)|~wise(lucy))))&
((?[X]:((funny(X)|~funny(X))))=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~tall(X)|generous(X))<=>(~humble(X)&kind(X))))&
(![X]:((happy(X)<~>tall(X))=>~generous(X)))&
(![X]:((~creative(X)<~>creative(X))=>(kind(X)<~>wise(X))))&
(((~kind(fred)<~>~patient(fred)))=>((~generous(fred)&~old(fred))))&
((?[X]:(patient(X)))=>((curious(paul)<~>~generous(paul))))&
(![X]:((brave(X)<~>~strong(X))<=>(kind(X)|brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(~calm(lucy))&
((patient(alice)|~creative(alice)))&
((~rich(susan)&quiet(susan)))&
((~creative(lucy)<~>curious(lucy)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X))) | funny(john) | [
"p7",
"p8",
"p10",
"p12",
"p14",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3962896354587613790139534
% SZS output start Proof for 3962896354587613790139534
8. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) | kind(X0))) [input p7]
9. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p12]
15. ! [X0] : ((kind(X0) | ~quiet(X0)) => (quiet(X0) | ~kind(X0))) [input p14]
20. ~quiet(john) & curious(john) [input p19]
22. ~funny(john) [input hypothesis]
32. ! [X0] : ((quiet(X0) | ~kind(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 15]
33. ! [X0] : (quiet(X0) | ~kind(X0) | (~kind(X0) & quiet(X0))) [flattening 32]
43. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 8]
44. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 43]
45. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 9]
46. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
50. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
51. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 50]
79. brave(X0) | kind(X0) | brave(X0) | strong(X0) [cnf transformation 44]
83. strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
84. ~calm(X0) | ~creative(X0) [cnf transformation 46]
86. ~calm(X0) | ~strong(X0) [cnf transformation 46]
94. ~patient(X0) | creative(X0) | calm(X0) | funny(X0) [cnf transformation 47]
99. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 47]
100. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 47]
107. patient(X0) | creative(X0) | kind(X0) [cnf transformation 51]
108. ~patient(X0) | kind(X0) | ~creative(X0) [cnf transformation 51]
120. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 33]
128. ~quiet(john) [cnf transformation 20]
130. ~funny(john) [cnf transformation 22]
132. ~kind(X0) | quiet(X0) [duplicate literal removal 120]
133. brave(X0) | kind(X0) | strong(X0) [duplicate literal removal 79]
134. ~brave(X0) | strong(X0) [duplicate literal removal 83]
206. strong(X0) | kind(X0) [subsumption resolution 133,134]
207. ~calm(X0) | patient(X0) | funny(X0) [subsumption resolution 100,84]
208. ~creative(X0) | patient(X0) | funny(X0) [subsumption resolution 99,207]
212. 16 <=> calm(john) [avatar definition]
213. ~calm(john) <- (~16) [avatar component clause 212]
214. calm(john) <- (16) [avatar component clause 212]
329. 28 <=> creative(john) [avatar definition]
330. ~creative(john) <- (~28) [avatar component clause 329]
331. creative(john) <- (28) [avatar component clause 329]
333. 29 <=> strong(john) [avatar definition]
334. ~strong(john) <- (~29) [avatar component clause 333]
345. ~strong(john) <- (16) [resolution 214,86]
348. ~29 | ~16 [avatar split clause 345,212,333]
420. kind(john) <- (~29) [resolution 334,206]
441. 37 <=> patient(john) [avatar definition]
442. ~patient(john) <- (~37) [avatar component clause 441]
443. patient(john) <- (37) [avatar component clause 441]
452. patient(john) | funny(john) <- (28) [resolution 331,208]
456. patient(john) <- (28) [subsumption resolution 452,130]
457. 37 | ~28 [avatar split clause 456,329,441]
473. quiet(john) <- (~29) [resolution 420,132]
474. $false <- (~29) [subsumption resolution 473,128]
475. 29 [avatar contradiction clause 474]
481. 39 <=> kind(john) [avatar definition]
482. ~kind(john) <- (~39) [avatar component clause 481]
483. kind(john) <- (39) [avatar component clause 481]
505. creative(john) | calm(john) | funny(john) <- (37) [resolution 443,94]
509. kind(john) | ~creative(john) <- (37) [resolution 443,108]
532. quiet(john) <- (39) [resolution 483,132]
533. $false <- (39) [subsumption resolution 532,128]
534. ~39 [avatar contradiction clause 533]
543. ~creative(john) <- (37, ~39) [subsumption resolution 509,482]
544. ~28 | ~37 | 39 [avatar split clause 543,481,441,329]
545. creative(john) | funny(john) <- (~16, 37) [subsumption resolution 505,213]
546. creative(john) <- (~16, 37) [subsumption resolution 545,130]
547. 28 | 16 | ~37 [avatar split clause 546,441,212,329]
566. creative(john) | kind(john) <- (~37) [resolution 442,107]
569. kind(john) <- (~28, ~37) [subsumption resolution 566,330]
570. $false <- (~28, ~37, ~39) [subsumption resolution 569,482]
571. 28 | 37 | 39 [avatar contradiction clause 570]
572. $false [avatar sat refutation 348,457,475,534,544,547,571]
% SZS output end Proof for 3962896354587613790139534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or strong then fred is either strong or kind and vice versa.
Everyone who is happy is wise or not old and vice versa.
Everyone who is both quiet and strong is either calm or not generous and vice versa.
If someone is both not curious and patient then someone is either kind or old.
Everyone who is both calm and not brave is both strong and quiet.
Everyone who is calm is not patient or humble and vice versa.
Everyone who is both quiet and not old is either old or not strong.
Everyone who is both kind and not quiet is quiet or not strong and vice versa.
Everyone who is either not wise or generous is not humble or not happy and vice versa.
Everyone who is humble is generous.
If fred is not curious or curious then susan is both not patient and not quiet.
Everyone who is either brave or not kind is calm.
If john is either not quiet or old then someone is kind.
If lucy is either rich or not strong then someone is not kind and vice versa.
Everyone who is not happy is both creative and not tall.
Everyone who is not curious or tall is not creative and vice versa.
John is both strong and not creative.
Someone is not wise or tall.
Lucy is either generous or happy.
Someone is generous or not old.
Fred is brave.
Alice is both wise and not calm.
Lucy is not generous.
Someone is brave or not funny. | Lucy is brave. | entailment | ((?[X]:((old(X)|strong(X))))<=>((strong(fred)<~>kind(fred))))&
(![X]:(happy(X)<=>(wise(X)|~old(X))))&
(![X]:((quiet(X)&strong(X))<=>(calm(X)<~>~generous(X))))&
((?[X]:((~curious(X)&patient(X))))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:((calm(X)&~brave(X))=>(strong(X)&quiet(X))))&
(![X]:(calm(X)<=>(~patient(X)|humble(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)<~>~strong(X))))&
(![X]:((kind(X)&~quiet(X))<=>(quiet(X)|~strong(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~humble(X)|~happy(X))))&
(![X]:(humble(X)=>generous(X)))&
(((~curious(fred)|curious(fred)))=>((~patient(susan)&~quiet(susan))))&
(![X]:((brave(X)<~>~kind(X))=>calm(X)))&
(((~quiet(john)<~>old(john)))=>(?[X]:(kind(X))))&
(((rich(lucy)<~>~strong(lucy)))<=>(?[X]:(~kind(X))))&
(![X]:(~happy(X)=>(creative(X)&~tall(X))))&
(![X]:((~curious(X)|tall(X))<=>~creative(X)))&
((strong(john)&~creative(john)))&
(?[X]:((~wise(X)|tall(X))))&
((generous(lucy)<~>happy(lucy)))&
(?[X]:((generous(X)|~old(X))))&
(brave(fred))&
((wise(alice)&~calm(alice)))&
(~generous(lucy))&
(?[X]:((brave(X)|~funny(X)))) | brave(lucy) | [
"p1",
"p2",
"p4",
"p7",
"p8",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 977630372086045786903560
% SZS output start Proof for 977630372086045786903560
2. ! [X0] : (happy(X0) <=> (~old(X0) | wise(X0))) [input p1]
3. ! [X0] : ((strong(X0) & quiet(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p2]
5. ! [X0] : ((~brave(X0) & calm(X0)) => (quiet(X0) & strong(X0))) [input p4]
8. ! [X0] : ((~quiet(X0) & kind(X0)) <=> (~strong(X0) | quiet(X0))) [input p7]
9. ! [X0] : ((~wise(X0) <~> generous(X0)) <=> (~happy(X0) | ~humble(X0))) [input p8]
19. generous(lucy) <~> happy(lucy) [input p18]
25. ~brave(lucy) [input hypothesis]
29. ! [X0] : ((quiet(X0) & strong(X0)) | (brave(X0) | ~calm(X0))) [ennf transformation 5]
30. ! [X0] : ((quiet(X0) & strong(X0)) | brave(X0) | ~calm(X0)) [flattening 29]
42. ! [X0] : ((happy(X0) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | ~happy(X0))) [nnf transformation 2]
43. ! [X0] : ((happy(X0) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | ~happy(X0))) [flattening 42]
44. ! [X0] : (((strong(X0) & quiet(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (~strong(X0) | ~quiet(X0)))) [nnf transformation 3]
45. ! [X0] : (((strong(X0) & quiet(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | ~strong(X0) | ~quiet(X0))) [flattening 44]
53. ! [X0] : (((~quiet(X0) & kind(X0)) | (strong(X0) & ~quiet(X0))) & ((~strong(X0) | quiet(X0)) | (quiet(X0) | ~kind(X0)))) [nnf transformation 8]
54. ! [X0] : (((~quiet(X0) & kind(X0)) | (strong(X0) & ~quiet(X0))) & (~strong(X0) | quiet(X0) | quiet(X0) | ~kind(X0))) [flattening 53]
55. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [flattening 55]
69. (~happy(lucy) | ~generous(lucy)) & (happy(lucy) | generous(lucy)) [nnf transformation 19]
79. ~wise(X0) | happy(X0) [cnf transformation 43]
84. generous(X0) | calm(X0) | quiet(X0) [cnf transformation 45]
90. ~calm(X0) | brave(X0) | quiet(X0) [cnf transformation 30]
99. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
106. ~generous(X0) | wise(X0) | happy(X0) [cnf transformation 56]
129. ~happy(lucy) | ~generous(lucy) [cnf transformation 69]
135. ~brave(lucy) [cnf transformation 25]
137. ~quiet(X0) [duplicate literal removal 99]
181. ~generous(X0) | happy(X0) [subsumption resolution 106,79]
231. ~generous(lucy) [subsumption resolution 129,181]
265. calm(lucy) | quiet(lucy) [resolution 84,231]
269. calm(lucy) [subsumption resolution 265,137]
303. brave(lucy) | quiet(lucy) [resolution 90,269]
306. quiet(lucy) [subsumption resolution 303,135]
307. $false [subsumption resolution 306,137]
% SZS output end Proof for 977630372086045786903560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either not curious or old.
If someone is both not rich and not generous then alice is not strong.
Everyone who is happy or not curious is either brave or not humble and vice versa.
If lucy is quiet or not wise then someone is not brave or kind.
Everyone who is not creative or quiet is both not creative and quiet and vice versa.
Everyone who is brave or not wise is both not rich and creative and vice versa.
Everyone who is curious is either curious or humble and vice versa.
If alice is either not creative or curious then mary is quiet.
If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa.
Everyone who is both calm and strong is both quiet and wise.
If lucy is both rich and not generous then paul is either creative or not tall and vice versa.
If someone is rich then paul is both not old and strong.
If someone is not creative or wise then fred is humble.
Everyone who is not kind or funny is either patient or tall and vice versa.
If alice is not patient then someone is brave.
Everyone who is either not funny or funny is either not kind or quiet and vice versa.
Lucy is both tall and brave.
Someone is calm or kind.
Someone is both calm and brave.
Someone is not funny. | Alice is not curious. | entailment | (![X]:(~old(X)=>(~curious(X)<~>old(X))))&
((?[X]:((~rich(X)&~generous(X))))=>(~strong(alice)))&
(![X]:((happy(X)|~curious(X))<=>(brave(X)<~>~humble(X))))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~kind(X)<~>quiet(X))))&
((tall(lucy)&brave(lucy)))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:(~funny(X))) | ~curious(alice) | [
"p4",
"p6",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 4969381292322038762154362
% SZS output start Proof for 4969381292322038762154362
5. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> (quiet(X0) & ~creative(X0))) [input p4]
7. ! [X0] : (curious(X0) <=> (curious(X0) <~> humble(X0))) [input p6]
8. (~creative(alice) <~> curious(alice)) => quiet(mary) [input p7]
13. ? [X0] : (wise(X0) | ~creative(X0)) => humble(fred) [input p12]
21. curious(alice) [input hypothesis]
25. quiet(mary) | (~creative(alice) <=> curious(alice)) [ennf transformation 8]
29. humble(fred) | ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 13]
36. ! [X0] : (((quiet(X0) | ~creative(X0)) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [nnf transformation 5]
37. ! [X0] : ((quiet(X0) | ~creative(X0) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [flattening 36]
40. ! [X0] : ((curious(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 7]
41. quiet(mary) | ((~creative(alice) | ~curious(alice)) & (curious(alice) | creative(alice))) [nnf transformation 25]
72. ~creative(X0) | ~quiet(X0) [cnf transformation 37]
82. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 40]
84. curious(X0) | curious(X0) | ~humble(X0) [cnf transformation 40]
86. quiet(mary) | ~creative(alice) | ~curious(alice) [cnf transformation 41]
103. humble(fred) | creative(X0) [cnf transformation 29]
126. curious(alice) [cnf transformation 21]
131. ~humble(X0) | ~curious(X0) [duplicate literal removal 82]
132. curious(X0) | ~humble(X0) [duplicate literal removal 84]
160. ~humble(X0) [subsumption resolution 131,132]
162. 7 <=> curious(alice) [avatar definition]
166. 8 <=> creative(alice) [avatar definition]
168. ~creative(alice) <- (~8) [avatar component clause 166]
170. 9 <=> quiet(mary) [avatar definition]
172. quiet(mary) <- (9) [avatar component clause 170]
173. ~7 | ~8 | 9 [avatar split clause 86,170,166,162]
224. creative(X0) [subsumption resolution 103,160]
245. 7 [avatar split clause 126,162]
248. $false <- (~8) [subsumption resolution 168,224]
249. 8 [avatar contradiction clause 248]
250. ~quiet(X0) [resolution 72,224]
251. $false <- (9) [resolution 250,172]
252. ~9 [avatar contradiction clause 251]
253. $false [avatar sat refutation 173,245,249,252]
% SZS output end Proof for 4969381292322038762154362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or strong is not quiet. If someone is not happy then lucy is both not patient and not generous and vice versa. Everyone who is tall is both not happy and rich and vice versa. Everyone who is both strong and happy is not wise or not quiet. If someone is either funny or curious then alice is both not generous and generous. Everyone who is generous is either not creative or not tall and vice versa. Everyone who is not tall or kind is not brave or old. Everyone who is both happy and brave is both patient and not patient and vice versa. Everyone who is not curious is both not kind and funny and vice versa. If paul is not old or not kind then mary is not rich or wise and vice versa. If someone is not curious or strong then john is either quiet or not wise. If lucy is either not tall or not curious then lucy is not kind and vice versa. If someone is both curious and not funny then lucy is both quiet and tall. Everyone who is either happy or patient is both patient and not humble. If paul is either tall or old then someone is patient. Someone is both humble and not quiet. Someone is either not old or wise. Paul is not happy or rich. John is either generous or humble. Mary is calm or generous. | John is creative. | neutral | (![X]:((wise(X)<~>strong(X))=>~quiet(X)))&
((?[X]:(~happy(X)))<=>((~patient(lucy)&~generous(lucy))))&
(![X]:(tall(X)<=>(~happy(X)&rich(X))))&
(![X]:((strong(X)&happy(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((funny(X)<~>curious(X))))=>((~generous(alice)&generous(alice))))&
(![X]:(generous(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~tall(X)|kind(X))=>(~brave(X)|old(X))))&
(![X]:((happy(X)&brave(X))<=>(patient(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~kind(X)&funny(X))))&
(((~old(paul)|~kind(paul)))<=>((~rich(mary)|wise(mary))))&
((?[X]:((~curious(X)|strong(X))))=>((quiet(john)<~>~wise(john))))&
(((~tall(lucy)<~>~curious(lucy)))<=>(~kind(lucy)))&
((?[X]:((curious(X)&~funny(X))))=>((quiet(lucy)&tall(lucy))))&
(![X]:((happy(X)<~>patient(X))=>(patient(X)&~humble(X))))&
(((tall(paul)<~>old(paul)))=>(?[X]:(patient(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((~old(X)<~>wise(X))))&
((~happy(paul)|rich(paul)))&
((generous(john)<~>humble(john)))&
((calm(mary)|generous(mary))) | creative(john) | []
| null | 0 |
Everyone who is creative is not humble and vice versa.
If someone is not tall or not humble then mary is both brave and curious and vice versa.
If fred is calm then someone is not quiet and vice versa.
Everyone who is both strong and not wise is not rich.
Everyone who is not creative is kind or quiet and vice versa.
Everyone who is both not happy and funny is either tall or brave and vice versa.
Everyone who is either old or not kind is creative.
Everyone who is both not quiet and not brave is both not quiet and curious and vice versa.
If paul is tall then fred is either old or creative.
Everyone who is not brave or curious is both strong and not kind.
Everyone who is humble or not generous is both not curious and happy.
If someone is not rich or patient then mary is brave.
Everyone who is either quiet or wise is not quiet and vice versa.
If fred is both not curious and not calm then someone is either not humble or not tall.
Everyone who is happy is either not generous or not rich.
If lucy is humble then someone is either creative or not generous and vice versa.
Mary is not brave or tall.
Someone is rich or not happy.
John is either not kind or patient. | Lucy is not tall. | contradiction | (![X]:(creative(X)<=>~humble(X)))&
((?[X]:((~tall(X)|~humble(X))))<=>((brave(mary)&curious(mary))))&
((calm(fred))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)&~wise(X))=>~rich(X)))&
(![X]:(~creative(X)<=>(kind(X)|quiet(X))))&
(![X]:((~happy(X)&funny(X))<=>(tall(X)<~>brave(X))))&
(![X]:((old(X)<~>~kind(X))=>creative(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(~quiet(X)&curious(X))))&
((tall(paul))=>((old(fred)<~>creative(fred))))&
(![X]:((~brave(X)|curious(X))=>(strong(X)&~kind(X))))&
(![X]:((humble(X)|~generous(X))=>(~curious(X)&happy(X))))&
((?[X]:((~rich(X)|patient(X))))=>(brave(mary)))&
(![X]:((quiet(X)<~>wise(X))<=>~quiet(X)))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(happy(X)=>(~generous(X)<~>~rich(X))))&
((humble(lucy))<=>(?[X]:((creative(X)<~>~generous(X)))))&
((~brave(mary)|tall(mary)))&
(?[X]:((rich(X)|~happy(X))))&
((~kind(john)<~>patient(john))) | ~tall(lucy) | [
"p0",
"p1",
"p4",
"p7",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 2132683282704294497816021
% SZS output start Proof for 2132683282704294497816021
1. ! [X0] : (creative(X0) <=> ~humble(X0)) [input p0]
2. ? [X0] : (~humble(X0) | ~tall(X0)) <=> (curious(mary) & brave(mary)) [input p1]
5. ! [X0] : (~creative(X0) <=> (quiet(X0) | kind(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (curious(X0) & ~quiet(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | humble(X0)) => (happy(X0) & ~curious(X0))) [input p10]
20. ~tall(lucy) [input hypothesis]
26. ! [X0] : ((happy(X0) & ~curious(X0)) | (generous(X0) & ~humble(X0))) [ennf transformation 11]
31. ! [X0] : ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))) [nnf transformation 1]
32. (? [X0] : (~humble(X0) | ~tall(X0)) | (~curious(mary) | ~brave(mary))) & ((curious(mary) & brave(mary)) | ! [X0] : (humble(X0) & tall(X0))) [nnf transformation 2]
33. (? [X0] : (~humble(X0) | ~tall(X0)) | ~curious(mary) | ~brave(mary)) & ((curious(mary) & brave(mary)) | ! [X0] : (humble(X0) & tall(X0))) [flattening 32]
34. (? [X0] : (~humble(X0) | ~tall(X0)) | ~curious(mary) | ~brave(mary)) & ((curious(mary) & brave(mary)) | ! [X1] : (humble(X1) & tall(X1))) [rectify 33]
35. ? [X0] : (~humble(X0) | ~tall(X0)) => (~humble(sK0) | ~tall(sK0)) [choice axiom]
36. ((~humble(sK0) | ~tall(sK0)) | ~curious(mary) | ~brave(mary)) & ((curious(mary) & brave(mary)) | ! [X1] : (humble(X1) & tall(X1))) [skolemisation 34,35]
41. ! [X0] : ((~creative(X0) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | creative(X0))) [nnf transformation 5]
42. ! [X0] : ((~creative(X0) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | creative(X0))) [flattening 41]
46. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | (brave(X0) | quiet(X0)))) [nnf transformation 8]
47. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | brave(X0) | quiet(X0))) [flattening 46]
62. humble(X0) | creative(X0) [cnf transformation 31]
63. brave(mary) | tall(X1) [cnf transformation 36]
65. curious(mary) | tall(X1) [cnf transformation 36]
73. ~quiet(X0) | ~creative(X0) [cnf transformation 42]
85. ~curious(X0) | ~brave(X0) | quiet(X0) [cnf transformation 47]
92. ~curious(X0) | ~humble(X0) [cnf transformation 26]
114. ~tall(lucy) [cnf transformation 20]
118. 1 <=> brave(mary) [avatar definition]
119. brave(mary) <- (1) [avatar component clause 118]
122. 2 <=> curious(mary) [avatar definition]
123. curious(mary) <- (2) [avatar component clause 122]
139. 6 <=> ! [X1] : tall(X1) [avatar definition]
140. tall(X1) <- (6) [avatar component clause 139]
141. 6 | 2 [avatar split clause 65,122,139]
143. 6 | 1 [avatar split clause 63,118,139]
242. $false <- (6) [resolution 140,114]
243. ~6 [avatar contradiction clause 242]
248. ~humble(mary) <- (2) [resolution 92,123]
254. creative(mary) <- (2) [resolution 248,62]
325. ~brave(mary) | quiet(mary) <- (2) [resolution 85,123]
332. quiet(mary) <- (1, 2) [subsumption resolution 325,119]
347. ~creative(mary) <- (1, 2) [resolution 332,73]
348. $false <- (1, 2) [subsumption resolution 347,254]
349. ~1 | ~2 [avatar contradiction clause 348]
350. $false [avatar sat refutation 141,143,243,349]
% SZS output end Proof for 2132683282704294497816021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or rich is not curious and vice versa. Everyone who is both not strong and rich is not patient or not humble and vice versa. Everyone who is kind or not patient is not creative or wise and vice versa. Everyone who is not old is either not calm or not wise and vice versa. Everyone who is wise is happy or brave and vice versa. Everyone who is both not generous and not quiet is not tall or not old. If someone is not wise then fred is both creative and not funny and vice versa. If alice is rich or not creative then fred is both not patient and brave and vice versa. If mary is both tall and not patient then someone is either not strong or not funny. If john is not patient or not rich then someone is both not kind and kind and vice versa. If someone is not wise then someone is either not calm or not quiet and vice versa. Everyone who is creative is both strong and not creative. If paul is either patient or not kind then someone is both tall and not creative. Everyone who is either not happy or rich is not calm or rich and vice versa. Everyone who is either humble or not humble is not humble. Paul is not kind or curious. John is quiet or not strong. Someone is happy. Someone is not strong. Susan is either humble or old. John is either old or not old. Mary is both tall and not kind. Someone is both generous and not quiet. | Paul is not creative. | entailment | (![X]:((wise(X)<~>rich(X))<=>~curious(X)))&
(![X]:((~strong(X)&rich(X))<=>(~patient(X)|~humble(X))))&
(![X]:((kind(X)|~patient(X))<=>(~creative(X)|wise(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>(strong(X)&~creative(X))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
(![X]:((humble(X)<~>~humble(X))=>~humble(X)))&
((~kind(paul)|curious(paul)))&
((quiet(john)|~strong(john)))&
(?[X]:(happy(X)))&
(?[X]:(~strong(X)))&
((humble(susan)<~>old(susan)))&
((old(john)<~>~old(john)))&
((tall(mary)&~kind(mary)))&
(?[X]:((generous(X)&~quiet(X)))) | ~creative(paul) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 2695763124671701971263222
% SZS output start Proof for 2695763124671701971263222
12. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p11]
24. creative(paul) [input hypothesis]
32. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 12]
115. ~creative(X0) | ~creative(X0) [cnf transformation 32]
139. creative(paul) [cnf transformation 24]
144. ~creative(X0) [duplicate literal removal 115]
271. $false [subsumption resolution 139,144]
% SZS output end Proof for 2695763124671701971263222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and happy is either rich or humble and vice versa.
Everyone who is both not strong and happy is either calm or patient.
If someone is either not quiet or humble then someone is both happy and old and vice versa.
Everyone who is both happy and not rich is not rich or not wise.
If mary is either happy or not wise then alice is both not curious and not wise and vice versa.
Everyone who is not wise is not kind and vice versa.
If someone is quiet or generous then lucy is both quiet and wise and vice versa.
Everyone who is not quiet or not brave is not happy and vice versa.
If someone is either not humble or humble then fred is not strong or strong and vice versa.
If john is not calm then mary is both creative and not kind and vice versa.
Everyone who is either not quiet or not curious is both calm and funny.
If mary is creative then someone is both not kind and wise and vice versa.
Everyone who is tall is either not old or not kind and vice versa.
If someone is happy then someone is both funny and brave and vice versa.
Everyone who is not humble is both quiet and not kind.
Everyone who is not calm is either creative or funny.
Someone is both strong and wise.
Someone is strong.
John is not kind.
Someone is tall.
Fred is both brave and not funny.
Alice is both patient and not wise.
Susan is either brave or happy.
Someone is quiet or funny. | Lucy is rich. | neutral | (![X]:((funny(X)&happy(X))<=>(rich(X)<~>humble(X))))&
(![X]:((~strong(X)&happy(X))=>(calm(X)<~>patient(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((happy(X)&~rich(X))=>(~rich(X)|~wise(X))))&
(((happy(mary)<~>~wise(mary)))<=>((~curious(alice)&~wise(alice))))&
(![X]:(~wise(X)<=>~kind(X)))&
((?[X]:((quiet(X)|generous(X))))<=>((quiet(lucy)&wise(lucy))))&
(![X]:((~quiet(X)|~brave(X))<=>~happy(X)))&
((?[X]:((~humble(X)<~>humble(X))))<=>((~strong(fred)|strong(fred))))&
((~calm(john))<=>((creative(mary)&~kind(mary))))&
(![X]:((~quiet(X)<~>~curious(X))=>(calm(X)&funny(X))))&
((creative(mary))<=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(tall(X)<=>(~old(X)<~>~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(~humble(X)=>(quiet(X)&~kind(X))))&
(![X]:(~calm(X)=>(creative(X)<~>funny(X))))&
(?[X]:((strong(X)&wise(X))))&
(?[X]:(strong(X)))&
(~kind(john))&
(?[X]:(tall(X)))&
((brave(fred)&~funny(fred)))&
((patient(alice)&~wise(alice)))&
((brave(susan)<~>happy(susan)))&
(?[X]:((quiet(X)|funny(X)))) | rich(lucy) | []
| null | 0 |
Everyone who is not wise or rich is both not humble and rich and vice versa.
If lucy is either not rich or strong then someone is either strong or kind and vice versa.
If lucy is quiet or not old then someone is humble or not calm.
If someone is old or rich then someone is either old or curious.
Everyone who is not tall is wise or quiet.
Everyone who is both not creative and not quiet is not strong or old and vice versa.
If someone is both not old and kind then someone is both not funny and funny.
If someone is either calm or kind then someone is curious and vice versa.
Everyone who is either brave or not strong is tall.
Everyone who is brave or wise is both strong and not strong and vice versa.
If mary is both not creative and not funny then someone is kind or funny.
Everyone who is either curious or strong is both strong and creative and vice versa.
If someone is either not generous or not happy then someone is either curious or quiet and vice versa.
If someone is humble then alice is both not generous and not calm and vice versa.
If someone is not calm then fred is either brave or humble and vice versa.
Everyone who is not patient or creative is both creative and not generous and vice versa.
Someone is calm.
Someone is either not curious or not humble.
Someone is quiet or creative.
Someone is both happy and not kind.
Lucy is tall. | Alice is generous. | neutral | (![X]:((~wise(X)|rich(X))<=>(~humble(X)&rich(X))))&
(((~rich(lucy)<~>strong(lucy)))<=>(?[X]:((strong(X)<~>kind(X)))))&
(((quiet(lucy)|~old(lucy)))=>(?[X]:((humble(X)|~calm(X)))))&
((?[X]:((old(X)|rich(X))))=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:(~tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|old(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)<~>~strong(X))=>tall(X)))&
(![X]:((brave(X)|wise(X))<=>(strong(X)&~strong(X))))&
(((~creative(mary)&~funny(mary)))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(strong(X)&creative(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:(humble(X)))<=>((~generous(alice)&~calm(alice))))&
((?[X]:(~calm(X)))<=>((brave(fred)<~>humble(fred))))&
(![X]:((~patient(X)|creative(X))<=>(creative(X)&~generous(X))))&
(?[X]:(calm(X)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((happy(X)&~kind(X))))&
(tall(lucy)) | generous(alice) | []
| null | 0 |
If someone is both generous and happy then mary is not curious.
If lucy is creative or not old then alice is patient.
If susan is wise then mary is both wise and brave.
If someone is both not wise and creative then mary is kind and vice versa.
Everyone who is not rich is not patient.
Everyone who is not happy or not curious is both tall and not curious and vice versa.
Everyone who is rich or not quiet is both happy and not happy and vice versa.
Everyone who is both not tall and not curious is either not generous or patient.
If susan is not old or not patient then someone is both brave and funny and vice versa.
Everyone who is strong is both calm and quiet.
Everyone who is not patient or not strong is not happy or happy.
If paul is both patient and old then paul is either not funny or quiet and vice versa.
Everyone who is not curious is rich or funny.
If lucy is patient then someone is both rich and funny.
Everyone who is either curious or brave is both not rich and not happy and vice versa.
Everyone who is curious is not humble.
Lucy is either kind or patient.
Someone is both happy and not rich.
Fred is kind.
Someone is kind or not wise.
Someone is either patient or brave.
Lucy is not tall or happy. | Paul is brave. | entailment | ((?[X]:((generous(X)&happy(X))))=>(~curious(mary)))&
(((creative(lucy)|~old(lucy)))=>(patient(alice)))&
((wise(susan))=>((wise(mary)&brave(mary))))&
((?[X]:((~wise(X)&creative(X))))<=>(kind(mary)))&
(![X]:(~rich(X)=>~patient(X)))&
(![X]:((~happy(X)|~curious(X))<=>(tall(X)&~curious(X))))&
(![X]:((rich(X)|~quiet(X))<=>(happy(X)&~happy(X))))&
(![X]:((~tall(X)&~curious(X))=>(~generous(X)<~>patient(X))))&
(((~old(susan)|~patient(susan)))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:(strong(X)=>(calm(X)&quiet(X))))&
(![X]:((~patient(X)|~strong(X))=>(~happy(X)|happy(X))))&
(((patient(paul)&old(paul)))<=>((~funny(paul)<~>quiet(paul))))&
(![X]:(~curious(X)=>(rich(X)|funny(X))))&
((patient(lucy))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((curious(X)<~>brave(X))<=>(~rich(X)&~happy(X))))&
(![X]:(curious(X)=>~humble(X)))&
((kind(lucy)<~>patient(lucy)))&
(?[X]:((happy(X)&~rich(X))))&
(kind(fred))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((patient(X)<~>brave(X))))&
((~tall(lucy)|happy(lucy))) | brave(paul) | [
"p4",
"p5",
"p6",
"p11",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1611316017696625680136620
% SZS output start Proof for 1611316017696625680136620
5. ! [X0] : (~rich(X0) => ~patient(X0)) [input p4]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (~curious(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (~happy(X0) & happy(X0))) [input p6]
12. (old(paul) & patient(paul)) <=> (~funny(paul) <~> quiet(paul)) [input p11]
13. ! [X0] : (~curious(X0) => (funny(X0) | rich(X0))) [input p12]
15. ! [X0] : ((curious(X0) <~> brave(X0)) <=> (~happy(X0) & ~rich(X0))) [input p14]
23. ~brave(paul) [input hypothesis]
29. ! [X0] : (~patient(X0) | rich(X0)) [ennf transformation 5]
35. ! [X0] : ((funny(X0) | rich(X0)) | curious(X0)) [ennf transformation 13]
36. ! [X0] : (funny(X0) | rich(X0) | curious(X0)) [flattening 35]
42. ! [X0] : (((~curious(X0) | ~happy(X0)) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 6]
43. ! [X0] : ((~curious(X0) | ~happy(X0) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | (curious(X0) & happy(X0)))) [flattening 42]
44. ! [X0] : (((~quiet(X0) | rich(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (quiet(X0) & ~rich(X0)))) [nnf transformation 7]
45. ! [X0] : ((~quiet(X0) | rich(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (quiet(X0) & ~rich(X0)))) [flattening 44]
52. ((old(paul) & patient(paul)) | ((~funny(paul) | ~quiet(paul)) & (quiet(paul) | funny(paul)))) & (((~quiet(paul) | funny(paul)) & (quiet(paul) | ~funny(paul))) | (~old(paul) | ~patient(paul))) [nnf transformation 12]
53. ((old(paul) & patient(paul)) | ((~funny(paul) | ~quiet(paul)) & (quiet(paul) | funny(paul)))) & (((~quiet(paul) | funny(paul)) & (quiet(paul) | ~funny(paul))) | ~old(paul) | ~patient(paul)) [flattening 52]
56. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [flattening 56]
74. ~patient(X0) | rich(X0) [cnf transformation 29]
77. ~curious(X0) | happy(X0) [cnf transformation 43]
80. happy(X0) | ~rich(X0) [cnf transformation 45]
81. happy(X0) | quiet(X0) [cnf transformation 45]
82. ~rich(X0) | ~happy(X0) [cnf transformation 45]
83. ~happy(X0) | quiet(X0) [cnf transformation 45]
98. patient(paul) | ~funny(paul) | ~quiet(paul) [cnf transformation 53]
101. funny(X0) | rich(X0) | curious(X0) [cnf transformation 36]
106. ~happy(X0) | brave(X0) | ~curious(X0) [cnf transformation 57]
119. ~brave(paul) [cnf transformation 23]
174. quiet(X0) [subsumption resolution 81,83]
175. ~rich(X0) [subsumption resolution 80,82]
202. 18 <=> funny(paul) [avatar definition]
204. ~funny(paul) <- (~18) [avatar component clause 202]
210. patient(paul) | ~funny(paul) [subsumption resolution 98,174]
212. 20 <=> patient(paul) [avatar definition]
214. patient(paul) <- (20) [avatar component clause 212]
215. ~18 | 20 [avatar split clause 210,212,202]
218. funny(X0) | curious(X0) [subsumption resolution 101,175]
232. ~curious(X0) | brave(X0) [subsumption resolution 106,77]
270. curious(paul) <- (~18) [resolution 218,204]
273. brave(paul) <- (~18) [resolution 232,270]
274. $false <- (~18) [subsumption resolution 273,119]
275. 18 [avatar contradiction clause 274]
276. rich(paul) <- (20) [resolution 214,74]
277. $false <- (20) [subsumption resolution 276,175]
278. ~20 [avatar contradiction clause 277]
279. $false [avatar sat refutation 215,275,278]
% SZS output end Proof for 1611316017696625680136620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and curious is not curious and vice versa.
Everyone who is not quiet is not kind or not curious.
Everyone who is happy is either curious or humble.
Everyone who is either curious or not happy is curious and vice versa.
If someone is both not kind and not curious then lucy is both not kind and not strong.
Everyone who is either generous or happy is humble or happy and vice versa.
If someone is both old and brave then alice is happy or not calm and vice versa.
Everyone who is not wise is either not funny or not quiet and vice versa.
Everyone who is either not strong or not wise is not kind.
If john is not happy then lucy is not old.
Everyone who is both generous and not creative is not wise and vice versa.
Everyone who is both not wise and not brave is either calm or not generous.
Everyone who is not brave is both humble and kind and vice versa.
If mary is both kind and strong then someone is both quiet and not quiet and vice versa.
Everyone who is both tall and calm is either not happy or not creative and vice versa.
Someone is both curious and not old.
Mary is not old.
Someone is brave.
Someone is old or funny.
Mary is tall.
Someone is not kind.
Fred is not quiet or not kind. | Mary is kind. | contradiction | (![X]:((~funny(X)&curious(X))<=>~curious(X)))&
(![X]:(~quiet(X)=>(~kind(X)|~curious(X))))&
(![X]:(happy(X)=>(curious(X)<~>humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>curious(X)))&
((?[X]:((~kind(X)&~curious(X))))=>((~kind(lucy)&~strong(lucy))))&
(![X]:((generous(X)<~>happy(X))<=>(humble(X)|happy(X))))&
((?[X]:((old(X)&brave(X))))<=>((happy(alice)|~calm(alice))))&
(![X]:(~wise(X)<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~strong(X)<~>~wise(X))=>~kind(X)))&
((~happy(john))=>(~old(lucy)))&
(![X]:((generous(X)&~creative(X))<=>~wise(X)))&
(![X]:((~wise(X)&~brave(X))=>(calm(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(((kind(mary)&strong(mary)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((tall(X)&calm(X))<=>(~happy(X)<~>~creative(X))))&
(?[X]:((curious(X)&~old(X))))&
(~old(mary))&
(?[X]:(brave(X)))&
(?[X]:((old(X)|funny(X))))&
(tall(mary))&
(?[X]:(~kind(X)))&
((~quiet(fred)|~kind(fred))) | kind(mary) | [
"p0",
"p3",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 9101371229075142706871259
% SZS output start Proof for 9101371229075142706871259
1. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~curious(X0)) [input p0]
4. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> curious(X0)) [input p3]
6. ! [X0] : ((generous(X0) <~> happy(X0)) <=> (happy(X0) | humble(X0))) [input p5]
9. ! [X0] : ((~strong(X0) <~> ~wise(X0)) => ~kind(X0)) [input p8]
11. ! [X0] : ((~creative(X0) & generous(X0)) <=> ~wise(X0)) [input p10]
14. (strong(mary) & kind(mary)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p13]
23. kind(mary) [input hypothesis]
28. ! [X0] : (~kind(X0) | (~strong(X0) <=> ~wise(X0))) [ennf transformation 9]
32. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 1]
33. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | funny(X0))) [flattening 32]
35. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 4]
36. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~happy(X0) & ~humble(X0))) & ((happy(X0) | humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 6]
37. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~happy(X0) & ~humble(X0))) & (happy(X0) | humble(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [flattening 36]
44. ! [X0] : (~kind(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) [nnf transformation 28]
45. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) | ~generous(X0)))) [nnf transformation 11]
46. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | creative(X0) | ~generous(X0))) [flattening 45]
50. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X0] : (~quiet(X0) & quiet(X0)) | (~strong(mary) | ~kind(mary))) [nnf transformation 14]
51. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X0] : (~quiet(X0) & quiet(X0)) | ~strong(mary) | ~kind(mary)) [flattening 50]
52. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ~strong(mary) | ~kind(mary)) [rectify 51]
53. ? [X1] : (~quiet(X1) & quiet(X1)) => (~quiet(sK1) & quiet(sK1)) [choice axiom]
54. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & ((~quiet(sK1) & quiet(sK1)) | ~strong(mary) | ~kind(mary)) [skolemisation 52,53]
67. curious(X0) | curious(X0) [cnf transformation 33]
74. happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 35]
82. ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 37]
92. ~wise(X0) | ~kind(X0) | strong(X0) [cnf transformation 44]
96. generous(X0) | wise(X0) [cnf transformation 46]
103. quiet(sK1) | ~strong(mary) | ~kind(mary) [cnf transformation 54]
104. ~quiet(sK1) | ~strong(mary) | ~kind(mary) [cnf transformation 54]
121. kind(mary) [cnf transformation 23]
123. ~happy(X0) | ~generous(X0) [duplicate literal removal 82]
125. happy(X0) | ~curious(X0) [duplicate literal removal 74]
127. curious(X0) [duplicate literal removal 67]
131. happy(X0) [subsumption resolution 125,127]
132. ~generous(X0) [subsumption resolution 123,131]
153. wise(X0) [subsumption resolution 96,132]
155. 4 <=> kind(mary) [avatar definition]
156. kind(mary) <- (4) [avatar component clause 155]
159. 5 <=> strong(mary) [avatar definition]
161. ~strong(mary) <- (~5) [avatar component clause 159]
163. 6 <=> quiet(sK1) [avatar definition]
166. ~4 | ~5 | ~6 [avatar split clause 104,163,159,155]
167. ~4 | ~5 | 6 [avatar split clause 103,163,159,155]
172. 4 [avatar split clause 121,155]
178. ~kind(X0) | strong(X0) [resolution 92,153]
179. strong(mary) <- (4) [resolution 178,156]
180. $false <- (4, ~5) [subsumption resolution 179,161]
181. ~4 | 5 [avatar contradiction clause 180]
182. $false [avatar sat refutation 166,167,172,181]
% SZS output end Proof for 9101371229075142706871259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is patient then someone is not curious or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Everyone who is both not happy and funny is either old or not creative.
If someone is tall or not quiet then paul is both not strong and not old and vice versa.
If susan is tall then someone is calm.
Everyone who is tall or rich is either not calm or rich.
If lucy is either quiet or not generous then susan is both strong and not old.
Everyone who is both humble and not old is both not old and rich and vice versa.
Everyone who is either patient or not humble is not old or curious and vice versa.
Everyone who is funny is both not brave and not wise and vice versa.
If someone is tall then someone is not strong and vice versa.
Everyone who is either not patient or creative is both not calm and rich.
If someone is either wise or not happy then paul is rich or tall.
Everyone who is either not kind or not humble is both curious and not creative and vice versa.
Everyone who is patient is both not generous and kind.
Everyone who is both not humble and tall is either not quiet or not happy and vice versa.
Someone is either not old or rich.
Paul is both not humble and rich.
Susan is both quiet and not brave.
Someone is either creative or tall.
Someone is either not creative or curious.
Someone is either not humble or kind. | Paul is not patient. | entailment | ((patient(fred))<=>(?[X]:((~curious(X)|curious(X)))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
(![X]:((~happy(X)&funny(X))=>(old(X)<~>~creative(X))))&
((?[X]:((tall(X)|~quiet(X))))<=>((~strong(paul)&~old(paul))))&
((tall(susan))=>(?[X]:(calm(X))))&
(![X]:((tall(X)|rich(X))=>(~calm(X)<~>rich(X))))&
(((quiet(lucy)<~>~generous(lucy)))=>((strong(susan)&~old(susan))))&
(![X]:((humble(X)&~old(X))<=>(~old(X)&rich(X))))&
(![X]:((patient(X)<~>~humble(X))<=>(~old(X)|curious(X))))&
(![X]:(funny(X)<=>(~brave(X)&~wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>((rich(paul)|tall(paul))))&
(![X]:((~kind(X)<~>~humble(X))<=>(curious(X)&~creative(X))))&
(![X]:(patient(X)=>(~generous(X)&kind(X))))&
(![X]:((~humble(X)&tall(X))<=>(~quiet(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((~humble(paul)&rich(paul)))&
((quiet(susan)&~brave(susan)))&
(?[X]:((creative(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p5",
"p7",
"p8",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7148278540211036073322882
% SZS output start Proof for 7148278540211036073322882
1. patient(fred) <=> ? [X0] : (curious(X0) | ~curious(X0)) [input p0]
2. (calm(fred) | old(fred)) <=> curious(paul) [input p1]
6. ! [X0] : ((rich(X0) | tall(X0)) => (~calm(X0) <~> rich(X0))) [input p5]
8. ! [X0] : ((~old(X0) & humble(X0)) <=> (rich(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> ~humble(X0)) <=> (curious(X0) | ~old(X0))) [input p8]
18. rich(paul) & ~humble(paul) [input p17]
23. patient(paul) [input hypothesis]
29. ! [X0] : ((~calm(X0) <~> rich(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 6]
37. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X0] : (curious(X0) | ~curious(X0)) | ~patient(fred)) [nnf transformation 1]
38. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X1] : (curious(X1) | ~curious(X1)) | ~patient(fred)) [rectify 37]
39. ? [X1] : (curious(X1) | ~curious(X1)) => (curious(sK0) | ~curious(sK0)) [choice axiom]
40. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & ((curious(sK0) | ~curious(sK0)) | ~patient(fred)) [skolemisation 38,39]
41. ((calm(fred) | old(fred)) | ~curious(paul)) & (curious(paul) | (~calm(fred) & ~old(fred))) [nnf transformation 2]
42. (calm(fred) | old(fred) | ~curious(paul)) & (curious(paul) | (~calm(fred) & ~old(fred))) [flattening 41]
51. ! [X0] : (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~rich(X0) & ~tall(X0))) [nnf transformation 29]
53. ! [X0] : (((~old(X0) & humble(X0)) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | (old(X0) | ~humble(X0)))) [nnf transformation 8]
54. ! [X0] : (((~old(X0) & humble(X0)) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | old(X0) | ~humble(X0))) [flattening 53]
55. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (~curious(X0) & old(X0))) & ((curious(X0) | ~old(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [nnf transformation 9]
56. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (~curious(X0) & old(X0))) & (curious(X0) | ~old(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [flattening 55]
81. patient(fred) | curious(X0) [cnf transformation 40]
82. patient(fred) | ~curious(X0) [cnf transformation 40]
83. curious(paul) | ~old(fred) [cnf transformation 42]
84. curious(paul) | ~calm(fred) [cnf transformation 42]
97. ~rich(X0) | calm(X0) | ~rich(X0) [cnf transformation 51]
103. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 54]
110. ~patient(X0) | humble(X0) | old(X0) [cnf transformation 56]
111. ~curious(X0) | ~patient(X0) | humble(X0) [cnf transformation 56]
137. ~humble(paul) [cnf transformation 18]
147. patient(paul) [cnf transformation 23]
148. ~rich(X0) | calm(X0) [duplicate literal removal 97]
150. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
151. ~curious(X0) <- (1) [avatar component clause 150]
153. 2 <=> patient(fred) [avatar definition]
155. patient(fred) <- (2) [avatar component clause 153]
156. 1 | 2 [avatar split clause 82,153,150]
158. 3 <=> ! [X0] : curious(X0) [avatar definition]
159. curious(X0) <- (3) [avatar component clause 158]
160. 3 | 2 [avatar split clause 81,153,158]
162. 4 <=> curious(paul) [avatar definition]
163. curious(paul) <- (4) [avatar component clause 162]
166. 5 <=> old(fred) [avatar definition]
167. ~old(fred) <- (~5) [avatar component clause 166]
170. 6 <=> calm(fred) [avatar definition]
171. ~calm(fred) <- (~6) [avatar component clause 170]
174. ~6 | 4 [avatar split clause 84,162,170]
175. ~5 | 4 [avatar split clause 83,162,166]
331. humble(fred) | old(fred) <- (2) [resolution 110,155]
332. humble(fred) <- (2, ~5) [subsumption resolution 331,167]
335. old(fred) | rich(fred) <- (2, ~5) [resolution 332,103]
336. rich(fred) <- (2, ~5) [subsumption resolution 335,167]
338. calm(fred) <- (2, ~5) [resolution 336,148]
339. $false <- (2, ~5, ~6) [subsumption resolution 338,171]
340. ~2 | 5 | 6 [avatar contradiction clause 339]
341. $false <- (1, 3) [subsumption resolution 151,159]
342. ~1 | ~3 [avatar contradiction clause 341]
352. ~patient(paul) | humble(paul) <- (4) [resolution 163,111]
353. humble(paul) <- (4) [subsumption resolution 352,147]
354. $false <- (4) [subsumption resolution 353,137]
355. ~4 [avatar contradiction clause 354]
356. $false [avatar sat refutation 156,160,174,175,340,342,355]
% SZS output end Proof for 7148278540211036073322882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is funny.
If someone is either not kind or not brave then lucy is not patient or not calm and vice versa.
Everyone who is both not wise and strong is either not creative or not humble.
Everyone who is not calm is both curious and calm.
If someone is not old then someone is both not wise and tall and vice versa.
If fred is either not wise or not happy then someone is either funny or not quiet.
Everyone who is both strong and funny is not tall or happy and vice versa.
Everyone who is either not funny or old is both not calm and brave.
Everyone who is both not happy and not kind is either patient or tall and vice versa.
Everyone who is either not rich or quiet is either curious or calm.
If fred is both brave and happy then fred is not humble.
Everyone who is funny or wise is curious.
Everyone who is both not patient and not old is not kind and vice versa.
If someone is either rich or not old then someone is wise or humble and vice versa.
Everyone who is funny or creative is patient.
Everyone who is both not brave and curious is both curious and creative and vice versa.
Lucy is patient.
Someone is calm or not creative.
Paul is both not quiet and strong.
Lucy is both calm and patient.
Mary is either kind or strong.
Susan is curious or not wise.
Someone is kind or not patient.
Lucy is not creative or not tall. | Susan is patient. | entailment | (![X]:(~old(X)=>funny(X)))&
((?[X]:((~kind(X)<~>~brave(X))))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((~wise(X)&strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~calm(X)=>(curious(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(curious(X)<~>calm(X))))&
(((brave(fred)&happy(fred)))=>(~humble(fred)))&
(![X]:((funny(X)|wise(X))=>curious(X)))&
(![X]:((~patient(X)&~old(X))<=>~kind(X)))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((funny(X)|creative(X))=>patient(X)))&
(![X]:((~brave(X)&curious(X))<=>(curious(X)&creative(X))))&
(patient(lucy))&
(?[X]:((calm(X)|~creative(X))))&
((~quiet(paul)&strong(paul)))&
((calm(lucy)&patient(lucy)))&
((kind(mary)<~>strong(mary)))&
((curious(susan)|~wise(susan)))&
(?[X]:((kind(X)|~patient(X))))&
((~creative(lucy)|~tall(lucy))) | patient(susan) | [
"p0",
"p6",
"p8",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1522738893254243490542730
% SZS output start Proof for 1522738893254243490542730
1. ! [X0] : (~old(X0) => funny(X0)) [input p0]
7. ! [X0] : ((funny(X0) & strong(X0)) <=> (happy(X0) | ~tall(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (patient(X0) <~> tall(X0))) [input p8]
13. ! [X0] : ((~old(X0) & ~patient(X0)) <=> ~kind(X0)) [input p12]
15. ! [X0] : ((creative(X0) | funny(X0)) => patient(X0)) [input p14]
25. ~patient(susan) [input hypothesis]
28. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 1]
38. ! [X0] : (patient(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 15]
53. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0)))) [nnf transformation 7]
54. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0))) [flattening 53]
56. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 9]
57. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | kind(X0) | happy(X0))) [flattening 56]
59. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | (old(X0) | patient(X0)))) [nnf transformation 13]
60. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | old(X0) | patient(X0))) [flattening 59]
73. funny(X0) | old(X0) [cnf transformation 28]
94. tall(X0) | funny(X0) [cnf transformation 54]
105. ~tall(X0) | patient(X0) | ~kind(X0) [cnf transformation 57]
114. ~patient(X0) | kind(X0) [cnf transformation 60]
115. ~old(X0) | kind(X0) [cnf transformation 60]
122. ~funny(X0) | patient(X0) [cnf transformation 38]
139. ~patient(susan) [cnf transformation 25]
287. patient(X0) | old(X0) [resolution 122,73]
322. patient(X0) | ~kind(X0) | funny(X0) [resolution 105,94]
348. ~kind(X0) | patient(X0) [subsumption resolution 322,122]
502. old(X1) | kind(X1) [resolution 287,114]
504. kind(X1) [subsumption resolution 502,115]
522. patient(X1) [resolution 504,348]
547. $false [resolution 522,139]
% SZS output end Proof for 1522738893254243490542730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or strong is funny or old and vice versa.
If fred is either funny or humble then someone is rich or not brave.
Everyone who is not wise is both not rich and curious.
If mary is quiet then john is not rich.
If alice is not quiet or quiet then someone is not patient or not quiet and vice versa.
Everyone who is either not humble or not kind is both not tall and not quiet and vice versa.
Everyone who is not old is not funny.
Everyone who is brave is either not funny or curious and vice versa.
Everyone who is either not quiet or not strong is strong.
Everyone who is not old or humble is not kind and vice versa.
If someone is wise or humble then someone is rich and vice versa.
If susan is not creative or humble then someone is not generous or quiet and vice versa.
Everyone who is either not calm or not generous is both not tall and not old and vice versa.
If mary is both quiet and rich then john is both not kind and not patient and vice versa.
If someone is both not brave and old then someone is not humble and vice versa.
Everyone who is quiet is both not patient and not calm and vice versa.
Someone is either rich or humble.
Someone is both brave and not humble.
John is either creative or not strong.
Alice is calm.
Alice is funny.
Susan is both creative and not kind.
Paul is either not generous or not calm.
Someone is not happy. | Fred is not quiet. | entailment | (![X]:((creative(X)|strong(X))<=>(funny(X)|old(X))))&
(((funny(fred)<~>humble(fred)))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:(~wise(X)=>(~rich(X)&curious(X))))&
((quiet(mary))=>(~rich(john)))&
(((~quiet(alice)|quiet(alice)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~tall(X)&~quiet(X))))&
(![X]:(~old(X)=>~funny(X)))&
(![X]:(brave(X)<=>(~funny(X)<~>curious(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>strong(X)))&
(![X]:((~old(X)|humble(X))<=>~kind(X)))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:(rich(X))))&
(((~creative(susan)|humble(susan)))<=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~tall(X)&~old(X))))&
(((quiet(mary)&rich(mary)))<=>((~kind(john)&~patient(john))))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:(~humble(X))))&
(![X]:(quiet(X)<=>(~patient(X)&~calm(X))))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((brave(X)&~humble(X))))&
((creative(john)<~>~strong(john)))&
(calm(alice))&
(funny(alice))&
((creative(susan)&~kind(susan)))&
((~generous(paul)<~>~calm(paul)))&
(?[X]:(~happy(X))) | ~quiet(fred) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 5921391008544419688210832
% SZS output start Proof for 5921391008544419688210832
1. ! [X0] : ((strong(X0) | creative(X0)) <=> (old(X0) | funny(X0))) [input p0]
6. ! [X0] : ((~humble(X0) <~> ~kind(X0)) <=> (~quiet(X0) & ~tall(X0))) [input p5]
7. ! [X0] : (~old(X0) => ~funny(X0)) [input p6]
9. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) => strong(X0)) [input p8]
10. ! [X0] : ((humble(X0) | ~old(X0)) <=> ~kind(X0)) [input p9]
25. quiet(fred) [input hypothesis]
32. ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 7]
33. ! [X0] : (strong(X0) | (~quiet(X0) <=> ~strong(X0))) [ennf transformation 9]
34. ! [X0] : (((strong(X0) | creative(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (~strong(X0) & ~creative(X0)))) [nnf transformation 1]
35. ! [X0] : ((strong(X0) | creative(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | (~strong(X0) & ~creative(X0)))) [flattening 34]
44. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [nnf transformation 6]
45. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [flattening 44]
47. ! [X0] : (strong(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) [nnf transformation 33]
48. ! [X0] : (((humble(X0) | ~old(X0)) | kind(X0)) & (~kind(X0) | (~humble(X0) & old(X0)))) [nnf transformation 10]
49. ! [X0] : ((humble(X0) | ~old(X0) | kind(X0)) & (~kind(X0) | (~humble(X0) & old(X0)))) [flattening 48]
79. ~strong(X0) | funny(X0) | old(X0) [cnf transformation 35]
93. ~kind(X0) | ~quiet(X0) | humble(X0) [cnf transformation 45]
94. ~quiet(X0) | ~humble(X0) | kind(X0) [cnf transformation 45]
97. ~funny(X0) | old(X0) [cnf transformation 32]
103. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 47]
105. ~kind(X0) | ~humble(X0) [cnf transformation 49]
106. ~old(X0) | humble(X0) | kind(X0) [cnf transformation 49]
142. quiet(fred) [cnf transformation 25]
143. ~quiet(X0) | strong(X0) [duplicate literal removal 103]
145. 1 <=> humble(fred) [avatar definition]
147. ~humble(fred) <- (~1) [avatar component clause 145]
314. strong(fred) [resolution 143,142]
317. funny(fred) | old(fred) [resolution 79,314]
318. old(fred) [subsumption resolution 317,97]
349. ~humble(fred) | kind(fred) [resolution 94,142]
350. ~humble(fred) [subsumption resolution 349,105]
351. ~1 [avatar split clause 350,145]
368. humble(fred) | kind(fred) [resolution 106,318]
372. kind(fred) <- (~1) [subsumption resolution 368,147]
557. ~quiet(fred) | humble(fred) <- (~1) [resolution 372,93]
560. humble(fred) <- (~1) [subsumption resolution 557,142]
561. $false <- (~1) [subsumption resolution 560,147]
562. 1 [avatar contradiction clause 561]
563. $false [avatar sat refutation 351,562]
% SZS output end Proof for 5921391008544419688210832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or curious is old or rich and vice versa.
Everyone who is not creative or not curious is either not tall or tall.
If someone is patient then mary is happy or rich.
If someone is not wise then fred is both funny and not tall and vice versa.
If someone is not patient then susan is quiet or not funny and vice versa.
Everyone who is curious is not tall or not happy and vice versa.
If mary is both not quiet and strong then someone is not quiet.
Everyone who is either not quiet or tall is both old and funny and vice versa.
If someone is either rich or not old then mary is either not humble or not happy.
If someone is not quiet then paul is brave and vice versa.
Everyone who is either not patient or humble is either not kind or not tall.
If alice is both not kind and not patient then someone is not quiet.
Everyone who is not rich or not curious is either not curious or tall and vice versa.
Everyone who is either not old or quiet is both not rich and not generous and vice versa.
Everyone who is either not rich or not brave is humble.
Everyone who is old is happy.
Someone is kind or old.
Someone is generous or not rich.
Paul is not kind or kind.
Someone is not tall or not creative.
Paul is happy or rich. | Susan is not brave. | neutral | (![X]:((old(X)<~>curious(X))<=>(old(X)|rich(X))))&
(![X]:((~creative(X)|~curious(X))=>(~tall(X)<~>tall(X))))&
((?[X]:(patient(X)))=>((happy(mary)|rich(mary))))&
((?[X]:(~wise(X)))<=>((funny(fred)&~tall(fred))))&
((?[X]:(~patient(X)))<=>((quiet(susan)|~funny(susan))))&
(![X]:(curious(X)<=>(~tall(X)|~happy(X))))&
(((~quiet(mary)&strong(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(old(X)&funny(X))))&
((?[X]:((rich(X)<~>~old(X))))=>((~humble(mary)<~>~happy(mary))))&
((?[X]:(~quiet(X)))<=>(brave(paul)))&
(![X]:((~patient(X)<~>humble(X))=>(~kind(X)<~>~tall(X))))&
(((~kind(alice)&~patient(alice)))=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)|~curious(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(~rich(X)&~generous(X))))&
(![X]:((~rich(X)<~>~brave(X))=>humble(X)))&
(![X]:(old(X)=>happy(X)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((generous(X)|~rich(X))))&
((~kind(paul)|kind(paul)))&
(?[X]:((~tall(X)|~creative(X))))&
((happy(paul)|rich(paul))) | ~brave(susan) | []
| null | 0 |
Everyone who is not strong or creative is wise and vice versa.
Everyone who is strong or curious is kind and vice versa.
If john is not happy then someone is both not creative and creative.
Everyone who is either not generous or not calm is either strong or old.
Everyone who is not tall is both not calm and not happy.
If someone is either strong or not patient then someone is either not tall or humble.
Everyone who is not creative or old is curious or not wise and vice versa.
If mary is not kind then john is either not funny or strong.
If john is either not brave or not humble then someone is both not strong and old and vice versa.
Everyone who is not wise or old is either not strong or patient and vice versa.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is not humble is either patient or not kind and vice versa.
If someone is both not kind and not strong then someone is both not calm and not generous and vice versa.
Everyone who is either wise or not old is both curious and not quiet.
If someone is either quiet or happy then someone is either not patient or not quiet.
Susan is brave or not quiet.
Someone is both wise and not quiet.
Susan is not old or funny.
Someone is both creative and not funny.
Someone is both not curious and calm.
Susan is wise or patient. | John is quiet. | neutral | (![X]:((~strong(X)|creative(X))<=>wise(X)))&
(![X]:((strong(X)|curious(X))<=>kind(X)))&
((~happy(john))=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((~generous(X)<~>~calm(X))=>(strong(X)<~>old(X))))&
(![X]:(~tall(X)=>(~calm(X)&~happy(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((~creative(X)|old(X))<=>(curious(X)|~wise(X))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
((brave(susan)|~quiet(susan)))&
(?[X]:((wise(X)&~quiet(X))))&
((~old(susan)|funny(susan)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~curious(X)&calm(X))))&
((wise(susan)|patient(susan))) | quiet(john) | []
| null | 0 |
Everyone who is wise is not quiet or not humble.
If alice is both not generous and kind then someone is patient.
If susan is patient then someone is not rich.
If someone is either creative or not calm then lucy is both happy and generous and vice versa.
Everyone who is not quiet or creative is either humble or not humble and vice versa.
Everyone who is happy or humble is both not humble and not strong.
If susan is happy then someone is both not brave and not curious.
If john is generous or calm then someone is either generous or rich.
Everyone who is tall or not curious is not creative.
If someone is both calm and rich then alice is humble.
If susan is not calm or not creative then someone is not kind or not funny.
If someone is not wise then someone is brave.
Everyone who is calm or generous is both brave and calm and vice versa.
If john is either not quiet or not happy then lucy is either creative or funny and vice versa.
If someone is not funny then john is both not wise and not strong and vice versa.
If susan is not old then alice is either quiet or not tall.
Someone is patient.
Someone is not creative.
Fred is both tall and rich.
Someone is strong or not tall.
Someone is not wise or not calm.
Someone is creative or not creative.
Someone is not strong.
Someone is not calm or old. | Alice is not humble. | entailment | (![X]:(wise(X)=>(~quiet(X)|~humble(X))))&
(((~generous(alice)&kind(alice)))=>(?[X]:(patient(X))))&
((patient(susan))=>(?[X]:(~rich(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>((happy(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|creative(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((happy(X)|humble(X))=>(~humble(X)&~strong(X))))&
((happy(susan))=>(?[X]:((~brave(X)&~curious(X)))))&
(((generous(john)|calm(john)))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~curious(X))=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))=>(humble(alice)))&
(((~calm(susan)|~creative(susan)))=>(?[X]:((~kind(X)|~funny(X)))))&
((?[X]:(~wise(X)))=>(?[X]:(brave(X))))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&calm(X))))&
(((~quiet(john)<~>~happy(john)))<=>((creative(lucy)<~>funny(lucy))))&
((?[X]:(~funny(X)))<=>((~wise(john)&~strong(john))))&
((~old(susan))=>((quiet(alice)<~>~tall(alice))))&
(?[X]:(patient(X)))&
(?[X]:(~creative(X)))&
((tall(fred)&rich(fred)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)|old(X)))) | ~humble(alice) | [
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 184674605161953028579279
% SZS output start Proof for 184674605161953028579279
6. ! [X0] : ((humble(X0) | happy(X0)) => (~strong(X0) & ~humble(X0))) [input p5]
25. humble(alice) [input hypothesis]
34. ! [X0] : ((~strong(X0) & ~humble(X0)) | (~humble(X0) & ~happy(X0))) [ennf transformation 6]
92. ~humble(X0) | ~humble(X0) [cnf transformation 34]
129. humble(alice) [cnf transformation 25]
130. ~humble(X0) [duplicate literal removal 92]
274. $false [subsumption resolution 129,130]
% SZS output end Proof for 184674605161953028579279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both quiet and patient then someone is not humble and vice versa.
If fred is not tall then someone is not kind or not generous.
Everyone who is not kind is either not patient or old.
Everyone who is strong or funny is both strong and kind.
If someone is either not calm or not rich then someone is not generous.
If someone is both not calm and creative then mary is both humble and not patient.
If someone is both not old and tall then someone is both calm and not creative.
Everyone who is not rich or old is not old and vice versa.
If someone is not creative then someone is both not old and not wise and vice versa.
Everyone who is both quiet and not curious is not kind and vice versa.
Everyone who is both old and not generous is both calm and humble.
Everyone who is not patient is both not quiet and quiet.
Everyone who is both happy and calm is humble and vice versa.
Everyone who is either not generous or not rich is both not funny and not creative and vice versa.
Everyone who is both not humble and old is either wise or brave and vice versa.
If someone is both brave and not wise then john is funny and vice versa.
John is not creative or not patient.
Someone is kind.
Someone is not humble.
Lucy is either not old or quiet.
Mary is either old or strong.
Alice is happy or not patient.
Fred is both not calm and quiet. | Lucy is kind. | entailment | (((quiet(susan)&patient(susan)))<=>(?[X]:(~humble(X))))&
((~tall(fred))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>old(X))))&
(![X]:((strong(X)|funny(X))=>(strong(X)&kind(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~calm(X)&creative(X))))=>((humble(mary)&~patient(mary))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((~rich(X)|old(X))<=>~old(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((quiet(X)&~curious(X))<=>~kind(X)))&
(![X]:((old(X)&~generous(X))=>(calm(X)&humble(X))))&
(![X]:(~patient(X)=>(~quiet(X)&quiet(X))))&
(![X]:((happy(X)&calm(X))<=>humble(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~funny(X)&~creative(X))))&
(![X]:((~humble(X)&old(X))<=>(wise(X)<~>brave(X))))&
((?[X]:((brave(X)&~wise(X))))<=>(funny(john)))&
((~creative(john)|~patient(john)))&
(?[X]:(kind(X)))&
(?[X]:(~humble(X)))&
((~old(lucy)<~>quiet(lucy)))&
((old(mary)<~>strong(mary)))&
((happy(alice)|~patient(alice)))&
((~calm(fred)&quiet(fred))) | kind(lucy) | [
"p7",
"p9",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 1624793893705112846238614
% SZS output start Proof for 1624793893705112846238614
8. ! [X0] : ((old(X0) | ~rich(X0)) <=> ~old(X0)) [input p7]
10. ! [X0] : ((~curious(X0) & quiet(X0)) <=> ~kind(X0)) [input p9]
20. ~old(lucy) <~> quiet(lucy) [input p19]
24. ~kind(lucy) [input hypothesis]
52. ! [X0] : (((old(X0) | ~rich(X0)) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [nnf transformation 8]
53. ! [X0] : ((old(X0) | ~rich(X0) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [flattening 52]
59. ! [X0] : (((~curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) | ~quiet(X0)))) [nnf transformation 10]
60. ! [X0] : (((~curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | curious(X0) | ~quiet(X0))) [flattening 59]
75. (~quiet(lucy) | old(lucy)) & (quiet(lucy) | ~old(lucy)) [nnf transformation 20]
94. ~old(X0) | ~old(X0) [cnf transformation 53]
100. kind(X0) | quiet(X0) [cnf transformation 60]
128. ~quiet(lucy) | old(lucy) [cnf transformation 75]
134. ~kind(lucy) [cnf transformation 24]
135. ~old(X0) [duplicate literal removal 94]
241. ~quiet(lucy) [subsumption resolution 128,135]
246. quiet(lucy) [resolution 100,134]
248. $false [subsumption resolution 246,241]
% SZS output end Proof for 1624793893705112846238614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall or funny then mary is not funny and vice versa. If someone is either not wise or not rich then susan is quiet. If someone is not quiet or tall then someone is kind or wise and vice versa. Everyone who is curious or generous is both not rich and not humble and vice versa. If someone is both not happy and happy then john is not curious or funny. Everyone who is not creative or not patient is happy or humble. Everyone who is both not curious and strong is either not humble or not quiet. If lucy is either tall or not patient then susan is strong or brave and vice versa. If someone is not tall then someone is brave or not quiet. Everyone who is generous is either humble or old. Everyone who is not rich or not generous is either curious or strong. If mary is not kind then fred is generous or not wise and vice versa. Everyone who is either not brave or calm is not calm and vice versa. If someone is patient or not creative then mary is creative. Everyone who is not creative is either curious or creative and vice versa. If someone is humble then susan is either not old or not rich and vice versa. Someone is not happy. Someone is not funny. Susan is either not creative or not generous. Someone is not old or old. Someone is both funny and not quiet. Someone is rich or not old. Someone is either funny or not funny. | John is quiet. | neutral | (((~tall(alice)|funny(alice)))<=>(~funny(mary)))&
((?[X]:((~wise(X)<~>~rich(X))))=>(quiet(susan)))&
((?[X]:((~quiet(X)|tall(X))))<=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((curious(X)|generous(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~happy(X)&happy(X))))=>((~curious(john)|funny(john))))&
(![X]:((~creative(X)|~patient(X))=>(happy(X)|humble(X))))&
(![X]:((~curious(X)&strong(X))=>(~humble(X)<~>~quiet(X))))&
(((tall(lucy)<~>~patient(lucy)))<=>((strong(susan)|brave(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(generous(X)=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|~generous(X))=>(curious(X)<~>strong(X))))&
((~kind(mary))<=>((generous(fred)|~wise(fred))))&
(![X]:((~brave(X)<~>calm(X))<=>~calm(X)))&
((?[X]:((patient(X)|~creative(X))))=>(creative(mary)))&
(![X]:(~creative(X)<=>(curious(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~old(susan)<~>~rich(susan))))&
(?[X]:(~happy(X)))&
(?[X]:(~funny(X)))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((funny(X)<~>~funny(X)))) | quiet(john) | []
| null | 0 |
Everyone who is both not strong and not rich is not happy or not strong.
If someone is both quiet and not strong then alice is both not old and brave.
Everyone who is not funny or not humble 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.
Everyone who is not humble or not tall is both old and not humble and vice versa.
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.
Someone is both not happy and kind. | Susan is patient. | entailment | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|~strong(X))))&
((?[X]:((quiet(X)&~strong(X))))=>((~old(alice)&brave(alice))))&
(![X]:((~funny(X)|~humble(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)))))&
(![X]:((~humble(X)|~tall(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)))&
(?[X]:((~happy(X)&kind(X)))) | patient(susan) | [
"p2",
"p6",
"p12",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 7497179792304340118732858
% SZS output start Proof for 7497179792304340118732858
3. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (brave(X0) & rich(X0))) [input p2]
7. ~tall(susan) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p6]
13. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~rich(X0) | strong(X0))) [input p12]
16. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p15]
21. ~old(susan) | ~strong(susan) [input p20]
23. ~patient(susan) [input hypothesis]
36. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 3]
37. ! [X0] : ((~humble(X0) | ~funny(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | (humble(X0) & funny(X0)))) [flattening 36]
43. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | tall(susan)) [nnf transformation 7]
44. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | tall(susan)) [rectify 43]
45. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
46. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | tall(susan)) [skolemisation 44,45]
60. ! [X0] : (((~generous(X0) | ~tall(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 13]
61. ! [X0] : ((~generous(X0) | ~tall(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (generous(X0) & tall(X0)))) [flattening 60]
68. ! [X0] : (((~tall(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 16]
69. ! [X0] : ((~tall(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [flattening 68]
83. humble(X0) | rich(X0) [cnf transformation 37]
97. ~tall(susan) | patient(X0) [cnf transformation 46]
112. ~rich(X0) | strong(X0) | tall(X0) [cnf transformation 61]
120. tall(X0) | old(X0) [cnf transformation 69]
122. ~humble(X0) | tall(X0) [cnf transformation 69]
129. ~old(susan) | ~strong(susan) [cnf transformation 21]
132. ~patient(susan) [cnf transformation 23]
190. 13 <=> ! [X0] : patient(X0) [avatar definition]
191. patient(X0) <- (13) [avatar component clause 190]
193. 14 <=> tall(susan) [avatar definition]
195. ~tall(susan) <- (~14) [avatar component clause 193]
196. 13 | ~14 [avatar split clause 97,193,190]
305. 38 <=> strong(susan) [avatar definition]
307. ~strong(susan) <- (~38) [avatar component clause 305]
309. 39 <=> old(susan) [avatar definition]
312. ~38 | ~39 [avatar split clause 129,309,305]
317. old(susan) <- (~14) [resolution 120,195]
320. 39 | 14 [avatar split clause 317,193,309]
321. $false <- (13) [resolution 191,132]
324. ~13 [avatar contradiction clause 321]
330. tall(X2) | rich(X2) [resolution 122,83]
422. rich(susan) <- (~14) [resolution 330,195]
455. strong(susan) | tall(susan) <- (~14) [resolution 422,112]
457. tall(susan) <- (~14, ~38) [subsumption resolution 455,307]
458. $false <- (~14, ~38) [subsumption resolution 457,195]
459. 14 | 38 [avatar contradiction clause 458]
460. $false [avatar sat refutation 196,312,320,324,459]
% SZS output end Proof for 7497179792304340118732858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and not creative is happy or not rich and vice versa.
Everyone who is either strong or not old is strong.
Everyone who is either tall or brave is not brave or not creative and vice versa.
If someone is both not quiet and old then someone is creative or not brave and vice versa.
Everyone who is both not happy and old is kind or curious.
Everyone who is both not quiet and rich is both kind and not happy.
Everyone who is not funny or not strong is not kind or not calm and vice versa.
Everyone who is not tall is patient.
If john is old then someone is not happy.
If someone is not creative or not patient then someone is both not creative and quiet and vice versa.
Everyone who is not generous or not creative is both kind and not curious.
Everyone who is either not curious or not wise is not patient.
If someone is either happy or funny then paul is not rich or calm.
Everyone who is either not brave or not humble is curious or not quiet.
Everyone who is wise is either not humble or not tall and vice versa.
If someone is both quiet and not humble then someone is not rich and vice versa.
Someone is either tall or old.
Alice is not generous or not wise.
Paul is either kind or happy.
Someone is old or not creative.
Someone is generous or not brave.
Alice is quiet.
Lucy is either creative or generous. | Paul is kind. | entailment | (![X]:((~tall(X)&~creative(X))<=>(happy(X)|~rich(X))))&
(![X]:((strong(X)<~>~old(X))=>strong(X)))&
(![X]:((tall(X)<~>brave(X))<=>(~brave(X)|~creative(X))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:((creative(X)|~brave(X)))))&
(![X]:((~happy(X)&old(X))=>(kind(X)|curious(X))))&
(![X]:((~quiet(X)&rich(X))=>(kind(X)&~happy(X))))&
(![X]:((~funny(X)|~strong(X))<=>(~kind(X)|~calm(X))))&
(![X]:(~tall(X)=>patient(X)))&
((old(john))=>(?[X]:(~happy(X))))&
((?[X]:((~creative(X)|~patient(X))))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~generous(X)|~creative(X))=>(kind(X)&~curious(X))))&
(![X]:((~curious(X)<~>~wise(X))=>~patient(X)))&
((?[X]:((happy(X)<~>funny(X))))=>((~rich(paul)|calm(paul))))&
(![X]:((~brave(X)<~>~humble(X))=>(curious(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~humble(X)<~>~tall(X))))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:(~rich(X))))&
(?[X]:((tall(X)<~>old(X))))&
((~generous(alice)|~wise(alice)))&
((kind(paul)<~>happy(paul)))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((generous(X)|~brave(X))))&
(quiet(alice))&
((creative(lucy)<~>generous(lucy))) | kind(paul) | [
"p0",
"p10",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6468028376491419835940761
% SZS output start Proof for 6468028376491419835940761
1. ! [X0] : ((~creative(X0) & ~tall(X0)) <=> (~rich(X0) | happy(X0))) [input p0]
11. ! [X0] : ((~creative(X0) | ~generous(X0)) => (~curious(X0) & kind(X0))) [input p10]
19. kind(paul) <~> happy(paul) [input p18]
24. ~kind(paul) [input hypothesis]
35. ! [X0] : ((~curious(X0) & kind(X0)) | (creative(X0) & generous(X0))) [ennf transformation 11]
41. ! [X0] : (((~creative(X0) & ~tall(X0)) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | (creative(X0) | tall(X0)))) [nnf transformation 1]
42. ! [X0] : (((~creative(X0) & ~tall(X0)) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | creative(X0) | tall(X0))) [flattening 41]
72. (~happy(paul) | ~kind(paul)) & (happy(paul) | kind(paul)) [nnf transformation 19]
81. ~happy(X0) | ~creative(X0) [cnf transformation 42]
111. kind(X0) | creative(X0) [cnf transformation 35]
130. happy(paul) | kind(paul) [cnf transformation 72]
137. ~kind(paul) [cnf transformation 24]
268. 30 <=> kind(paul) [avatar definition]
270. ~kind(paul) <- (~30) [avatar component clause 268]
272. 31 <=> happy(paul) [avatar definition]
273. happy(paul) <- (31) [avatar component clause 272]
276. 30 | 31 [avatar split clause 130,272,268]
305. ~30 [avatar split clause 137,268]
312. ~creative(paul) <- (31) [resolution 81,273]
318. creative(paul) <- (~30) [resolution 111,270]
319. $false <- (~30, 31) [subsumption resolution 318,312]
320. 30 | ~31 [avatar contradiction clause 319]
321. $false [avatar sat refutation 276,305,320]
% SZS output end Proof for 6468028376491419835940761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Susan is creative. | 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))) | creative(susan) | []
| null | 0 |
Everyone who is either not curious or wise is both not rich and strong and vice versa. Everyone who is either not old or creative is both not kind and not curious and vice versa. If john is either not quiet or not happy then fred is both not strong and not wise. Everyone who is both curious and not humble is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. If lucy is curious or kind then mary is not brave and vice versa. Someone is happy or rich. Someone is generous. Susan is kind or not kind. Someone is either calm or not kind. Someone is both not kind and not generous. Someone is not quiet or not patient. Someone is rich or calm. Alice is both quiet and not creative. | Alice is not humble. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X))))&
((quiet(alice)&~creative(alice))) | ~humble(alice) | []
| null | 0 |
Everyone who is both curious and not patient is both not curious and strong.
If someone is not patient then paul is quiet.
If paul is both not generous and old then someone is both not old and not curious and vice versa.
Everyone who is kind or not generous is not brave and vice versa.
Everyone who is brave is not quiet or kind.
If someone is either creative or patient then someone is both generous and old.
If alice is both not generous and tall then mary is not patient or wise.
Everyone who is happy is humble.
If alice is not generous then someone is either wise or not creative and vice versa.
Everyone who is not kind or not patient is happy or calm and vice versa.
If someone is strong then someone is not tall or not generous.
Everyone who is both not happy and calm is not wise and vice versa.
Everyone who is funny or not rich is both not patient and calm.
If fred is not generous or not strong then someone is both not patient and not rich and vice versa.
Everyone who is not tall is either not kind or not happy and vice versa.
Everyone who is not kind or not patient is not generous or tall.
Paul is old or happy.
Fred is either brave or happy.
Mary is not patient.
Someone is both not old and not tall.
Someone is either brave or creative.
Paul is not patient.
Someone is either patient or generous.
Someone is either kind or curious. | Paul is not quiet. | contradiction | (![X]:((curious(X)&~patient(X))=>(~curious(X)&strong(X))))&
((?[X]:(~patient(X)))=>(quiet(paul)))&
(((~generous(paul)&old(paul)))<=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((kind(X)|~generous(X))<=>~brave(X)))&
(![X]:(brave(X)=>(~quiet(X)|kind(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:((generous(X)&old(X)))))&
(((~generous(alice)&tall(alice)))=>((~patient(mary)|wise(mary))))&
(![X]:(happy(X)=>humble(X)))&
((~generous(alice))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(![X]:((~kind(X)|~patient(X))<=>(happy(X)|calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((~happy(X)&calm(X))<=>~wise(X)))&
(![X]:((funny(X)|~rich(X))=>(~patient(X)&calm(X))))&
(((~generous(fred)|~strong(fred)))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:(~tall(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:((~kind(X)|~patient(X))=>(~generous(X)|tall(X))))&
((old(paul)|happy(paul)))&
((brave(fred)<~>happy(fred)))&
(~patient(mary))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(~patient(paul))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((kind(X)<~>curious(X)))) | ~quiet(paul) | [
"p1",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5090092694874183409163326
% SZS output start Proof for 5090092694874183409163326
2. ? [X0] : ~patient(X0) => quiet(paul) [input p1]
22. ~patient(paul) [input p21]
25. ~quiet(paul) [input hypothesis]
32. quiet(paul) | ! [X0] : patient(X0) [ennf transformation 2]
84. quiet(paul) | patient(X0) [cnf transformation 32]
131. ~patient(paul) [cnf transformation 22]
136. ~quiet(paul) [cnf transformation 25]
139. 1 <=> ! [X0] : patient(X0) [avatar definition]
140. patient(X0) <- (1) [avatar component clause 139]
142. 2 <=> quiet(paul) [avatar definition]
145. 1 | 2 [avatar split clause 84,142,139]
306. ~2 [avatar split clause 136,142]
307. $false <- (1) [resolution 140,131]
308. ~1 [avatar contradiction clause 307]
309. $false [avatar sat refutation 145,306,308]
% SZS output end Proof for 5090092694874183409163326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not brave is both tall and not calm.
Everyone who is either not funny or brave is either not humble or happy.
Everyone who is both old and calm is quiet and vice versa.
Everyone who is either not funny or not patient is both not kind and kind.
Everyone who is not creative is funny.
Everyone who is both funny and wise is either not kind or not happy and vice versa.
If someone is either not kind or rich then paul is both not quiet and not creative.
If mary is rich then someone is either not tall or happy and vice versa.
Everyone who is both wise and old is quiet.
If lucy is funny then john is both calm and rich and vice versa.
Everyone who is not rich or calm is wise.
Everyone who is either not tall or not creative is both not humble and strong and vice versa.
Everyone who is either brave or curious is not creative and vice versa.
Everyone who is humble or patient is both not old and not happy and vice versa.
Everyone who is either curious or not funny is not old and vice versa.
Everyone who is either creative or not humble is humble or not generous and vice versa.
Fred is not tall.
Someone is not tall or not funny.
Someone is either patient or not creative.
Susan is either curious or humble.
Someone is not old.
John is not quiet or not happy. | Fred is happy. | contradiction | (![X]:((~humble(X)<~>~brave(X))=>(tall(X)&~calm(X))))&
(![X]:((~funny(X)<~>brave(X))=>(~humble(X)<~>happy(X))))&
(![X]:((old(X)&calm(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~patient(X))=>(~kind(X)&kind(X))))&
(![X]:(~creative(X)=>funny(X)))&
(![X]:((funny(X)&wise(X))<=>(~kind(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>rich(X))))=>((~quiet(paul)&~creative(paul))))&
((rich(mary))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((wise(X)&old(X))=>quiet(X)))&
((funny(lucy))<=>((calm(john)&rich(john))))&
(![X]:((~rich(X)|calm(X))=>wise(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~humble(X)&strong(X))))&
(![X]:((brave(X)<~>curious(X))<=>~creative(X)))&
(![X]:((humble(X)|patient(X))<=>(~old(X)&~happy(X))))&
(![X]:((curious(X)<~>~funny(X))<=>~old(X)))&
(![X]:((creative(X)<~>~humble(X))<=>(humble(X)|~generous(X))))&
(~tall(fred))&
(?[X]:((~tall(X)|~funny(X))))&
(?[X]:((patient(X)<~>~creative(X))))&
((curious(susan)<~>humble(susan)))&
(?[X]:(~old(X)))&
((~quiet(john)|~happy(john))) | happy(fred) | [
"p0",
"p1",
"p3",
"p13",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2476336304777106361944463
% SZS output start Proof for 2476336304777106361944463
1. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => (~calm(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~humble(X0) <~> happy(X0))) [input p1]
4. ! [X0] : ((~funny(X0) <~> ~patient(X0)) => (kind(X0) & ~kind(X0))) [input p3]
14. ! [X0] : ((patient(X0) | humble(X0)) <=> (~happy(X0) & ~old(X0))) [input p13]
17. ~tall(fred) [input p16]
23. happy(fred) [input hypothesis]
24. ! [X0] : ((~calm(X0) & tall(X0)) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 1]
25. ! [X0] : ((~humble(X0) <~> happy(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 2]
26. ! [X0] : ((kind(X0) & ~kind(X0)) | (~funny(X0) <=> ~patient(X0))) [ennf transformation 4]
32. ! [X0] : ((~calm(X0) & tall(X0)) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 24]
33. ! [X0] : (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 25]
36. ! [X0] : ((kind(X0) & ~kind(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 26]
49. ! [X0] : (((patient(X0) | humble(X0)) | (happy(X0) | old(X0))) & ((~happy(X0) & ~old(X0)) | (~patient(X0) & ~humble(X0)))) [nnf transformation 14]
50. ! [X0] : ((patient(X0) | humble(X0) | happy(X0) | old(X0)) & ((~happy(X0) & ~old(X0)) | (~patient(X0) & ~humble(X0)))) [flattening 49]
62. ~brave(X0) | tall(X0) | humble(X0) [cnf transformation 32]
68. ~happy(X0) | humble(X0) | brave(X0) | funny(X0) [cnf transformation 33]
74. ~kind(X0) | ~funny(X0) | patient(X0) [cnf transformation 36]
76. ~funny(X0) | kind(X0) | patient(X0) [cnf transformation 36]
110. ~happy(X0) | ~humble(X0) [cnf transformation 50]
111. ~patient(X0) | ~happy(X0) [cnf transformation 50]
123. ~tall(fred) [cnf transformation 17]
131. happy(fred) [cnf transformation 23]
134. ~funny(X0) | patient(X0) [subsumption resolution 74,76]
233. ~humble(fred) [resolution 110,131]
255. 22 <=> funny(fred) [avatar definition]
257. funny(fred) <- (22) [avatar component clause 255]
400. humble(fred) | brave(fred) | funny(fred) [resolution 68,131]
401. brave(fred) | funny(fred) [subsumption resolution 400,233]
403. 38 <=> brave(fred) [avatar definition]
405. brave(fred) <- (38) [avatar component clause 403]
406. 22 | 38 [avatar split clause 401,403,255]
407. tall(fred) | humble(fred) <- (38) [resolution 405,62]
408. humble(fred) <- (38) [subsumption resolution 407,123]
409. $false <- (38) [subsumption resolution 408,233]
410. ~38 [avatar contradiction clause 409]
415. patient(fred) <- (22) [resolution 257,134]
459. ~happy(fred) <- (22) [resolution 415,111]
461. $false <- (22) [subsumption resolution 459,131]
462. ~22 [avatar contradiction clause 461]
464. $false [avatar sat refutation 406,410,462]
% SZS output end Proof for 2476336304777106361944463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious then john is not brave and vice versa.
Everyone who is not patient is humble.
If someone is calm or not brave then lucy is not patient or curious and vice versa.
Everyone who is not funny or kind is not calm or not brave and vice versa.
If someone is quiet then john is both not curious and not happy and vice versa.
If someone is not creative or not strong then someone is either not strong or happy.
If someone is either wise or not generous then lucy is wise and vice versa.
If someone is not curious or happy then paul is either not quiet or quiet and vice versa.
If someone is either patient or rich then someone is both not brave and not calm.
Everyone who is both not happy and quiet is both not wise and generous and vice versa.
If someone is not calm or quiet then someone is patient or not funny and vice versa.
Everyone who is both humble and not kind is humble.
Everyone who is not curious or happy is generous.
Everyone who is tall or humble is not brave or not calm.
If someone is strong or not brave then susan is creative or old.
Everyone who is generous or strong is not quiet.
Someone is patient.
Alice is not quiet or not generous.
Someone is both not patient and not calm.
Someone is curious.
Someone is either not rich or not generous.
John is either patient or not strong.
Susan is curious or quiet. | Lucy is not quiet. | entailment | ((curious(susan))<=>(~brave(john)))&
(![X]:(~patient(X)=>humble(X)))&
((?[X]:((calm(X)|~brave(X))))<=>((~patient(lucy)|curious(lucy))))&
(![X]:((~funny(X)|kind(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(quiet(X)))<=>((~curious(john)&~happy(john))))&
((?[X]:((~creative(X)|~strong(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((wise(X)<~>~generous(X))))<=>(wise(lucy)))&
((?[X]:((~curious(X)|happy(X))))<=>((~quiet(paul)<~>quiet(paul))))&
((?[X]:((patient(X)<~>rich(X))))=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(~wise(X)&generous(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((humble(X)&~kind(X))=>humble(X)))&
(![X]:((~curious(X)|happy(X))=>generous(X)))&
(![X]:((tall(X)|humble(X))=>(~brave(X)|~calm(X))))&
((?[X]:((strong(X)|~brave(X))))=>((creative(susan)|old(susan))))&
(![X]:((generous(X)|strong(X))=>~quiet(X)))&
(?[X]:(patient(X)))&
((~quiet(alice)|~generous(alice)))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)<~>~generous(X))))&
((patient(john)<~>~strong(john)))&
((curious(susan)|quiet(susan))) | ~quiet(lucy) | [
"p4",
"p9",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7936629250880897400874906
% SZS output start Proof for 7936629250880897400874906
5. ? [X0] : quiet(X0) <=> (~happy(john) & ~curious(john)) [input p4]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (generous(X0) & ~wise(X0))) [input p9]
13. ! [X0] : ((happy(X0) | ~curious(X0)) => generous(X0)) [input p12]
16. ! [X0] : ((strong(X0) | generous(X0)) => ~quiet(X0)) [input p15]
24. quiet(lucy) [input hypothesis]
36. ! [X0] : (generous(X0) | (~happy(X0) & curious(X0))) [ennf transformation 13]
39. ! [X0] : (~quiet(X0) | (~strong(X0) & ~generous(X0))) [ennf transformation 16]
48. (? [X0] : quiet(X0) | (happy(john) | curious(john))) & ((~happy(john) & ~curious(john)) | ! [X0] : ~quiet(X0)) [nnf transformation 5]
49. (? [X0] : quiet(X0) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X0] : ~quiet(X0)) [flattening 48]
50. (? [X0] : quiet(X0) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X1] : ~quiet(X1)) [rectify 49]
51. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
52. (quiet(sK1) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X1] : ~quiet(X1)) [skolemisation 50,51]
69. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
70. ! [X0] : (((quiet(X0) & ~happy(X0)) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | ~quiet(X0) | happy(X0))) [flattening 69]
97. ~curious(john) | ~quiet(X1) [cnf transformation 52]
98. ~happy(john) | ~quiet(X1) [cnf transformation 52]
99. quiet(sK1) | happy(john) | curious(john) [cnf transformation 52]
117. ~quiet(X0) | generous(X0) | happy(X0) [cnf transformation 70]
126. ~happy(X0) | generous(X0) [cnf transformation 36]
128. ~generous(X0) | ~quiet(X0) [cnf transformation 39]
140. quiet(lucy) [cnf transformation 24]
180. 9 <=> curious(john) [avatar definition]
184. 10 <=> happy(john) [avatar definition]
188. 11 <=> quiet(sK1) [avatar definition]
190. quiet(sK1) <- (11) [avatar component clause 188]
191. 9 | 10 | 11 [avatar split clause 99,188,184,180]
193. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
194. ~quiet(X1) <- (12) [avatar component clause 193]
195. 12 | ~10 [avatar split clause 98,184,193]
196. 12 | ~9 [avatar split clause 97,180,193]
327. generous(sK1) | happy(sK1) <- (11) [resolution 117,190]
328. generous(sK1) <- (11) [subsumption resolution 327,126]
332. ~quiet(sK1) <- (11) [resolution 328,128]
342. $false <- (11) [subsumption resolution 332,190]
343. ~11 [avatar contradiction clause 342]
345. $false <- (12) [resolution 194,140]
346. ~12 [avatar contradiction clause 345]
347. $false [avatar sat refutation 191,195,196,343,346]
% SZS output end Proof for 7936629250880897400874906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or patient then mary is either rich or not quiet.
Everyone who is funny is either tall or old.
Everyone who is not generous or not wise is not wise.
Everyone who is funny is both tall and old.
Everyone who is either kind or not generous is not wise or not calm.
Everyone who is either not rich or wise is creative.
If alice is either wise or not generous then someone is both wise and not kind and vice versa.
Everyone who is either not humble or not tall is patient or quiet.
Everyone who is either quiet or not funny is not tall.
Everyone who is either patient or not curious is either not tall or wise and vice versa.
Everyone who is both tall and curious is both happy and not kind and vice versa.
If lucy is strong or kind then someone is kind or not humble.
Everyone who is old is either quiet or not rich.
Everyone who is not strong is either curious or not tall.
If fred is not brave then someone is rich and vice versa.
Everyone who is both not creative and not funny is not old.
Fred is kind.
Someone is not calm.
Susan is both humble and not quiet.
Someone is either not creative or kind.
Alice is either funny or not kind.
Susan is happy. | Lucy is not strong. | neutral | ((?[X]:((old(X)<~>patient(X))))=>((rich(mary)<~>~quiet(mary))))&
(![X]:(funny(X)=>(tall(X)<~>old(X))))&
(![X]:((~generous(X)|~wise(X))=>~wise(X)))&
(![X]:(funny(X)=>(tall(X)&old(X))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~humble(X)<~>~tall(X))=>(patient(X)|quiet(X))))&
(![X]:((quiet(X)<~>~funny(X))=>~tall(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((tall(X)&curious(X))<=>(happy(X)&~kind(X))))&
(((strong(lucy)|kind(lucy)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:(old(X)=>(quiet(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(curious(X)<~>~tall(X))))&
((~brave(fred))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)&~funny(X))=>~old(X)))&
(kind(fred))&
(?[X]:(~calm(X)))&
((humble(susan)&~quiet(susan)))&
(?[X]:((~creative(X)<~>kind(X))))&
((funny(alice)<~>~kind(alice)))&
(happy(susan)) | ~strong(lucy) | []
| null | 0 |
If someone is both strong and not quiet then someone is both rich and humble. If paul is both curious and wise then fred is either not humble or not curious. Everyone who is not wise or not brave is either quiet or not curious. Everyone who is not humble is not happy or not brave. If someone is both not patient and happy then susan is either not strong or tall and vice versa. Everyone who is not patient is not brave. Everyone who is either rich or not happy is both not patient and not curious. If someone is either not wise or kind then lucy is both not wise and not happy and vice versa. If paul is both brave and quiet then mary is both strong and rich. If someone is humble or quiet then alice is not wise and vice versa. Everyone who is not brave is both not calm and not old and vice versa. Everyone who is both curious and not generous is either rich or kind and vice versa. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Someone is not strong or funny. Someone is not tall. Susan is both funny and not kind. Alice is rich or not quiet. Lucy is either old or not rich. Someone is strong or kind. Someone is generous. Paul is brave. | Lucy is not patient. | contradiction | ((?[X]:((strong(X)&~quiet(X))))=>(?[X]:((rich(X)&humble(X)))))&
(((curious(paul)&wise(paul)))=>((~humble(fred)<~>~curious(fred))))&
(![X]:((~wise(X)|~brave(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(~humble(X)=>(~happy(X)|~brave(X))))&
((?[X]:((~patient(X)&happy(X))))<=>((~strong(susan)<~>tall(susan))))&
(![X]:(~patient(X)=>~brave(X)))&
(![X]:((rich(X)<~>~happy(X))=>(~patient(X)&~curious(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((~wise(lucy)&~happy(lucy))))&
(((brave(paul)&quiet(paul)))=>((strong(mary)&rich(mary))))&
((?[X]:((humble(X)|quiet(X))))<=>(~wise(alice)))&
(![X]:(~brave(X)<=>(~calm(X)&~old(X))))&
(![X]:((curious(X)&~generous(X))<=>(rich(X)<~>kind(X))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(?[X]:((~strong(X)|funny(X))))&
(?[X]:(~tall(X)))&
((funny(susan)&~kind(susan)))&
((rich(alice)|~quiet(alice)))&
((old(lucy)<~>~rich(lucy)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:(generous(X)))&
(brave(paul)) | ~patient(lucy) | [
"p5",
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3198168606087025001588967
% SZS output start Proof for 3198168606087025001588967
6. ! [X0] : (~patient(X0) => ~brave(X0)) [input p5]
11. ! [X0] : (~brave(X0) <=> (~old(X0) & ~calm(X0))) [input p10]
16. ! [X0] : (~patient(X0) <=> (generous(X0) & calm(X0))) [input p15]
25. ~patient(lucy) [input hypothesis]
33. ! [X0] : (~brave(X0) | patient(X0)) [ennf transformation 6]
56. ! [X0] : ((~brave(X0) | (old(X0) | calm(X0))) & ((~old(X0) & ~calm(X0)) | brave(X0))) [nnf transformation 11]
57. ! [X0] : ((~brave(X0) | old(X0) | calm(X0)) & ((~old(X0) & ~calm(X0)) | brave(X0))) [flattening 56]
71. ! [X0] : ((~patient(X0) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | patient(X0))) [nnf transformation 16]
72. ! [X0] : ((~patient(X0) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | patient(X0))) [flattening 71]
97. ~brave(X0) | patient(X0) [cnf transformation 33]
113. ~calm(X0) | brave(X0) [cnf transformation 57]
138. calm(X0) | patient(X0) [cnf transformation 72]
151. ~patient(lucy) [cnf transformation 25]
364. patient(X0) | brave(X0) [resolution 138,113]
365. patient(X0) [subsumption resolution 364,97]
366. $false [resolution 365,151]
% SZS output end Proof for 3198168606087025001588967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not calm then john is not funny or brave and vice versa. If someone is both calm and funny then someone is old and vice versa. If alice is rich then fred is curious. If fred is not wise or not old then someone is both not rich and funny and vice versa. If susan is humble or not strong then mary is both not rich and humble and vice versa. Everyone who is funny is either generous or old and vice versa. If someone is both wise and humble then lucy is both not old and quiet and vice versa. If alice is not creative then susan is either patient or not quiet. Everyone who is funny or not patient is not humble and vice versa. If susan is both not rich and brave then mary is happy or not kind and vice versa. If john is tall or patient then someone is both not calm and not old and vice versa. Everyone who is strong or not strong is calm. If lucy is both not strong and not wise then paul is both patient and not brave. If lucy is both patient and creative then someone is either patient or not rich. Everyone who is rich is either not tall or not calm and vice versa. Everyone who is either quiet or old is not old and vice versa. Someone is either not quiet or creative. Paul is both curious and not brave. Lucy is both not wise and calm. Someone is either not patient or not tall. Susan is either tall or happy. Lucy is either rich or not curious. Someone is patient or not old. | Paul is not patient. | neutral | ((?[X]:((funny(X)&~calm(X))))<=>((~funny(john)|brave(john))))&
((?[X]:((calm(X)&funny(X))))<=>(?[X]:(old(X))))&
((rich(alice))=>(curious(fred)))&
(((~wise(fred)|~old(fred)))<=>(?[X]:((~rich(X)&funny(X)))))&
(((humble(susan)|~strong(susan)))<=>((~rich(mary)&humble(mary))))&
(![X]:(funny(X)<=>(generous(X)<~>old(X))))&
((?[X]:((wise(X)&humble(X))))<=>((~old(lucy)&quiet(lucy))))&
((~creative(alice))=>((patient(susan)<~>~quiet(susan))))&
(![X]:((funny(X)|~patient(X))<=>~humble(X)))&
(((~rich(susan)&brave(susan)))<=>((happy(mary)|~kind(mary))))&
(((tall(john)|patient(john)))<=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((strong(X)|~strong(X))=>calm(X)))&
(((~strong(lucy)&~wise(lucy)))=>((patient(paul)&~brave(paul))))&
(((patient(lucy)&creative(lucy)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:(rich(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>old(X))<=>~old(X)))&
(?[X]:((~quiet(X)<~>creative(X))))&
((curious(paul)&~brave(paul)))&
((~wise(lucy)&calm(lucy)))&
(?[X]:((~patient(X)<~>~tall(X))))&
((tall(susan)<~>happy(susan)))&
((rich(lucy)<~>~curious(lucy)))&
(?[X]:((patient(X)|~old(X)))) | ~patient(paul) | []
| null | 0 |
Everyone who is both calm and not generous is either creative or not calm. If someone is either rich or not generous then fred is quiet. If paul is quiet or patient then paul is not brave or patient and vice versa. Everyone who is both funny and generous is happy and vice versa. Everyone who is humble or not creative is calm. Everyone who is both wise and not patient is both curious and not curious. Everyone who is both not curious and not strong is creative or not quiet and vice versa. Everyone who is curious or not rich is either happy or not brave. If mary is wise or not curious then susan is both humble and old. Everyone who is kind or happy is both not brave and curious and vice versa. Everyone who is quiet or not humble is not quiet or quiet and vice versa. Everyone who is not kind is either quiet or humble and vice versa. Everyone who is either not funny or patient is either humble or not quiet and vice versa. If someone is rich or not tall then someone is either creative or generous and vice versa. John is either curious or not creative. Someone is either not patient or patient. Lucy is either not happy or not humble. Someone is both rich and wise. Someone is not tall or quiet. Someone is both brave and not generous. Someone is either not patient or curious. Someone is either rich or not old. | John is happy. | contradiction | (![X]:((calm(X)&~generous(X))=>(creative(X)<~>~calm(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>(quiet(fred)))&
(((quiet(paul)|patient(paul)))<=>((~brave(paul)|patient(paul))))&
(![X]:((funny(X)&generous(X))<=>happy(X)))&
(![X]:((humble(X)|~creative(X))=>calm(X)))&
(![X]:((wise(X)&~patient(X))=>(curious(X)&~curious(X))))&
(![X]:((~curious(X)&~strong(X))<=>(creative(X)|~quiet(X))))&
(![X]:((curious(X)|~rich(X))=>(happy(X)<~>~brave(X))))&
(((wise(mary)|~curious(mary)))=>((humble(susan)&old(susan))))&
(![X]:((kind(X)|happy(X))<=>(~brave(X)&curious(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~kind(X)<=>(quiet(X)<~>humble(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(humble(X)<~>~quiet(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((creative(X)<~>generous(X)))))&
((curious(john)<~>~creative(john)))&
(?[X]:((~patient(X)<~>patient(X))))&
((~happy(lucy)<~>~humble(lucy)))&
(?[X]:((rich(X)&wise(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((rich(X)<~>~old(X)))) | happy(john) | [
"p6",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1047309258395869038652617
% SZS output start Proof for 1047309258395869038652617
7. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> (~quiet(X0) | creative(X0))) [input p6]
10. ! [X0] : ((happy(X0) | kind(X0)) <=> (curious(X0) & ~brave(X0))) [input p9]
15. curious(john) <~> ~creative(john) [input p14]
23. happy(john) [input hypothesis]
39. ! [X0] : (((~strong(X0) & ~curious(X0)) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | (strong(X0) | curious(X0)))) [nnf transformation 7]
40. ! [X0] : (((~strong(X0) & ~curious(X0)) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | strong(X0) | curious(X0))) [flattening 39]
42. ! [X0] : (((happy(X0) | kind(X0)) | (~curious(X0) | brave(X0))) & ((curious(X0) & ~brave(X0)) | (~happy(X0) & ~kind(X0)))) [nnf transformation 10]
43. ! [X0] : ((happy(X0) | kind(X0) | ~curious(X0) | brave(X0)) & ((curious(X0) & ~brave(X0)) | (~happy(X0) & ~kind(X0)))) [flattening 42]
53. (creative(john) | ~curious(john)) & (~creative(john) | curious(john)) [nnf transformation 15]
86. ~curious(X0) | ~creative(X0) [cnf transformation 40]
101. ~happy(X0) | curious(X0) [cnf transformation 43]
126. creative(john) | ~curious(john) [cnf transformation 53]
140. happy(john) [cnf transformation 23]
232. ~curious(john) [subsumption resolution 126,86]
283. curious(john) [resolution 101,140]
285. $false [subsumption resolution 283,232]
% SZS output end Proof for 1047309258395869038652617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and generous then paul is not tall.
Everyone who is tall or wise is both old and not creative.
Everyone who is both not curious and not rich is not calm or not creative.
Everyone who is either tall or patient is both not quiet and old and vice versa.
Everyone who is either happy or not generous is not kind and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is quiet or funny is calm or kind and vice versa.
Everyone who is brave or not brave is either rich or wise.
If fred is calm or tall then john is both not brave and not tall and vice versa.
Everyone who is brave or strong is not creative and vice versa.
If alice is rich then someone is both not brave and not humble and vice versa.
Everyone who is not kind or not quiet is both tall and not wise and vice versa.
Everyone who is patient or not kind is not happy.
If someone is either wise or not kind then john is not kind.
Everyone who is either not rich or creative is not patient or old and vice versa.
If fred is both quiet and funny then someone is either creative or not generous.
Fred is both calm and kind.
Alice is either not old or not generous.
John is funny.
Susan is either not brave or humble.
Someone is either not creative or happy.
Someone is calm or not brave. | Susan is patient. | contradiction | ((?[X]:((~tall(X)&generous(X))))=>(~tall(paul)))&
(![X]:((tall(X)|wise(X))=>(old(X)&~creative(X))))&
(![X]:((~curious(X)&~rich(X))=>(~calm(X)|~creative(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~quiet(X)&old(X))))&
(![X]:((happy(X)<~>~generous(X))<=>~kind(X)))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((quiet(X)|funny(X))<=>(calm(X)|kind(X))))&
(![X]:((brave(X)|~brave(X))=>(rich(X)<~>wise(X))))&
(((calm(fred)|tall(fred)))<=>((~brave(john)&~tall(john))))&
(![X]:((brave(X)|strong(X))<=>~creative(X)))&
((rich(alice))<=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((~kind(X)|~quiet(X))<=>(tall(X)&~wise(X))))&
(![X]:((patient(X)|~kind(X))=>~happy(X)))&
((?[X]:((wise(X)<~>~kind(X))))=>(~kind(john)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)|old(X))))&
(((quiet(fred)&funny(fred)))=>(?[X]:((creative(X)<~>~generous(X)))))&
((calm(fred)&kind(fred)))&
((~old(alice)<~>~generous(alice)))&
(funny(john))&
((~brave(susan)<~>humble(susan)))&
(?[X]:((~creative(X)<~>happy(X))))&
(?[X]:((calm(X)|~brave(X)))) | patient(susan) | [
"p1",
"p3",
"p5",
"p7",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 459853066820568085272757
% SZS output start Proof for 459853066820568085272757
2. ! [X0] : ((wise(X0) | tall(X0)) => (~creative(X0) & old(X0))) [input p1]
4. ! [X0] : ((tall(X0) <~> patient(X0)) <=> (old(X0) & ~quiet(X0))) [input p3]
6. ! [X0] : (~old(X0) <=> wise(X0)) [input p5]
8. ! [X0] : ((~brave(X0) | brave(X0)) => (rich(X0) <~> wise(X0))) [input p7]
12. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (~wise(X0) & tall(X0))) [input p11]
15. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (old(X0) | ~patient(X0))) [input p14]
23. patient(susan) [input hypothesis]
26. ! [X0] : ((~creative(X0) & old(X0)) | (~wise(X0) & ~tall(X0))) [ennf transformation 2]
27. ! [X0] : ((rich(X0) <~> wise(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 8]
32. ! [X0] : ((((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))))) [nnf transformation 4]
33. ! [X0] : ((((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))))) [flattening 32]
35. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 6]
38. ! [X0] : (((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (brave(X0) & ~brave(X0))) [nnf transformation 27]
47. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (wise(X0) | ~tall(X0))) & ((~wise(X0) & tall(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 12]
48. ! [X0] : ((~quiet(X0) | ~kind(X0) | wise(X0) | ~tall(X0)) & ((~wise(X0) & tall(X0)) | (quiet(X0) & kind(X0)))) [flattening 47]
50. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 50]
64. ~wise(X0) | old(X0) [cnf transformation 26]
65. ~creative(X0) | ~tall(X0) [cnf transformation 26]
68. ~quiet(X0) | tall(X0) | ~patient(X0) [cnf transformation 33]
77. wise(X0) | old(X0) [cnf transformation 35]
78. ~old(X0) | ~wise(X0) [cnf transformation 35]
83. wise(X0) | rich(X0) | ~brave(X0) [cnf transformation 38]
84. wise(X0) | rich(X0) | brave(X0) [cnf transformation 38]
99. quiet(X0) | tall(X0) [cnf transformation 48]
110. creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 51]
125. patient(susan) [cnf transformation 23]
136. ~wise(X0) [subsumption resolution 78,64]
137. old(X0) [subsumption resolution 77,136]
138. brave(X0) | rich(X0) [subsumption resolution 84,136]
139. rich(X0) | ~brave(X0) [subsumption resolution 83,136]
140. rich(X0) [subsumption resolution 139,138]
174. creative(X0) | ~old(X0) [subsumption resolution 110,140]
175. creative(X0) [subsumption resolution 174,137]
212. ~tall(X0) [resolution 65,175]
226. tall(X0) | ~patient(X0) | tall(X0) [resolution 68,99]
227. tall(X0) | ~patient(X0) [duplicate literal removal 226]
228. ~patient(X0) [subsumption resolution 227,212]
229. $false [resolution 228,125]
% SZS output end Proof for 459853066820568085272757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either strong or happy and vice versa. Everyone who is old is calm or not wise and vice versa. Everyone who is happy or strong is not strong. Everyone who is both quiet and not brave is either tall or not brave and vice versa. If lucy is both old and not generous then paul is either calm or not tall. Everyone who is creative or wise is either calm or strong and vice versa. Everyone who is either not wise or not kind is both not strong and funny. Everyone who is both not patient and not happy is creative. Everyone who is brave or rich is not curious and vice versa. Everyone who is generous or brave is not quiet or wise. If someone is calm or not wise then someone is either happy or not funny. If paul is both not old and not quiet then mary is either calm or creative and vice versa. If someone is both not curious and old then paul is strong and vice versa. If susan is quiet then mary is patient and vice versa. If john is not old or not patient then mary is both strong and old and vice versa. Everyone who is both creative and not old is not kind or calm. Alice is both not generous and happy. Someone is both kind and not generous. Someone is both not tall and not humble. Mary is wise. Someone is old or rich. Paul is not tall. Paul is both not wise and not tall. | John is not rich. | entailment | (![X]:(curious(X)<=>(strong(X)<~>happy(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(![X]:((happy(X)|strong(X))=>~strong(X)))&
(![X]:((quiet(X)&~brave(X))<=>(tall(X)<~>~brave(X))))&
(((old(lucy)&~generous(lucy)))=>((calm(paul)<~>~tall(paul))))&
(![X]:((creative(X)|wise(X))<=>(calm(X)<~>strong(X))))&
(![X]:((~wise(X)<~>~kind(X))=>(~strong(X)&funny(X))))&
(![X]:((~patient(X)&~happy(X))=>creative(X)))&
(![X]:((brave(X)|rich(X))<=>~curious(X)))&
(![X]:((generous(X)|brave(X))=>(~quiet(X)|wise(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((happy(X)<~>~funny(X)))))&
(((~old(paul)&~quiet(paul)))<=>((calm(mary)<~>creative(mary))))&
((?[X]:((~curious(X)&old(X))))<=>(strong(paul)))&
((quiet(susan))<=>(patient(mary)))&
(((~old(john)|~patient(john)))<=>((strong(mary)&old(mary))))&
(![X]:((creative(X)&~old(X))=>(~kind(X)|calm(X))))&
((~generous(alice)&happy(alice)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((~tall(X)&~humble(X))))&
(wise(mary))&
(?[X]:((old(X)|rich(X))))&
(~tall(paul))&
((~wise(paul)&~tall(paul))) | ~rich(john) | [
"p1",
"p2",
"p5",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 230294452605618455772051
% SZS output start Proof for 230294452605618455772051
2. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p1]
3. ! [X0] : ((strong(X0) | happy(X0)) => ~strong(X0)) [input p2]
6. ! [X0] : ((wise(X0) | creative(X0)) <=> (calm(X0) <~> strong(X0))) [input p5]
9. ! [X0] : ((rich(X0) | brave(X0)) <=> ~curious(X0)) [input p8]
13. ? [X0] : (old(X0) & ~curious(X0)) <=> strong(paul) [input p12]
24. rich(john) [input hypothesis]
27. ! [X0] : (~strong(X0) | (~strong(X0) & ~happy(X0))) [ennf transformation 3]
39. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 39]
44. ! [X0] : (((wise(X0) | creative(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((wise(X0) | creative(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [flattening 44]
47. ! [X0] : (((rich(X0) | brave(X0)) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [nnf transformation 9]
48. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [flattening 47]
55. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X0] : (~old(X0) | curious(X0))) [nnf transformation 13]
56. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [rectify 55]
57. ? [X0] : (old(X0) & ~curious(X0)) => (old(sK1) & ~curious(sK1)) [choice axiom]
58. ((old(sK1) & ~curious(sK1)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [skolemisation 56,57]
73. ~calm(X0) | old(X0) [cnf transformation 40]
74. wise(X0) | old(X0) [cnf transformation 40]
76. ~strong(X0) | ~strong(X0) [cnf transformation 27]
86. strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 45]
97. ~rich(X0) | ~curious(X0) [cnf transformation 48]
111. strong(paul) | ~old(X1) | curious(X1) [cnf transformation 58]
132. rich(john) [cnf transformation 24]
135. ~strong(X0) [duplicate literal removal 76]
156. ~wise(X0) | calm(X0) [subsumption resolution 86,135]
198. ~old(X1) | curious(X1) [subsumption resolution 111,135]
244. ~curious(john) [resolution 97,132]
246. calm(X0) | old(X0) [resolution 156,74]
249. old(X0) [subsumption resolution 246,73]
253. curious(X0) [resolution 198,249]
257. $false [resolution 253,244]
% SZS output end Proof for 230294452605618455772051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or funny is quiet or wise. If alice is not strong then mary is happy or not generous and vice versa. If someone is both not funny and quiet then alice is strong or humble. Everyone who is both not humble and patient is both quiet and old. Everyone who is either old or not funny is both old and generous. Everyone who is strong is humble or patient and vice versa. Everyone who is both calm and happy is both quiet and old and vice versa. If susan is either not strong or not happy then susan is not tall. Everyone who is not brave or generous is either kind or not rich and vice versa. Everyone who is rich or patient is both curious and not happy. If susan is old or calm then john is not strong or not generous and vice versa. If mary is both humble and patient then fred is either brave or old and vice versa. If fred is both not rich and brave then someone is not creative or not funny and vice versa. If paul is both calm and not patient then mary is not kind or calm and vice versa. If someone is both tall and not tall then john is both not humble and kind. Everyone who is quiet is either not tall or not strong. Susan is either not humble or brave. Someone is either happy or not patient. Fred is strong or not curious. Susan is either kind or not humble. Fred is both generous and not calm. Someone is tall or quiet. Someone is quiet. Someone is brave. | Alice is strong. | neutral | (![X]:((~happy(X)<~>funny(X))=>(quiet(X)|wise(X))))&
((~strong(alice))<=>((happy(mary)|~generous(mary))))&
((?[X]:((~funny(X)&quiet(X))))=>((strong(alice)|humble(alice))))&
(![X]:((~humble(X)&patient(X))=>(quiet(X)&old(X))))&
(![X]:((old(X)<~>~funny(X))=>(old(X)&generous(X))))&
(![X]:(strong(X)<=>(humble(X)|patient(X))))&
(![X]:((calm(X)&happy(X))<=>(quiet(X)&old(X))))&
(((~strong(susan)<~>~happy(susan)))=>(~tall(susan)))&
(![X]:((~brave(X)|generous(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((rich(X)|patient(X))=>(curious(X)&~happy(X))))&
(((old(susan)|calm(susan)))<=>((~strong(john)|~generous(john))))&
(((humble(mary)&patient(mary)))<=>((brave(fred)<~>old(fred))))&
(((~rich(fred)&brave(fred)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((calm(paul)&~patient(paul)))<=>((~kind(mary)|calm(mary))))&
((?[X]:((tall(X)&~tall(X))))=>((~humble(john)&kind(john))))&
(![X]:(quiet(X)=>(~tall(X)<~>~strong(X))))&
((~humble(susan)<~>brave(susan)))&
(?[X]:((happy(X)<~>~patient(X))))&
((strong(fred)|~curious(fred)))&
((kind(susan)<~>~humble(susan)))&
((generous(fred)&~calm(fred)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:(quiet(X)))&
(?[X]:(brave(X))) | strong(alice) | []
| null | 0 |
If alice is either not tall or tall then someone is rich or calm.
If someone is either kind or not old then susan is generous or kind and vice versa.
Everyone who is not rich or not generous is not quiet or curious and vice versa.
Everyone who is brave is not wise.
If someone is both curious and not strong then someone is either not happy or not funny and vice versa.
If someone is both not funny and not generous then john is either not generous or not brave.
Everyone who is not generous or quiet is both not strong and not brave and vice versa.
If someone is both not kind and not happy then fred is generous and vice versa.
If someone is both not kind and curious then someone is generous.
Everyone who is kind or not humble is both patient and not generous.
If john is not calm or not funny then someone is either generous or not brave.
If someone is not old or not happy then john is both humble and not happy.
If someone is either not happy or not strong then someone is both not patient and humble and vice versa.
Everyone who is patient or not tall is not strong or tall and vice versa.
Everyone who is both tall and not quiet is both not happy and happy.
Everyone who is not strong is either brave or not wise.
Someone is both not tall and funny.
Someone is both calm and not patient.
Someone is either not strong or humble.
Alice is either quiet or humble.
Someone is either funny or rich.
Susan is either calm or humble.
Someone is either not calm or happy.
Someone is both old and not brave. | Alice is not generous. | entailment | (((~tall(alice)<~>tall(alice)))=>(?[X]:((rich(X)|calm(X)))))&
((?[X]:((kind(X)<~>~old(X))))<=>((generous(susan)|kind(susan))))&
(![X]:((~rich(X)|~generous(X))<=>(~quiet(X)|curious(X))))&
(![X]:(brave(X)=>~wise(X)))&
((?[X]:((curious(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((?[X]:((~funny(X)&~generous(X))))=>((~generous(john)<~>~brave(john))))&
(![X]:((~generous(X)|quiet(X))<=>(~strong(X)&~brave(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>(generous(fred)))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:(generous(X))))&
(![X]:((kind(X)|~humble(X))=>(patient(X)&~generous(X))))&
(((~calm(john)|~funny(john)))=>(?[X]:((generous(X)<~>~brave(X)))))&
((?[X]:((~old(X)|~happy(X))))=>((humble(john)&~happy(john))))&
((?[X]:((~happy(X)<~>~strong(X))))<=>(?[X]:((~patient(X)&humble(X)))))&
(![X]:((patient(X)|~tall(X))<=>(~strong(X)|tall(X))))&
(![X]:((tall(X)&~quiet(X))=>(~happy(X)&happy(X))))&
(![X]:(~strong(X)=>(brave(X)<~>~wise(X))))&
(?[X]:((~tall(X)&funny(X))))&
(?[X]:((calm(X)&~patient(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
((quiet(alice)<~>humble(alice)))&
(?[X]:((funny(X)<~>rich(X))))&
((calm(susan)<~>humble(susan)))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:((old(X)&~brave(X)))) | ~generous(alice) | [
"p3",
"p6",
"p9",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 1827621817111469131188198
% SZS output start Proof for 1827621817111469131188198
4. ! [X0] : (brave(X0) => ~wise(X0)) [input p3]
7. ! [X0] : ((quiet(X0) | ~generous(X0)) <=> (~brave(X0) & ~strong(X0))) [input p6]
10. ! [X0] : ((~humble(X0) | kind(X0)) => (~generous(X0) & patient(X0))) [input p9]
14. ! [X0] : ((~tall(X0) | patient(X0)) <=> (tall(X0) | ~strong(X0))) [input p13]
15. ! [X0] : ((~quiet(X0) & tall(X0)) => (happy(X0) & ~happy(X0))) [input p14]
16. ! [X0] : (~strong(X0) => (brave(X0) <~> ~wise(X0))) [input p15]
20. quiet(alice) <~> humble(alice) [input p19]
25. generous(alice) [input hypothesis]
30. ! [X0] : (~wise(X0) | ~brave(X0)) [ennf transformation 4]
33. ! [X0] : ((~generous(X0) & patient(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 10]
36. ! [X0] : ((happy(X0) & ~happy(X0)) | (quiet(X0) | ~tall(X0))) [ennf transformation 15]
37. ! [X0] : ((happy(X0) & ~happy(X0)) | quiet(X0) | ~tall(X0)) [flattening 36]
38. ! [X0] : ((brave(X0) <~> ~wise(X0)) | strong(X0)) [ennf transformation 16]
55. ! [X0] : (((quiet(X0) | ~generous(X0)) | (brave(X0) | strong(X0))) & ((~brave(X0) & ~strong(X0)) | (~quiet(X0) & generous(X0)))) [nnf transformation 7]
56. ! [X0] : ((quiet(X0) | ~generous(X0) | brave(X0) | strong(X0)) & ((~brave(X0) & ~strong(X0)) | (~quiet(X0) & generous(X0)))) [flattening 55]
72. ! [X0] : (((~tall(X0) | patient(X0)) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | (tall(X0) & ~patient(X0)))) [nnf transformation 14]
73. ! [X0] : ((~tall(X0) | patient(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | (tall(X0) & ~patient(X0)))) [flattening 72]
74. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | strong(X0)) [nnf transformation 38]
82. (~humble(alice) | ~quiet(alice)) & (humble(alice) | quiet(alice)) [nnf transformation 20]
104. ~wise(X0) | ~brave(X0) [cnf transformation 30]
117. ~generous(X0) | quiet(X0) | brave(X0) | strong(X0) [cnf transformation 56]
125. ~generous(X0) | humble(X0) [cnf transformation 33]
141. tall(X0) | ~strong(X0) | tall(X0) [cnf transformation 73]
144. ~happy(X0) | quiet(X0) | ~tall(X0) [cnf transformation 37]
145. ~tall(X0) | quiet(X0) | happy(X0) [cnf transformation 37]
147. wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 74]
155. ~humble(alice) | ~quiet(alice) [cnf transformation 82]
164. generous(alice) [cnf transformation 25]
165. ~strong(X0) | tall(X0) [duplicate literal removal 141]
170. 1 <=> tall(alice) [avatar definition]
171. tall(alice) <- (1) [avatar component clause 170]
350. ~tall(X0) | quiet(X0) [subsumption resolution 144,145]
351. ~brave(X0) | strong(X0) [subsumption resolution 147,104]
364. 43 <=> quiet(alice) [avatar definition]
366. ~quiet(alice) <- (~43) [avatar component clause 364]
368. 44 <=> humble(alice) [avatar definition]
371. ~43 | ~44 [avatar split clause 155,368,364]
417. humble(alice) [resolution 125,164]
420. 44 [avatar split clause 417,368]
472. quiet(alice) | brave(alice) | strong(alice) [resolution 117,164]
474. brave(alice) | strong(alice) <- (~43) [subsumption resolution 472,366]
475. strong(alice) <- (~43) [subsumption resolution 474,351]
483. tall(alice) <- (~43) [resolution 475,165]
486. 1 | 43 [avatar split clause 483,364,170]
488. quiet(alice) <- (1) [resolution 171,350]
491. $false <- (1, ~43) [subsumption resolution 488,366]
492. ~1 | 43 [avatar contradiction clause 491]
493. $false [avatar sat refutation 371,420,486,492]
% SZS output end Proof for 1827621817111469131188198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or curious then fred is either not wise or patient. If fred is either not strong or not wise then someone is either calm or curious. If lucy is not kind then someone is either generous or quiet and vice versa. If someone is calm or tall then someone is generous or not kind and vice versa. If someone is calm then paul is either not strong or curious. Everyone who is either not generous or not old is strong and vice versa. If someone is not curious or not rich then lucy is either funny or not happy. If alice is not calm or funny then someone is kind. Everyone who is not generous or rich is brave and vice versa. Everyone who is either tall or not old is happy. If someone is both not creative and tall then lucy is both curious and happy and vice versa. Everyone who is not creative is not humble or quiet and vice versa. If someone is patient or not generous then mary is either calm or strong. Everyone who is not wise is not kind or not funny. If someone is patient then someone is not kind. Everyone who is wise is brave. Someone is both not happy and funny. Someone is either not rich or humble. Someone is either not quiet or not creative. Someone is both generous and not wise. Someone is both creative and not patient. John is not rich or not strong. Someone is not tall. Mary is not kind or not funny. | Fred is wise. | neutral | ((?[X]:((old(X)|curious(X))))=>((~wise(fred)<~>patient(fred))))&
(((~strong(fred)<~>~wise(fred)))=>(?[X]:((calm(X)<~>curious(X)))))&
((~kind(lucy))<=>(?[X]:((generous(X)<~>quiet(X)))))&
((?[X]:((calm(X)|tall(X))))<=>(?[X]:((generous(X)|~kind(X)))))&
((?[X]:(calm(X)))=>((~strong(paul)<~>curious(paul))))&
(![X]:((~generous(X)<~>~old(X))<=>strong(X)))&
((?[X]:((~curious(X)|~rich(X))))=>((funny(lucy)<~>~happy(lucy))))&
(((~calm(alice)|funny(alice)))=>(?[X]:(kind(X))))&
(![X]:((~generous(X)|rich(X))<=>brave(X)))&
(![X]:((tall(X)<~>~old(X))=>happy(X)))&
((?[X]:((~creative(X)&tall(X))))<=>((curious(lucy)&happy(lucy))))&
(![X]:(~creative(X)<=>(~humble(X)|quiet(X))))&
((?[X]:((patient(X)|~generous(X))))=>((calm(mary)<~>strong(mary))))&
(![X]:(~wise(X)=>(~kind(X)|~funny(X))))&
((?[X]:(patient(X)))=>(?[X]:(~kind(X))))&
(![X]:(wise(X)=>brave(X)))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:((generous(X)&~wise(X))))&
(?[X]:((creative(X)&~patient(X))))&
((~rich(john)|~strong(john)))&
(?[X]:(~tall(X)))&
((~kind(mary)|~funny(mary))) | wise(fred) | []
| null | 0 |
If lucy is not brave or creative then alice is both strong and not curious.
If mary is brave or calm then someone is either not old or old and vice versa.
Everyone who is both not happy and curious is funny or not tall.
If susan is not curious or kind then someone is not creative or funny and vice versa.
Everyone who is not quiet is not creative.
If someone is not calm then someone is humble or not calm.
If alice is brave or generous then someone is both humble and not happy.
Everyone who is either not tall or kind is curious.
Everyone who is both not curious and old is both curious and not strong.
If lucy is either funny or curious then someone is generous and vice versa.
If someone is kind or not curious then lucy is both not curious and humble and vice versa.
Everyone who is patient is both not patient and quiet and vice versa.
Everyone who is both not old and quiet is either quiet or not rich and vice versa.
Everyone who is not strong is generous.
If someone is calm or not curious then someone is not patient and vice versa.
If fred is generous then mary is not curious or strong.
Someone is rich or funny.
Someone is not happy or curious.
Someone is not creative.
Someone is either tall or not old.
John is either tall or not rich.
Someone is either kind or funny.
Susan is either old or not humble. | Lucy is not old. | entailment | (((~brave(lucy)|creative(lucy)))=>((strong(alice)&~curious(alice))))&
(((brave(mary)|calm(mary)))<=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((~happy(X)&curious(X))=>(funny(X)|~tall(X))))&
(((~curious(susan)|kind(susan)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:(~quiet(X)=>~creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:((humble(X)|~calm(X)))))&
(((brave(alice)|generous(alice)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:((~tall(X)<~>kind(X))=>curious(X)))&
(![X]:((~curious(X)&old(X))=>(curious(X)&~strong(X))))&
(((funny(lucy)<~>curious(lucy)))<=>(?[X]:(generous(X))))&
((?[X]:((kind(X)|~curious(X))))<=>((~curious(lucy)&humble(lucy))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
(![X]:((~old(X)&quiet(X))<=>(quiet(X)<~>~rich(X))))&
(![X]:(~strong(X)=>generous(X)))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(~patient(X))))&
((generous(fred))=>((~curious(mary)|strong(mary))))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)<~>~old(X))))&
((tall(john)<~>~rich(john)))&
(?[X]:((kind(X)<~>funny(X))))&
((old(susan)<~>~humble(susan))) | ~old(lucy) | [
"p3",
"p8",
"p10",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4084863467804340784755675
% SZS output start Proof for 4084863467804340784755675
4. (kind(susan) | ~curious(susan)) <=> ? [X0] : (funny(X0) | ~creative(X0)) [input p3]
9. ! [X0] : ((old(X0) & ~curious(X0)) => (~strong(X0) & curious(X0))) [input p8]
11. ? [X0] : (~curious(X0) | kind(X0)) <=> (humble(lucy) & ~curious(lucy)) [input p10]
19. ? [X0] : ~creative(X0) [input p18]
24. old(lucy) [input hypothesis]
34. ! [X0] : ((~strong(X0) & curious(X0)) | (~old(X0) | curious(X0))) [ennf transformation 9]
35. ! [X0] : ((~strong(X0) & curious(X0)) | ~old(X0) | curious(X0)) [flattening 34]
44. ((kind(susan) | ~curious(susan)) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X0] : (funny(X0) | ~creative(X0)) | (~kind(susan) & curious(susan))) [nnf transformation 4]
45. (kind(susan) | ~curious(susan) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X0] : (funny(X0) | ~creative(X0)) | (~kind(susan) & curious(susan))) [flattening 44]
46. (kind(susan) | ~curious(susan) | ! [X0] : (~funny(X0) & creative(X0))) & (? [X1] : (funny(X1) | ~creative(X1)) | (~kind(susan) & curious(susan))) [rectify 45]
47. ? [X1] : (funny(X1) | ~creative(X1)) => (funny(sK1) | ~creative(sK1)) [choice axiom]
48. (kind(susan) | ~curious(susan) | ! [X0] : (~funny(X0) & creative(X0))) & ((funny(sK1) | ~creative(sK1)) | (~kind(susan) & curious(susan))) [skolemisation 46,47]
59. (? [X0] : (~curious(X0) | kind(X0)) | (~humble(lucy) | curious(lucy))) & ((humble(lucy) & ~curious(lucy)) | ! [X0] : (curious(X0) & ~kind(X0))) [nnf transformation 11]
60. (? [X0] : (~curious(X0) | kind(X0)) | ~humble(lucy) | curious(lucy)) & ((humble(lucy) & ~curious(lucy)) | ! [X0] : (curious(X0) & ~kind(X0))) [flattening 59]
61. (? [X0] : (~curious(X0) | kind(X0)) | ~humble(lucy) | curious(lucy)) & ((humble(lucy) & ~curious(lucy)) | ! [X1] : (curious(X1) & ~kind(X1))) [rectify 60]
62. ? [X0] : (~curious(X0) | kind(X0)) => (~curious(sK5) | kind(sK5)) [choice axiom]
63. ((~curious(sK5) | kind(sK5)) | ~humble(lucy) | curious(lucy)) & ((humble(lucy) & ~curious(lucy)) | ! [X1] : (curious(X1) & ~kind(X1))) [skolemisation 61,62]
77. ? [X0] : ~creative(X0) => ~creative(sK10) [choice axiom]
78. ~creative(sK10) [skolemisation 19,77]
100. kind(susan) | ~curious(susan) | creative(X0) [cnf transformation 48]
110. curious(X0) | ~old(X0) | curious(X0) [cnf transformation 35]
116. ~curious(lucy) | ~kind(X1) [cnf transformation 63]
117. ~curious(lucy) | curious(X1) [cnf transformation 63]
137. ~creative(sK10) [cnf transformation 78]
146. old(lucy) [cnf transformation 24]
151. ~old(X0) | curious(X0) [duplicate literal removal 110]
194. 10 <=> curious(susan) [avatar definition]
196. ~curious(susan) <- (~10) [avatar component clause 194]
198. 11 <=> kind(susan) [avatar definition]
200. kind(susan) <- (11) [avatar component clause 198]
203. 12 <=> ! [X0] : creative(X0) [avatar definition]
204. creative(X0) <- (12) [avatar component clause 203]
205. 12 | ~10 | 11 [avatar split clause 100,198,194,203]
256. 24 <=> curious(lucy) [avatar definition]
281. 29 <=> ! [X1] : curious(X1) [avatar definition]
282. curious(X1) <- (29) [avatar component clause 281]
285. 30 <=> ! [X1] : ~kind(X1) [avatar definition]
286. ~kind(X1) <- (30) [avatar component clause 285]
288. 29 | ~24 [avatar split clause 117,256,281]
289. 30 | ~24 [avatar split clause 116,256,285]
377. curious(lucy) [resolution 151,146]
380. 24 [avatar split clause 377,256]
383. $false <- (~10, 29) [resolution 282,196]
388. 10 | ~29 [avatar contradiction clause 383]
391. $false <- (11, 30) [subsumption resolution 200,286]
392. ~11 | ~30 [avatar contradiction clause 391]
400. $false <- (12) [resolution 204,137]
401. ~12 [avatar contradiction clause 400]
404. $false [avatar sat refutation 205,288,289,380,388,392,401]
% SZS output end Proof for 4084863467804340784755675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong then someone is humble and vice versa.
If someone is both not kind and not wise then susan is either kind or generous.
Everyone who is not happy is both not funny and happy.
If someone is patient or not happy then fred is either not old or not curious and vice versa.
Everyone who is kind or humble is not humble.
If someone is either wise or curious then someone is either not brave or strong.
If someone is not wise or funny then mary is both old and tall and vice versa.
If someone is not old then paul is both not generous and tall.
If someone is rich or creative then paul is old and vice versa.
Everyone who is wise or strong is not old or not wise.
Everyone who is either funny or not patient is not kind or not old.
Everyone who is happy or old is both brave and wise.
Everyone who is generous or not kind is curious.
If someone is either not patient or kind then someone is wise or not happy.
If someone is both not happy and strong then someone is generous or not patient.
Someone is curious.
Susan is not generous.
Fred is either not rich or not happy.
Someone is patient.
Someone is both not creative and not old.
John is both wise and not quiet.
Someone is either quiet or happy. | Paul is not funny. | entailment | ((?[X]:((tall(X)<~>~strong(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~kind(X)&~wise(X))))=>((kind(susan)<~>generous(susan))))&
(![X]:(~happy(X)=>(~funny(X)&happy(X))))&
((?[X]:((patient(X)|~happy(X))))<=>((~old(fred)<~>~curious(fred))))&
(![X]:((kind(X)|humble(X))=>~humble(X)))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:((~wise(X)|funny(X))))<=>((old(mary)&tall(mary))))&
((?[X]:(~old(X)))=>((~generous(paul)&tall(paul))))&
((?[X]:((rich(X)|creative(X))))<=>(old(paul)))&
(![X]:((wise(X)|strong(X))=>(~old(X)|~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~kind(X)|~old(X))))&
(![X]:((happy(X)|old(X))=>(brave(X)&wise(X))))&
(![X]:((generous(X)|~kind(X))=>curious(X)))&
((?[X]:((~patient(X)<~>kind(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((?[X]:((~happy(X)&strong(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(?[X]:(curious(X)))&
(~generous(susan))&
((~rich(fred)<~>~happy(fred)))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)&~old(X))))&
((wise(john)&~quiet(john)))&
(?[X]:((quiet(X)<~>happy(X)))) | ~funny(paul) | [
"p6",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6818137848778399416859498
% SZS output start Proof for 6818137848778399416859498
7. ? [X0] : (funny(X0) | ~wise(X0)) <=> (tall(mary) & old(mary)) [input p6]
10. ! [X0] : ((strong(X0) | wise(X0)) => (~wise(X0) | ~old(X0))) [input p9]
12. ! [X0] : ((old(X0) | happy(X0)) => (wise(X0) & brave(X0))) [input p11]
23. funny(paul) [input hypothesis]
33. ! [X0] : ((~wise(X0) | ~old(X0)) | (~strong(X0) & ~wise(X0))) [ennf transformation 10]
34. ! [X0] : (~wise(X0) | ~old(X0) | (~strong(X0) & ~wise(X0))) [flattening 33]
37. ! [X0] : ((wise(X0) & brave(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 12]
55. (? [X0] : (funny(X0) | ~wise(X0)) | (~tall(mary) | ~old(mary))) & ((tall(mary) & old(mary)) | ! [X0] : (~funny(X0) & wise(X0))) [nnf transformation 7]
56. (? [X0] : (funny(X0) | ~wise(X0)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X0] : (~funny(X0) & wise(X0))) [flattening 55]
57. (? [X0] : (funny(X0) | ~wise(X0)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X1] : (~funny(X1) & wise(X1))) [rectify 56]
58. ? [X0] : (funny(X0) | ~wise(X0)) => (funny(sK4) | ~wise(sK4)) [choice axiom]
59. ((funny(sK4) | ~wise(sK4)) | ~tall(mary) | ~old(mary)) & ((tall(mary) & old(mary)) | ! [X1] : (~funny(X1) & wise(X1))) [skolemisation 57,58]
103. old(mary) | ~funny(X1) [cnf transformation 59]
112. ~wise(X0) | ~old(X0) | ~wise(X0) [cnf transformation 34]
119. wise(X0) | ~old(X0) [cnf transformation 37]
136. funny(paul) [cnf transformation 23]
137. ~wise(X0) | ~old(X0) [duplicate literal removal 112]
219. 18 <=> old(mary) [avatar definition]
220. old(mary) <- (18) [avatar component clause 219]
236. 22 <=> ! [X1] : ~funny(X1) [avatar definition]
237. ~funny(X1) <- (22) [avatar component clause 236]
243. 22 | 18 [avatar split clause 103,219,236]
279. ~old(X0) [subsumption resolution 119,137]
306. $false <- (18) [subsumption resolution 220,279]
307. ~18 [avatar contradiction clause 306]
312. $false <- (22) [resolution 237,136]
313. ~22 [avatar contradiction clause 312]
314. $false [avatar sat refutation 243,307,313]
% SZS output end Proof for 6818137848778399416859498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both happy and patient.
Everyone who is both old and happy is tall.
Everyone who is either not kind or quiet is either not kind or generous.
Everyone who is either not wise or not quiet is kind and vice versa.
Everyone who is kind or not generous is both not strong and wise.
Everyone who is creative or quiet is either strong or not generous.
Everyone who is not kind or not happy is both not curious and not happy and vice versa.
If mary is happy or patient then someone is either brave or not brave and vice versa.
Everyone who is both patient and quiet is both not calm and happy and vice versa.
If someone is not old then someone is generous or kind and vice versa.
If paul is strong or not patient then fred is both not creative and not strong.
If alice is not brave or wise then someone is not tall and vice versa.
Everyone who is not quiet or not rich is not brave.
Lucy is either not wise or not patient.
Mary is humble or not tall.
Someone is either not brave or brave.
Someone is humble.
Lucy is not humble.
Alice is either rich or quiet.
John is not tall or not kind.
Lucy is both not curious and not creative. | Mary is calm. | entailment | (![X]:(~strong(X)=>(happy(X)&patient(X))))&
(![X]:((old(X)&happy(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((kind(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((creative(X)|quiet(X))=>(strong(X)<~>~generous(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~curious(X)&~happy(X))))&
(((happy(mary)|patient(mary)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((patient(X)&quiet(X))<=>(~calm(X)&happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:((generous(X)|kind(X)))))&
(((strong(paul)|~patient(paul)))=>((~creative(fred)&~strong(fred))))&
(((~brave(alice)|wise(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~quiet(X)|~rich(X))=>~brave(X)))&
((~wise(lucy)<~>~patient(lucy)))&
((humble(mary)|~tall(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
((rich(alice)<~>quiet(alice)))&
((~tall(john)|~kind(john)))&
((~curious(lucy)&~creative(lucy))) | calm(mary) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 147565709971908367254642
% SZS output start Proof for 147565709971908367254642
1. ! [X0] : (~strong(X0) => (patient(X0) & happy(X0))) [input p0]
3. ! [X0] : ((~kind(X0) <~> quiet(X0)) => (~kind(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p3]
5. ! [X0] : ((~generous(X0) | kind(X0)) => (wise(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((quiet(X0) | creative(X0)) => (strong(X0) <~> ~generous(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | ~kind(X0)) <=> (~happy(X0) & ~curious(X0))) [input p6]
8. (patient(mary) | happy(mary)) <=> ? [X0] : (brave(X0) <~> ~brave(X0)) [input p7]
9. ! [X0] : ((quiet(X0) & patient(X0)) <=> (happy(X0) & ~calm(X0))) [input p8]
22. ~calm(mary) [input hypothesis]
26. ! [X0] : (quiet(X0) => (strong(X0) <~> ~generous(X0))) [pure predicate removal 6]
27. ! [X0] : ((patient(X0) & happy(X0)) | strong(X0)) [ennf transformation 1]
30. ! [X0] : ((~kind(X0) <~> generous(X0)) | (~kind(X0) <=> quiet(X0))) [ennf transformation 3]
31. ! [X0] : ((wise(X0) & ~strong(X0)) | (generous(X0) & ~kind(X0))) [ennf transformation 5]
32. ! [X0] : ((strong(X0) <~> ~generous(X0)) | ~quiet(X0)) [ennf transformation 26]
35. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) [nnf transformation 30]
36. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~kind(X0)) & (kind(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 4]
37. ! [X0] : (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ~quiet(X0)) [nnf transformation 32]
38. ! [X0] : (((~happy(X0) | ~kind(X0)) | (happy(X0) | curious(X0))) & ((~happy(X0) & ~curious(X0)) | (happy(X0) & kind(X0)))) [nnf transformation 7]
39. ! [X0] : ((~happy(X0) | ~kind(X0) | happy(X0) | curious(X0)) & ((~happy(X0) & ~curious(X0)) | (happy(X0) & kind(X0)))) [flattening 38]
40. ((patient(mary) | happy(mary)) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~patient(mary) & ~happy(mary))) [nnf transformation 8]
41. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~patient(mary) & ~happy(mary))) [flattening 40]
42. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) | (~patient(mary) & ~happy(mary))) [rectify 41]
43. ? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) => ((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) [choice axiom]
44. (patient(mary) | happy(mary) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) | (~patient(mary) & ~happy(mary))) [skolemisation 42,43]
45. ! [X0] : (((quiet(X0) & patient(X0)) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | (~quiet(X0) | ~patient(X0)))) [nnf transformation 9]
46. ! [X0] : (((quiet(X0) & patient(X0)) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | ~quiet(X0) | ~patient(X0))) [flattening 45]
64. happy(X0) | strong(X0) [cnf transformation 27]
68. generous(X0) | ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 35]
69. ~generous(X0) | kind(X0) | quiet(X0) | kind(X0) [cnf transformation 35]
72. ~wise(X0) | kind(X0) | quiet(X0) [cnf transformation 36]
75. ~kind(X0) | ~strong(X0) [cnf transformation 31]
78. wise(X0) | generous(X0) [cnf transformation 31]
79. ~generous(X0) | strong(X0) | ~quiet(X0) [cnf transformation 37]
83. ~happy(X0) | kind(X0) [cnf transformation 39]
90. patient(mary) | happy(mary) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
91. patient(mary) | happy(mary) | brave(X0) | brave(X0) [cnf transformation 44]
93. ~quiet(X0) | happy(X0) | ~patient(X0) [cnf transformation 46]
95. ~happy(X0) | quiet(X0) | calm(X0) [cnf transformation 46]
117. ~calm(mary) [cnf transformation 22]
118. patient(mary) | happy(mary) | ~brave(X0) [duplicate literal removal 90]
119. patient(mary) | happy(mary) | brave(X0) [duplicate literal removal 91]
120. ~quiet(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 68]
121. ~generous(X0) | kind(X0) | quiet(X0) [duplicate literal removal 69]
123. 1 <=> ! [X0] : brave(X0) [avatar definition]
124. brave(X0) <- (1) [avatar component clause 123]
126. 2 <=> happy(mary) [avatar definition]
127. ~happy(mary) <- (~2) [avatar component clause 126]
128. happy(mary) <- (2) [avatar component clause 126]
130. 3 <=> patient(mary) [avatar definition]
132. patient(mary) <- (3) [avatar component clause 130]
133. 1 | 2 | 3 [avatar split clause 119,130,126,123]
135. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
136. ~brave(X0) <- (4) [avatar component clause 135]
137. 4 | 2 | 3 [avatar split clause 118,130,126,135]
249. kind(X1) | quiet(X1) | generous(X1) [resolution 72,78]
260. quiet(X1) | kind(X1) [subsumption resolution 249,121]
289. strong(mary) <- (~2) [resolution 127,64]
294. happy(X0) | ~patient(X0) | kind(X0) [resolution 93,260]
300. calm(X0) | quiet(X0) | strong(X0) [resolution 95,64]
317. ~patient(X0) | kind(X0) [subsumption resolution 294,83]
341. quiet(mary) | strong(mary) [resolution 300,117]
349. kind(mary) <- (3) [resolution 317,132]
352. ~strong(mary) <- (3) [resolution 349,75]
353. $false <- (~2, 3) [subsumption resolution 352,289]
354. 2 | ~3 [avatar contradiction clause 353]
355. $false <- (1, 4) [subsumption resolution 124,136]
356. ~1 | ~4 [avatar contradiction clause 355]
358. 33 <=> strong(mary) [avatar definition]
359. ~strong(mary) <- (~33) [avatar component clause 358]
362. 34 <=> quiet(mary) [avatar definition]
364. quiet(mary) <- (34) [avatar component clause 362]
365. 33 | 34 [avatar split clause 341,362,358]
372. kind(mary) <- (2) [resolution 128,83]
399. ~strong(mary) <- (2) [resolution 372,75]
400. ~33 | ~2 [avatar split clause 399,126,358]
401. ~kind(mary) | generous(mary) <- (34) [resolution 364,120]
404. generous(mary) <- (2, 34) [subsumption resolution 401,372]
409. strong(mary) | ~quiet(mary) <- (2, 34) [resolution 404,79]
410. ~quiet(mary) <- (2, ~33, 34) [subsumption resolution 409,359]
411. $false <- (2, ~33, 34) [subsumption resolution 410,364]
412. ~2 | 33 | ~34 [avatar contradiction clause 411]
413. $false [avatar sat refutation 133,137,354,356,365,400,412]
% SZS output end Proof for 147565709971908367254642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and rich then lucy is either patient or happy.
Everyone who is not rich or quiet is not generous or calm and vice versa.
Everyone who is not happy is not kind.
Everyone who is kind is patient.
Everyone who is strong or not patient is either curious or not strong.
Everyone who is not curious is tall or strong and vice versa.
Everyone who is not funny or not generous is calm and vice versa.
If john is either not curious or not brave then susan is not wise.
Everyone who is humble or not strong is either strong or not kind and vice versa.
If someone is not brave then john is not strong or not wise and vice versa.
Everyone who is patient or not happy is either not humble or brave.
If someone is not happy then paul is not wise and vice versa.
If susan is either not generous or not calm then paul is not happy and vice versa.
Everyone who is both brave and not tall is both not humble and creative.
Everyone who is either funny or not tall is both not strong and not wise and vice versa.
If someone is not kind then someone is not creative.
Susan is both not wise and not curious.
Alice is both creative and not funny.
Lucy is both not happy and not generous.
Fred is strong or happy.
Paul is either not brave or not tall.
Someone is either not old or humble.
Someone is not calm.
Someone is either not tall or not curious. | Susan is not strong. | entailment | ((?[X]:((funny(X)&rich(X))))=>((patient(lucy)<~>happy(lucy))))&
(![X]:((~rich(X)|quiet(X))<=>(~generous(X)|calm(X))))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((strong(X)|~patient(X))=>(curious(X)<~>~strong(X))))&
(![X]:(~curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>calm(X)))&
(((~curious(john)<~>~brave(john)))=>(~wise(susan)))&
(![X]:((humble(X)|~strong(X))<=>(strong(X)<~>~kind(X))))&
((?[X]:(~brave(X)))<=>((~strong(john)|~wise(john))))&
(![X]:((patient(X)|~happy(X))=>(~humble(X)<~>brave(X))))&
((?[X]:(~happy(X)))<=>(~wise(paul)))&
(((~generous(susan)<~>~calm(susan)))<=>(~happy(paul)))&
(![X]:((brave(X)&~tall(X))=>(~humble(X)&creative(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~strong(X)&~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~creative(X))))&
((~wise(susan)&~curious(susan)))&
((creative(alice)&~funny(alice)))&
((~happy(lucy)&~generous(lucy)))&
((strong(fred)|happy(fred)))&
((~brave(paul)<~>~tall(paul)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~strong(susan) | [
"p4",
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 107287303211761903883238
% SZS output start Proof for 107287303211761903883238
5. ! [X0] : ((~patient(X0) | strong(X0)) => (curious(X0) <~> ~strong(X0))) [input p4]
6. ! [X0] : (~curious(X0) <=> (strong(X0) | tall(X0))) [input p5]
25. strong(susan) [input hypothesis]
30. ! [X0] : ((curious(X0) <~> ~strong(X0)) | (patient(X0) & ~strong(X0))) [ennf transformation 5]
39. ! [X0] : (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (patient(X0) & ~strong(X0))) [nnf transformation 30]
40. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | curious(X0))) [nnf transformation 6]
41. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | curious(X0))) [flattening 40]
80. ~strong(X0) | curious(X0) | ~strong(X0) [cnf transformation 39]
86. ~curious(X0) | ~strong(X0) [cnf transformation 41]
134. strong(susan) [cnf transformation 25]
137. ~strong(X0) | curious(X0) [duplicate literal removal 80]
151. ~strong(X0) [subsumption resolution 86,137]
235. $false [subsumption resolution 134,151]
% SZS output end Proof for 107287303211761903883238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or tall then someone is not calm and vice versa.
If alice is both not strong and not rich then lucy is not kind or not brave and vice versa.
Everyone who is not curious or tall is both not humble and not curious and vice versa.
If someone is both not calm and calm then john is calm or creative and vice versa.
Everyone who is not humble is both not old and wise and vice versa.
Everyone who is either not strong or not tall is both happy and not wise.
If someone is either curious or not funny then someone is creative or happy.
Everyone who is not curious or not patient is both old and not funny.
If alice is funny then someone is both not quiet and humble.
Everyone who is not funny or not kind is either not quiet or not strong and vice versa.
If someone is either kind or wise then susan is rich or kind and vice versa.
Everyone who is both generous and not brave is not wise and vice versa.
If lucy is both rich and brave then someone is either calm or not brave and vice versa.
Everyone who is funny is both old and not creative.
Everyone who is both not old and wise is humble or wise and vice versa.
If john is both old and wise then fred is both rich and not tall.
Someone is calm or not curious.
Lucy is not strong or not curious.
Someone is happy or not patient.
Someone is both not strong and not old.
Someone is curious or patient. | Alice is quiet. | entailment | ((?[X]:((generous(X)|tall(X))))<=>(?[X]:(~calm(X))))&
(((~strong(alice)&~rich(alice)))<=>((~kind(lucy)|~brave(lucy))))&
(![X]:((~curious(X)|tall(X))<=>(~humble(X)&~curious(X))))&
((?[X]:((~calm(X)&calm(X))))<=>((calm(john)|creative(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)&~wise(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~curious(X)|~patient(X))=>(old(X)&~funny(X))))&
((funny(alice))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(~quiet(X)<~>~strong(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>((rich(susan)|kind(susan))))&
(![X]:((generous(X)&~brave(X))<=>~wise(X)))&
(((rich(lucy)&brave(lucy)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(old(X)&~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(humble(X)|wise(X))))&
(((old(john)&wise(john)))=>((rich(fred)&~tall(fred))))&
(?[X]:((calm(X)|~curious(X))))&
((~strong(lucy)|~curious(lucy)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:((curious(X)|patient(X)))) | quiet(alice) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 4611856062691392925726699
% SZS output start Proof for 4611856062691392925726699
3. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (~curious(X0) & ~humble(X0))) [input p2]
5. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p4]
6. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~wise(X0) & happy(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | ~curious(X0)) => (~funny(X0) & old(X0))) [input p7]
9. funny(alice) => ? [X0] : (humble(X0) & ~quiet(X0)) [input p8]
10. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (~quiet(X0) <~> ~strong(X0))) [input p9]
15. ! [X0] : ((wise(X0) & ~old(X0)) <=> (wise(X0) | humble(X0))) [input p14]
22. ~quiet(alice) [input hypothesis]
25. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => ~wise(X0)) [pure predicate removal 6]
29. ! [X0] : (~curious(X0) => (~funny(X0) & old(X0))) [pure predicate removal 8]
30. ! [X0] : (~wise(X0) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 25]
31. ! [X0] : ((~funny(X0) & old(X0)) | curious(X0)) [ennf transformation 29]
32. ? [X0] : (humble(X0) & ~quiet(X0)) | ~funny(alice) [ennf transformation 9]
43. ! [X0] : (((tall(X0) | ~curious(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 3]
44. ! [X0] : ((tall(X0) | ~curious(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (~tall(X0) & curious(X0)))) [flattening 43]
50. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 5]
51. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 50]
52. ! [X0] : (~wise(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 30]
53. ? [X0] : (humble(X0) & ~quiet(X0)) => (humble(sK3) & ~quiet(sK3)) [choice axiom]
54. (humble(sK3) & ~quiet(sK3)) | ~funny(alice) [skolemisation 32,53]
55. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 10]
56. ! [X0] : ((~kind(X0) | ~funny(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | (kind(X0) & funny(X0)))) [flattening 55]
69. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 15]
70. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~wise(X0) | old(X0))) [flattening 69]
83. ~humble(X0) | curious(X0) [cnf transformation 44]
86. ~curious(X0) | ~tall(X0) [cnf transformation 44]
93. ~old(X0) | humble(X0) [cnf transformation 51]
94. wise(X0) | humble(X0) [cnf transformation 51]
95. ~wise(X0) | ~humble(X0) | old(X0) [cnf transformation 51]
97. ~wise(X0) | ~strong(X0) | tall(X0) [cnf transformation 52]
98. old(X0) | curious(X0) [cnf transformation 31]
101. humble(sK3) | ~funny(alice) [cnf transformation 54]
104. quiet(X0) | strong(X0) | funny(X0) [cnf transformation 56]
127. ~old(X0) | ~wise(X0) [cnf transformation 70]
128. wise(X0) | ~humble(X0) [cnf transformation 70]
136. ~quiet(alice) [cnf transformation 22]
150. 4 <=> ! [X3] : ~tall(X3) [avatar definition]
151. ~tall(X3) <- (4) [avatar component clause 150]
199. 14 <=> funny(alice) [avatar definition]
203. 15 <=> humble(sK3) [avatar definition]
205. humble(sK3) <- (15) [avatar component clause 203]
206. ~14 | 15 [avatar split clause 101,203,199]
264. wise(X0) [subsumption resolution 128,94]
265. ~old(X0) [subsumption resolution 127,264]
286. curious(X0) | humble(X0) [resolution 98,93]
288. curious(X0) [subsumption resolution 286,83]
291. ~tall(X0) [resolution 288,86]
294. 4 [avatar split clause 291,150]
300. ~humble(X2) | old(X2) [resolution 95,264]
302. ~humble(X2) [subsumption resolution 300,265]
307. ~strong(X1) | tall(X1) | humble(X1) [resolution 97,94]
310. ~strong(X1) | humble(X1) <- (4) [subsumption resolution 307,151]
311. ~strong(X1) <- (4) [subsumption resolution 310,302]
312. strong(alice) | funny(alice) [resolution 104,136]
319. funny(alice) <- (4) [subsumption resolution 312,311]
324. 14 | ~4 [avatar split clause 319,150,199]
325. $false <- (15) [subsumption resolution 205,302]
326. ~15 [avatar contradiction clause 325]
327. $false [avatar sat refutation 206,294,324,326]
% SZS output end Proof for 4611856062691392925726699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not kind is not old and vice versa. Everyone who is both brave and patient is wise and vice versa. Everyone who is both not creative and not brave is kind or not humble and vice versa. If susan is either not humble or not quiet then john is both brave and kind and vice versa. Everyone who is either happy or not strong is not happy or patient and vice versa. If alice is not funny then paul is both not happy and not wise and vice versa. Everyone who is both not kind and not strong is not strong and vice versa. If paul is either not patient or wise then someone is generous. Everyone who is generous is both kind and not kind and vice versa. If someone is funny or creative then someone is not strong or not tall. Everyone who is both calm and not tall is both happy and brave. Everyone who is not curious is creative or brave and vice versa. Everyone who is not funny or humble is not brave or not funny and vice versa. If someone is strong then mary is generous and vice versa. Everyone who is either rich or not kind is either not generous or rich. Alice is not tall or not happy. Someone is not humble. Someone is both not wise and creative. Paul is not curious or strong. Susan is not generous. Someone is not tall. Susan is not quiet. Someone is brave. | Alice is funny. | contradiction | (![X]:((~tall(X)|~kind(X))<=>~old(X)))&
(![X]:((brave(X)&patient(X))<=>wise(X)))&
(![X]:((~creative(X)&~brave(X))<=>(kind(X)|~humble(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>((brave(john)&kind(john))))&
(![X]:((happy(X)<~>~strong(X))<=>(~happy(X)|patient(X))))&
((~funny(alice))<=>((~happy(paul)&~wise(paul))))&
(![X]:((~kind(X)&~strong(X))<=>~strong(X)))&
(((~patient(paul)<~>wise(paul)))=>(?[X]:(generous(X))))&
(![X]:(generous(X)<=>(kind(X)&~kind(X))))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((calm(X)&~tall(X))=>(happy(X)&brave(X))))&
(![X]:(~curious(X)<=>(creative(X)|brave(X))))&
(![X]:((~funny(X)|humble(X))<=>(~brave(X)|~funny(X))))&
((?[X]:(strong(X)))<=>(generous(mary)))&
(![X]:((rich(X)<~>~kind(X))=>(~generous(X)<~>rich(X))))&
((~tall(alice)|~happy(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~wise(X)&creative(X))))&
((~curious(paul)|strong(paul)))&
(~generous(susan))&
(?[X]:(~tall(X)))&
(~quiet(susan))&
(?[X]:(brave(X))) | funny(alice) | [
"p1",
"p4",
"p5",
"p7",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5836923374480337829482849
% SZS output start Proof for 5836923374480337829482849
2. ! [X0] : ((patient(X0) & brave(X0)) <=> wise(X0)) [input p1]
5. ! [X0] : ((happy(X0) <~> ~strong(X0)) <=> (patient(X0) | ~happy(X0))) [input p4]
6. ~funny(alice) <=> (~wise(paul) & ~happy(paul)) [input p5]
8. (~patient(paul) <~> wise(paul)) => ? [X0] : generous(X0) [input p7]
9. ! [X0] : (generous(X0) <=> (~kind(X0) & kind(X0))) [input p8]
14. ? [X0] : strong(X0) <=> generous(mary) [input p13]
24. funny(alice) [input hypothesis]
31. ? [X0] : generous(X0) | (~patient(paul) <=> wise(paul)) [ennf transformation 8]
35. ! [X0] : (((patient(X0) & brave(X0)) | ~wise(X0)) & (wise(X0) | (~patient(X0) | ~brave(X0)))) [nnf transformation 2]
36. ! [X0] : (((patient(X0) & brave(X0)) | ~wise(X0)) & (wise(X0) | ~patient(X0) | ~brave(X0))) [flattening 35]
41. ! [X0] : ((((strong(X0) | ~happy(X0)) & (~strong(X0) | happy(X0))) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))))) [nnf transformation 5]
42. ! [X0] : ((((strong(X0) | ~happy(X0)) & (~strong(X0) | happy(X0))) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))))) [flattening 41]
43. (~funny(alice) | (wise(paul) | happy(paul))) & ((~wise(paul) & ~happy(paul)) | funny(alice)) [nnf transformation 6]
44. (~funny(alice) | wise(paul) | happy(paul)) & ((~wise(paul) & ~happy(paul)) | funny(alice)) [flattening 43]
47. ? [X0] : generous(X0) | ((~patient(paul) | ~wise(paul)) & (wise(paul) | patient(paul))) [nnf transformation 31]
48. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
49. generous(sK0) | ((~patient(paul) | ~wise(paul)) & (wise(paul) | patient(paul))) [skolemisation 47,48]
50. ! [X0] : ((generous(X0) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | ~generous(X0))) [nnf transformation 9]
51. ! [X0] : ((generous(X0) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ~generous(X0))) [flattening 50]
54. (? [X0] : strong(X0) | ~generous(mary)) & (generous(mary) | ! [X0] : ~strong(X0)) [nnf transformation 14]
55. (? [X0] : strong(X0) | ~generous(mary)) & (generous(mary) | ! [X1] : ~strong(X1)) [rectify 54]
56. ? [X0] : strong(X0) => strong(sK1) [choice axiom]
57. (strong(sK1) | ~generous(mary)) & (generous(mary) | ! [X1] : ~strong(X1)) [skolemisation 55,56]
67. ~wise(X0) | patient(X0) [cnf transformation 36]
84. ~happy(X0) | strong(X0) | ~patient(X0) [cnf transformation 42]
87. ~funny(alice) | wise(paul) | happy(paul) [cnf transformation 44]
91. generous(sK0) | wise(paul) | patient(paul) [cnf transformation 49]
92. generous(sK0) | ~patient(paul) | ~wise(paul) [cnf transformation 49]
93. kind(X0) | ~generous(X0) [cnf transformation 51]
94. ~generous(X0) | ~kind(X0) [cnf transformation 51]
101. generous(mary) | ~strong(X1) [cnf transformation 57]
114. funny(alice) [cnf transformation 24]
141. 5 <=> happy(paul) [avatar definition]
143. happy(paul) <- (5) [avatar component clause 141]
145. 6 <=> wise(paul) [avatar definition]
149. 7 <=> funny(alice) [avatar definition]
152. 5 | 6 | ~7 [avatar split clause 87,149,145,141]
155. generous(sK0) | ~wise(paul) [subsumption resolution 92,67]
157. 8 <=> generous(sK0) [avatar definition]
159. generous(sK0) <- (8) [avatar component clause 157]
160. ~6 | 8 [avatar split clause 155,157,145]
161. generous(sK0) | patient(paul) [subsumption resolution 91,67]
163. 9 <=> patient(paul) [avatar definition]
165. patient(paul) <- (9) [avatar component clause 163]
166. 9 | 8 [avatar split clause 161,157,163]
167. ~generous(X0) [subsumption resolution 93,94]
170. ~strong(X1) [subsumption resolution 101,167]
174. 7 [avatar split clause 114,149]
175. $false <- (8) [subsumption resolution 159,167]
176. ~8 [avatar contradiction clause 175]
185. strong(paul) | ~patient(paul) <- (5) [resolution 84,143]
186. ~patient(paul) <- (5) [subsumption resolution 185,170]
187. $false <- (5, 9) [subsumption resolution 186,165]
188. ~5 | ~9 [avatar contradiction clause 187]
189. $false [avatar sat refutation 152,160,166,174,176,188]
% SZS output end Proof for 5836923374480337829482849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not strong is old and vice versa.
If fred is not quiet or not funny then alice is either not happy or quiet.
Everyone who is either curious or not calm is not wise.
Everyone who is both not old and old is either strong or not humble.
Everyone who is either not strong or strong is not creative and vice versa.
Everyone who is kind is not kind or humble.
Everyone who is either creative or not quiet is either not curious or not rich and vice versa.
If fred is both patient and not strong then alice is both not tall and generous.
Everyone who is humble is both quiet and strong.
If someone is patient then alice is both old and wise.
If someone is not humble then paul is not curious or not rich.
If someone is kind or not kind then alice is not calm.
If someone is either funny or curious then someone is old or not happy and vice versa.
If fred is either brave or curious then lucy is not old or funny.
Everyone who is not funny is both tall and rich.
If alice is either not generous or not brave then someone is both happy and not generous.
Someone is tall.
Someone is tall or humble.
Susan is kind.
Paul is patient or wise.
Someone is both not brave and old.
John is curious or not kind.
Mary is both not old and tall. | Fred is not patient. | entailment | (![X]:((calm(X)&~strong(X))<=>old(X)))&
(((~quiet(fred)|~funny(fred)))=>((~happy(alice)<~>quiet(alice))))&
(![X]:((curious(X)<~>~calm(X))=>~wise(X)))&
(![X]:((~old(X)&old(X))=>(strong(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>strong(X))<=>~creative(X)))&
(![X]:(kind(X)=>(~kind(X)|humble(X))))&
(![X]:((creative(X)<~>~quiet(X))<=>(~curious(X)<~>~rich(X))))&
(((patient(fred)&~strong(fred)))=>((~tall(alice)&generous(alice))))&
(![X]:(humble(X)=>(quiet(X)&strong(X))))&
((?[X]:(patient(X)))=>((old(alice)&wise(alice))))&
((?[X]:(~humble(X)))=>((~curious(paul)|~rich(paul))))&
((?[X]:((kind(X)|~kind(X))))=>(~calm(alice)))&
((?[X]:((funny(X)<~>curious(X))))<=>(?[X]:((old(X)|~happy(X)))))&
(((brave(fred)<~>curious(fred)))=>((~old(lucy)|funny(lucy))))&
(![X]:(~funny(X)=>(tall(X)&rich(X))))&
(((~generous(alice)<~>~brave(alice)))=>(?[X]:((happy(X)&~generous(X)))))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)|humble(X))))&
(kind(susan))&
((patient(paul)|wise(paul)))&
(?[X]:((~brave(X)&old(X))))&
((curious(john)|~kind(john)))&
((~old(mary)&tall(mary))) | ~patient(fred) | [
"p0",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 193217227268457635621177
% SZS output start Proof for 193217227268457635621177
1. ! [X0] : ((~strong(X0) & calm(X0)) <=> old(X0)) [input p0]
10. ? [X0] : patient(X0) => (wise(alice) & old(alice)) [input p9]
12. ? [X0] : (~kind(X0) | kind(X0)) => ~calm(alice) [input p11]
24. patient(fred) [input hypothesis]
35. (wise(alice) & old(alice)) | ! [X0] : ~patient(X0) [ennf transformation 10]
38. ~calm(alice) | ! [X0] : (kind(X0) & ~kind(X0)) [ennf transformation 12]
43. ! [X0] : (((~strong(X0) & calm(X0)) | ~old(X0)) & (old(X0) | (strong(X0) | ~calm(X0)))) [nnf transformation 1]
44. ! [X0] : (((~strong(X0) & calm(X0)) | ~old(X0)) & (old(X0) | strong(X0) | ~calm(X0))) [flattening 43]
66. ~old(X0) | calm(X0) [cnf transformation 44]
93. old(alice) | ~patient(X0) [cnf transformation 35]
96. ~calm(alice) | ~kind(X0) [cnf transformation 38]
97. ~calm(alice) | kind(X0) [cnf transformation 38]
121. patient(fred) [cnf transformation 24]
151. 5 <=> patient(fred) [avatar definition]
152. patient(fred) <- (5) [avatar component clause 151]
169. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
170. ~patient(X0) <- (9) [avatar component clause 169]
177. 11 <=> old(alice) [avatar definition]
179. old(alice) <- (11) [avatar component clause 177]
180. 9 | 11 [avatar split clause 93,177,169]
194. 15 <=> ! [X0] : kind(X0) [avatar definition]
195. kind(X0) <- (15) [avatar component clause 194]
197. 16 <=> calm(alice) [avatar definition]
200. 15 | ~16 [avatar split clause 97,197,194]
202. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
203. ~kind(X0) <- (17) [avatar component clause 202]
204. 17 | ~16 [avatar split clause 96,197,202]
300. 5 [avatar split clause 121,151]
301. $false <- (5, 9) [subsumption resolution 152,170]
302. ~5 | ~9 [avatar contradiction clause 301]
304. calm(alice) <- (11) [resolution 66,179]
307. 16 | ~11 [avatar split clause 304,177,197]
308. $false <- (15, 17) [subsumption resolution 195,203]
309. ~15 | ~17 [avatar contradiction clause 308]
310. $false [avatar sat refutation 180,200,204,300,302,307,309]
% SZS output end Proof for 193217227268457635621177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and brave then susan is either not old or not happy and vice versa. Everyone who is either rich or patient is both not tall and not quiet and vice versa. Everyone who is both strong and not happy is either not wise or funny. If someone is both funny and not calm then someone is not rich or not wise. Everyone who is either tall or humble is not funny and vice versa. Everyone who is both rich and curious is patient or not creative and vice versa. If john is both not tall and not rich then paul is tall or not calm. If someone is either not strong or brave then john is either old or strong. If lucy is both quiet and patient then fred is not wise. If fred is either humble or patient then someone is both strong and patient and vice versa. If paul is both not quiet and not kind then fred is either not old or curious. If someone is curious then alice is either curious or tall. Everyone who is both not curious and not funny is rich and vice versa. Everyone who is both not old and not strong is not patient and vice versa. Everyone who is rich is kind or happy and vice versa. If someone is either not old or wise then paul is generous or patient. Lucy is either strong or calm. John is either not rich or not old. Fred is either patient or quiet. Someone is not wise or kind. Lucy is curious or patient. Someone is not curious. Someone is funny or not patient. | John is brave. | entailment | ((?[X]:((~wise(X)&brave(X))))<=>((~old(susan)<~>~happy(susan))))&
(![X]:((rich(X)<~>patient(X))<=>(~tall(X)&~quiet(X))))&
(![X]:((strong(X)&~happy(X))=>(~wise(X)<~>funny(X))))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((tall(X)<~>humble(X))<=>~funny(X)))&
(![X]:((rich(X)&curious(X))<=>(patient(X)|~creative(X))))&
(((~tall(john)&~rich(john)))=>((tall(paul)|~calm(paul))))&
((?[X]:((~strong(X)<~>brave(X))))=>((old(john)<~>strong(john))))&
(((quiet(lucy)&patient(lucy)))=>(~wise(fred)))&
(((humble(fred)<~>patient(fred)))<=>(?[X]:((strong(X)&patient(X)))))&
(((~quiet(paul)&~kind(paul)))=>((~old(fred)<~>curious(fred))))&
((?[X]:(curious(X)))=>((curious(alice)<~>tall(alice))))&
(![X]:((~curious(X)&~funny(X))<=>rich(X)))&
(![X]:((~old(X)&~strong(X))<=>~patient(X)))&
(![X]:(rich(X)<=>(kind(X)|happy(X))))&
((?[X]:((~old(X)<~>wise(X))))=>((generous(paul)|patient(paul))))&
((strong(lucy)<~>calm(lucy)))&
((~rich(john)<~>~old(john)))&
((patient(fred)<~>quiet(fred)))&
(?[X]:((~wise(X)|kind(X))))&
((curious(lucy)|patient(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((funny(X)|~patient(X)))) | brave(john) | [
"p5",
"p7",
"p9",
"p12",
"p13",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 3215954118821073132633548
% SZS output start Proof for 3215954118821073132633548
6. ! [X0] : ((curious(X0) & rich(X0)) <=> (~creative(X0) | patient(X0))) [input p5]
8. ? [X0] : (~strong(X0) <~> brave(X0)) => (old(john) <~> strong(john)) [input p7]
10. (humble(fred) <~> patient(fred)) <=> ? [X0] : (patient(X0) & strong(X0)) [input p9]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> rich(X0)) [input p12]
14. ! [X0] : ((~strong(X0) & ~old(X0)) <=> ~patient(X0)) [input p13]
18. ~rich(john) <~> ~old(john) [input p17]
24. ~brave(john) [input hypothesis]
32. (old(john) <~> strong(john)) | ! [X0] : (~strong(X0) <=> brave(X0)) [ennf transformation 8]
49. ! [X0] : (((curious(X0) & rich(X0)) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | (~curious(X0) | ~rich(X0)))) [nnf transformation 6]
50. ! [X0] : (((curious(X0) & rich(X0)) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ~curious(X0) | ~rich(X0))) [flattening 49]
51. ((~strong(john) | ~old(john)) & (strong(john) | old(john))) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))) [nnf transformation 32]
52. (((~patient(fred) | ~humble(fred)) & (patient(fred) | humble(fred))) | ! [X0] : (~patient(X0) | ~strong(X0))) & (? [X0] : (patient(X0) & strong(X0)) | ((humble(fred) | ~patient(fred)) & (patient(fred) | ~humble(fred)))) [nnf transformation 10]
53. (((~patient(fred) | ~humble(fred)) & (patient(fred) | humble(fred))) | ! [X0] : (~patient(X0) | ~strong(X0))) & (? [X1] : (patient(X1) & strong(X1)) | ((humble(fred) | ~patient(fred)) & (patient(fred) | ~humble(fred)))) [rectify 52]
54. ? [X1] : (patient(X1) & strong(X1)) => (patient(sK2) & strong(sK2)) [choice axiom]
55. (((~patient(fred) | ~humble(fred)) & (patient(fred) | humble(fred))) | ! [X0] : (~patient(X0) | ~strong(X0))) & ((patient(sK2) & strong(sK2)) | ((humble(fred) | ~patient(fred)) & (patient(fred) | ~humble(fred)))) [skolemisation 53,54]
58. ! [X0] : (((~funny(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | (funny(X0) | curious(X0)))) [nnf transformation 13]
59. ! [X0] : (((~funny(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | funny(X0) | curious(X0))) [flattening 58]
60. ! [X0] : (((~strong(X0) & ~old(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) | old(X0)))) [nnf transformation 14]
61. ! [X0] : (((~strong(X0) & ~old(X0)) | patient(X0)) & (~patient(X0) | strong(X0) | old(X0))) [flattening 60]
65. (old(john) | rich(john)) & (~old(john) | ~rich(john)) [nnf transformation 18]
93. ~patient(X0) | rich(X0) [cnf transformation 50]
95. ~patient(X0) | curious(X0) [cnf transformation 50]
98. strong(john) | old(john) | brave(X0) | strong(X0) [cnf transformation 51]
105. patient(sK2) | patient(fred) | ~humble(fred) [cnf transformation 55]
107. patient(fred) | humble(fred) | ~patient(X0) | ~strong(X0) [cnf transformation 55]
114. ~curious(X0) | ~rich(X0) [cnf transformation 59]
117. ~old(X0) | patient(X0) [cnf transformation 61]
118. ~strong(X0) | patient(X0) [cnf transformation 61]
124. ~old(john) | ~rich(john) [cnf transformation 65]
132. ~brave(john) [cnf transformation 24]
175. 10 <=> rich(john) [avatar definition]
176. ~rich(john) <- (~10) [avatar component clause 175]
191. 14 <=> old(john) [avatar definition]
192. old(john) <- (14) [avatar component clause 191]
195. 15 <=> strong(john) [avatar definition]
196. strong(john) <- (15) [avatar component clause 195]
200. 16 <=> ! [X0] : (brave(X0) | strong(X0)) [avatar definition]
201. brave(X0) | strong(X0) <- (16) [avatar component clause 200]
204. 16 | 14 | 15 [avatar split clause 98,195,191,200]
219. 20 <=> ! [X0] : (~patient(X0) | ~strong(X0)) [avatar definition]
220. ~patient(X0) | ~strong(X0) <- (20) [avatar component clause 219]
222. 21 <=> humble(fred) [avatar definition]
226. 22 <=> patient(fred) [avatar definition]
227. patient(fred) <- (22) [avatar component clause 226]
230. 20 | 21 | 22 [avatar split clause 107,226,222,219]
232. 23 <=> patient(sK2) [avatar definition]
234. patient(sK2) <- (23) [avatar component clause 232]
236. ~21 | 22 | 23 [avatar split clause 105,232,226,222]
256. 28 <=> curious(fred) [avatar definition]
257. curious(fred) <- (28) [avatar component clause 256]
285. ~10 | ~14 [avatar split clause 124,191,175]
316. rich(fred) <- (22) [resolution 93,227]
317. rich(sK2) <- (23) [resolution 93,234]
318. curious(fred) <- (22) [resolution 95,227]
319. curious(sK2) <- (23) [resolution 95,234]
322. 28 | ~22 [avatar split clause 318,226,256]
324. ~rich(fred) <- (28) [resolution 114,257]
326. ~rich(sK2) <- (23) [resolution 114,319]
327. $false <- (22, 28) [subsumption resolution 324,316]
328. ~22 | ~28 [avatar contradiction clause 327]
329. $false <- (23) [subsumption resolution 326,317]
330. ~23 [avatar contradiction clause 329]
331. ~strong(X0) <- (20) [subsumption resolution 220,118]
335. patient(john) <- (14) [resolution 117,192]
339. rich(john) <- (14) [resolution 335,93]
340. $false <- (~10, 14) [subsumption resolution 339,176]
341. 10 | ~14 [avatar contradiction clause 340]
342. $false <- (15, 20) [subsumption resolution 196,331]
343. ~15 | ~20 [avatar contradiction clause 342]
344. brave(X0) <- (16, 20) [subsumption resolution 201,331]
345. $false <- (16, 20) [resolution 344,132]
346. ~16 | ~20 [avatar contradiction clause 345]
347. $false [avatar sat refutation 204,230,236,285,322,328,330,341,343,346]
% SZS output end Proof for 3215954118821073132633548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not quiet is either not brave or not curious and vice versa.
Everyone who is not humble or kind is curious or not curious and vice versa.
If lucy is both wise and curious then paul is either funny or tall and vice versa.
If paul is not tall or not kind then mary is tall.
Everyone who is either not calm or not old is both not humble and humble and vice versa.
Everyone who is funny is both humble and patient and vice versa.
If alice is not quiet or not happy then alice is either not funny or curious and vice versa.
Everyone who is not old is old.
Everyone who is tall or not happy is either not humble or not happy.
If someone is either curious or quiet then someone is not funny.
Everyone who is either not kind or not patient is both happy and not happy.
Everyone who is both creative and not brave is not brave or not wise.
Everyone who is either curious or generous is not wise or kind and vice versa.
If mary is both not funny and wise then fred is both not wise and not old and vice versa.
If someone is curious then susan is not strong and vice versa.
If someone is both kind and not strong then someone is both not humble and not funny and vice versa.
Fred is funny.
Alice is wise or strong.
Someone is not generous.
Paul is not quiet.
Someone is either tall or not tall.
Paul is not calm or wise.
Someone is either not brave or calm. | Susan is not strong. | neutral | (![X]:((curious(X)<~>~quiet(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~humble(X)|kind(X))<=>(curious(X)|~curious(X))))&
(((wise(lucy)&curious(lucy)))<=>((funny(paul)<~>tall(paul))))&
(((~tall(paul)|~kind(paul)))=>(tall(mary)))&
(![X]:((~calm(X)<~>~old(X))<=>(~humble(X)&humble(X))))&
(![X]:(funny(X)<=>(humble(X)&patient(X))))&
(((~quiet(alice)|~happy(alice)))<=>((~funny(alice)<~>curious(alice))))&
(![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)|~happy(X))=>(~humble(X)<~>~happy(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>~patient(X))=>(happy(X)&~happy(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)|~wise(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~wise(X)|kind(X))))&
(((~funny(mary)&wise(mary)))<=>((~wise(fred)&~old(fred))))&
((?[X]:(curious(X)))<=>(~strong(susan)))&
((?[X]:((kind(X)&~strong(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(funny(fred))&
((wise(alice)|strong(alice)))&
(?[X]:(~generous(X)))&
(~quiet(paul))&
(?[X]:((tall(X)<~>~tall(X))))&
((~calm(paul)|wise(paul)))&
(?[X]:((~brave(X)<~>calm(X)))) | ~strong(susan) | []
| null | 0 |
Everyone who is not tall is old.
Everyone who is either happy or not kind is both happy and calm.
Everyone who is not generous is strong.
If paul is creative then someone is wise or patient and vice versa.
Everyone who is not brave is both not humble and kind.
Everyone who is both not curious and brave is not funny or tall and vice versa.
Everyone who is happy or kind is not rich or not funny.
Everyone who is either not tall or funny is wise or not tall.
Everyone who is not wise or wise is not old.
If someone is not happy then lucy is not quiet or wise and vice versa.
Everyone who is either curious or not creative is quiet.
Everyone who is not kind or generous is either not happy or not creative.
Everyone who is either not calm or not humble is strong and vice versa.
If john is tall then someone is either old or not patient.
If fred is not old or creative then alice is not strong.
If someone is not curious or funny then paul is not rich and vice versa.
Someone is not quiet or not rich.
Someone is either funny or old.
Someone is either not funny or tall.
Lucy is both generous and calm.
Someone is not old.
Paul is not calm or strong.
Mary is not calm. | Lucy is not happy. | neutral | (![X]:(~tall(X)=>old(X)))&
(![X]:((happy(X)<~>~kind(X))=>(happy(X)&calm(X))))&
(![X]:(~generous(X)=>strong(X)))&
((creative(paul))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:(~brave(X)=>(~humble(X)&kind(X))))&
(![X]:((~curious(X)&brave(X))<=>(~funny(X)|tall(X))))&
(![X]:((happy(X)|kind(X))=>(~rich(X)|~funny(X))))&
(![X]:((~tall(X)<~>funny(X))=>(wise(X)|~tall(X))))&
(![X]:((~wise(X)|wise(X))=>~old(X)))&
((?[X]:(~happy(X)))<=>((~quiet(lucy)|wise(lucy))))&
(![X]:((curious(X)<~>~creative(X))=>quiet(X)))&
(![X]:((~kind(X)|generous(X))=>(~happy(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>strong(X)))&
((tall(john))=>(?[X]:((old(X)<~>~patient(X)))))&
(((~old(fred)|creative(fred)))=>(~strong(alice)))&
((?[X]:((~curious(X)|funny(X))))<=>(~rich(paul)))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:((funny(X)<~>old(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
((generous(lucy)&calm(lucy)))&
(?[X]:(~old(X)))&
((~calm(paul)|strong(paul)))&
(~calm(mary)) | ~happy(lucy) | []
| null | 0 |
If mary is both wise and not happy then someone is not happy or generous. Everyone who is either strong or not rich is both patient and old. Everyone who is not curious or not tall is either not rich or not curious and vice versa. Everyone who is patient or not old is both patient and tall. Everyone who is not funny is not generous. Everyone who is creative or not calm is creative and vice versa. If susan is patient or not happy then fred is both funny and not patient. If john is not quiet or brave then someone is old or funny and vice versa. Everyone who is not patient or not calm is either not quiet or patient and vice versa. Everyone who is not humble or not generous is generous. If paul is either kind or not generous then paul is not rich. If mary is both humble and not quiet then someone is either not funny or not brave and vice versa. Everyone who is not happy is humble. Everyone who is either old or not brave is not old or not kind. If john is not brave then mary is either wise or kind and vice versa. Everyone who is both calm and not funny is either not kind or not curious and vice versa. Alice is either not strong or not patient. Someone is not wise or funny. John is either patient or not quiet. Someone is old. Fred is both not happy and patient. Fred is either kind or not curious. | Alice is not strong. | neutral | (((wise(mary)&~happy(mary)))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((strong(X)<~>~rich(X))=>(patient(X)&old(X))))&
(![X]:((~curious(X)|~tall(X))<=>(~rich(X)<~>~curious(X))))&
(![X]:((patient(X)|~old(X))=>(patient(X)&tall(X))))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:((creative(X)|~calm(X))<=>creative(X)))&
(((patient(susan)|~happy(susan)))=>((funny(fred)&~patient(fred))))&
(((~quiet(john)|brave(john)))<=>(?[X]:((old(X)|funny(X)))))&
(![X]:((~patient(X)|~calm(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((~humble(X)|~generous(X))=>generous(X)))&
(((kind(paul)<~>~generous(paul)))=>(~rich(paul)))&
(((humble(mary)&~quiet(mary)))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:(~happy(X)=>humble(X)))&
(![X]:((old(X)<~>~brave(X))=>(~old(X)|~kind(X))))&
((~brave(john))<=>((wise(mary)<~>kind(mary))))&
(![X]:((calm(X)&~funny(X))<=>(~kind(X)<~>~curious(X))))&
((~strong(alice)<~>~patient(alice)))&
(?[X]:((~wise(X)|funny(X))))&
((patient(john)<~>~quiet(john)))&
(?[X]:(old(X)))&
((~happy(fred)&patient(fred)))&
((kind(fred)<~>~curious(fred))) | ~strong(alice) | []
| null | 0 |
Everyone who is kind is either not happy or not quiet. Everyone who is both strong and not tall is not rich and vice versa. Everyone who is both generous and not humble is tall and vice versa. Everyone who is either tall or not creative is patient or not humble and vice versa. Everyone who is not calm is both old and not creative and vice versa. Everyone who is brave or funny is not quiet or brave. Everyone who is both not funny and funny is both generous and old. If paul is not funny then someone is not humble or strong. Everyone who is both not creative and kind is wise or not curious. Everyone who is either calm or funny is not kind and vice versa. Everyone who is both rich and funny is either curious or funny and vice versa. Everyone who is not tall is both kind and not creative. Everyone who is humble or not rich is not happy or strong and vice versa. Everyone who is patient is both curious and humble and vice versa. If alice is not rich then susan is both not curious and wise and vice versa. If someone is not patient or wise then mary is either humble or not calm and vice versa. Susan is not curious or happy. John is not curious or not wise. Someone is tall or not creative. Someone is not creative. Someone is rich. Susan is either not patient or calm. Someone is either curious or wise. Lucy is not quiet. | Susan is not patient. | neutral | (![X]:(kind(X)=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)&~tall(X))<=>~rich(X)))&
(![X]:((generous(X)&~humble(X))<=>tall(X)))&
(![X]:((tall(X)<~>~creative(X))<=>(patient(X)|~humble(X))))&
(![X]:(~calm(X)<=>(old(X)&~creative(X))))&
(![X]:((brave(X)|funny(X))=>(~quiet(X)|brave(X))))&
(![X]:((~funny(X)&funny(X))=>(generous(X)&old(X))))&
((~funny(paul))=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:((~creative(X)&kind(X))=>(wise(X)|~curious(X))))&
(![X]:((calm(X)<~>funny(X))<=>~kind(X)))&
(![X]:((rich(X)&funny(X))<=>(curious(X)<~>funny(X))))&
(![X]:(~tall(X)=>(kind(X)&~creative(X))))&
(![X]:((humble(X)|~rich(X))<=>(~happy(X)|strong(X))))&
(![X]:(patient(X)<=>(curious(X)&humble(X))))&
((~rich(alice))<=>((~curious(susan)&wise(susan))))&
((?[X]:((~patient(X)|wise(X))))<=>((humble(mary)<~>~calm(mary))))&
((~curious(susan)|happy(susan)))&
((~curious(john)|~wise(john)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:(~creative(X)))&
(?[X]:(rich(X)))&
((~patient(susan)<~>calm(susan)))&
(?[X]:((curious(X)<~>wise(X))))&
(~quiet(lucy)) | ~patient(susan) | []
| null | 0 |
Everyone who is either generous or not creative is both not old and not patient. If someone is creative then susan is not tall. If alice is either not brave or patient then someone is either kind or not creative and vice versa. If lucy is humble or not patient then paul is either old or happy. Everyone who is both quiet and not kind is either not kind or not humble and vice versa. Everyone who is not tall is strong and vice versa. Everyone who is old or not kind is brave and vice versa. Everyone who is both not brave and not calm is curious. If someone is creative then susan is either patient or calm. If someone is humble then someone is both not creative and not brave and vice versa. Everyone who is not funny or not strong is wise or calm. If someone is not kind or generous then someone is not rich or not calm. If alice is either not funny or not wise then someone is either not humble or creative. Everyone who is both kind and happy is patient and vice versa. Everyone who is both tall and strong is curious or not generous and vice versa. Everyone who is creative or not happy is both not humble and not happy. Alice is calm. Susan is both strong and not brave. Paul is both old and not creative. Someone is rich or not curious. John is either creative or not calm. Someone is wise. | Alice is happy. | entailment | (![X]:((generous(X)<~>~creative(X))=>(~old(X)&~patient(X))))&
((?[X]:(creative(X)))=>(~tall(susan)))&
(((~brave(alice)<~>patient(alice)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
(((humble(lucy)|~patient(lucy)))=>((old(paul)<~>happy(paul))))&
(![X]:((quiet(X)&~kind(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:(~tall(X)<=>strong(X)))&
(![X]:((old(X)|~kind(X))<=>brave(X)))&
(![X]:((~brave(X)&~calm(X))=>curious(X)))&
((?[X]:(creative(X)))=>((patient(susan)<~>calm(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~funny(X)|~strong(X))=>(wise(X)|calm(X))))&
((?[X]:((~kind(X)|generous(X))))=>(?[X]:((~rich(X)|~calm(X)))))&
(((~funny(alice)<~>~wise(alice)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((kind(X)&happy(X))<=>patient(X)))&
(![X]:((tall(X)&strong(X))<=>(curious(X)|~generous(X))))&
(![X]:((creative(X)|~happy(X))=>(~humble(X)&~happy(X))))&
(calm(alice))&
((strong(susan)&~brave(susan)))&
((old(paul)&~creative(paul)))&
(?[X]:((rich(X)|~curious(X))))&
((creative(john)<~>~calm(john)))&
(?[X]:(wise(X))) | happy(alice) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7380795207227689315832526
% SZS output start Proof for 7380795207227689315832526
1. ! [X0] : ((generous(X0) <~> ~creative(X0)) => (~patient(X0) & ~old(X0))) [input p0]
3. (~brave(alice) <~> patient(alice)) <=> ? [X0] : (kind(X0) <~> ~creative(X0)) [input p2]
4. (~patient(lucy) | humble(lucy)) => (old(paul) <~> happy(paul)) [input p3]
5. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p4]
6. ! [X0] : (~tall(X0) <=> strong(X0)) [input p5]
7. ! [X0] : ((~kind(X0) | old(X0)) <=> brave(X0)) [input p6]
14. ! [X0] : ((happy(X0) & kind(X0)) <=> patient(X0)) [input p13]
15. ! [X0] : ((strong(X0) & tall(X0)) <=> (~generous(X0) | curious(X0))) [input p14]
16. ! [X0] : ((~happy(X0) | creative(X0)) => (~happy(X0) & ~humble(X0))) [input p15]
19. ~creative(paul) & old(paul) [input p18]
23. ~happy(alice) [input hypothesis]
26. ! [X0] : ((~patient(X0) & ~old(X0)) | (generous(X0) <=> ~creative(X0))) [ennf transformation 1]
28. (old(paul) <~> happy(paul)) | (patient(lucy) & ~humble(lucy)) [ennf transformation 4]
36. ! [X0] : ((~happy(X0) & ~humble(X0)) | (happy(X0) & ~creative(X0))) [ennf transformation 16]
37. ! [X0] : ((~patient(X0) & ~old(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) [nnf transformation 26]
38. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (? [X0] : ((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [nnf transformation 3]
39. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (? [X1] : ((creative(X1) | ~kind(X1)) & (~creative(X1) | kind(X1))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [rectify 38]
40. ? [X1] : ((creative(X1) | ~kind(X1)) & (~creative(X1) | kind(X1))) => ((creative(sK0) | ~kind(sK0)) & (~creative(sK0) | kind(sK0))) [choice axiom]
41. (((~patient(alice) | brave(alice)) & (patient(alice) | ~brave(alice))) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0)))) & (((creative(sK0) | ~kind(sK0)) & (~creative(sK0) | kind(sK0))) | ((~brave(alice) | ~patient(alice)) & (patient(alice) | brave(alice)))) [skolemisation 39,40]
42. ((~happy(paul) | ~old(paul)) & (happy(paul) | old(paul))) | (patient(lucy) & ~humble(lucy)) [nnf transformation 28]
43. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (kind(X0) | ~quiet(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | kind(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))) [nnf transformation 6]
46. ! [X0] : (((~kind(X0) | old(X0)) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~old(X0)))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | old(X0) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~old(X0)))) [flattening 46]
60. ! [X0] : (((happy(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~happy(X0) | ~kind(X0)))) [nnf transformation 14]
61. ! [X0] : (((happy(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~happy(X0) | ~kind(X0))) [flattening 60]
62. ! [X0] : (((strong(X0) & tall(X0)) | (generous(X0) & ~curious(X0))) & ((~generous(X0) | curious(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((strong(X0) & tall(X0)) | (generous(X0) & ~curious(X0))) & (~generous(X0) | curious(X0) | ~strong(X0) | ~tall(X0))) [flattening 62]
71. ~patient(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 37]
79. patient(alice) | ~brave(alice) | kind(X0) | creative(X0) [cnf transformation 41]
84. ~happy(paul) | ~old(paul) | ~humble(lucy) [cnf transformation 42]
85. ~happy(paul) | ~old(paul) | patient(lucy) [cnf transformation 42]
91. ~kind(X0) | ~kind(X0) | humble(X0) [cnf transformation 44]
93. ~strong(X0) | ~tall(X0) [cnf transformation 45]
95. kind(X0) | brave(X0) [cnf transformation 47]
113. ~patient(X0) | happy(X0) [cnf transformation 61]
116. tall(X0) | generous(X0) [cnf transformation 63]
118. strong(X0) | generous(X0) [cnf transformation 63]
120. ~humble(X0) | happy(X0) [cnf transformation 36]
126. old(paul) [cnf transformation 19]
127. ~creative(paul) [cnf transformation 19]
132. ~happy(alice) [cnf transformation 23]
134. ~kind(X0) | humble(X0) [duplicate literal removal 91]
144. 3 <=> ! [X0] : (kind(X0) | creative(X0)) [avatar definition]
145. kind(X0) | creative(X0) <- (3) [avatar component clause 144]
147. 4 <=> brave(alice) [avatar definition]
151. 5 <=> patient(alice) [avatar definition]
152. patient(alice) <- (5) [avatar component clause 151]
159. 3 | ~4 | 5 [avatar split clause 79,151,147,144]
174. 9 <=> patient(lucy) [avatar definition]
176. patient(lucy) <- (9) [avatar component clause 174]
178. 10 <=> old(paul) [avatar definition]
182. 11 <=> happy(paul) [avatar definition]
184. ~happy(paul) <- (~11) [avatar component clause 182]
185. 9 | ~10 | ~11 [avatar split clause 85,182,178,174]
187. 12 <=> humble(lucy) [avatar definition]
189. ~humble(lucy) <- (~12) [avatar component clause 187]
190. ~12 | ~10 | ~11 [avatar split clause 84,182,178,187]
261. 10 [avatar split clause 126,178]
288. generous(X0) | ~tall(X0) [resolution 118,93]
289. generous(X0) [subsumption resolution 288,116]
291. humble(X0) | brave(X0) [resolution 134,95]
307. happy(X0) | brave(X0) [resolution 291,120]
310. brave(alice) [resolution 307,132]
315. 4 [avatar split clause 310,147]
317. happy(alice) <- (5) [resolution 152,113]
320. $false <- (5) [subsumption resolution 317,132]
321. ~5 [avatar contradiction clause 320]
323. humble(X0) | creative(X0) <- (3) [resolution 145,134]
331. happy(X0) | creative(X0) <- (3) [resolution 323,120]
449. creative(paul) <- (3, ~11) [resolution 331,184]
452. $false <- (3, ~11) [subsumption resolution 449,127]
453. ~3 | 11 [avatar contradiction clause 452]
456. ~creative(lucy) | ~generous(lucy) <- (9) [resolution 176,71]
459. ~creative(lucy) <- (9) [subsumption resolution 456,289]
462. creative(lucy) <- (3, ~12) [resolution 189,323]
464. $false <- (3, 9, ~12) [subsumption resolution 462,459]
465. ~3 | ~9 | 12 [avatar contradiction clause 464]
466. $false [avatar sat refutation 159,185,190,261,315,321,453,465]
% SZS output end Proof for 7380795207227689315832526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is either generous or quiet and vice versa.
Everyone who is wise is funny or not tall.
Everyone who is tall is both rich and funny and vice versa.
Everyone who is either creative or strong is both not calm and not brave and vice versa.
Everyone who is not tall or rich is both tall and calm.
Everyone who is generous or patient is quiet or not quiet and vice versa.
Everyone who is both tall and humble is creative or kind and vice versa.
Everyone who is both not happy and quiet is calm or patient and vice versa.
Everyone who is strong is either kind or not humble and vice versa.
If lucy is funny or not rich then paul is either not brave or not happy and vice versa.
If someone is both happy and not humble then fred is both not funny and not brave and vice versa.
Everyone who is either creative or calm is happy.
Everyone who is not old or not brave is both not quiet and humble.
Everyone who is not tall is either not rich or patient and vice versa.
Someone is either generous or not calm.
Paul is not tall or wise.
Someone is tall or not strong.
Someone is not curious.
Someone is either not old or brave. | Paul is tall. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:(wise(X)=>(funny(X)|~tall(X))))&
(![X]:(tall(X)<=>(rich(X)&funny(X))))&
(![X]:((creative(X)<~>strong(X))<=>(~calm(X)&~brave(X))))&
(![X]:((~tall(X)|rich(X))=>(tall(X)&calm(X))))&
(![X]:((generous(X)|patient(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((tall(X)&humble(X))<=>(creative(X)|kind(X))))&
(![X]:((~happy(X)&quiet(X))<=>(calm(X)|patient(X))))&
(![X]:(strong(X)<=>(kind(X)<~>~humble(X))))&
(((funny(lucy)|~rich(lucy)))<=>((~brave(paul)<~>~happy(paul))))&
((?[X]:((happy(X)&~humble(X))))<=>((~funny(fred)&~brave(fred))))&
(![X]:((creative(X)<~>calm(X))=>happy(X)))&
(![X]:((~old(X)|~brave(X))=>(~quiet(X)&humble(X))))&
(![X]:(~tall(X)<=>(~rich(X)<~>patient(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
((~tall(paul)|wise(paul)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~old(X)<~>brave(X)))) | tall(paul) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 450398999189647410810965
% SZS output start Proof for 450398999189647410810965
5. ! [X0] : ((rich(X0) | ~tall(X0)) => (calm(X0) & tall(X0))) [input p4]
20. ~tall(paul) [input hypothesis]
25. ! [X0] : ((calm(X0) & tall(X0)) | (~rich(X0) & tall(X0))) [ennf transformation 5]
75. tall(X0) | tall(X0) [cnf transformation 25]
123. ~tall(paul) [cnf transformation 20]
124. tall(X0) [duplicate literal removal 75]
138. 4 <=> ! [X3] : tall(X3) [avatar definition]
139. tall(X3) <- (4) [avatar component clause 138]
150. 4 [avatar split clause 124,138]
214. 18 <=> tall(paul) [avatar definition]
216. ~tall(paul) <- (~18) [avatar component clause 214]
241. ~18 [avatar split clause 123,214]
244. $false <- (4, ~18) [resolution 216,139]
245. ~4 | 18 [avatar contradiction clause 244]
246. $false [avatar sat refutation 150,241,245]
% SZS output end Proof for 450398999189647410810965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not curious is either humble or not humble.
Everyone who is either not happy or kind is creative or not strong and vice versa.
If john is both brave and not humble then someone is happy or kind and vice versa.
If someone is happy then fred is both calm and not curious and vice versa.
If someone is either kind or not generous then someone is not rich or creative and vice versa.
Everyone who is either brave or not old is old or not brave and vice versa.
Everyone who is either not wise or strong is kind.
Everyone who is happy is both patient and not rich.
Everyone who is not creative is not generous.
If someone is either not old or not quiet then mary is both not strong and creative and vice versa.
If alice is brave or funny then someone is not happy and vice versa.
If susan is either not kind or not happy then paul is either quiet or tall and vice versa.
If alice is generous or happy then fred is both not tall and kind and vice versa.
Everyone who is either calm or happy is either not rich or rich.
If paul is not happy then someone is not kind.
Everyone who is happy or not kind is both quiet and not happy and vice versa.
Lucy is wise or calm.
Someone is not strong or strong.
Someone is not old or curious.
Alice is not funny or humble.
Susan is both funny and not curious.
Fred is either kind or funny.
Someone is not creative or generous. | Paul is not curious. | neutral | (![X]:((~wise(X)&~curious(X))=>(humble(X)<~>~humble(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(creative(X)|~strong(X))))&
(((brave(john)&~humble(john)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:(happy(X)))<=>((calm(fred)&~curious(fred))))&
((?[X]:((kind(X)<~>~generous(X))))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(old(X)|~brave(X))))&
(![X]:((~wise(X)<~>strong(X))=>kind(X)))&
(![X]:(happy(X)=>(patient(X)&~rich(X))))&
(![X]:(~creative(X)=>~generous(X)))&
((?[X]:((~old(X)<~>~quiet(X))))<=>((~strong(mary)&creative(mary))))&
(((brave(alice)|funny(alice)))<=>(?[X]:(~happy(X))))&
(((~kind(susan)<~>~happy(susan)))<=>((quiet(paul)<~>tall(paul))))&
(((generous(alice)|happy(alice)))<=>((~tall(fred)&kind(fred))))&
(![X]:((calm(X)<~>happy(X))=>(~rich(X)<~>rich(X))))&
((~happy(paul))=>(?[X]:(~kind(X))))&
(![X]:((happy(X)|~kind(X))<=>(quiet(X)&~happy(X))))&
((wise(lucy)|calm(lucy)))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:((~old(X)|curious(X))))&
((~funny(alice)|humble(alice)))&
((funny(susan)&~curious(susan)))&
((kind(fred)<~>funny(fred)))&
(?[X]:((~creative(X)|generous(X)))) | ~curious(paul) | []
| null | 0 |
Everyone who is not happy is curious and vice versa.
Everyone who is either generous or not old is either tall or calm and vice versa.
If someone is creative then alice is generous or strong.
If john is either humble or funny then paul is both not rich and not calm.
If someone is both not patient and not happy then susan is generous or not funny.
Everyone who is not strong is both not happy and not calm and vice versa.
Everyone who is both not happy and not strong is both not creative and patient.
If lucy is both not funny and not happy then paul is humble or rich and vice versa.
If mary is not brave then susan is both not funny and not strong and vice versa.
If someone is generous or kind then lucy is curious and vice versa.
Everyone who is both not generous and wise is wise or kind and vice versa.
Everyone who is creative is both happy and humble and vice versa.
If someone is either not creative or kind then someone is either kind or not brave and vice versa.
Everyone who is both curious and wise is not rich.
If someone is humble then lucy is both happy and not brave.
Everyone who is either not rich or kind is both brave and not humble.
Fred is rich.
Alice is not tall or not kind.
Someone is not old or kind.
Fred is not curious or old.
Someone is either brave or wise.
Paul is not tall or brave.
Fred is creative or not quiet.
Someone is either not curious or not kind. | Lucy is not tall. | neutral | (![X]:(~happy(X)<=>curious(X)))&
(![X]:((generous(X)<~>~old(X))<=>(tall(X)<~>calm(X))))&
((?[X]:(creative(X)))=>((generous(alice)|strong(alice))))&
(((humble(john)<~>funny(john)))=>((~rich(paul)&~calm(paul))))&
((?[X]:((~patient(X)&~happy(X))))=>((generous(susan)|~funny(susan))))&
(![X]:(~strong(X)<=>(~happy(X)&~calm(X))))&
(![X]:((~happy(X)&~strong(X))=>(~creative(X)&patient(X))))&
(((~funny(lucy)&~happy(lucy)))<=>((humble(paul)|rich(paul))))&
((~brave(mary))<=>((~funny(susan)&~strong(susan))))&
((?[X]:((generous(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~generous(X)&wise(X))<=>(wise(X)|kind(X))))&
(![X]:(creative(X)<=>(happy(X)&humble(X))))&
((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((curious(X)&wise(X))=>~rich(X)))&
((?[X]:(humble(X)))=>((happy(lucy)&~brave(lucy))))&
(![X]:((~rich(X)<~>kind(X))=>(brave(X)&~humble(X))))&
(rich(fred))&
((~tall(alice)|~kind(alice)))&
(?[X]:((~old(X)|kind(X))))&
((~curious(fred)|old(fred)))&
(?[X]:((brave(X)<~>wise(X))))&
((~tall(paul)|brave(paul)))&
((creative(fred)|~quiet(fred)))&
(?[X]:((~curious(X)<~>~kind(X)))) | ~tall(lucy) | []
| null | 0 |
If john is either generous or wise then susan is not curious or not happy.
Everyone who is quiet or curious is not old or old and vice versa.
Everyone who is kind or funny is either not curious or not quiet and vice versa.
Everyone who is either not quiet or not strong is both wise and rich.
Everyone who is not quiet is both tall and patient and vice versa.
Everyone who is funny is both rich and humble.
Everyone who is creative or not patient is kind or not rich.
If someone is both not patient and not curious then someone is humble or not strong and vice versa.
If someone is not rich then someone is strong or not old and vice versa.
Everyone who is old or not humble is curious or not funny.
If someone is both not wise and funny then someone is either strong or not generous and vice versa.
Everyone who is either calm or brave is strong or funny.
If someone is both generous and quiet then someone is not creative or not humble and vice versa.
If someone is both not brave and humble then someone is calm and vice versa.
If john is quiet then susan is not generous or not quiet and vice versa.
Everyone who is either not strong or funny is both not calm and strong and vice versa.
Fred is not strong or not creative.
Lucy is either not patient or not old.
Someone is old.
Fred is curious or old.
Alice is brave.
Someone is both calm and not wise.
Someone is both not kind and curious.
John is both not kind and not humble. | Lucy is patient. | neutral | (((generous(john)<~>wise(john)))=>((~curious(susan)|~happy(susan))))&
(![X]:((quiet(X)|curious(X))<=>(~old(X)|old(X))))&
(![X]:((kind(X)|funny(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>(wise(X)&rich(X))))&
(![X]:(~quiet(X)<=>(tall(X)&patient(X))))&
(![X]:(funny(X)=>(rich(X)&humble(X))))&
(![X]:((creative(X)|~patient(X))=>(kind(X)|~rich(X))))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)|~humble(X))=>(curious(X)|~funny(X))))&
((?[X]:((~wise(X)&funny(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>brave(X))=>(strong(X)|funny(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:(calm(X))))&
((quiet(john))<=>((~generous(susan)|~quiet(susan))))&
(![X]:((~strong(X)<~>funny(X))<=>(~calm(X)&strong(X))))&
((~strong(fred)|~creative(fred)))&
((~patient(lucy)<~>~old(lucy)))&
(?[X]:(old(X)))&
((curious(fred)|old(fred)))&
(brave(alice))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((~kind(X)&curious(X))))&
((~kind(john)&~humble(john))) | patient(lucy) | []
| null | 0 |
Everyone who is not curious is either calm or not generous.
Everyone who is humble or strong is both not creative and not funny and vice versa.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is both not old and old is not kind and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
If mary is not kind or happy then lucy is either not creative or quiet.
If someone is both not strong and not old then someone is both curious and not funny.
Everyone who is either not strong or not creative is both not tall and creative.
If mary is either not funny or not rich then someone is funny.
Everyone who is curious is either not creative or curious and vice versa.
If john is not curious or not wise then someone is either old or not funny.
If someone is both not patient and not calm then mary is curious or patient.
Everyone who is either creative or kind is both creative and quiet and vice versa.
Someone is calm or wise.
John is both old and generous.
Susan is funny or calm.
Mary is either not old or not happy.
Fred is both not funny and not old.
Someone is either tall or not generous.
Someone is either generous or not generous.
Lucy is happy or not kind. | John is old. | entailment | (![X]:(~curious(X)=>(calm(X)<~>~generous(X))))&
(![X]:((humble(X)|strong(X))<=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~old(X)&old(X))<=>~kind(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(((~kind(mary)|happy(mary)))=>((~creative(lucy)<~>quiet(lucy))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~tall(X)&creative(X))))&
(((~funny(mary)<~>~rich(mary)))=>(?[X]:(funny(X))))&
(![X]:(curious(X)<=>(~creative(X)<~>curious(X))))&
(((~curious(john)|~wise(john)))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~calm(X))))=>((curious(mary)|patient(mary))))&
(![X]:((creative(X)<~>kind(X))<=>(creative(X)&quiet(X))))&
(?[X]:((calm(X)|wise(X))))&
((old(john)&generous(john)))&
((funny(susan)|calm(susan)))&
((~old(mary)<~>~happy(mary)))&
((~funny(fred)&~old(fred)))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:((generous(X)<~>~generous(X))))&
((happy(lucy)|~kind(lucy))) | old(john) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8780069995013880488424803
% SZS output start Proof for 8780069995013880488424803
17. generous(john) & old(john) [input p16]
24. ~old(john) [input hypothesis]
131. old(john) [cnf transformation 17]
143. ~old(john) [cnf transformation 24]
297. $false [subsumption resolution 143,131]
% SZS output end Proof for 8780069995013880488424803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not creative then susan is both generous and not rich. Everyone who is old or wise is not tall or happy. Everyone who is generous or not patient is both not brave and old. Everyone who is either not funny or not brave is not brave or wise and vice versa. Everyone who is funny is rich or not tall and vice versa. Everyone who is wise is not strong and vice versa. Everyone who is either strong or rich is both not rich and not curious and vice versa. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. Everyone who is both curious and happy is strong or not brave and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Fred is happy. Someone is rich or not old. Someone is either calm or rich. Someone is not patient or happy. Lucy is both brave and not generous. Someone is not calm. Someone is both kind and not old. | Susan is strong. | entailment | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((old(X)|wise(X))=>(~tall(X)|happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~brave(X)&old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~brave(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|~tall(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
((brave(lucy)&~generous(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((kind(X)&~old(X)))) | strong(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7096242266430850377177023
% SZS output start Proof for 7096242266430850377177023
2. ! [X0] : ((wise(X0) | old(X0)) => (happy(X0) | ~tall(X0))) [input p1]
4. ! [X0] : ((~funny(X0) <~> ~brave(X0)) <=> (wise(X0) | ~brave(X0))) [input p3]
5. ! [X0] : (funny(X0) <=> (~tall(X0) | rich(X0))) [input p4]
6. ! [X0] : (wise(X0) <=> ~strong(X0)) [input p5]
7. ! [X0] : ((strong(X0) <~> rich(X0)) <=> (~curious(X0) & ~rich(X0))) [input p6]
10. ! [X0] : ((~humble(X0) <~> funny(X0)) => strong(X0)) [input p9]
12. ! [X0] : (funny(X0) => (humble(X0) <~> tall(X0))) [input p11]
14. ! [X0] : ((happy(X0) & curious(X0)) <=> (~brave(X0) | strong(X0))) [input p13]
15. ? [X0] : (curious(X0) & ~funny(X0)) <=> (~happy(lucy) & ~creative(lucy)) [input p14]
23. ~strong(susan) [input hypothesis]
26. ! [X0] : ((happy(X0) | ~tall(X0)) | (~wise(X0) & ~old(X0))) [ennf transformation 2]
27. ! [X0] : (happy(X0) | ~tall(X0) | (~wise(X0) & ~old(X0))) [flattening 26]
31. ! [X0] : (strong(X0) | (~humble(X0) <=> funny(X0))) [ennf transformation 10]
33. ! [X0] : ((humble(X0) <~> tall(X0)) | ~funny(X0)) [ennf transformation 12]
35. ! [X0] : ((((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0))))) [nnf transformation 4]
36. ! [X0] : ((((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0))))) [flattening 35]
37. ! [X0] : ((funny(X0) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 5]
38. ! [X0] : ((funny(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 6]
40. ! [X0] : ((((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))))) [nnf transformation 7]
41. ! [X0] : ((((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))))) [flattening 40]
45. ! [X0] : (strong(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 31]
47. ! [X0] : (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~funny(X0)) [nnf transformation 33]
50. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 14]
51. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~happy(X0) | ~curious(X0))) [flattening 50]
52. (? [X0] : (curious(X0) & ~funny(X0)) | (happy(lucy) | creative(lucy))) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [nnf transformation 15]
53. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [flattening 52]
54. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [rectify 53]
55. ? [X0] : (curious(X0) & ~funny(X0)) => (curious(sK0) & ~funny(sK0)) [choice axiom]
56. ((curious(sK0) & ~funny(sK0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [skolemisation 54,55]
73. ~tall(X0) | happy(X0) | ~wise(X0) [cnf transformation 27]
78. wise(X0) | ~brave(X0) | ~brave(X0) | funny(X0) [cnf transformation 36]
82. brave(X0) | funny(X0) | brave(X0) [cnf transformation 36]
84. ~funny(X0) | rich(X0) | ~tall(X0) [cnf transformation 38]
85. ~rich(X0) | funny(X0) [cnf transformation 38]
86. funny(X0) | tall(X0) [cnf transformation 38]
88. strong(X0) | wise(X0) [cnf transformation 39]
90. ~rich(X0) | strong(X0) | ~rich(X0) [cnf transformation 41]
91. ~curious(X0) | rich(X0) | ~strong(X0) [cnf transformation 41]
93. rich(X0) | strong(X0) | curious(X0) | rich(X0) [cnf transformation 41]
103. ~humble(X0) | strong(X0) | ~funny(X0) [cnf transformation 45]
106. tall(X0) | humble(X0) | ~funny(X0) [cnf transformation 47]
114. ~curious(X0) | strong(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 51]
116. curious(X0) | brave(X0) [cnf transformation 51]
119. ~creative(lucy) | ~curious(X1) | funny(X1) [cnf transformation 56]
120. ~happy(lucy) | ~curious(X1) | funny(X1) [cnf transformation 56]
121. ~funny(sK0) | happy(lucy) | creative(lucy) [cnf transformation 56]
122. curious(sK0) | happy(lucy) | creative(lucy) [cnf transformation 56]
133. ~strong(susan) [cnf transformation 23]
136. ~rich(X0) | strong(X0) [duplicate literal removal 90]
137. curious(X0) | strong(X0) | rich(X0) [duplicate literal removal 93]
138. wise(X0) | ~brave(X0) | funny(X0) [duplicate literal removal 78]
139. funny(X0) | brave(X0) [duplicate literal removal 82]
144. 2 <=> rich(susan) [avatar definition]
145. rich(susan) <- (2) [avatar component clause 144]
146. ~rich(susan) <- (~2) [avatar component clause 144]
158. funny(X0) | wise(X0) [subsumption resolution 138,139]
160. 5 <=> curious(susan) [avatar definition]
161. curious(susan) <- (5) [avatar component clause 160]
162. ~curious(susan) <- (~5) [avatar component clause 160]
169. 7 <=> brave(susan) [avatar definition]
170. brave(susan) <- (7) [avatar component clause 169]
181. humble(X0) | tall(X0) [subsumption resolution 106,86]
197. 11 <=> creative(lucy) [avatar definition]
201. 12 <=> happy(lucy) [avatar definition]
205. 13 <=> curious(sK0) [avatar definition]
207. curious(sK0) <- (13) [avatar component clause 205]
208. 11 | 12 | 13 [avatar split clause 122,205,201,197]
210. 14 <=> funny(sK0) [avatar definition]
212. ~funny(sK0) <- (~14) [avatar component clause 210]
213. 11 | 12 | ~14 [avatar split clause 121,210,201,197]
215. 15 <=> ! [X1] : (~curious(X1) | funny(X1)) [avatar definition]
216. ~curious(X1) | funny(X1) <- (15) [avatar component clause 215]
217. 15 | ~12 [avatar split clause 120,201,215]
218. 15 | ~11 [avatar split clause 119,197,215]
252. tall(sK0) <- (~14) [resolution 86,212]
253. wise(susan) [resolution 88,133]
266. wise(sK0) <- (~14) [resolution 158,212]
273. 23 <=> happy(sK0) [avatar definition]
275. happy(sK0) <- (23) [avatar component clause 273]
277. happy(sK0) | ~wise(sK0) <- (~14) [resolution 73,252]
278. happy(sK0) <- (~14) [subsumption resolution 277,266]
279. 23 | 14 [avatar split clause 278,210,273]
280. funny(susan) <- (5, 15) [resolution 216,161]
293. 25 <=> brave(sK0) [avatar definition]
294. brave(sK0) <- (25) [avatar component clause 293]
307. rich(susan) | ~tall(susan) <- (5, 15) [resolution 84,280]
313. 27 <=> rich(sK0) [avatar definition]
315. rich(sK0) <- (27) [avatar component clause 313]
317. ~tall(susan) <- (~2, 5, 15) [subsumption resolution 307,146]
319. rich(sK0) | ~strong(sK0) <- (13) [resolution 91,207]
322. 28 <=> strong(sK0) [avatar definition]
324. ~strong(sK0) <- (~28) [avatar component clause 322]
325. ~28 | 27 | ~13 [avatar split clause 319,205,313,322]
332. strong(X1) | ~funny(X1) | tall(X1) [resolution 103,181]
334. strong(X1) | tall(X1) [subsumption resolution 332,86]
341. funny(sK0) <- (27) [resolution 315,85]
354. strong(X0) | ~happy(X0) | ~brave(X0) | strong(X0) | rich(X0) [resolution 114,137]
356. strong(X0) | ~happy(X0) | ~brave(X0) | rich(X0) [duplicate literal removal 354]
357. ~brave(X0) | ~happy(X0) | strong(X0) [subsumption resolution 356,136]
365. tall(susan) [resolution 334,133]
369. $false <- (~2, 5, 15) [subsumption resolution 365,317]
370. 2 | ~5 | ~15 [avatar contradiction clause 369]
373. brave(susan) <- (~5) [resolution 162,116]
380. 7 | 5 [avatar split clause 373,160,169]
381. strong(susan) <- (2) [resolution 145,136]
383. $false <- (2) [subsumption resolution 381,133]
384. ~2 [avatar contradiction clause 383]
385. 14 | ~27 [avatar split clause 341,313,210]
394. brave(sK0) <- (~14) [resolution 212,139]
410. happy(susan) | ~wise(susan) [resolution 365,73]
412. happy(susan) [subsumption resolution 410,253]
424. ~happy(susan) | strong(susan) <- (7) [resolution 357,170]
426. ~happy(sK0) | strong(sK0) <- (25) [resolution 357,294]
427. strong(susan) <- (7) [subsumption resolution 424,412]
428. $false <- (7) [subsumption resolution 427,133]
429. ~7 [avatar contradiction clause 428]
430. strong(sK0) <- (23, 25) [subsumption resolution 426,275]
431. $false <- (23, 25, ~28) [subsumption resolution 430,324]
432. ~23 | ~25 | 28 [avatar contradiction clause 431]
433. 25 | 14 [avatar split clause 394,210,293]
434. $false [avatar sat refutation 208,213,217,218,279,325,370,380,384,385,429,432,433]
% SZS output end Proof for 7096242266430850377177023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or patient is either not calm or tall and vice versa.
If susan is not brave or quiet then susan is not kind or wise.
Everyone who is either not strong or curious is not patient and vice versa.
If john is generous or not creative then paul is both not kind and not calm.
If mary is both strong and not brave then alice is either not humble or rich and vice versa.
Everyone who is not generous is either patient or not generous and vice versa.
Everyone who is not quiet is not patient.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Everyone who is both not old and not strong is strong or not strong and vice versa.
If someone is calm then alice is strong or humble and vice versa.
If paul is either happy or not brave then john is both not funny and not old.
Everyone who is both brave and not patient is either not humble or strong and vice versa.
If someone is either not strong or kind then fred is either tall or not old.
Everyone who is either not quiet or quiet is calm and vice versa.
If someone is not generous then paul is humble and vice versa.
Someone is either not wise or rich.
Fred is either tall or wise.
Susan is both not happy and not brave.
Someone is patient or not old.
Susan is not tall.
Paul is either not funny or wise.
Mary is either kind or happy.
Mary is either not patient or not wise. | Alice is rich. | contradiction | (![X]:((happy(X)<~>patient(X))<=>(~calm(X)<~>tall(X))))&
(((~brave(susan)|quiet(susan)))=>((~kind(susan)|wise(susan))))&
(![X]:((~strong(X)<~>curious(X))<=>~patient(X)))&
(((generous(john)|~creative(john)))=>((~kind(paul)&~calm(paul))))&
(((strong(mary)&~brave(mary)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~old(X)&~strong(X))<=>(strong(X)|~strong(X))))&
((?[X]:(calm(X)))<=>((strong(alice)|humble(alice))))&
(((happy(paul)<~>~brave(paul)))=>((~funny(john)&~old(john))))&
(![X]:((brave(X)&~patient(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((~strong(X)<~>kind(X))))=>((tall(fred)<~>~old(fred))))&
(![X]:((~quiet(X)<~>quiet(X))<=>calm(X)))&
((?[X]:(~generous(X)))<=>(humble(paul)))&
(?[X]:((~wise(X)<~>rich(X))))&
((tall(fred)<~>wise(fred)))&
((~happy(susan)&~brave(susan)))&
(?[X]:((patient(X)|~old(X))))&
(~tall(susan))&
((~funny(paul)<~>wise(paul)))&
((kind(mary)<~>happy(mary)))&
((~patient(mary)<~>~wise(mary))) | rich(alice) | [
"p4",
"p9",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8820793078648428988415931
% SZS output start Proof for 8820793078648428988415931
5. (~brave(mary) & strong(mary)) <=> (~humble(alice) <~> rich(alice)) [input p4]
10. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~strong(X0) | strong(X0))) [input p9]
11. ? [X0] : calm(X0) <=> (humble(alice) | strong(alice)) [input p10]
15. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> calm(X0)) [input p14]
25. rich(alice) [input hypothesis]
36. ((~brave(mary) & strong(mary)) | ((~humble(alice) | ~rich(alice)) & (rich(alice) | humble(alice)))) & (((~rich(alice) | humble(alice)) & (rich(alice) | ~humble(alice))) | (brave(mary) | ~strong(mary))) [nnf transformation 5]
37. ((~brave(mary) & strong(mary)) | ((~humble(alice) | ~rich(alice)) & (rich(alice) | humble(alice)))) & (((~rich(alice) | humble(alice)) & (rich(alice) | ~humble(alice))) | brave(mary) | ~strong(mary)) [flattening 36]
47. ! [X0] : (((~strong(X0) & ~old(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (strong(X0) | old(X0)))) [nnf transformation 10]
48. ! [X0] : (((~strong(X0) & ~old(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | strong(X0) | old(X0))) [flattening 47]
49. (? [X0] : calm(X0) | (~humble(alice) & ~strong(alice))) & ((humble(alice) | strong(alice)) | ! [X0] : ~calm(X0)) [nnf transformation 11]
50. (? [X0] : calm(X0) | (~humble(alice) & ~strong(alice))) & (humble(alice) | strong(alice) | ! [X0] : ~calm(X0)) [flattening 49]
51. (? [X0] : calm(X0) | (~humble(alice) & ~strong(alice))) & (humble(alice) | strong(alice) | ! [X1] : ~calm(X1)) [rectify 50]
52. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
53. (calm(sK2) | (~humble(alice) & ~strong(alice))) & (humble(alice) | strong(alice) | ! [X1] : ~calm(X1)) [skolemisation 51,52]
58. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~calm(X0)) & (calm(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 15]
91. strong(mary) | ~humble(alice) | ~rich(alice) [cnf transformation 37]
107. ~strong(X0) | ~strong(X0) [cnf transformation 48]
109. humble(alice) | strong(alice) | ~calm(X1) [cnf transformation 53]
126. calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 58]
127. calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 58]
146. rich(alice) [cnf transformation 25]
147. calm(X0) | quiet(X0) [duplicate literal removal 126]
148. calm(X0) | ~quiet(X0) [duplicate literal removal 127]
150. ~strong(X0) [duplicate literal removal 107]
186. 8 <=> rich(alice) [avatar definition]
190. 9 <=> humble(alice) [avatar definition]
200. 11 <=> strong(mary) [avatar definition]
202. strong(mary) <- (11) [avatar component clause 200]
203. ~8 | ~9 | 11 [avatar split clause 91,200,190,186]
246. humble(alice) | ~calm(X1) [subsumption resolution 109,150]
248. 20 <=> ! [X1] : ~calm(X1) [avatar definition]
249. ~calm(X1) <- (20) [avatar component clause 248]
250. 20 | 9 [avatar split clause 246,190,248]
278. calm(X0) [subsumption resolution 147,148]
330. 8 [avatar split clause 146,186]
331. $false <- (11) [subsumption resolution 202,150]
332. ~11 [avatar contradiction clause 331]
335. $false <- (20) [subsumption resolution 249,278]
336. ~20 [avatar contradiction clause 335]
337. $false [avatar sat refutation 203,250,330,332,336]
% SZS output end Proof for 8820793078648428988415931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or funny is funny and vice versa.
Everyone who is not wise or generous is both not calm and tall and vice versa.
If someone is rich or not rich then someone is both not quiet and old.
If paul is not funny then someone is funny and vice versa.
Everyone who is either kind or brave is either old or creative and vice versa.
Everyone who is both not tall and not generous is not happy or not funny.
Everyone who is wise is both humble and not kind and vice versa.
Everyone who is either funny or not humble is not tall or kind and vice versa.
Everyone who is not generous is not quiet.
If fred is both brave and calm then paul is both not humble and rich.
If fred is not tall or rich then someone is both tall and not happy and vice versa.
If john is not happy or not calm then someone is kind and vice versa.
If lucy is strong or not creative then lucy is not tall or not rich and vice versa.
Everyone who is both quiet and not funny is either not quiet or funny.
Everyone who is either not creative or patient is quiet and vice versa.
Everyone who is either funny or creative is not patient or not curious.
Someone is patient.
Someone is either rich or not funny.
Fred is not patient or not calm.
Mary is both happy and rich.
John is not generous.
Someone is curious or calm.
Someone is quiet.
Someone is either not kind or generous. | John is not quiet. | entailment | (![X]:((creative(X)<~>funny(X))<=>funny(X)))&
(![X]:((~wise(X)|generous(X))<=>(~calm(X)&tall(X))))&
((?[X]:((rich(X)|~rich(X))))=>(?[X]:((~quiet(X)&old(X)))))&
((~funny(paul))<=>(?[X]:(funny(X))))&
(![X]:((kind(X)<~>brave(X))<=>(old(X)<~>creative(X))))&
(![X]:((~tall(X)&~generous(X))=>(~happy(X)|~funny(X))))&
(![X]:(wise(X)<=>(humble(X)&~kind(X))))&
(![X]:((funny(X)<~>~humble(X))<=>(~tall(X)|kind(X))))&
(![X]:(~generous(X)=>~quiet(X)))&
(((brave(fred)&calm(fred)))=>((~humble(paul)&rich(paul))))&
(((~tall(fred)|rich(fred)))<=>(?[X]:((tall(X)&~happy(X)))))&
(((~happy(john)|~calm(john)))<=>(?[X]:(kind(X))))&
(((strong(lucy)|~creative(lucy)))<=>((~tall(lucy)|~rich(lucy))))&
(![X]:((quiet(X)&~funny(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~creative(X)<~>patient(X))<=>quiet(X)))&
(![X]:((funny(X)<~>creative(X))=>(~patient(X)|~curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)<~>~funny(X))))&
((~patient(fred)|~calm(fred)))&
((happy(mary)&rich(mary)))&
(~generous(john))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)<~>generous(X)))) | ~quiet(john) | [
"p8",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 7685302729086012629715959
% SZS output start Proof for 7685302729086012629715959
9. ! [X0] : (~generous(X0) => ~quiet(X0)) [input p8]
21. ~generous(john) [input p20]
25. quiet(john) [input hypothesis]
30. ! [X0] : (~quiet(X0) | generous(X0)) [ennf transformation 9]
112. ~quiet(X0) | generous(X0) [cnf transformation 30]
141. ~generous(john) [cnf transformation 21]
146. quiet(john) [cnf transformation 25]
307. generous(john) [resolution 112,146]
308. $false [subsumption resolution 307,141]
% SZS output end Proof for 7685302729086012629715959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or old is not quiet or kind.
Everyone who is both not generous and not wise is either not old or not curious and vice versa.
Everyone who is not happy is kind or humble and vice versa.
Everyone who is happy or wise is brave or curious.
If paul is not brave then lucy is both not old and not funny and vice versa.
Everyone who is either not happy or not rich is not patient.
If someone is tall then someone is either happy or rich and vice versa.
Everyone who is not strong or not kind is both not quiet and rich and vice versa.
Everyone who is both curious and not patient is not rich.
Everyone who is not patient or not funny is both old and not patient.
Everyone who is both patient and not generous is either not kind or not funny.
Everyone who is curious or tall is not rich and vice versa.
Everyone who is both curious and strong is both patient and not funny.
Everyone who is both wise and not humble is both generous and not brave and vice versa.
Everyone who is not old is both not quiet and not brave.
Everyone who is both not calm and not generous is either not calm or not brave.
Someone is both happy and not wise.
Someone is both humble and not generous.
Alice is patient.
Someone is either not happy or not kind.
Fred is creative.
Lucy is either old or creative.
John is either not kind or not humble.
Someone is either not strong or not old. | Alice is kind. | contradiction | (![X]:((~curious(X)<~>old(X))=>(~quiet(X)|kind(X))))&
(![X]:((~generous(X)&~wise(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(kind(X)|humble(X))))&
(![X]:((happy(X)|wise(X))=>(brave(X)|curious(X))))&
((~brave(paul))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~happy(X)<~>~rich(X))=>~patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((happy(X)<~>rich(X)))))&
(![X]:((~strong(X)|~kind(X))<=>(~quiet(X)&rich(X))))&
(![X]:((curious(X)&~patient(X))=>~rich(X)))&
(![X]:((~patient(X)|~funny(X))=>(old(X)&~patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
(![X]:((curious(X)&strong(X))=>(patient(X)&~funny(X))))&
(![X]:((wise(X)&~humble(X))<=>(generous(X)&~brave(X))))&
(![X]:(~old(X)=>(~quiet(X)&~brave(X))))&
(![X]:((~calm(X)&~generous(X))=>(~calm(X)<~>~brave(X))))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((humble(X)&~generous(X))))&
(patient(alice))&
(?[X]:((~happy(X)<~>~kind(X))))&
(creative(fred))&
((old(lucy)<~>creative(lucy)))&
((~kind(john)<~>~humble(john)))&
(?[X]:((~strong(X)<~>~old(X)))) | kind(alice) | [
"p1",
"p3",
"p7",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5851718650658732478511340
% SZS output start Proof for 5851718650658732478511340
2. ! [X0] : ((~wise(X0) & ~generous(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : ((wise(X0) | happy(X0)) => (curious(X0) | brave(X0))) [input p3]
8. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (rich(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p9]
11. ! [X0] : ((~generous(X0) & patient(X0)) => (~kind(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : ((tall(X0) | curious(X0)) <=> ~rich(X0)) [input p11]
13. ! [X0] : ((strong(X0) & curious(X0)) => (~funny(X0) & patient(X0))) [input p12]
14. ! [X0] : ((~humble(X0) & wise(X0)) <=> (~brave(X0) & generous(X0))) [input p13]
15. ! [X0] : (~old(X0) => (~brave(X0) & ~quiet(X0))) [input p14]
19. patient(alice) [input p18]
25. kind(alice) [input hypothesis]
29. ! [X0] : ((curious(X0) | brave(X0)) | (~wise(X0) & ~happy(X0))) [ennf transformation 4]
30. ! [X0] : (curious(X0) | brave(X0) | (~wise(X0) & ~happy(X0))) [flattening 29]
34. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 10]
35. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | (generous(X0) | ~patient(X0))) [ennf transformation 11]
36. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | generous(X0) | ~patient(X0)) [flattening 35]
37. ! [X0] : ((~funny(X0) & patient(X0)) | (~strong(X0) | ~curious(X0))) [ennf transformation 13]
38. ! [X0] : ((~funny(X0) & patient(X0)) | ~strong(X0) | ~curious(X0)) [flattening 37]
39. ! [X0] : ((~brave(X0) & ~quiet(X0)) | old(X0)) [ennf transformation 15]
43. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (wise(X0) | generous(X0)))) [nnf transformation 2]
44. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | wise(X0) | generous(X0))) [flattening 43]
55. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | ~strong(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [flattening 55]
57. ! [X0] : (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | generous(X0) | ~patient(X0)) [nnf transformation 36]
58. ! [X0] : (((tall(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 12]
59. ! [X0] : ((tall(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [flattening 58]
60. ! [X0] : (((~humble(X0) & wise(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (humble(X0) | ~wise(X0)))) [nnf transformation 14]
61. ! [X0] : (((~humble(X0) & wise(X0)) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | humble(X0) | ~wise(X0))) [flattening 60]
78. wise(X0) | old(X0) | curious(X0) | generous(X0) [cnf transformation 44]
80. ~generous(X0) | ~old(X0) | curious(X0) [cnf transformation 44]
87. ~wise(X0) | brave(X0) | curious(X0) [cnf transformation 30]
99. strong(X0) | rich(X0) [cnf transformation 56]
104. funny(X0) | old(X0) [cnf transformation 34]
106. ~patient(X0) | funny(X0) [cnf transformation 34]
107. ~funny(X0) | ~kind(X0) | generous(X0) | ~patient(X0) [cnf transformation 57]
109. ~rich(X0) | ~curious(X0) [cnf transformation 59]
113. ~strong(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 38]
116. ~generous(X0) | brave(X0) | wise(X0) [cnf transformation 61]
119. ~brave(X0) | old(X0) [cnf transformation 39]
126. patient(alice) [cnf transformation 19]
136. kind(alice) [cnf transformation 25]
178. ~patient(X0) | generous(X0) | ~kind(X0) [subsumption resolution 107,106]
224. funny(alice) [resolution 106,126]
273. ~funny(X0) | ~curious(X0) | rich(X0) [resolution 113,99]
318. ~funny(X0) | ~curious(X0) [subsumption resolution 273,109]
360. generous(alice) | ~kind(alice) [resolution 178,126]
362. generous(alice) [subsumption resolution 360,136]
402. old(X1) | curious(X1) | generous(X1) | brave(X1) | curious(X1) [resolution 78,87]
410. old(X1) | curious(X1) | generous(X1) | brave(X1) [duplicate literal removal 402]
412. generous(X1) | curious(X1) | old(X1) [subsumption resolution 410,119]
431. ~old(alice) | curious(alice) [resolution 362,80]
443. 43 <=> curious(alice) [avatar definition]
447. 44 <=> old(alice) [avatar definition]
449. ~old(alice) <- (~44) [avatar component clause 447]
450. 43 | ~44 [avatar split clause 431,447,443]
454. ~curious(X0) | old(X0) [resolution 318,104]
455. ~curious(alice) [resolution 318,224]
502. curious(X0) | old(X0) | brave(X0) | wise(X0) [resolution 412,116]
508. curious(X0) | old(X0) | brave(X0) [subsumption resolution 502,87]
509. old(X0) | brave(X0) [subsumption resolution 508,454]
510. old(X0) [subsumption resolution 509,119]
577. $false <- (~44) [resolution 510,449]
578. 44 [avatar contradiction clause 577]
580. ~43 [avatar split clause 455,443]
583. $false [avatar sat refutation 450,578,580]
% SZS output end Proof for 5851718650658732478511340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and kind then someone is both generous and funny. Everyone who is creative or not calm is not kind or not curious and vice versa. Everyone who is rich or not strong is not brave or not kind and vice versa. Everyone who is not kind or patient is both not brave and not tall. Everyone who is creative is rich and vice versa. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Everyone who is either not old or not funny is both kind and not strong and vice versa. Everyone who is quiet is generous and vice versa. If fred is either creative or not wise then someone is both brave and not patient. Susan is not humble. Someone is humble or brave. Mary is either funny or patient. Someone is wise. Someone is either not rich or rich. Paul is both strong and not kind. Someone is not brave or calm. | Mary is wise. | contradiction | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((humble(X)|brave(X))))&
((funny(mary)<~>patient(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | wise(mary) | [
"p3",
"p9",
"p10",
"p12",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 8198797031436040072543718
% SZS output start Proof for 8198797031436040072543718
4. ! [X0] : ((patient(X0) | ~kind(X0)) => (~tall(X0) & ~brave(X0))) [input p3]
10. ! [X0] : ((~tall(X0) & quiet(X0)) <=> (~wise(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p12]
15. ! [X0] : (quiet(X0) <=> generous(X0)) [input p14]
19. funny(mary) <~> patient(mary) [input p18]
24. wise(mary) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~brave(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 4]
31. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | (tall(X0) | ~quiet(X0)))) [nnf transformation 10]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | tall(X0) | ~quiet(X0))) [flattening 49]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 13]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 52]
56. ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))) [nnf transformation 15]
62. (~patient(mary) | ~funny(mary)) & (patient(mary) | funny(mary)) [nnf transformation 19]
83. ~patient(X0) | ~tall(X0) [cnf transformation 27]
99. ~wise(X0) | tall(X0) | ~quiet(X0) [cnf transformation 50]
103. generous(X0) | generous(X0) [cnf transformation 31]
109. ~funny(X0) | patient(X0) [cnf transformation 53]
118. quiet(X0) | ~generous(X0) [cnf transformation 56]
125. patient(mary) | funny(mary) [cnf transformation 62]
126. ~patient(mary) | ~funny(mary) [cnf transformation 62]
133. wise(mary) [cnf transformation 24]
135. generous(X0) [duplicate literal removal 103]
150. 4 <=> patient(mary) [avatar definition]
151. patient(mary) <- (4) [avatar component clause 150]
178. quiet(X0) [subsumption resolution 118,135]
208. ~funny(mary) [subsumption resolution 126,109]
209. patient(mary) [subsumption resolution 125,208]
210. 4 [avatar split clause 209,150]
221. ~tall(mary) <- (4) [resolution 83,151]
294. tall(mary) | ~quiet(mary) [resolution 99,133]
298. ~quiet(mary) <- (4) [subsumption resolution 294,221]
299. $false <- (4) [subsumption resolution 298,178]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 210,300]
% SZS output end Proof for 8198797031436040072543718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not curious is patient and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is either brave or not patient is either tall or not humble.
If fred is not patient then someone is either not brave or not wise and vice versa.
Everyone who is either not brave or not patient is both happy and rich and vice versa.
Everyone who is generous is either not kind or tall.
Everyone who is either tall or not tall is either not generous or not humble and vice versa.
Everyone who is either rich or wise is not kind or strong.
If someone is either not old or kind then alice is either rich or quiet and vice versa.
Everyone who is tall is both strong and funny and vice versa.
Everyone who is not rich is not funny or strong.
Everyone who is either not curious or rich is both not patient and quiet.
If paul is either quiet or generous then lucy is both creative and happy and vice versa.
Everyone who is either strong or old is both brave and old and vice versa.
Everyone who is humble is wise.
Everyone who is humble or not strong is both not rich and brave and vice versa.
Mary is strong or old.
Someone is both old and strong.
Someone is not humble.
Mary is not quiet or funny.
Someone is generous or not wise. | Lucy is not creative. | neutral | (![X]:((funny(X)&~curious(X))<=>patient(X)))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:((brave(X)<~>~patient(X))=>(tall(X)<~>~humble(X))))&
((~patient(fred))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((~brave(X)<~>~patient(X))<=>(happy(X)&rich(X))))&
(![X]:(generous(X)=>(~kind(X)<~>tall(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((rich(X)<~>wise(X))=>(~kind(X)|strong(X))))&
((?[X]:((~old(X)<~>kind(X))))<=>((rich(alice)<~>quiet(alice))))&
(![X]:(tall(X)<=>(strong(X)&funny(X))))&
(![X]:(~rich(X)=>(~funny(X)|strong(X))))&
(![X]:((~curious(X)<~>rich(X))=>(~patient(X)&quiet(X))))&
(((quiet(paul)<~>generous(paul)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>old(X))<=>(brave(X)&old(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((humble(X)|~strong(X))<=>(~rich(X)&brave(X))))&
((strong(mary)|old(mary)))&
(?[X]:((old(X)&strong(X))))&
(?[X]:(~humble(X)))&
((~quiet(mary)|funny(mary)))&
(?[X]:((generous(X)|~wise(X)))) | ~creative(lucy) | []
| null | 0 |
Everyone who is kind is happy or not tall. If john is both not quiet and humble then susan is funny. Everyone who is both kind and brave is both wise and funny. Everyone who is not happy or patient is patient and vice versa. Everyone who is both not humble and old is not kind. Everyone who is not humble is not creative. If someone is not funny then someone is both not humble and patient. Everyone who is old is either wise or calm and vice versa. Everyone who is not funny is both brave and creative and vice versa. If lucy is both strong and not strong then someone is either not happy or not humble. If someone is kind then susan is tall and vice versa. Everyone who is not tall is either not curious or not funny and vice versa. If lucy is either not old or strong then someone is either not patient or tall and vice versa. Everyone who is either not curious or creative is both not happy and patient and vice versa. Everyone who is both happy and not rich is both kind and happy. If susan is both rich and curious then mary is curious or not brave. Someone is both not funny and not rich. Someone is either not quiet or not old. Someone is not calm. Someone is wise. Alice is either tall or not creative. Paul is both kind and not calm. Someone is generous. Someone is not kind or not brave. | Alice is funny. | neutral | (![X]:(kind(X)=>(happy(X)|~tall(X))))&
(((~quiet(john)&humble(john)))=>(funny(susan)))&
(![X]:((kind(X)&brave(X))=>(wise(X)&funny(X))))&
(![X]:((~happy(X)|patient(X))<=>patient(X)))&
(![X]:((~humble(X)&old(X))=>~kind(X)))&
(![X]:(~humble(X)=>~creative(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(old(X)<=>(wise(X)<~>calm(X))))&
(![X]:(~funny(X)<=>(brave(X)&creative(X))))&
(((strong(lucy)&~strong(lucy)))=>(?[X]:((~happy(X)<~>~humble(X)))))&
((?[X]:(kind(X)))<=>(tall(susan)))&
(![X]:(~tall(X)<=>(~curious(X)<~>~funny(X))))&
(((~old(lucy)<~>strong(lucy)))<=>(?[X]:((~patient(X)<~>tall(X)))))&
(![X]:((~curious(X)<~>creative(X))<=>(~happy(X)&patient(X))))&
(![X]:((happy(X)&~rich(X))=>(kind(X)&happy(X))))&
(((rich(susan)&curious(susan)))=>((curious(mary)|~brave(mary))))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((~quiet(X)<~>~old(X))))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
((tall(alice)<~>~creative(alice)))&
((kind(paul)&~calm(paul)))&
(?[X]:(generous(X)))&
(?[X]:((~kind(X)|~brave(X)))) | funny(alice) | []
| null | 0 |
Everyone who is both not old and humble is kind or not rich. Everyone who is not wise is not brave and vice versa. Everyone who is both wise and not old is both not quiet and not tall and vice versa. Everyone who is not calm is not patient and vice versa. Everyone who is generous is both not patient and not tall. Everyone who is not old is either not rich or not humble. Everyone who is either not curious or humble is either kind or not curious and vice versa. If someone is either not wise or not patient then susan is either generous or not quiet and vice versa. If someone is quiet then mary is not tall. Everyone who is not patient is both not brave and not quiet and vice versa. If john is tall or creative then someone is happy and vice versa. If someone is either not wise or not creative then someone is not generous. Everyone who is not old is not calm. If someone is either tall or quiet then susan is quiet or generous and vice versa. Everyone who is both not rich and curious is both not calm and wise and vice versa. Everyone who is either not tall or not humble is quiet. Mary is both funny and happy. John is not humble or not quiet. Fred is not brave or not old. Paul is not strong or strong. Susan is either not strong or generous. Lucy is not wise. | Susan is not strong. | entailment | (![X]:((~old(X)&humble(X))=>(kind(X)|~rich(X))))&
(![X]:(~wise(X)<=>~brave(X)))&
(![X]:((wise(X)&~old(X))<=>(~quiet(X)&~tall(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(![X]:(generous(X)=>(~patient(X)&~tall(X))))&
(![X]:(~old(X)=>(~rich(X)<~>~humble(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>((generous(susan)<~>~quiet(susan))))&
((?[X]:(quiet(X)))=>(~tall(mary)))&
(![X]:(~patient(X)<=>(~brave(X)&~quiet(X))))&
(((tall(john)|creative(john)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)<~>~creative(X))))=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>~calm(X)))&
((?[X]:((tall(X)<~>quiet(X))))<=>((quiet(susan)|generous(susan))))&
(![X]:((~rich(X)&curious(X))<=>(~calm(X)&wise(X))))&
(![X]:((~tall(X)<~>~humble(X))=>quiet(X)))&
((funny(mary)&happy(mary)))&
((~humble(john)|~quiet(john)))&
((~brave(fred)|~old(fred)))&
((~strong(paul)|strong(paul)))&
((~strong(susan)<~>generous(susan)))&
(~wise(lucy)) | ~strong(susan) | [
"p2",
"p4",
"p7",
"p9",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 4562646117213029876759
% SZS output start Proof for 4562646117213029876759
3. ! [X0] : ((~old(X0) & wise(X0)) <=> (~tall(X0) & ~quiet(X0))) [input p2]
5. ! [X0] : (generous(X0) => (~tall(X0) & ~patient(X0))) [input p4]
8. ? [X0] : (~wise(X0) <~> ~patient(X0)) <=> (generous(susan) <~> ~quiet(susan)) [input p7]
10. ! [X0] : (~patient(X0) <=> (~quiet(X0) & ~brave(X0))) [input p9]
21. ~strong(susan) <~> generous(susan) [input p20]
23. strong(susan) [input hypothesis]
28. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~generous(X0)) [ennf transformation 5]
35. ! [X0] : (((~old(X0) & wise(X0)) | (tall(X0) | quiet(X0))) & ((~tall(X0) & ~quiet(X0)) | (old(X0) | ~wise(X0)))) [nnf transformation 3]
36. ! [X0] : (((~old(X0) & wise(X0)) | tall(X0) | quiet(X0)) & ((~tall(X0) & ~quiet(X0)) | old(X0) | ~wise(X0))) [flattening 35]
40. (? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) [nnf transformation 8]
41. (? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X1] : ((~wise(X1) | patient(X1)) & (~patient(X1) | wise(X1)))) [rectify 40]
42. ? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) => ((patient(sK0) | wise(sK0)) & (~patient(sK0) | ~wise(sK0))) [choice axiom]
43. (((patient(sK0) | wise(sK0)) & (~patient(sK0) | ~wise(sK0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X1] : ((~wise(X1) | patient(X1)) & (~patient(X1) | wise(X1)))) [skolemisation 41,42]
44. ! [X0] : ((~patient(X0) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 10]
45. ! [X0] : ((~patient(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [flattening 44]
63. (~generous(susan) | strong(susan)) & (generous(susan) | ~strong(susan)) [nnf transformation 21]
69. tall(X0) | wise(X0) | quiet(X0) [cnf transformation 36]
73. ~generous(X0) | ~patient(X0) [cnf transformation 28]
74. ~generous(X0) | ~tall(X0) [cnf transformation 28]
88. quiet(susan) | ~generous(susan) | ~wise(X1) | patient(X1) [cnf transformation 43]
95. ~quiet(X0) | patient(X0) [cnf transformation 45]
119. generous(susan) | ~strong(susan) [cnf transformation 63]
122. strong(susan) [cnf transformation 23]
130. 1 <=> quiet(susan) [avatar definition]
131. ~quiet(susan) <- (~1) [avatar component clause 130]
132. quiet(susan) <- (1) [avatar component clause 130]
134. 2 <=> generous(susan) [avatar definition]
136. generous(susan) <- (2) [avatar component clause 134]
150. 5 <=> ! [X1] : (~wise(X1) | patient(X1)) [avatar definition]
151. ~wise(X1) | patient(X1) <- (5) [avatar component clause 150]
152. 5 | ~2 | 1 [avatar split clause 88,130,134,150]
236. 24 <=> strong(susan) [avatar definition]
240. ~24 | 2 [avatar split clause 119,134,236]
241. 24 [avatar split clause 122,236]
244. ~patient(susan) <- (2) [resolution 73,136]
245. ~tall(susan) <- (2) [resolution 74,136]
257. wise(susan) | quiet(susan) <- (2) [resolution 69,245]
260. wise(susan) <- (~1, 2) [subsumption resolution 257,131]
275. patient(susan) <- (~1, 2, 5) [resolution 260,151]
277. $false <- (~1, 2, 5) [subsumption resolution 275,244]
278. 1 | ~2 | ~5 [avatar contradiction clause 277]
285. patient(susan) <- (1) [resolution 132,95]
291. $false <- (1, 2) [subsumption resolution 285,244]
292. ~1 | ~2 [avatar contradiction clause 291]
293. $false [avatar sat refutation 152,240,241,278,292]
% SZS output end Proof for 4562646117213029876759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is old then someone is either generous or old.
If someone is not quiet or not generous then susan is either not tall or brave.
If someone is not strong then someone is either calm or patient and vice versa.
If someone is old or quiet then mary is brave or not generous and vice versa.
If someone is happy then alice is both quiet and humble.
Everyone who is not kind or not humble is both not generous and not strong and vice versa.
Everyone who is not brave is both not kind and not patient.
If john is both not funny and not curious then someone is either rich or not kind and vice versa.
If someone is patient or not strong then someone is both generous and not kind.
Everyone who is not brave is humble.
If susan is not creative then mary is humble.
Everyone who is both not old and not strong is calm.
If someone is either not brave or happy then someone is both not humble and not generous.
Everyone who is either not old or generous is either not funny or not quiet.
If someone is curious or strong then fred is both not curious and not creative and vice versa.
If someone is patient then susan is not rich or not creative and vice versa.
Fred is not funny.
Someone is not happy.
Fred is not patient.
Fred is rich or quiet.
Someone is either not strong or curious.
Someone is either not strong or creative.
Fred is not wise. | Paul is humble. | entailment | ((old(paul))=>(?[X]:((generous(X)<~>old(X)))))&
((?[X]:((~quiet(X)|~generous(X))))=>((~tall(susan)<~>brave(susan))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)<~>patient(X)))))&
((?[X]:((old(X)|quiet(X))))<=>((brave(mary)|~generous(mary))))&
((?[X]:(happy(X)))=>((quiet(alice)&humble(alice))))&
(![X]:((~kind(X)|~humble(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~brave(X)=>(~kind(X)&~patient(X))))&
(((~funny(john)&~curious(john)))<=>(?[X]:((rich(X)<~>~kind(X)))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:(~brave(X)=>humble(X)))&
((~creative(susan))=>(humble(mary)))&
(![X]:((~old(X)&~strong(X))=>calm(X)))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((~old(X)<~>generous(X))=>(~funny(X)<~>~quiet(X))))&
((?[X]:((curious(X)|strong(X))))<=>((~curious(fred)&~creative(fred))))&
((?[X]:(patient(X)))<=>((~rich(susan)|~creative(susan))))&
(~funny(fred))&
(?[X]:(~happy(X)))&
(~patient(fred))&
((rich(fred)|quiet(fred)))&
(?[X]:((~strong(X)<~>curious(X))))&
(?[X]:((~strong(X)<~>creative(X))))&
(~wise(fred)) | humble(paul) | [
"p5",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 7009486916030317505205926
% SZS output start Proof for 7009486916030317505205926
6. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (~strong(X0) & ~generous(X0))) [input p5]
9. ? [X0] : (~strong(X0) | patient(X0)) => ? [X0] : (~kind(X0) & generous(X0)) [input p8]
24. ~humble(paul) [input hypothesis]
26. ? [X0] : (~strong(X0) | patient(X0)) => ? [X1] : (~kind(X1) & generous(X1)) [rectify 9]
33. ? [X1] : (~kind(X1) & generous(X1)) | ! [X0] : (strong(X0) & ~patient(X0)) [ennf transformation 26]
54. ! [X0] : (((~humble(X0) | ~kind(X0)) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 6]
55. ! [X0] : ((~humble(X0) | ~kind(X0) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | (humble(X0) & kind(X0)))) [flattening 54]
61. ? [X0] : (~kind(X0) & generous(X0)) | ! [X1] : (strong(X1) & ~patient(X1)) [rectify 33]
62. ? [X0] : (~kind(X0) & generous(X0)) => (~kind(sK5) & generous(sK5)) [choice axiom]
63. (~kind(sK5) & generous(sK5)) | ! [X1] : (strong(X1) & ~patient(X1)) [skolemisation 61,62]
103. ~generous(X0) | kind(X0) [cnf transformation 55]
106. ~strong(X0) | humble(X0) [cnf transformation 55]
117. generous(sK5) | strong(X1) [cnf transformation 63]
119. ~kind(sK5) | strong(X1) [cnf transformation 63]
147. ~humble(paul) [cnf transformation 24]
193. 11 <=> ! [X3] : strong(X3) [avatar definition]
194. strong(X3) <- (11) [avatar component clause 193]
273. 29 <=> kind(sK5) [avatar definition]
275. ~kind(sK5) <- (~29) [avatar component clause 273]
276. 11 | ~29 [avatar split clause 119,273,193]
282. 31 <=> generous(sK5) [avatar definition]
284. generous(sK5) <- (31) [avatar component clause 282]
285. 11 | 31 [avatar split clause 117,282,193]
388. kind(sK5) <- (31) [resolution 103,284]
389. $false <- (~29, 31) [subsumption resolution 388,275]
390. 29 | ~31 [avatar contradiction clause 389]
397. humble(X0) <- (11) [resolution 106,194]
412. $false <- (11) [resolution 397,147]
415. ~11 [avatar contradiction clause 412]
416. $false [avatar sat refutation 276,285,390,415]
% SZS output end Proof for 7009486916030317505205926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or patient then mary is not strong.
If alice is not old then fred is not tall and vice versa.
Everyone who is not old or not strong is either quiet or not tall and vice versa.
If susan is both generous and quiet then fred is not brave and vice versa.
Everyone who is both not brave and strong is either patient or tall and vice versa.
If someone is both funny and tall then someone is both not brave and kind and vice versa.
If susan is either not happy or not patient then john is patient or not tall and vice versa.
Everyone who is both not calm and generous is not brave or happy and vice versa.
Everyone who is creative or happy is both curious and not kind and vice versa.
Everyone who is not generous is either creative or brave.
If alice is either brave or not calm then someone is tall or not creative.
Everyone who is either happy or not brave is not old.
Everyone who is either not strong or not creative is either wise or not strong and vice versa.
Everyone who is strong is not funny and vice versa.
Everyone who is both not funny and not calm is either not kind or kind and vice versa.
If john is not kind or not brave then john is both not quiet and not happy and vice versa.
Mary is either patient or not tall.
Someone is either not kind or old.
Alice is both not calm and not curious.
Mary is either rich or not rich.
Someone is either calm or happy.
Someone is patient or wise.
Alice is happy or quiet. | Mary is not wise. | neutral | ((?[X]:((~wise(X)<~>patient(X))))=>(~strong(mary)))&
((~old(alice))<=>(~tall(fred)))&
(![X]:((~old(X)|~strong(X))<=>(quiet(X)<~>~tall(X))))&
(((generous(susan)&quiet(susan)))<=>(~brave(fred)))&
(![X]:((~brave(X)&strong(X))<=>(patient(X)<~>tall(X))))&
((?[X]:((funny(X)&tall(X))))<=>(?[X]:((~brave(X)&kind(X)))))&
(((~happy(susan)<~>~patient(susan)))<=>((patient(john)|~tall(john))))&
(![X]:((~calm(X)&generous(X))<=>(~brave(X)|happy(X))))&
(![X]:((creative(X)|happy(X))<=>(curious(X)&~kind(X))))&
(![X]:(~generous(X)=>(creative(X)<~>brave(X))))&
(((brave(alice)<~>~calm(alice)))=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:((happy(X)<~>~brave(X))=>~old(X)))&
(![X]:((~strong(X)<~>~creative(X))<=>(wise(X)<~>~strong(X))))&
(![X]:(strong(X)<=>~funny(X)))&
(![X]:((~funny(X)&~calm(X))<=>(~kind(X)<~>kind(X))))&
(((~kind(john)|~brave(john)))<=>((~quiet(john)&~happy(john))))&
((patient(mary)<~>~tall(mary)))&
(?[X]:((~kind(X)<~>old(X))))&
((~calm(alice)&~curious(alice)))&
((rich(mary)<~>~rich(mary)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((patient(X)|wise(X))))&
((happy(alice)|quiet(alice))) | ~wise(mary) | []
| null | 0 |
Everyone who is both not quiet and not old is not brave or curious.
Everyone who is both strong and kind is both happy and humble and vice versa.
If someone is not quiet then susan is wise.
If john is either kind or wise then someone is either kind or not brave and vice versa.
Everyone who is both curious and not strong is not funny.
If fred is not happy or not strong then someone is happy.
Everyone who is brave is both not funny and not quiet and vice versa.
Everyone who is quiet or not rich is brave and vice versa.
Everyone who is not patient or funny is strong and vice versa.
Everyone who is both not kind and not brave is not quiet and vice versa.
Everyone who is either quiet or not humble is tall and vice versa.
Everyone who is not kind or old is either wise or generous.
Everyone who is curious is either not kind or not curious and vice versa.
Everyone who is both old and not wise is both strong and old.
If susan is either kind or not brave then someone is either not funny or humble.
Someone is rich.
Someone is not patient or generous.
Someone is not happy.
Fred is either wise or happy.
Someone is both not creative and not humble.
Susan is generous or not generous.
Mary is either not generous or not humble.
Someone is either not calm or not funny. | Fred is creative. | neutral | (![X]:((~quiet(X)&~old(X))=>(~brave(X)|curious(X))))&
(![X]:((strong(X)&kind(X))<=>(happy(X)&humble(X))))&
((?[X]:(~quiet(X)))=>(wise(susan)))&
(((kind(john)<~>wise(john)))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((curious(X)&~strong(X))=>~funny(X)))&
(((~happy(fred)|~strong(fred)))=>(?[X]:(happy(X))))&
(![X]:(brave(X)<=>(~funny(X)&~quiet(X))))&
(![X]:((quiet(X)|~rich(X))<=>brave(X)))&
(![X]:((~patient(X)|funny(X))<=>strong(X)))&
(![X]:((~kind(X)&~brave(X))<=>~quiet(X)))&
(![X]:((quiet(X)<~>~humble(X))<=>tall(X)))&
(![X]:((~kind(X)|old(X))=>(wise(X)<~>generous(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>~curious(X))))&
(![X]:((old(X)&~wise(X))=>(strong(X)&old(X))))&
(((kind(susan)<~>~brave(susan)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)|generous(X))))&
(?[X]:(~happy(X)))&
((wise(fred)<~>happy(fred)))&
(?[X]:((~creative(X)&~humble(X))))&
((generous(susan)|~generous(susan)))&
((~generous(mary)<~>~humble(mary)))&
(?[X]:((~calm(X)<~>~funny(X)))) | creative(fred) | []
| null | 0 |
Everyone who is strong or funny is both strong and kind.
Everyone who is not rich or not brave is either patient or not kind.
If someone is not wise or not tall then someone is not wise or rich.
If john is both not quiet and not kind then someone is either not quiet or humble.
If someone is happy then someone is both not tall and curious.
If alice is both not strong and old then someone is rich or humble and vice versa.
Everyone who is kind or rich is both not old and kind.
Everyone who is brave or not old is brave or not rich and vice versa.
If alice is not kind then lucy is creative or not calm.
If someone is either not creative or strong then someone is rich and vice versa.
Everyone who is not old or rich is kind or curious and vice versa.
Everyone who is either not kind or not old is both rich and not quiet.
Everyone who is not wise or happy is rich or funny.
If susan is either rich or not patient then fred is both not kind and brave.
If someone is either not funny or not humble then susan is both not tall and tall.
Mary is generous.
Susan is not strong or tall.
Fred is not patient or not brave.
Paul is not curious or generous. | Fred is happy. | contradiction | (![X]:((strong(X)|funny(X))=>(strong(X)&kind(X))))&
(![X]:((~rich(X)|~brave(X))=>(patient(X)<~>~kind(X))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((~wise(X)|rich(X)))))&
(((~quiet(john)&~kind(john)))=>(?[X]:((~quiet(X)<~>humble(X)))))&
((?[X]:(happy(X)))=>(?[X]:((~tall(X)&curious(X)))))&
(((~strong(alice)&old(alice)))<=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((kind(X)|rich(X))=>(~old(X)&kind(X))))&
(![X]:((brave(X)|~old(X))<=>(brave(X)|~rich(X))))&
((~kind(alice))=>((creative(lucy)|~calm(lucy))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)|rich(X))<=>(kind(X)|curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(rich(X)|funny(X))))&
(((rich(susan)<~>~patient(susan)))=>((~kind(fred)&brave(fred))))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~tall(susan)&tall(susan))))&
(generous(mary))&
((~strong(susan)|tall(susan)))&
((~patient(fred)|~brave(fred)))&
((~curious(paul)|generous(paul))) | happy(fred) | [
"p2",
"p4",
"p5",
"p6",
"p11",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 6339085063275777047588620
% SZS output start Proof for 6339085063275777047588620
3. ? [X0] : (~tall(X0) | ~wise(X0)) => ? [X0] : (rich(X0) | ~wise(X0)) [input p2]
5. ? [X0] : happy(X0) => ? [X0] : (curious(X0) & ~tall(X0)) [input p4]
6. (old(alice) & ~strong(alice)) <=> ? [X0] : (humble(X0) | rich(X0)) [input p5]
7. ! [X0] : ((rich(X0) | kind(X0)) => (kind(X0) & ~old(X0))) [input p6]
12. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (~quiet(X0) & rich(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~wise(X0)) => (funny(X0) | rich(X0))) [input p12]
15. ? [X0] : (~funny(X0) <~> ~humble(X0)) => (tall(susan) & ~tall(susan)) [input p14]
20. happy(fred) [input hypothesis]
21. ? [X0] : (~tall(X0) | ~wise(X0)) => ? [X1] : (rich(X1) | ~wise(X1)) [rectify 3]
22. ? [X0] : happy(X0) => ? [X1] : (curious(X1) & ~tall(X1)) [rectify 5]
29. ? [X1] : (rich(X1) | ~wise(X1)) | ! [X0] : (tall(X0) & wise(X0)) [ennf transformation 21]
32. ? [X1] : (curious(X1) & ~tall(X1)) | ! [X0] : ~happy(X0) [ennf transformation 22]
33. ! [X0] : ((kind(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 7]
34. ! [X0] : ((~quiet(X0) & rich(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 12]
35. ! [X0] : ((funny(X0) | rich(X0)) | (~happy(X0) & wise(X0))) [ennf transformation 13]
36. ! [X0] : (funny(X0) | rich(X0) | (~happy(X0) & wise(X0))) [flattening 35]
38. (tall(susan) & ~tall(susan)) | ! [X0] : (~funny(X0) <=> ~humble(X0)) [ennf transformation 15]
40. ? [X0] : (rich(X0) | ~wise(X0)) | ! [X1] : (tall(X1) & wise(X1)) [rectify 29]
41. ? [X0] : (rich(X0) | ~wise(X0)) => (rich(sK0) | ~wise(sK0)) [choice axiom]
42. (rich(sK0) | ~wise(sK0)) | ! [X1] : (tall(X1) & wise(X1)) [skolemisation 40,41]
46. ? [X0] : (curious(X0) & ~tall(X0)) | ! [X1] : ~happy(X1) [rectify 32]
47. ? [X0] : (curious(X0) & ~tall(X0)) => (curious(sK2) & ~tall(sK2)) [choice axiom]
48. (curious(sK2) & ~tall(sK2)) | ! [X1] : ~happy(X1) [skolemisation 46,47]
49. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | (~old(alice) | strong(alice))) [nnf transformation 6]
50. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | ~old(alice) | strong(alice)) [flattening 49]
51. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X1] : (humble(X1) | rich(X1)) | ~old(alice) | strong(alice)) [rectify 50]
52. ? [X1] : (humble(X1) | rich(X1)) => (humble(sK3) | rich(sK3)) [choice axiom]
53. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & ((humble(sK3) | rich(sK3)) | ~old(alice) | strong(alice)) [skolemisation 51,52]
63. ! [X0] : ((~quiet(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 34]
65. (tall(susan) & ~tall(susan)) | ! [X0] : ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))) [nnf transformation 38]
75. rich(sK0) | ~wise(sK0) | tall(X1) [cnf transformation 42]
78. ~tall(sK2) | ~happy(X1) [cnf transformation 48]
83. old(alice) | ~rich(X0) [cnf transformation 53]
84. old(alice) | ~humble(X0) [cnf transformation 53]
85. ~old(X0) | ~kind(X0) [cnf transformation 33]
86. ~old(X0) | ~rich(X0) [cnf transformation 33]
101. rich(X0) | ~old(X0) | kind(X0) [cnf transformation 63]
105. wise(X0) | rich(X0) | funny(X0) [cnf transformation 36]
112. ~tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 65]
114. tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 65]
117. happy(fred) [cnf transformation 20]
119. 1 <=> ! [X1] : tall(X1) [avatar definition]
120. tall(X1) <- (1) [avatar component clause 119]
122. 2 <=> wise(sK0) [avatar definition]
124. ~wise(sK0) <- (~2) [avatar component clause 122]
126. 3 <=> rich(sK0) [avatar definition]
128. rich(sK0) <- (3) [avatar component clause 126]
129. 1 | ~2 | 3 [avatar split clause 75,126,122,119]
153. 9 <=> ! [X1] : ~happy(X1) [avatar definition]
154. ~happy(X1) <- (9) [avatar component clause 153]
161. 11 <=> tall(sK2) [avatar definition]
163. ~tall(sK2) <- (~11) [avatar component clause 161]
164. 9 | ~11 [avatar split clause 78,161,153]
166. 12 <=> ! [X0] : ~humble(X0) [avatar definition]
167. ~humble(X0) <- (12) [avatar component clause 166]
169. 13 <=> old(alice) [avatar definition]
171. old(alice) <- (13) [avatar component clause 169]
172. 12 | 13 [avatar split clause 84,169,166]
174. 14 <=> ! [X0] : ~rich(X0) [avatar definition]
175. ~rich(X0) <- (14) [avatar component clause 174]
176. 14 | 13 [avatar split clause 83,169,174]
220. ~old(X0) | kind(X0) [subsumption resolution 101,86]
221. ~old(X0) [subsumption resolution 220,85]
243. 27 <=> ! [X0] : (~funny(X0) | humble(X0)) [avatar definition]
244. ~funny(X0) | humble(X0) <- (27) [avatar component clause 243]
246. 28 <=> tall(susan) [avatar definition]
249. 27 | 28 [avatar split clause 114,246,243]
254. 27 | ~28 [avatar split clause 112,246,243]
266. $false <- (13) [subsumption resolution 171,221]
267. ~13 [avatar contradiction clause 266]
268. $false <- (9) [resolution 154,117]
269. ~9 [avatar contradiction clause 268]
301. rich(sK0) | funny(sK0) <- (~2) [resolution 105,124]
302. funny(sK0) <- (~2, 14) [subsumption resolution 301,175]
303. humble(sK0) <- (~2, 14, 27) [resolution 302,244]
306. $false <- (~2, 12, 14, 27) [subsumption resolution 303,167]
307. 2 | ~12 | ~14 | ~27 [avatar contradiction clause 306]
308. $false <- (3, 14) [subsumption resolution 128,175]
309. ~3 | ~14 [avatar contradiction clause 308]
310. $false <- (1, ~11) [resolution 120,163]
311. ~1 | 11 [avatar contradiction clause 310]
312. $false [avatar sat refutation 129,164,172,176,249,254,267,269,307,309,311]
% SZS output end Proof for 6339085063275777047588620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not creative is not tall or happy and vice versa.
Everyone who is both happy and not brave is either old or not curious and vice versa.
Everyone who is curious or quiet is not brave.
Everyone who is either curious or happy is happy and vice versa.
Everyone who is not humble or happy is both curious and not quiet and vice versa.
Everyone who is not calm is not old or creative and vice versa.
If someone is both happy and not humble then susan is funny or humble.
If someone is either not calm or tall then someone is strong or happy and vice versa.
Everyone who is both humble and not kind is patient or not kind and vice versa.
If someone is rich then someone is either strong or not wise.
Everyone who is both calm and not patient is either humble or brave and vice versa.
If someone is both quiet and not patient then someone is patient and vice versa.
If someone is not curious or strong then someone is not rich or not creative and vice versa.
If someone is either not wise or not curious then john is not strong and vice versa.
Everyone who is not brave is either not generous or not rich.
If fred is rich or not brave then mary is not curious.
Someone is either not calm or strong.
Fred is rich.
Someone is both patient and rich.
Mary is either not funny or brave.
Fred is not funny.
Paul is tall or creative.
Susan is not rich. | Mary is curious. | contradiction | (![X]:((~happy(X)&~creative(X))<=>(~tall(X)|happy(X))))&
(![X]:((happy(X)&~brave(X))<=>(old(X)<~>~curious(X))))&
(![X]:((curious(X)|quiet(X))=>~brave(X)))&
(![X]:((curious(X)<~>happy(X))<=>happy(X)))&
(![X]:((~humble(X)|happy(X))<=>(curious(X)&~quiet(X))))&
(![X]:(~calm(X)<=>(~old(X)|creative(X))))&
((?[X]:((happy(X)&~humble(X))))=>((funny(susan)|humble(susan))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:((strong(X)|happy(X)))))&
(![X]:((humble(X)&~kind(X))<=>(patient(X)|~kind(X))))&
((?[X]:(rich(X)))=>(?[X]:((strong(X)<~>~wise(X)))))&
(![X]:((calm(X)&~patient(X))<=>(humble(X)<~>brave(X))))&
((?[X]:((quiet(X)&~patient(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~curious(X)|strong(X))))<=>(?[X]:((~rich(X)|~creative(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(~strong(john)))&
(![X]:(~brave(X)=>(~generous(X)<~>~rich(X))))&
(((rich(fred)|~brave(fred)))=>(~curious(mary)))&
(?[X]:((~calm(X)<~>strong(X))))&
(rich(fred))&
(?[X]:((patient(X)&rich(X))))&
((~funny(mary)<~>brave(mary)))&
(~funny(fred))&
((tall(paul)|creative(paul)))&
(~rich(susan)) | curious(mary) | [
"p0",
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 271825407105798013825275
% SZS output start Proof for 271825407105798013825275
1. ! [X0] : ((~creative(X0) & ~happy(X0)) <=> (happy(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((curious(X0) <~> happy(X0)) <=> happy(X0)) [input p3]
24. curious(mary) [input hypothesis]
35. ! [X0] : (((~creative(X0) & ~happy(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (creative(X0) | happy(X0)))) [nnf transformation 1]
36. ! [X0] : (((~creative(X0) & ~happy(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | creative(X0) | happy(X0))) [flattening 35]
39. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ~happy(X0)) & (happy(X0) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 4]
80. ~happy(X0) | ~happy(X0) [cnf transformation 36]
91. happy(X0) | happy(X0) | ~curious(X0) [cnf transformation 39]
148. curious(mary) [cnf transformation 24]
149. happy(X0) | ~curious(X0) [duplicate literal removal 91]
152. ~happy(X0) [duplicate literal removal 80]
156. ~curious(X0) [subsumption resolution 149,152]
269. $false [subsumption resolution 148,156]
% SZS output end Proof for 271825407105798013825275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is strong. Everyone who is not old is either not funny or not tall and vice versa. Everyone who is not generous is not strong and vice versa. Everyone who is not funny is both not wise and not happy. If alice is either not creative or not strong then mary is strong or tall. If someone is either calm or not old then john is not generous. Everyone who is kind or not old is either tall or calm. If someone is either not old or not calm then someone is not humble. Everyone who is both not kind and humble is either generous or not humble and vice versa. Everyone who is strong is not humble. Everyone who is not curious is not brave or not calm. If susan is both not happy and kind then someone is not funny or tall. If susan is not happy then paul is humble. Everyone who is both not strong and not tall is quiet or patient and vice versa. Everyone who is not tall is creative or not humble. Everyone who is not patient is either tall or not calm. Someone is either not brave or not old. Lucy is both not generous and not curious. Fred is wise. Susan is both not funny and kind. Alice is funny or not brave. Someone is kind. | Alice is not patient. | neutral | (![X]:(curious(X)=>strong(X)))&
(![X]:(~old(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:(~funny(X)=>(~wise(X)&~happy(X))))&
(((~creative(alice)<~>~strong(alice)))=>((strong(mary)|tall(mary))))&
((?[X]:((calm(X)<~>~old(X))))=>(~generous(john)))&
(![X]:((kind(X)|~old(X))=>(tall(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)&humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:(strong(X)=>~humble(X)))&
(![X]:(~curious(X)=>(~brave(X)|~calm(X))))&
(((~happy(susan)&kind(susan)))=>(?[X]:((~funny(X)|tall(X)))))&
((~happy(susan))=>(humble(paul)))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(creative(X)|~humble(X))))&
(![X]:(~patient(X)=>(tall(X)<~>~calm(X))))&
(?[X]:((~brave(X)<~>~old(X))))&
((~generous(lucy)&~curious(lucy)))&
(wise(fred))&
((~funny(susan)&kind(susan)))&
((funny(alice)|~brave(alice)))&
(?[X]:(kind(X))) | ~patient(alice) | []
| null | 0 |
Everyone who is funny is not generous.
Everyone who is wise is not happy and vice versa.
Everyone who is not quiet is not generous or wise.
Everyone who is strong is both creative and calm.
Everyone who is strong is strong or not patient.
If john is brave or not funny then someone is quiet or not quiet.
If john is not calm then alice is not kind or old.
Everyone who is both tall and old is both not tall and generous and vice versa.
Everyone who is generous is calm or not wise and vice versa.
If lucy is both not funny and strong then someone is not old.
If alice is either not kind or not happy then john is generous.
If alice is either happy or calm then lucy is either quiet or strong and vice versa.
If someone is creative then lucy is happy.
Everyone who is both not funny and happy is funny or humble.
Everyone who is either not patient or not funny is curious or not tall and vice versa.
If paul is curious then someone is either not creative or not brave and vice versa.
Paul is not happy.
John is not wise or not creative.
Mary is old.
Lucy is either not tall or not creative.
Someone is either curious or not generous.
Alice is both not humble and not calm.
Susan is wise. | John is not wise. | neutral | (![X]:(funny(X)=>~generous(X)))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:(~quiet(X)=>(~generous(X)|wise(X))))&
(![X]:(strong(X)=>(creative(X)&calm(X))))&
(![X]:(strong(X)=>(strong(X)|~patient(X))))&
(((brave(john)|~funny(john)))=>(?[X]:((quiet(X)|~quiet(X)))))&
((~calm(john))=>((~kind(alice)|old(alice))))&
(![X]:((tall(X)&old(X))<=>(~tall(X)&generous(X))))&
(![X]:(generous(X)<=>(calm(X)|~wise(X))))&
(((~funny(lucy)&strong(lucy)))=>(?[X]:(~old(X))))&
(((~kind(alice)<~>~happy(alice)))=>(generous(john)))&
(((happy(alice)<~>calm(alice)))<=>((quiet(lucy)<~>strong(lucy))))&
((?[X]:(creative(X)))=>(happy(lucy)))&
(![X]:((~funny(X)&happy(X))=>(funny(X)|humble(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(curious(X)|~tall(X))))&
((curious(paul))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(~happy(paul))&
((~wise(john)|~creative(john)))&
(old(mary))&
((~tall(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)<~>~generous(X))))&
((~humble(alice)&~calm(alice)))&
(wise(susan)) | ~wise(john) | []
| null | 0 |
If someone is both not wise and quiet then susan is both not happy and not humble and vice versa.
Everyone who is happy is either quiet or not creative.
If someone is either not strong or not humble then someone is not brave.
Everyone who is not creative is humble or strong.
If someone is both not wise and humble then mary is both funny and not happy.
Everyone who is not rich or not wise is both not old and kind.
If fred is either creative or humble then alice is either happy or not happy and vice versa.
If lucy is both not creative and not happy then someone is not generous or patient and vice versa.
Everyone who is not curious or kind is curious and vice versa.
Everyone who is not happy or tall is both not wise and not generous.
If john is both wise and brave then someone is both not strong and not patient and vice versa.
Everyone who is either not strong or kind is not rich or not humble and vice versa.
Everyone who is brave or strong is not tall or not brave and vice versa.
If susan is not creative or patient then someone is both not rich and not quiet.
Everyone who is both not creative and not funny is both not quiet and not kind.
Everyone who is not kind or not tall is both brave and not strong and vice versa.
Someone is both old and quiet.
Someone is either happy or not kind.
Someone is humble.
Lucy is humble or not wise.
Someone is both quiet and happy. | Lucy is not kind. | contradiction | ((?[X]:((~wise(X)&quiet(X))))<=>((~happy(susan)&~humble(susan))))&
(![X]:(happy(X)=>(quiet(X)<~>~creative(X))))&
((?[X]:((~strong(X)<~>~humble(X))))=>(?[X]:(~brave(X))))&
(![X]:(~creative(X)=>(humble(X)|strong(X))))&
((?[X]:((~wise(X)&humble(X))))=>((funny(mary)&~happy(mary))))&
(![X]:((~rich(X)|~wise(X))=>(~old(X)&kind(X))))&
(((creative(fred)<~>humble(fred)))<=>((happy(alice)<~>~happy(alice))))&
(((~creative(lucy)&~happy(lucy)))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((~curious(X)|kind(X))<=>curious(X)))&
(![X]:((~happy(X)|tall(X))=>(~wise(X)&~generous(X))))&
(((wise(john)&brave(john)))<=>(?[X]:((~strong(X)&~patient(X)))))&
(![X]:((~strong(X)<~>kind(X))<=>(~rich(X)|~humble(X))))&
(![X]:((brave(X)|strong(X))<=>(~tall(X)|~brave(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)&~funny(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~kind(X)|~tall(X))<=>(brave(X)&~strong(X))))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:(humble(X)))&
((humble(lucy)|~wise(lucy)))&
(?[X]:((quiet(X)&happy(X)))) | ~kind(lucy) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 7294655272716812804450836
% SZS output start Proof for 7294655272716812804450836
9. ! [X0] : ((kind(X0) | ~curious(X0)) <=> curious(X0)) [input p8]
22. ~kind(lucy) [input hypothesis]
50. ! [X0] : (((kind(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 9]
51. ! [X0] : ((kind(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & curious(X0)))) [flattening 50]
101. curious(X0) | curious(X0) [cnf transformation 51]
103. kind(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 51]
139. ~kind(lucy) [cnf transformation 22]
142. curious(X0) [duplicate literal removal 101]
143. ~curious(X0) | kind(X0) [duplicate literal removal 103]
335. kind(X0) [resolution 143,142]
336. $false [resolution 335,139]
% SZS output end Proof for 7294655272716812804450836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or humble then someone is happy. If someone is both wise and calm then someone is either not kind or not humble and vice versa. Everyone who is both not wise and not kind is either funny or humble and vice versa. If someone is both not kind and not brave then someone is either rich or brave and vice versa. Everyone who is either not creative or quiet is not calm. Everyone who is happy is either not old or not kind. Everyone who is not humble or not happy is both not old and not happy and vice versa. If someone is not wise then someone is either not strong or happy and vice versa. Everyone who is wise or not wise is wise or not curious. If mary is not kind or funny then someone is not wise. Everyone who is rich is not tall and vice versa. If susan is not tall then fred is both not generous and not creative and vice versa. Everyone who is either rich or strong is not wise or not humble and vice versa. Everyone who is not funny is both not happy and not creative and vice versa. Everyone who is not patient or not humble is either strong or not tall and vice versa. Everyone who is strong is either not generous or funny. Someone is either not humble or not funny. John is patient. Someone is both rich and humble. Someone is happy or not humble. Mary is not kind or not creative. Susan is generous or not old. Someone is either old or not brave. Someone is kind or not brave. | Susan is not quiet. | neutral | ((?[X]:((~creative(X)|humble(X))))=>(?[X]:(happy(X))))&
((?[X]:((wise(X)&calm(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
(![X]:((~wise(X)&~kind(X))<=>(funny(X)<~>humble(X))))&
((?[X]:((~kind(X)&~brave(X))))<=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:((~creative(X)<~>quiet(X))=>~calm(X)))&
(![X]:(happy(X)=>(~old(X)<~>~kind(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~old(X)&~happy(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((wise(X)|~wise(X))=>(wise(X)|~curious(X))))&
(((~kind(mary)|funny(mary)))=>(?[X]:(~wise(X))))&
(![X]:(rich(X)<=>~tall(X)))&
((~tall(susan))<=>((~generous(fred)&~creative(fred))))&
(![X]:((rich(X)<~>strong(X))<=>(~wise(X)|~humble(X))))&
(![X]:(~funny(X)<=>(~happy(X)&~creative(X))))&
(![X]:((~patient(X)|~humble(X))<=>(strong(X)<~>~tall(X))))&
(![X]:(strong(X)=>(~generous(X)<~>funny(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
(patient(john))&
(?[X]:((rich(X)&humble(X))))&
(?[X]:((happy(X)|~humble(X))))&
((~kind(mary)|~creative(mary)))&
((generous(susan)|~old(susan)))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((kind(X)|~brave(X)))) | ~quiet(susan) | []
| null | 0 |
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