premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is either not happy or strong then someone is either not happy or patient.
Everyone who is both not generous and generous is tall or wise.
If alice is both funny and happy then someone is both not kind and generous and vice versa.
If someone is either not old or not generous then someone is not old or creative.
If someone is both old and tall then someone is tall.
Everyone who is curious is both not brave and rich.
If someone is either old or not tall then someone is happy.
If someone is not creative then someone is either humble or not rich and vice versa.
If fred is both not patient and not tall then mary is not strong or strong.
Everyone who is both strong and not rich is not rich or not calm and vice versa.
If someone is not strong then someone is either funny or not kind and vice versa.
Everyone who is either not wise or not brave is not creative or not kind.
If someone is not patient or not rich then john is kind.
Everyone who is quiet or humble is both not kind and calm and vice versa.
If john is funny then someone is creative and vice versa.
Everyone who is not calm or quiet is not quiet.
Someone is not creative.
Fred is creative or curious.
Mary is not kind.
Mary is either strong or not brave.
Someone is not generous or not quiet.
Someone is tall.
Someone is both not happy and not creative.
Someone is either funny or curious. | Fred is creative. | neutral | ((?[X]:((~happy(X)<~>strong(X))))=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((~generous(X)&generous(X))=>(tall(X)|wise(X))))&
(((funny(alice)&happy(alice)))<=>(?[X]:((~kind(X)&generous(X)))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:((~old(X)|creative(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:(tall(X))))&
(![X]:(curious(X)=>(~brave(X)&rich(X))))&
((?[X]:((old(X)<~>~tall(X))))=>(?[X]:(happy(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)<~>~rich(X)))))&
(((~patient(fred)&~tall(fred)))=>((~strong(mary)|strong(mary))))&
(![X]:((strong(X)&~rich(X))<=>(~rich(X)|~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~kind(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)|~kind(X))))&
((?[X]:((~patient(X)|~rich(X))))=>(kind(john)))&
(![X]:((quiet(X)|humble(X))<=>(~kind(X)&calm(X))))&
((funny(john))<=>(?[X]:(creative(X))))&
(![X]:((~calm(X)|quiet(X))=>~quiet(X)))&
(?[X]:(~creative(X)))&
((creative(fred)|curious(fred)))&
(~kind(mary))&
((strong(mary)<~>~brave(mary)))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(tall(X)))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:((funny(X)<~>curious(X)))) | creative(fred) | [] | null | 0 |
Everyone who is quiet or not brave is both not strong and not kind and vice versa.
Everyone who is both generous and quiet is not wise or not patient.
If susan is patient or not wise then lucy is both not brave and not kind and vice versa.
Everyone who is both tall and not humble is not happy or strong and vice versa.
If susan is both not happy and quiet then lucy is either not funny or creative and vice versa.
Everyone who is not quiet or not curious is either funny or rich and vice versa.
Everyone who is both wise and not rich is brave or humble and vice versa.
Everyone who is not tall is calm and vice versa.
If someone is either not kind or happy then someone is both not patient and not creative and vice versa.
Everyone who is not tall or not humble is not curious or patient.
If someone is calm or tall then susan is either not humble or not patient.
Everyone who is humble or patient is calm or generous and vice versa.
If someone is both not kind and not quiet then someone is humble or funny.
Everyone who is not strong is both not brave and patient and vice versa.
If susan is calm then mary is wise or rich.
Everyone who is either quiet or not calm is wise and vice versa.
Lucy is brave or not tall.
Susan is calm or creative.
Someone is either not old or not creative.
Fred is either rich or not strong.
Someone is both wise and not quiet.
Alice is both creative and not happy.
Someone is either not patient or tall.
Someone is either happy or calm. | Fred is strong. | contradiction | (![X]:((quiet(X)|~brave(X))<=>(~strong(X)&~kind(X))))&
(![X]:((generous(X)&quiet(X))=>(~wise(X)|~patient(X))))&
(((patient(susan)|~wise(susan)))<=>((~brave(lucy)&~kind(lucy))))&
(![X]:((tall(X)&~humble(X))<=>(~happy(X)|strong(X))))&
(((~happy(susan)&quiet(susan)))<=>((~funny(lucy)<~>creative(lucy))))&
(![X]:((~quiet(X)|~curious(X))<=>(funny(X)<~>rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(brave(X)|humble(X))))&
(![X]:(~tall(X)<=>calm(X)))&
((?[X]:((~kind(X)<~>happy(X))))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((~tall(X)|~humble(X))=>(~curious(X)|patient(X))))&
((?[X]:((calm(X)|tall(X))))=>((~humble(susan)<~>~patient(susan))))&
(![X]:((humble(X)|patient(X))<=>(calm(X)|generous(X))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:(~strong(X)<=>(~brave(X)&patient(X))))&
((calm(susan))=>((wise(mary)|rich(mary))))&
(![X]:((quiet(X)<~>~calm(X))<=>wise(X)))&
((brave(lucy)|~tall(lucy)))&
((calm(susan)|creative(susan)))&
(?[X]:((~old(X)<~>~creative(X))))&
((rich(fred)<~>~strong(fred)))&
(?[X]:((wise(X)&~quiet(X))))&
((creative(alice)&~happy(alice)))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((happy(X)<~>calm(X)))) | strong(fred) | [
"p0",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6470966268609486990756447
% SZS output start Proof for 6470966268609486990756447
1. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (~kind(X0) & ~strong(X0))) [input p0]
7. ! [X0] : ((~rich(X0) & wise(X0)) <=> (humble(X0) | brave(X0))) [input p6]
20. rich(fred) <~> ~strong(fred) [input p19]
25. strong(fred) [input hypothesis]
36. ! [X0] : (((~brave(X0) | quiet(X0)) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | quiet(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0)))) [flattening 36]
46. ! [X0] : (((~rich(X0) & wise(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (rich(X0) | ~wise(X0)))) [nnf transformation 7]
47. ! [X0] : (((~rich(X0) & wise(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | rich(X0) | ~wise(X0))) [flattening 46]
66. (strong(fred) | ~rich(fred)) & (~strong(fred) | rich(fred)) [nnf transformation 20]
76. ~strong(X0) | brave(X0) [cnf transformation 37]
106. ~rich(X0) | ~brave(X0) [cnf transformation 47]
139. ~strong(fred) | rich(fred) [cnf transformation 66]
149. strong(fred) [cnf transformation 25]
285. 29 <=> rich(fred) [avatar definition]
286. rich(fred) <- (29) [avatar component clause 285]
289. 30 <=> strong(fred) [avatar definition]
291. strong(fred) <- (30) [avatar component clause 289]
293. 29 | ~30 [avatar split clause 139,289,285]
314. 30 [avatar split clause 149,289]
316. brave(fred) <- (30) [resolution 76,291]
321. ~brave(fred) <- (29) [resolution 106,286]
322. $false <- (29, 30) [subsumption resolution 321,316]
323. ~29 | ~30 [avatar contradiction clause 322]
324. $false [avatar sat refutation 293,314,323]
% SZS output end Proof for 6470966268609486990756447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or humble is either generous or not tall.
If someone is either creative or happy then susan is quiet or not patient and vice versa.
If someone is calm or generous then mary is both not quiet and tall.
If someone is either creative or not funny then someone is not creative or wise 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.
Someone is either old or strong.
Someone is either not generous or brave.
Alice is either not curious or not generous.
Someone is either kind or brave.
John is not strong.
Someone is not kind or not wise.
Someone is not calm or strong. | Lucy is not curious. | entailment | (![X]:((~rich(X)<~>humble(X))=>(generous(X)<~>~tall(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>((quiet(susan)|~patient(susan))))&
((?[X]:((calm(X)|generous(X))))=>((~quiet(mary)&tall(mary))))&
((?[X]:((creative(X)<~>~funny(X))))<=>(?[X]:((~creative(X)|wise(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]:((old(X)<~>strong(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
((~curious(alice)<~>~generous(alice)))&
(?[X]:((kind(X)<~>brave(X))))&
(~strong(john))&
(?[X]:((~kind(X)|~wise(X))))&
(?[X]:((~calm(X)|strong(X)))) | ~curious(lucy) | [
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8467540619587668494134502
% SZS output start Proof for 8467540619587668494134502
9. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (rich(X0) & ~quiet(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & curious(X0)) => ~rich(X0)) [input p9]
11. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p10]
13. ! [X0] : ((tall(X0) | curious(X0)) <=> ~rich(X0)) [input p12]
14. ! [X0] : ((strong(X0) & curious(X0)) => (~funny(X0) & patient(X0))) [input p13]
24. curious(lucy) [input hypothesis]
34. ! [X0] : (~rich(X0) | (patient(X0) | ~curious(X0))) [ennf transformation 10]
35. ! [X0] : (~rich(X0) | patient(X0) | ~curious(X0)) [flattening 34]
36. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 11]
39. ! [X0] : ((~funny(X0) & patient(X0)) | (~strong(X0) | ~curious(X0))) [ennf transformation 14]
40. ! [X0] : ((~funny(X0) & patient(X0)) | ~strong(X0) | ~curious(X0)) [flattening 39]
61. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 9]
62. ! [X0] : ((~kind(X0) | ~strong(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [flattening 61]
64. ! [X0] : (((tall(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 13]
65. ! [X0] : ((tall(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [flattening 64]
111. strong(X0) | rich(X0) [cnf transformation 62]
114. ~curious(X0) | patient(X0) | ~rich(X0) [cnf transformation 35]
118. ~patient(X0) | funny(X0) [cnf transformation 36]
121. ~curious(X0) | ~rich(X0) [cnf transformation 65]
124. ~strong(X0) | patient(X0) | ~curious(X0) [cnf transformation 40]
125. ~strong(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 40]
142. curious(lucy) [cnf transformation 24]
223. 19 <=> funny(lucy) [avatar definition]
224. ~funny(lucy) <- (~19) [avatar component clause 223]
367. patient(X0) | ~curious(X0) | rich(X0) [resolution 124,111]
368. ~curious(X0) | patient(X0) [subsumption resolution 367,114]
369. ~funny(X0) | ~curious(X0) | rich(X0) [resolution 125,111]
370. ~curious(X0) | ~funny(X0) [subsumption resolution 369,121]
371. patient(lucy) [resolution 368,142]
406. ~funny(lucy) [resolution 370,142]
413. ~19 [avatar split clause 406,223]
551. funny(lucy) [resolution 371,118]
553. $false <- (~19) [subsumption resolution 551,224]
554. 19 [avatar contradiction clause 553]
555. $false [avatar sat refutation 413,554]
% SZS output end Proof for 8467540619587668494134502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is tall then someone is both not old and not brave and vice versa.
If paul is generous or kind then alice is both not generous and not kind and vice versa.
If someone is either not wise or wise then someone is not happy or not wise and vice versa.
If someone is not patient then someone is not calm or not humble.
If someone is both humble and not kind then paul is both tall and not rich and vice versa.
If alice is both not tall and generous then susan is not humble.
If paul is either not wise or humble then mary is either not creative or not strong and vice versa.
If someone is not happy then susan is not tall or not curious and vice versa.
If mary is both not creative and happy then alice is tall.
Everyone who is either not generous or funny is either not creative or kind and vice versa.
Everyone who is either wise or quiet is creative and vice versa.
Everyone who is not curious or not tall is not rich and vice versa.
Everyone who is both not generous and kind is happy and vice versa.
Everyone who is not rich is tall and vice versa.
If mary is either rich or not humble then someone is either not happy or calm.
If lucy is both not funny and funny then john is both not happy and not strong and vice versa.
Mary is not curious.
Fred is either not creative or not quiet.
John is both not humble and not wise.
Paul is kind or tall.
Someone is either not patient or patient.
Someone is calm.
Lucy is both old and not strong.
John is either not generous or strong. | Paul is curious. | contradiction | ((tall(paul))<=>(?[X]:((~old(X)&~brave(X)))))&
(((generous(paul)|kind(paul)))<=>((~generous(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>wise(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((humble(X)&~kind(X))))<=>((tall(paul)&~rich(paul))))&
(((~tall(alice)&generous(alice)))=>(~humble(susan)))&
(((~wise(paul)<~>humble(paul)))<=>((~creative(mary)<~>~strong(mary))))&
((?[X]:(~happy(X)))<=>((~tall(susan)|~curious(susan))))&
(((~creative(mary)&happy(mary)))=>(tall(alice)))&
(![X]:((~generous(X)<~>funny(X))<=>(~creative(X)<~>kind(X))))&
(![X]:((wise(X)<~>quiet(X))<=>creative(X)))&
(![X]:((~curious(X)|~tall(X))<=>~rich(X)))&
(![X]:((~generous(X)&kind(X))<=>happy(X)))&
(![X]:(~rich(X)<=>tall(X)))&
(((rich(mary)<~>~humble(mary)))=>(?[X]:((~happy(X)<~>calm(X)))))&
(((~funny(lucy)&funny(lucy)))<=>((~happy(john)&~strong(john))))&
(~curious(mary))&
((~creative(fred)<~>~quiet(fred)))&
((~humble(john)&~wise(john)))&
((kind(paul)|tall(paul)))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:(calm(X)))&
((old(lucy)&~strong(lucy)))&
((~generous(john)<~>strong(john))) | curious(paul) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 316025537474431256793033
% SZS output start Proof for 316025537474431256793033
12. ! [X0] : ((~tall(X0) | ~curious(X0)) <=> ~rich(X0)) [input p11]
14. ! [X0] : (~rich(X0) <=> tall(X0)) [input p13]
25. curious(paul) [input hypothesis]
61. ! [X0] : (((~tall(X0) | ~curious(X0)) | rich(X0)) & (~rich(X0) | (tall(X0) & curious(X0)))) [nnf transformation 12]
62. ! [X0] : ((~tall(X0) | ~curious(X0) | rich(X0)) & (~rich(X0) | (tall(X0) & curious(X0)))) [flattening 61]
65. ! [X0] : ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))) [nnf transformation 14]
123. ~rich(X0) | tall(X0) [cnf transformation 62]
124. ~curious(X0) | ~tall(X0) | rich(X0) [cnf transformation 62]
128. tall(X0) | rich(X0) [cnf transformation 65]
129. ~rich(X0) | ~tall(X0) [cnf transformation 65]
151. curious(paul) [cnf transformation 25]
296. ~rich(X0) [subsumption resolution 129,123]
297. tall(X0) [subsumption resolution 128,296]
351. ~tall(paul) | rich(paul) [resolution 124,151]
352. rich(paul) [subsumption resolution 351,297]
353. $false [subsumption resolution 352,296]
% SZS output end Proof for 316025537474431256793033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not curious and vice versa.
Everyone who is happy is both kind and curious.
Everyone who is both curious and not humble is not kind or not patient and vice versa.
Everyone who is both not wise and brave is either not wise or wise and vice versa.
Everyone who is happy or quiet is not funny and vice versa.
If john is both not creative and not brave then someone is humble and vice versa.
Everyone who is both not creative and not strong is both not generous and brave.
Everyone who is either kind or wise is both not wise and patient.
If john is funny then paul is quiet.
If mary is calm or not brave then lucy is strong or not rich.
Everyone who is either strong or generous is both not old and not wise and vice versa.
If someone is not old or not creative then someone is both not curious and calm and vice versa.
Everyone who is strong is not wise.
Everyone who is not happy or rich is both rich and generous.
If john is calm then paul is generous.
Everyone who is curious is both old and not funny.
Someone is both generous and kind.
Fred is rich.
Alice is not humble or not rich.
Mary is calm.
Paul is either not wise or not old.
John is either humble or curious. | Lucy is creative. | neutral | (![X]:(~tall(X)<=>~curious(X)))&
(![X]:(happy(X)=>(kind(X)&curious(X))))&
(![X]:((curious(X)&~humble(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~wise(X)&brave(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((happy(X)|quiet(X))<=>~funny(X)))&
(((~creative(john)&~brave(john)))<=>(?[X]:(humble(X))))&
(![X]:((~creative(X)&~strong(X))=>(~generous(X)&brave(X))))&
(![X]:((kind(X)<~>wise(X))=>(~wise(X)&patient(X))))&
((funny(john))=>(quiet(paul)))&
(((calm(mary)|~brave(mary)))=>((strong(lucy)|~rich(lucy))))&
(![X]:((strong(X)<~>generous(X))<=>(~old(X)&~wise(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(strong(X)=>~wise(X)))&
(![X]:((~happy(X)|rich(X))=>(rich(X)&generous(X))))&
((calm(john))=>(generous(paul)))&
(![X]:(curious(X)=>(old(X)&~funny(X))))&
(?[X]:((generous(X)&kind(X))))&
(rich(fred))&
((~humble(alice)|~rich(alice)))&
(calm(mary))&
((~wise(paul)<~>~old(paul)))&
((humble(john)<~>curious(john))) | creative(lucy) | [] | null | 0 |
If someone is tall then someone is strong or patient. If someone is wise then someone is not quiet. Everyone who is both old and not curious is rich. If someone is brave or not brave then lucy is creative or not humble. If someone is both funny and happy then someone is either quiet or not kind. Everyone who is happy or not wise is either tall or old and vice versa. If someone is brave then someone is both not strong and rich. If mary is either old or not curious then mary is both not wise and not strong and vice versa. Everyone who is patient or wise is not tall and vice versa. If lucy is generous or not creative then fred is either not generous or calm. Everyone who is not happy or not quiet is both not wise and wise. Everyone who is both not happy and not quiet is not calm or not tall and vice versa. Everyone who is either not calm or tall is both not curious and tall. Everyone who is not old is both not funny and rich. If lucy is not happy then lucy is both rich and not strong and vice versa. If john is either not kind or not humble then susan is both kind and strong. Alice is calm or funny. Lucy is rich or not funny. Lucy is either creative or kind. Lucy is both not old and kind. Someone is either old or not creative. Fred is either not rich or not funny. | Lucy is not wise. | entailment | ((?[X]:(tall(X)))=>(?[X]:((strong(X)|patient(X)))))&
((?[X]:(wise(X)))=>(?[X]:(~quiet(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
((?[X]:((brave(X)|~brave(X))))=>((creative(lucy)|~humble(lucy))))&
((?[X]:((funny(X)&happy(X))))=>(?[X]:((quiet(X)<~>~kind(X)))))&
(![X]:((happy(X)|~wise(X))<=>(tall(X)<~>old(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)&rich(X)))))&
(((old(mary)<~>~curious(mary)))<=>((~wise(mary)&~strong(mary))))&
(![X]:((patient(X)|wise(X))<=>~tall(X)))&
(((generous(lucy)|~creative(lucy)))=>((~generous(fred)<~>calm(fred))))&
(![X]:((~happy(X)|~quiet(X))=>(~wise(X)&wise(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(~calm(X)|~tall(X))))&
(![X]:((~calm(X)<~>tall(X))=>(~curious(X)&tall(X))))&
(![X]:(~old(X)=>(~funny(X)&rich(X))))&
((~happy(lucy))<=>((rich(lucy)&~strong(lucy))))&
(((~kind(john)<~>~humble(john)))=>((kind(susan)&strong(susan))))&
((calm(alice)|funny(alice)))&
((rich(lucy)|~funny(lucy)))&
((creative(lucy)<~>kind(lucy)))&
((~old(lucy)&kind(lucy)))&
(?[X]:((old(X)<~>~creative(X))))&
((~rich(fred)<~>~funny(fred))) | ~wise(lucy) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4951157031989230621754959
% SZS output start Proof for 4951157031989230621754959
2. ? [X0] : wise(X0) => ? [X0] : ~quiet(X0) [input p1]
11. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (wise(X0) & ~wise(X0))) [input p10]
23. wise(lucy) [input hypothesis]
25. ? [X0] : wise(X0) => ? [X1] : ~quiet(X1) [rectify 2]
29. ? [X1] : ~quiet(X1) | ! [X0] : ~wise(X0) [ennf transformation 25]
37. ! [X0] : ((wise(X0) & ~wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 11]
44. ? [X0] : ~quiet(X0) | ! [X1] : ~wise(X1) [rectify 29]
45. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
46. ~quiet(sK1) | ! [X1] : ~wise(X1) [skolemisation 44,45]
73. ~quiet(sK1) | ~wise(X1) [cnf transformation 46]
101. ~wise(X0) | quiet(X0) [cnf transformation 37]
103. wise(X0) | quiet(X0) [cnf transformation 37]
132. wise(lucy) [cnf transformation 23]
147. 4 <=> ! [X1] : ~wise(X1) [avatar definition]
148. ~wise(X1) <- (4) [avatar component clause 147]
150. 5 <=> quiet(sK1) [avatar definition]
152. ~quiet(sK1) <- (~5) [avatar component clause 150]
153. 4 | ~5 [avatar split clause 73,150,147]
231. quiet(X0) [subsumption resolution 101,103]
303. $false <- (~5) [subsumption resolution 152,231]
304. 5 [avatar contradiction clause 303]
306. $false <- (4) [resolution 148,132]
307. ~4 [avatar contradiction clause 306]
308. $false [avatar sat refutation 153,304,307]
% SZS output end Proof for 4951157031989230621754959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or calm is both not patient and old. Everyone who is either kind or not tall is both calm and not creative and vice versa. Everyone who is either not wise or curious is both quiet and humble and vice versa. If someone is both not brave and not wise then susan is both not happy and not patient and vice versa. Everyone who is not creative or creative is quiet or wise and vice versa. If paul is both funny and tall then someone is either not funny or old and vice versa. Everyone who is not generous or calm is both not quiet and not calm and vice versa. If someone is kind then someone is not curious. If lucy is both calm and kind then susan is not calm or not generous. Everyone who is either not tall or not happy is not humble or not old. Everyone who is not happy is humble and vice versa. Everyone who is either not old or not kind is both not happy and curious. Everyone who is brave or not quiet is not patient or curious and vice versa. Everyone who is both not funny and curious is not happy and vice versa. Everyone who is either not calm or creative is not creative. If someone is not strong then someone is not creative or not strong. Alice is not humble or old. Someone is humble or tall. Alice is either humble or not patient. Alice is both not brave and happy. Someone is patient or quiet. Fred is humble. Alice is quiet or not kind. Mary is either calm or not rich. | Susan is humble. | contradiction | (![X]:((quiet(X)<~>calm(X))=>(~patient(X)&old(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(calm(X)&~creative(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(quiet(X)&humble(X))))&
((?[X]:((~brave(X)&~wise(X))))<=>((~happy(susan)&~patient(susan))))&
(![X]:((~creative(X)|creative(X))<=>(quiet(X)|wise(X))))&
(((funny(paul)&tall(paul)))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~generous(X)|calm(X))<=>(~quiet(X)&~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:(~curious(X))))&
(((calm(lucy)&kind(lucy)))=>((~calm(susan)|~generous(susan))))&
(![X]:((~tall(X)<~>~happy(X))=>(~humble(X)|~old(X))))&
(![X]:(~happy(X)<=>humble(X)))&
(![X]:((~old(X)<~>~kind(X))=>(~happy(X)&curious(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~funny(X)&curious(X))<=>~happy(X)))&
(![X]:((~calm(X)<~>creative(X))=>~creative(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~strong(X)))))&
((~humble(alice)|old(alice)))&
(?[X]:((humble(X)|tall(X))))&
((humble(alice)<~>~patient(alice)))&
((~brave(alice)&happy(alice)))&
(?[X]:((patient(X)|quiet(X))))&
(humble(fred))&
((quiet(alice)|~kind(alice)))&
((calm(mary)<~>~rich(mary))) | humble(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6207617928529430407623422
% SZS output start Proof for 6207617928529430407623422
1. ! [X0] : ((quiet(X0) <~> calm(X0)) => (old(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (humble(X0) & quiet(X0))) [input p2]
4. ? [X0] : (~wise(X0) & ~brave(X0)) <=> (~patient(susan) & ~happy(susan)) [input p3]
5. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (wise(X0) | quiet(X0))) [input p4]
7. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~calm(X0) & ~quiet(X0))) [input p6]
11. ! [X0] : (~happy(X0) <=> humble(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (curious(X0) | ~patient(X0))) [input p12]
14. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~happy(X0)) [input p13]
25. humble(susan) [input hypothesis]
28. ! [X0] : ((old(X0) & ~patient(X0)) | (quiet(X0) <=> calm(X0))) [ennf transformation 1]
37. ! [X0] : ((old(X0) & ~patient(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) [nnf transformation 28]
40. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 40]
42. (? [X0] : (~wise(X0) & ~brave(X0)) | (patient(susan) | happy(susan))) & ((~patient(susan) & ~happy(susan)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 4]
43. (? [X0] : (~wise(X0) & ~brave(X0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X0] : (wise(X0) | brave(X0))) [flattening 42]
44. (? [X0] : (~wise(X0) & ~brave(X0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X1] : (wise(X1) | brave(X1))) [rectify 43]
45. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK0) & ~brave(sK0)) [choice axiom]
46. ((~wise(sK0) & ~brave(sK0)) | patient(susan) | happy(susan)) & ((~patient(susan) & ~happy(susan)) | ! [X1] : (wise(X1) | brave(X1))) [skolemisation 44,45]
47. ! [X0] : (((creative(X0) | ~creative(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 5]
48. ! [X0] : ((creative(X0) | ~creative(X0) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | (~creative(X0) & creative(X0)))) [flattening 47]
54. ! [X0] : (((calm(X0) | ~generous(X0)) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 7]
55. ! [X0] : ((calm(X0) | ~generous(X0) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & generous(X0)))) [flattening 54]
60. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 11]
62. ! [X0] : (((~quiet(X0) | brave(X0)) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 13]
63. ! [X0] : ((~quiet(X0) | brave(X0) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | (quiet(X0) & ~brave(X0)))) [flattening 62]
64. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 14]
65. ! [X0] : (((curious(X0) & ~funny(X0)) | happy(X0)) & (~happy(X0) | ~curious(X0) | funny(X0))) [flattening 64]
76. ~patient(X0) | calm(X0) | ~quiet(X0) [cnf transformation 37]
87. ~curious(X0) | ~wise(X0) | quiet(X0) [cnf transformation 41]
88. humble(X0) | curious(X0) | wise(X0) [cnf transformation 41]
94. ~brave(sK0) | patient(susan) | happy(susan) [cnf transformation 46]
95. ~wise(sK0) | patient(susan) | happy(susan) [cnf transformation 46]
96. wise(X0) | quiet(X0) | creative(X0) [cnf transformation 48]
97. ~creative(X0) | quiet(X0) | wise(X0) [cnf transformation 48]
109. ~calm(X0) | ~calm(X0) [cnf transformation 55]
116. ~happy(X0) | ~humble(X0) [cnf transformation 60]
124. ~curious(X0) | brave(X0) | ~quiet(X0) [cnf transformation 63]
127. happy(X0) | curious(X0) [cnf transformation 65]
142. humble(susan) [cnf transformation 25]
144. ~calm(X0) [duplicate literal removal 109]
147. 1 <=> happy(susan) [avatar definition]
149. happy(susan) <- (1) [avatar component clause 147]
151. 2 <=> patient(susan) [avatar definition]
153. patient(susan) <- (2) [avatar component clause 151]
155. 3 <=> wise(sK0) [avatar definition]
158. 1 | 2 | ~3 [avatar split clause 95,155,151,147]
160. 4 <=> brave(sK0) [avatar definition]
162. ~brave(sK0) <- (~4) [avatar component clause 160]
163. 1 | 2 | ~4 [avatar split clause 94,160,151,147]
165. 5 <=> ! [X1] : (wise(X1) | brave(X1)) [avatar definition]
166. brave(X1) | wise(X1) <- (5) [avatar component clause 165]
169. wise(X0) | quiet(X0) [subsumption resolution 96,97]
265. ~humble(X0) | curious(X0) [resolution 127,116]
278. curious(susan) [resolution 265,142]
300. curious(X1) | wise(X1) | curious(X1) [resolution 88,265]
301. curious(X1) | wise(X1) [duplicate literal removal 300]
358. ~humble(susan) <- (1) [resolution 149,116]
360. $false <- (1) [subsumption resolution 358,142]
361. ~1 [avatar contradiction clause 360]
366. calm(susan) | ~quiet(susan) <- (2) [resolution 153,76]
367. ~quiet(susan) <- (2) [subsumption resolution 366,144]
394. wise(sK0) <- (~4, 5) [resolution 166,162]
464. ~wise(susan) | quiet(susan) [resolution 278,87]
465. ~wise(susan) <- (2) [subsumption resolution 464,367]
592. wise(X1) | brave(X1) | ~quiet(X1) [resolution 301,124]
606. quiet(susan) <- (2) [resolution 465,169]
607. $false <- (2) [subsumption resolution 606,367]
608. ~2 [avatar contradiction clause 607]
613. 3 | 4 | ~5 [avatar split clause 394,165,160,155]
614. wise(X1) | brave(X1) [subsumption resolution 592,169]
615. 5 [avatar split clause 614,165]
616. $false [avatar sat refutation 158,163,361,608,613,615]
% SZS output end Proof for 6207617928529430407623422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy then someone is not humble.
Everyone who is not creative is both not brave and wise.
Everyone who is not strong is generous.
Everyone who is brave is either tall or not creative and vice versa.
Everyone who is both not happy and not old is both tall and not strong.
If someone is both creative and not quiet then someone is not strong and vice versa.
If someone is not generous then lucy is brave.
If lucy is either not quiet or not generous then someone is either not curious or not wise.
If lucy is both not rich and funny then someone is not funny.
If paul is not generous or quiet then alice is not happy or generous and vice versa.
Everyone who is strong is either humble or old and vice versa.
Everyone who is not happy or not kind is creative or not happy and vice versa.
If someone is both brave and not curious then someone is both not calm and not patient.
Everyone who is wise is either brave or not strong.
Everyone who is not quiet or not calm is not curious.
Everyone who is either curious or not humble is funny and vice versa.
Someone is both brave and kind.
Paul is either not brave or rich.
Alice is not strong or not brave.
Susan is either quiet or not brave.
Alice is both creative and curious.
Susan is either not generous or not brave.
Lucy is either not curious or not humble.
Susan is old. | Lucy is curious. | neutral | ((?[X]:(~happy(X)))=>(?[X]:(~humble(X))))&
(![X]:(~creative(X)=>(~brave(X)&wise(X))))&
(![X]:(~strong(X)=>generous(X)))&
(![X]:(brave(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((~happy(X)&~old(X))=>(tall(X)&~strong(X))))&
((?[X]:((creative(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
((?[X]:(~generous(X)))=>(brave(lucy)))&
(((~quiet(lucy)<~>~generous(lucy)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(((~rich(lucy)&funny(lucy)))=>(?[X]:(~funny(X))))&
(((~generous(paul)|quiet(paul)))<=>((~happy(alice)|generous(alice))))&
(![X]:(strong(X)<=>(humble(X)<~>old(X))))&
(![X]:((~happy(X)|~kind(X))<=>(creative(X)|~happy(X))))&
((?[X]:((brave(X)&~curious(X))))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:(wise(X)=>(brave(X)<~>~strong(X))))&
(![X]:((~quiet(X)|~calm(X))=>~curious(X)))&
(![X]:((curious(X)<~>~humble(X))<=>funny(X)))&
(?[X]:((brave(X)&kind(X))))&
((~brave(paul)<~>rich(paul)))&
((~strong(alice)|~brave(alice)))&
((quiet(susan)<~>~brave(susan)))&
((creative(alice)&curious(alice)))&
((~generous(susan)<~>~brave(susan)))&
((~curious(lucy)<~>~humble(lucy)))&
(old(susan)) | curious(lucy) | [] | null | 0 |
Everyone who is creative is funny or not funny and vice versa.
If lucy is both not funny and curious then someone is tall or not strong and vice versa.
Everyone who is not happy is strong and vice versa.
Everyone who is either old or not tall is rich or patient.
Everyone who is generous or tall is not kind or not rich and vice versa.
Everyone who is not tall or kind is both kind and not quiet.
Everyone who is either not funny or not creative is both not creative and not rich.
If someone is wise then john is both wise and not kind.
If fred is generous or not old then someone is both rich and brave.
If someone is both not brave and not kind then someone is either not wise or not patient and vice versa.
Everyone who is not humble is either not creative or not patient.
If someone is both humble and not happy then someone is either not generous or not kind.
If someone is either not brave or old then lucy is funny or not rich and vice versa.
If fred is both not quiet and not wise then someone is either brave or not funny.
Everyone who is both not kind and strong is patient or not creative and vice versa.
Everyone who is either not humble or generous is both curious and not happy.
Someone is either not strong or not curious.
Fred is not wise or not kind.
Someone is not rich or happy.
Someone is not quiet or happy.
Alice is both generous and curious. | Fred is strong. | entailment | (![X]:(creative(X)<=>(funny(X)|~funny(X))))&
(((~funny(lucy)&curious(lucy)))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((old(X)<~>~tall(X))=>(rich(X)|patient(X))))&
(![X]:((generous(X)|tall(X))<=>(~kind(X)|~rich(X))))&
(![X]:((~tall(X)|kind(X))=>(kind(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~creative(X)&~rich(X))))&
((?[X]:(wise(X)))=>((wise(john)&~kind(john))))&
(((generous(fred)|~old(fred)))=>(?[X]:((rich(X)&brave(X)))))&
((?[X]:((~brave(X)&~kind(X))))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(~humble(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((humble(X)&~happy(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
((?[X]:((~brave(X)<~>old(X))))<=>((funny(lucy)|~rich(lucy))))&
(((~quiet(fred)&~wise(fred)))=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((~kind(X)&strong(X))<=>(patient(X)|~creative(X))))&
(![X]:((~humble(X)<~>generous(X))=>(curious(X)&~happy(X))))&
(?[X]:((~strong(X)<~>~curious(X))))&
((~wise(fred)|~kind(fred)))&
(?[X]:((~rich(X)|happy(X))))&
(?[X]:((~quiet(X)|happy(X))))&
((generous(alice)&curious(alice))) | strong(fred) | [
"p0",
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8843657163677089966312004
% SZS output start Proof for 8843657163677089966312004
1. ! [X0] : (creative(X0) <=> (~funny(X0) | funny(X0))) [input p0]
2. (curious(lucy) & ~funny(lucy)) <=> ? [X0] : (~strong(X0) | tall(X0)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~creative(X0)) => (~rich(X0) & ~creative(X0))) [input p6]
22. ~strong(fred) [input hypothesis]
28. ! [X0] : ((~rich(X0) & ~creative(X0)) | (~funny(X0) <=> ~creative(X0))) [ennf transformation 7]
36. ! [X0] : ((creative(X0) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | ~creative(X0))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | ~creative(X0))) [flattening 36]
38. ((curious(lucy) & ~funny(lucy)) | ! [X0] : (strong(X0) & ~tall(X0))) & (? [X0] : (~strong(X0) | tall(X0)) | (~curious(lucy) | funny(lucy))) [nnf transformation 2]
39. ((curious(lucy) & ~funny(lucy)) | ! [X0] : (strong(X0) & ~tall(X0))) & (? [X0] : (~strong(X0) | tall(X0)) | ~curious(lucy) | funny(lucy)) [flattening 38]
40. ((curious(lucy) & ~funny(lucy)) | ! [X0] : (strong(X0) & ~tall(X0))) & (? [X1] : (~strong(X1) | tall(X1)) | ~curious(lucy) | funny(lucy)) [rectify 39]
41. ? [X1] : (~strong(X1) | tall(X1)) => (~strong(sK0) | tall(sK0)) [choice axiom]
42. ((curious(lucy) & ~funny(lucy)) | ! [X0] : (strong(X0) & ~tall(X0))) & ((~strong(sK0) | tall(sK0)) | ~curious(lucy) | funny(lucy)) [skolemisation 40,41]
47. ! [X0] : ((~rich(X0) & ~creative(X0)) | ((~funny(X0) | creative(X0)) & (~creative(X0) | funny(X0)))) [nnf transformation 28]
79. creative(X0) | ~funny(X0) [cnf transformation 37]
80. creative(X0) | funny(X0) [cnf transformation 37]
83. ~funny(lucy) | strong(X0) [cnf transformation 42]
98. ~creative(X0) | ~creative(X0) | funny(X0) [cnf transformation 47]
142. ~strong(fred) [cnf transformation 22]
143. ~creative(X0) | funny(X0) [duplicate literal removal 98]
144. creative(X0) [subsumption resolution 79,80]
146. 1 <=> ! [X0] : strong(X0) [avatar definition]
147. strong(X0) <- (1) [avatar component clause 146]
158. 4 <=> funny(lucy) [avatar definition]
160. ~funny(lucy) <- (~4) [avatar component clause 158]
161. 1 | ~4 [avatar split clause 83,158,146]
173. funny(X0) [subsumption resolution 143,144]
318. $false <- (~4) [subsumption resolution 160,173]
319. 4 [avatar contradiction clause 318]
320. $false <- (1) [resolution 147,142]
321. ~1 [avatar contradiction clause 320]
322. $false [avatar sat refutation 161,319,321]
% SZS output end Proof for 8843657163677089966312004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not old is either not funny or creative.
Everyone who is either not old or not humble is both not patient and not rich and vice versa.
If lucy is rich or patient then someone is both not patient and not wise and vice versa.
If someone is not kind or calm then john is both creative and not patient.
If someone is not quiet then someone is either not patient or curious and vice versa.
If john is either not happy or not humble then someone is not humble or not calm.
If paul is either quiet or not funny then john is either not creative or strong and vice versa.
If someone is either not humble or generous then alice is either not rich or not humble.
If someone is either not brave or not curious then paul is either not creative or calm and vice versa.
If susan is either quiet or creative then susan is either not patient or not curious and vice versa.
Everyone who is not patient or not funny is either not wise or not happy.
If john is both not funny and humble then someone is not humble or not funny.
If someone is not funny or kind then someone is curious and vice versa.
If someone is either not funny or not rich then someone is not rich and vice versa.
If someone is funny or patient then someone is not old and vice versa.
If john is both not patient and not strong then susan is either creative or not creative.
Someone is not old or not wise.
Someone is brave.
Mary is wise.
Someone is either not patient or not happy.
Someone is both not brave and not humble.
Lucy is either kind or not quiet.
Someone is both quiet and not creative.
Someone is either happy or not old. | Lucy is not strong. | neutral | (![X]:((~curious(X)<~>~old(X))=>(~funny(X)<~>creative(X))))&
(![X]:((~old(X)<~>~humble(X))<=>(~patient(X)&~rich(X))))&
(((rich(lucy)|patient(lucy)))<=>(?[X]:((~patient(X)&~wise(X)))))&
((?[X]:((~kind(X)|calm(X))))=>((creative(john)&~patient(john))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(((~happy(john)<~>~humble(john)))=>(?[X]:((~humble(X)|~calm(X)))))&
(((quiet(paul)<~>~funny(paul)))<=>((~creative(john)<~>strong(john))))&
((?[X]:((~humble(X)<~>generous(X))))=>((~rich(alice)<~>~humble(alice))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((~creative(paul)<~>calm(paul))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>~curious(susan))))&
(![X]:((~patient(X)|~funny(X))=>(~wise(X)<~>~happy(X))))&
(((~funny(john)&humble(john)))=>(?[X]:((~humble(X)|~funny(X)))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((funny(X)|patient(X))))<=>(?[X]:(~old(X))))&
(((~patient(john)&~strong(john)))=>((creative(susan)<~>~creative(susan))))&
(?[X]:((~old(X)|~wise(X))))&
(?[X]:(brave(X)))&
(wise(mary))&
(?[X]:((~patient(X)<~>~happy(X))))&
(?[X]:((~brave(X)&~humble(X))))&
((kind(lucy)<~>~quiet(lucy)))&
(?[X]:((quiet(X)&~creative(X))))&
(?[X]:((happy(X)<~>~old(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either not calm or not quiet is both not happy and not calm and vice versa.
If someone is both strong and humble then someone is both not strong and brave and vice versa.
If lucy is either not funny or happy then mary is not funny and vice versa.
Everyone who is funny or tall is both quiet and not rich and vice versa.
Everyone who is not patient or not generous is both not quiet and not rich.
Everyone who is both not strong and not creative is not humble or curious and vice versa.
If someone is strong or not tall then alice is both not humble and generous and vice versa.
Everyone who is happy is either not creative or quiet.
Everyone who is both wise and funny is not funny.
Everyone who is both not rich and generous is both brave and patient and vice versa.
If someone is quiet or rich then someone is calm.
Everyone who is not humble is either not calm or happy and vice versa.
If john is both strong and brave then paul is both not humble and not strong and vice versa.
If someone is either calm or not wise then alice is not curious or funny.
Everyone who is not kind is wise or generous and vice versa.
If fred is either not curious or not rich then someone is generous or not wise.
Someone is not generous or quiet.
Someone is both not creative and not brave.
Someone is calm.
Susan is both not patient and not rich.
Someone is not strong or happy.
Someone is either not old or brave.
Susan is not tall. | Susan is not funny. | entailment | (![X]:((~calm(X)<~>~quiet(X))<=>(~happy(X)&~calm(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~strong(X)&brave(X)))))&
(((~funny(lucy)<~>happy(lucy)))<=>(~funny(mary)))&
(![X]:((funny(X)|tall(X))<=>(quiet(X)&~rich(X))))&
(![X]:((~patient(X)|~generous(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~strong(X)&~creative(X))<=>(~humble(X)|curious(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~humble(alice)&generous(alice))))&
(![X]:(happy(X)=>(~creative(X)<~>quiet(X))))&
(![X]:((wise(X)&funny(X))=>~funny(X)))&
(![X]:((~rich(X)&generous(X))<=>(brave(X)&patient(X))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(((strong(john)&brave(john)))<=>((~humble(paul)&~strong(paul))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~curious(alice)|funny(alice))))&
(![X]:(~kind(X)<=>(wise(X)|generous(X))))&
(((~curious(fred)<~>~rich(fred)))=>(?[X]:((generous(X)|~wise(X)))))&
(?[X]:((~generous(X)|quiet(X))))&
(?[X]:((~creative(X)&~brave(X))))&
(?[X]:(calm(X)))&
((~patient(susan)&~rich(susan)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(~tall(susan)) | ~funny(susan) | [
"p3",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 523551078847840233422317
% SZS output start Proof for 523551078847840233422317
4. ! [X0] : ((tall(X0) | funny(X0)) <=> (~rich(X0) & quiet(X0))) [input p3]
5. ! [X0] : ((~generous(X0) | ~patient(X0)) => (~rich(X0) & ~quiet(X0))) [input p4]
20. ~rich(susan) & ~patient(susan) [input p19]
24. funny(susan) [input hypothesis]
27. ! [X0] : ((~rich(X0) & ~quiet(X0)) | (generous(X0) & patient(X0))) [ennf transformation 5]
43. ! [X0] : (((tall(X0) | funny(X0)) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | (~tall(X0) & ~funny(X0)))) [nnf transformation 4]
44. ! [X0] : ((tall(X0) | funny(X0) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | (~tall(X0) & ~funny(X0)))) [flattening 43]
90. ~funny(X0) | quiet(X0) [cnf transformation 44]
95. ~quiet(X0) | patient(X0) [cnf transformation 27]
134. ~patient(susan) [cnf transformation 20]
140. funny(susan) [cnf transformation 24]
316. quiet(susan) [resolution 90,140]
317. patient(susan) [resolution 95,316]
318. $false [subsumption resolution 317,134]
% SZS output end Proof for 523551078847840233422317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and humble is both tall and humble. Everyone who is not funny or patient is not funny or quiet and vice versa. Everyone who is both not creative and not strong is brave or creative and vice versa. If mary is not rich or wise then someone is both not creative and tall and vice versa. If someone is either tall or not curious then someone is either not funny or funny. Everyone who is old or not calm is both curious and not calm. If someone is not humble or humble then someone is both not quiet and tall. If mary is both not generous and not tall then someone is both not humble and not quiet. Everyone who is both not curious and not calm is both not calm and not creative and vice versa. Everyone who is either wise or not old is both not happy and not curious and vice versa. If fred is brave or not calm then someone is both not curious and curious and vice versa. If lucy is either not curious or funny then someone is not brave and vice versa. If john is not kind or not happy then alice is both kind and not generous and vice versa. If someone is both not patient and not generous then someone is not humble. Everyone who is not creative or wise is not calm or not quiet and vice versa. If someone is not quiet then someone is not quiet or not wise. John is not old or not strong. Someone is both not tall and not generous. Someone is either calm or rich. Alice is not happy. Fred is humble or not humble. Mary is both not kind and funny. | Mary is not calm. | contradiction | (![X]:((~wise(X)&humble(X))=>(tall(X)&humble(X))))&
(![X]:((~funny(X)|patient(X))<=>(~funny(X)|quiet(X))))&
(![X]:((~creative(X)&~strong(X))<=>(brave(X)|creative(X))))&
(((~rich(mary)|wise(mary)))<=>(?[X]:((~creative(X)&tall(X)))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((~funny(X)<~>funny(X)))))&
(![X]:((old(X)|~calm(X))=>(curious(X)&~calm(X))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:((~quiet(X)&tall(X)))))&
(((~generous(mary)&~tall(mary)))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:((~curious(X)&~calm(X))<=>(~calm(X)&~creative(X))))&
(![X]:((wise(X)<~>~old(X))<=>(~happy(X)&~curious(X))))&
(((brave(fred)|~calm(fred)))<=>(?[X]:((~curious(X)&curious(X)))))&
(((~curious(lucy)<~>funny(lucy)))<=>(?[X]:(~brave(X))))&
(((~kind(john)|~happy(john)))<=>((kind(alice)&~generous(alice))))&
((?[X]:((~patient(X)&~generous(X))))=>(?[X]:(~humble(X))))&
(![X]:((~creative(X)|wise(X))<=>(~calm(X)|~quiet(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~quiet(X)|~wise(X)))))&
((~old(john)|~strong(john)))&
(?[X]:((~tall(X)&~generous(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(~happy(alice))&
((humble(fred)|~humble(fred)))&
((~kind(mary)&funny(mary))) | ~calm(mary) | [
"p2",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 393404449440550413382782
% SZS output start Proof for 393404449440550413382782
3. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (creative(X0) | brave(X0))) [input p2]
6. ! [X0] : ((~calm(X0) | old(X0)) => (~calm(X0) & curious(X0))) [input p5]
9. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (~creative(X0) & ~calm(X0))) [input p8]
23. ~calm(mary) [input hypothesis]
31. ! [X0] : ((~calm(X0) & curious(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 6]
39. ! [X0] : (((~strong(X0) & ~creative(X0)) | (~creative(X0) & ~brave(X0))) & ((creative(X0) | brave(X0)) | (strong(X0) | creative(X0)))) [nnf transformation 3]
40. ! [X0] : (((~strong(X0) & ~creative(X0)) | (~creative(X0) & ~brave(X0))) & (creative(X0) | brave(X0) | strong(X0) | creative(X0))) [flattening 39]
55. ! [X0] : (((~calm(X0) & ~curious(X0)) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | (calm(X0) | curious(X0)))) [nnf transformation 9]
56. ! [X0] : (((~calm(X0) & ~curious(X0)) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | calm(X0) | curious(X0))) [flattening 55]
91. ~creative(X0) | ~creative(X0) [cnf transformation 40]
104. curious(X0) | calm(X0) [cnf transformation 31]
115. ~curious(X0) | creative(X0) | calm(X0) [cnf transformation 56]
152. ~calm(mary) [cnf transformation 23]
154. ~creative(X0) [duplicate literal removal 91]
211. ~curious(X0) | calm(X0) [subsumption resolution 115,154]
212. calm(X0) [subsumption resolution 211,104]
286. $false [subsumption resolution 152,212]
% SZS output end Proof for 393404449440550413382782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not curious or not patient then someone is both old and funny and vice versa.
If someone is both brave and not strong then paul is strong.
Everyone who is either not generous or kind is creative or not wise.
If someone is happy then someone is either wise or not generous.
Everyone who is either calm or rich is not generous or not happy and vice versa.
Everyone who is both rich and strong is tall or not creative.
If someone is creative or wise then susan is funny and vice versa.
Everyone who is both strong and happy is not creative or wise and vice versa.
Everyone who is either brave or tall is both not funny and not rich and vice versa.
Everyone who is old or not tall is both not calm and strong and vice versa.
If someone is either brave or not brave then paul is not humble and vice versa.
Everyone who is not wise or not generous is humble or funny and vice versa.
Everyone who is both not quiet and not calm is not funny or curious.
Everyone who is both not old and not kind is both not quiet and kind.
If lucy is both curious and not funny then paul is either strong or old and vice versa.
If someone is old or not creative then someone is both strong and not curious and vice versa.
Lucy is both not old and patient.
Paul is both not kind and not brave.
Someone is both not funny and not happy.
Mary is wise or curious.
Fred is both not wise and curious.
Mary is not quiet.
Someone is not creative. | Mary is rich. | neutral | (((~curious(alice)|~patient(alice)))<=>(?[X]:((old(X)&funny(X)))))&
((?[X]:((brave(X)&~strong(X))))=>(strong(paul)))&
(![X]:((~generous(X)<~>kind(X))=>(creative(X)|~wise(X))))&
((?[X]:(happy(X)))=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>rich(X))<=>(~generous(X)|~happy(X))))&
(![X]:((rich(X)&strong(X))=>(tall(X)|~creative(X))))&
((?[X]:((creative(X)|wise(X))))<=>(funny(susan)))&
(![X]:((strong(X)&happy(X))<=>(~creative(X)|wise(X))))&
(![X]:((brave(X)<~>tall(X))<=>(~funny(X)&~rich(X))))&
(![X]:((old(X)|~tall(X))<=>(~calm(X)&strong(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:((~wise(X)|~generous(X))<=>(humble(X)|funny(X))))&
(![X]:((~quiet(X)&~calm(X))=>(~funny(X)|curious(X))))&
(![X]:((~old(X)&~kind(X))=>(~quiet(X)&kind(X))))&
(((curious(lucy)&~funny(lucy)))<=>((strong(paul)<~>old(paul))))&
((?[X]:((old(X)|~creative(X))))<=>(?[X]:((strong(X)&~curious(X)))))&
((~old(lucy)&patient(lucy)))&
((~kind(paul)&~brave(paul)))&
(?[X]:((~funny(X)&~happy(X))))&
((wise(mary)|curious(mary)))&
((~wise(fred)&curious(fred)))&
(~quiet(mary))&
(?[X]:(~creative(X))) | rich(mary) | [] | null | 0 |
If john is either calm or generous then lucy is not brave and vice versa.
If susan is both old and quiet then alice is either curious or creative and vice versa.
Everyone who is both not generous and happy is both not tall and brave.
If someone is not generous then someone is both tall and not strong and vice versa.
Everyone who is happy is not tall and vice versa.
If someone is both rich and tall then john is either not happy or quiet.
Everyone who is both curious and generous is either not wise or curious and vice versa.
If someone is both not old and not patient then someone is brave or not patient.
Everyone who is both humble and brave is either happy or creative.
Everyone who is both not funny and not happy is not calm and vice versa.
Everyone who is both funny and not curious is both not generous and funny and vice versa.
Everyone who is both not brave and humble is old or not generous and vice versa.
If lucy is kind then someone is rich.
Everyone who is creative is not patient or not generous and vice versa.
Everyone who is not generous is both strong and not brave and vice versa.
Everyone who is both not calm and not brave is calm or tall and vice versa.
Fred is not curious or strong.
Someone is both not quiet and not kind.
Someone is rich or kind.
Fred is either not happy or not patient.
Someone is not patient or not brave.
Mary is either not patient or creative.
Fred is either wise or strong. | Susan is not tall. | contradiction | (((calm(john)<~>generous(john)))<=>(~brave(lucy)))&
(((old(susan)&quiet(susan)))<=>((curious(alice)<~>creative(alice))))&
(![X]:((~generous(X)&happy(X))=>(~tall(X)&brave(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:(happy(X)<=>~tall(X)))&
((?[X]:((rich(X)&tall(X))))=>((~happy(john)<~>quiet(john))))&
(![X]:((curious(X)&generous(X))<=>(~wise(X)<~>curious(X))))&
((?[X]:((~old(X)&~patient(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:((humble(X)&brave(X))=>(happy(X)<~>creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>~calm(X)))&
(![X]:((funny(X)&~curious(X))<=>(~generous(X)&funny(X))))&
(![X]:((~brave(X)&humble(X))<=>(old(X)|~generous(X))))&
((kind(lucy))=>(?[X]:(rich(X))))&
(![X]:(creative(X)<=>(~patient(X)|~generous(X))))&
(![X]:(~generous(X)<=>(strong(X)&~brave(X))))&
(![X]:((~calm(X)&~brave(X))<=>(calm(X)|tall(X))))&
((~curious(fred)|strong(fred)))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((rich(X)|kind(X))))&
((~happy(fred)<~>~patient(fred)))&
(?[X]:((~patient(X)|~brave(X))))&
((~patient(mary)<~>creative(mary)))&
((wise(fred)<~>strong(fred))) | ~tall(susan) | [
"p4",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 764148100587562121583882
% SZS output start Proof for 764148100587562121583882
5. ! [X0] : (happy(X0) <=> ~tall(X0)) [input p4]
10. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> ~calm(X0)) [input p9]
16. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> (tall(X0) | calm(X0))) [input p15]
24. ~tall(susan) [input hypothesis]
42. ! [X0] : ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))) [nnf transformation 5]
50. ! [X0] : (((~happy(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | (happy(X0) | funny(X0)))) [nnf transformation 10]
51. ! [X0] : (((~happy(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | happy(X0) | funny(X0))) [flattening 50]
62. ! [X0] : (((~brave(X0) & ~calm(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (brave(X0) | calm(X0)))) [nnf transformation 16]
63. ! [X0] : (((~brave(X0) & ~calm(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | brave(X0) | calm(X0))) [flattening 62]
89. tall(X0) | happy(X0) [cnf transformation 42]
103. ~happy(X0) | calm(X0) [cnf transformation 51]
121. ~calm(X0) | ~calm(X0) [cnf transformation 63]
136. ~tall(susan) [cnf transformation 24]
138. ~calm(X0) [duplicate literal removal 121]
287. happy(susan) [resolution 89,136]
290. calm(susan) [resolution 103,287]
293. $false [subsumption resolution 290,138]
% SZS output end Proof for 764148100587562121583882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or kind then someone is strong and vice versa.
Everyone who is not kind is not rich.
Everyone who is tall or not calm is both not happy and kind.
Everyone who is not old is either not rich or not humble.
If susan is either tall or not old then susan is either generous or strong and vice versa.
If fred is quiet then someone is either not strong or patient and vice versa.
If someone is either quiet or not funny then susan is both not rich and rich and vice versa.
Everyone who is quiet is rich or strong.
Everyone who is not kind or not happy is not calm.
Everyone who is both not tall and patient is both creative and tall and vice versa.
If someone is quiet then susan is funny.
If john is both strong and not brave then someone is both tall and not calm and vice versa.
If john is both humble and not generous then someone is not curious or funny and vice versa.
If someone is not calm or brave then john is old.
If mary is both patient and not quiet then mary is not brave or not patient and vice versa.
If paul is either calm or not strong then someone is not quiet and vice versa.
Fred is not rich or not curious.
Alice is happy.
Someone is calm or not patient.
Mary is wise.
John is both tall and old.
Mary is either happy or not quiet.
Someone is either calm or quiet.
Someone is rich or funny. | John is not strong. | contradiction | ((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(strong(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((tall(X)|~calm(X))=>(~happy(X)&kind(X))))&
(![X]:(~old(X)=>(~rich(X)<~>~humble(X))))&
(((tall(susan)<~>~old(susan)))<=>((generous(susan)<~>strong(susan))))&
((quiet(fred))<=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:((quiet(X)<~>~funny(X))))<=>((~rich(susan)&rich(susan))))&
(![X]:(quiet(X)=>(rich(X)|strong(X))))&
(![X]:((~kind(X)|~happy(X))=>~calm(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)&tall(X))))&
((?[X]:(quiet(X)))=>(funny(susan)))&
(((strong(john)&~brave(john)))<=>(?[X]:((tall(X)&~calm(X)))))&
(((humble(john)&~generous(john)))<=>(?[X]:((~curious(X)|funny(X)))))&
((?[X]:((~calm(X)|brave(X))))=>(old(john)))&
(((patient(mary)&~quiet(mary)))<=>((~brave(mary)|~patient(mary))))&
(((calm(paul)<~>~strong(paul)))<=>(?[X]:(~quiet(X))))&
((~rich(fred)|~curious(fred)))&
(happy(alice))&
(?[X]:((calm(X)|~patient(X))))&
(wise(mary))&
((tall(john)&old(john)))&
((happy(mary)<~>~quiet(mary)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((rich(X)|funny(X)))) | ~strong(john) | [
"p2",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2990271471905876785792872
% SZS output start Proof for 2990271471905876785792872
3. ! [X0] : ((~calm(X0) | tall(X0)) => (kind(X0) & ~happy(X0))) [input p2]
9. ! [X0] : ((~happy(X0) | ~kind(X0)) => ~calm(X0)) [input p8]
10. ! [X0] : ((patient(X0) & ~tall(X0)) <=> (tall(X0) & creative(X0))) [input p9]
12. (~brave(john) & strong(john)) <=> ? [X0] : (~calm(X0) & tall(X0)) [input p11]
15. (~quiet(mary) & patient(mary)) <=> (~patient(mary) | ~brave(mary)) [input p14]
25. ~strong(john) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~happy(X0)) | (calm(X0) & ~tall(X0))) [ennf transformation 3]
33. ! [X0] : (~calm(X0) | (happy(X0) & kind(X0))) [ennf transformation 9]
52. ! [X0] : (((patient(X0) & ~tall(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (~patient(X0) | tall(X0)))) [nnf transformation 10]
53. ! [X0] : (((patient(X0) & ~tall(X0)) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | ~patient(X0) | tall(X0))) [flattening 52]
54. ((~brave(john) & strong(john)) | ! [X0] : (calm(X0) | ~tall(X0))) & (? [X0] : (~calm(X0) & tall(X0)) | (brave(john) | ~strong(john))) [nnf transformation 12]
55. ((~brave(john) & strong(john)) | ! [X0] : (calm(X0) | ~tall(X0))) & (? [X0] : (~calm(X0) & tall(X0)) | brave(john) | ~strong(john)) [flattening 54]
56. ((~brave(john) & strong(john)) | ! [X0] : (calm(X0) | ~tall(X0))) & (? [X1] : (~calm(X1) & tall(X1)) | brave(john) | ~strong(john)) [rectify 55]
57. ? [X1] : (~calm(X1) & tall(X1)) => (~calm(sK4) & tall(sK4)) [choice axiom]
58. ((~brave(john) & strong(john)) | ! [X0] : (calm(X0) | ~tall(X0))) & ((~calm(sK4) & tall(sK4)) | brave(john) | ~strong(john)) [skolemisation 56,57]
64. ((~quiet(mary) & patient(mary)) | (patient(mary) & brave(mary))) & ((~patient(mary) | ~brave(mary)) | (quiet(mary) | ~patient(mary))) [nnf transformation 15]
65. ((~quiet(mary) & patient(mary)) | (patient(mary) & brave(mary))) & (~patient(mary) | ~brave(mary) | quiet(mary) | ~patient(mary)) [flattening 64]
83. ~happy(X0) | ~tall(X0) [cnf transformation 29]
109. ~calm(X0) | happy(X0) [cnf transformation 33]
111. tall(X0) | ~patient(X0) | tall(X0) [cnf transformation 53]
117. strong(john) | calm(X0) | ~tall(X0) [cnf transformation 58]
128. patient(mary) | patient(mary) [cnf transformation 65]
145. ~strong(john) [cnf transformation 25]
147. patient(mary) [duplicate literal removal 128]
148. ~patient(X0) | tall(X0) [duplicate literal removal 111]
245. 21 <=> ! [X0] : (calm(X0) | ~tall(X0)) [avatar definition]
246. ~tall(X0) | calm(X0) <- (21) [avatar component clause 245]
253. 23 <=> strong(john) [avatar definition]
256. 21 | 23 [avatar split clause 117,253,245]
307. 35 <=> patient(mary) [avatar definition]
309. patient(mary) <- (35) [avatar component clause 307]
320. 35 [avatar split clause 147,307]
362. 46 <=> happy(mary) [avatar definition]
363. happy(mary) <- (46) [avatar component clause 362]
386. ~23 [avatar split clause 145,253]
411. tall(mary) <- (35) [resolution 148,309]
419. calm(mary) <- (21, 35) [resolution 246,411]
425. happy(mary) <- (21, 35) [resolution 419,109]
428. 46 | ~21 | ~35 [avatar split clause 425,307,245,362]
430. ~tall(mary) <- (46) [resolution 363,83]
431. $false <- (35, 46) [subsumption resolution 430,411]
432. ~35 | ~46 [avatar contradiction clause 431]
433. $false [avatar sat refutation 256,320,386,428,432]
% SZS output end Proof for 2990271471905876785792872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not humble or not calm then lucy is either creative or patient and vice versa.
Everyone who is both not kind and not brave is either not calm or generous and vice versa.
If alice is either happy or not strong then mary is rich and vice versa.
If mary is either not generous or not tall then someone is both kind and not calm and vice versa.
If someone is both curious and happy then fred is not strong.
Everyone who is both old and not rich is rich.
Everyone who is not humble or not generous is either quiet or not patient.
If someone is either not tall or happy then susan is not calm or not strong.
Everyone who is either not quiet or not wise is either tall or not curious and vice versa.
If john is not patient then someone is not calm and vice versa.
Everyone who is not tall or wise is either not wise or old.
If someone is tall then lucy is both not curious and not tall.
Everyone who is either not tall or not calm is both calm and not calm and vice versa.
Everyone who is not calm is rich and vice versa.
If mary is either generous or not calm then john is both not creative and patient and vice versa.
Everyone who is both happy and not strong is calm and vice versa.
Someone is both not generous and patient.
Susan is old.
Someone is both patient and creative.
Mary is either rich or quiet.
Someone is both kind and not rich.
Someone is not tall.
Alice is not generous. | Lucy is not happy. | neutral | (((~humble(paul)<~>~calm(paul)))<=>((creative(lucy)<~>patient(lucy))))&
(![X]:((~kind(X)&~brave(X))<=>(~calm(X)<~>generous(X))))&
(((happy(alice)<~>~strong(alice)))<=>(rich(mary)))&
(((~generous(mary)<~>~tall(mary)))<=>(?[X]:((kind(X)&~calm(X)))))&
((?[X]:((curious(X)&happy(X))))=>(~strong(fred)))&
(![X]:((old(X)&~rich(X))=>rich(X)))&
(![X]:((~humble(X)|~generous(X))=>(quiet(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>happy(X))))=>((~calm(susan)|~strong(susan))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(tall(X)<~>~curious(X))))&
((~patient(john))<=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)|wise(X))=>(~wise(X)<~>old(X))))&
((?[X]:(tall(X)))=>((~curious(lucy)&~tall(lucy))))&
(![X]:((~tall(X)<~>~calm(X))<=>(calm(X)&~calm(X))))&
(![X]:(~calm(X)<=>rich(X)))&
(((generous(mary)<~>~calm(mary)))<=>((~creative(john)&patient(john))))&
(![X]:((happy(X)&~strong(X))<=>calm(X)))&
(?[X]:((~generous(X)&patient(X))))&
(old(susan))&
(?[X]:((patient(X)&creative(X))))&
((rich(mary)<~>quiet(mary)))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:(~tall(X)))&
(~generous(alice)) | ~happy(lucy) | [] | null | 0 |
Everyone who is not kind or not quiet is both happy and wise.
If paul is either calm or humble then fred is not funny or strong and vice versa.
Everyone who is happy or not creative is not tall or not old and vice versa.
If lucy is either quiet or not brave then someone is either strong or not creative and vice versa.
Everyone who is either creative or kind is either humble or not rich.
Everyone who is either wise or humble is either not quiet or humble.
Everyone who is patient or not wise is strong or brave.
If someone is quiet then fred is either kind or tall and vice versa.
If someone is happy then mary is happy or generous and vice versa.
Everyone who is either not funny or not humble is both not tall and tall.
If someone is creative then susan is rich or not generous and vice versa.
Everyone who is happy is not kind or kind and vice versa.
If someone is not happy then someone is patient or funny and vice versa.
If fred is both not old and not rich then paul is both not strong and old and vice versa.
Everyone who is patient is both creative and not creative and vice versa.
Susan is not funny.
Someone is either kind or humble.
Someone is both happy and kind.
Someone is creative or funny.
Someone is not patient or not kind.
Someone is either tall or not patient.
Lucy is not humble. | Fred is patient. | contradiction | (![X]:((~kind(X)|~quiet(X))=>(happy(X)&wise(X))))&
(((calm(paul)<~>humble(paul)))<=>((~funny(fred)|strong(fred))))&
(![X]:((happy(X)|~creative(X))<=>(~tall(X)|~old(X))))&
(((quiet(lucy)<~>~brave(lucy)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((creative(X)<~>kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:((wise(X)<~>humble(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((patient(X)|~wise(X))=>(strong(X)|brave(X))))&
((?[X]:(quiet(X)))<=>((kind(fred)<~>tall(fred))))&
((?[X]:(happy(X)))<=>((happy(mary)|generous(mary))))&
(![X]:((~funny(X)<~>~humble(X))=>(~tall(X)&tall(X))))&
((?[X]:(creative(X)))<=>((rich(susan)|~generous(susan))))&
(![X]:(happy(X)<=>(~kind(X)|kind(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|funny(X)))))&
(((~old(fred)&~rich(fred)))<=>((~strong(paul)&old(paul))))&
(![X]:(patient(X)<=>(creative(X)&~creative(X))))&
(~funny(susan))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:((happy(X)&kind(X))))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(~humble(lucy)) | patient(fred) | [
"p0",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 758068938509822576856224
% SZS output start Proof for 758068938509822576856224
1. ! [X0] : ((~quiet(X0) | ~kind(X0)) => (wise(X0) & happy(X0))) [input p0]
12. ! [X0] : (happy(X0) <=> (kind(X0) | ~kind(X0))) [input p11]
13. ? [X0] : ~happy(X0) <=> ? [X0] : (funny(X0) | patient(X0)) [input p12]
23. patient(fred) [input hypothesis]
24. ? [X0] : ~happy(X0) <=> ? [X1] : (funny(X1) | patient(X1)) [rectify 13]
25. ! [X0] : ((wise(X0) & happy(X0)) | (quiet(X0) & kind(X0))) [ennf transformation 1]
56. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ~happy(X0))) [nnf transformation 12]
57. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ~happy(X0))) [flattening 56]
58. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X1] : (funny(X1) | patient(X1)) | ! [X0] : happy(X0)) [nnf transformation 24]
59. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X2] : (funny(X2) | patient(X2)) | ! [X3] : happy(X3)) [rectify 58]
60. ? [X0] : ~happy(X0) => ~happy(sK4) [choice axiom]
61. ? [X2] : (funny(X2) | patient(X2)) => (funny(sK5) | patient(sK5)) [choice axiom]
62. (~happy(sK4) | ! [X1] : (~funny(X1) & ~patient(X1))) & ((funny(sK5) | patient(sK5)) | ! [X3] : happy(X3)) [skolemisation 59,61,60]
79. happy(X0) | kind(X0) [cnf transformation 25]
127. happy(X0) | ~kind(X0) [cnf transformation 57]
129. ~happy(sK4) | ~patient(X1) [cnf transformation 62]
148. patient(fred) [cnf transformation 23]
260. happy(X0) [subsumption resolution 127,79]
262. ~patient(X1) [subsumption resolution 129,260]
295. $false [subsumption resolution 148,262]
% SZS output end Proof for 758068938509822576856224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or patient is brave and vice versa. If someone is both old and brave then someone is either creative or not strong and vice versa. Everyone who is both creative and not wise is not humble or funny and vice versa. Everyone who is funny is both rich and not creative and vice versa. If paul is either not calm or kind then mary is both not funny and calm and vice versa. Everyone who is either not patient or not rich is not tall. If susan is both calm and not creative then mary is either not patient or not funny. If mary is humble then fred is either not wise or not curious. Everyone who is quiet or not rich is both not old and wise and vice versa. If someone is not happy then someone is humble or old. Everyone who is not happy or funny is kind and vice versa. Everyone who is either not creative or not brave is not calm or not funny and vice versa. Everyone who is not curious or not kind is either not rich or not generous. If alice is either not creative or happy then john is either not wise or creative and vice versa. Everyone who is not creative or generous is not humble and vice versa. If someone is both funny and not calm then someone is patient or brave and vice versa. Lucy is either not strong or calm. Someone is strong or happy. Lucy is not creative or not brave. Susan is quiet. Lucy is not old or not curious. Someone is either kind or not brave. | Alice is wise. | neutral | (![X]:((~curious(X)|patient(X))<=>brave(X)))&
((?[X]:((old(X)&brave(X))))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((creative(X)&~wise(X))<=>(~humble(X)|funny(X))))&
(![X]:(funny(X)<=>(rich(X)&~creative(X))))&
(((~calm(paul)<~>kind(paul)))<=>((~funny(mary)&calm(mary))))&
(![X]:((~patient(X)<~>~rich(X))=>~tall(X)))&
(((calm(susan)&~creative(susan)))=>((~patient(mary)<~>~funny(mary))))&
((humble(mary))=>((~wise(fred)<~>~curious(fred))))&
(![X]:((quiet(X)|~rich(X))<=>(~old(X)&wise(X))))&
((?[X]:(~happy(X)))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~happy(X)|funny(X))<=>kind(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~calm(X)|~funny(X))))&
(![X]:((~curious(X)|~kind(X))=>(~rich(X)<~>~generous(X))))&
(((~creative(alice)<~>happy(alice)))<=>((~wise(john)<~>creative(john))))&
(![X]:((~creative(X)|generous(X))<=>~humble(X)))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((patient(X)|brave(X)))))&
((~strong(lucy)<~>calm(lucy)))&
(?[X]:((strong(X)|happy(X))))&
((~creative(lucy)|~brave(lucy)))&
(quiet(susan))&
((~old(lucy)|~curious(lucy)))&
(?[X]:((kind(X)<~>~brave(X)))) | wise(alice) | [] | null | 0 |
Everyone who is calm or not humble is generous. Everyone who is either not curious or funny is happy or curious. If someone is not calm or not strong then someone is both not creative and not old and vice versa. Everyone who is not creative or humble is either tall or not old and vice versa. Everyone who is both not strong and creative is not quiet or not patient and vice versa. If paul is both old and not quiet then someone is both not happy and old and vice versa. If alice is patient then someone is quiet and vice versa. Everyone who is both kind and wise is both not humble and happy and vice versa. If alice is either not funny or quiet then someone is both not tall and curious. If someone is both generous and humble then someone is both rich and kind and vice versa. Everyone who is either brave or not rich is either quiet or not kind and vice versa. Everyone who is either tall or old is either kind or not patient and vice versa. Everyone who is both tall and not creative is both not strong and not happy and vice versa. If someone is either not creative or not brave then fred is tall or not strong. If fred is creative or not brave then someone is wise and vice versa. If someone is kind or not funny then someone is either not wise or not tall. Someone is both calm and old. Someone is not old. John is either not generous or humble. Someone is quiet. Fred is not old. Fred is rich. Someone is not humble. Someone is humble or not brave. | John is patient. | neutral | (![X]:((calm(X)|~humble(X))=>generous(X)))&
(![X]:((~curious(X)<~>funny(X))=>(happy(X)|curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((~creative(X)|humble(X))<=>(tall(X)<~>~old(X))))&
(![X]:((~strong(X)&creative(X))<=>(~quiet(X)|~patient(X))))&
(((old(paul)&~quiet(paul)))<=>(?[X]:((~happy(X)&old(X)))))&
((patient(alice))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&wise(X))<=>(~humble(X)&happy(X))))&
(((~funny(alice)<~>quiet(alice)))=>(?[X]:((~tall(X)&curious(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:((tall(X)<~>old(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((tall(X)&~creative(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((~creative(X)<~>~brave(X))))=>((tall(fred)|~strong(fred))))&
(((creative(fred)|~brave(fred)))<=>(?[X]:(wise(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((~wise(X)<~>~tall(X)))))&
(?[X]:((calm(X)&old(X))))&
(?[X]:(~old(X)))&
((~generous(john)<~>humble(john)))&
(?[X]:(quiet(X)))&
(~old(fred))&
(rich(fred))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|~brave(X)))) | patient(john) | [] | null | 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa. If susan is both not curious and not rich then someone is creative or not calm. Everyone who is both happy and not rich is funny or not creative and vice versa. Everyone who is either not tall or not curious is both humble and not funny and vice versa. Everyone who is either not funny or tall is not wise. If someone is both rich and old then someone is brave or humble. If lucy is tall or brave then someone is both patient and not patient. If mary is old then john is either not old or funny and vice versa. Everyone who is both funny and old is both not curious and not calm and vice versa. If someone is rich or funny then john is creative or not calm. Everyone who is humble is both not funny and not old. Everyone who is not old is not happy and vice versa. Everyone who is quiet is both not humble and wise and vice versa. Everyone who is either old or not wise is both not curious and not generous and vice versa. Everyone who is either not kind or tall is not wise and vice versa. If paul is both not wise and not happy then someone is kind or tall and vice versa. Someone is either humble or happy. Paul is both generous and not humble. Someone is tall or patient. Someone is not generous or generous. Someone is either not strong or not happy. Someone is happy or rich. Someone is not funny. | Susan is humble. | contradiction | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((~curious(susan)&~rich(susan)))=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((happy(X)&~rich(X))<=>(funny(X)|~creative(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>(humble(X)&~funny(X))))&
(![X]:((~funny(X)<~>tall(X))=>~wise(X)))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((brave(X)|humble(X)))))&
(((tall(lucy)|brave(lucy)))=>(?[X]:((patient(X)&~patient(X)))))&
((old(mary))<=>((~old(john)<~>funny(john))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(((~wise(paul)&~happy(paul)))<=>(?[X]:((kind(X)|tall(X)))))&
(?[X]:((humble(X)<~>happy(X))))&
((generous(paul)&~humble(paul)))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(~funny(X))) | humble(susan) | [
"p0",
"p3",
"p4",
"p10",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 759885661171357572023842
% SZS output start Proof for 759885661171357572023842
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
4. ! [X0] : ((~tall(X0) <~> ~curious(X0)) <=> (~funny(X0) & humble(X0))) [input p3]
5. ! [X0] : ((~funny(X0) <~> tall(X0)) => ~wise(X0)) [input p4]
11. ! [X0] : (humble(X0) => (~old(X0) & ~funny(X0))) [input p10]
14. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (~generous(X0) & ~curious(X0))) [input p13]
16. (~happy(paul) & ~wise(paul)) <=> ? [X0] : (tall(X0) | kind(X0)) [input p15]
18. ~humble(paul) & generous(paul) [input p17]
24. humble(susan) [input hypothesis]
28. ! [X0] : (~wise(X0) | (~funny(X0) <=> tall(X0))) [ennf transformation 5]
33. ! [X0] : ((~old(X0) & ~funny(X0)) | ~humble(X0)) [ennf transformation 11]
34. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
35. ! [X0] : ((funny(X0) | ~funny(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [flattening 34]
40. ! [X0] : ((((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | (funny(X0) | ~humble(X0))) & ((~funny(X0) & humble(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0))))) [nnf transformation 4]
41. ! [X0] : ((((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | funny(X0) | ~humble(X0)) & ((~funny(X0) & humble(X0)) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0))))) [flattening 40]
42. ! [X0] : (~wise(X0) | ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0)))) [nnf transformation 28]
52. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 14]
53. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [flattening 52]
55. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | (happy(paul) | wise(paul))) [nnf transformation 16]
56. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | happy(paul) | wise(paul)) [flattening 55]
57. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X1] : (tall(X1) | kind(X1)) | happy(paul) | wise(paul)) [rectify 56]
58. ? [X1] : (tall(X1) | kind(X1)) => (tall(sK3) | kind(sK3)) [choice axiom]
59. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & ((tall(sK3) | kind(sK3)) | happy(paul) | wise(paul)) [skolemisation 57,58]
76. ~generous(X0) | happy(X0) | funny(X0) [cnf transformation 35]
77. ~generous(X0) | happy(X0) | ~funny(X0) [cnf transformation 35]
91. ~humble(X0) | tall(X0) | funny(X0) | curious(X0) [cnf transformation 41]
92. ~wise(X0) | tall(X0) | funny(X0) [cnf transformation 42]
109. ~humble(X0) | ~funny(X0) [cnf transformation 33]
110. ~old(X0) | ~humble(X0) [cnf transformation 33]
114. ~curious(X0) | old(X0) | wise(X0) [cnf transformation 53]
127. ~happy(paul) | ~tall(X0) [cnf transformation 59]
130. generous(paul) [cnf transformation 18]
138. humble(susan) [cnf transformation 24]
139. ~generous(X0) | happy(X0) [subsumption resolution 76,77]
142. 1 <=> curious(susan) [avatar definition]
144. curious(susan) <- (1) [avatar component clause 142]
219. 18 <=> ! [X0] : ~tall(X0) [avatar definition]
220. ~tall(X0) <- (18) [avatar component clause 219]
222. 19 <=> happy(paul) [avatar definition]
225. 18 | ~19 [avatar split clause 127,222,219]
288. ~funny(susan) [resolution 109,138]
298. happy(paul) [resolution 139,130]
301. 19 [avatar split clause 298,222]
441. tall(susan) | funny(susan) | curious(susan) [resolution 91,138]
444. funny(susan) | curious(susan) <- (18) [subsumption resolution 441,220]
445. curious(susan) <- (18) [subsumption resolution 444,288]
446. 1 | ~18 [avatar split clause 445,219,142]
449. old(susan) | wise(susan) <- (1) [resolution 144,114]
453. 46 <=> wise(susan) [avatar definition]
455. wise(susan) <- (46) [avatar component clause 453]
457. 47 <=> old(susan) [avatar definition]
459. old(susan) <- (47) [avatar component clause 457]
460. 46 | 47 | ~1 [avatar split clause 449,142,457,453]
481. tall(susan) | funny(susan) <- (46) [resolution 455,92]
485. funny(susan) <- (18, 46) [subsumption resolution 481,220]
486. $false <- (18, 46) [subsumption resolution 485,288]
487. ~18 | ~46 [avatar contradiction clause 486]
490. ~humble(susan) <- (47) [resolution 459,110]
496. $false <- (47) [subsumption resolution 490,138]
497. ~47 [avatar contradiction clause 496]
498. $false [avatar sat refutation 225,301,446,460,487,497]
% SZS output end Proof for 759885661171357572023842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or creative is either not tall or happy.
Everyone who is both not calm and not tall is either not generous or old and vice versa.
Everyone who is both not brave and not wise is either not brave or funny and vice versa.
Everyone who is both calm and not funny is both not creative and not humble and vice versa.
If paul is not tall or not happy then someone is both quiet and not happy and vice versa.
If someone is both not wise and strong then someone is both not wise and quiet.
If fred is not old then someone is both creative and not brave and vice versa.
Everyone who is either strong or rich is either strong or not calm.
Everyone who is not rich is both not rich and quiet.
Everyone who is both not humble and calm is either creative or patient.
Everyone who is tall or not patient is humble.
Everyone who is both not wise and not humble is not tall or not creative and vice versa.
Everyone who is not happy is both wise and kind.
Everyone who is either not brave or not kind is rich or calm and vice versa.
Everyone who is quiet or not old is both funny and brave.
If fred is both not calm and funny then someone is curious and vice versa.
Someone is either not brave or wise.
Fred is either not strong or not creative.
Someone is not quiet. | Fred is not happy. | contradiction | (![X]:((~happy(X)<~>creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~calm(X)&~tall(X))<=>(~generous(X)<~>old(X))))&
(![X]:((~brave(X)&~wise(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((calm(X)&~funny(X))<=>(~creative(X)&~humble(X))))&
(((~tall(paul)|~happy(paul)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:((~wise(X)&quiet(X)))))&
((~old(fred))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((strong(X)<~>rich(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(~rich(X)&quiet(X))))&
(![X]:((~humble(X)&calm(X))=>(creative(X)<~>patient(X))))&
(![X]:((tall(X)|~patient(X))=>humble(X)))&
(![X]:((~wise(X)&~humble(X))<=>(~tall(X)|~creative(X))))&
(![X]:(~happy(X)=>(wise(X)&kind(X))))&
(![X]:((~brave(X)<~>~kind(X))<=>(rich(X)|calm(X))))&
(![X]:((quiet(X)|~old(X))=>(funny(X)&brave(X))))&
(((~calm(fred)&funny(fred)))<=>(?[X]:(curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
((~strong(fred)<~>~creative(fred)))&
(?[X]:(~quiet(X))) | ~happy(fred) | [
"p2",
"p4",
"p6",
"p8",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2973828473321358583337675
% SZS output start Proof for 2973828473321358583337675
3. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> (~brave(X0) <~> funny(X0))) [input p2]
5. (~happy(paul) | ~tall(paul)) <=> ? [X0] : (~happy(X0) & quiet(X0)) [input p4]
7. ~old(fred) <=> ? [X0] : (~brave(X0) & creative(X0)) [input p6]
9. ! [X0] : (~rich(X0) => (quiet(X0) & ~rich(X0))) [input p8]
12. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (~creative(X0) | ~tall(X0))) [input p11]
13. ! [X0] : (~happy(X0) => (kind(X0) & wise(X0))) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~kind(X0)) <=> (calm(X0) | rich(X0))) [input p13]
15. ! [X0] : ((~old(X0) | quiet(X0)) => (brave(X0) & funny(X0))) [input p14]
20. ~happy(fred) [input hypothesis]
25. ! [X0] : ((quiet(X0) & ~rich(X0)) | rich(X0)) [ennf transformation 9]
29. ! [X0] : ((kind(X0) & wise(X0)) | happy(X0)) [ennf transformation 13]
30. ! [X0] : ((brave(X0) & funny(X0)) | (old(X0) & ~quiet(X0))) [ennf transformation 15]
34. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (wise(X0) | brave(X0)))) [nnf transformation 3]
35. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | wise(X0) | brave(X0))) [flattening 34]
38. ((~happy(paul) | ~tall(paul)) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X0] : (~happy(X0) & quiet(X0)) | (happy(paul) & tall(paul))) [nnf transformation 5]
39. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X0] : (~happy(X0) & quiet(X0)) | (happy(paul) & tall(paul))) [flattening 38]
40. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X1] : (~happy(X1) & quiet(X1)) | (happy(paul) & tall(paul))) [rectify 39]
41. ? [X1] : (~happy(X1) & quiet(X1)) => (~happy(sK0) & quiet(sK0)) [choice axiom]
42. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & ((~happy(sK0) & quiet(sK0)) | (happy(paul) & tall(paul))) [skolemisation 40,41]
46. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & (? [X0] : (~brave(X0) & creative(X0)) | old(fred)) [nnf transformation 7]
47. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & (? [X1] : (~brave(X1) & creative(X1)) | old(fred)) [rectify 46]
48. ? [X1] : (~brave(X1) & creative(X1)) => (~brave(sK2) & creative(sK2)) [choice axiom]
49. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & ((~brave(sK2) & creative(sK2)) | old(fred)) [skolemisation 47,48]
52. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 12]
53. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | humble(X0) | wise(X0))) [flattening 52]
54. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [nnf transformation 14]
55. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [flattening 54]
80. ~brave(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 35]
87. quiet(sK0) | tall(paul) [cnf transformation 42]
88. quiet(sK0) | happy(paul) [cnf transformation 42]
91. ~happy(paul) | ~tall(paul) | happy(X0) | ~quiet(X0) [cnf transformation 42]
96. ~old(fred) | brave(X0) | ~creative(X0) [cnf transformation 49]
102. rich(X0) | quiet(X0) [cnf transformation 25]
109. ~wise(X0) | creative(X0) [cnf transformation 53]
112. wise(X0) | happy(X0) [cnf transformation 29]
113. kind(X0) | happy(X0) [cnf transformation 29]
116. ~kind(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 55]
120. ~quiet(X0) | funny(X0) [cnf transformation 30]
121. funny(X0) | old(X0) [cnf transformation 30]
122. ~quiet(X0) | brave(X0) [cnf transformation 30]
123. brave(X0) | old(X0) [cnf transformation 30]
132. ~happy(fred) [cnf transformation 20]
136. ~funny(X0) | ~brave(X0) [duplicate literal removal 80]
141. 1 <=> ! [X0] : (happy(X0) | ~quiet(X0)) [avatar definition]
142. ~quiet(X0) | happy(X0) <- (1) [avatar component clause 141]
144. 2 <=> tall(paul) [avatar definition]
148. 3 <=> happy(paul) [avatar definition]
151. 1 | ~2 | ~3 [avatar split clause 91,148,144,141]
159. 5 <=> quiet(sK0) [avatar definition]
161. quiet(sK0) <- (5) [avatar component clause 159]
162. 3 | 5 [avatar split clause 88,159,148]
163. 2 | 5 [avatar split clause 87,159,144]
178. 9 <=> ! [X0] : (brave(X0) | ~creative(X0)) [avatar definition]
179. ~creative(X0) | brave(X0) <- (9) [avatar component clause 178]
181. 10 <=> old(fred) [avatar definition]
183. ~old(fred) <- (~10) [avatar component clause 181]
184. 9 | ~10 [avatar split clause 96,181,178]
238. creative(X0) | happy(X0) [resolution 112,109]
240. funny(sK0) <- (5) [resolution 120,161]
242. brave(sK0) <- (5) [resolution 122,161]
244. ~brave(sK0) <- (5) [resolution 136,240]
245. ~brave(X0) | old(X0) [resolution 136,121]
246. $false <- (5) [subsumption resolution 244,242]
247. ~5 [avatar contradiction clause 246]
248. old(X0) [subsumption resolution 245,123]
285. happy(X0) | brave(X0) <- (9) [resolution 238,179]
307. ~brave(X0) | ~rich(X0) | happy(X0) [resolution 116,113]
308. ~rich(X0) | happy(X0) <- (9) [subsumption resolution 307,285]
309. happy(X0) | quiet(X0) <- (9) [resolution 308,102]
310. happy(X0) <- (1, 9) [subsumption resolution 309,142]
312. $false <- (1, 9) [resolution 310,132]
315. ~1 | ~9 [avatar contradiction clause 312]
316. $false <- (~10) [subsumption resolution 183,248]
317. 10 [avatar contradiction clause 316]
318. $false [avatar sat refutation 151,162,163,184,247,315,317]
% SZS output end Proof for 2973828473321358583337675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both calm and not generous.
Everyone who is either not humble or not wise is generous.
If alice is either brave or rich then fred is not funny or not calm and vice versa.
If someone is both happy and not tall then mary is strong or not happy.
Everyone who is not tall or quiet is both creative and calm and vice versa.
If someone is both tall and not funny then susan is not brave or not curious.
If someone is either not humble or not wise then susan is patient or tall and vice versa.
Everyone who is either kind or not curious is not creative or curious.
Everyone who is either curious or strong is either brave or not generous.
Everyone who is either not curious or generous is either not old or not kind and vice versa.
Everyone who is quiet is old and vice versa.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is either not happy or happy is curious and vice versa.
Everyone who is brave is generous and vice versa.
If fred is calm or creative then someone is both not tall and generous and vice versa.
Everyone who is both strong and happy is both creative and calm and vice versa.
Someone is not old.
Someone is not rich or kind.
Someone is patient or not rich.
Someone is curious or not brave.
Someone is both brave and not kind.
Someone is not funny or not humble. | Alice is funny. | neutral | (![X]:(rich(X)=>(calm(X)&~generous(X))))&
(![X]:((~humble(X)<~>~wise(X))=>generous(X)))&
(((brave(alice)<~>rich(alice)))<=>((~funny(fred)|~calm(fred))))&
((?[X]:((happy(X)&~tall(X))))=>((strong(mary)|~happy(mary))))&
(![X]:((~tall(X)|quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:((tall(X)&~funny(X))))=>((~brave(susan)|~curious(susan))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>((patient(susan)|tall(susan))))&
(![X]:((kind(X)<~>~curious(X))=>(~creative(X)|curious(X))))&
(![X]:((curious(X)<~>strong(X))=>(brave(X)<~>~generous(X))))&
(![X]:((~curious(X)<~>generous(X))<=>(~old(X)<~>~kind(X))))&
(![X]:(quiet(X)<=>old(X)))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>happy(X))<=>curious(X)))&
(![X]:(brave(X)<=>generous(X)))&
(((calm(fred)|creative(fred)))<=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((strong(X)&happy(X))<=>(creative(X)&calm(X))))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((patient(X)|~rich(X))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((~funny(X)|~humble(X)))) | funny(alice) | [] | null | 0 |
If john is not patient or not wise then john is either not quiet or not calm.
If lucy is quiet then someone is not brave or kind.
If mary is generous then someone is not creative and vice versa.
Everyone who is either not quiet or not calm is either creative or happy.
Everyone who is not old or not humble is both patient and not quiet and vice versa.
Everyone who is not creative is calm or not calm.
If paul is both not kind and not happy then susan is both not brave and not wise.
Everyone who is not rich is not generous or calm.
If someone is both quiet and not brave then mary is either patient or not creative and vice versa.
If someone is either not tall or not kind then someone is funny or not strong and vice versa.
If someone is both creative and tall then someone is both calm and strong and vice versa.
Everyone who is either not happy or not wise is either not generous or not kind and vice versa.
If fred is not quiet or generous then someone is not kind and vice versa.
If someone is old or brave then paul is calm or not brave.
If someone is wise or not funny then paul is strong and vice versa.
Everyone who is tall is not strong or calm.
Mary is either creative or not humble.
Someone is not creative or creative.
Paul is both not brave and not quiet.
Someone is both funny and calm.
Paul is wise or kind.
Someone is either creative or tall.
Someone is both not brave and tall.
Someone is not strong or old. | Paul is not brave. | entailment | (((~patient(john)|~wise(john)))=>((~quiet(john)<~>~calm(john))))&
((quiet(lucy))=>(?[X]:((~brave(X)|kind(X)))))&
((generous(mary))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>(creative(X)<~>happy(X))))&
(![X]:((~old(X)|~humble(X))<=>(patient(X)&~quiet(X))))&
(![X]:(~creative(X)=>(calm(X)|~calm(X))))&
(((~kind(paul)&~happy(paul)))=>((~brave(susan)&~wise(susan))))&
(![X]:(~rich(X)=>(~generous(X)|calm(X))))&
((?[X]:((quiet(X)&~brave(X))))<=>((patient(mary)<~>~creative(mary))))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((funny(X)|~strong(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~generous(X)<~>~kind(X))))&
(((~quiet(fred)|generous(fred)))<=>(?[X]:(~kind(X))))&
((?[X]:((old(X)|brave(X))))=>((calm(paul)|~brave(paul))))&
((?[X]:((wise(X)|~funny(X))))<=>(strong(paul)))&
(![X]:(tall(X)=>(~strong(X)|calm(X))))&
((creative(mary)<~>~humble(mary)))&
(?[X]:((~creative(X)|creative(X))))&
((~brave(paul)&~quiet(paul)))&
(?[X]:((funny(X)&calm(X))))&
((wise(paul)|kind(paul)))&
(?[X]:((creative(X)<~>tall(X))))&
(?[X]:((~brave(X)&tall(X))))&
(?[X]:((~strong(X)|old(X)))) | ~brave(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 75005562097824506152861
% SZS output start Proof for 75005562097824506152861
19. ~quiet(paul) & ~brave(paul) [input p18]
25. brave(paul) [input hypothesis]
141. ~brave(paul) [cnf transformation 19]
151. brave(paul) [cnf transformation 25]
327. 40 <=> brave(paul) [avatar definition]
362. ~40 [avatar split clause 141,327]
387. 40 [avatar split clause 151,327]
388. $false [avatar sat refutation 362,387]
% SZS output end Proof for 75005562097824506152861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
If mary is either not happy or not calm then susan is not tall.
Everyone who is curious or not curious is generous.
If someone is strong or humble then someone is both kind and generous and vice versa.
Everyone who is not curious or not generous is both patient and not funny.
If someone is funny then someone is not creative or not calm and vice versa.
Everyone who is either not tall or not generous is not creative or creative and vice versa.
If fred is both not creative and not funny then someone is both not wise and kind and vice versa.
If someone is humble or wise then fred is not rich and vice versa.
If someone is not happy or funny then mary is creative.
Everyone who is both not happy and patient is either not patient or not calm.
Everyone who is old or not happy is either generous or not tall and vice versa.
Everyone who is not kind or not strong is calm or not quiet and vice versa.
Lucy is calm or rich.
Someone is both not kind and not brave.
Someone is creative or humble.
Someone is rich or curious.
John is brave or not humble.
Someone is creative or not kind.
Someone is wise or not wise. | Mary is not old. | entailment | (![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
(((~happy(mary)<~>~calm(mary)))=>(~tall(susan)))&
(![X]:((curious(X)|~curious(X))=>generous(X)))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((kind(X)&generous(X)))))&
(![X]:((~curious(X)|~generous(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~creative(X)|creative(X))))&
(((~creative(fred)&~funny(fred)))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((humble(X)|wise(X))))<=>(~rich(fred)))&
((?[X]:((~happy(X)|funny(X))))=>(creative(mary)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((old(X)|~happy(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((~kind(X)|~strong(X))<=>(calm(X)|~quiet(X))))&
((calm(lucy)|rich(lucy)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((rich(X)|curious(X))))&
((brave(john)|~humble(john)))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((wise(X)|~wise(X)))) | ~old(mary) | [
"p4",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8398039603024053298410235
% SZS output start Proof for 8398039603024053298410235
5. ! [X0] : ((~curious(X0) | curious(X0)) => generous(X0)) [input p4]
9. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (creative(X0) | ~creative(X0))) [input p8]
14. ! [X0] : ((~happy(X0) | old(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p13]
23. old(mary) [input hypothesis]
28. ! [X0] : (generous(X0) | (curious(X0) & ~curious(X0))) [ennf transformation 5]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 9]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
61. ! [X0] : (((~happy(X0) | old(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [nnf transformation 14]
62. ! [X0] : ((~happy(X0) | old(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (happy(X0) & ~old(X0)))) [flattening 61]
88. generous(X0) | ~curious(X0) [cnf transformation 28]
89. generous(X0) | curious(X0) [cnf transformation 28]
104. ~generous(X0) | ~tall(X0) | creative(X0) [cnf transformation 50]
105. ~generous(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 50]
121. tall(X0) | ~generous(X0) | ~old(X0) [cnf transformation 62]
137. old(mary) [cnf transformation 23]
155. generous(X0) [subsumption resolution 88,89]
205. ~tall(X0) | ~creative(X0) [subsumption resolution 105,155]
206. ~tall(X0) | creative(X0) [subsumption resolution 104,155]
207. ~tall(X0) [subsumption resolution 206,205]
246. ~generous(X0) | ~old(X0) [subsumption resolution 121,207]
247. ~old(X0) [subsumption resolution 246,155]
276. $false [subsumption resolution 137,247]
% SZS output end Proof for 8398039603024053298410235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or creative is not wise and vice versa.
Everyone who is both not funny and strong is either patient or kind.
Everyone who is both funny and happy is strong or happy and vice versa.
If someone is both funny and patient then paul is 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.
Everyone who is not calm is curious 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.
Susan is not old or funny.
Someone is both creative and not funny.
John is not tall.
Someone is both not curious and calm. | Paul is generous. | neutral | (![X]:((~strong(X)|creative(X))<=>~wise(X)))&
(![X]:((~funny(X)&strong(X))=>(patient(X)<~>kind(X))))&
(![X]:((funny(X)&happy(X))<=>(strong(X)|happy(X))))&
((?[X]:((funny(X)&patient(X))))=>(old(paul)))&
(![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]:(~calm(X)<=>curious(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)))&
((~old(susan)|funny(susan)))&
(?[X]:((creative(X)&~funny(X))))&
(~tall(john))&
(?[X]:((~curious(X)&calm(X)))) | generous(paul) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is not humble or funny is both not curious and tall.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
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.
Someone is not brave or patient.
Someone is either not old or tall.
Susan is not brave.
Fred is both funny and not creative.
Susan is either old or kind. | Fred is not quiet. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((~humble(X)|funny(X))=>(~curious(X)&tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(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)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~old(X)<~>tall(X))))&
(~brave(susan))&
((funny(fred)&~creative(fred)))&
((old(susan)<~>kind(susan))) | ~quiet(fred) | [
"p2",
"p3",
"p7",
"p8",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3429978134566582842634405
% SZS output start Proof for 3429978134566582842634405
3. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p2]
4. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p3]
8. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p7]
9. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p8]
12. ? [X0] : ~wise(X0) <=> ? [X0] : (~calm(X0) <~> ~quiet(X0)) [input p11]
13. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
20. ~creative(fred) & funny(fred) [input p19]
22. quiet(fred) [input hypothesis]
23. ? [X0] : ~wise(X0) <=> ? [X1] : (~calm(X1) <~> ~quiet(X1)) [rectify 12]
25. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 3]
32. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 13]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 4]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 8]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
45. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 9]
46. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 45]
55. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X1] : ((quiet(X1) | calm(X1)) & (~quiet(X1) | ~calm(X1))) | ! [X0] : wise(X0)) [nnf transformation 23]
56. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) | ! [X3] : wise(X3)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. ? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) => ((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) [choice axiom]
59. (~wise(sK3) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) | ! [X3] : wise(X3)) [skolemisation 56,58,57]
63. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 63]
80. ~rich(X0) | happy(X0) [cnf transformation 25]
84. ~happy(X0) | creative(X0) | patient(X0) [cnf transformation 36]
93. ~funny(fred) | wise(X1) [cnf transformation 44]
96. ~patient(fred) | creative(alice) [cnf transformation 46]
109. ~wise(sK3) | ~quiet(X1) | calm(X1) [cnf transformation 59]
112. ~creative(X0) | ~creative(X0) [cnf transformation 32]
117. rich(X0) | ~calm(X0) | rich(X0) | happy(X0) [cnf transformation 64]
129. funny(fred) [cnf transformation 20]
133. quiet(fred) [cnf transformation 22]
136. rich(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 117]
138. ~creative(X0) [duplicate literal removal 112]
144. 2 <=> funny(fred) [avatar definition]
153. 4 <=> ! [X1] : wise(X1) [avatar definition]
154. wise(X1) <- (4) [avatar component clause 153]
155. 4 | ~2 [avatar split clause 93,144,153]
158. 5 <=> patient(fred) [avatar definition]
170. 8 <=> creative(alice) [avatar definition]
171. creative(alice) <- (8) [avatar component clause 170]
176. 8 | ~5 [avatar split clause 96,158,170]
216. 17 <=> wise(sK3) [avatar definition]
218. ~wise(sK3) <- (~17) [avatar component clause 216]
221. 18 <=> ! [X1] : (~quiet(X1) | calm(X1)) [avatar definition]
222. ~quiet(X1) | calm(X1) <- (18) [avatar component clause 221]
223. 18 | ~17 [avatar split clause 109,216,221]
248. ~calm(X0) | happy(X0) [subsumption resolution 136,80]
268. 2 [avatar split clause 129,144]
279. $false <- (4, ~17) [resolution 218,154]
280. ~4 | 17 [avatar contradiction clause 279]
292. calm(fred) <- (18) [resolution 222,133]
294. happy(fred) <- (18) [resolution 248,292]
307. creative(fred) | patient(fred) <- (18) [resolution 84,294]
309. patient(fred) <- (18) [subsumption resolution 307,138]
312. 5 | ~18 [avatar split clause 309,221,158]
313. $false <- (8) [subsumption resolution 171,138]
314. ~8 [avatar contradiction clause 313]
315. $false [avatar sat refutation 155,176,223,268,280,312,314]
% SZS output end Proof for 3429978134566582842634405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or strong is wise and vice versa. If someone is not patient then someone is not tall or not strong and vice versa. If lucy is not generous or not rich then lucy is strong or generous and vice versa. If someone is not curious or not rich then john is either not happy or not patient. Everyone who is humble or quiet is not generous. If someone is either not brave or creative then someone is not calm and vice versa. If someone is not wise then someone is creative or not calm. If john is either not rich or generous then fred is both not happy and old and vice versa. If someone is either not old or not generous then john is both strong and not happy and vice versa. If fred is brave or calm then someone is rich or not generous and vice versa. Everyone who is both strong and not tall is not tall or not wise. If someone is both not kind and funny then someone is both kind and curious. If someone is both not generous and curious then mary is not brave and vice versa. Everyone who is generous is both not creative and not brave and vice versa. If someone is not wise then someone is funny or not rich and vice versa. If someone is old then lucy is either not strong or humble and vice versa. Paul is kind. Someone is not happy. Someone is both wise and brave. Fred is both not old and not humble. Someone is not humble or not generous. Mary is either not happy or not old. Lucy is old. Fred is not quiet. | Mary is not rich. | contradiction | (![X]:((~strong(X)|strong(X))<=>wise(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((~tall(X)|~strong(X)))))&
(((~generous(lucy)|~rich(lucy)))<=>((strong(lucy)|generous(lucy))))&
((?[X]:((~curious(X)|~rich(X))))=>((~happy(john)<~>~patient(john))))&
(![X]:((humble(X)|quiet(X))=>~generous(X)))&
((?[X]:((~brave(X)<~>creative(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~wise(X)))=>(?[X]:((creative(X)|~calm(X)))))&
(((~rich(john)<~>generous(john)))<=>((~happy(fred)&old(fred))))&
((?[X]:((~old(X)<~>~generous(X))))<=>((strong(john)&~happy(john))))&
(((brave(fred)|calm(fred)))<=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((strong(X)&~tall(X))=>(~tall(X)|~wise(X))))&
((?[X]:((~kind(X)&funny(X))))=>(?[X]:((kind(X)&curious(X)))))&
((?[X]:((~generous(X)&curious(X))))<=>(~brave(mary)))&
(![X]:(generous(X)<=>(~creative(X)&~brave(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((funny(X)|~rich(X)))))&
((?[X]:(old(X)))<=>((~strong(lucy)<~>humble(lucy))))&
(kind(paul))&
(?[X]:(~happy(X)))&
(?[X]:((wise(X)&brave(X))))&
((~old(fred)&~humble(fred)))&
(?[X]:((~humble(X)|~generous(X))))&
((~happy(mary)<~>~old(mary)))&
(old(lucy))&
(~quiet(fred)) | ~rich(mary) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4285036560936290536340109
% SZS output start Proof for 4285036560936290536340109
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> wise(X0)) [input p0]
15. ? [X0] : ~wise(X0) <=> ? [X0] : (~rich(X0) | funny(X0)) [input p14]
25. ~rich(mary) [input hypothesis]
30. ? [X0] : ~wise(X0) <=> ? [X1] : (~rich(X1) | funny(X1)) [rectify 15]
40. ! [X0] : (((strong(X0) | ~strong(X0)) | ~wise(X0)) & (wise(X0) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
41. ! [X0] : ((strong(X0) | ~strong(X0) | ~wise(X0)) & (wise(X0) | (~strong(X0) & strong(X0)))) [flattening 40]
76. (? [X0] : ~wise(X0) | ! [X1] : (rich(X1) & ~funny(X1))) & (? [X1] : (~rich(X1) | funny(X1)) | ! [X0] : wise(X0)) [nnf transformation 30]
77. (? [X0] : ~wise(X0) | ! [X1] : (rich(X1) & ~funny(X1))) & (? [X2] : (~rich(X2) | funny(X2)) | ! [X3] : wise(X3)) [rectify 76]
78. ? [X0] : ~wise(X0) => ~wise(sK8) [choice axiom]
79. ? [X2] : (~rich(X2) | funny(X2)) => (~rich(sK9) | funny(sK9)) [choice axiom]
80. (~wise(sK8) | ! [X1] : (rich(X1) & ~funny(X1))) & ((~rich(sK9) | funny(sK9)) | ! [X3] : wise(X3)) [skolemisation 77,79,78]
92. wise(X0) | strong(X0) [cnf transformation 41]
93. wise(X0) | ~strong(X0) [cnf transformation 41]
137. ~wise(sK8) | rich(X1) [cnf transformation 80]
151. ~rich(mary) [cnf transformation 25]
154. wise(X0) [subsumption resolution 92,93]
196. 10 <=> ! [X0] : rich(X0) [avatar definition]
197. rich(X0) <- (10) [avatar component clause 196]
328. rich(X1) [subsumption resolution 137,154]
329. 10 [avatar split clause 328,196]
359. $false <- (10) [resolution 197,151]
360. ~10 [avatar contradiction clause 359]
361. $false [avatar sat refutation 329,360]
% SZS output end Proof for 4285036560936290536340109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind then susan is either not generous or not strong and vice versa.
Everyone who is either not kind or kind is humble and vice versa.
Everyone who is not rich or humble is not tall or not generous and vice versa.
Everyone who is funny is either not patient or not calm.
Everyone who is either happy or patient is both not calm and not creative.
Everyone who is rich or curious is both not creative and patient.
If susan is either not kind or quiet then paul is both not calm and happy.
If fred is tall or brave then paul is either not curious or not generous.
Everyone who is kind or not generous is rich and vice versa.
Everyone who is rich is both wise and not rich.
If susan is either not creative or humble then someone is not wise or brave.
Everyone who is not patient is funny or not creative.
Everyone who is not funny or not curious is both not strong and not happy and vice versa.
If someone is not curious or humble then someone is generous or not generous.
Everyone who is both not creative and not curious is creative or not rich.
Everyone who is both not funny and not happy is rich.
Someone is generous or curious.
Someone is either creative or not happy.
Alice is both not old and funny.
John is patient.
Mary is either not rich or kind.
Someone is either kind or creative. | John is funny. | entailment | ((~kind(alice))<=>((~generous(susan)<~>~strong(susan))))&
(![X]:((~kind(X)<~>kind(X))<=>humble(X)))&
(![X]:((~rich(X)|humble(X))<=>(~tall(X)|~generous(X))))&
(![X]:(funny(X)=>(~patient(X)<~>~calm(X))))&
(![X]:((happy(X)<~>patient(X))=>(~calm(X)&~creative(X))))&
(![X]:((rich(X)|curious(X))=>(~creative(X)&patient(X))))&
(((~kind(susan)<~>quiet(susan)))=>((~calm(paul)&happy(paul))))&
(((tall(fred)|brave(fred)))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((kind(X)|~generous(X))<=>rich(X)))&
(![X]:(rich(X)=>(wise(X)&~rich(X))))&
(((~creative(susan)<~>humble(susan)))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(~patient(X)=>(funny(X)|~creative(X))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((~curious(X)|humble(X))))=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((~creative(X)&~curious(X))=>(creative(X)|~rich(X))))&
(![X]:((~funny(X)&~happy(X))=>rich(X)))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((~old(alice)&funny(alice)))&
(patient(john))&
((~rich(mary)<~>kind(mary)))&
(?[X]:((kind(X)<~>creative(X)))) | funny(john) | [
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8239755250592029090237850
% SZS output start Proof for 8239755250592029090237850
10. ! [X0] : (rich(X0) => (~rich(X0) & wise(X0))) [input p9]
13. ! [X0] : ((~curious(X0) | ~funny(X0)) <=> (~happy(X0) & ~strong(X0))) [input p12]
16. ! [X0] : ((~happy(X0) & ~funny(X0)) => rich(X0)) [input p15]
23. ~funny(john) [input hypothesis]
31. ! [X0] : ((~rich(X0) & wise(X0)) | ~rich(X0)) [ennf transformation 10]
38. ! [X0] : (rich(X0) | (happy(X0) | funny(X0))) [ennf transformation 16]
39. ! [X0] : (rich(X0) | happy(X0) | funny(X0)) [flattening 38]
53. ! [X0] : (((~curious(X0) | ~funny(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (curious(X0) & funny(X0)))) [nnf transformation 13]
54. ! [X0] : ((~curious(X0) | ~funny(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (curious(X0) & funny(X0)))) [flattening 53]
101. ~rich(X0) | ~rich(X0) [cnf transformation 31]
107. ~happy(X0) | funny(X0) [cnf transformation 54]
113. rich(X0) | happy(X0) | funny(X0) [cnf transformation 39]
123. ~funny(john) [cnf transformation 23]
125. ~rich(X0) [duplicate literal removal 101]
200. happy(X0) | funny(X0) [subsumption resolution 113,125]
201. funny(X0) [subsumption resolution 200,107]
231. $false [subsumption resolution 123,201]
% SZS output end Proof for 8239755250592029090237850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both funny and brave.
Everyone who is both not kind and not brave is not quiet or not generous.
If mary is strong then john is not generous or curious.
If john is not old then lucy is either not patient or not happy and vice versa.
If someone is both brave and not generous then alice is either funny or kind.
Everyone who is both not quiet and humble is either calm or not kind and vice versa.
Everyone who is not curious is both tall and not humble.
Everyone who is happy is both patient and not generous and vice versa.
If someone is both not creative and not calm then someone is calm or brave.
Everyone who is tall or not curious is funny or not rich.
Everyone who is strong is either tall or not quiet.
If lucy is both not creative and strong then someone is either not rich or not humble and vice versa.
Everyone who is not generous is either not old or not patient and vice versa.
Everyone who is either humble or old is either quiet or not quiet and vice versa.
If someone is not happy or not patient then someone is either not humble or not curious.
Everyone who is not humble or curious is both not patient and not rich.
Alice is not happy.
Mary is either brave or kind.
Paul is not curious.
Someone is not tall.
John is both wise and not patient.
Someone is both not quiet and calm. | John is not happy. | entailment | (![X]:(happy(X)=>(funny(X)&brave(X))))&
(![X]:((~kind(X)&~brave(X))=>(~quiet(X)|~generous(X))))&
((strong(mary))=>((~generous(john)|curious(john))))&
((~old(john))<=>((~patient(lucy)<~>~happy(lucy))))&
((?[X]:((brave(X)&~generous(X))))=>((funny(alice)<~>kind(alice))))&
(![X]:((~quiet(X)&humble(X))<=>(calm(X)<~>~kind(X))))&
(![X]:(~curious(X)=>(tall(X)&~humble(X))))&
(![X]:(happy(X)<=>(patient(X)&~generous(X))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:((calm(X)|brave(X)))))&
(![X]:((tall(X)|~curious(X))=>(funny(X)|~rich(X))))&
(![X]:(strong(X)=>(tall(X)<~>~quiet(X))))&
(((~creative(lucy)&strong(lucy)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:(~generous(X)<=>(~old(X)<~>~patient(X))))&
(![X]:((humble(X)<~>old(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~humble(X)|curious(X))=>(~patient(X)&~rich(X))))&
(~happy(alice))&
((brave(mary)<~>kind(mary)))&
(~curious(paul))&
(?[X]:(~tall(X)))&
((wise(john)&~patient(john)))&
(?[X]:((~quiet(X)&calm(X)))) | ~happy(john) | [
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9135972958298371162967296
% SZS output start Proof for 9135972958298371162967296
8. ! [X0] : (happy(X0) <=> (~generous(X0) & patient(X0))) [input p7]
21. ~patient(john) & wise(john) [input p20]
23. happy(john) [input hypothesis]
26. ~patient(john) [pure predicate removal 21]
44. ! [X0] : ((happy(X0) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | ~happy(X0))) [nnf transformation 8]
45. ! [X0] : ((happy(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | ~happy(X0))) [flattening 44]
84. ~happy(X0) | patient(X0) [cnf transformation 45]
123. ~patient(john) [cnf transformation 26]
126. happy(john) [cnf transformation 23]
253. patient(john) [resolution 84,126]
255. $false [subsumption resolution 253,123]
% SZS output end Proof for 9135972958298371162967296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not humble is tall and vice versa.
Everyone who is both rich and not curious is both not happy and patient.
If someone is not calm or not quiet then lucy is creative or calm and vice versa.
Everyone who is not creative is both not curious and rich.
Everyone who is strong is either not quiet or kind and vice versa.
If alice is not calm then john is either humble or not tall and vice versa.
If fred is not curious or not wise then lucy is funny and vice versa.
Everyone who is strong or not kind is either not generous or not creative and vice versa.
If someone is either brave or humble then alice is either tall or not kind.
Everyone who is both old and humble is not curious or not happy and vice versa.
Everyone who is not brave is either not kind or humble.
If lucy is either strong or calm then john is either rich or not brave and vice versa.
Everyone who is not happy is both tall and kind.
Everyone who is not funny or patient is either not humble or not patient.
Everyone who is both humble and not happy is either generous or calm and vice versa.
If someone is either not happy or curious then someone is both not curious and funny.
Lucy is both not brave and not quiet.
Someone is both brave and creative.
Fred is happy.
Lucy is tall or creative.
Someone is funny.
Someone is not generous or brave.
Paul is not calm. | Fred is not old. | neutral | (![X]:((funny(X)|~humble(X))<=>tall(X)))&
(![X]:((rich(X)&~curious(X))=>(~happy(X)&patient(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((creative(lucy)|calm(lucy))))&
(![X]:(~creative(X)=>(~curious(X)&rich(X))))&
(![X]:(strong(X)<=>(~quiet(X)<~>kind(X))))&
((~calm(alice))<=>((humble(john)<~>~tall(john))))&
(((~curious(fred)|~wise(fred)))<=>(funny(lucy)))&
(![X]:((strong(X)|~kind(X))<=>(~generous(X)<~>~creative(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((tall(alice)<~>~kind(alice))))&
(![X]:((old(X)&humble(X))<=>(~curious(X)|~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)<~>humble(X))))&
(((strong(lucy)<~>calm(lucy)))<=>((rich(john)<~>~brave(john))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
(![X]:((~funny(X)|patient(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((humble(X)&~happy(X))<=>(generous(X)<~>calm(X))))&
((?[X]:((~happy(X)<~>curious(X))))=>(?[X]:((~curious(X)&funny(X)))))&
((~brave(lucy)&~quiet(lucy)))&
(?[X]:((brave(X)&creative(X))))&
(happy(fred))&
((tall(lucy)|creative(lucy)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|brave(X))))&
(~calm(paul)) | ~old(fred) | [] | null | 0 |
Everyone who is either not humble or humble is not brave and vice versa. If someone is either strong or old then someone is not curious or kind and vice versa. If someone is brave then someone is both not calm and not brave. If fred is both not strong and not humble then someone 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. | Susan is not tall. | entailment | (![X]:((~humble(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:((~curious(X)|kind(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(((~strong(fred)&~humble(fred)))=>(?[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)))) | ~tall(susan) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4776981963109949125982568
% SZS output start Proof for 4776981963109949125982568
1. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~brave(X0)) [input p0]
5. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p4]
8. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p7]
9. ! [X0] : (old(X0) => brave(X0)) [input p8]
11. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~happy(X0) | old(X0))) [input p10]
22. tall(susan) [input hypothesis]
34. ! [X0] : (brave(X0) | ~old(X0)) [ennf transformation 9]
35. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | brave(X0)) & (~brave(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 1]
47. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 5]
49. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0) | tall(X0))) [flattening 49]
51. ! [X0] : (((~curious(X0) | ~calm(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 11]
52. ! [X0] : ((~curious(X0) | ~calm(X0) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | (curious(X0) & calm(X0)))) [flattening 51]
75. ~brave(X0) | humble(X0) | humble(X0) [cnf transformation 35]
76. ~brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 35]
90. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 47]
92. kind(X0) | kind(X0) | happy(X0) [cnf transformation 47]
97. ~tall(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 50]
101. brave(X0) | ~old(X0) [cnf transformation 34]
102. ~happy(X0) | old(X0) | calm(X0) [cnf transformation 52]
122. tall(susan) [cnf transformation 22]
123. happy(X0) | ~kind(X0) [duplicate literal removal 90]
124. happy(X0) | kind(X0) [duplicate literal removal 92]
125. ~brave(X0) | humble(X0) [duplicate literal removal 75]
126. ~brave(X0) | ~humble(X0) [duplicate literal removal 76]
127. ~brave(X0) [subsumption resolution 125,126]
176. happy(X0) [subsumption resolution 123,124]
178. ~tall(X0) | ~calm(X0) [subsumption resolution 97,176]
180. ~old(X0) [subsumption resolution 101,127]
184. old(X0) | calm(X0) [subsumption resolution 102,176]
185. calm(X0) [subsumption resolution 184,180]
226. ~calm(susan) [resolution 178,122]
227. $false [subsumption resolution 226,185]
% SZS output end Proof for 4776981963109949125982568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both patient and humble.
Everyone who is both brave and old is either humble or not curious and vice versa.
Everyone who is either old or generous is not brave.
Everyone who is brave is either not curious or tall.
If someone is either not old or not rich then someone is either not brave or not curious.
If someone is either not humble or not strong then lucy is either curious or rich and vice versa.
If someone is not rich then paul is either not funny or not generous.
If someone is not generous or not happy then mary is both not kind and not happy.
Everyone who is either brave or not happy is either not generous or not strong.
Everyone who is both not old and not patient is not wise or quiet.
Everyone who is either humble or not funny is both not generous and rich and vice versa.
If someone is both quiet and generous then someone is either curious or not tall.
Everyone who is either not humble or not brave is funny.
Everyone who is both happy and tall is not tall or wise and vice versa.
If john is quiet or creative then paul is both quiet and not humble.
If lucy is wise then john is not curious and vice versa.
Fred is either not old or humble.
Lucy is both tall and not curious.
John is both not kind and happy.
Fred is either calm or not funny.
Someone is not happy or strong.
Lucy is either tall or not happy.
Someone is either funny or kind.
Paul is either tall or not quiet. | Lucy is rich. | entailment | (![X]:(~calm(X)=>(patient(X)&humble(X))))&
(![X]:((brave(X)&old(X))<=>(humble(X)<~>~curious(X))))&
(![X]:((old(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)=>(~curious(X)<~>tall(X))))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>((curious(lucy)<~>rich(lucy))))&
((?[X]:(~rich(X)))=>((~funny(paul)<~>~generous(paul))))&
((?[X]:((~generous(X)|~happy(X))))=>((~kind(mary)&~happy(mary))))&
(![X]:((brave(X)<~>~happy(X))=>(~generous(X)<~>~strong(X))))&
(![X]:((~old(X)&~patient(X))=>(~wise(X)|quiet(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~generous(X)&rich(X))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>funny(X)))&
(![X]:((happy(X)&tall(X))<=>(~tall(X)|wise(X))))&
(((quiet(john)|creative(john)))=>((quiet(paul)&~humble(paul))))&
((wise(lucy))<=>(~curious(john)))&
((~old(fred)<~>humble(fred)))&
((tall(lucy)&~curious(lucy)))&
((~kind(john)&happy(john)))&
((calm(fred)<~>~funny(fred)))&
(?[X]:((~happy(X)|strong(X))))&
((tall(lucy)<~>~happy(lucy)))&
(?[X]:((funny(X)<~>kind(X))))&
((tall(paul)<~>~quiet(paul))) | rich(lucy) | [
"p1",
"p3",
"p10",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8157847013966898858808913
% SZS output start Proof for 8157847013966898858808913
2. ! [X0] : ((old(X0) & brave(X0)) <=> (humble(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : (brave(X0) => (~curious(X0) <~> tall(X0))) [input p3]
11. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (rich(X0) & ~generous(X0))) [input p10]
13. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => funny(X0)) [input p12]
14. ! [X0] : ((tall(X0) & happy(X0)) <=> (wise(X0) | ~tall(X0))) [input p13]
18. ~curious(lucy) & tall(lucy) [input p17]
25. ~rich(lucy) [input hypothesis]
33. ! [X0] : ((~curious(X0) <~> tall(X0)) | ~brave(X0)) [ennf transformation 4]
39. ! [X0] : (funny(X0) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 13]
41. ! [X0] : (((old(X0) & brave(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~old(X0) | ~brave(X0)))) [nnf transformation 2]
42. ! [X0] : (((old(X0) & brave(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0)))) & (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | ~old(X0) | ~brave(X0))) [flattening 41]
44. ! [X0] : (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~brave(X0)) [nnf transformation 33]
55. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 55]
61. ! [X0] : (funny(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 39]
62. ! [X0] : (((tall(X0) & happy(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~tall(X0) | ~happy(X0)))) [nnf transformation 14]
63. ! [X0] : (((tall(X0) & happy(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ~tall(X0) | ~happy(X0))) [flattening 62]
78. curious(X0) | humble(X0) | brave(X0) [cnf transformation 42]
84. ~tall(X0) | curious(X0) | ~brave(X0) [cnf transformation 44]
109. ~funny(X0) | rich(X0) | ~humble(X0) [cnf transformation 56]
116. ~humble(X0) | funny(X0) | brave(X0) [cnf transformation 61]
120. tall(X0) | tall(X0) [cnf transformation 63]
129. ~curious(lucy) [cnf transformation 18]
141. ~rich(lucy) [cnf transformation 25]
143. tall(X0) [duplicate literal removal 120]
163. 5 <=> rich(lucy) [avatar definition]
165. ~rich(lucy) <- (~5) [avatar component clause 163]
167. 6 <=> curious(lucy) [avatar definition]
168. ~curious(lucy) <- (~6) [avatar component clause 167]
271. ~6 [avatar split clause 129,167]
304. ~5 [avatar split clause 141,163]
327. humble(lucy) | brave(lucy) <- (~6) [resolution 78,168]
333. 34 <=> brave(lucy) [avatar definition]
335. brave(lucy) <- (34) [avatar component clause 333]
337. 35 <=> humble(lucy) [avatar definition]
339. humble(lucy) <- (35) [avatar component clause 337]
340. 34 | 35 | 6 [avatar split clause 327,167,337,333]
410. ~brave(X0) | curious(X0) [resolution 84,143]
435. funny(lucy) | brave(lucy) <- (35) [resolution 116,339]
551. curious(lucy) <- (34) [resolution 410,335]
554. $false <- (~6, 34) [subsumption resolution 551,168]
555. 6 | ~34 [avatar contradiction clause 554]
564. 63 <=> funny(lucy) [avatar definition]
566. funny(lucy) <- (63) [avatar component clause 564]
567. 34 | 63 | ~35 [avatar split clause 435,337,564,333]
604. rich(lucy) | ~humble(lucy) <- (63) [resolution 566,109]
606. ~humble(lucy) <- (~5, 63) [subsumption resolution 604,165]
607. $false <- (~5, 35, 63) [subsumption resolution 606,339]
608. 5 | ~35 | ~63 [avatar contradiction clause 607]
611. $false [avatar sat refutation 271,304,340,555,567,608]
% SZS output end Proof for 8157847013966898858808913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or strong is either not quiet or humble and vice versa.
Everyone who is not humble is either not curious or funny.
Everyone who is both not kind and curious is generous and vice versa.
If someone is either not old or rich then someone is not funny and vice versa.
Everyone who is not generous is not tall or kind.
If someone is tall then alice is not patient or not curious.
Everyone who is either not strong or funny is not rich or not creative and vice versa.
Everyone who is both curious and rich is tall and vice versa.
If someone is strong then someone is patient or old.
Everyone who is either rich or quiet is both not kind and funny.
Everyone who is either brave or old is curious or calm and vice versa.
Everyone who is either not tall or generous is either not funny or calm.
If someone is both not rich and not kind then someone is rich.
Everyone who is not curious or patient is wise or not patient.
If someone is either patient or not brave then john is both generous and kind.
If susan is both not kind and funny then someone is either tall or not patient and vice versa.
Someone is not quiet.
Someone is either happy or humble.
John is both not happy and not strong.
Fred is both not calm and brave.
John is either not tall or tall.
John is both creative and curious.
Someone is not patient or not funny.
Alice is not funny or old. | Susan is funny. | neutral | (![X]:((rich(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~humble(X)=>(~curious(X)<~>funny(X))))&
(![X]:((~kind(X)&curious(X))<=>generous(X)))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~generous(X)=>(~tall(X)|kind(X))))&
((?[X]:(tall(X)))=>((~patient(alice)|~curious(alice))))&
(![X]:((~strong(X)<~>funny(X))<=>(~rich(X)|~creative(X))))&
(![X]:((curious(X)&rich(X))<=>tall(X)))&
((?[X]:(strong(X)))=>(?[X]:((patient(X)|old(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((brave(X)<~>old(X))<=>(curious(X)|calm(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~funny(X)<~>calm(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(rich(X))))&
(![X]:((~curious(X)|patient(X))=>(wise(X)|~patient(X))))&
((?[X]:((patient(X)<~>~brave(X))))=>((generous(john)&kind(john))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((tall(X)<~>~patient(X)))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)<~>humble(X))))&
((~happy(john)&~strong(john)))&
((~calm(fred)&brave(fred)))&
((~tall(john)<~>tall(john)))&
((creative(john)&curious(john)))&
(?[X]:((~patient(X)|~funny(X))))&
((~funny(alice)|old(alice))) | funny(susan) | [] | null | 0 |
Everyone who is both not tall and not kind is not brave or curious.
Everyone who is both tall and not curious is humble.
If john is generous or kind then someone is not kind.
Everyone who is not patient or not creative is either not strong or not generous and vice versa.
If someone is both not generous and creative then someone is not brave or not strong.
If john is not creative or kind then someone is 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.
Fred is both not curious and not wise.
Someone is not generous.
Mary is not old.
Someone is not patient.
Someone is tall or quiet.
Susan is quiet or generous.
Someone is both not rich and curious. | Mary is patient. | entailment | (![X]:((~tall(X)&~kind(X))=>(~brave(X)|curious(X))))&
(![X]:((tall(X)&~curious(X))=>humble(X)))&
(((generous(john)|kind(john)))=>(?[X]:(~kind(X))))&
(![X]:((~patient(X)|~creative(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:((~generous(X)&creative(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
(((~creative(john)|kind(john)))=>(?[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))))&
((~curious(fred)&~wise(fred)))&
(?[X]:(~generous(X)))&
(~old(mary))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|quiet(X))))&
((quiet(susan)|generous(susan)))&
(?[X]:((~rich(X)&curious(X)))) | patient(mary) | [
"p7",
"p9",
"p12",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8916668152894025607303905
% SZS output start Proof for 8916668152894025607303905
8. ! [X0] : ((~old(X0) & wise(X0)) <=> (~tall(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : (generous(X0) => (~tall(X0) & ~patient(X0))) [input p9]
13. ? [X0] : (~wise(X0) <~> ~patient(X0)) <=> (generous(susan) <~> ~quiet(susan)) [input p12]
14. ? [X0] : quiet(X0) => ~tall(mary) [input p13]
15. ! [X0] : (~patient(X0) <=> (~quiet(X0) & ~brave(X0))) [input p14]
22. generous(susan) | quiet(susan) [input p21]
24. ~patient(mary) [input hypothesis]
33. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~generous(X0)) [ennf transformation 10]
35. ~tall(mary) | ! [X0] : ~quiet(X0) [ennf transformation 14]
46. ! [X0] : (((~old(X0) & wise(X0)) | (tall(X0) | quiet(X0))) & ((~tall(X0) & ~quiet(X0)) | (old(X0) | ~wise(X0)))) [nnf transformation 8]
47. ! [X0] : (((~old(X0) & wise(X0)) | tall(X0) | quiet(X0)) & ((~tall(X0) & ~quiet(X0)) | old(X0) | ~wise(X0))) [flattening 46]
50. (? [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 13]
51. (? [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 50]
52. ? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) => ((patient(sK3) | wise(sK3)) & (~patient(sK3) | ~wise(sK3))) [choice axiom]
53. (((patient(sK3) | wise(sK3)) & (~patient(sK3) | ~wise(sK3))) | ((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 51,52]
54. ! [X0] : ((~patient(X0) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 15]
55. ! [X0] : ((~patient(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [flattening 54]
86. quiet(X0) | tall(X0) | wise(X0) [cnf transformation 47]
88. ~patient(X0) | ~generous(X0) [cnf transformation 33]
89. ~generous(X0) | ~tall(X0) [cnf transformation 33]
101. ~quiet(susan) | generous(susan) | ~wise(X1) | patient(X1) [cnf transformation 53]
103. quiet(susan) | ~generous(susan) | ~wise(X1) | patient(X1) [cnf transformation 53]
108. ~tall(mary) | ~quiet(X0) [cnf transformation 35]
110. ~quiet(X0) | patient(X0) [cnf transformation 55]
121. generous(susan) | quiet(susan) [cnf transformation 22]
124. ~patient(mary) [cnf transformation 24]
168. 9 <=> quiet(susan) [avatar definition]
170. quiet(susan) <- (9) [avatar component clause 168]
172. 10 <=> generous(susan) [avatar definition]
174. generous(susan) <- (10) [avatar component clause 172]
188. 13 <=> ! [X1] : (~wise(X1) | patient(X1)) [avatar definition]
189. ~wise(X1) | patient(X1) <- (13) [avatar component clause 188]
190. 13 | ~10 | 9 [avatar split clause 103,168,172,188]
195. 13 | 10 | ~9 [avatar split clause 101,168,172,188]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
201. 16 <=> tall(mary) [avatar definition]
204. 15 | ~16 [avatar split clause 108,201,198]
228. 9 | 10 [avatar split clause 121,172,168]
236. patient(susan) <- (9) [resolution 110,170]
237. ~generous(susan) <- (9) [resolution 236,88]
240. ~10 | ~9 [avatar split clause 237,168,172]
296. tall(X1) | wise(X1) | patient(X1) [resolution 86,110]
297. patient(X1) | tall(X1) <- (13) [subsumption resolution 296,189]
302. tall(X1) | ~generous(X1) <- (13) [resolution 297,88]
303. tall(mary) <- (13) [resolution 297,124]
305. ~generous(X1) <- (13) [subsumption resolution 302,89]
308. 16 | ~13 [avatar split clause 303,188,201]
309. $false <- (9, 15) [resolution 199,170]
311. ~9 | ~15 [avatar contradiction clause 309]
312. $false <- (10, 13) [subsumption resolution 174,305]
313. ~10 | ~13 [avatar contradiction clause 312]
314. $false [avatar sat refutation 190,195,204,228,240,308,311,313]
% SZS output end Proof for 8916668152894025607303905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is humble and vice versa.
If someone is old or not funny then someone is not old and vice versa.
If someone is both not kind and wise then someone is either brave or not rich.
Everyone who is not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Someone is either quiet or strong.
Someone is not brave or creative.
Someone is not rich.
Someone is both strong and not rich.
Someone is not creative. | Susan is calm. | entailment | (![X]:(~funny(X)<=>humble(X)))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(~creative(X))) | calm(susan) | [
"p4",
"p5",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6187208808130785571451168
% SZS output start Proof for 6187208808130785571451168
5. (calm(susan) & ~curious(susan)) <=> ? [X0] : (~rich(X0) & ~patient(X0)) [input p4]
6. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p5]
9. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p8]
17. ? [X0] : ~rich(X0) [input p16]
20. ~calm(susan) [input hypothesis]
23. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 6]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 9]
44. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | (~calm(susan) | curious(susan))) [nnf transformation 5]
45. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | ~calm(susan) | curious(susan)) [flattening 44]
46. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X1] : (~rich(X1) & ~patient(X1)) | ~calm(susan) | curious(susan)) [rectify 45]
47. ? [X1] : (~rich(X1) & ~patient(X1)) => (~rich(sK3) & ~patient(sK3)) [choice axiom]
48. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & ((~rich(sK3) & ~patient(sK3)) | ~calm(susan) | curious(susan)) [skolemisation 46,47]
49. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 23]
50. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 49]
51. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK4) & creative(sK4)) [choice axiom]
52. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK5) | patient(sK5)) [choice axiom]
53. ((curious(sK4) & creative(sK4)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK5) | patient(sK5)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 50,52,51]
71. ? [X0] : ~rich(X0) => ~rich(sK10) [choice axiom]
72. ~rich(sK10) [skolemisation 17,71]
89. calm(susan) | rich(X0) | patient(X0) [cnf transformation 48]
91. creative(sK4) | ~patient(X1) [cnf transformation 53]
102. ~creative(X0) | ~creative(X0) [cnf transformation 31]
125. ~rich(sK10) [cnf transformation 72]
129. ~calm(susan) [cnf transformation 20]
132. ~creative(X0) [duplicate literal removal 102]
171. 10 <=> ! [X0] : (rich(X0) | patient(X0)) [avatar definition]
172. rich(X0) | patient(X0) <- (10) [avatar component clause 171]
174. 11 <=> calm(susan) [avatar definition]
177. 10 | 11 [avatar split clause 89,174,171]
199. 16 <=> ! [X1] : ~patient(X1) [avatar definition]
200. ~patient(X1) <- (16) [avatar component clause 199]
203. 17 <=> creative(sK4) [avatar definition]
205. creative(sK4) <- (17) [avatar component clause 203]
207. 16 | 17 [avatar split clause 91,203,199]
280. ~11 [avatar split clause 129,174]
283. rich(X0) <- (10, 16) [subsumption resolution 172,200]
290. $false <- (17) [subsumption resolution 205,132]
291. ~17 [avatar contradiction clause 290]
299. $false <- (10, 16) [resolution 283,125]
302. ~10 | ~16 [avatar contradiction clause 299]
303. $false [avatar sat refutation 177,207,280,291,302]
% SZS output end Proof for 6187208808130785571451168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not happy then someone is not old.
Everyone who is both creative and not humble is both not brave and wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
Someone is either not funny or not wise.
Susan is not wise or not patient.
Alice is humble.
Susan is rich or tall.
Susan is generous. | Mary is not calm. | contradiction | ((?[X]:((~generous(X)|~happy(X))))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~humble(X))<=>(~brave(X)&wise(X))))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
(humble(alice))&
((rich(susan)|tall(susan)))&
(generous(susan)) | ~calm(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8484772329495431840831759
% SZS output start Proof for 8484772329495431840831759
13. ! [X0] : ((calm(X0) & funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
22. ~calm(mary) [input hypothesis]
59. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~calm(X0) | ~funny(X0)))) [nnf transformation 13]
60. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~calm(X0) | ~funny(X0))) [flattening 59]
115. calm(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 60]
116. calm(X0) | tall(X0) | tall(X0) [cnf transformation 60]
137. ~calm(mary) [cnf transformation 22]
140. calm(X0) | ~tall(X0) [duplicate literal removal 115]
141. calm(X0) | tall(X0) [duplicate literal removal 116]
210. calm(X0) [subsumption resolution 140,141]
243. $false [subsumption resolution 137,210]
% SZS output end Proof for 8484772329495431840831759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not patient.
If mary is both not strong and generous then paul is not quiet or creative and vice versa.
If susan is not wise then mary is kind.
If alice is both old and rich then someone is either patient or calm.
Everyone who is either not old or not kind is both not generous and not happy.
If fred is rich or not brave then mary is either not generous or not kind and vice versa.
If paul is generous or tall then fred is not wise or quiet and vice versa.
Everyone who is both not happy and not quiet is humble and vice versa.
If mary is curious or not tall then mary is quiet and vice versa.
If john is not humble then someone is both not tall and funny.
Everyone who is both not funny and not old is both not strong and happy and vice versa.
Everyone who is not patient is both not tall and not calm and vice versa.
Everyone who is either not quiet or not calm is either not creative or rich and vice versa.
Everyone who is either patient or rich is not curious or quiet.
Everyone who is both old and calm is happy or not old.
Everyone who is both brave and happy is either not brave or generous.
Someone is both funny and not creative.
Someone is both not tall and generous.
Alice is not creative.
Someone is both not strong and not brave.
Mary is either rich or kind.
Someone is not quiet or not rich.
John is both not patient and kind.
Someone is either not strong or quiet. | Paul is quiet. | neutral | (![X]:(old(X)=>~patient(X)))&
(((~strong(mary)&generous(mary)))<=>((~quiet(paul)|creative(paul))))&
((~wise(susan))=>(kind(mary)))&
(((old(alice)&rich(alice)))=>(?[X]:((patient(X)<~>calm(X)))))&
(![X]:((~old(X)<~>~kind(X))=>(~generous(X)&~happy(X))))&
(((rich(fred)|~brave(fred)))<=>((~generous(mary)<~>~kind(mary))))&
(((generous(paul)|tall(paul)))<=>((~wise(fred)|quiet(fred))))&
(![X]:((~happy(X)&~quiet(X))<=>humble(X)))&
(((curious(mary)|~tall(mary)))<=>(quiet(mary)))&
((~humble(john))=>(?[X]:((~tall(X)&funny(X)))))&
(![X]:((~funny(X)&~old(X))<=>(~strong(X)&happy(X))))&
(![X]:(~patient(X)<=>(~tall(X)&~calm(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((patient(X)<~>rich(X))=>(~curious(X)|quiet(X))))&
(![X]:((old(X)&calm(X))=>(happy(X)|~old(X))))&
(![X]:((brave(X)&happy(X))=>(~brave(X)<~>generous(X))))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~tall(X)&generous(X))))&
(~creative(alice))&
(?[X]:((~strong(X)&~brave(X))))&
((rich(mary)<~>kind(mary)))&
(?[X]:((~quiet(X)|~rich(X))))&
((~patient(john)&kind(john)))&
(?[X]:((~strong(X)<~>quiet(X)))) | quiet(paul) | [] | null | 0 |
If susan is either old or not brave then susan is quiet and vice versa. Everyone who is either not old or not quiet is not kind. Everyone who is both kind and old is both not strong and brave. If alice is both funny and not funny then mary is both not wise and not calm. Everyone who is both not calm and not brave is kind and vice versa. If fred is not old or not quiet then lucy is either not calm or brave and vice versa. If someone is calm or not creative then someone is either humble or not old. Everyone who is strong or not brave is quiet or not humble and vice versa. Everyone who is either not happy or not wise is not creative. If susan is both curious and patient then susan is either strong or tall. If someone is both calm and happy then mary is either kind or not quiet. Everyone who is both not calm and not wise is both wise and calm and vice versa. If paul is both not wise and rich then someone is tall. Everyone who is not creative or not calm is both not kind and creative and vice versa. Everyone who is rich is both not kind and creative and vice versa. Everyone who is either strong or tall is not rich and vice versa. Mary is not curious or not humble. John is either not patient or calm. Mary is creative or not brave. Someone is not quiet. Someone is funny or old. Fred is both old and generous. | Paul is old. | neutral | (((old(susan)<~>~brave(susan)))<=>(quiet(susan)))&
(![X]:((~old(X)<~>~quiet(X))=>~kind(X)))&
(![X]:((kind(X)&old(X))=>(~strong(X)&brave(X))))&
(((funny(alice)&~funny(alice)))=>((~wise(mary)&~calm(mary))))&
(![X]:((~calm(X)&~brave(X))<=>kind(X)))&
(((~old(fred)|~quiet(fred)))<=>((~calm(lucy)<~>brave(lucy))))&
((?[X]:((calm(X)|~creative(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
(![X]:((strong(X)|~brave(X))<=>(quiet(X)|~humble(X))))&
(![X]:((~happy(X)<~>~wise(X))=>~creative(X)))&
(((curious(susan)&patient(susan)))=>((strong(susan)<~>tall(susan))))&
((?[X]:((calm(X)&happy(X))))=>((kind(mary)<~>~quiet(mary))))&
(![X]:((~calm(X)&~wise(X))<=>(wise(X)&calm(X))))&
(((~wise(paul)&rich(paul)))=>(?[X]:(tall(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&creative(X))))&
(![X]:(rich(X)<=>(~kind(X)&creative(X))))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
((~curious(mary)|~humble(mary)))&
((~patient(john)<~>calm(john)))&
((creative(mary)|~brave(mary)))&
(?[X]:(~quiet(X)))&
(?[X]:((funny(X)|old(X))))&
((old(fred)&generous(fred))) | old(paul) | [] | null | 0 |
Everyone who is not kind or calm is generous.
Everyone who is brave or wise is not old and vice versa.
Everyone who is not calm or not generous is not strong.
If someone is both strong and rich then someone is either kind or not generous and vice versa.
If someone is both not tall and not quiet then susan is both curious and brave.
Everyone who is either not curious or old is tall and vice versa.
Everyone who is either generous or tall is old and vice versa.
If john is not tall or not wise then fred is not tall.
Everyone who is tall is not rich or not strong and vice versa.
Everyone who is tall or not tall is both not kind and not creative and vice versa.
If susan is both not humble and old then someone is both not rich and not strong.
Everyone who is both not rich and not humble is either not generous or wise and vice versa.
Everyone who is not calm is both not brave and not funny and vice versa.
If someone is not old then lucy is not creative or not strong.
If fred is both not old and curious then john is either funny or brave and vice versa.
Lucy is either not calm or not generous.
Someone is old or happy.
John is quiet or kind.
Someone is strong or not curious. | Lucy is old. | contradiction | (![X]:((~kind(X)|calm(X))=>generous(X)))&
(![X]:((brave(X)|wise(X))<=>~old(X)))&
(![X]:((~calm(X)|~generous(X))=>~strong(X)))&
((?[X]:((strong(X)&rich(X))))<=>(?[X]:((kind(X)<~>~generous(X)))))&
((?[X]:((~tall(X)&~quiet(X))))=>((curious(susan)&brave(susan))))&
(![X]:((~curious(X)<~>old(X))<=>tall(X)))&
(![X]:((generous(X)<~>tall(X))<=>old(X)))&
(((~tall(john)|~wise(john)))=>(~tall(fred)))&
(![X]:(tall(X)<=>(~rich(X)|~strong(X))))&
(![X]:((tall(X)|~tall(X))<=>(~kind(X)&~creative(X))))&
(((~humble(susan)&old(susan)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:(~calm(X)<=>(~brave(X)&~funny(X))))&
((?[X]:(~old(X)))=>((~creative(lucy)|~strong(lucy))))&
(((~old(fred)&curious(fred)))<=>((funny(john)<~>brave(john))))&
((~calm(lucy)<~>~generous(lucy)))&
(?[X]:((old(X)|happy(X))))&
((quiet(john)|kind(john)))&
(?[X]:((strong(X)|~curious(X)))) | old(lucy) | [
"p0",
"p2",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5950721377316831607343644
% SZS output start Proof for 5950721377316831607343644
1. ! [X0] : ((calm(X0) | ~kind(X0)) => generous(X0)) [input p0]
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => ~strong(X0)) [input p2]
7. ! [X0] : ((generous(X0) <~> tall(X0)) <=> old(X0)) [input p6]
9. ! [X0] : (tall(X0) <=> (~strong(X0) | ~rich(X0))) [input p8]
16. ~calm(lucy) <~> ~generous(lucy) [input p15]
20. old(lucy) [input hypothesis]
25. ! [X0] : (generous(X0) | (~calm(X0) & kind(X0))) [ennf transformation 1]
26. ! [X0] : (~strong(X0) | (generous(X0) & calm(X0))) [ennf transformation 3]
40. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ~old(X0)) & (old(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 7]
41. ! [X0] : ((tall(X0) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | ~tall(X0))) [nnf transformation 9]
42. ! [X0] : ((tall(X0) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ~tall(X0))) [flattening 41]
53. (generous(lucy) | calm(lucy)) & (~generous(lucy) | ~calm(lucy)) [nnf transformation 16]
57. ~calm(X0) | generous(X0) [cnf transformation 25]
61. ~strong(X0) | calm(X0) [cnf transformation 26]
76. ~tall(X0) | ~generous(X0) | ~old(X0) [cnf transformation 40]
81. tall(X0) | strong(X0) [cnf transformation 42]
105. ~generous(lucy) | ~calm(lucy) [cnf transformation 53]
106. generous(lucy) | calm(lucy) [cnf transformation 53]
108. old(lucy) [cnf transformation 20]
193. generous(lucy) [subsumption resolution 106,57]
194. ~calm(lucy) [subsumption resolution 105,193]
301. ~old(X0) | ~generous(X0) | strong(X0) [resolution 76,81]
356. 32 <=> strong(lucy) [avatar definition]
357. ~strong(lucy) <- (~32) [avatar component clause 356]
358. strong(lucy) <- (32) [avatar component clause 356]
366. calm(lucy) <- (32) [resolution 358,61]
367. $false <- (32) [subsumption resolution 366,194]
368. ~32 [avatar contradiction clause 367]
372. ~generous(lucy) | strong(lucy) [resolution 301,108]
375. strong(lucy) [subsumption resolution 372,193]
376. $false <- (~32) [subsumption resolution 375,357]
377. 32 [avatar contradiction clause 376]
378. $false [avatar sat refutation 368,377]
% SZS output end Proof for 5950721377316831607343644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Paul is not funny. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~funny(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2597314663851810193226743
% SZS output start Proof for 2597314663851810193226743
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p1]
3. ? [X0] : ~old(X0) <=> ~calm(susan) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) => ~curious(X0)) [input p3]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
8. ? [X0] : brave(X0) <=> (~rich(fred) & kind(fred)) [input p7]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> old(X0)) => (humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (~strong(X0) => brave(X0)) [input p11]
21. ~funny(paul) [input hypothesis]
22. ! [X0] : (~curious(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> generous(X0)) | (~creative(X0) <=> old(X0))) [ennf transformation 10]
24. ! [X0] : (brave(X0) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
30. ! [X0] : (((~humble(X0) | ~curious(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | ~curious(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [flattening 30]
32. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X0] : old(X0)) [nnf transformation 3]
33. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [rectify 32]
34. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
35. (~old(sK0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [skolemisation 33,34]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
45. (? [X0] : brave(X0) | (rich(fred) | ~kind(fred))) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
46. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
49. (brave(sK2) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 23]
66. brave(X0) | generous(X0) | rich(X0) [cnf transformation 29]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
68. brave(X0) | calm(X0) | rich(X0) [cnf transformation 29]
70. ~creative(X0) | ~calm(X0) | curious(X0) [cnf transformation 31]
76. ~calm(susan) | old(X1) [cnf transformation 35]
77. ~old(sK0) | calm(susan) [cnf transformation 35]
78. ~strong(X0) | ~curious(X0) [cnf transformation 22]
80. old(X0) | humble(X0) | brave(X0) | rich(X0) [cnf transformation 37]
85. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
97. kind(fred) | ~brave(X1) [cnf transformation 49]
98. ~rich(fred) | ~brave(X1) [cnf transformation 49]
99. brave(sK2) | rich(fred) | ~kind(fred) [cnf transformation 49]
100. ~old(X0) | brave(X0) | funny(X0) [cnf transformation 51]
101. ~funny(X0) | old(X0) [cnf transformation 51]
102. ~brave(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~generous(X0) | old(X0) | creative(X0) [cnf transformation 52]
113. strong(X0) | brave(X0) [cnf transformation 24]
132. ~funny(paul) [cnf transformation 21]
134. 1 <=> calm(susan) [avatar definition]
138. 2 <=> old(sK0) [avatar definition]
140. ~old(sK0) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 77,138,134]
143. 3 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (3) [avatar component clause 143]
145. 3 | ~1 [avatar split clause 76,134,143]
175. 10 <=> kind(fred) [avatar definition]
179. 11 <=> rich(fred) [avatar definition]
183. 12 <=> brave(sK2) [avatar definition]
185. brave(sK2) <- (12) [avatar component clause 183]
186. ~10 | 11 | 12 [avatar split clause 99,183,179,175]
188. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (13) [avatar component clause 188]
190. 13 | ~11 [avatar split clause 98,179,188]
191. 13 | 10 [avatar split clause 97,175,188]
201. 16 <=> funny(paul) [avatar definition]
202. ~funny(paul) <- (~16) [avatar component clause 201]
265. ~16 [avatar split clause 132,201]
273. old(sK2) <- (12) [resolution 102,185]
274. ~curious(X0) | brave(X0) [resolution 113,78]
288. ~rich(sK2) | generous(sK2) <- (12) [resolution 67,185]
292. ~rich(sK2) <- (12) [subsumption resolution 288,87]
343. rich(sK2) | ~brave(sK2) <- (12) [resolution 85,273]
350. ~brave(sK2) <- (12) [subsumption resolution 343,292]
351. $false <- (12) [subsumption resolution 350,185]
352. ~12 [avatar contradiction clause 351]
367. rich(X0) | calm(X0) <- (13) [resolution 189,68]
368. rich(X1) | generous(X1) <- (13) [resolution 189,66]
430. humble(sK0) | brave(sK0) | rich(sK0) <- (~2) [resolution 80,140]
437. humble(sK0) | rich(sK0) <- (~2, 13) [subsumption resolution 430,189]
439. 40 <=> rich(sK0) [avatar definition]
440. ~rich(sK0) <- (~40) [avatar component clause 439]
441. rich(sK0) <- (40) [avatar component clause 439]
443. 41 <=> humble(sK0) [avatar definition]
445. humble(sK0) <- (41) [avatar component clause 443]
446. 40 | 41 | 2 | ~13 [avatar split clause 437,188,138,443,439]
450. funny(sK0) <- (40) [resolution 441,88]
454. 42 <=> generous(sK0) [avatar definition]
458. 43 <=> calm(sK0) [avatar definition]
459. calm(sK0) <- (43) [avatar component clause 458]
465. old(sK0) <- (40) [resolution 450,101]
466. $false <- (~2, 40) [subsumption resolution 465,140]
467. 2 | ~40 [avatar contradiction clause 466]
491. 46 <=> curious(sK0) [avatar definition]
493. curious(sK0) <- (46) [avatar component clause 491]
583. calm(sK0) <- (13, ~40) [resolution 367,440]
586. 43 | ~13 | 40 [avatar split clause 583,439,188,458]
593. brave(X2) | funny(X2) <- (3) [resolution 144,100]
597. funny(X2) <- (3, 13) [subsumption resolution 593,189]
600. ~generous(sK0) | old(sK0) | creative(sK0) <- (41) [resolution 445,105]
606. $false <- (3, 13, ~16) [resolution 597,202]
609. ~3 | ~13 | 16 [avatar contradiction clause 606]
617. generous(sK0) <- (13, ~40) [resolution 368,440]
624. 42 | ~13 | 40 [avatar split clause 617,439,188,454]
625. ~generous(sK0) | creative(sK0) <- (~2, 41) [subsumption resolution 600,140]
627. 58 <=> creative(sK0) [avatar definition]
629. creative(sK0) <- (58) [avatar component clause 627]
630. 58 | ~42 | 2 | ~41 [avatar split clause 625,443,138,454,627]
680. ~calm(sK0) | curious(sK0) <- (58) [resolution 629,70]
681. curious(sK0) <- (43, 58) [subsumption resolution 680,459]
682. 46 | ~43 | ~58 [avatar split clause 681,627,458,491]
683. brave(sK0) <- (46) [resolution 493,274]
685. $false <- (13, 46) [subsumption resolution 683,189]
686. ~13 | ~46 [avatar contradiction clause 685]
687. $false [avatar sat refutation 141,145,186,190,191,265,352,446,467,586,609,624,630,682,686]
% SZS output end Proof for 2597314663851810193226743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not curious is not brave and vice versa. If someone is both strong and brave then someone is not brave or not kind. Everyone who is quiet or calm is both not humble and wise and vice versa. Everyone who is either not quiet or not happy is not patient. If someone is both happy and funny then someone is strong. Everyone who is both patient and not rich is humble and vice versa. Everyone who is both not rich and not quiet is not calm or not brave and vice versa. If someone is rich then someone is strong. Everyone who is not rich or not kind is not quiet and vice versa. Everyone who is both happy and not happy is kind and vice versa. If alice is funny then mary is either not humble or generous. If john is old then someone is not creative or patient. If lucy is not creative or not funny then alice is either not strong or curious and vice versa. If john is rich then lucy is either curious or humble. Everyone who is both generous and not happy is not quiet. If someone is both curious and funny then susan is old and vice versa. Someone is rich or not rich. Mary is either not patient or not wise. Fred is not old or not wise. Susan is both strong and not brave. Fred is both brave and not generous. Someone is both not quiet and not rich. | Mary is not kind. | entailment | (![X]:((calm(X)|~curious(X))<=>~brave(X)))&
((?[X]:((strong(X)&brave(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~humble(X)&wise(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>~patient(X)))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(strong(X))))&
(![X]:((patient(X)&~rich(X))<=>humble(X)))&
(![X]:((~rich(X)&~quiet(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(rich(X)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)|~kind(X))<=>~quiet(X)))&
(![X]:((happy(X)&~happy(X))<=>kind(X)))&
((funny(alice))=>((~humble(mary)<~>generous(mary))))&
((old(john))=>(?[X]:((~creative(X)|patient(X)))))&
(((~creative(lucy)|~funny(lucy)))<=>((~strong(alice)<~>curious(alice))))&
((rich(john))=>((curious(lucy)<~>humble(lucy))))&
(![X]:((generous(X)&~happy(X))=>~quiet(X)))&
((?[X]:((curious(X)&funny(X))))<=>(old(susan)))&
(?[X]:((rich(X)|~rich(X))))&
((~patient(mary)<~>~wise(mary)))&
((~old(fred)|~wise(fred)))&
((strong(susan)&~brave(susan)))&
((brave(fred)&~generous(fred)))&
(?[X]:((~quiet(X)&~rich(X)))) | ~kind(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8338539827389042542848318
% SZS output start Proof for 8338539827389042542848318
10. ! [X0] : ((~happy(X0) & happy(X0)) <=> kind(X0)) [input p9]
23. kind(mary) [input hypothesis]
56. ! [X0] : (((~happy(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | (happy(X0) | ~happy(X0)))) [nnf transformation 10]
57. ! [X0] : (((~happy(X0) & happy(X0)) | ~kind(X0)) & (kind(X0) | happy(X0) | ~happy(X0))) [flattening 56]
98. happy(X0) | ~kind(X0) [cnf transformation 57]
99. ~happy(X0) | ~kind(X0) [cnf transformation 57]
125. kind(mary) [cnf transformation 23]
154. ~kind(X0) [subsumption resolution 98,99]
255. $false [subsumption resolution 125,154]
% SZS output end Proof for 8338539827389042542848318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not funny or wise and vice versa. Everyone who is either happy or not generous is not funny or old and vice versa. Everyone who is not creative is not generous or not curious. Everyone who is not brave is brave or not generous and vice versa. If someone is brave or patient then alice is either not humble or not funny and vice versa. If someone is tall then someone is not humble. If lucy is generous then someone is creative or funny. If paul is funny then mary is not rich and vice versa. If someone is not wise or strong then someone is not kind or creative. If susan is either not quiet or not tall then someone is brave and vice versa. If someone is either curious or patient then susan is either not patient or not curious. Everyone who is kind is either not tall or not quiet and vice versa. If someone is both not strong and humble then fred is not rich or not creative and vice versa. Everyone who is generous or brave is either not humble or rich. Everyone who is both brave and not humble is either not creative or calm. Everyone who is both not old and not funny is patient or not calm and vice versa. Mary is both kind and funny. Alice is either calm or patient. Someone is rich or not happy. Someone is either calm or generous. Fred is either funny or wise. Someone is quiet or not generous. Someone is not brave. Someone is not brave or not quiet. | Alice is not generous. | entailment | (![X]:(~tall(X)<=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~funny(X)|old(X))))&
(![X]:(~creative(X)=>(~generous(X)|~curious(X))))&
(![X]:(~brave(X)<=>(brave(X)|~generous(X))))&
((?[X]:((brave(X)|patient(X))))<=>((~humble(alice)<~>~funny(alice))))&
((?[X]:(tall(X)))=>(?[X]:(~humble(X))))&
((generous(lucy))=>(?[X]:((creative(X)|funny(X)))))&
((funny(paul))<=>(~rich(mary)))&
((?[X]:((~wise(X)|strong(X))))=>(?[X]:((~kind(X)|creative(X)))))&
(((~quiet(susan)<~>~tall(susan)))<=>(?[X]:(brave(X))))&
((?[X]:((curious(X)<~>patient(X))))=>((~patient(susan)<~>~curious(susan))))&
(![X]:(kind(X)<=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&humble(X))))<=>((~rich(fred)|~creative(fred))))&
(![X]:((generous(X)|brave(X))=>(~humble(X)<~>rich(X))))&
(![X]:((brave(X)&~humble(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~old(X)&~funny(X))<=>(patient(X)|~calm(X))))&
((kind(mary)&funny(mary)))&
((calm(alice)<~>patient(alice)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((calm(X)<~>generous(X))))&
((funny(fred)<~>wise(fred)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|~quiet(X)))) | ~generous(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 880890022853272224867569
% SZS output start Proof for 880890022853272224867569
4. ! [X0] : (~brave(X0) <=> (~generous(X0) | brave(X0))) [input p3]
25. generous(alice) [input hypothesis]
41. ! [X0] : ((~brave(X0) | (generous(X0) & ~brave(X0))) & ((~generous(X0) | brave(X0)) | brave(X0))) [nnf transformation 4]
42. ! [X0] : ((~brave(X0) | (generous(X0) & ~brave(X0))) & (~generous(X0) | brave(X0) | brave(X0))) [flattening 41]
94. ~generous(X0) | brave(X0) | brave(X0) [cnf transformation 42]
95. ~brave(X0) | ~brave(X0) [cnf transformation 42]
149. generous(alice) [cnf transformation 25]
150. ~generous(X0) | brave(X0) [duplicate literal removal 94]
151. ~brave(X0) [duplicate literal removal 95]
152. ~generous(X0) [subsumption resolution 150,151]
292. $false [subsumption resolution 149,152]
% SZS output end Proof for 880890022853272224867569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both wise and not generous and vice versa. If mary is both wise and not kind then someone is either humble or brave. Everyone who is both happy and strong is not humble. Everyone who is not happy or not tall is not humble. Everyone who is either not brave or not happy is either not quiet or not happy. Everyone who is both quiet and not curious is either old or not strong. If someone is not funny then someone is both not calm and not brave. Everyone who is creative is not creative or happy. Everyone who is not strong is both not funny and not brave and vice versa. If mary is either quiet or generous then someone is old or not happy and vice versa. Everyone who is not quiet is either not quiet or funny. Everyone who is either not curious or not humble is both not tall and rich. Everyone who is either not creative or kind is either not quiet or not wise. Everyone who is either not kind or quiet is not calm or happy and vice versa. If lucy is not wise or not kind then someone is tall and vice versa. Someone is both strong and not humble. Someone is not funny. Alice is not wise or generous. Someone is both not calm and not tall. Someone is funny or humble. Lucy is both quiet and happy. Someone is brave or not calm. | Alice is not humble. | entailment | (![X]:(~wise(X)<=>(wise(X)&~generous(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((happy(X)&strong(X))=>~humble(X)))&
(![X]:((~happy(X)|~tall(X))=>~humble(X)))&
(![X]:((~brave(X)<~>~happy(X))=>(~quiet(X)<~>~happy(X))))&
(![X]:((quiet(X)&~curious(X))=>(old(X)<~>~strong(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:(creative(X)=>(~creative(X)|happy(X))))&
(![X]:(~strong(X)<=>(~funny(X)&~brave(X))))&
(((quiet(mary)<~>generous(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:(~quiet(X)=>(~quiet(X)<~>funny(X))))&
(![X]:((~curious(X)<~>~humble(X))=>(~tall(X)&rich(X))))&
(![X]:((~creative(X)<~>kind(X))=>(~quiet(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~calm(X)|happy(X))))&
(((~wise(lucy)|~kind(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:((strong(X)&~humble(X))))&
(?[X]:(~funny(X)))&
((~wise(alice)|generous(alice)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((funny(X)|humble(X))))&
((quiet(lucy)&happy(lucy)))&
(?[X]:((brave(X)|~calm(X)))) | ~humble(alice) | [
"p0",
"p3",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3658056939820050331520983
% SZS output start Proof for 3658056939820050331520983
1. ! [X0] : (~wise(X0) <=> (~generous(X0) & wise(X0))) [input p0]
4. ! [X0] : ((~tall(X0) | ~happy(X0)) => ~humble(X0)) [input p3]
14. ! [X0] : ((~kind(X0) <~> quiet(X0)) <=> (happy(X0) | ~calm(X0))) [input p13]
15. (~kind(lucy) | ~wise(lucy)) <=> ? [X0] : tall(X0) [input p14]
21. happy(lucy) & quiet(lucy) [input p20]
23. humble(alice) [input hypothesis]
30. ! [X0] : (~humble(X0) | (tall(X0) & happy(X0))) [ennf transformation 4]
40. ! [X0] : ((~wise(X0) | (generous(X0) | ~wise(X0))) & ((~generous(X0) & wise(X0)) | wise(X0))) [nnf transformation 1]
41. ! [X0] : ((~wise(X0) | generous(X0) | ~wise(X0)) & ((~generous(X0) & wise(X0)) | wise(X0))) [flattening 40]
59. ! [X0] : ((((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0))))) [flattening 59]
61. ((~kind(lucy) | ~wise(lucy)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (kind(lucy) & wise(lucy))) [nnf transformation 15]
62. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (kind(lucy) & wise(lucy))) [flattening 61]
63. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | (kind(lucy) & wise(lucy))) [rectify 62]
64. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
65. (~kind(lucy) | ~wise(lucy) | ! [X0] : ~tall(X0)) & (tall(sK3) | (kind(lucy) & wise(lucy))) [skolemisation 63,64]
76. wise(X0) | wise(X0) [cnf transformation 41]
83. ~humble(X0) | tall(X0) [cnf transformation 30]
115. ~quiet(X0) | kind(X0) | ~happy(X0) [cnf transformation 60]
118. ~kind(lucy) | ~wise(lucy) | ~tall(X0) [cnf transformation 65]
126. quiet(lucy) [cnf transformation 21]
127. happy(lucy) [cnf transformation 21]
129. humble(alice) [cnf transformation 23]
134. wise(X0) [duplicate literal removal 76]
196. ~kind(lucy) | ~tall(X0) [subsumption resolution 118,134]
198. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
199. ~tall(X0) <- (13) [avatar component clause 198]
201. 14 <=> kind(lucy) [avatar definition]
203. ~kind(lucy) <- (~14) [avatar component clause 201]
204. 13 | ~14 [avatar split clause 196,201,198]
230. tall(alice) [resolution 83,129]
232. $false <- (13) [subsumption resolution 230,199]
233. ~13 [avatar contradiction clause 232]
309. kind(lucy) | ~happy(lucy) [resolution 115,126]
310. ~happy(lucy) <- (~14) [subsumption resolution 309,203]
311. $false <- (~14) [subsumption resolution 310,127]
312. 14 [avatar contradiction clause 311]
313. $false [avatar sat refutation 204,233,312]
% SZS output end Proof for 3658056939820050331520983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not patient is patient or not old. Everyone who is not quiet or wise is calm. If someone is not calm or quiet then alice is both generous and humble. Everyone who is either curious or tall is either not wise or not quiet. If someone is either kind or not kind then alice is kind or not happy. If mary is either not brave or tall then alice is either wise or tall and vice versa. If susan is both old and calm then paul is either not kind or not quiet and vice versa. Everyone who is either not patient or not old is either not calm or not old. If someone is calm then someone is either not brave or not generous and vice versa. If alice is old then someone is either not calm or not happy and vice versa. Everyone who is either tall or old is not tall or kind and vice versa. If someone is either humble or not kind then someone is not patient or not tall and vice versa. Everyone who is not calm or not curious is both patient and wise. If susan is either not strong or not happy then someone is either not wise or not old. Everyone who is both not generous and creative is either not patient or humble and vice versa. Someone is both curious and not strong. Mary is either quiet or curious. Mary is either tall or brave. Someone is creative. Mary is either not rich or happy. John is not wise or not kind. | Alice is not tall. | contradiction | (![X]:((~tall(X)<~>~patient(X))=>(patient(X)|~old(X))))&
(![X]:((~quiet(X)|wise(X))=>calm(X)))&
((?[X]:((~calm(X)|quiet(X))))=>((generous(alice)&humble(alice))))&
(![X]:((curious(X)<~>tall(X))=>(~wise(X)<~>~quiet(X))))&
((?[X]:((kind(X)<~>~kind(X))))=>((kind(alice)|~happy(alice))))&
(((~brave(mary)<~>tall(mary)))<=>((wise(alice)<~>tall(alice))))&
(((old(susan)&calm(susan)))<=>((~kind(paul)<~>~quiet(paul))))&
(![X]:((~patient(X)<~>~old(X))=>(~calm(X)<~>~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((old(alice))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((tall(X)<~>old(X))<=>(~tall(X)|kind(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~calm(X)|~curious(X))=>(patient(X)&wise(X))))&
(((~strong(susan)<~>~happy(susan)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(?[X]:((curious(X)&~strong(X))))&
((quiet(mary)<~>curious(mary)))&
((tall(mary)<~>brave(mary)))&
(?[X]:(creative(X)))&
((~rich(mary)<~>happy(mary)))&
((~wise(john)|~kind(john))) | ~tall(alice) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3541735168247820848843284
% SZS output start Proof for 3541735168247820848843284
3. ? [X0] : (quiet(X0) | ~calm(X0)) => (humble(alice) & generous(alice)) [input p2]
4. ! [X0] : ((curious(X0) <~> tall(X0)) => (~wise(X0) <~> ~quiet(X0))) [input p3]
6. (~brave(mary) <~> tall(mary)) <=> (wise(alice) <~> tall(alice)) [input p5]
8. ! [X0] : ((~patient(X0) <~> ~old(X0)) => (~calm(X0) <~> ~old(X0))) [input p7]
11. ! [X0] : ((tall(X0) <~> old(X0)) <=> (kind(X0) | ~tall(X0))) [input p10]
13. ! [X0] : ((~curious(X0) | ~calm(X0)) => (wise(X0) & patient(X0))) [input p12]
15. ! [X0] : ((creative(X0) & ~generous(X0)) <=> (~patient(X0) <~> humble(X0))) [input p14]
18. tall(mary) <~> brave(mary) [input p17]
22. ~tall(alice) [input hypothesis]
28. (humble(alice) & generous(alice)) | ! [X0] : (~quiet(X0) & calm(X0)) [ennf transformation 3]
29. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 4]
32. ! [X0] : ((~calm(X0) <~> ~old(X0)) | (~patient(X0) <=> ~old(X0))) [ennf transformation 8]
33. ! [X0] : ((wise(X0) & patient(X0)) | (curious(X0) & calm(X0))) [ennf transformation 13]
36. ! [X0] : (((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 29]
38. (((~tall(mary) | brave(mary)) & (tall(mary) | ~brave(mary))) | ((wise(alice) | ~tall(alice)) & (tall(alice) | ~wise(alice)))) & (((~tall(alice) | ~wise(alice)) & (tall(alice) | wise(alice))) | ((~brave(mary) | ~tall(mary)) & (tall(mary) | brave(mary)))) [nnf transformation 6]
41. ! [X0] : (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) [nnf transformation 32]
51. ! [X0] : ((((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | (~kind(X0) & tall(X0))) & ((kind(X0) | ~tall(X0)) | ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | (~kind(X0) & tall(X0))) & (kind(X0) | ~tall(X0) | ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))))) [flattening 51]
61. ! [X0] : (((creative(X0) & ~generous(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~creative(X0) | generous(X0)))) [nnf transformation 15]
62. ! [X0] : (((creative(X0) & ~generous(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0)))) & (((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | ~creative(X0) | generous(X0))) [flattening 61]
66. (~brave(mary) | ~tall(mary)) & (brave(mary) | tall(mary)) [nnf transformation 18]
75. generous(alice) | ~quiet(X0) [cnf transformation 28]
77. humble(alice) | ~quiet(X0) [cnf transformation 28]
80. ~curious(X0) | wise(X0) | tall(X0) | quiet(X0) [cnf transformation 36]
88. tall(mary) | ~brave(mary) | tall(alice) | ~wise(alice) [cnf transformation 38]
90. ~tall(mary) | brave(mary) | tall(alice) | ~wise(alice) [cnf transformation 38]
98. ~old(X0) | ~calm(X0) | ~old(X0) | patient(X0) [cnf transformation 41]
112. old(X0) | tall(X0) | tall(X0) [cnf transformation 52]
122. calm(X0) | patient(X0) [cnf transformation 33]
125. curious(X0) | wise(X0) [cnf transformation 33]
133. ~humble(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 62]
140. brave(mary) | tall(mary) [cnf transformation 66]
141. ~brave(mary) | ~tall(mary) [cnf transformation 66]
146. ~tall(alice) [cnf transformation 22]
148. old(X0) | tall(X0) [duplicate literal removal 112]
149. ~calm(X0) | ~old(X0) | patient(X0) [duplicate literal removal 98]
155. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
156. ~quiet(X0) <- (1) [avatar component clause 155]
158. 2 <=> humble(alice) [avatar definition]
160. humble(alice) <- (2) [avatar component clause 158]
161. 1 | 2 [avatar split clause 77,158,155]
167. 4 <=> generous(alice) [avatar definition]
169. generous(alice) <- (4) [avatar component clause 167]
170. 1 | 4 [avatar split clause 75,167,155]
189. 9 <=> tall(alice) [avatar definition]
191. ~tall(alice) <- (~9) [avatar component clause 189]
193. 10 <=> wise(alice) [avatar definition]
194. ~wise(alice) <- (~10) [avatar component clause 193]
197. 11 <=> brave(mary) [avatar definition]
201. 12 <=> tall(mary) [avatar definition]
205. ~10 | 9 | 11 | ~12 [avatar split clause 90,201,197,189,193]
207. ~10 | 9 | ~11 | 12 [avatar split clause 88,201,197,189,193]
263. 24 <=> old(alice) [avatar definition]
264. ~old(alice) <- (~24) [avatar component clause 263]
265. old(alice) <- (24) [avatar component clause 263]
348. ~12 | ~11 [avatar split clause 141,197,201]
349. 12 | 11 [avatar split clause 140,197,201]
369. ~9 [avatar split clause 146,189]
378. tall(alice) <- (~24) [resolution 148,264]
380. $false <- (~9, ~24) [subsumption resolution 378,191]
381. 9 | 24 [avatar contradiction clause 380]
401. ~patient(alice) | ~generous(alice) <- (2) [resolution 133,160]
402. ~patient(alice) <- (2, 4) [subsumption resolution 401,169]
404. ~old(X0) | patient(X0) | patient(X0) [resolution 149,122]
407. ~old(X0) | patient(X0) [duplicate literal removal 404]
410. patient(alice) <- (24) [resolution 407,265]
414. $false <- (2, 4, 24) [subsumption resolution 410,402]
415. ~2 | ~4 | ~24 [avatar contradiction clause 414]
432. wise(X0) | tall(X0) | quiet(X0) | wise(X0) [resolution 80,125]
435. wise(X0) | tall(X0) | quiet(X0) [duplicate literal removal 432]
446. wise(X0) | tall(X0) <- (1) [subsumption resolution 435,156]
451. tall(alice) <- (1, ~10) [resolution 446,194]
454. $false <- (1, ~9, ~10) [subsumption resolution 451,191]
455. ~1 | 9 | 10 [avatar contradiction clause 454]
456. $false [avatar sat refutation 161,170,205,207,348,349,369,381,415,455]
% SZS output end Proof for 3541735168247820848843284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not creative is wise and vice versa.
Everyone who is not calm is both not generous and happy and vice versa.
If fred is not old then someone is not creative or brave and vice versa.
Everyone who is curious is not curious or not rich and vice versa.
If alice is not creative then john is kind or curious.
Everyone who is both brave and wise is either not patient or not strong.
Everyone who is either generous or not happy is either wise or creative.
If someone is either wise or patient then fred is not brave.
Everyone who is not quiet or not brave is not generous.
Everyone who is either brave or not wise is either kind or not patient and vice versa.
If someone is both calm and patient then someone is either not curious or strong.
Everyone who is not happy is either patient or funny and vice versa.
Everyone who is not funny is quiet.
Everyone who is not old or calm is kind or funny and vice versa.
If lucy is either not creative or not strong then alice is not rich.
If someone is strong then someone is patient.
John is either generous or calm.
Someone is not old.
Someone is both brave and curious.
Paul is either not tall or strong.
Someone is not wise.
Someone is generous.
Someone is not creative. | Alice is kind. | neutral | (![X]:((quiet(X)<~>~creative(X))<=>wise(X)))&
(![X]:(~calm(X)<=>(~generous(X)&happy(X))))&
((~old(fred))<=>(?[X]:((~creative(X)|brave(X)))))&
(![X]:(curious(X)<=>(~curious(X)|~rich(X))))&
((~creative(alice))=>((kind(john)|curious(john))))&
(![X]:((brave(X)&wise(X))=>(~patient(X)<~>~strong(X))))&
(![X]:((generous(X)<~>~happy(X))=>(wise(X)<~>creative(X))))&
((?[X]:((wise(X)<~>patient(X))))=>(~brave(fred)))&
(![X]:((~quiet(X)|~brave(X))=>~generous(X)))&
(![X]:((brave(X)<~>~wise(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:(~happy(X)<=>(patient(X)<~>funny(X))))&
(![X]:(~funny(X)=>quiet(X)))&
(![X]:((~old(X)|calm(X))<=>(kind(X)|funny(X))))&
(((~creative(lucy)<~>~strong(lucy)))=>(~rich(alice)))&
((?[X]:(strong(X)))=>(?[X]:(patient(X))))&
((generous(john)<~>calm(john)))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)&curious(X))))&
((~tall(paul)<~>strong(paul)))&
(?[X]:(~wise(X)))&
(?[X]:(generous(X)))&
(?[X]:(~creative(X))) | kind(alice) | [] | null | 0 |
If lucy is either not wise or tall then someone is both not creative and not kind and vice versa.
Everyone who is not tall is either not creative or not kind and vice versa.
Everyone who is creative or not quiet is not wise.
Everyone who is not brave or not old is not happy and vice versa.
Everyone who is wise is happy.
Everyone who is both creative and brave is not tall or not calm.
Everyone who is either rich or not wise is either not quiet or not wise.
If someone is creative then fred is creative and vice versa.
If someone is generous or not happy then mary is both not quiet and humble.
Everyone who is rich or quiet is wise.
Everyone who is not quiet or not tall is either tall or kind and vice versa.
If alice is either not old or not creative then someone is quiet and vice versa.
If mary is either not generous or not quiet then someone is either curious or not strong and vice versa.
If paul is both not calm and not kind then someone is both rich and brave and vice versa.
Everyone who is either generous or not funny is either strong or happy and vice versa.
Someone is rich or not creative.
Someone is kind or brave.
Someone is either not creative or not strong.
John is happy.
Mary is either not patient or calm. | Mary is funny. | neutral | (((~wise(lucy)<~>tall(lucy)))<=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(~tall(X)<=>(~creative(X)<~>~kind(X))))&
(![X]:((creative(X)|~quiet(X))=>~wise(X)))&
(![X]:((~brave(X)|~old(X))<=>~happy(X)))&
(![X]:(wise(X)=>happy(X)))&
(![X]:((creative(X)&brave(X))=>(~tall(X)|~calm(X))))&
(![X]:((rich(X)<~>~wise(X))=>(~quiet(X)<~>~wise(X))))&
((?[X]:(creative(X)))<=>(creative(fred)))&
((?[X]:((generous(X)|~happy(X))))=>((~quiet(mary)&humble(mary))))&
(![X]:((rich(X)|quiet(X))=>wise(X)))&
(![X]:((~quiet(X)|~tall(X))<=>(tall(X)<~>kind(X))))&
(((~old(alice)<~>~creative(alice)))<=>(?[X]:(quiet(X))))&
(((~generous(mary)<~>~quiet(mary)))<=>(?[X]:((curious(X)<~>~strong(X)))))&
(((~calm(paul)&~kind(paul)))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(strong(X)<~>happy(X))))&
(?[X]:((rich(X)|~creative(X))))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~creative(X)<~>~strong(X))))&
(happy(john))&
((~patient(mary)<~>calm(mary))) | funny(mary) | [] | null | 0 |
If fred is generous then someone is rich and vice versa.
If someone is not curious then someone is not happy or not patient.
If paul is tall then alice is both curious and not old.
Everyone who is generous or not kind is quiet.
If paul is either funny or not kind then someone is either not curious or calm.
Everyone who is both not old and not kind is both not creative and old and vice versa.
Everyone who is both not wise and tall is not old.
Everyone who is funny or not strong is not happy.
Everyone who is patient or not kind is both not quiet and not generous and vice versa.
Everyone who is generous is tall or happy and vice versa.
If someone is curious or not rich then fred is both kind and not funny.
Everyone who is not tall is not calm.
Everyone who is not quiet or rich is brave or not strong.
Everyone who is rich or not happy is either strong or generous and vice versa.
If mary is strong or curious then john is creative or not tall and vice versa.
Everyone who is not happy or old is tall.
Susan is either not creative or not brave.
Someone is not patient or not creative.
Someone is not happy.
Someone is both creative and old.
Someone is both generous and kind.
Someone is not generous or happy. | Fred is generous. | entailment | ((generous(fred))<=>(?[X]:(rich(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~happy(X)|~patient(X)))))&
((tall(paul))=>((curious(alice)&~old(alice))))&
(![X]:((generous(X)|~kind(X))=>quiet(X)))&
(((funny(paul)<~>~kind(paul)))=>(?[X]:((~curious(X)<~>calm(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~creative(X)&old(X))))&
(![X]:((~wise(X)&tall(X))=>~old(X)))&
(![X]:((funny(X)|~strong(X))=>~happy(X)))&
(![X]:((patient(X)|~kind(X))<=>(~quiet(X)&~generous(X))))&
(![X]:(generous(X)<=>(tall(X)|happy(X))))&
((?[X]:((curious(X)|~rich(X))))=>((kind(fred)&~funny(fred))))&
(![X]:(~tall(X)=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))=>(brave(X)|~strong(X))))&
(![X]:((rich(X)|~happy(X))<=>(strong(X)<~>generous(X))))&
(((strong(mary)|curious(mary)))<=>((creative(john)|~tall(john))))&
(![X]:((~happy(X)|old(X))=>tall(X)))&
((~creative(susan)<~>~brave(susan)))&
(?[X]:((~patient(X)|~creative(X))))&
(?[X]:(~happy(X)))&
(?[X]:((creative(X)&old(X))))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:((~generous(X)|happy(X)))) | generous(fred) | [
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6178272428759667894137953
% SZS output start Proof for 6178272428759667894137953
10. ! [X0] : (generous(X0) <=> (happy(X0) | tall(X0))) [input p9]
16. ! [X0] : ((old(X0) | ~happy(X0)) => tall(X0)) [input p15]
23. ~generous(fred) [input hypothesis]
35. ! [X0] : (tall(X0) | (~old(X0) & happy(X0))) [ennf transformation 16]
50. ! [X0] : ((generous(X0) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | ~generous(X0))) [nnf transformation 10]
51. ! [X0] : ((generous(X0) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ~generous(X0))) [flattening 50]
90. ~tall(X0) | generous(X0) [cnf transformation 51]
91. ~happy(X0) | generous(X0) [cnf transformation 51]
109. tall(X0) | happy(X0) [cnf transformation 35]
120. ~generous(fred) [cnf transformation 23]
127. 2 <=> generous(fred) [avatar definition]
128. ~generous(fred) <- (~2) [avatar component clause 127]
246. ~2 [avatar split clause 120,127]
256. happy(X0) | generous(X0) [resolution 109,90]
257. generous(X0) [subsumption resolution 256,91]
261. $false <- (~2) [resolution 257,128]
266. 2 [avatar contradiction clause 261]
267. $false [avatar sat refutation 246,266]
% SZS output end Proof for 6178272428759667894137953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either calm or not strong.
Everyone who is not brave is not kind and vice versa.
Everyone who is not old or not curious is either not old or curious.
Everyone who is either brave or patient is either happy or calm.
If lucy is both not kind and not happy then someone is not rich or calm and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either patient or strong is either wise or not brave and vice versa.
If susan is both quiet and not curious then someone is either not quiet or not happy.
Everyone who is not brave or not rich is both not funny and kind and vice versa.
Everyone who is curious or not patient is either funny or not quiet.
If someone is both not tall and kind then john is both not old and not wise.
Everyone who is tall or calm is either not funny or patient.
If alice is either creative or curious then paul is either brave or curious.
If someone is both happy and humble then lucy is not old or wise and vice versa.
If john is either not rich or not old then someone is wise and vice versa.
Someone is both creative and tall.
Susan is both kind and generous.
Mary is brave or not generous.
Someone is rich.
Someone is either not wise or humble.
Someone is not quiet or strong. | Susan is not funny. | contradiction | (![X]:(~humble(X)=>(calm(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>~kind(X)))&
(![X]:((~old(X)|~curious(X))=>(~old(X)<~>curious(X))))&
(![X]:((brave(X)<~>patient(X))=>(happy(X)<~>calm(X))))&
(((~kind(lucy)&~happy(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((patient(X)<~>strong(X))<=>(wise(X)<~>~brave(X))))&
(((quiet(susan)&~curious(susan)))=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~rich(X))<=>(~funny(X)&kind(X))))&
(![X]:((curious(X)|~patient(X))=>(funny(X)<~>~quiet(X))))&
((?[X]:((~tall(X)&kind(X))))=>((~old(john)&~wise(john))))&
(![X]:((tall(X)|calm(X))=>(~funny(X)<~>patient(X))))&
(((creative(alice)<~>curious(alice)))=>((brave(paul)<~>curious(paul))))&
((?[X]:((happy(X)&humble(X))))<=>((~old(lucy)|wise(lucy))))&
(((~rich(john)<~>~old(john)))<=>(?[X]:(wise(X))))&
(?[X]:((creative(X)&tall(X))))&
((kind(susan)&generous(susan)))&
((brave(mary)|~generous(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((~quiet(X)|strong(X)))) | ~funny(susan) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6713347795141868220419042
% SZS output start Proof for 6713347795141868220419042
2. ! [X0] : (~brave(X0) <=> ~kind(X0)) [input p1]
5. (~happy(lucy) & ~kind(lucy)) <=> ? [X0] : (calm(X0) | ~rich(X0)) [input p4]
9. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> (kind(X0) & ~funny(X0))) [input p8]
22. ~funny(susan) [input hypothesis]
33. ! [X0] : ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))) [nnf transformation 2]
36. ((~happy(lucy) & ~kind(lucy)) | ! [X0] : (~calm(X0) & rich(X0))) & (? [X0] : (calm(X0) | ~rich(X0)) | (happy(lucy) | kind(lucy))) [nnf transformation 5]
37. ((~happy(lucy) & ~kind(lucy)) | ! [X0] : (~calm(X0) & rich(X0))) & (? [X0] : (calm(X0) | ~rich(X0)) | happy(lucy) | kind(lucy)) [flattening 36]
38. ((~happy(lucy) & ~kind(lucy)) | ! [X0] : (~calm(X0) & rich(X0))) & (? [X1] : (calm(X1) | ~rich(X1)) | happy(lucy) | kind(lucy)) [rectify 37]
39. ? [X1] : (calm(X1) | ~rich(X1)) => (calm(sK0) | ~rich(sK0)) [choice axiom]
40. ((~happy(lucy) & ~kind(lucy)) | ! [X0] : (~calm(X0) & rich(X0))) & ((calm(sK0) | ~rich(sK0)) | happy(lucy) | kind(lucy)) [skolemisation 38,39]
46. ! [X0] : (((~rich(X0) | ~brave(X0)) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | (rich(X0) & brave(X0)))) [nnf transformation 9]
47. ! [X0] : ((~rich(X0) | ~brave(X0) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | (rich(X0) & brave(X0)))) [flattening 46]
71. ~kind(X0) | brave(X0) [cnf transformation 33]
72. ~brave(X0) | kind(X0) [cnf transformation 33]
82. ~kind(lucy) | rich(X0) [cnf transformation 40]
100. kind(X0) | brave(X0) [cnf transformation 47]
102. ~rich(X0) | ~brave(X0) | ~kind(X0) | funny(X0) [cnf transformation 47]
135. ~funny(susan) [cnf transformation 22]
147. 3 <=> ! [X0] : rich(X0) [avatar definition]
148. rich(X0) <- (3) [avatar component clause 147]
151. 4 <=> kind(lucy) [avatar definition]
153. ~kind(lucy) <- (~4) [avatar component clause 151]
155. 3 | ~4 [avatar split clause 82,151,147]
183. ~rich(X0) | ~kind(X0) | funny(X0) [subsumption resolution 102,71]
184. kind(X0) [subsumption resolution 100,72]
289. $false <- (~4) [subsumption resolution 153,184]
290. 4 [avatar contradiction clause 289]
318. ~kind(X1) | funny(X1) <- (3) [resolution 183,148]
320. funny(X1) <- (3) [subsumption resolution 318,184]
338. $false <- (3) [resolution 320,135]
347. ~3 [avatar contradiction clause 338]
348. $false [avatar sat refutation 155,290,347]
% SZS output end Proof for 6713347795141868220419042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or quiet is both funny and wise and vice versa.
Everyone who is kind is either calm or not funny and vice versa.
If someone is both patient and not curious then someone is calm and vice versa.
If lucy is funny then paul is either wise or not kind and vice versa.
If someone is both creative and not generous then someone is both brave and funny and vice versa.
If paul is both funny and not calm then someone is not patient.
Everyone who is calm is both not curious and creative.
If alice is both calm and not strong then someone is both not quiet and not brave.
Everyone who is not strong or strong is both wise and not patient.
If john is both brave and not generous then susan is either not creative or humble.
Everyone who is either brave or not happy is not creative or old and vice versa.
If paul is both not generous and not curious then someone is either wise or not happy.
If someone is either not curious or patient then paul is not calm and vice versa.
Everyone who is either not old or patient is both not happy and not kind.
Mary is either generous or not old.
Fred is either not patient or patient.
Someone is either humble or not strong.
Paul is not generous or strong.
Lucy is both old and brave.
Someone is either not rich or not quiet.
John is not wise or old.
Fred is both not generous and not quiet. | John is not patient. | entailment | (![X]:((old(X)<~>quiet(X))<=>(funny(X)&wise(X))))&
(![X]:(kind(X)<=>(calm(X)<~>~funny(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:(calm(X))))&
((funny(lucy))<=>((wise(paul)<~>~kind(paul))))&
((?[X]:((creative(X)&~generous(X))))<=>(?[X]:((brave(X)&funny(X)))))&
(((funny(paul)&~calm(paul)))=>(?[X]:(~patient(X))))&
(![X]:(calm(X)=>(~curious(X)&creative(X))))&
(((calm(alice)&~strong(alice)))=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:((~strong(X)|strong(X))=>(wise(X)&~patient(X))))&
(((brave(john)&~generous(john)))=>((~creative(susan)<~>humble(susan))))&
(![X]:((brave(X)<~>~happy(X))<=>(~creative(X)|old(X))))&
(((~generous(paul)&~curious(paul)))=>(?[X]:((wise(X)<~>~happy(X)))))&
((?[X]:((~curious(X)<~>patient(X))))<=>(~calm(paul)))&
(![X]:((~old(X)<~>patient(X))=>(~happy(X)&~kind(X))))&
((generous(mary)<~>~old(mary)))&
((~patient(fred)<~>patient(fred)))&
(?[X]:((humble(X)<~>~strong(X))))&
((~generous(paul)|strong(paul)))&
((old(lucy)&brave(lucy)))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((~wise(john)|old(john)))&
((~generous(fred)&~quiet(fred))) | ~patient(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4725722045701246269697142
% SZS output start Proof for 4725722045701246269697142
9. ! [X0] : ((strong(X0) | ~strong(X0)) => (~patient(X0) & wise(X0))) [input p8]
23. patient(john) [input hypothesis]
31. ! [X0] : ((~patient(X0) & wise(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 9]
102. ~patient(X0) | strong(X0) [cnf transformation 31]
103. ~patient(X0) | ~strong(X0) [cnf transformation 31]
136. patient(john) [cnf transformation 23]
231. ~patient(X0) [subsumption resolution 102,103]
314. $false [subsumption resolution 136,231]
% SZS output end Proof for 4725722045701246269697142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not funny and vice versa. If someone is either old or patient then john is either generous or wise. Everyone who is calm is both not humble and quiet and vice versa. Everyone who is either happy or not curious is old or not patient. If someone is not generous then paul is not kind or not funny. Everyone who is both old and not wise is patient or happy and vice versa. If someone is not funny or not rich then mary is either not wise or curious. Everyone who is not calm is not old and vice versa. If someone is both not humble and patient then susan is either not patient or not brave and vice versa. If someone is both not funny and not patient then someone is either not generous or rich. Everyone who is not brave is both not humble and curious. If someone is not quiet then lucy is both not patient and not curious and vice versa. Everyone who is both wise and not patient is both old and not old. If john is not happy or not quiet then someone is wise and vice versa. Everyone who is either generous or not funny is either not creative or tall and vice versa. If mary is both funny and not kind then lucy is both quiet and not kind. Someone is not humble or not creative. Mary is not quiet. Someone is not brave or not generous. Mary is both creative and not calm. Someone is either kind or not tall. Lucy is either strong or not creative. Someone is either not kind or funny. Someone is not generous or tall. | Mary is not funny. | contradiction | (![X]:(happy(X)<=>~funny(X)))&
((?[X]:((old(X)<~>patient(X))))=>((generous(john)<~>wise(john))))&
(![X]:(calm(X)<=>(~humble(X)&quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>(old(X)|~patient(X))))&
((?[X]:(~generous(X)))=>((~kind(paul)|~funny(paul))))&
(![X]:((old(X)&~wise(X))<=>(patient(X)|happy(X))))&
((?[X]:((~funny(X)|~rich(X))))=>((~wise(mary)<~>curious(mary))))&
(![X]:(~calm(X)<=>~old(X)))&
((?[X]:((~humble(X)&patient(X))))<=>((~patient(susan)<~>~brave(susan))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:(~brave(X)=>(~humble(X)&curious(X))))&
((?[X]:(~quiet(X)))<=>((~patient(lucy)&~curious(lucy))))&
(![X]:((wise(X)&~patient(X))=>(old(X)&~old(X))))&
(((~happy(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~creative(X)<~>tall(X))))&
(((funny(mary)&~kind(mary)))=>((quiet(lucy)&~kind(lucy))))&
(?[X]:((~humble(X)|~creative(X))))&
(~quiet(mary))&
(?[X]:((~brave(X)|~generous(X))))&
((creative(mary)&~calm(mary)))&
(?[X]:((kind(X)<~>~tall(X))))&
((strong(lucy)<~>~creative(lucy)))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:((~generous(X)|tall(X)))) | ~funny(mary) | [
"p0",
"p5",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2910434157874251388827068
% SZS output start Proof for 2910434157874251388827068
1. ! [X0] : (happy(X0) <=> ~funny(X0)) [input p0]
6. ! [X0] : ((~wise(X0) & old(X0)) <=> (happy(X0) | patient(X0))) [input p5]
8. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p7]
20. ~calm(mary) & creative(mary) [input p19]
25. ~funny(mary) [input hypothesis]
39. ! [X0] : ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))) [nnf transformation 1]
44. ! [X0] : (((~wise(X0) & old(X0)) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~wise(X0) & old(X0)) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | wise(X0) | ~old(X0))) [flattening 44]
47. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 8]
81. funny(X0) | happy(X0) [cnf transformation 39]
94. ~happy(X0) | old(X0) [cnf transformation 45]
101. ~old(X0) | calm(X0) [cnf transformation 47]
135. ~calm(mary) [cnf transformation 20]
143. ~funny(mary) [cnf transformation 25]
255. 24 <=> funny(mary) [avatar definition]
257. ~funny(mary) <- (~24) [avatar component clause 255]
329. ~24 [avatar split clause 143,255]
334. happy(mary) <- (~24) [resolution 81,257]
338. old(mary) <- (~24) [resolution 94,334]
342. calm(mary) <- (~24) [resolution 101,338]
343. $false <- (~24) [subsumption resolution 342,135]
344. 24 [avatar contradiction clause 343]
345. $false [avatar sat refutation 329,344]
% SZS output end Proof for 2910434157874251388827068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not generous is calm or creative and vice versa.
If susan is not brave then alice is not curious.
If someone is both not calm and happy then susan is either kind or wise and vice versa.
If someone is both not quiet and not calm then susan is both tall and not creative.
Everyone who is not patient is strong and vice versa.
Everyone who is either not kind or not strong is creative and vice versa.
Everyone who is both not quiet and not happy is creative or not rich.
If someone is either not humble or creative then fred is not calm or not humble and vice versa.
Everyone who is either calm or kind is both old and humble.
If someone is both kind and not calm then someone is not creative or generous and vice versa.
Everyone who is both kind and not kind is not tall.
Everyone who is calm is kind or wise and vice versa.
Everyone who is generous is both not rich and not old and vice versa.
Everyone who is not tall or tall is not rich and vice versa.
If paul is old then someone is both calm and patient.
If someone is either not wise or not generous then someone is not patient or not quiet and vice versa.
Someone is wise.
Someone is both curious and calm.
Someone is calm or not tall.
Someone is both creative and not brave.
Paul is either brave or wise.
Someone is both not strong and patient. | Paul is generous. | contradiction | (![X]:((old(X)&~generous(X))<=>(calm(X)|creative(X))))&
((~brave(susan))=>(~curious(alice)))&
((?[X]:((~calm(X)&happy(X))))<=>((kind(susan)<~>wise(susan))))&
((?[X]:((~quiet(X)&~calm(X))))=>((tall(susan)&~creative(susan))))&
(![X]:(~patient(X)<=>strong(X)))&
(![X]:((~kind(X)<~>~strong(X))<=>creative(X)))&
(![X]:((~quiet(X)&~happy(X))=>(creative(X)|~rich(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>((~calm(fred)|~humble(fred))))&
(![X]:((calm(X)<~>kind(X))=>(old(X)&humble(X))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~creative(X)|generous(X)))))&
(![X]:((kind(X)&~kind(X))=>~tall(X)))&
(![X]:(calm(X)<=>(kind(X)|wise(X))))&
(![X]:(generous(X)<=>(~rich(X)&~old(X))))&
(![X]:((~tall(X)|tall(X))<=>~rich(X)))&
((old(paul))=>(?[X]:((calm(X)&patient(X)))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|~quiet(X)))))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
((brave(paul)<~>wise(paul)))&
(?[X]:((~strong(X)&patient(X)))) | generous(paul) | [
"p0",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7475332572849421924966431
% SZS output start Proof for 7475332572849421924966431
1. ! [X0] : ((~generous(X0) & old(X0)) <=> (creative(X0) | calm(X0))) [input p0]
10. ? [X0] : (~calm(X0) & kind(X0)) <=> ? [X0] : (generous(X0) | ~creative(X0)) [input p9]
12. ! [X0] : (calm(X0) <=> (wise(X0) | kind(X0))) [input p11]
13. ! [X0] : (generous(X0) <=> (~old(X0) & ~rich(X0))) [input p12]
23. generous(paul) [input hypothesis]
24. ? [X0] : (~calm(X0) & kind(X0)) <=> ? [X1] : (generous(X1) | ~creative(X1)) [rectify 10]
34. ! [X0] : (((~generous(X0) & old(X0)) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | (generous(X0) | ~old(X0)))) [nnf transformation 1]
35. ! [X0] : (((~generous(X0) & old(X0)) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | generous(X0) | ~old(X0))) [flattening 34]
48. (? [X0] : (~calm(X0) & kind(X0)) | ! [X1] : (~generous(X1) & creative(X1))) & (? [X1] : (generous(X1) | ~creative(X1)) | ! [X0] : (calm(X0) | ~kind(X0))) [nnf transformation 24]
49. (? [X0] : (~calm(X0) & kind(X0)) | ! [X1] : (~generous(X1) & creative(X1))) & (? [X2] : (generous(X2) | ~creative(X2)) | ! [X3] : (calm(X3) | ~kind(X3))) [rectify 48]
50. ? [X0] : (~calm(X0) & kind(X0)) => (~calm(sK2) & kind(sK2)) [choice axiom]
51. ? [X2] : (generous(X2) | ~creative(X2)) => (generous(sK3) | ~creative(sK3)) [choice axiom]
52. ((~calm(sK2) & kind(sK2)) | ! [X1] : (~generous(X1) & creative(X1))) & ((generous(sK3) | ~creative(sK3)) | ! [X3] : (calm(X3) | ~kind(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((calm(X0) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | ~calm(X0))) [nnf transformation 12]
54. ! [X0] : ((calm(X0) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~calm(X0))) [flattening 53]
55. ! [X0] : ((generous(X0) | (old(X0) | rich(X0))) & ((~old(X0) & ~rich(X0)) | ~generous(X0))) [nnf transformation 13]
56. ! [X0] : ((generous(X0) | old(X0) | rich(X0)) & ((~old(X0) & ~rich(X0)) | ~generous(X0))) [flattening 55]
79. ~creative(X0) | old(X0) [cnf transformation 35]
109. kind(sK2) | creative(X1) [cnf transformation 52]
111. ~calm(sK2) | creative(X1) [cnf transformation 52]
115. calm(X0) | ~kind(X0) [cnf transformation 54]
118. ~generous(X0) | ~old(X0) [cnf transformation 56]
141. generous(paul) [cnf transformation 23]
222. 18 <=> calm(sK2) [avatar definition]
224. ~calm(sK2) <- (~18) [avatar component clause 222]
227. 19 <=> ! [X1] : creative(X1) [avatar definition]
228. creative(X1) <- (19) [avatar component clause 227]
229. 19 | ~18 [avatar split clause 111,222,227]
231. 20 <=> kind(sK2) [avatar definition]
233. kind(sK2) <- (20) [avatar component clause 231]
235. 19 | 20 [avatar split clause 109,231,227]
238. 21 <=> ! [X3] : (calm(X3) | ~kind(X3)) [avatar definition]
239. ~kind(X3) | calm(X3) <- (21) [avatar component clause 238]
245. 21 [avatar split clause 115,238]
248. 23 <=> old(paul) [avatar definition]
250. ~old(paul) <- (~23) [avatar component clause 248]
320. old(X0) <- (19) [resolution 79,228]
322. $false <- (19, ~23) [resolution 320,250]
323. ~19 | 23 [avatar contradiction clause 322]
336. ~old(paul) [resolution 118,141]
339. ~23 [avatar split clause 336,248]
345. calm(sK2) <- (20, 21) [resolution 239,233]
346. $false <- (~18, 20, 21) [subsumption resolution 345,224]
347. 18 | ~20 | ~21 [avatar contradiction clause 346]
348. $false [avatar sat refutation 229,235,245,323,339,347]
% SZS output end Proof for 7475332572849421924966431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not tall or not strong then fred is patient or curious and vice versa.
If someone is creative then someone is both wise and not funny.
Everyone who is not quiet is both happy and brave.
Everyone who is not rich is either generous or not rich.
Everyone who is not strong is patient or funny.
Everyone who is not kind or not tall is either happy or generous.
If fred is either not generous or quiet then someone is not calm or happy and vice versa.
If someone is either not curious or not tall then someone is both not patient and funny.
Everyone who is not patient is both not generous and not curious and vice versa.
Everyone who is not wise or not old is brave and vice versa.
Everyone who is strong is either patient or not generous and vice versa.
If john is not calm then someone is both happy and brave.
If john is both not brave and not funny then someone is generous and vice versa.
If someone is either quiet or not patient then mary is generous.
Everyone who is both not patient and not curious is not humble or not curious and vice versa.
Everyone who is quiet or tall is either not generous or patient and vice versa.
Someone is not old.
John is either brave or funny.
Lucy is either humble or not generous.
Someone is not tall.
Someone is humble or happy.
Lucy is either not quiet or happy.
Someone is either brave or curious.
Someone is either strong or not kind. | Fred is strong. | contradiction | (((~tall(paul)|~strong(paul)))<=>((patient(fred)|curious(fred))))&
((?[X]:(creative(X)))=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:(~quiet(X)=>(happy(X)&brave(X))))&
(![X]:(~rich(X)=>(generous(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(patient(X)|funny(X))))&
(![X]:((~kind(X)|~tall(X))=>(happy(X)<~>generous(X))))&
(((~generous(fred)<~>quiet(fred)))<=>(?[X]:((~calm(X)|happy(X)))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:(~patient(X)<=>(~generous(X)&~curious(X))))&
(![X]:((~wise(X)|~old(X))<=>brave(X)))&
(![X]:(strong(X)<=>(patient(X)<~>~generous(X))))&
((~calm(john))=>(?[X]:((happy(X)&brave(X)))))&
(((~brave(john)&~funny(john)))<=>(?[X]:(generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))=>(generous(mary)))&
(![X]:((~patient(X)&~curious(X))<=>(~humble(X)|~curious(X))))&
(![X]:((quiet(X)|tall(X))<=>(~generous(X)<~>patient(X))))&
(?[X]:(~old(X)))&
((brave(john)<~>funny(john)))&
((humble(lucy)<~>~generous(lucy)))&
(?[X]:(~tall(X)))&
(?[X]:((humble(X)|happy(X))))&
((~quiet(lucy)<~>happy(lucy)))&
(?[X]:((brave(X)<~>curious(X))))&
(?[X]:((strong(X)<~>~kind(X)))) | strong(fred) | [
"p2",
"p6",
"p10",
"p12",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 696049487986755728447356
% SZS output start Proof for 696049487986755728447356
3. ! [X0] : (~quiet(X0) => (brave(X0) & happy(X0))) [input p2]
7. (~generous(fred) <~> quiet(fred)) <=> ? [X0] : (happy(X0) | ~calm(X0)) [input p6]
11. ! [X0] : (strong(X0) <=> (patient(X0) <~> ~generous(X0))) [input p10]
13. (~funny(john) & ~brave(john)) <=> ? [X0] : generous(X0) [input p12]
14. ? [X0] : (quiet(X0) <~> ~patient(X0)) => generous(mary) [input p13]
18. brave(john) <~> funny(john) [input p17]
22. ~quiet(lucy) <~> happy(lucy) [input p21]
25. strong(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) & happy(X0)) | quiet(X0)) [ennf transformation 3]
36. generous(mary) | ! [X0] : (quiet(X0) <=> ~patient(X0)) [ennf transformation 14]
41. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & (? [X0] : (happy(X0) | ~calm(X0)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [nnf transformation 7]
42. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & (? [X1] : (happy(X1) | ~calm(X1)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [rectify 41]
43. ? [X1] : (happy(X1) | ~calm(X1)) => (happy(sK0) | ~calm(sK0)) [choice axiom]
44. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & ((happy(sK0) | ~calm(sK0)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [skolemisation 42,43]
53. ! [X0] : ((strong(X0) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 11]
56. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (funny(john) | brave(john))) [nnf transformation 13]
57. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | funny(john) | brave(john)) [flattening 56]
58. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | funny(john) | brave(john)) [rectify 57]
59. ? [X1] : generous(X1) => generous(sK3) [choice axiom]
60. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (generous(sK3) | funny(john) | brave(john)) [skolemisation 58,59]
61. generous(mary) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))) [nnf transformation 36]
68. (~funny(john) | ~brave(john)) & (funny(john) | brave(john)) [nnf transformation 18]
74. (~happy(lucy) | quiet(lucy)) & (happy(lucy) | ~quiet(lucy)) [nnf transformation 22]
85. happy(X0) | quiet(X0) [cnf transformation 29]
99. ~quiet(fred) | generous(fred) | ~happy(X0) [cnf transformation 44]
111. ~patient(X0) | generous(X0) | ~strong(X0) [cnf transformation 53]
117. ~brave(john) | ~generous(X0) [cnf transformation 60]
118. ~funny(john) | ~generous(X0) [cnf transformation 60]
120. generous(mary) | quiet(X0) | patient(X0) [cnf transformation 61]
133. funny(john) | brave(john) [cnf transformation 68]
139. happy(lucy) | ~quiet(lucy) [cnf transformation 74]
140. ~happy(lucy) | quiet(lucy) [cnf transformation 74]
145. strong(fred) [cnf transformation 25]
161. 4 <=> patient(fred) [avatar definition]
162. patient(fred) <- (4) [avatar component clause 161]
163. ~patient(fred) <- (~4) [avatar component clause 161]
168. 5 <=> ! [X0] : ~happy(X0) [avatar definition]
169. ~happy(X0) <- (5) [avatar component clause 168]
171. 6 <=> generous(fred) [avatar definition]
173. generous(fred) <- (6) [avatar component clause 171]
175. 7 <=> quiet(fred) [avatar definition]
177. ~quiet(fred) <- (~7) [avatar component clause 175]
178. 5 | 6 | ~7 [avatar split clause 99,175,171,168]
230. 18 <=> ! [X0] : ~generous(X0) [avatar definition]
231. ~generous(X0) <- (18) [avatar component clause 230]
233. 19 <=> funny(john) [avatar definition]
236. 18 | ~19 [avatar split clause 118,233,230]
238. 20 <=> brave(john) [avatar definition]
241. 18 | ~20 [avatar split clause 117,238,230]
248. 22 <=> ! [X0] : (quiet(X0) | patient(X0)) [avatar definition]
249. quiet(X0) | patient(X0) <- (22) [avatar component clause 248]
251. 23 <=> generous(mary) [avatar definition]
253. generous(mary) <- (23) [avatar component clause 251]
254. 22 | 23 [avatar split clause 120,251,248]
262. 20 | 19 [avatar split clause 133,233,238]
282. quiet(lucy) [subsumption resolution 140,85]
283. happy(lucy) [subsumption resolution 139,282]
304. $false <- (18, 23) [resolution 253,231]
305. ~18 | ~23 [avatar contradiction clause 304]
313. patient(fred) <- (~7, 22) [resolution 249,177]
314. $false <- (~4, ~7, 22) [subsumption resolution 313,163]
315. 4 | 7 | ~22 [avatar contradiction clause 314]
316. $false <- (6, 18) [subsumption resolution 173,231]
317. ~6 | ~18 [avatar contradiction clause 316]
318. $false <- (5) [resolution 169,283]
320. ~5 [avatar contradiction clause 318]
353. generous(fred) | ~strong(fred) <- (4) [resolution 111,162]
354. ~strong(fred) <- (4, 18) [subsumption resolution 353,231]
355. $false <- (4, 18) [subsumption resolution 354,145]
356. ~4 | ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 178,236,241,254,262,305,315,317,320,356]
% SZS output end Proof for 696049487986755728447356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is humble or patient.
Everyone who is either humble or brave is both wise and generous.
If someone is both not strong and creative then susan is both strong and not creative and vice versa.
Everyone who is either not quiet or happy is both old and wise.
Everyone who is both not happy and quiet is both brave and rich and vice versa.
If alice is both rich and kind then fred is either not wise or quiet and vice versa.
If someone is both kind and not kind then john is not calm or patient.
Everyone who is brave is either rich or curious.
If susan is either wise or not strong then john is either not quiet or kind and vice versa.
Everyone who is both not wise and not brave is not humble and vice versa.
Everyone who is either not wise or curious is both not strong and strong and vice versa.
Everyone who is kind or brave is kind and vice versa.
If someone is generous then someone is both not happy and generous and vice versa.
If lucy is curious then fred is quiet or not brave and vice versa.
Everyone who is either not curious or quiet is both humble and not calm.
Someone is quiet or not brave.
Someone is not patient.
John is either brave or quiet.
Susan is generous.
Someone is both tall and not quiet.
Someone is old or not strong.
Someone is not tall or not kind. | Alice is not tall. | neutral | ((?[X]:(funny(X)))=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((humble(X)<~>brave(X))=>(wise(X)&generous(X))))&
((?[X]:((~strong(X)&creative(X))))<=>((strong(susan)&~creative(susan))))&
(![X]:((~quiet(X)<~>happy(X))=>(old(X)&wise(X))))&
(![X]:((~happy(X)&quiet(X))<=>(brave(X)&rich(X))))&
(((rich(alice)&kind(alice)))<=>((~wise(fred)<~>quiet(fred))))&
((?[X]:((kind(X)&~kind(X))))=>((~calm(john)|patient(john))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(((wise(susan)<~>~strong(susan)))<=>((~quiet(john)<~>kind(john))))&
(![X]:((~wise(X)&~brave(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>curious(X))<=>(~strong(X)&strong(X))))&
(![X]:((kind(X)|brave(X))<=>kind(X)))&
((?[X]:(generous(X)))<=>(?[X]:((~happy(X)&generous(X)))))&
((curious(lucy))<=>((quiet(fred)|~brave(fred))))&
(![X]:((~curious(X)<~>quiet(X))=>(humble(X)&~calm(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:(~patient(X)))&
((brave(john)<~>quiet(john)))&
(generous(susan))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((old(X)|~strong(X))))&
(?[X]:((~tall(X)|~kind(X)))) | ~tall(alice) | [] | null | 0 |
If someone is not humble or not funny then someone is not creative and vice versa.
Everyone who is not patient is not strong and vice versa.
If someone is rich then someone is either quiet or wise and vice versa.
If mary is not curious then john is not funny.
Everyone who is not old is both patient and not happy.
If someone is old then paul is happy and vice versa.
Everyone who is either curious or creative is not brave or not rich.
If mary is happy then someone is not humble or not generous and vice versa.
Everyone who is either not humble or not calm is either strong or not strong and vice versa.
Everyone who is either happy or curious is strong.
If someone is humble or funny then someone is either not creative or not calm.
Everyone who is not funny or kind is generous or rich.
Everyone who is both not tall and not old is either wise or not rich.
If john is either not old or calm then someone is not quiet or tall.
If someone is both not curious and calm then lucy is both patient and tall.
Everyone who is not humble or not quiet is not curious and vice versa.
Someone is patient.
Someone is not humble or not old.
Someone is either humble or happy.
Paul is not old.
Someone is curious or not creative.
Fred is not calm.
Someone is either calm or generous. | John is not calm. | entailment | ((?[X]:((~humble(X)|~funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~patient(X)<=>~strong(X)))&
((?[X]:(rich(X)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
((~curious(mary))=>(~funny(john)))&
(![X]:(~old(X)=>(patient(X)&~happy(X))))&
((?[X]:(old(X)))<=>(happy(paul)))&
(![X]:((curious(X)<~>creative(X))=>(~brave(X)|~rich(X))))&
((happy(mary))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((happy(X)<~>curious(X))=>strong(X)))&
((?[X]:((humble(X)|funny(X))))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~funny(X)|kind(X))=>(generous(X)|rich(X))))&
(![X]:((~tall(X)&~old(X))=>(wise(X)<~>~rich(X))))&
(((~old(john)<~>calm(john)))=>(?[X]:((~quiet(X)|tall(X)))))&
((?[X]:((~curious(X)&calm(X))))=>((patient(lucy)&tall(lucy))))&
(![X]:((~humble(X)|~quiet(X))<=>~curious(X)))&
(?[X]:(patient(X)))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((humble(X)<~>happy(X))))&
(~old(paul))&
(?[X]:((curious(X)|~creative(X))))&
(~calm(fred))&
(?[X]:((calm(X)<~>generous(X)))) | ~calm(john) | [
"p4",
"p5",
"p7",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1812756622786715791122468
% SZS output start Proof for 1812756622786715791122468
5. ! [X0] : (~old(X0) => (~happy(X0) & patient(X0))) [input p4]
6. ? [X0] : old(X0) <=> happy(paul) [input p5]
8. happy(mary) <=> ? [X0] : (~generous(X0) | ~humble(X0)) [input p7]
9. ! [X0] : ((~humble(X0) <~> ~calm(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p8]
20. ~old(paul) [input p19]
24. calm(john) [input hypothesis]
36. ! [X0] : ((~happy(X0) & patient(X0)) | old(X0)) [ennf transformation 5]
52. (? [X0] : old(X0) | ~happy(paul)) & (happy(paul) | ! [X0] : ~old(X0)) [nnf transformation 6]
53. (? [X0] : old(X0) | ~happy(paul)) & (happy(paul) | ! [X1] : ~old(X1)) [rectify 52]
54. ? [X0] : old(X0) => old(sK4) [choice axiom]
55. (old(sK4) | ~happy(paul)) & (happy(paul) | ! [X1] : ~old(X1)) [skolemisation 53,54]
56. (happy(mary) | ! [X0] : (generous(X0) & humble(X0))) & (? [X0] : (~generous(X0) | ~humble(X0)) | ~happy(mary)) [nnf transformation 8]
57. (happy(mary) | ! [X0] : (generous(X0) & humble(X0))) & (? [X1] : (~generous(X1) | ~humble(X1)) | ~happy(mary)) [rectify 56]
58. ? [X1] : (~generous(X1) | ~humble(X1)) => (~generous(sK5) | ~humble(sK5)) [choice axiom]
59. (happy(mary) | ! [X0] : (generous(X0) & humble(X0))) & ((~generous(sK5) | ~humble(sK5)) | ~happy(mary)) [skolemisation 57,58]
60. ! [X0] : ((((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0))))) [nnf transformation 9]
90. ~happy(X0) | old(X0) [cnf transformation 36]
91. happy(paul) | ~old(X1) [cnf transformation 55]
94. happy(mary) | humble(X0) [cnf transformation 59]
100. ~calm(X0) | ~humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 60]
101. ~calm(X0) | ~humble(X0) | strong(X0) | strong(X0) [cnf transformation 60]
119. ~old(paul) [cnf transformation 20]
124. calm(john) [cnf transformation 24]
125. ~calm(X0) | ~humble(X0) | ~strong(X0) [duplicate literal removal 100]
126. ~calm(X0) | ~humble(X0) | strong(X0) [duplicate literal removal 101]
150. 6 <=> ! [X3] : humble(X3) [avatar definition]
151. humble(X3) <- (6) [avatar component clause 150]
188. 15 <=> happy(paul) [avatar definition]
189. happy(paul) <- (15) [avatar component clause 188]
197. 17 <=> ! [X1] : ~old(X1) [avatar definition]
198. ~old(X1) <- (17) [avatar component clause 197]
199. 17 | 15 [avatar split clause 91,188,197]
204. 19 <=> happy(mary) [avatar definition]
206. happy(mary) <- (19) [avatar component clause 204]
208. 6 | 19 [avatar split clause 94,204,150]
219. ~calm(X0) | ~humble(X0) [subsumption resolution 125,126]
294. old(paul) <- (15) [resolution 90,189]
295. old(mary) <- (19) [resolution 90,206]
296. $false <- (15) [subsumption resolution 294,119]
297. ~15 [avatar contradiction clause 296]
302. $false <- (17, 19) [resolution 295,198]
303. ~17 | ~19 [avatar contradiction clause 302]
310. ~humble(john) [resolution 219,124]
312. $false <- (6) [subsumption resolution 310,151]
313. ~6 [avatar contradiction clause 312]
314. $false [avatar sat refutation 199,208,297,303,313]
% SZS output end Proof for 1812756622786715791122468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or funny is not quiet and vice versa.
Everyone who is not happy or kind is either creative or happy.
Everyone who is either curious or brave is not old or not generous and vice versa.
Everyone who is kind or humble is not curious and vice versa.
If someone is not curious then mary is both creative and kind and vice versa.
If paul is patient then john is humble and vice versa.
Everyone who is either not funny or not brave is quiet.
If someone is both not patient and not calm then alice is either not happy or not wise.
If john is not old then mary is either not patient or kind and vice versa.
Everyone who is not happy or patient is either brave or rich.
Everyone who is old or not tall is tall or patient and vice versa.
If mary is both not patient and not curious then someone is wise or not old and vice versa.
If someone is not quiet then paul is not tall or not strong and vice versa.
If someone is either not calm or not funny then someone is both funny and not creative.
Everyone who is not creative or not wise is both not calm and calm.
Everyone who is either patient or kind is both not strong and generous and vice versa.
John is humble.
Someone is not calm or calm.
Someone is both strong and not happy.
Alice is both strong and patient.
Someone is humble or not strong. | Alice is not calm. | neutral | (![X]:((~brave(X)<~>funny(X))<=>~quiet(X)))&
(![X]:((~happy(X)|kind(X))=>(creative(X)<~>happy(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~old(X)|~generous(X))))&
(![X]:((kind(X)|humble(X))<=>~curious(X)))&
((?[X]:(~curious(X)))<=>((creative(mary)&kind(mary))))&
((patient(paul))<=>(humble(john)))&
(![X]:((~funny(X)<~>~brave(X))=>quiet(X)))&
((?[X]:((~patient(X)&~calm(X))))=>((~happy(alice)<~>~wise(alice))))&
((~old(john))<=>((~patient(mary)<~>kind(mary))))&
(![X]:((~happy(X)|patient(X))=>(brave(X)<~>rich(X))))&
(![X]:((old(X)|~tall(X))<=>(tall(X)|patient(X))))&
(((~patient(mary)&~curious(mary)))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:(~quiet(X)))<=>((~tall(paul)|~strong(paul))))&
((?[X]:((~calm(X)<~>~funny(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:((~creative(X)|~wise(X))=>(~calm(X)&calm(X))))&
(![X]:((patient(X)<~>kind(X))<=>(~strong(X)&generous(X))))&
(humble(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((strong(X)&~happy(X))))&
((strong(alice)&patient(alice)))&
(?[X]:((humble(X)|~strong(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is curious or not calm is happy. If paul is both not old and happy then someone is either kind or not kind and vice versa. If someone is both patient and humble then fred is either curious or not kind. Everyone who is both tall and not creative is curious. If someone is both funny and not curious then someone is humble. If john is both not wise and curious then someone is rich or not calm and vice versa. If susan is both quiet and not happy then paul is either wise or patient. If someone is old or not humble then lucy is either not wise or kind and vice versa. If someone is either not wise or tall then someone is both not curious and not strong. Everyone who is either not brave or happy is generous. Everyone who is both generous and funny is not generous. Everyone who is both strong and curious is either not old or not funny and vice versa. If lucy is both not strong and generous then alice is either not curious or not generous. Everyone who is either old or happy is either quiet or strong and vice versa. Everyone who is calm is patient or rich. Someone is either not generous or funny. Paul is either not humble or not patient. Someone is not old. Someone is happy or not rich. Someone is happy. Someone is calm or not tall. Lucy is both generous and happy. | Fred is patient. | neutral | (![X]:((curious(X)|~calm(X))=>happy(X)))&
(((~old(paul)&happy(paul)))<=>(?[X]:((kind(X)<~>~kind(X)))))&
((?[X]:((patient(X)&humble(X))))=>((curious(fred)<~>~kind(fred))))&
(![X]:((tall(X)&~creative(X))=>curious(X)))&
((?[X]:((funny(X)&~curious(X))))=>(?[X]:(humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((rich(X)|~calm(X)))))&
(((quiet(susan)&~happy(susan)))=>((wise(paul)<~>patient(paul))))&
((?[X]:((old(X)|~humble(X))))<=>((~wise(lucy)<~>kind(lucy))))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((~curious(X)&~strong(X)))))&
(![X]:((~brave(X)<~>happy(X))=>generous(X)))&
(![X]:((generous(X)&funny(X))=>~generous(X)))&
(![X]:((strong(X)&curious(X))<=>(~old(X)<~>~funny(X))))&
(((~strong(lucy)&generous(lucy)))=>((~curious(alice)<~>~generous(alice))))&
(![X]:((old(X)<~>happy(X))<=>(quiet(X)<~>strong(X))))&
(![X]:(calm(X)=>(patient(X)|rich(X))))&
(?[X]:((~generous(X)<~>funny(X))))&
((~humble(paul)<~>~patient(paul)))&
(?[X]:(~old(X)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:(happy(X)))&
(?[X]:((calm(X)|~tall(X))))&
((generous(lucy)&happy(lucy))) | patient(fred) | [] | null | 0 |
If alice is not generous then someone is either not calm or funny.
If lucy is either creative or generous then mary is both not wise and not brave.
If someone is either not rich or not calm then paul is both not happy and wise and vice versa.
Everyone who is not humble is brave and vice versa.
Everyone who is tall is patient and vice versa.
If someone is either not humble or funny then susan is either not rich or patient.
If someone is both not tall and humble then someone is not brave and vice versa.
Everyone who is generous or humble is kind and vice versa.
If lucy is not generous or brave then susan is both creative and brave and vice versa.
Everyone who is kind or generous is happy or not tall and vice versa.
Everyone who is curious is strong or happy.
Everyone who is both happy and not generous is funny.
If alice is not generous then mary is strong or humble and vice versa.
Everyone who is both old and not wise is both generous and not curious.
Everyone who is either generous or not quiet is either not old or not tall and vice versa.
Everyone who is tall is both strong and not generous.
Alice is not humble.
Someone is both not happy and not funny.
Someone is both not funny and rich.
Someone is strong.
Someone is both not humble and patient.
John is calm or not generous.
John is either not curious or wise. | John is not patient. | neutral | ((~generous(alice))=>(?[X]:((~calm(X)<~>funny(X)))))&
(((creative(lucy)<~>generous(lucy)))=>((~wise(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~calm(X))))<=>((~happy(paul)&wise(paul))))&
(![X]:(~humble(X)<=>brave(X)))&
(![X]:(tall(X)<=>patient(X)))&
((?[X]:((~humble(X)<~>funny(X))))=>((~rich(susan)<~>patient(susan))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((generous(X)|humble(X))<=>kind(X)))&
(((~generous(lucy)|brave(lucy)))<=>((creative(susan)&brave(susan))))&
(![X]:((kind(X)|generous(X))<=>(happy(X)|~tall(X))))&
(![X]:(curious(X)=>(strong(X)|happy(X))))&
(![X]:((happy(X)&~generous(X))=>funny(X)))&
((~generous(alice))<=>((strong(mary)|humble(mary))))&
(![X]:((old(X)&~wise(X))=>(generous(X)&~curious(X))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:(tall(X)=>(strong(X)&~generous(X))))&
(~humble(alice))&
(?[X]:((~happy(X)&~funny(X))))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:(strong(X)))&
(?[X]:((~humble(X)&patient(X))))&
((calm(john)|~generous(john)))&
((~curious(john)<~>wise(john))) | ~patient(john) | [] | null | 0 |
Everyone who is not funny or calm is either not generous or not patient and vice versa. Everyone who is both not tall and humble is not tall and vice versa. Everyone who is strong is not kind. If paul is strong or old then someone is either not brave or old and vice versa. If fred is funny then someone is either not generous or not wise and vice versa. Everyone who is both generous and strong is rich or humble and vice versa. Everyone who is patient or not curious is either wise or patient and vice versa. Everyone who is both not funny and kind is both not funny and not generous. Everyone who is not humble is humble. If lucy is brave or funny then someone is not quiet. Everyone who is both old and generous is either tall or not brave. Everyone who is not generous is not wise. If susan is either brave or rich then mary is tall or creative. Everyone who is not strong or strong is either not creative or not calm. Everyone who is creative or patient is either not funny or not kind. Everyone who is either humble or quiet is not calm. Alice is not calm or not strong. Mary is both not patient and happy. John is not calm. Someone is both not happy and not quiet. Lucy is not creative. | Susan is tall. | neutral | (![X]:((~funny(X)|calm(X))<=>(~generous(X)<~>~patient(X))))&
(![X]:((~tall(X)&humble(X))<=>~tall(X)))&
(![X]:(strong(X)=>~kind(X)))&
(((strong(paul)|old(paul)))<=>(?[X]:((~brave(X)<~>old(X)))))&
((funny(fred))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((generous(X)&strong(X))<=>(rich(X)|humble(X))))&
(![X]:((patient(X)|~curious(X))<=>(wise(X)<~>patient(X))))&
(![X]:((~funny(X)&kind(X))=>(~funny(X)&~generous(X))))&
(![X]:(~humble(X)=>humble(X)))&
(((brave(lucy)|funny(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:((old(X)&generous(X))=>(tall(X)<~>~brave(X))))&
(![X]:(~generous(X)=>~wise(X)))&
(((brave(susan)<~>rich(susan)))=>((tall(mary)|creative(mary))))&
(![X]:((~strong(X)|strong(X))=>(~creative(X)<~>~calm(X))))&
(![X]:((creative(X)|patient(X))=>(~funny(X)<~>~kind(X))))&
(![X]:((humble(X)<~>quiet(X))=>~calm(X)))&
((~calm(alice)|~strong(alice)))&
((~patient(mary)&happy(mary)))&
(~calm(john))&
(?[X]:((~happy(X)&~quiet(X))))&
(~creative(lucy)) | tall(susan) | [] | null | 0 |
Everyone who is not rich or not old is either not wise or not patient.
Everyone who is either not kind or creative is not strong and vice versa.
If mary is generous then susan is not calm and vice versa.
Everyone who is not generous is not curious and vice versa.
Everyone who is both not creative and not curious is not kind or not patient and vice versa.
If someone is both not tall and not happy then susan is strong.
If john is both generous and kind then someone is either quiet or not rich.
If someone is either not creative or strong then someone is not generous or funny.
Everyone who is humble is both happy and not strong.
Everyone who is rich or not calm is either strong or humble.
Everyone who is not curious or wise is either not patient or not curious.
Everyone who is not patient or not funny is either not wise or not happy.
If john is both not funny and humble then someone is not humble or not funny.
If someone is not funny or kind then someone is curious and vice versa.
If someone is either not funny or not rich then someone is not rich and vice versa.
If someone is funny or patient then someone is not old and vice versa.
Someone is kind.
Someone is both not old and not generous.
Fred is not happy.
John is either happy or rich.
Someone is wise or brave.
Paul is either tall or calm.
Someone is generous. | John is not wise. | entailment | (![X]:((~rich(X)|~old(X))=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>creative(X))<=>~strong(X)))&
((generous(mary))<=>(~calm(susan)))&
(![X]:(~generous(X)<=>~curious(X)))&
(![X]:((~creative(X)&~curious(X))<=>(~kind(X)|~patient(X))))&
((?[X]:((~tall(X)&~happy(X))))=>(strong(susan)))&
(((generous(john)&kind(john)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~creative(X)<~>strong(X))))=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:(humble(X)=>(happy(X)&~strong(X))))&
(![X]:((rich(X)|~calm(X))=>(strong(X)<~>humble(X))))&
(![X]:((~curious(X)|wise(X))=>(~patient(X)<~>~curious(X))))&
(![X]:((~patient(X)|~funny(X))=>(~wise(X)<~>~happy(X))))&
(((~funny(john)&humble(john)))=>(?[X]:((~humble(X)|~funny(X)))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((funny(X)|patient(X))))<=>(?[X]:(~old(X))))&
(?[X]:(kind(X)))&
(?[X]:((~old(X)&~generous(X))))&
(~happy(fred))&
((happy(john)<~>rich(john)))&
(?[X]:((wise(X)|brave(X))))&
((tall(paul)<~>calm(paul)))&
(?[X]:(generous(X))) | ~wise(john) | [
"p0",
"p1",
"p4",
"p8",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4890275007614117298469461
% SZS output start Proof for 4890275007614117298469461
1. ! [X0] : ((~old(X0) | ~rich(X0)) => (~wise(X0) <~> ~patient(X0))) [input p0]
2. ! [X0] : ((~kind(X0) <~> creative(X0)) <=> ~strong(X0)) [input p1]
5. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (~patient(X0) | ~kind(X0))) [input p4]
9. ! [X0] : (humble(X0) => (~strong(X0) & happy(X0))) [input p8]
10. ! [X0] : ((~calm(X0) | rich(X0)) => (strong(X0) <~> humble(X0))) [input p9]
11. ! [X0] : ((wise(X0) | ~curious(X0)) => (~patient(X0) <~> ~curious(X0))) [input p10]
20. happy(john) <~> rich(john) [input p19]
24. wise(john) [input hypothesis]
30. ! [X0] : ((~wise(X0) <~> ~patient(X0)) | (old(X0) & rich(X0))) [ennf transformation 1]
35. ! [X0] : ((~strong(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 9]
36. ! [X0] : ((strong(X0) <~> humble(X0)) | (calm(X0) & ~rich(X0))) [ennf transformation 10]
37. ! [X0] : ((~patient(X0) <~> ~curious(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 11]
41. ! [X0] : (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (old(X0) & rich(X0))) [nnf transformation 30]
42. ! [X0] : ((((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | strong(X0)) & (~strong(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))))) [nnf transformation 2]
45. ! [X0] : (((~curious(X0) & ~creative(X0)) | (patient(X0) & kind(X0))) & ((~patient(X0) | ~kind(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 5]
46. ! [X0] : (((~curious(X0) & ~creative(X0)) | (patient(X0) & kind(X0))) & (~patient(X0) | ~kind(X0) | curious(X0) | creative(X0))) [flattening 45]
54. ! [X0] : (((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | (calm(X0) & ~rich(X0))) [nnf transformation 36]
55. ! [X0] : (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (~wise(X0) & curious(X0))) [nnf transformation 37]
78. (~rich(john) | ~happy(john)) & (rich(john) | happy(john)) [nnf transformation 20]
82. ~patient(X0) | ~wise(X0) | rich(X0) [cnf transformation 41]
86. ~strong(X0) | creative(X0) | kind(X0) [cnf transformation 42]
87. ~strong(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 42]
94. ~kind(X0) | ~patient(X0) | curious(X0) | creative(X0) [cnf transformation 46]
95. ~creative(X0) | kind(X0) [cnf transformation 46]
98. ~curious(X0) | patient(X0) [cnf transformation 46]
104. ~humble(X0) | happy(X0) [cnf transformation 35]
106. ~rich(X0) | strong(X0) | humble(X0) [cnf transformation 54]
111. ~curious(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 55]
112. curious(X0) | patient(X0) | curious(X0) [cnf transformation 55]
134. ~rich(john) | ~happy(john) [cnf transformation 78]
138. wise(john) [cnf transformation 24]
139. curious(X0) | patient(X0) [duplicate literal removal 112]
163. 6 <=> kind(john) [avatar definition]
164. kind(john) <- (6) [avatar component clause 163]
193. patient(X0) [subsumption resolution 139,98]
194. ~curious(X0) | ~wise(X0) [subsumption resolution 111,193]
200. 14 <=> humble(john) [avatar definition]
201. humble(john) <- (14) [avatar component clause 200]
202. ~humble(john) <- (~14) [avatar component clause 200]
263. 29 <=> happy(john) [avatar definition]
265. ~happy(john) <- (~29) [avatar component clause 263]
267. 30 <=> rich(john) [avatar definition]
268. rich(john) <- (30) [avatar component clause 267]
270. ~29 | ~30 [avatar split clause 134,267,263]
301. ~wise(X0) | rich(X0) [resolution 82,193]
309. rich(john) [resolution 301,138]
312. 30 [avatar split clause 309,267]
383. strong(john) | humble(john) <- (30) [resolution 106,268]
384. strong(john) <- (~14, 30) [subsumption resolution 383,202]
422. ~kind(john) | ~creative(john) <- (~14, 30) [resolution 384,87]
423. creative(john) | kind(john) <- (~14, 30) [resolution 384,86]
424. ~creative(john) <- (~14, 30) [subsumption resolution 422,95]
425. kind(john) <- (~14, 30) [subsumption resolution 423,424]
426. 6 | 14 | ~30 [avatar split clause 425,267,200,163]
428. 46 <=> strong(john) [avatar definition]
430. strong(john) <- (46) [avatar component clause 428]
431. 14 | 46 | ~30 [avatar split clause 383,267,428,200]
433. happy(john) <- (14) [resolution 201,104]
435. $false <- (14, ~29) [subsumption resolution 433,265]
436. ~14 | 29 [avatar contradiction clause 435]
437. ~patient(john) | curious(john) | creative(john) <- (6) [resolution 164,94]
439. curious(john) | creative(john) <- (6) [subsumption resolution 437,193]
441. 47 <=> creative(john) [avatar definition]
445. 48 <=> curious(john) [avatar definition]
447. curious(john) <- (48) [avatar component clause 445]
448. 47 | 48 | ~6 [avatar split clause 439,163,445,441]
464. ~kind(john) | ~creative(john) <- (46) [resolution 430,87]
466. ~creative(john) <- (6, 46) [subsumption resolution 464,164]
469. ~47 | ~6 | ~46 [avatar split clause 466,428,163,441]
470. ~wise(john) <- (48) [resolution 447,194]
474. $false <- (48) [subsumption resolution 470,138]
475. ~48 [avatar contradiction clause 474]
478. $false [avatar sat refutation 270,312,426,431,436,448,469,475]
% SZS output end Proof for 4890275007614117298469461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is rich and vice versa.
Everyone who is not wise is not curious or not patient and vice versa.
Everyone who is either brave or strong is not creative or happy and vice versa.
If someone is old then someone is brave or not funny and vice versa.
If someone is strong or brave then lucy is not humble or calm.
If john is not humble or not quiet then john is either kind or not strong and vice versa.
If alice is not strong then someone is both not kind and not old.
If someone is calm then fred is wise or not quiet.
Everyone who is both not old and not generous is both not curious and rich.
Everyone who is not kind is happy or kind.
Everyone who is tall or kind is both curious and not generous.
If someone is either rich or generous then susan is both strong and not creative and vice versa.
If alice is either funny or not calm then mary is brave and vice versa.
Everyone who is not wise is not happy or generous and vice versa.
Everyone who is both not strong and brave is creative and vice versa.
If fred is both not happy and not rich then someone is curious or not patient and vice versa.
Alice is either calm or not tall.
Paul is both not patient and funny.
John is not old.
Lucy is funny.
Lucy is both not curious and generous.
Someone is both kind and not strong.
Fred is both not calm and not generous.
Paul is both old and not brave. | Susan is generous. | neutral | (![X]:(~kind(X)<=>rich(X)))&
(![X]:(~wise(X)<=>(~curious(X)|~patient(X))))&
(![X]:((brave(X)<~>strong(X))<=>(~creative(X)|happy(X))))&
((?[X]:(old(X)))<=>(?[X]:((brave(X)|~funny(X)))))&
((?[X]:((strong(X)|brave(X))))=>((~humble(lucy)|calm(lucy))))&
(((~humble(john)|~quiet(john)))<=>((kind(john)<~>~strong(john))))&
((~strong(alice))=>(?[X]:((~kind(X)&~old(X)))))&
((?[X]:(calm(X)))=>((wise(fred)|~quiet(fred))))&
(![X]:((~old(X)&~generous(X))=>(~curious(X)&rich(X))))&
(![X]:(~kind(X)=>(happy(X)|kind(X))))&
(![X]:((tall(X)|kind(X))=>(curious(X)&~generous(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>((strong(susan)&~creative(susan))))&
(((funny(alice)<~>~calm(alice)))<=>(brave(mary)))&
(![X]:(~wise(X)<=>(~happy(X)|generous(X))))&
(![X]:((~strong(X)&brave(X))<=>creative(X)))&
(((~happy(fred)&~rich(fred)))<=>(?[X]:((curious(X)|~patient(X)))))&
((calm(alice)<~>~tall(alice)))&
((~patient(paul)&funny(paul)))&
(~old(john))&
(funny(lucy))&
((~curious(lucy)&generous(lucy)))&
(?[X]:((kind(X)&~strong(X))))&
((~calm(fred)&~generous(fred)))&
((old(paul)&~brave(paul))) | generous(susan) | [] | null | 0 |
Everyone who is old or not strong is wise or not calm.
Everyone who is either not strong or happy is not quiet and vice versa.
Everyone who is humble is wise and vice versa.
If john is both not calm and not strong then susan is not curious.
Everyone who is both rich and creative is not wise.
Everyone who is not generous or not kind is either wise or not strong and vice versa.
Everyone who is tall or not strong is not kind or not strong.
Everyone who is either not tall or strong is not creative or not brave and vice versa.
Everyone who is not humble is both tall and calm and vice versa.
If someone is brave or not old then someone is either wise or not brave and vice versa.
Everyone who is either not patient or not brave is both not kind and not rich and vice versa.
Everyone who is not wise or creative is both not calm and strong.
If someone is either patient or funny then john is quiet or not generous.
Everyone who is both not kind and generous is not strong or not old and vice versa.
Everyone who is both curious and not kind is either not wise or not happy and vice versa.
Everyone who is both generous and not curious is either brave or patient and vice versa.
Mary is not tall.
Fred is not rich or old.
Someone is quiet.
Someone is either not old or not patient.
Lucy is both old and not kind.
Susan is either not generous or not tall.
Someone is kind. | Lucy is not tall. | contradiction | (![X]:((old(X)|~strong(X))=>(wise(X)|~calm(X))))&
(![X]:((~strong(X)<~>happy(X))<=>~quiet(X)))&
(![X]:(humble(X)<=>wise(X)))&
(((~calm(john)&~strong(john)))=>(~curious(susan)))&
(![X]:((rich(X)&creative(X))=>~wise(X)))&
(![X]:((~generous(X)|~kind(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~humble(X)<=>(tall(X)&calm(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((quiet(john)|~generous(john))))&
(![X]:((~kind(X)&generous(X))<=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&~kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((generous(X)&~curious(X))<=>(brave(X)<~>patient(X))))&
(~tall(mary))&
((~rich(fred)|old(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~patient(X))))&
((old(lucy)&~kind(lucy)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(kind(X))) | ~tall(lucy) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 447943783523960904451344
% SZS output start Proof for 447943783523960904451344
3. ! [X0] : (humble(X0) <=> wise(X0)) [input p2]
5. ! [X0] : ((creative(X0) & rich(X0)) => ~wise(X0)) [input p4]
6. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p5]
8. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~brave(X0) | ~creative(X0))) [input p7]
9. ! [X0] : (~humble(X0) <=> (calm(X0) & tall(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~rich(X0) & ~kind(X0))) [input p10]
12. ! [X0] : ((creative(X0) | ~wise(X0)) => (strong(X0) & ~calm(X0))) [input p11]
14. ! [X0] : ((generous(X0) & ~kind(X0)) <=> (~old(X0) | ~strong(X0))) [input p13]
16. ! [X0] : ((~curious(X0) & generous(X0)) <=> (brave(X0) <~> patient(X0))) [input p15]
21. ~kind(lucy) & old(lucy) [input p20]
24. ~tall(lucy) [input hypothesis]
32. ! [X0] : (~wise(X0) | (~creative(X0) | ~rich(X0))) [ennf transformation 5]
33. ! [X0] : (~wise(X0) | ~creative(X0) | ~rich(X0)) [flattening 32]
36. ! [X0] : ((strong(X0) & ~calm(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 12]
40. ! [X0] : ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0))) [nnf transformation 3]
41. ! [X0] : (((~kind(X0) | ~generous(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [nnf transformation 6]
42. ! [X0] : ((~kind(X0) | ~generous(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [flattening 41]
43. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & ((~brave(X0) | ~creative(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 8]
44. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & (~brave(X0) | ~creative(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 43]
45. ! [X0] : ((~humble(X0) | (~calm(X0) | ~tall(X0))) & ((calm(X0) & tall(X0)) | humble(X0))) [nnf transformation 9]
46. ! [X0] : ((~humble(X0) | ~calm(X0) | ~tall(X0)) & ((calm(X0) & tall(X0)) | humble(X0))) [flattening 45]
52. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 11]
53. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 52]
55. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | (~generous(X0) | kind(X0)))) [nnf transformation 14]
56. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ~generous(X0) | kind(X0))) [flattening 55]
59. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (curious(X0) | ~generous(X0)))) [nnf transformation 16]
60. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | curious(X0) | ~generous(X0))) [flattening 59]
73. ~humble(X0) | wise(X0) [cnf transformation 40]
76. ~creative(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 33]
80. ~wise(X0) | strong(X0) | kind(X0) [cnf transformation 42]
89. ~strong(X0) | tall(X0) | creative(X0) [cnf transformation 44]
92. humble(X0) | calm(X0) [cnf transformation 46]
104. ~patient(X0) | ~brave(X0) | rich(X0) | kind(X0) [cnf transformation 53]
105. patient(X0) | brave(X0) | rich(X0) | kind(X0) [cnf transformation 53]
106. ~calm(X0) | wise(X0) [cnf transformation 36]
112. ~generous(X0) | ~strong(X0) | ~old(X0) | kind(X0) [cnf transformation 56]
113. ~kind(X0) | strong(X0) [cnf transformation 56]
125. ~brave(X0) | patient(X0) | generous(X0) [cnf transformation 60]
126. ~patient(X0) | brave(X0) | generous(X0) [cnf transformation 60]
134. old(lucy) [cnf transformation 21]
135. ~kind(lucy) [cnf transformation 21]
139. ~tall(lucy) [cnf transformation 24]
235. calm(X0) | wise(X0) [resolution 92,73]
236. wise(X0) [subsumption resolution 235,106]
274. strong(X0) | kind(X0) [resolution 80,236]
277. strong(X0) [subsumption resolution 274,113]
283. tall(X0) | creative(X0) [resolution 89,277]
296. creative(lucy) [resolution 283,139]
327. ~wise(lucy) | ~rich(lucy) [resolution 296,76]
330. ~rich(lucy) [subsumption resolution 327,236]
402. brave(X2) | rich(X2) | kind(X2) | brave(X2) | generous(X2) [resolution 105,126]
407. brave(X2) | rich(X2) | kind(X2) | generous(X2) [duplicate literal removal 402]
488. rich(X3) | kind(X3) | generous(X3) | patient(X3) | generous(X3) [resolution 407,125]
491. patient(X3) | kind(X3) | generous(X3) | rich(X3) [duplicate literal removal 488]
548. kind(X1) | generous(X1) | rich(X1) | ~brave(X1) | rich(X1) | kind(X1) [resolution 491,104]
554. kind(X1) | generous(X1) | rich(X1) | ~brave(X1) [duplicate literal removal 548]
555. kind(X1) | generous(X1) | rich(X1) [subsumption resolution 554,407]
571. generous(lucy) | rich(lucy) [resolution 555,135]
574. generous(lucy) [subsumption resolution 571,330]
578. ~strong(lucy) | ~old(lucy) | kind(lucy) [resolution 574,112]
592. ~old(lucy) | kind(lucy) [subsumption resolution 578,277]
593. kind(lucy) [subsumption resolution 592,134]
594. $false [subsumption resolution 593,135]
% SZS output end Proof for 447943783523960904451344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is wise then someone is both not wise and kind and vice versa. If someone is rich or not happy then someone is not wise and vice versa. Everyone who is both rich and calm is either curious or strong. If mary is curious or kind then paul is not patient. Everyone who is not strong or patient is not generous and vice versa. If lucy is wise or funny then someone is both happy and old and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. If someone is not curious or not generous then fred is both creative and old and vice versa. Someone is either funny or not calm. Lucy is not wise or calm. Susan is rich. Susan is not calm. Someone is both humble and rich. Someone is generous or wise. Paul is not strong or not generous. Alice is not generous. | Paul is not strong. | neutral | ((wise(mary))<=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((rich(X)|~happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((rich(X)&calm(X))=>(curious(X)<~>strong(X))))&
(((curious(mary)|kind(mary)))=>(~patient(paul)))&
(![X]:((~strong(X)|patient(X))<=>~generous(X)))&
(((wise(lucy)|funny(lucy)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X))))&
((~strong(paul)|~generous(paul)))&
(~generous(alice)) | ~strong(paul) | [] | null | 0 |
Everyone who is both humble and not calm is calm and vice versa.
Everyone who is either wise or patient is not creative or calm and vice versa.
Everyone who is kind or brave is either not calm or curious.
Everyone who is either not happy or curious is not brave and vice versa.
Everyone who is calm or humble is both not old and not generous and vice versa.
Everyone who is either creative or tall is not wise or patient.
Everyone who is either not happy or wise is either not rich or not old and vice versa.
Everyone who is tall or not curious is either happy or not tall and vice versa.
Everyone who is either not brave or rich is both not quiet and humble and vice versa.
If someone is rich then someone is not kind or not creative and vice versa.
If paul is both not curious and not rich then susan is not curious or not happy and vice versa.
Everyone who is not creative is either brave or not rich and vice versa.
If fred is not strong or calm then someone is either not tall or humble.
If alice is either rich or funny then lucy is both humble and not kind.
If fred is both not generous and not creative then john is not curious or brave.
Fred is brave.
Mary is not tall or curious.
Someone is both creative and funny.
Someone is not brave or kind.
Someone is not calm or not tall.
Mary is either not creative or tall.
Alice is not calm.
Someone is either generous or not old. | Alice is not funny. | neutral | (![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((wise(X)<~>patient(X))<=>(~creative(X)|calm(X))))&
(![X]:((kind(X)|brave(X))=>(~calm(X)<~>curious(X))))&
(![X]:((~happy(X)<~>curious(X))<=>~brave(X)))&
(![X]:((calm(X)|humble(X))<=>(~old(X)&~generous(X))))&
(![X]:((creative(X)<~>tall(X))=>(~wise(X)|patient(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(~rich(X)<~>~old(X))))&
(![X]:((tall(X)|~curious(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~quiet(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~kind(X)|~creative(X)))))&
(((~curious(paul)&~rich(paul)))<=>((~curious(susan)|~happy(susan))))&
(![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(((~strong(fred)|calm(fred)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(((rich(alice)<~>funny(alice)))=>((humble(lucy)&~kind(lucy))))&
(((~generous(fred)&~creative(fred)))=>((~curious(john)|brave(john))))&
(brave(fred))&
((~tall(mary)|curious(mary)))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((~brave(X)|kind(X))))&
(?[X]:((~calm(X)|~tall(X))))&
((~creative(mary)<~>tall(mary)))&
(~calm(alice))&
(?[X]:((generous(X)<~>~old(X)))) | ~funny(alice) | [] | null | 0 |
If someone is either not humble or creative then someone is not wise.
Everyone who is not funny is both not strong and not kind and vice versa.
If lucy is both not curious and not humble then john is both not creative and not calm and vice versa.
If someone is not rich then someone is not humble or curious and vice versa.
Everyone who is both not humble and not brave is both not strong and generous and vice versa.
If someone is either not quiet or brave then susan is creative and vice versa.
Everyone who is either not quiet or brave is either rich or patient and vice versa.
If someone is funny or not humble then fred is not creative or not calm.
If lucy is both patient and creative then someone is either not generous or strong.
Everyone who is not tall is curious or brave and vice versa.
Everyone who is not curious or not generous is curious.
If lucy is both not wise and not quiet then john is both not curious and quiet.
Everyone who is both funny and not old is both not strong and creative.
Everyone who is both not brave and not patient is both brave and tall.
Everyone who is either creative or tall is not old or wise and vice versa.
Everyone who is either not rich or not strong is not wise.
Someone is either not strong or not creative.
Someone is quiet.
Someone is old.
Someone is both not strong and not quiet.
Paul is rich.
Mary is either calm or not strong.
Mary is either not rich or happy.
Someone is strong or not strong. | Paul is tall. | contradiction | ((?[X]:((~humble(X)<~>creative(X))))=>(?[X]:(~wise(X))))&
(![X]:(~funny(X)<=>(~strong(X)&~kind(X))))&
(((~curious(lucy)&~humble(lucy)))<=>((~creative(john)&~calm(john))))&
((?[X]:(~rich(X)))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:((~humble(X)&~brave(X))<=>(~strong(X)&generous(X))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>(creative(susan)))&
(![X]:((~quiet(X)<~>brave(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((funny(X)|~humble(X))))=>((~creative(fred)|~calm(fred))))&
(((patient(lucy)&creative(lucy)))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(~tall(X)<=>(curious(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>curious(X)))&
(((~wise(lucy)&~quiet(lucy)))=>((~curious(john)&quiet(john))))&
(![X]:((funny(X)&~old(X))=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))=>(brave(X)&tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~old(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~wise(X)))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:(quiet(X)))&
(?[X]:(old(X)))&
(?[X]:((~strong(X)&~quiet(X))))&
(rich(paul))&
((calm(mary)<~>~strong(mary)))&
((~rich(mary)<~>happy(mary)))&
(?[X]:((strong(X)|~strong(X)))) | tall(paul) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1084622943776074434325616
% SZS output start Proof for 1084622943776074434325616
10. ! [X0] : (~tall(X0) <=> (brave(X0) | curious(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => curious(X0)) [input p10]
25. tall(paul) [input hypothesis]
36. ! [X0] : (curious(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
65. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | tall(X0))) [nnf transformation 10]
66. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | tall(X0))) [flattening 65]
114. ~tall(X0) | ~curious(X0) [cnf transformation 66]
116. curious(X0) | curious(X0) [cnf transformation 36]
144. tall(paul) [cnf transformation 25]
146. curious(X0) [duplicate literal removal 116]
305. ~curious(paul) [resolution 114,144]
306. $false [subsumption resolution 305,146]
% SZS output end Proof for 1084622943776074434325616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or kind is not kind and vice versa.
If john is not old then john is either not tall or not curious and vice versa.
If someone is not tall then someone is both not generous and patient and vice versa.
If lucy is strong or not wise then fred is brave or not strong.
If someone is both not curious and not quiet then susan is either rich or not happy and vice versa.
Everyone who is not quiet is both not wise and funny.
If someone is both not kind and calm then susan is both not generous and tall.
If someone is either creative or not humble then someone is quiet and vice versa.
If susan is not tall or not funny then someone is quiet.
Everyone who is not calm is either happy or not curious and vice versa.
Everyone who is both kind and not happy is not tall or patient.
If someone is brave or not quiet then someone is kind and vice versa.
If mary is both not curious and not old then someone is creative or curious.
If fred is both old and not happy then someone is either generous or not quiet.
Everyone who is not funny or happy is humble and vice versa.
If someone is both curious and not humble then someone is rich or happy.
Alice is either not kind or strong.
Susan is not creative.
Alice is not wise.
Alice is brave or not wise.
Someone is not funny or not humble.
Someone is both curious and rich.
John is happy. | Mary is tall. | entailment | (![X]:((generous(X)|kind(X))<=>~kind(X)))&
((~old(john))<=>((~tall(john)<~>~curious(john))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)&patient(X)))))&
(((strong(lucy)|~wise(lucy)))=>((brave(fred)|~strong(fred))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((rich(susan)<~>~happy(susan))))&
(![X]:(~quiet(X)=>(~wise(X)&funny(X))))&
((?[X]:((~kind(X)&calm(X))))=>((~generous(susan)&tall(susan))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:(quiet(X))))&
(((~tall(susan)|~funny(susan)))=>(?[X]:(quiet(X))))&
(![X]:(~calm(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((kind(X)&~happy(X))=>(~tall(X)|patient(X))))&
((?[X]:((brave(X)|~quiet(X))))<=>(?[X]:(kind(X))))&
(((~curious(mary)&~old(mary)))=>(?[X]:((creative(X)|curious(X)))))&
(((old(fred)&~happy(fred)))=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((~funny(X)|happy(X))<=>humble(X)))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((rich(X)|happy(X)))))&
((~kind(alice)<~>strong(alice)))&
(~creative(susan))&
(~wise(alice))&
((brave(alice)|~wise(alice)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((curious(X)&rich(X))))&
(happy(john)) | tall(mary) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 248382311910722288323058
% SZS output start Proof for 248382311910722288323058
1. ! [X0] : ((kind(X0) | generous(X0)) <=> ~kind(X0)) [input p0]
3. ? [X0] : ~tall(X0) <=> ? [X0] : (patient(X0) & ~generous(X0)) [input p2]
24. ~tall(mary) [input hypothesis]
25. ? [X0] : ~tall(X0) <=> ? [X1] : (patient(X1) & ~generous(X1)) [rectify 3]
43. ! [X0] : (((kind(X0) | generous(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | generous(X0) | kind(X0)) & (~kind(X0) | (~kind(X0) & ~generous(X0)))) [flattening 43]
46. (? [X0] : ~tall(X0) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X1] : (patient(X1) & ~generous(X1)) | ! [X0] : tall(X0)) [nnf transformation 25]
47. (? [X0] : ~tall(X0) | ! [X1] : (~patient(X1) | generous(X1))) & (? [X2] : (patient(X2) & ~generous(X2)) | ! [X3] : tall(X3)) [rectify 46]
48. ? [X0] : ~tall(X0) => ~tall(sK0) [choice axiom]
49. ? [X2] : (patient(X2) & ~generous(X2)) => (patient(sK1) & ~generous(sK1)) [choice axiom]
50. (~tall(sK0) | ! [X1] : (~patient(X1) | generous(X1))) & ((patient(sK1) & ~generous(sK1)) | ! [X3] : tall(X3)) [skolemisation 47,49,48]
84. ~kind(X0) | ~kind(X0) [cnf transformation 44]
85. kind(X0) | generous(X0) | kind(X0) [cnf transformation 44]
90. ~generous(sK1) | tall(X3) [cnf transformation 50]
133. ~tall(mary) [cnf transformation 24]
134. ~kind(X0) [duplicate literal removal 84]
135. kind(X0) | generous(X0) [duplicate literal removal 85]
161. 6 <=> ! [X3] : tall(X3) [avatar definition]
162. tall(X3) <- (6) [avatar component clause 161]
169. 8 <=> generous(sK1) [avatar definition]
171. ~generous(sK1) <- (~8) [avatar component clause 169]
172. 6 | ~8 [avatar split clause 90,169,161]
325. $false <- (6) [resolution 162,133]
326. ~6 [avatar contradiction clause 325]
332. generous(X0) [resolution 135,134]
333. $false <- (~8) [resolution 332,171]
336. 8 [avatar contradiction clause 333]
337. $false [avatar sat refutation 172,326,336]
% SZS output end Proof for 248382311910722288323058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is old or funny and vice versa. If john is strong then susan is not generous or curious. If susan is either happy or humble then paul is funny or creative and vice versa. Everyone who is either not generous or funny is rich and vice versa. Everyone who is not creative is both wise and not strong and vice versa. If susan is not old then lucy is either not humble or not generous and vice versa. Everyone who is old or not humble is both old and not tall. Everyone who is not old or not quiet is tall or not calm. If alice is both brave and not happy then mary is strong. Everyone who is not kind or not quiet is not calm or patient and vice versa. Everyone who is either happy or not humble is not curious. If susan is wise or not patient then paul is not quiet. If paul is both not creative and funny then alice is calm or not strong. If someone is either tall or not wise then someone is both humble and kind and vice versa. Everyone who is not calm or quiet is quiet or not humble and vice versa. Mary is old or tall. Someone is both not strong and wise. Susan is not creative. Lucy is either rich or not patient. Someone is brave or old. Fred is funny or not curious. | John is not wise. | neutral | (![X]:(~old(X)<=>(old(X)|funny(X))))&
((strong(john))=>((~generous(susan)|curious(susan))))&
(((happy(susan)<~>humble(susan)))<=>((funny(paul)|creative(paul))))&
(![X]:((~generous(X)<~>funny(X))<=>rich(X)))&
(![X]:(~creative(X)<=>(wise(X)&~strong(X))))&
((~old(susan))<=>((~humble(lucy)<~>~generous(lucy))))&
(![X]:((old(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((~old(X)|~quiet(X))=>(tall(X)|~calm(X))))&
(((brave(alice)&~happy(alice)))=>(strong(mary)))&
(![X]:((~kind(X)|~quiet(X))<=>(~calm(X)|patient(X))))&
(![X]:((happy(X)<~>~humble(X))=>~curious(X)))&
(((wise(susan)|~patient(susan)))=>(~quiet(paul)))&
(((~creative(paul)&funny(paul)))=>((calm(alice)|~strong(alice))))&
((?[X]:((tall(X)<~>~wise(X))))<=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((~calm(X)|quiet(X))<=>(quiet(X)|~humble(X))))&
((old(mary)|tall(mary)))&
(?[X]:((~strong(X)&wise(X))))&
(~creative(susan))&
((rich(lucy)<~>~patient(lucy)))&
(?[X]:((brave(X)|old(X))))&
((funny(fred)|~curious(fred))) | ~wise(john) | [] | null | 0 |
Everyone who is humble is either not curious or not quiet and vice versa.
Everyone who is not calm is not quiet or tall and vice versa.
Everyone who is humble is both creative and kind and vice versa.
If someone is not happy then susan is either brave or rich and vice versa.
Everyone who is calm or not humble is not happy or not curious and vice versa.
Everyone who is not old or not quiet is not brave and vice versa.
Everyone who is old is patient and vice versa.
Everyone who is not humble is brave and vice versa.
If someone is either not calm or happy then someone is not old or not wise.
Everyone who is not kind is not humble and vice versa.
If someone is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Someone is not happy or not humble.
Paul is rich or not strong.
Someone is strong.
Lucy is not wise.
Someone is not generous.
Someone is either quiet or not generous. | Paul is not rich. | neutral | (![X]:(humble(X)<=>(~curious(X)<~>~quiet(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|tall(X))))&
(![X]:(humble(X)<=>(creative(X)&kind(X))))&
((?[X]:(~happy(X)))<=>((brave(susan)<~>rich(susan))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(?[X]:((~happy(X)|~humble(X))))&
((rich(paul)|~strong(paul)))&
(?[X]:(strong(X)))&
(~wise(lucy))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>~generous(X)))) | ~rich(paul) | [] | null | 0 |
If fred is either not patient or not creative then mary is both not humble and patient. Everyone who is not funny or wise is either generous or not quiet. Everyone who is not creative is not creative or not rich. If susan is rich or not quiet then susan is not creative or not tall and vice versa. Everyone who is happy or not curious is not rich and vice versa. If mary is not rich or happy then someone is not funny or brave. Everyone who is either not funny or not strong is either curious or quiet. Everyone who is either not brave or old is rich or not kind and vice versa. If mary is funny or generous then alice is either not wise or patient. Everyone who is either not kind or not calm is not rich. Everyone who is either not funny or funny is not rich or not quiet and vice versa. If someone is not happy then paul is not generous and vice versa. If someone is both not curious and not humble then someone is not calm. If fred is strong then someone is both old and not patient. If lucy is not brave or wise then someone is either curious or not kind and vice versa. Everyone who is both not funny and not kind is both humble and creative and vice versa. Lucy is both calm and not curious. Alice is tall or old. Fred is not humble or humble. Someone is not creative or not funny. Paul is old. Someone is not curious or not patient. Someone is not curious. Someone is either happy or not patient. | Lucy is not rich. | entailment | (((~patient(fred)<~>~creative(fred)))=>((~humble(mary)&patient(mary))))&
(![X]:((~funny(X)|wise(X))=>(generous(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>(~creative(X)|~rich(X))))&
(((rich(susan)|~quiet(susan)))<=>((~creative(susan)|~tall(susan))))&
(![X]:((happy(X)|~curious(X))<=>~rich(X)))&
(((~rich(mary)|happy(mary)))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>(curious(X)<~>quiet(X))))&
(![X]:((~brave(X)<~>old(X))<=>(rich(X)|~kind(X))))&
(((funny(mary)|generous(mary)))=>((~wise(alice)<~>patient(alice))))&
(![X]:((~kind(X)<~>~calm(X))=>~rich(X)))&
(![X]:((~funny(X)<~>funny(X))<=>(~rich(X)|~quiet(X))))&
((?[X]:(~happy(X)))<=>(~generous(paul)))&
((?[X]:((~curious(X)&~humble(X))))=>(?[X]:(~calm(X))))&
((strong(fred))=>(?[X]:((old(X)&~patient(X)))))&
(((~brave(lucy)|wise(lucy)))<=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(humble(X)&creative(X))))&
((calm(lucy)&~curious(lucy)))&
((tall(alice)|old(alice)))&
((~humble(fred)|humble(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(old(paul))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~patient(X)))) | ~rich(lucy) | [
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7130131227728676528691706
% SZS output start Proof for 7130131227728676528691706
5. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~rich(X0)) [input p4]
17. ~curious(lucy) & calm(lucy) [input p16]
25. rich(lucy) [input hypothesis]
41. ! [X0] : (((~curious(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 5]
42. ! [X0] : ((~curious(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (curious(X0) & ~happy(X0)))) [flattening 41]
91. ~rich(X0) | curious(X0) [cnf transformation 42]
133. ~curious(lucy) [cnf transformation 17]
142. rich(lucy) [cnf transformation 25]
324. curious(lucy) [resolution 91,142]
325. $false [subsumption resolution 324,133]
% SZS output end Proof for 7130131227728676528691706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either tall or strong then someone is humble and vice versa.
Everyone who is not quiet or kind is happy or calm.
Everyone who is both not old and happy is both not curious and not creative and vice versa.
Everyone who is kind or tall is either wise or happy.
Everyone who is not humble or funny is either not strong or not calm.
Everyone who is wise is not humble or kind and vice versa.
If mary is both not humble and patient then alice is generous or not patient and vice versa.
Everyone who is both generous and rich is not generous.
If someone is not generous then someone is either wise or not strong and vice versa.
If fred is either not calm or wise then lucy is not strong.
Everyone who is both old and patient is either not tall or patient and vice versa.
If someone is not calm or not happy then john is both curious and not patient.
Everyone who is both not brave and not old is old.
Everyone who is old or not rich is both not tall and rich.
Everyone who is both not generous and not humble is not tall or tall and vice versa.
Everyone who is patient is curious or brave.
John is both not creative and strong.
Susan is not funny or old.
Someone is not old or not creative.
Someone is either quiet or patient.
Someone is not funny or tall.
Someone is either not strong or not tall.
Lucy is not wise or not happy. | John is not happy. | entailment | (((tall(mary)<~>strong(mary)))<=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(happy(X)|calm(X))))&
(![X]:((~old(X)&happy(X))<=>(~curious(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))=>(wise(X)<~>happy(X))))&
(![X]:((~humble(X)|funny(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~humble(X)|kind(X))))&
(((~humble(mary)&patient(mary)))<=>((generous(alice)|~patient(alice))))&
(![X]:((generous(X)&rich(X))=>~generous(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(fred)<~>wise(fred)))=>(~strong(lucy)))&
(![X]:((old(X)&patient(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((curious(john)&~patient(john))))&
(![X]:((~brave(X)&~old(X))=>old(X)))&
(![X]:((old(X)|~rich(X))=>(~tall(X)&rich(X))))&
(![X]:((~generous(X)&~humble(X))<=>(~tall(X)|tall(X))))&
(![X]:(patient(X)=>(curious(X)|brave(X))))&
((~creative(john)&strong(john)))&
((~funny(susan)|old(susan)))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((~strong(X)<~>~tall(X))))&
((~wise(lucy)|~happy(lucy))) | ~happy(john) | [
"p2",
"p5",
"p10",
"p11",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1986517820654813822399647
% SZS output start Proof for 1986517820654813822399647
3. ! [X0] : ((happy(X0) & ~old(X0)) <=> (~creative(X0) & ~curious(X0))) [input p2]
6. ! [X0] : (wise(X0) <=> (kind(X0) | ~humble(X0))) [input p5]
11. ! [X0] : ((patient(X0) & old(X0)) <=> (~tall(X0) <~> patient(X0))) [input p10]
12. ? [X0] : (~happy(X0) | ~calm(X0)) => (~patient(john) & curious(john)) [input p11]
14. ! [X0] : ((~rich(X0) | old(X0)) => (rich(X0) & ~tall(X0))) [input p13]
15. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (tall(X0) | ~tall(X0))) [input p14]
23. ~happy(lucy) | ~wise(lucy) [input p22]
24. happy(john) [input hypothesis]
38. (~patient(john) & curious(john)) | ! [X0] : (happy(X0) & calm(X0)) [ennf transformation 12]
39. ! [X0] : ((rich(X0) & ~tall(X0)) | (rich(X0) & ~old(X0))) [ennf transformation 14]
44. ! [X0] : (((happy(X0) & ~old(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (~happy(X0) | old(X0)))) [nnf transformation 3]
45. ! [X0] : (((happy(X0) & ~old(X0)) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | ~happy(X0) | old(X0))) [flattening 44]
48. ! [X0] : ((wise(X0) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 6]
49. ! [X0] : ((wise(X0) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~wise(X0))) [flattening 48]
58. ! [X0] : (((patient(X0) & old(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | (~patient(X0) | ~old(X0)))) [nnf transformation 11]
59. ! [X0] : (((patient(X0) & old(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~patient(X0) | ~old(X0))) [flattening 58]
60. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 15]
61. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | humble(X0) | generous(X0))) [flattening 60]
76. ~curious(X0) | ~happy(X0) | old(X0) [cnf transformation 45]
87. wise(X0) | humble(X0) [cnf transformation 49]
102. ~patient(X0) | tall(X0) | ~patient(X0) | ~old(X0) [cnf transformation 59]
105. patient(X0) | patient(X0) | tall(X0) [cnf transformation 59]
108. curious(john) | happy(X0) [cnf transformation 38]
111. ~tall(X0) | ~old(X0) [cnf transformation 39]
118. ~humble(X0) | tall(X0) [cnf transformation 61]
119. ~humble(X0) | ~tall(X0) [cnf transformation 61]
127. ~happy(lucy) | ~wise(lucy) [cnf transformation 23]
128. happy(john) [cnf transformation 24]
130. ~patient(X0) | tall(X0) | ~old(X0) [duplicate literal removal 102]
131. patient(X0) | tall(X0) [duplicate literal removal 105]
134. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
135. ~humble(X0) <- (1) [avatar component clause 134]
212. ~old(X0) | tall(X0) [subsumption resolution 130,131]
214. 18 <=> ! [X0] : happy(X0) [avatar definition]
215. happy(X0) <- (18) [avatar component clause 214]
226. 21 <=> curious(john) [avatar definition]
228. curious(john) <- (21) [avatar component clause 226]
229. 18 | 21 [avatar split clause 108,226,214]
231. ~old(X0) [subsumption resolution 111,212]
232. ~humble(X0) [subsumption resolution 118,119]
233. 1 [avatar split clause 232,134]
256. 26 <=> wise(lucy) [avatar definition]
258. ~wise(lucy) <- (~26) [avatar component clause 256]
260. 27 <=> happy(lucy) [avatar definition]
262. ~happy(lucy) <- (~27) [avatar component clause 260]
263. ~26 | ~27 [avatar split clause 127,260,256]
264. $false <- (18, ~27) [resolution 262,215]
265. ~18 | 27 [avatar contradiction clause 264]
278. ~happy(john) | old(john) <- (21) [resolution 76,228]
279. old(john) <- (21) [subsumption resolution 278,128]
280. $false <- (21) [subsumption resolution 279,231]
281. ~21 [avatar contradiction clause 280]
282. humble(lucy) <- (~26) [resolution 258,87]
283. $false <- (1, ~26) [subsumption resolution 282,135]
284. ~1 | 26 [avatar contradiction clause 283]
285. $false [avatar sat refutation 229,233,263,265,281,284]
% SZS output end Proof for 1986517820654813822399647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or quiet is either not rich or tall.
Everyone who is happy or tall is either wise or tall.
If someone is either rich or not curious then lucy is either humble or not kind and vice versa.
Everyone who is kind or not humble is curious.
Everyone who is both not patient and not tall is calm or not old and vice versa.
If someone is both strong and generous then someone is either generous or happy.
If alice is creative or old then someone is not calm and vice versa.
Everyone who is not tall or tall is not tall or rich.
Everyone who is both kind and brave is not patient or not wise.
If someone is not patient then fred is quiet and vice versa.
If someone is wise or not strong then someone is either not strong or brave.
Everyone who is generous is funny or not calm and vice versa.
Everyone who is old is wise and vice versa.
If someone is brave or generous then mary is either not creative or generous and vice versa.
Everyone who is both quiet and not quiet is both not funny and not patient and vice versa.
Everyone who is either not brave or brave is strong and vice versa.
Susan is kind.
Mary is not rich.
Alice is funny or brave.
Someone is not curious or humble.
Someone is not tall.
Someone is both not rich and wise.
Someone is patient.
Paul is either not old or not patient. | Paul is strong. | entailment | (![X]:((generous(X)<~>quiet(X))=>(~rich(X)<~>tall(X))))&
(![X]:((happy(X)|tall(X))=>(wise(X)<~>tall(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((humble(lucy)<~>~kind(lucy))))&
(![X]:((kind(X)|~humble(X))=>curious(X)))&
(![X]:((~patient(X)&~tall(X))<=>(calm(X)|~old(X))))&
((?[X]:((strong(X)&generous(X))))=>(?[X]:((generous(X)<~>happy(X)))))&
(((creative(alice)|old(alice)))<=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)|rich(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)|~wise(X))))&
((?[X]:(~patient(X)))<=>(quiet(fred)))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(generous(X)<=>(funny(X)|~calm(X))))&
(![X]:(old(X)<=>wise(X)))&
((?[X]:((brave(X)|generous(X))))<=>((~creative(mary)<~>generous(mary))))&
(![X]:((quiet(X)&~quiet(X))<=>(~funny(X)&~patient(X))))&
(![X]:((~brave(X)<~>brave(X))<=>strong(X)))&
(kind(susan))&
(~rich(mary))&
((funny(alice)|brave(alice)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)&wise(X))))&
(?[X]:(patient(X)))&
((~old(paul)<~>~patient(paul))) | strong(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 300126026020642297607841
% SZS output start Proof for 300126026020642297607841
16. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> strong(X0)) [input p15]
25. ~strong(paul) [input hypothesis]
71. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~strong(X0)) & (strong(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 16]
133. strong(X0) | brave(X0) | brave(X0) [cnf transformation 71]
134. strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 71]
147. ~strong(paul) [cnf transformation 25]
148. strong(X0) | brave(X0) [duplicate literal removal 133]
149. strong(X0) | ~brave(X0) [duplicate literal removal 134]
227. 17 <=> ! [X1] : strong(X1) [avatar definition]
228. strong(X1) <- (17) [avatar component clause 227]
273. strong(X0) [subsumption resolution 148,149]
274. 17 [avatar split clause 273,227]
291. $false <- (17) [resolution 228,147]
292. ~17 [avatar contradiction clause 291]
293. $false [avatar sat refutation 274,292]
% SZS output end Proof for 300126026020642297607841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not wise is not creative or not patient and vice versa. If alice is not tall then someone is either patient or quiet and vice versa. If someone is not rich or not curious then someone is both not creative and not curious. If mary is either not tall or not rich then alice is both funny and quiet. Everyone who is kind or not brave is either strong or not old and vice versa. If lucy is not tall then someone is rich or not creative and vice versa. If susan is wise then paul is not strong or not quiet and vice versa. If paul is both funny and not funny then susan is funny or brave and vice versa. If paul is happy then someone is both not curious and calm and vice versa. If alice is not funny then john is rich and vice versa. If someone is tall then mary is either not rich or rich and vice versa. Everyone who is either not wise or happy is humble or rich. Everyone who is both not brave and not calm is either not tall or not creative and vice versa. Everyone who is both not humble and not rich is either not curious or generous. Everyone who is either calm or not creative is both generous and curious and vice versa. Everyone who is either curious or not creative is both quiet and brave. Mary is not wise. Fred is brave or generous. Alice is not happy. John is either not wise or strong. Alice is both not calm and not brave. John is both generous and strong. Mary is not funny or brave. Alice is not brave. | Mary is not tall. | neutral | (![X]:((patient(X)&~wise(X))<=>(~creative(X)|~patient(X))))&
((~tall(alice))<=>(?[X]:((patient(X)<~>quiet(X)))))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((~creative(X)&~curious(X)))))&
(((~tall(mary)<~>~rich(mary)))=>((funny(alice)&quiet(alice))))&
(![X]:((kind(X)|~brave(X))<=>(strong(X)<~>~old(X))))&
((~tall(lucy))<=>(?[X]:((rich(X)|~creative(X)))))&
((wise(susan))<=>((~strong(paul)|~quiet(paul))))&
(((funny(paul)&~funny(paul)))<=>((funny(susan)|brave(susan))))&
((happy(paul))<=>(?[X]:((~curious(X)&calm(X)))))&
((~funny(alice))<=>(rich(john)))&
((?[X]:(tall(X)))<=>((~rich(mary)<~>rich(mary))))&
(![X]:((~wise(X)<~>happy(X))=>(humble(X)|rich(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((~humble(X)&~rich(X))=>(~curious(X)<~>generous(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(generous(X)&curious(X))))&
(![X]:((curious(X)<~>~creative(X))=>(quiet(X)&brave(X))))&
(~wise(mary))&
((brave(fred)|generous(fred)))&
(~happy(alice))&
((~wise(john)<~>strong(john)))&
((~calm(alice)&~brave(alice)))&
((generous(john)&strong(john)))&
((~funny(mary)|brave(mary)))&
(~brave(alice)) | ~tall(mary) | [] | null | 0 |
If someone is not creative or quiet then someone is either humble or not tall and vice versa.
If someone is both old and not tall then alice is quiet.
Everyone who is not tall or tall is either not strong or strong and vice versa.
Everyone who is either not quiet or quiet is either not brave or not old.
If someone is either not generous or kind then someone is not kind.
If someone is either not rich or not calm then alice is both not happy and old.
Everyone who is not generous is not old and vice versa.
Everyone who is strong or old is not kind and vice versa.
Everyone who is quiet or not strong is not patient or rich and vice versa.
If alice is both tall and curious then someone is either happy or not tall and vice versa.
Everyone who is not wise or not humble is either rich or quiet and vice versa.
Everyone who is both generous and not brave is strong.
If susan is either not generous or not calm then susan is not creative or kind.
If someone is not kind then paul is both funny and calm.
Everyone who is both brave and not rich is either humble or not brave and vice versa.
Everyone who is both old and not strong is not brave and vice versa.
Fred is either curious or not humble.
John is not patient.
Fred is not generous or not funny.
Fred is not wise.
Someone is not tall or not happy.
Alice is either not creative or rich.
Susan is either funny or patient. | Susan is kind. | neutral | ((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((humble(X)<~>~tall(X)))))&
((?[X]:((old(X)&~tall(X))))=>(quiet(alice)))&
(![X]:((~tall(X)|tall(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~brave(X)<~>~old(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:(~kind(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~happy(alice)&old(alice))))&
(![X]:(~generous(X)<=>~old(X)))&
(![X]:((strong(X)|old(X))<=>~kind(X)))&
(![X]:((quiet(X)|~strong(X))<=>(~patient(X)|rich(X))))&
(((tall(alice)&curious(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)<~>quiet(X))))&
(![X]:((generous(X)&~brave(X))=>strong(X)))&
(((~generous(susan)<~>~calm(susan)))=>((~creative(susan)|kind(susan))))&
((?[X]:(~kind(X)))=>((funny(paul)&calm(paul))))&
(![X]:((brave(X)&~rich(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((old(X)&~strong(X))<=>~brave(X)))&
((curious(fred)<~>~humble(fred)))&
(~patient(john))&
((~generous(fred)|~funny(fred)))&
(~wise(fred))&
(?[X]:((~tall(X)|~happy(X))))&
((~creative(alice)<~>rich(alice)))&
((funny(susan)<~>patient(susan))) | kind(susan) | [] | null | 0 |
If someone is both old and not funny then someone is happy and vice versa.
Everyone who is kind or not quiet is both not rich and not curious.
Everyone who is both not calm and not kind is not wise or generous and vice versa.
If someone is not kind or not strong then paul is generous.
Everyone who is either not old or old is generous and vice versa.
Everyone who is calm or not strong is creative and vice versa.
If alice is not kind or generous then someone is brave and vice versa.
Everyone who is both not tall and not funny is either funny or not calm.
Everyone who is either generous or not old is not creative.
If john is both not happy and quiet then lucy is not funny or happy.
If someone is either not funny or patient then fred is not curious and vice versa.
If john is either happy or tall then someone is both not humble and not strong and vice versa.
Everyone who is both not tall and not creative is either rich or strong.
Everyone who is both curious and not old is either not old or strong.
If someone is not humble then someone is not creative.
If someone is either not wise or old then lucy is both not kind and not funny.
Alice is both not wise and not calm.
Someone is both not tall and not kind.
Someone is both not quiet and humble.
Fred is quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich. | Lucy is happy. | neutral | ((?[X]:((old(X)&~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)|~quiet(X))=>(~rich(X)&~curious(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(generous(paul)))&
(![X]:((~old(X)<~>old(X))<=>generous(X)))&
(![X]:((calm(X)|~strong(X))<=>creative(X)))&
(((~kind(alice)|generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((~tall(X)&~funny(X))=>(funny(X)<~>~calm(X))))&
(![X]:((generous(X)<~>~old(X))=>~creative(X)))&
(((~happy(john)&quiet(john)))=>((~funny(lucy)|happy(lucy))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
((~wise(alice)&~calm(alice)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(quiet(fred))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul)) | happy(lucy) | [] | null | 0 |
If someone is humble then someone is either not patient or not rich and vice versa. If alice is brave or funny then someone is either not quiet or not funny and vice versa. Everyone who is both funny and brave is not curious or calm and vice versa. Everyone who is either strong or not happy is both tall and generous. Everyone who is either wise or tall is not brave or calm and vice versa. If alice is calm then someone is both not curious and brave and vice versa. Everyone who is calm is either rich or calm. Everyone who is both brave and curious is either old or not patient and vice versa. Everyone who is calm is old or not happy. If john is both quiet and funny then john is both creative and happy and vice versa. Everyone who is either tall or happy is curious and vice versa. If someone is both not funny and generous then someone is not quiet or curious. If someone is old then someone is either not humble or not funny and vice versa. Everyone who is humble is not patient or not kind. If fred is both happy and not calm then john is not wise or quiet and vice versa. Everyone who is happy or calm is not calm. Mary is both quiet and not humble. Lucy is either not generous or strong. Someone is tall or not strong. Someone is not humble. Someone is not happy or not funny. Someone is both humble and not funny. Someone is both happy and not patient. | John is not creative. | neutral | ((?[X]:(humble(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((brave(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(![X]:((funny(X)&brave(X))<=>(~curious(X)|calm(X))))&
(![X]:((strong(X)<~>~happy(X))=>(tall(X)&generous(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)|calm(X))))&
((calm(alice))<=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:(calm(X)=>(rich(X)<~>calm(X))))&
(![X]:((brave(X)&curious(X))<=>(old(X)<~>~patient(X))))&
(![X]:(calm(X)=>(old(X)|~happy(X))))&
(((quiet(john)&funny(john)))<=>((creative(john)&happy(john))))&
(![X]:((tall(X)<~>happy(X))<=>curious(X)))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:((~quiet(X)|curious(X)))))&
((?[X]:(old(X)))<=>(?[X]:((~humble(X)<~>~funny(X)))))&
(![X]:(humble(X)=>(~patient(X)|~kind(X))))&
(((happy(fred)&~calm(fred)))<=>((~wise(john)|quiet(john))))&
(![X]:((happy(X)|calm(X))=>~calm(X)))&
((quiet(mary)&~humble(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:((humble(X)&~funny(X))))&
(?[X]:((happy(X)&~patient(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is not happy or patient is either not happy or not patient. If paul is either not old or curious then someone is not patient or curious and vice versa. Everyone who is not rich or not calm is not happy and vice versa. Everyone who is both tall and strong is both not strong and kind and vice versa. Everyone who is old or not tall is both not creative and not humble. Everyone who is both calm and rich is not funny or not brave and vice versa. If susan is curious or not strong then paul is both not tall and not brave and vice versa. If lucy is not curious or generous then paul is not strong or calm. If susan is brave or not patient then john is not funny or creative. If someone is not generous or not strong then fred is creative and vice versa. If paul is both rich and not quiet then someone is not curious. Everyone who is happy is both not kind and funny and vice versa. If john is both not rich and not creative then someone is patient or funny. If someone is both not quiet and not funny then alice is both not happy and tall and vice versa. Everyone who is either not happy or old is happy or not creative. Everyone who is not patient is both happy and creative. Lucy is not calm. Paul is brave. Someone is brave or humble. Someone is quiet or not brave. Someone is either quiet or not quiet. | John is not kind. | entailment | (![X]:((~happy(X)|patient(X))=>(~happy(X)<~>~patient(X))))&
(((~old(paul)<~>curious(paul)))<=>(?[X]:((~patient(X)|curious(X)))))&
(![X]:((~rich(X)|~calm(X))<=>~happy(X)))&
(![X]:((tall(X)&strong(X))<=>(~strong(X)&kind(X))))&
(![X]:((old(X)|~tall(X))=>(~creative(X)&~humble(X))))&
(![X]:((calm(X)&rich(X))<=>(~funny(X)|~brave(X))))&
(((curious(susan)|~strong(susan)))<=>((~tall(paul)&~brave(paul))))&
(((~curious(lucy)|generous(lucy)))=>((~strong(paul)|calm(paul))))&
(((brave(susan)|~patient(susan)))=>((~funny(john)|creative(john))))&
((?[X]:((~generous(X)|~strong(X))))<=>(creative(fred)))&
(((rich(paul)&~quiet(paul)))=>(?[X]:(~curious(X))))&
(![X]:(happy(X)<=>(~kind(X)&funny(X))))&
(((~rich(john)&~creative(john)))=>(?[X]:((patient(X)|funny(X)))))&
((?[X]:((~quiet(X)&~funny(X))))<=>((~happy(alice)&tall(alice))))&
(![X]:((~happy(X)<~>old(X))=>(happy(X)|~creative(X))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(~calm(lucy))&
(brave(paul))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~kind(john) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 919873536022791061886353
% SZS output start Proof for 919873536022791061886353
1. ! [X0] : ((patient(X0) | ~happy(X0)) => (~happy(X0) <~> ~patient(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((strong(X0) & tall(X0)) <=> (kind(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((~tall(X0) | old(X0)) => (~humble(X0) & ~creative(X0))) [input p4]
6. ! [X0] : ((rich(X0) & calm(X0)) <=> (~brave(X0) | ~funny(X0))) [input p5]
9. (~patient(susan) | brave(susan)) => (creative(john) | ~funny(john)) [input p8]
12. ! [X0] : (happy(X0) <=> (funny(X0) & ~kind(X0))) [input p11]
22. kind(john) [input hypothesis]
23. ! [X0] : ((~happy(X0) <~> ~patient(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 1]
24. ! [X0] : ((~humble(X0) & ~creative(X0)) | (tall(X0) & ~old(X0))) [ennf transformation 5]
27. (creative(john) | ~funny(john)) | (patient(susan) & ~brave(susan)) [ennf transformation 9]
28. creative(john) | ~funny(john) | (patient(susan) & ~brave(susan)) [flattening 27]
36. ! [X0] : (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | (~patient(X0) & happy(X0))) [nnf transformation 23]
41. ! [X0] : (((~calm(X0) | ~rich(X0)) | happy(X0)) & (~happy(X0) | (calm(X0) & rich(X0)))) [nnf transformation 3]
42. ! [X0] : ((~calm(X0) | ~rich(X0) | happy(X0)) & (~happy(X0) | (calm(X0) & rich(X0)))) [flattening 41]
43. ! [X0] : (((strong(X0) & tall(X0)) | (~kind(X0) | strong(X0))) & ((kind(X0) & ~strong(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 4]
44. ! [X0] : (((strong(X0) & tall(X0)) | ~kind(X0) | strong(X0)) & ((kind(X0) & ~strong(X0)) | ~strong(X0) | ~tall(X0))) [flattening 43]
45. ! [X0] : (((rich(X0) & calm(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (~rich(X0) | ~calm(X0)))) [nnf transformation 6]
46. ! [X0] : (((rich(X0) & calm(X0)) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ~rich(X0) | ~calm(X0))) [flattening 45]
55. ! [X0] : ((happy(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | ~happy(X0))) [nnf transformation 12]
56. ! [X0] : ((happy(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ~happy(X0))) [flattening 55]
73. ~patient(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 36]
84. ~calm(X0) | ~rich(X0) | happy(X0) [cnf transformation 42]
85. ~strong(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 44]
88. strong(X0) | ~kind(X0) | strong(X0) [cnf transformation 44]
90. ~creative(X0) | tall(X0) [cnf transformation 24]
94. funny(X0) | calm(X0) [cnf transformation 46]
95. brave(X0) | calm(X0) [cnf transformation 46]
96. funny(X0) | rich(X0) [cnf transformation 46]
97. brave(X0) | rich(X0) [cnf transformation 46]
105. creative(john) | ~funny(john) | ~brave(susan) [cnf transformation 28]
106. creative(john) | ~funny(john) | patient(susan) [cnf transformation 28]
111. ~kind(X0) | ~happy(X0) [cnf transformation 56]
129. kind(john) [cnf transformation 22]
131. ~strong(X0) | ~tall(X0) [duplicate literal removal 85]
132. ~kind(X0) | strong(X0) [duplicate literal removal 88]
133. ~patient(X0) | ~happy(X0) [duplicate literal removal 73]
203. 15 <=> patient(susan) [avatar definition]
205. patient(susan) <- (15) [avatar component clause 203]
207. 16 <=> funny(john) [avatar definition]
209. ~funny(john) <- (~16) [avatar component clause 207]
211. 17 <=> creative(john) [avatar definition]
213. creative(john) <- (17) [avatar component clause 211]
214. 15 | ~16 | 17 [avatar split clause 106,211,207,203]
216. 18 <=> brave(susan) [avatar definition]
218. ~brave(susan) <- (~18) [avatar component clause 216]
219. ~18 | ~16 | 17 [avatar split clause 105,211,207,216]
255. 27 <=> rich(john) [avatar definition]
256. ~rich(john) <- (~27) [avatar component clause 255]
257. rich(john) <- (27) [avatar component clause 255]
312. tall(john) <- (17) [resolution 90,213]
318. ~happy(john) [resolution 111,129]
322. strong(john) [resolution 132,129]
323. ~tall(john) [resolution 322,131]
324. $false <- (17) [subsumption resolution 323,312]
325. ~17 [avatar contradiction clause 324]
327. calm(john) <- (~16) [resolution 209,94]
342. ~rich(john) | happy(john) <- (~16) [resolution 84,327]
345. happy(john) <- (~16, 27) [subsumption resolution 342,257]
346. $false <- (~16, 27) [subsumption resolution 345,318]
347. 16 | ~27 [avatar contradiction clause 346]
348. ~happy(susan) <- (15) [resolution 205,133]
349. rich(susan) <- (~18) [resolution 218,97]
350. calm(susan) <- (~18) [resolution 218,95]
375. ~rich(susan) | happy(susan) <- (~18) [resolution 350,84]
376. happy(susan) <- (~18) [subsumption resolution 375,349]
377. $false <- (15, ~18) [subsumption resolution 376,348]
378. ~15 | 18 [avatar contradiction clause 377]
379. rich(john) <- (~16) [resolution 209,96]
381. $false <- (~16, ~27) [subsumption resolution 379,256]
382. 16 | 27 [avatar contradiction clause 381]
383. $false [avatar sat refutation 214,219,325,347,378,382]
% SZS output end Proof for 919873536022791061886353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not tall and not happy then someone is not rich or funny. Everyone who is both not creative and kind is either happy or not humble. If someone is not patient or quiet then alice is curious or creative and vice versa. If alice is both strong and not kind then someone is either quiet or not curious. Everyone who is both not humble and not curious is either not happy or not patient and vice versa. If someone is both not rich and not tall then fred is happy or not happy and vice versa. If someone is humble or old then alice is not quiet. Everyone who is both not wise and not humble is either not happy or rich and vice versa. Everyone who is calm is both patient and kind. Everyone who is both not creative and not brave is kind and vice versa. Everyone who is humble is not happy and vice versa. If someone is happy or creative then alice is not wise or humble and vice versa. Everyone who is either not tall or calm is either not brave or not quiet. Everyone who is either kind or patient is either not brave or humble. Everyone who is either not old or not tall is both not curious and old. If someone is both rich and curious then someone is happy or not brave and vice versa. Paul is both not strong and not rich. Someone is not kind. Someone is generous or not humble. Someone is either not strong or not happy. Paul is not humble. Paul is not kind or patient. Mary is not creative or patient. John is generous. | Mary is calm. | contradiction | (((~tall(fred)&~happy(fred)))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~creative(X)&kind(X))=>(happy(X)<~>~humble(X))))&
((?[X]:((~patient(X)|quiet(X))))<=>((curious(alice)|creative(alice))))&
(((strong(alice)&~kind(alice)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((~humble(X)&~curious(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((~rich(X)&~tall(X))))<=>((happy(fred)|~happy(fred))))&
((?[X]:((humble(X)|old(X))))=>(~quiet(alice)))&
(![X]:((~wise(X)&~humble(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(calm(X)=>(patient(X)&kind(X))))&
(![X]:((~creative(X)&~brave(X))<=>kind(X)))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:((happy(X)|creative(X))))<=>((~wise(alice)|humble(alice))))&
(![X]:((~tall(X)<~>calm(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>patient(X))=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)<~>~tall(X))=>(~curious(X)&old(X))))&
((?[X]:((rich(X)&curious(X))))<=>(?[X]:((happy(X)|~brave(X)))))&
((~strong(paul)&~rich(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(~humble(paul))&
((~kind(paul)|patient(paul)))&
((~creative(mary)|patient(mary)))&
(generous(john)) | calm(mary) | [
"p1",
"p4",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5526503830308882861838493
% SZS output start Proof for 5526503830308882861838493
2. ! [X0] : ((kind(X0) & ~creative(X0)) => (happy(X0) <~> ~humble(X0))) [input p1]
5. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (~happy(X0) <~> ~patient(X0))) [input p4]
9. ! [X0] : (calm(X0) => (kind(X0) & patient(X0))) [input p8]
10. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> kind(X0)) [input p9]
11. ! [X0] : (humble(X0) <=> ~happy(X0)) [input p10]
25. calm(mary) [input hypothesis]
30. ! [X0] : ((happy(X0) <~> ~humble(X0)) | (~kind(X0) | creative(X0))) [ennf transformation 2]
31. ! [X0] : ((happy(X0) <~> ~humble(X0)) | ~kind(X0) | creative(X0)) [flattening 30]
35. ! [X0] : ((kind(X0) & patient(X0)) | ~calm(X0)) [ennf transformation 9]
39. ! [X0] : (((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | ~kind(X0) | creative(X0)) [nnf transformation 31]
48. ! [X0] : (((~curious(X0) & ~humble(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | (curious(X0) | humble(X0)))) [nnf transformation 5]
49. ! [X0] : (((~curious(X0) & ~humble(X0)) | ((~happy(X0) | patient(X0)) & (~patient(X0) | happy(X0)))) & (((patient(X0) | happy(X0)) & (~patient(X0) | ~happy(X0))) | curious(X0) | humble(X0))) [flattening 48]
57. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | (brave(X0) | creative(X0)))) [nnf transformation 10]
58. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | brave(X0) | creative(X0))) [flattening 57]
59. ! [X0] : ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0))) [nnf transformation 11]
79. ~kind(X0) | ~happy(X0) | humble(X0) | creative(X0) [cnf transformation 39]
88. ~patient(X0) | ~humble(X0) | happy(X0) [cnf transformation 49]
105. ~calm(X0) | patient(X0) [cnf transformation 35]
106. ~calm(X0) | kind(X0) [cnf transformation 35]
108. ~kind(X0) | ~creative(X0) [cnf transformation 58]
110. ~humble(X0) | ~happy(X0) [cnf transformation 59]
111. humble(X0) | happy(X0) [cnf transformation 59]
141. calm(mary) [cnf transformation 25]
290. 33 <=> creative(mary) [avatar definition]
292. ~creative(mary) <- (~33) [avatar component clause 290]
294. 34 <=> patient(mary) [avatar definition]
296. patient(mary) <- (34) [avatar component clause 294]
302. patient(mary) [resolution 105,141]
303. 34 [avatar split clause 302,294]
304. kind(mary) [resolution 106,141]
305. ~creative(mary) [resolution 304,108]
310. ~humble(mary) | happy(mary) <- (34) [resolution 88,296]
311. happy(mary) <- (34) [subsumption resolution 310,111]
377. ~happy(mary) | humble(mary) | creative(mary) [resolution 79,304]
378. humble(mary) | creative(mary) <- (34) [subsumption resolution 377,311]
379. humble(mary) <- (~33, 34) [subsumption resolution 378,292]
385. ~happy(mary) <- (~33, 34) [resolution 379,110]
387. $false <- (~33, 34) [subsumption resolution 385,311]
388. 33 | ~34 [avatar contradiction clause 387]
394. ~33 [avatar split clause 305,290]
395. $false [avatar sat refutation 303,388,394]
% SZS output end Proof for 5526503830308882861838493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not kind is either tall or happy and vice versa. Everyone who is happy or not creative is either calm or not happy and vice versa. Everyone who is both rich and creative is both not old and calm and vice versa. If paul is not calm or patient then someone is happy and vice versa. Everyone who is either not funny or not creative is both not rich and not patient and vice versa. If mary is not tall or not curious then fred is both not brave and not creative. Everyone who is calm or curious is either not funny or not brave and vice versa. If someone is not curious then fred is rich or not funny and vice versa. If fred is tall or wise then someone is either not kind or kind and vice versa. If susan is curious or not brave then fred is either creative or not generous. If susan is both tall and not brave then someone is funny. Everyone who is both not generous and not quiet is not brave or not generous. Everyone who is not generous or rich is not funny. If mary is both not funny and not generous then someone is both not curious and not wise. If someone is either not wise or not curious then someone is rich and vice versa. If someone is not calm then someone is not calm or funny and vice versa. Susan is not patient. Fred is funny or brave. Susan is not wise. Someone is both not calm and strong. Someone is not generous or not quiet. Someone is not happy. Someone is strong or not patient. Lucy is either quiet or not curious. | Lucy is old. | neutral | (![X]:((~patient(X)<~>~kind(X))<=>(tall(X)<~>happy(X))))&
(![X]:((happy(X)|~creative(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((rich(X)&creative(X))<=>(~old(X)&calm(X))))&
(((~calm(paul)|patient(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~rich(X)&~patient(X))))&
(((~tall(mary)|~curious(mary)))=>((~brave(fred)&~creative(fred))))&
(![X]:((calm(X)|curious(X))<=>(~funny(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>((rich(fred)|~funny(fred))))&
(((tall(fred)|wise(fred)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(((curious(susan)|~brave(susan)))=>((creative(fred)<~>~generous(fred))))&
(((tall(susan)&~brave(susan)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)|rich(X))=>~funny(X)))&
(((~funny(mary)&~generous(mary)))=>(?[X]:((~curious(X)&~wise(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(~patient(susan))&
((funny(fred)|brave(fred)))&
(~wise(susan))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(~happy(X)))&
(?[X]:((strong(X)|~patient(X))))&
((quiet(lucy)<~>~curious(lucy))) | old(lucy) | [] | null | 0 |
If paul is creative or brave then someone is either old or kind and vice versa. Everyone who is tall is both quiet and not rich and vice versa. Everyone who is not calm is not patient and vice versa. If paul is either not quiet or patient then fred is both brave and not kind. If someone is quiet or tall then someone is not brave or humble. Everyone who is tall or happy is not wise. Everyone who is strong or not rich is not quiet or not funny and vice versa. Everyone who is calm or generous is wise or not creative. Everyone who is rich or curious is both not brave and not funny and vice versa. Everyone who is not creative or not kind is either not happy or humble and vice versa. Everyone who is humble or not rich is either old or not funny. Everyone who is not funny or patient is not old and vice versa. If fred is either not quiet or generous then someone is both humble and not funny and vice versa. Everyone who is not funny is both tall and not patient. If paul is happy then someone is either old or patient. Everyone who is generous is wise or not calm. Someone is patient or tall. John is either curious or tall. Someone is not tall or not happy. Someone is not wise or rich. Fred is both happy and not old. Paul is old or rich. | Paul is tall. | contradiction | (((creative(paul)|brave(paul)))<=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(quiet(X)&~rich(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(((~quiet(paul)<~>patient(paul)))=>((brave(fred)&~kind(fred))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((tall(X)|happy(X))=>~wise(X)))&
(![X]:((strong(X)|~rich(X))<=>(~quiet(X)|~funny(X))))&
(![X]:((calm(X)|generous(X))=>(wise(X)|~creative(X))))&
(![X]:((rich(X)|curious(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((humble(X)|~rich(X))=>(old(X)<~>~funny(X))))&
(![X]:((~funny(X)|patient(X))<=>~old(X)))&
(((~quiet(fred)<~>generous(fred)))<=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:(~funny(X)=>(tall(X)&~patient(X))))&
((happy(paul))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(generous(X)=>(wise(X)|~calm(X))))&
(?[X]:((patient(X)|tall(X))))&
((curious(john)<~>tall(john)))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~wise(X)|rich(X))))&
((happy(fred)&~old(fred)))&
((old(paul)|rich(paul))) | tall(paul) | [
"p1",
"p6",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3694245959655701603361849
% SZS output start Proof for 3694245959655701603361849
2. ! [X0] : (tall(X0) <=> (~rich(X0) & quiet(X0))) [input p1]
7. ! [X0] : ((~rich(X0) | strong(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p6]
9. ! [X0] : ((curious(X0) | rich(X0)) <=> (~funny(X0) & ~brave(X0))) [input p8]
12. ! [X0] : ((patient(X0) | ~funny(X0)) <=> ~old(X0)) [input p11]
14. ! [X0] : (~funny(X0) => (~patient(X0) & tall(X0))) [input p13]
22. rich(paul) | old(paul) [input p21]
23. tall(paul) [input hypothesis]
33. ! [X0] : ((~patient(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
42. ! [X0] : ((tall(X0) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 2]
43. ! [X0] : ((tall(X0) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | ~tall(X0))) [flattening 42]
48. ! [X0] : (((~rich(X0) | strong(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (rich(X0) & ~strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((~rich(X0) | strong(X0) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | (rich(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((curious(X0) | rich(X0)) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [nnf transformation 9]
51. ! [X0] : ((curious(X0) | rich(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0)))) [flattening 50]
55. ! [X0] : (((patient(X0) | ~funny(X0)) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((patient(X0) | ~funny(X0) | old(X0)) & (~old(X0) | (~patient(X0) & funny(X0)))) [flattening 55]
77. ~tall(X0) | quiet(X0) [cnf transformation 43]
78. ~rich(X0) | ~tall(X0) [cnf transformation 43]
90. ~funny(X0) | ~quiet(X0) | rich(X0) [cnf transformation 49]
97. ~funny(X0) | ~rich(X0) [cnf transformation 51]
110. ~old(X0) | funny(X0) [cnf transformation 56]
119. funny(X0) | tall(X0) [cnf transformation 33]
131. rich(paul) | old(paul) [cnf transformation 22]
132. tall(paul) [cnf transformation 23]
166. 8 <=> quiet(paul) [avatar definition]
167. quiet(paul) <- (8) [avatar component clause 166]
274. 31 <=> old(paul) [avatar definition]
276. old(paul) <- (31) [avatar component clause 274]
278. 32 <=> rich(paul) [avatar definition]
280. rich(paul) <- (32) [avatar component clause 278]
281. 31 | 32 [avatar split clause 131,278,274]
282. quiet(paul) [resolution 77,132]
285. 8 [avatar split clause 282,166]
290. funny(paul) <- (31) [resolution 110,276]
293. tall(X0) | ~rich(X0) [resolution 119,97]
295. ~rich(X0) [subsumption resolution 293,78]
328. ~quiet(paul) | rich(paul) <- (31) [resolution 90,290]
330. rich(paul) <- (8, 31) [subsumption resolution 328,167]
331. $false <- (8, 31) [subsumption resolution 330,295]
332. ~8 | ~31 [avatar contradiction clause 331]
335. $false <- (32) [subsumption resolution 280,295]
336. ~32 [avatar contradiction clause 335]
337. $false [avatar sat refutation 281,285,332,336]
% SZS output end Proof for 3694245959655701603361849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is creative or not creative and vice versa.
Everyone who is both not quiet and not wise is both rich and not funny and vice versa.
If alice is both curious and not happy then alice is not old or tall and vice versa.
If lucy is both calm and not creative then someone is both funny and old.
If mary is both not rich and creative then susan is not happy or not creative and vice versa.
If fred is curious or wise then someone is both happy and old.
If someone is strong then someone is both not patient and patient.
Everyone who is both not kind and creative is calm.
If someone is both patient and calm then lucy is brave or quiet.
If someone is both not creative and wise then mary is both wise and not old and vice versa.
Everyone who is not strong or not calm is curious or not strong and vice versa.
If susan is not generous then someone is not funny.
Everyone who is generous or not generous is both not brave and not wise and vice versa.
Everyone who is funny is both not strong and not kind and vice versa.
If someone is either happy or not old then paul is both not quiet and not kind.
Everyone who is kind or not strong is both not funny and not humble.
Someone is both not creative and not generous.
Fred is either patient or curious.
Someone is either rich or generous.
Someone is not creative or not funny.
Someone is both not humble and not curious. | Lucy is not patient. | neutral | (![X]:((brave(X)|~strong(X))<=>(creative(X)|~creative(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(rich(X)&~funny(X))))&
(((curious(alice)&~happy(alice)))<=>((~old(alice)|tall(alice))))&
(((calm(lucy)&~creative(lucy)))=>(?[X]:((funny(X)&old(X)))))&
(((~rich(mary)&creative(mary)))<=>((~happy(susan)|~creative(susan))))&
(((curious(fred)|wise(fred)))=>(?[X]:((happy(X)&old(X)))))&
((?[X]:(strong(X)))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(?[X]:((~creative(X)&~generous(X))))&
((patient(fred)<~>curious(fred)))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~humble(X)&~curious(X)))) | ~patient(lucy) | [] | null | 0 |
Everyone who is not funny or patient is either kind or not creative and vice versa.
If someone is both brave and not wise then someone is old and vice versa.
Everyone who is tall is both humble and patient.
Everyone who is either creative or generous is both not creative and not patient.
If lucy is either not calm or generous then susan is rich.
Everyone who is generous or not tall is either not curious or funny and vice versa.
If mary is either not creative or tall then someone is either kind or funny and vice versa.
Everyone who is either creative or generous is not calm or not happy.
Everyone who is tall or not generous is strong or not generous and vice versa.
Everyone who is not kind is not brave and vice versa.
Everyone who is kind is curious or old.
Everyone who is both not tall and not generous is both not generous and not patient and vice versa.
If fred is both not wise and not old then alice is both not funny and patient.
If john is either not curious or not calm then someone is kind or calm and vice versa.
If lucy is not tall or generous then someone is not wise or not happy.
Someone is either rich or not patient.
Someone is not humble.
Mary is either patient or not creative.
Someone is both not funny and humble.
John is humble or not wise. | Mary is not patient. | neutral | (![X]:((~funny(X)|patient(X))<=>(kind(X)<~>~creative(X))))&
((?[X]:((brave(X)&~wise(X))))<=>(?[X]:(old(X))))&
(![X]:(tall(X)=>(humble(X)&patient(X))))&
(![X]:((creative(X)<~>generous(X))=>(~creative(X)&~patient(X))))&
(((~calm(lucy)<~>generous(lucy)))=>(rich(susan)))&
(![X]:((generous(X)|~tall(X))<=>(~curious(X)<~>funny(X))))&
(((~creative(mary)<~>tall(mary)))<=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((creative(X)<~>generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((tall(X)|~generous(X))<=>(strong(X)|~generous(X))))&
(![X]:(~kind(X)<=>~brave(X)))&
(![X]:(kind(X)=>(curious(X)|old(X))))&
(![X]:((~tall(X)&~generous(X))<=>(~generous(X)&~patient(X))))&
(((~wise(fred)&~old(fred)))=>((~funny(alice)&patient(alice))))&
(((~curious(john)<~>~calm(john)))<=>(?[X]:((kind(X)|calm(X)))))&
(((~tall(lucy)|generous(lucy)))=>(?[X]:((~wise(X)|~happy(X)))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:(~humble(X)))&
((patient(mary)<~>~creative(mary)))&
(?[X]:((~funny(X)&humble(X))))&
((humble(john)|~wise(john))) | ~patient(mary) | [] | null | 0 |
If mary is humble or generous then mary is quiet or curious and vice versa.
If john is tall or rich then fred is not creative or old.
If someone is not curious then lucy is funny or patient and vice versa.
If alice is both not kind and not happy then someone is calm or not curious and vice versa.
Everyone who is both old and not wise is either rich or not quiet and vice versa.
Everyone who is funny is creative.
Everyone who is either not generous or strong is both funny and happy and vice versa.
If susan is both calm and not humble then someone is both creative and strong.
Everyone who is both not happy and not strong is not funny or not rich and vice versa.
Everyone who is either quiet or creative is wise or kind.
Everyone who is either not kind or not old is either not generous or not curious and vice versa.
Everyone who is not funny or generous is humble.
If someone is not wise then susan is creative or not patient and vice versa.
Everyone who is not wise or generous is either not tall or funny and vice versa.
If john is either patient or old then lucy is both not calm and generous and vice versa.
Everyone who is brave is either not generous or not brave.
Someone is not wise or not rich.
Someone is calm or not strong.
Someone is both curious and not humble.
Someone is both not old and not wise.
Someone is either strong or not creative.
Mary is both not creative and not tall.
Someone is not strong or curious. | Alice is happy. | neutral | (((humble(mary)|generous(mary)))<=>((quiet(mary)|curious(mary))))&
(((tall(john)|rich(john)))=>((~creative(fred)|old(fred))))&
((?[X]:(~curious(X)))<=>((funny(lucy)|patient(lucy))))&
(((~kind(alice)&~happy(alice)))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((old(X)&~wise(X))<=>(rich(X)<~>~quiet(X))))&
(![X]:(funny(X)=>creative(X)))&
(![X]:((~generous(X)<~>strong(X))<=>(funny(X)&happy(X))))&
(((calm(susan)&~humble(susan)))=>(?[X]:((creative(X)&strong(X)))))&
(![X]:((~happy(X)&~strong(X))<=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)<~>creative(X))=>(wise(X)|kind(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:((~funny(X)|generous(X))=>humble(X)))&
((?[X]:(~wise(X)))<=>((creative(susan)|~patient(susan))))&
(![X]:((~wise(X)|generous(X))<=>(~tall(X)<~>funny(X))))&
(((patient(john)<~>old(john)))<=>((~calm(lucy)&generous(lucy))))&
(![X]:(brave(X)=>(~generous(X)<~>~brave(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((curious(X)&~humble(X))))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((~creative(mary)&~tall(mary)))&
(?[X]:((~strong(X)|curious(X)))) | happy(alice) | [] | null | 0 |
Everyone who is creative or not old is wise or not brave and vice versa. Everyone who is not rich or not happy is patient or not rich. Everyone who is either not patient or quiet is calm and vice versa. If paul is both not patient and wise then someone is not old or brave and vice versa. Everyone who is old or not rich is brave or not old and vice versa. Everyone who is happy is quiet. Everyone who is not patient or not generous is generous and vice versa. If mary is either kind or rich then someone is both not calm and generous. If paul is patient or kind then someone is not creative. If someone is both not happy and happy then someone is patient. If alice is both happy and not calm then someone is not old or brave. Everyone who is both humble and not calm is not calm and vice versa. If someone is both not humble and tall then lucy is either happy or kind. Everyone who is not quiet or wise is not rich or patient and vice versa. If fred is generous then someone is strong. Someone is either generous or creative. John is creative or not creative. Someone is tall or not quiet. Alice is both not wise and not strong. Someone is both curious and old. | Paul is not rich. | entailment | (![X]:((creative(X)|~old(X))<=>(wise(X)|~brave(X))))&
(![X]:((~rich(X)|~happy(X))=>(patient(X)|~rich(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>calm(X)))&
(((~patient(paul)&wise(paul)))<=>(?[X]:((~old(X)|brave(X)))))&
(![X]:((old(X)|~rich(X))<=>(brave(X)|~old(X))))&
(![X]:(happy(X)=>quiet(X)))&
(![X]:((~patient(X)|~generous(X))<=>generous(X)))&
(((kind(mary)<~>rich(mary)))=>(?[X]:((~calm(X)&generous(X)))))&
(((patient(paul)|kind(paul)))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)&happy(X))))=>(?[X]:(patient(X))))&
(((happy(alice)&~calm(alice)))=>(?[X]:((~old(X)|brave(X)))))&
(![X]:((humble(X)&~calm(X))<=>~calm(X)))&
((?[X]:((~humble(X)&tall(X))))=>((happy(lucy)<~>kind(lucy))))&
(![X]:((~quiet(X)|wise(X))<=>(~rich(X)|patient(X))))&
((generous(fred))=>(?[X]:(strong(X))))&
(?[X]:((generous(X)<~>creative(X))))&
((creative(john)|~creative(john)))&
(?[X]:((tall(X)|~quiet(X))))&
((~wise(alice)&~strong(alice)))&
(?[X]:((curious(X)&old(X)))) | ~rich(paul) | [
"p3",
"p4",
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6828825526685346732596384
% SZS output start Proof for 6828825526685346732596384
4. (wise(paul) & ~patient(paul)) <=> ? [X0] : (brave(X0) | ~old(X0)) [input p3]
5. ! [X0] : ((~rich(X0) | old(X0)) <=> (~old(X0) | brave(X0))) [input p4]
7. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> generous(X0)) [input p6]
14. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (patient(X0) | ~rich(X0))) [input p13]
20. ? [X0] : (old(X0) & curious(X0)) [input p19]
21. rich(paul) [input hypothesis]
23. ? [X0] : old(X0) [pure predicate removal 20]
37. ((wise(paul) & ~patient(paul)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X0] : (brave(X0) | ~old(X0)) | (~wise(paul) | patient(paul))) [nnf transformation 4]
38. ((wise(paul) & ~patient(paul)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X0] : (brave(X0) | ~old(X0)) | ~wise(paul) | patient(paul)) [flattening 37]
39. ((wise(paul) & ~patient(paul)) | ! [X0] : (~brave(X0) & old(X0))) & (? [X1] : (brave(X1) | ~old(X1)) | ~wise(paul) | patient(paul)) [rectify 38]
40. ? [X1] : (brave(X1) | ~old(X1)) => (brave(sK0) | ~old(sK0)) [choice axiom]
41. ((wise(paul) & ~patient(paul)) | ! [X0] : (~brave(X0) & old(X0))) & ((brave(sK0) | ~old(sK0)) | ~wise(paul) | patient(paul)) [skolemisation 39,40]
42. ! [X0] : (((~rich(X0) | old(X0)) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | (rich(X0) & ~old(X0)))) [nnf transformation 5]
43. ! [X0] : ((~rich(X0) | old(X0) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | (rich(X0) & ~old(X0)))) [flattening 42]
44. ! [X0] : (((~generous(X0) | ~patient(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & patient(X0)))) [nnf transformation 7]
45. ! [X0] : ((~generous(X0) | ~patient(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & patient(X0)))) [flattening 44]
59. ! [X0] : (((wise(X0) | ~quiet(X0)) | (~patient(X0) & rich(X0))) & ((patient(X0) | ~rich(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 14]
60. ! [X0] : ((wise(X0) | ~quiet(X0) | (~patient(X0) & rich(X0))) & (patient(X0) | ~rich(X0) | (~wise(X0) & quiet(X0)))) [flattening 59]
68. ? [X0] : old(X0) => old(sK8) [choice axiom]
69. old(sK8) [skolemisation 23,68]
84. wise(paul) | ~brave(X0) [cnf transformation 41]
85. ~old(X0) | brave(X0) | ~old(X0) [cnf transformation 43]
91. generous(X0) | generous(X0) [cnf transformation 45]
92. ~generous(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 45]
107. ~rich(X0) | patient(X0) | ~wise(X0) [cnf transformation 60]
117. old(sK8) [cnf transformation 69]
118. rich(paul) [cnf transformation 21]
119. generous(X0) [duplicate literal removal 91]
120. ~generous(X0) | ~patient(X0) [duplicate literal removal 92]
121. ~old(X0) | brave(X0) [duplicate literal removal 85]
124. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
125. ~brave(X0) <- (1) [avatar component clause 124]
127. 2 <=> wise(paul) [avatar definition]
130. 1 | 2 [avatar split clause 84,127,124]
198. ~patient(X0) [resolution 120,119]
199. brave(sK8) [resolution 121,117]
233. patient(paul) | ~wise(paul) [resolution 107,118]
237. ~wise(paul) [subsumption resolution 233,198]
244. ~2 [avatar split clause 237,127]
250. $false <- (1) [resolution 125,199]
253. ~1 [avatar contradiction clause 250]
254. $false [avatar sat refutation 130,244,253]
% SZS output end Proof for 6828825526685346732596384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not strong then someone is both old and not kind.
Everyone who is not kind is either not creative or patient.
If paul is not patient or not funny then someone is both not curious and not quiet and vice versa.
Everyone who is either humble or not curious is either not tall or not wise.
Everyone who is tall is either patient or strong and vice versa.
Everyone who is both happy and not calm is strong or not patient.
If someone is either not strong or not humble then someone is strong and vice versa.
If someone is wise or kind then fred is not patient and vice versa.
If someone is not strong or happy then fred is either calm or not kind and vice versa.
Everyone who is either humble or not strong is not strong or not kind.
If someone is either quiet or patient then someone is not happy or strong and vice versa.
Everyone who is not rich or calm is both creative and not tall and vice versa.
Everyone who is either calm or tall is not old or funny and vice versa.
Everyone who is either not brave or not rich is both not quiet and patient and vice versa.
If john is not creative then lucy is not patient and vice versa.
Everyone who is calm or curious is creative and vice versa.
Someone is strong or not funny.
Someone is not rich or not old.
Someone is either not quiet or old.
Someone is both kind and not creative.
Someone is not funny.
Lucy is either strong or not generous.
Fred is either happy or not quiet.
Someone is both old and curious. | Fred is old. | neutral | ((?[X]:((~calm(X)|~strong(X))))=>(?[X]:((old(X)&~kind(X)))))&
(![X]:(~kind(X)=>(~creative(X)<~>patient(X))))&
(((~patient(paul)|~funny(paul)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((humble(X)<~>~curious(X))=>(~tall(X)<~>~wise(X))))&
(![X]:(tall(X)<=>(patient(X)<~>strong(X))))&
(![X]:((happy(X)&~calm(X))=>(strong(X)|~patient(X))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>(?[X]:(strong(X))))&
((?[X]:((wise(X)|kind(X))))<=>(~patient(fred)))&
((?[X]:((~strong(X)|happy(X))))<=>((calm(fred)<~>~kind(fred))))&
(![X]:((humble(X)<~>~strong(X))=>(~strong(X)|~kind(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~rich(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~rich(X))<=>(~quiet(X)&patient(X))))&
((~creative(john))<=>(~patient(lucy)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~funny(X)))&
((strong(lucy)<~>~generous(lucy)))&
((happy(fred)<~>~quiet(fred)))&
(?[X]:((old(X)&curious(X)))) | old(fred) | [] | null | 0 |
Everyone who is brave is not funny or creative. Everyone who is happy or tall is either not funny or happy. If john is either not old or not patient then someone is quiet and vice versa. If someone is both not generous and happy then someone is not funny or creative and vice versa. Everyone who is not happy is either not generous or not old and vice versa. If john is both not brave and not quiet then someone is both brave and not generous. If someone is either not kind or not rich then someone is both not generous and not kind. Everyone who is either rich or not kind is not happy or not wise and vice versa. If alice is wise then someone is both generous and not brave and vice versa. Everyone who is tall or funny is both not strong and calm and vice versa. If fred is not brave then someone is happy or not happy. Everyone who is not kind or quiet is not kind or not funny and vice versa. Everyone who is generous or not rich is creative or kind. If someone is generous or not tall then someone is both curious and not old. Everyone who is not humble or wise is calm and vice versa. John is either not generous or not patient. Lucy is both not kind and calm. Fred is both not humble and not creative. John is either old or not rich. Paul is both generous and not old. Alice is both funny and quiet. | John is funny. | entailment | (![X]:(brave(X)=>(~funny(X)|creative(X))))&
(![X]:((happy(X)|tall(X))=>(~funny(X)<~>happy(X))))&
(((~old(john)<~>~patient(john)))<=>(?[X]:(quiet(X))))&
((?[X]:((~generous(X)&happy(X))))<=>(?[X]:((~funny(X)|creative(X)))))&
(![X]:(~happy(X)<=>(~generous(X)<~>~old(X))))&
(((~brave(john)&~quiet(john)))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~kind(X)<~>~rich(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:((rich(X)<~>~kind(X))<=>(~happy(X)|~wise(X))))&
((wise(alice))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((tall(X)|funny(X))<=>(~strong(X)&calm(X))))&
((~brave(fred))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~kind(X)|quiet(X))<=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)|~rich(X))=>(creative(X)|kind(X))))&
((?[X]:((generous(X)|~tall(X))))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~humble(X)|wise(X))<=>calm(X)))&
((~generous(john)<~>~patient(john)))&
((~kind(lucy)&calm(lucy)))&
((~humble(fred)&~creative(fred)))&
((old(john)<~>~rich(john)))&
((generous(paul)&~old(paul)))&
((funny(alice)&quiet(alice))) | funny(john) | [
"p1",
"p2",
"p4",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5711450746168784704882481
% SZS output start Proof for 5711450746168784704882481
2. ! [X0] : ((tall(X0) | happy(X0)) => (~funny(X0) <~> happy(X0))) [input p1]
3. (~old(john) <~> ~patient(john)) <=> ? [X0] : quiet(X0) [input p2]
5. ! [X0] : (~happy(X0) <=> (~generous(X0) <~> ~old(X0))) [input p4]
16. ~generous(john) <~> ~patient(john) [input p15]
21. quiet(alice) & funny(alice) [input p20]
22. ~funny(john) [input hypothesis]
29. ! [X0] : ((~funny(X0) <~> happy(X0)) | (~tall(X0) & ~happy(X0))) [ennf transformation 2]
37. ! [X0] : (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~tall(X0) & ~happy(X0))) [nnf transformation 29]
38. (((patient(john) | old(john)) & (~patient(john) | ~old(john))) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ((~old(john) | patient(john)) & (~patient(john) | old(john)))) [nnf transformation 3]
39. (((patient(john) | old(john)) & (~patient(john) | ~old(john))) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ((~old(john) | patient(john)) & (~patient(john) | old(john)))) [rectify 38]
40. ? [X1] : quiet(X1) => quiet(sK0) [choice axiom]
41. (((patient(john) | old(john)) & (~patient(john) | ~old(john))) | ! [X0] : ~quiet(X0)) & (quiet(sK0) | ((~old(john) | patient(john)) & (~patient(john) | old(john)))) [skolemisation 39,40]
47. ! [X0] : ((~happy(X0) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) & (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | happy(X0))) [nnf transformation 5]
71. (patient(john) | generous(john)) & (~patient(john) | ~generous(john)) [nnf transformation 16]
76. ~happy(X0) | funny(X0) | ~happy(X0) [cnf transformation 37]
80. ~patient(john) | ~old(john) | ~quiet(X0) [cnf transformation 41]
81. patient(john) | old(john) | ~quiet(X0) [cnf transformation 41]
87. ~generous(X0) | ~old(X0) | happy(X0) [cnf transformation 47]
88. generous(X0) | old(X0) | happy(X0) [cnf transformation 47]
123. ~patient(john) | ~generous(john) [cnf transformation 71]
124. patient(john) | generous(john) [cnf transformation 71]
134. quiet(alice) [cnf transformation 21]
135. ~funny(john) [cnf transformation 22]
136. ~happy(X0) | funny(X0) [duplicate literal removal 76]
138. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
139. ~quiet(X0) <- (1) [avatar component clause 138]
141. 2 <=> old(john) [avatar definition]
142. ~old(john) <- (~2) [avatar component clause 141]
143. old(john) <- (2) [avatar component clause 141]
145. 3 <=> patient(john) [avatar definition]
148. 1 | 2 | 3 [avatar split clause 81,145,141,138]
149. 1 | ~2 | ~3 [avatar split clause 80,145,141,138]
253. 27 <=> generous(john) [avatar definition]
254. ~generous(john) <- (~27) [avatar component clause 253]
255. generous(john) <- (27) [avatar component clause 253]
256. 27 | 3 [avatar split clause 124,145,253]
257. ~27 | ~3 [avatar split clause 123,145,253]
292. old(john) | happy(john) <- (~27) [resolution 88,254]
296. happy(john) <- (~2, ~27) [subsumption resolution 292,142]
309. funny(john) <- (~2, ~27) [resolution 296,136]
310. $false <- (~2, ~27) [subsumption resolution 309,135]
311. 2 | 27 [avatar contradiction clause 310]
312. ~old(john) | happy(john) <- (27) [resolution 255,87]
314. happy(john) <- (2, 27) [subsumption resolution 312,143]
325. funny(john) <- (2, 27) [resolution 314,136]
326. $false <- (2, 27) [subsumption resolution 325,135]
327. ~2 | ~27 [avatar contradiction clause 326]
333. $false <- (1) [resolution 139,134]
336. ~1 [avatar contradiction clause 333]
337. $false [avatar sat refutation 148,149,256,257,311,327,336]
% SZS output end Proof for 5711450746168784704882481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or quiet is not strong or happy. If someone is either not patient or calm then lucy is either brave or patient. If fred is both not happy and old then alice is curious or not funny and vice versa. If fred is both happy and not rich then someone is either tall or not calm and vice versa. If lucy is not strong or brave then someone is both not humble and calm. Everyone who is both quiet and strong is not humble. Everyone who is patient or brave is funny and vice versa. Everyone who is not tall is not old or not rich. If john is either not rich or strong then john is not strong or not curious and vice versa. If someone is rich or not wise then someone is not brave or not happy and vice versa. Everyone who is either rich or not quiet is either not funny or not tall. Everyone who is curious is either creative or wise and vice versa. Everyone who is not tall or not old is curious or wise and vice versa. Everyone who is either funny or calm is wise or quiet and vice versa. If john is both strong and brave then someone is both not tall and strong. If mary is wise or tall then susan is not funny or generous. Alice is creative. Someone is either funny or not humble. Mary is both not creative and old. Someone is creative or strong. Lucy is not rich. Mary is patient or not strong. Fred is calm or not calm. Paul is both calm and strong. | Fred is not calm. | neutral | (![X]:((~creative(X)|quiet(X))=>(~strong(X)|happy(X))))&
((?[X]:((~patient(X)<~>calm(X))))=>((brave(lucy)<~>patient(lucy))))&
(((~happy(fred)&old(fred)))<=>((curious(alice)|~funny(alice))))&
(((happy(fred)&~rich(fred)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((~strong(lucy)|brave(lucy)))=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((quiet(X)&strong(X))=>~humble(X)))&
(![X]:((patient(X)|brave(X))<=>funny(X)))&
(![X]:(~tall(X)=>(~old(X)|~rich(X))))&
(((~rich(john)<~>strong(john)))<=>((~strong(john)|~curious(john))))&
((?[X]:((rich(X)|~wise(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((rich(X)<~>~quiet(X))=>(~funny(X)<~>~tall(X))))&
(![X]:(curious(X)<=>(creative(X)<~>wise(X))))&
(![X]:((~tall(X)|~old(X))<=>(curious(X)|wise(X))))&
(![X]:((funny(X)<~>calm(X))<=>(wise(X)|quiet(X))))&
(((strong(john)&brave(john)))=>(?[X]:((~tall(X)&strong(X)))))&
(((wise(mary)|tall(mary)))=>((~funny(susan)|generous(susan))))&
(creative(alice))&
(?[X]:((funny(X)<~>~humble(X))))&
((~creative(mary)&old(mary)))&
(?[X]:((creative(X)|strong(X))))&
(~rich(lucy))&
((patient(mary)|~strong(mary)))&
((calm(fred)|~calm(fred)))&
((calm(paul)&strong(paul))) | ~calm(fred) | [] | null | 0 |
Everyone who is not old is both not rich and rich.
Everyone who is either wise or not calm is either not strong or strong and vice versa.
Everyone who is either tall or humble is patient and vice versa.
Everyone who is both calm and not funny is either not old or not strong.
Everyone who is generous or kind is not humble or calm.
If alice is not brave or calm then someone is either old or not brave.
If john is either kind or happy then someone is either kind or not brave.
Everyone who is not generous is either not kind or not tall.
If susan is either not kind or funny then someone is not old and vice versa.
Everyone who is both not old and old is both patient and not generous.
If alice is rich then paul is not brave and vice versa.
Everyone who is not rich is either funny or not creative and vice versa.
If fred is not generous or generous then alice is both not happy and not kind.
Everyone who is rich is either brave or tall.
If someone is either not generous or kind then someone is either not kind or not curious and vice versa.
If someone is not creative then paul is either not calm or funny and vice versa.
Fred is either calm or not humble.
Mary is both happy and generous.
Someone is not happy.
Someone is either tall or curious.
Susan is both brave and kind.
Someone is either calm or tall.
Alice is both not funny and not kind.
John is funny or not brave. | Alice is not happy. | entailment | (![X]:(~old(X)=>(~rich(X)&rich(X))))&
(![X]:((wise(X)<~>~calm(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((tall(X)<~>humble(X))<=>patient(X)))&
(![X]:((calm(X)&~funny(X))=>(~old(X)<~>~strong(X))))&
(![X]:((generous(X)|kind(X))=>(~humble(X)|calm(X))))&
(((~brave(alice)|calm(alice)))=>(?[X]:((old(X)<~>~brave(X)))))&
(((kind(john)<~>happy(john)))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~tall(X))))&
(((~kind(susan)<~>funny(susan)))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)&old(X))=>(patient(X)&~generous(X))))&
((rich(alice))<=>(~brave(paul)))&
(![X]:(~rich(X)<=>(funny(X)<~>~creative(X))))&
(((~generous(fred)|generous(fred)))=>((~happy(alice)&~kind(alice))))&
(![X]:(rich(X)=>(brave(X)<~>tall(X))))&
((?[X]:((~generous(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
((?[X]:(~creative(X)))<=>((~calm(paul)<~>funny(paul))))&
((calm(fred)<~>~humble(fred)))&
((happy(mary)&generous(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((tall(X)<~>curious(X))))&
((brave(susan)&kind(susan)))&
(?[X]:((calm(X)<~>tall(X))))&
((~funny(alice)&~kind(alice)))&
((funny(john)|~brave(john))) | ~happy(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1075763504338141024814750
% SZS output start Proof for 1075763504338141024814750
13. (generous(fred) | ~generous(fred)) => (~kind(alice) & ~happy(alice)) [input p12]
25. happy(alice) [input hypothesis]
39. (~kind(alice) & ~happy(alice)) | (~generous(fred) & generous(fred)) [ennf transformation 13]
114. ~happy(alice) | generous(fred) [cnf transformation 39]
115. ~happy(alice) | ~generous(fred) [cnf transformation 39]
146. happy(alice) [cnf transformation 25]
214. 12 <=> generous(fred) [avatar definition]
224. 14 <=> happy(alice) [avatar definition]
227. ~12 | ~14 [avatar split clause 115,224,214]
228. 12 | ~14 [avatar split clause 114,224,214]
325. 14 [avatar split clause 146,224]
326. $false [avatar sat refutation 227,228,325]
% SZS output end Proof for 1075763504338141024814750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not humble then someone is not rich or not tall.
Everyone who is both humble and tall is not humble or rich.
Everyone who is not creative is not rich and vice versa.
Everyone who is both old and wise is not patient and vice versa.
If someone is either not wise or quiet then someone is either not brave or old and vice versa.
Everyone who is not patient is either rich or not old and vice versa.
Everyone who is not rich or not old is both funny and not patient.
If fred is both patient and not kind then someone is either generous or not creative and vice versa.
Everyone who is either not patient or patient is both not brave and not kind and vice versa.
If mary is both wise and not creative then mary is patient or not calm and vice versa.
If someone is both creative and not wise then fred is patient.
If someone is both quiet and not happy then alice is not old.
If mary is humble then mary is both generous and strong and vice versa.
If someone is curious then john is both not creative and brave and vice versa.
Everyone who is either not funny or not generous is both not creative and brave.
If someone is both rich and not calm then someone is calm or not strong.
Someone is both not calm and creative.
Someone is either not strong or humble.
Someone is not happy or not humble.
Someone is either not old or not calm. | Alice is not old. | contradiction | ((?[X]:((~strong(X)|~humble(X))))=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((humble(X)&tall(X))=>(~humble(X)|rich(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:((old(X)&wise(X))<=>~patient(X)))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:(~patient(X)<=>(rich(X)<~>~old(X))))&
(![X]:((~rich(X)|~old(X))=>(funny(X)&~patient(X))))&
(((patient(fred)&~kind(fred)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~patient(X)<~>patient(X))<=>(~brave(X)&~kind(X))))&
(((wise(mary)&~creative(mary)))<=>((patient(mary)|~calm(mary))))&
((?[X]:((creative(X)&~wise(X))))=>(patient(fred)))&
((?[X]:((quiet(X)&~happy(X))))=>(~old(alice)))&
((humble(mary))<=>((generous(mary)&strong(mary))))&
((?[X]:(curious(X)))<=>((~creative(john)&brave(john))))&
(![X]:((~funny(X)<~>~generous(X))=>(~creative(X)&brave(X))))&
((?[X]:((rich(X)&~calm(X))))=>(?[X]:((calm(X)|~strong(X)))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~old(X)<~>~calm(X)))) | ~old(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1385203307230001008617444
% SZS output start Proof for 1385203307230001008617444
4. ! [X0] : ((wise(X0) & old(X0)) <=> ~patient(X0)) [input p3]
7. ! [X0] : ((~old(X0) | ~rich(X0)) => (~patient(X0) & funny(X0))) [input p6]
21. ~old(alice) [input hypothesis]
27. ! [X0] : ((~patient(X0) & funny(X0)) | (old(X0) & rich(X0))) [ennf transformation 7]
33. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | (~wise(X0) | ~old(X0)))) [nnf transformation 4]
34. ! [X0] : (((wise(X0) & old(X0)) | patient(X0)) & (~patient(X0) | ~wise(X0) | ~old(X0))) [flattening 33]
74. old(X0) | patient(X0) [cnf transformation 34]
91. ~patient(X0) | old(X0) [cnf transformation 27]
129. ~old(alice) [cnf transformation 21]
172. old(X0) [subsumption resolution 91,74]
283. $false [subsumption resolution 129,172]
% SZS output end Proof for 1385203307230001008617444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is both not tall and strong.
Everyone who is both not wise and curious is not quiet and vice versa.
Everyone who is either old or not rich is both not old and calm and vice versa.
Everyone who is both not happy and kind is either not generous or not funny.
If someone is rich then lucy is quiet and vice versa.
Everyone who is not strong or not creative is not tall and vice versa.
If someone is both strong and brave then someone is not funny and vice versa.
If someone is both funny and creative then mary is both not funny and not old and vice versa.
Everyone who is not curious or old is both curious and happy.
If someone is curious then mary is patient.
Everyone who is humble or old is not strong.
If someone is not strong then fred is funny and vice versa.
Everyone who is both rich and not calm is not strong or not wise and vice versa.
If someone is either not funny or quiet then someone is either not rich or creative and vice versa.
If someone is not generous then fred is either rich or kind and vice versa.
If mary is not happy or humble then someone is not happy or not generous and vice versa.
Someone is both not humble and not generous.
Someone is generous.
Lucy is both tall and kind.
Paul is both not funny and rich.
Mary is either generous or not old.
Someone is not old.
Someone is not funny or not brave. | Lucy is rich. | contradiction | (![X]:((~creative(X)<~>brave(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)&curious(X))<=>~quiet(X)))&
(![X]:((old(X)<~>~rich(X))<=>(~old(X)&calm(X))))&
(![X]:((~happy(X)&kind(X))=>(~generous(X)<~>~funny(X))))&
((?[X]:(rich(X)))<=>(quiet(lucy)))&
(![X]:((~strong(X)|~creative(X))<=>~tall(X)))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((funny(X)&creative(X))))<=>((~funny(mary)&~old(mary))))&
(![X]:((~curious(X)|old(X))=>(curious(X)&happy(X))))&
((?[X]:(curious(X)))=>(patient(mary)))&
(![X]:((humble(X)|old(X))=>~strong(X)))&
((?[X]:(~strong(X)))<=>(funny(fred)))&
(![X]:((rich(X)&~calm(X))<=>(~strong(X)|~wise(X))))&
((?[X]:((~funny(X)<~>quiet(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
((?[X]:(~generous(X)))<=>((rich(fred)<~>kind(fred))))&
(((~happy(mary)|humble(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:(generous(X)))&
((tall(lucy)&kind(lucy)))&
((~funny(paul)&rich(paul)))&
((generous(mary)<~>~old(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)|~brave(X)))) | rich(lucy) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p12",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 692395170027352807695703
% SZS output start Proof for 692395170027352807695703
2. ! [X0] : ((curious(X0) & ~wise(X0)) <=> ~quiet(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (calm(X0) & ~old(X0))) [input p2]
5. ? [X0] : rich(X0) <=> quiet(lucy) [input p4]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> ~tall(X0)) [input p5]
9. ! [X0] : ((old(X0) | ~curious(X0)) => (happy(X0) & curious(X0))) [input p8]
11. ! [X0] : ((old(X0) | humble(X0)) => ~strong(X0)) [input p10]
13. ! [X0] : ((~calm(X0) & rich(X0)) <=> (~wise(X0) | ~strong(X0))) [input p12]
19. kind(lucy) & tall(lucy) [input p18]
20. rich(paul) & ~funny(paul) [input p19]
24. rich(lucy) [input hypothesis]
31. ! [X0] : ((happy(X0) & curious(X0)) | (~old(X0) & curious(X0))) [ennf transformation 9]
32. ! [X0] : (~strong(X0) | (~old(X0) & ~humble(X0))) [ennf transformation 11]
34. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | (~curious(X0) | wise(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | ~curious(X0) | wise(X0))) [flattening 34]
36. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 3]
37. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [flattening 36]
39. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X0] : ~rich(X0)) [nnf transformation 5]
40. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [rectify 39]
41. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
42. (rich(sK0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [skolemisation 40,41]
43. ! [X0] : (((~creative(X0) | ~strong(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [nnf transformation 6]
44. ! [X0] : ((~creative(X0) | ~strong(X0) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [flattening 43]
59. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | calm(X0) | ~rich(X0))) [flattening 59]
88. ~quiet(X0) | ~curious(X0) | wise(X0) [cnf transformation 35]
91. ~old(X0) | ~rich(X0) | ~old(X0) [cnf transformation 37]
95. ~rich(X0) | old(X0) | ~calm(X0) | old(X0) [cnf transformation 37]
99. quiet(lucy) | ~rich(X1) [cnf transformation 42]
101. ~tall(X0) | strong(X0) [cnf transformation 44]
111. curious(X0) | curious(X0) [cnf transformation 31]
116. ~old(X0) | ~strong(X0) [cnf transformation 32]
119. ~rich(X0) | ~strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 60]
120. rich(X0) | strong(X0) [cnf transformation 60]
143. tall(lucy) [cnf transformation 19]
146. rich(paul) [cnf transformation 20]
151. rich(lucy) [cnf transformation 24]
152. curious(X0) [duplicate literal removal 111]
153. ~rich(X0) | ~old(X0) [duplicate literal removal 91]
154. ~calm(X0) | old(X0) | ~rich(X0) [duplicate literal removal 95]
156. 1 <=> quiet(lucy) [avatar definition]
157. quiet(lucy) <- (1) [avatar component clause 156]
165. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
166. ~rich(X1) <- (3) [avatar component clause 165]
167. 3 | 1 [avatar split clause 99,156,165]
318. $false <- (3) [resolution 166,146]
321. ~3 [avatar contradiction clause 318]
325. strong(lucy) [resolution 101,143]
335. ~old(X1) | strong(X1) [resolution 153,120]
339. ~old(X1) [subsumption resolution 335,116]
356. ~curious(lucy) | wise(lucy) <- (1) [resolution 88,157]
359. wise(lucy) <- (1) [subsumption resolution 356,152]
421. ~strong(lucy) | calm(lucy) | ~wise(lucy) [resolution 119,151]
425. calm(lucy) | ~wise(lucy) [subsumption resolution 421,325]
426. calm(lucy) <- (1) [subsumption resolution 425,359]
457. old(lucy) | ~rich(lucy) <- (1) [resolution 426,154]
460. ~rich(lucy) <- (1) [subsumption resolution 457,339]
461. $false <- (1) [subsumption resolution 460,151]
462. ~1 [avatar contradiction clause 461]
463. $false [avatar sat refutation 167,321,462]
% SZS output end Proof for 692395170027352807695703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either not kind or creative and vice versa.
Everyone who is calm or quiet is not funny and vice versa.
If susan is happy then someone is both not creative and tall.
Everyone who is either curious or brave is either tall or not funny and vice versa.
If fred is both creative and quiet then someone is both not strong and not generous and vice versa.
Everyone who is not rich or calm is quiet or not rich and vice versa.
If someone is not wise then susan is not generous or brave and vice versa.
Everyone who is both not curious and creative is either tall or happy and vice versa.
Everyone who is tall or generous is humble and vice versa.
Everyone who is humble or not calm is humble or tall and vice versa.
Everyone who is not rich is either rich or not kind and vice versa.
Everyone who is both not old and strong is not brave or humble and vice versa.
If mary is not creative or wise then john is either rich or not humble.
Everyone who is strong or rich is either generous or creative and vice versa.
Everyone who is curious or not old is not humble or rich.
If fred is not brave then someone is not brave.
Someone is either not brave or not patient.
Paul is both not happy and funny.
Lucy is both not quiet and brave.
Someone is either kind or wise.
John is both not creative and generous.
Fred is either not patient or tall.
John is not humble or happy. | Paul is generous. | entailment | (![X]:(funny(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((calm(X)|quiet(X))<=>~funny(X)))&
((happy(susan))=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((curious(X)<~>brave(X))<=>(tall(X)<~>~funny(X))))&
(((creative(fred)&quiet(fred)))<=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(~wise(X)))<=>((~generous(susan)|brave(susan))))&
(![X]:((~curious(X)&creative(X))<=>(tall(X)<~>happy(X))))&
(![X]:((tall(X)|generous(X))<=>humble(X)))&
(![X]:((humble(X)|~calm(X))<=>(humble(X)|tall(X))))&
(![X]:(~rich(X)<=>(rich(X)<~>~kind(X))))&
(![X]:((~old(X)&strong(X))<=>(~brave(X)|humble(X))))&
(((~creative(mary)|wise(mary)))=>((rich(john)<~>~humble(john))))&
(![X]:((strong(X)|rich(X))<=>(generous(X)<~>creative(X))))&
(![X]:((curious(X)|~old(X))=>(~humble(X)|rich(X))))&
((~brave(fred))=>(?[X]:(~brave(X))))&
(?[X]:((~brave(X)<~>~patient(X))))&
((~happy(paul)&funny(paul)))&
((~quiet(lucy)&brave(lucy)))&
(?[X]:((kind(X)<~>wise(X))))&
((~creative(john)&generous(john)))&
((~patient(fred)<~>tall(fred)))&
((~humble(john)|happy(john))) | generous(paul) | [
"p0",
"p1",
"p7",
"p8",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 659703981403414704123559
% SZS output start Proof for 659703981403414704123559
1. ! [X0] : (funny(X0) <=> (~kind(X0) <~> creative(X0))) [input p0]
2. ! [X0] : ((quiet(X0) | calm(X0)) <=> ~funny(X0)) [input p1]
8. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (tall(X0) <~> happy(X0))) [input p7]
9. ! [X0] : ((generous(X0) | tall(X0)) <=> humble(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | humble(X0)) <=> (tall(X0) | humble(X0))) [input p9]
11. ! [X0] : (~rich(X0) <=> (rich(X0) <~> ~kind(X0))) [input p10]
18. funny(paul) & ~happy(paul) [input p17]
24. ~generous(paul) [input hypothesis]
30. ! [X0] : ((funny(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~funny(X0))) [nnf transformation 1]
31. ! [X0] : (((quiet(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 2]
32. ! [X0] : ((quiet(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (~quiet(X0) & ~calm(X0)))) [flattening 31]
48. ! [X0] : (((creative(X0) & ~curious(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (~creative(X0) | curious(X0)))) [nnf transformation 8]
49. ! [X0] : (((creative(X0) & ~curious(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | ~creative(X0) | curious(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) | tall(X0)) | ~humble(X0)) & (humble(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 9]
51. ! [X0] : ((generous(X0) | tall(X0) | ~humble(X0)) & (humble(X0) | (~generous(X0) & ~tall(X0)))) [flattening 50]
52. ! [X0] : (((~calm(X0) | humble(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (calm(X0) & ~humble(X0)))) [nnf transformation 10]
53. ! [X0] : ((~calm(X0) | humble(X0) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | (calm(X0) & ~humble(X0)))) [flattening 52]
54. ! [X0] : ((~rich(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | rich(X0))) [nnf transformation 11]
70. ~creative(X0) | kind(X0) | ~funny(X0) [cnf transformation 30]
73. ~calm(X0) | ~funny(X0) [cnf transformation 32]
101. ~tall(X0) | happy(X0) | creative(X0) [cnf transformation 49]
103. ~tall(X0) | humble(X0) [cnf transformation 51]
105. ~humble(X0) | tall(X0) | generous(X0) [cnf transformation 51]
107. tall(X0) | humble(X0) | calm(X0) [cnf transformation 53]
110. ~kind(X0) | rich(X0) | rich(X0) [cnf transformation 54]
112. ~rich(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 54]
134. ~happy(paul) [cnf transformation 18]
135. funny(paul) [cnf transformation 18]
145. ~generous(paul) [cnf transformation 24]
146. ~kind(X0) | rich(X0) [duplicate literal removal 110]
147. ~rich(X0) | ~kind(X0) [duplicate literal removal 112]
203. humble(X0) | calm(X0) [subsumption resolution 107,103]
204. ~kind(X0) [subsumption resolution 146,147]
342. generous(X0) | tall(X0) | calm(X0) [resolution 105,203]
525. tall(paul) | calm(paul) [resolution 342,145]
538. 48 <=> calm(paul) [avatar definition]
540. calm(paul) <- (48) [avatar component clause 538]
542. 49 <=> tall(paul) [avatar definition]
544. tall(paul) <- (49) [avatar component clause 542]
545. 48 | 49 [avatar split clause 525,542,538]
593. 56 <=> creative(paul) [avatar definition]
595. creative(paul) <- (56) [avatar component clause 593]
746. ~funny(paul) <- (48) [resolution 540,73]
747. $false <- (48) [subsumption resolution 746,135]
748. ~48 [avatar contradiction clause 747]
751. happy(paul) | creative(paul) <- (49) [resolution 544,101]
753. creative(paul) <- (49) [subsumption resolution 751,134]
754. 56 | ~49 [avatar split clause 753,542,593]
764. kind(paul) | ~funny(paul) <- (56) [resolution 595,70]
775. ~funny(paul) <- (56) [subsumption resolution 764,204]
776. $false <- (56) [subsumption resolution 775,135]
777. ~56 [avatar contradiction clause 776]
778. $false [avatar sat refutation 545,748,754,777]
% SZS output end Proof for 659703981403414704123559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not generous is not strong and vice versa.
Everyone who is both not kind and not calm is not strong.
Everyone who is not patient or kind is either generous or humble.
Everyone who is both humble and wise is not happy or rich.
If someone is both kind and not tall then fred is not humble or humble.
Everyone who is quiet is not calm or not funny.
If someone is humble or not tall then someone is both funny and not happy and vice versa.
Everyone who is both not calm and not wise is both funny and creative and vice versa.
Everyone who is not creative is strong.
If fred is either quiet or not wise then someone is either rich or creative.
Everyone who is generous is not brave and vice versa.
If someone is not quiet or wise then someone is not kind or wise and vice versa.
Everyone who is not humble is rich and vice versa.
If someone is not funny or not tall then someone is not patient and vice versa.
Everyone who is both strong and not quiet is curious or strong and vice versa.
Everyone who is either calm or not kind is not brave and vice versa.
Lucy is strong.
Someone is not funny.
Someone is both curious and not generous.
Paul is not creative.
Susan is either quiet or curious.
Paul is old or generous.
Someone is both creative and patient.
Alice is either not quiet or not patient. | Paul is not quiet. | entailment | (![X]:((happy(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((~kind(X)&~calm(X))=>~strong(X)))&
(![X]:((~patient(X)|kind(X))=>(generous(X)<~>humble(X))))&
(![X]:((humble(X)&wise(X))=>(~happy(X)|rich(X))))&
((?[X]:((kind(X)&~tall(X))))=>((~humble(fred)|humble(fred))))&
(![X]:(quiet(X)=>(~calm(X)|~funny(X))))&
((?[X]:((humble(X)|~tall(X))))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((~calm(X)&~wise(X))<=>(funny(X)&creative(X))))&
(![X]:(~creative(X)=>strong(X)))&
(((quiet(fred)<~>~wise(fred)))=>(?[X]:((rich(X)<~>creative(X)))))&
(![X]:(generous(X)<=>~brave(X)))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
(![X]:(~humble(X)<=>rich(X)))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:(~patient(X))))&
(![X]:((strong(X)&~quiet(X))<=>(curious(X)|strong(X))))&
(![X]:((calm(X)<~>~kind(X))<=>~brave(X)))&
(strong(lucy))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)&~generous(X))))&
(~creative(paul))&
((quiet(susan)<~>curious(susan)))&
((old(paul)|generous(paul)))&
(?[X]:((creative(X)&patient(X))))&
((~quiet(alice)<~>~patient(alice))) | ~quiet(paul) | [
"p8",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 412833581238372020278606
% SZS output start Proof for 412833581238372020278606
9. ! [X0] : (~creative(X0) => strong(X0)) [input p8]
15. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (strong(X0) | curious(X0))) [input p14]
20. ~creative(paul) [input p19]
25. quiet(paul) [input hypothesis]
39. ! [X0] : (strong(X0) | creative(X0)) [ennf transformation 9]
65. ! [X0] : (((~quiet(X0) & strong(X0)) | (~strong(X0) & ~curious(X0))) & ((strong(X0) | curious(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 15]
66. ! [X0] : (((~quiet(X0) & strong(X0)) | (~strong(X0) & ~curious(X0))) & (strong(X0) | curious(X0) | quiet(X0) | ~strong(X0))) [flattening 65]
97. creative(X0) | strong(X0) [cnf transformation 39]
117. ~quiet(X0) | ~strong(X0) [cnf transformation 66]
126. ~creative(paul) [cnf transformation 20]
133. quiet(paul) [cnf transformation 25]
255. strong(paul) [resolution 97,126]
261. ~strong(paul) [resolution 117,133]
264. $false [subsumption resolution 261,255]
% SZS output end Proof for 412833581238372020278606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either kind or not strong and vice versa.
Everyone who is quiet is both not tall and patient.
If fred is either quiet or rich then mary is both tall and not happy.
If mary is both not creative and patient then someone is either not quiet or not brave.
Everyone who is both generous and quiet is not patient.
If someone is not humble then alice is not rich and vice versa.
Everyone who is not wise is brave or not patient.
If john is either not humble or not quiet then someone is not generous or tall and vice versa.
Everyone who is not old is not rich or old and vice versa.
Everyone who is quiet is not curious.
If fred is both tall and calm then someone is both not generous and happy.
Everyone who is not brave or not funny is not old.
If someone is both rich and calm then someone is both not brave and not happy and vice versa.
If someone is not humble or not brave then someone is not creative and vice versa.
If alice is both curious and not strong then susan is brave or not strong and vice versa.
If someone is either happy or not kind then someone is both not creative and not quiet.
Mary is not brave or happy.
John is humble or not funny.
Someone is not generous or not tall.
Someone is not generous.
Someone is funny.
John is not rich.
Mary is strong or not kind. | Fred is quiet. | contradiction | (![X]:(funny(X)<=>(kind(X)<~>~strong(X))))&
(![X]:(quiet(X)=>(~tall(X)&patient(X))))&
(((quiet(fred)<~>rich(fred)))=>((tall(mary)&~happy(mary))))&
(((~creative(mary)&patient(mary)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((generous(X)&quiet(X))=>~patient(X)))&
((?[X]:(~humble(X)))<=>(~rich(alice)))&
(![X]:(~wise(X)=>(brave(X)|~patient(X))))&
(((~humble(john)<~>~quiet(john)))<=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:(~old(X)<=>(~rich(X)|old(X))))&
(![X]:(quiet(X)=>~curious(X)))&
(((tall(fred)&calm(fred)))=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((~brave(X)|~funny(X))=>~old(X)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((~brave(X)&~happy(X)))))&
((?[X]:((~humble(X)|~brave(X))))<=>(?[X]:(~creative(X))))&
(((curious(alice)&~strong(alice)))<=>((brave(susan)|~strong(susan))))&
((?[X]:((happy(X)<~>~kind(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
((~brave(mary)|happy(mary)))&
((humble(john)|~funny(john)))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:(~generous(X)))&
(?[X]:(funny(X)))&
(~rich(john))&
((strong(mary)|~kind(mary))) | quiet(fred) | [
"p2",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5647119066220845924282807
% SZS output start Proof for 5647119066220845924282807
3. (quiet(fred) <~> rich(fred)) => (~happy(mary) & tall(mary)) [input p2]
9. ! [X0] : (~old(X0) <=> (old(X0) | ~rich(X0))) [input p8]
13. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X0] : (~happy(X0) & ~brave(X0)) [input p12]
17. happy(mary) | ~brave(mary) [input p16]
24. quiet(fred) [input hypothesis]
25. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X1] : (~happy(X1) & ~brave(X1)) [rectify 13]
30. (~happy(mary) & tall(mary)) | (quiet(fred) <=> rich(fred)) [ennf transformation 3]
41. (~happy(mary) & tall(mary)) | ((quiet(fred) | ~rich(fred)) & (rich(fred) | ~quiet(fred))) [nnf transformation 30]
53. ! [X0] : ((~old(X0) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | old(X0))) [nnf transformation 9]
54. ! [X0] : ((~old(X0) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | old(X0))) [flattening 53]
57. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : (happy(X1) | brave(X1))) & (? [X1] : (~happy(X1) & ~brave(X1)) | ! [X0] : (~calm(X0) | ~rich(X0))) [nnf transformation 25]
58. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : (happy(X1) | brave(X1))) & (? [X2] : (~happy(X2) & ~brave(X2)) | ! [X3] : (~calm(X3) | ~rich(X3))) [rectify 57]
59. ? [X0] : (calm(X0) & rich(X0)) => (calm(sK4) & rich(sK4)) [choice axiom]
60. ? [X2] : (~happy(X2) & ~brave(X2)) => (~happy(sK5) & ~brave(sK5)) [choice axiom]
61. ((calm(sK4) & rich(sK4)) | ! [X1] : (happy(X1) | brave(X1))) & ((~happy(sK5) & ~brave(sK5)) | ! [X3] : (~calm(X3) | ~rich(X3))) [skolemisation 58,60,59]
87. ~happy(mary) | rich(fred) | ~quiet(fred) [cnf transformation 41]
100. old(X0) | ~rich(X0) | old(X0) [cnf transformation 54]
102. ~old(X0) | ~old(X0) [cnf transformation 54]
110. rich(sK4) | happy(X1) | brave(X1) [cnf transformation 61]
124. happy(mary) | ~brave(mary) [cnf transformation 17]
131. quiet(fred) [cnf transformation 24]
132. old(X0) | ~rich(X0) [duplicate literal removal 100]
133. ~old(X0) [duplicate literal removal 102]
135. 1 <=> rich(fred) [avatar definition]
136. rich(fred) <- (1) [avatar component clause 135]
139. 2 <=> quiet(fred) [avatar definition]
143. 3 <=> happy(mary) [avatar definition]
147. ~2 | 1 | ~3 [avatar split clause 87,143,135,139]
214. ~rich(X0) [subsumption resolution 132,133]
234. 22 <=> ! [X1] : (happy(X1) | brave(X1)) [avatar definition]
235. brave(X1) | happy(X1) <- (22) [avatar component clause 234]
241. happy(X1) | brave(X1) [subsumption resolution 110,214]
242. 22 [avatar split clause 241,234]
304. 37 <=> brave(mary) [avatar definition]
306. ~brave(mary) <- (~37) [avatar component clause 304]
307. ~37 | 3 [avatar split clause 124,143,304]
331. 2 [avatar split clause 131,139]
336. happy(mary) <- (22, ~37) [resolution 235,306]
339. 3 | ~22 | 37 [avatar split clause 336,304,234,143]
340. $false <- (1) [subsumption resolution 136,214]
341. ~1 [avatar contradiction clause 340]
342. $false [avatar sat refutation 147,242,307,331,339,341]
% SZS output end Proof for 5647119066220845924282807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and wise and vice versa.
Everyone who is both not happy and patient is curious and vice versa.
If lucy is either curious or not curious then lucy is either curious or rich and vice versa.
If john is either creative or not generous then someone is either not tall or not wise and vice versa.
Everyone who is not old is either tall or old.
If someone is patient then lucy is not tall or old and vice versa.
If someone is both curious and not rich then someone is both curious and creative and vice versa.
If john is generous or tall then mary is both tall and brave and vice versa.
If someone is not strong or creative then someone is not tall or not calm and vice versa.
If someone is not happy then mary is not strong.
Everyone who is either not rich or not kind is old.
Everyone who is not old is not calm and vice versa.
Everyone who is either not creative or brave is either tall or not strong and vice versa.
Everyone who is tall is not quiet.
Everyone who is either wise or not creative is kind or funny and vice versa.
Everyone who is not patient or tall is both not rich and patient.
Someone is not kind.
Someone is not curious or not funny.
Someone is either not tall or not happy.
Paul is not calm.
Someone is both not curious and not funny.
Someone is both not quiet and humble. | Paul is not rich. | entailment | (![X]:(~strong(X)<=>(~old(X)&wise(X))))&
(![X]:((~happy(X)&patient(X))<=>curious(X)))&
(((curious(lucy)<~>~curious(lucy)))<=>((curious(lucy)<~>rich(lucy))))&
(((creative(john)<~>~generous(john)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:(~old(X)=>(tall(X)<~>old(X))))&
((?[X]:(patient(X)))<=>((~tall(lucy)|old(lucy))))&
((?[X]:((curious(X)&~rich(X))))<=>(?[X]:((curious(X)&creative(X)))))&
(((generous(john)|tall(john)))<=>((tall(mary)&brave(mary))))&
((?[X]:((~strong(X)|creative(X))))<=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:(~happy(X)))=>(~strong(mary)))&
(![X]:((~rich(X)<~>~kind(X))=>old(X)))&
(![X]:(~old(X)<=>~calm(X)))&
(![X]:((~creative(X)<~>brave(X))<=>(tall(X)<~>~strong(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((wise(X)<~>~creative(X))<=>(kind(X)|funny(X))))&
(![X]:((~patient(X)|tall(X))=>(~rich(X)&patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((~tall(X)<~>~happy(X))))&
(~calm(paul))&
(?[X]:((~curious(X)&~funny(X))))&
(?[X]:((~quiet(X)&humble(X)))) | ~rich(paul) | [
"p4",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2492490722364376699497874
% SZS output start Proof for 2492490722364376699497874
5. ! [X0] : (~old(X0) => (tall(X0) <~> old(X0))) [input p4]
12. ! [X0] : (~old(X0) <=> ~calm(X0)) [input p11]
16. ! [X0] : ((tall(X0) | ~patient(X0)) => (patient(X0) & ~rich(X0))) [input p15]
20. ~calm(paul) [input p19]
23. rich(paul) [input hypothesis]
29. ! [X0] : ((tall(X0) <~> old(X0)) | old(X0)) [ennf transformation 5]
32. ! [X0] : ((patient(X0) & ~rich(X0)) | (~tall(X0) & patient(X0))) [ennf transformation 16]
42. ! [X0] : (((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | old(X0)) [nnf transformation 29]
61. ! [X0] : ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0))) [nnf transformation 12]
96. old(X0) | tall(X0) | old(X0) [cnf transformation 42]
118. ~old(X0) | calm(X0) [cnf transformation 61]
134. ~tall(X0) | ~rich(X0) [cnf transformation 32]
141. ~calm(paul) [cnf transformation 20]
144. rich(paul) [cnf transformation 23]
146. tall(X0) | old(X0) [duplicate literal removal 96]
324. ~rich(X1) | old(X1) [resolution 146,134]
369. 41 <=> old(paul) [avatar definition]
370. ~old(paul) <- (~41) [avatar component clause 369]
371. old(paul) <- (41) [avatar component clause 369]
438. calm(paul) <- (41) [resolution 371,118]
440. $false <- (41) [subsumption resolution 438,141]
441. ~41 [avatar contradiction clause 440]
499. old(paul) [resolution 324,144]
501. $false <- (~41) [subsumption resolution 499,370]
502. 41 [avatar contradiction clause 501]
503. $false [avatar sat refutation 441,502]
% SZS output end Proof for 2492490722364376699497874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is either not kind or humble. Everyone who is not funny is both not rich and curious. Everyone who is both happy and not creative is not happy and vice versa. If someone is either not old or creative then someone is both old and not old. Everyone who is both creative and funny is curious. Everyone who is either tall or not curious is both generous and not strong and vice versa. If lucy is not curious or not strong then john is both old and not tall. If someone is not humble or not funny then alice is either old or kind. If someone is both not generous and not funny then lucy is not brave or not humble and vice versa. If fred is not patient or funny then someone is both not funny and not brave. If alice is both not creative and not rich then paul is not patient or not brave and vice versa. If fred is both kind and not curious then john is humble or calm. Everyone who is both strong and not happy is both quiet and funny and vice versa. Everyone who is not patient or quiet is quiet or happy. Everyone who is not patient is not curious. Mary is both happy and not kind. Someone is either humble or not calm. Someone is quiet or brave. Someone is either curious or strong. | Lucy is tall. | contradiction | (![X]:(quiet(X)=>(~kind(X)<~>humble(X))))&
(![X]:(~funny(X)=>(~rich(X)&curious(X))))&
(![X]:((happy(X)&~creative(X))<=>~happy(X)))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((creative(X)&funny(X))=>curious(X)))&
(![X]:((tall(X)<~>~curious(X))<=>(generous(X)&~strong(X))))&
(((~curious(lucy)|~strong(lucy)))=>((old(john)&~tall(john))))&
((?[X]:((~humble(X)|~funny(X))))=>((old(alice)<~>kind(alice))))&
((?[X]:((~generous(X)&~funny(X))))<=>((~brave(lucy)|~humble(lucy))))&
(((~patient(fred)|funny(fred)))=>(?[X]:((~funny(X)&~brave(X)))))&
(((~creative(alice)&~rich(alice)))<=>((~patient(paul)|~brave(paul))))&
(((kind(fred)&~curious(fred)))=>((humble(john)|calm(john))))&
(![X]:((strong(X)&~happy(X))<=>(quiet(X)&funny(X))))&
(![X]:((~patient(X)|quiet(X))=>(quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
((happy(mary)&~kind(mary)))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((curious(X)<~>strong(X)))) | tall(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2697050907993301672631713
% SZS output start Proof for 2697050907993301672631713
2. ! [X0] : (~funny(X0) => (curious(X0) & ~rich(X0))) [input p1]
3. ! [X0] : ((~creative(X0) & happy(X0)) <=> ~happy(X0)) [input p2]
4. ? [X0] : (~old(X0) <~> creative(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p3]
5. ! [X0] : ((funny(X0) & creative(X0)) => curious(X0)) [input p4]
6. ! [X0] : ((tall(X0) <~> ~curious(X0)) <=> (~strong(X0) & generous(X0))) [input p5]
7. (~strong(lucy) | ~curious(lucy)) => (~tall(john) & old(john)) [input p6]
20. tall(lucy) [input hypothesis]
21. ? [X0] : (~old(X0) <~> creative(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 4]
23. ! [X0] : ((curious(X0) & ~rich(X0)) | funny(X0)) [ennf transformation 2]
24. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (~old(X0) <=> creative(X0)) [ennf transformation 21]
25. ! [X0] : (curious(X0) | (~funny(X0) | ~creative(X0))) [ennf transformation 5]
26. ! [X0] : (curious(X0) | ~funny(X0) | ~creative(X0)) [flattening 25]
27. (~tall(john) & old(john)) | (strong(lucy) & curious(lucy)) [ennf transformation 7]
36. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | (creative(X0) | ~happy(X0)))) [nnf transformation 3]
37. ! [X0] : (((~creative(X0) & happy(X0)) | happy(X0)) & (~happy(X0) | creative(X0) | ~happy(X0))) [flattening 36]
38. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))) [nnf transformation 24]
39. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~old(X1) | ~creative(X1)) & (creative(X1) | old(X1))) [rectify 38]
40. ? [X0] : (~old(X0) & old(X0)) => (~old(sK0) & old(sK0)) [choice axiom]
41. (~old(sK0) & old(sK0)) | ! [X1] : ((~old(X1) | ~creative(X1)) & (creative(X1) | old(X1))) [skolemisation 39,40]
42. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [nnf transformation 6]
43. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [flattening 42]
67. curious(X0) | funny(X0) [cnf transformation 23]
68. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 37]
69. happy(X0) | happy(X0) [cnf transformation 37]
72. old(sK0) | ~old(X1) | ~creative(X1) [cnf transformation 41]
74. ~old(sK0) | ~old(X1) | ~creative(X1) [cnf transformation 41]
75. curious(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 26]
78. ~strong(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 43]
83. old(john) | strong(lucy) [cnf transformation 27]
119. tall(lucy) [cnf transformation 20]
120. ~happy(X0) | creative(X0) [duplicate literal removal 68]
121. happy(X0) [duplicate literal removal 69]
122. creative(X0) [subsumption resolution 120,121]
123. ~old(sK0) | ~old(X1) [subsumption resolution 74,122]
125. 1 <=> ! [X1] : ~old(X1) [avatar definition]
126. ~old(X1) <- (1) [avatar component clause 125]
128. 2 <=> old(sK0) [avatar definition]
131. 1 | ~2 [avatar split clause 123,128,125]
132. old(sK0) | ~old(X1) [subsumption resolution 72,122]
133. 1 | 2 [avatar split clause 132,128,125]
134. curious(X0) | ~funny(X0) [subsumption resolution 75,122]
135. curious(X0) [subsumption resolution 134,67]
137. ~strong(X0) | ~tall(X0) [subsumption resolution 78,135]
140. 3 <=> strong(lucy) [avatar definition]
142. strong(lucy) <- (3) [avatar component clause 140]
149. 5 <=> old(john) [avatar definition]
151. old(john) <- (5) [avatar component clause 149]
152. 3 | 5 [avatar split clause 83,149,140]
258. ~tall(lucy) <- (3) [resolution 137,142]
259. $false <- (3) [subsumption resolution 258,119]
260. ~3 [avatar contradiction clause 259]
261. $false <- (1, 5) [subsumption resolution 151,126]
262. ~1 | ~5 [avatar contradiction clause 261]
263. $false [avatar sat refutation 131,133,152,260,262]
% SZS output end Proof for 2697050907993301672631713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not humble is either rich or tall.
If john is quiet or not funny then john is not humble.
If someone is both old and not quiet then paul is either creative or humble.
If mary is both curious and kind then someone is brave.
If someone is not funny then alice is either curious or not wise and vice versa.
If someone is both not brave and not happy then someone is funny and vice versa.
If someone is not wise or not humble then paul is not strong or not happy and vice versa.
Everyone who is not brave is kind and vice versa.
Everyone who is rich or not calm is both not strong and humble.
Everyone who is either calm or generous is not calm and vice versa.
Everyone who is either kind or not happy is both tall and curious and vice versa.
If someone is both not patient and not strong then someone is both calm and rich and vice versa.
Everyone who is not humble is not old or rich and vice versa.
If someone is either old or generous then lucy is both humble and kind and vice versa.
Everyone who is both not happy and creative is brave and vice versa.
If mary is both not rich and not funny then someone is both rich and patient and vice versa.
Someone is either calm or kind.
Someone is kind or not strong.
Susan is happy.
Someone is either not kind or wise.
Lucy is either kind or tall.
John is either not kind or not old.
Lucy is either curious or not quiet. | John is happy. | contradiction | (![X]:((humble(X)|~humble(X))=>(rich(X)<~>tall(X))))&
(((quiet(john)|~funny(john)))=>(~humble(john)))&
((?[X]:((old(X)&~quiet(X))))=>((creative(paul)<~>humble(paul))))&
(((curious(mary)&kind(mary)))=>(?[X]:(brave(X))))&
((?[X]:(~funny(X)))<=>((curious(alice)<~>~wise(alice))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>((~strong(paul)|~happy(paul))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((rich(X)|~calm(X))=>(~strong(X)&humble(X))))&
(![X]:((calm(X)<~>generous(X))<=>~calm(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)&curious(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:(~humble(X)<=>(~old(X)|rich(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((humble(lucy)&kind(lucy))))&
(![X]:((~happy(X)&creative(X))<=>brave(X)))&
(((~rich(mary)&~funny(mary)))<=>(?[X]:((rich(X)&patient(X)))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((kind(X)|~strong(X))))&
(happy(susan))&
(?[X]:((~kind(X)<~>wise(X))))&
((kind(lucy)<~>tall(lucy)))&
((~kind(john)<~>~old(john)))&
((curious(lucy)<~>~quiet(lucy))) | happy(john) | [
"p0",
"p7",
"p8",
"p9",
"p12",
"p13",
"p14",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2182585851154671151947635
% SZS output start Proof for 2182585851154671151947635
1. ! [X0] : ((~humble(X0) | humble(X0)) => (rich(X0) <~> tall(X0))) [input p0]
8. ! [X0] : (~brave(X0) <=> kind(X0)) [input p7]
9. ! [X0] : ((~calm(X0) | rich(X0)) => (humble(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((calm(X0) <~> generous(X0)) <=> ~calm(X0)) [input p9]
13. ! [X0] : (~humble(X0) <=> (rich(X0) | ~old(X0))) [input p12]
14. ? [X0] : (old(X0) <~> generous(X0)) <=> (kind(lucy) & humble(lucy)) [input p13]
15. ! [X0] : ((creative(X0) & ~happy(X0)) <=> brave(X0)) [input p14]
21. kind(lucy) <~> tall(lucy) [input p20]
22. ~kind(john) <~> ~old(john) [input p21]
24. happy(john) [input hypothesis]
27. ! [X0] : ((rich(X0) <~> tall(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 1]
32. ! [X0] : ((humble(X0) & ~strong(X0)) | (calm(X0) & ~rich(X0))) [ennf transformation 9]
33. ! [X0] : (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (humble(X0) & ~humble(X0))) [nnf transformation 27]
51. ! [X0] : ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))) [nnf transformation 8]
52. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | calm(X0)) & (~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 10]
60. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | humble(X0))) [nnf transformation 13]
61. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | humble(X0))) [flattening 60]
62. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~kind(lucy) | ~humble(lucy))) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 14]
63. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [flattening 62]
64. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [rectify 63]
65. ? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) => ((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) [choice axiom]
66. (((~generous(sK7) | ~old(sK7)) & (generous(sK7) | old(sK7))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [skolemisation 64,65]
67. ! [X0] : (((creative(X0) & ~happy(X0)) | ~brave(X0)) & (brave(X0) | (~creative(X0) | happy(X0)))) [nnf transformation 15]
68. ! [X0] : (((creative(X0) & ~happy(X0)) | ~brave(X0)) & (brave(X0) | ~creative(X0) | happy(X0))) [flattening 67]
82. (~tall(lucy) | ~kind(lucy)) & (tall(lucy) | kind(lucy)) [nnf transformation 21]
83. (old(john) | kind(john)) & (~old(john) | ~kind(john)) [nnf transformation 22]
85. tall(X0) | rich(X0) | ~humble(X0) [cnf transformation 33]
86. tall(X0) | rich(X0) | humble(X0) [cnf transformation 33]
105. brave(X0) | kind(X0) [cnf transformation 51]
109. ~rich(X0) | humble(X0) [cnf transformation 32]
111. ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 52]
113. generous(X0) | calm(X0) | calm(X0) [cnf transformation 52]
127. ~humble(X0) | ~rich(X0) [cnf transformation 61]
131. kind(lucy) | old(X1) | ~generous(X1) [cnf transformation 66]
135. ~happy(X0) | ~brave(X0) [cnf transformation 68]
148. ~tall(lucy) | ~kind(lucy) [cnf transformation 82]
149. ~old(john) | ~kind(john) [cnf transformation 83]
153. happy(john) [cnf transformation 24]
154. ~calm(X0) | generous(X0) [duplicate literal removal 111]
155. generous(X0) | calm(X0) [duplicate literal removal 113]
157. tall(X0) | rich(X0) [subsumption resolution 85,86]
264. generous(X0) [subsumption resolution 154,155]
291. ~rich(X0) [subsumption resolution 127,109]
299. 32 <=> kind(lucy) [avatar definition]
307. kind(lucy) | old(X1) [subsumption resolution 131,264]
309. 34 <=> ! [X1] : old(X1) [avatar definition]
310. old(X1) <- (34) [avatar component clause 309]
311. 34 | 32 [avatar split clause 307,299,309]
357. 43 <=> tall(lucy) [avatar definition]
359. ~tall(lucy) <- (~43) [avatar component clause 357]
360. ~32 | ~43 [avatar split clause 148,357,299]
363. 44 <=> kind(john) [avatar definition]
367. 45 <=> old(john) [avatar definition]
368. ~old(john) <- (~45) [avatar component clause 367]
371. ~44 | ~45 [avatar split clause 149,367,363]
386. ~brave(john) [resolution 135,153]
389. kind(john) [resolution 386,105]
390. rich(lucy) <- (~43) [resolution 157,359]
392. $false <- (~43) [subsumption resolution 390,291]
393. 43 [avatar contradiction clause 392]
395. $false <- (34, ~45) [resolution 310,368]
396. ~34 | 45 [avatar contradiction clause 395]
398. 44 [avatar split clause 389,363]
399. $false [avatar sat refutation 311,360,371,393,396,398]
% SZS output end Proof for 2182585851154671151947635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is not generous.
Everyone who is strong is brave or not kind and vice versa.
If someone is strong or quiet then someone is both not quiet and not patient and vice versa.
Everyone who is not kind or not humble is strong or creative.
If john is not kind then someone is both not curious and not quiet.
Everyone who is both quiet and not tall is both kind and generous.
Everyone who is not rich is not wise or not old and vice versa.
Everyone who is both not rich and brave is not happy or not funny.
Everyone who is curious or funny is not wise.
Everyone who is either not strong or kind is not funny or strong.
Everyone who is kind is not old.
Everyone who is either brave or happy is both wise and not generous.
If someone is both kind and not quiet then someone is both curious and humble and vice versa.
Everyone who is both funny and wise is not wise.
If someone is both tall and not curious then john is kind or creative.
Everyone who is either quiet or not old is both not wise and rich and vice versa.
Someone is both strong and rich.
Mary is patient.
Mary is not funny or not humble.
Someone is either curious or wise.
Someone is either not funny or not kind.
Fred is both not tall and funny.
Someone is not quiet.
Susan is not funny. | Fred is not happy. | entailment | (![X]:((~old(X)|happy(X))=>~generous(X)))&
(![X]:(strong(X)<=>(brave(X)|~kind(X))))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((~kind(X)|~humble(X))=>(strong(X)|creative(X))))&
((~kind(john))=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((quiet(X)&~tall(X))=>(kind(X)&generous(X))))&
(![X]:(~rich(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)&brave(X))=>(~happy(X)|~funny(X))))&
(![X]:((curious(X)|funny(X))=>~wise(X)))&
(![X]:((~strong(X)<~>kind(X))=>(~funny(X)|strong(X))))&
(![X]:(kind(X)=>~old(X)))&
(![X]:((brave(X)<~>happy(X))=>(wise(X)&~generous(X))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((curious(X)&humble(X)))))&
(![X]:((funny(X)&wise(X))=>~wise(X)))&
((?[X]:((tall(X)&~curious(X))))=>((kind(john)|creative(john))))&
(![X]:((quiet(X)<~>~old(X))<=>(~wise(X)&rich(X))))&
(?[X]:((strong(X)&rich(X))))&
(patient(mary))&
((~funny(mary)|~humble(mary)))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((~funny(X)<~>~kind(X))))&
((~tall(fred)&funny(fred)))&
(?[X]:(~quiet(X)))&
(~funny(susan)) | ~happy(fred) | [
"p6",
"p7",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7960658029002510587927037
% SZS output start Proof for 7960658029002510587927037
7. ! [X0] : (~rich(X0) <=> (~old(X0) | ~wise(X0))) [input p6]
8. ! [X0] : ((brave(X0) & ~rich(X0)) => (~funny(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((funny(X0) | curious(X0)) => ~wise(X0)) [input p8]
12. ! [X0] : ((brave(X0) <~> happy(X0)) => (~generous(X0) & wise(X0))) [input p11]
22. funny(fred) & ~tall(fred) [input p21]
25. happy(fred) [input hypothesis]
34. ! [X0] : ((~funny(X0) | ~happy(X0)) | (~brave(X0) | rich(X0))) [ennf transformation 8]
35. ! [X0] : (~funny(X0) | ~happy(X0) | ~brave(X0) | rich(X0)) [flattening 34]
36. ! [X0] : (~wise(X0) | (~funny(X0) & ~curious(X0))) [ennf transformation 9]
40. ! [X0] : ((~generous(X0) & wise(X0)) | (brave(X0) <=> happy(X0))) [ennf transformation 12]
52. ! [X0] : ((~rich(X0) | (old(X0) & wise(X0))) & ((~old(X0) | ~wise(X0)) | rich(X0))) [nnf transformation 7]
53. ! [X0] : ((~rich(X0) | (old(X0) & wise(X0))) & (~old(X0) | ~wise(X0) | rich(X0))) [flattening 52]
55. ! [X0] : ((~generous(X0) & wise(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) [nnf transformation 40]
88. ~rich(X0) | wise(X0) [cnf transformation 53]
90. ~funny(X0) | ~happy(X0) | ~brave(X0) | rich(X0) [cnf transformation 35]
92. ~funny(X0) | ~wise(X0) [cnf transformation 36]
97. ~happy(X0) | brave(X0) | wise(X0) [cnf transformation 55]
120. funny(fred) [cnf transformation 22]
123. happy(fred) [cnf transformation 25]
230. ~wise(fred) [resolution 92,120]
247. brave(fred) | wise(fred) [resolution 97,123]
248. brave(fred) [subsumption resolution 247,230]
255. ~happy(fred) | ~brave(fred) | rich(fred) [resolution 90,120]
257. ~brave(fred) | rich(fred) [subsumption resolution 255,123]
258. rich(fred) [subsumption resolution 257,248]
273. wise(fred) [resolution 258,88]
274. $false [subsumption resolution 273,230]
% SZS output end Proof for 7960658029002510587927037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is wise or quiet.
Everyone who is either not curious or rich is rich.
If john is both not curious and not humble then lucy is either not wise or old.
If susan is either not kind or not generous then susan is both tall and not kind.
Everyone who is either not rich or not curious is both strong and not calm.
Everyone who is patient or not old is generous or curious.
Everyone who is either wise or not generous is strong.
Everyone who is either wise or not curious is not patient.
Everyone who is not happy or not rich is not creative.
If lucy is not generous or calm then paul is not old or not calm and vice versa.
Everyone who is both curious and not quiet is both not calm and happy.
If john is both not tall and not strong then fred is both not humble and not old and vice versa.
If mary is either old or not calm then susan is not creative or brave and vice versa.
If lucy is either not quiet or funny then susan is either not kind or creative.
Everyone who is creative or calm is not old and vice versa.
If someone is not rich or patient then someone is funny.
Fred is both rich and strong.
Susan is both funny and not rich.
Someone is either not kind or quiet.
Someone is either generous or not rich.
Fred is patient.
Fred is quiet or not kind. | Fred is humble. | neutral | (![X]:(tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~curious(X)<~>rich(X))=>rich(X)))&
(((~curious(john)&~humble(john)))=>((~wise(lucy)<~>old(lucy))))&
(((~kind(susan)<~>~generous(susan)))=>((tall(susan)&~kind(susan))))&
(![X]:((~rich(X)<~>~curious(X))=>(strong(X)&~calm(X))))&
(![X]:((patient(X)|~old(X))=>(generous(X)|curious(X))))&
(![X]:((wise(X)<~>~generous(X))=>strong(X)))&
(![X]:((wise(X)<~>~curious(X))=>~patient(X)))&
(![X]:((~happy(X)|~rich(X))=>~creative(X)))&
(((~generous(lucy)|calm(lucy)))<=>((~old(paul)|~calm(paul))))&
(![X]:((curious(X)&~quiet(X))=>(~calm(X)&happy(X))))&
(((~tall(john)&~strong(john)))<=>((~humble(fred)&~old(fred))))&
(((old(mary)<~>~calm(mary)))<=>((~creative(susan)|brave(susan))))&
(((~quiet(lucy)<~>funny(lucy)))=>((~kind(susan)<~>creative(susan))))&
(![X]:((creative(X)|calm(X))<=>~old(X)))&
((?[X]:((~rich(X)|patient(X))))=>(?[X]:(funny(X))))&
((rich(fred)&strong(fred)))&
((funny(susan)&~rich(susan)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(patient(fred))&
((quiet(fred)|~kind(fred))) | humble(fred) | [] | null | 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not generous or not quiet then mary is both creative and brave.
If someone is generous then alice is tall or not tall.
If john is not rich then someone is patient.
Everyone who is either not old or rich is both not strong and not calm and vice versa.
If someone is either not funny or not creative then john is either brave or not tall.
If someone is either patient or happy then someone is humble and vice versa.
If john is not happy or not kind then someone is either tall or kind and vice versa.
Everyone who is strong is both not kind and old and vice versa.
Everyone who is creative or not strong is not calm or not happy.
If someone is either not kind or patient then susan is both not happy and wise.
Everyone who is old is both not strong and strong.
Everyone who is happy is either not humble or not happy.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Someone is not strong.
John is both not calm and not wise.
Mary is not happy.
Someone is both wise and not kind.
Mary is both not brave and wise.
Someone is either curious or kind.
Someone is not kind or patient. | John is rich. | contradiction | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>((creative(mary)&brave(mary))))&
((?[X]:(generous(X)))=>((tall(alice)|~tall(alice))))&
((~rich(john))=>(?[X]:(patient(X))))&
(![X]:((~old(X)<~>rich(X))<=>(~strong(X)&~calm(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((brave(john)<~>~tall(john))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(((~happy(john)|~kind(john)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(?[X]:(~strong(X)))&
((~calm(john)&~wise(john)))&
(~happy(mary))&
(?[X]:((wise(X)&~kind(X))))&
((~brave(mary)&wise(mary)))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((~kind(X)|patient(X)))) | rich(john) | [
"p4",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8197876446966933128714056
% SZS output start Proof for 8197876446966933128714056
5. ! [X0] : ((~old(X0) <~> rich(X0)) <=> (~calm(X0) & ~strong(X0))) [input p4]
9. ! [X0] : (strong(X0) <=> (old(X0) & ~kind(X0))) [input p8]
12. ! [X0] : (old(X0) => (strong(X0) & ~strong(X0))) [input p11]
18. ~wise(john) & ~calm(john) [input p17]
24. rich(john) [input hypothesis]
35. ! [X0] : ((strong(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 12]
42. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [flattening 42]
55. ! [X0] : ((strong(X0) | (~old(X0) | kind(X0))) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~old(X0) | kind(X0)) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [flattening 55]
88. ~rich(X0) | old(X0) | calm(X0) | strong(X0) [cnf transformation 43]
104. ~strong(X0) | old(X0) [cnf transformation 56]
112. ~strong(X0) | ~old(X0) [cnf transformation 35]
113. ~old(X0) | strong(X0) [cnf transformation 35]
131. ~calm(john) [cnf transformation 18]
141. rich(john) [cnf transformation 24]
159. 4 <=> rich(john) [avatar definition]
161. rich(john) <- (4) [avatar component clause 159]
256. ~strong(X0) [subsumption resolution 112,104]
311. 4 [avatar split clause 141,159]
357. 42 <=> old(john) [avatar definition]
359. old(john) <- (42) [avatar component clause 357]
364. old(john) | calm(john) | strong(john) <- (4) [resolution 88,161]
365. old(john) | strong(john) <- (4) [subsumption resolution 364,131]
366. old(john) <- (4) [subsumption resolution 365,256]
367. 42 | ~4 [avatar split clause 366,159,357]
373. strong(john) <- (42) [resolution 359,113]
375. $false <- (42) [subsumption resolution 373,256]
376. ~42 [avatar contradiction clause 375]
377. $false [avatar sat refutation 311,367,376]
% SZS output end Proof for 8197876446966933128714056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is rich or not generous.
If someone is kind then someone is both rich and not strong.
Everyone who is both wise and not kind is not rich and vice versa.
If someone is both not strong and not curious then mary is either generous or not kind.
Everyone who is not creative is not calm.
Everyone who is both not curious and not tall is both brave and not calm and vice versa.
Everyone who is old or not brave is both not generous and not old and vice versa.
Everyone who is both not old and not kind is not curious.
If someone is either tall or old then someone is either patient or tall and vice versa.
If someone is not curious then fred is either happy or old.
If someone is either not tall or kind then someone is wise or not old and vice versa.
If someone is wise or not curious then paul is either not patient or wise and vice versa.
Everyone who is either not funny or happy is not funny or quiet.
If fred is happy then alice is not creative.
If susan is either calm or wise then fred is not curious and vice versa.
Everyone who is not creative is not curious.
Paul is both not happy and tall.
Fred is either creative or not tall.
Paul is curious.
Someone is either calm or not happy.
John is calm.
Someone is not happy.
Someone is rich or not curious.
Susan is happy or strong. | John is old. | contradiction | (![X]:((kind(X)&creative(X))=>(rich(X)|~generous(X))))&
((?[X]:(kind(X)))=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((wise(X)&~kind(X))<=>~rich(X)))&
((?[X]:((~strong(X)&~curious(X))))=>((generous(mary)<~>~kind(mary))))&
(![X]:(~creative(X)=>~calm(X)))&
(![X]:((~curious(X)&~tall(X))<=>(brave(X)&~calm(X))))&
(![X]:((old(X)|~brave(X))<=>(~generous(X)&~old(X))))&
(![X]:((~old(X)&~kind(X))=>~curious(X)))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:(~curious(X)))=>((happy(fred)<~>old(fred))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:((wise(X)|~curious(X))))<=>((~patient(paul)<~>wise(paul))))&
(![X]:((~funny(X)<~>happy(X))=>(~funny(X)|quiet(X))))&
((happy(fred))=>(~creative(alice)))&
(((calm(susan)<~>wise(susan)))<=>(~curious(fred)))&
(![X]:(~creative(X)=>~curious(X)))&
((~happy(paul)&tall(paul)))&
((creative(fred)<~>~tall(fred)))&
(curious(paul))&
(?[X]:((calm(X)<~>~happy(X))))&
(calm(john))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)|~curious(X))))&
((happy(susan)|strong(susan))) | old(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4045079880188083572273673
% SZS output start Proof for 4045079880188083572273673
7. ! [X0] : ((~brave(X0) | old(X0)) <=> (~old(X0) & ~generous(X0))) [input p6]
25. old(john) [input hypothesis]
49. ! [X0] : (((~brave(X0) | old(X0)) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | (brave(X0) & ~old(X0)))) [nnf transformation 7]
50. ! [X0] : ((~brave(X0) | old(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | (brave(X0) & ~old(X0)))) [flattening 49]
88. ~old(X0) | ~old(X0) [cnf transformation 50]
131. old(john) [cnf transformation 25]
132. ~old(X0) [duplicate literal removal 88]
297. $false [subsumption resolution 131,132]
% SZS output end Proof for 4045079880188083572273673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.044 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not patient or patient and vice versa.
If john is both not strong and not wise then someone is both curious and brave and vice versa.
If john is quiet then someone is both not quiet and funny and vice versa.
Everyone who is tall is either not brave or quiet and vice versa.
If fred is generous or wise then someone is not quiet and vice versa.
Everyone who is both happy and calm is both not tall and old.
If someone is either curious or wise then paul is not happy or funny and vice versa.
Everyone who is not strong is not kind and vice versa.
Everyone who is not tall is not generous or old.
Everyone who is either not quiet or not calm is calm.
Everyone who is brave is either strong or calm and vice versa.
If alice is rich or creative then someone is both not brave and wise and vice versa.
Everyone who is both not strong and strong is both strong and wise.
If paul is not humble or strong then someone is not quiet or calm.
Everyone who is not kind is old or not tall and vice versa.
Everyone who is both calm and kind is both kind and generous and vice versa.
John is both not wise and not creative.
Someone is either not rich or wise.
Paul is either not happy or not tall.
Someone is tall.
Someone is either not funny or curious.
Alice is not tall. | Paul is happy. | contradiction | (![X]:(~old(X)<=>(~patient(X)|patient(X))))&
(((~strong(john)&~wise(john)))<=>(?[X]:((curious(X)&brave(X)))))&
((quiet(john))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:(tall(X)<=>(~brave(X)<~>quiet(X))))&
(((generous(fred)|wise(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)&calm(X))=>(~tall(X)&old(X))))&
((?[X]:((curious(X)<~>wise(X))))<=>((~happy(paul)|funny(paul))))&
(![X]:(~strong(X)<=>~kind(X)))&
(![X]:(~tall(X)=>(~generous(X)|old(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>calm(X)))&
(![X]:(brave(X)<=>(strong(X)<~>calm(X))))&
(((rich(alice)|creative(alice)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:((~strong(X)&strong(X))=>(strong(X)&wise(X))))&
(((~humble(paul)|strong(paul)))=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:(~kind(X)<=>(old(X)|~tall(X))))&
(![X]:((calm(X)&kind(X))<=>(kind(X)&generous(X))))&
((~wise(john)&~creative(john)))&
(?[X]:((~rich(X)<~>wise(X))))&
((~happy(paul)<~>~tall(paul)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)<~>curious(X))))&
(~tall(alice)) | happy(paul) | [
"p0",
"p3",
"p5",
"p7",
"p9",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 63050374604920177135573
% SZS output start Proof for 63050374604920177135573
1. ! [X0] : (~old(X0) <=> (patient(X0) | ~patient(X0))) [input p0]
4. ! [X0] : (tall(X0) <=> (~brave(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : ((calm(X0) & happy(X0)) => (old(X0) & ~tall(X0))) [input p5]
8. ! [X0] : (~strong(X0) <=> ~kind(X0)) [input p7]
10. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) => calm(X0)) [input p9]
11. ! [X0] : (brave(X0) <=> (strong(X0) <~> calm(X0))) [input p10]
15. ! [X0] : (~kind(X0) <=> (~tall(X0) | old(X0))) [input p14]
19. ~happy(paul) <~> ~tall(paul) [input p18]
23. happy(paul) [input hypothesis]
25. ! [X0] : ((old(X0) & ~tall(X0)) | (~calm(X0) | ~happy(X0))) [ennf transformation 6]
26. ! [X0] : ((old(X0) & ~tall(X0)) | ~calm(X0) | ~happy(X0)) [flattening 25]
29. ! [X0] : (calm(X0) | (~quiet(X0) <=> ~calm(X0))) [ennf transformation 10]
33. ! [X0] : ((~old(X0) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | old(X0))) [nnf transformation 1]
34. ! [X0] : ((~old(X0) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | old(X0))) [flattening 33]
44. ! [X0] : ((tall(X0) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) & (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | ~tall(X0))) [nnf transformation 4]
55. ! [X0] : ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))) [nnf transformation 8]
56. ! [X0] : (calm(X0) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) [nnf transformation 29]
57. ! [X0] : ((brave(X0) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ~brave(X0))) [nnf transformation 11]
65. ! [X0] : ((~kind(X0) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | kind(X0))) [nnf transformation 15]
66. ! [X0] : ((~kind(X0) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | kind(X0))) [flattening 65]
72. (tall(paul) | happy(paul)) & (~tall(paul) | ~happy(paul)) [nnf transformation 19]
79. ~old(X0) | patient(X0) [cnf transformation 34]
80. ~patient(X0) | ~old(X0) [cnf transformation 34]
90. tall(X0) | quiet(X0) | brave(X0) [cnf transformation 44]
96. old(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 26]
104. ~strong(X0) | kind(X0) [cnf transformation 55]
107. calm(X0) | ~quiet(X0) | calm(X0) [cnf transformation 56]
108. ~brave(X0) | strong(X0) | calm(X0) [cnf transformation 57]
122. ~kind(X0) | tall(X0) [cnf transformation 66]
131. ~tall(paul) | ~happy(paul) [cnf transformation 72]
137. happy(paul) [cnf transformation 23]
139. ~quiet(X0) | calm(X0) [duplicate literal removal 107]
140. ~old(X0) [subsumption resolution 79,80]
200. ~calm(X0) | ~happy(X0) [subsumption resolution 96,140]
215. 17 <=> happy(paul) [avatar definition]
217. happy(paul) <- (17) [avatar component clause 215]
267. 27 <=> tall(paul) [avatar definition]
268. ~tall(paul) <- (~27) [avatar component clause 267]
271. ~17 | ~27 [avatar split clause 131,267,215]
282. 17 [avatar split clause 137,215]
325. quiet(paul) | brave(paul) <- (~27) [resolution 90,268]
341. 36 <=> brave(paul) [avatar definition]
343. brave(paul) <- (36) [avatar component clause 341]
345. 37 <=> quiet(paul) [avatar definition]
347. quiet(paul) <- (37) [avatar component clause 345]
348. 36 | 37 | 27 [avatar split clause 325,267,345,341]
388. strong(paul) | calm(paul) <- (36) [resolution 343,108]
390. 44 <=> calm(paul) [avatar definition]
391. ~calm(paul) <- (~44) [avatar component clause 390]
392. calm(paul) <- (44) [avatar component clause 390]
394. 45 <=> strong(paul) [avatar definition]
396. strong(paul) <- (45) [avatar component clause 394]
397. 44 | 45 | ~36 [avatar split clause 388,341,394,390]
512. ~happy(paul) <- (44) [resolution 392,200]
515. $false <- (17, 44) [subsumption resolution 512,217]
516. ~17 | ~44 [avatar contradiction clause 515]
518. calm(paul) <- (37) [resolution 347,139]
519. $false <- (37, ~44) [subsumption resolution 518,391]
520. ~37 | 44 [avatar contradiction clause 519]
523. kind(paul) <- (45) [resolution 396,104]
580. tall(paul) <- (45) [resolution 523,122]
583. $false <- (~27, 45) [subsumption resolution 580,268]
584. 27 | ~45 [avatar contradiction clause 583]
585. $false [avatar sat refutation 271,282,348,397,516,520,584]
% SZS output end Proof for 63050374604920177135573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not wise is tall.
If paul is either not wise or not funny then fred is not curious or not funny and vice versa.
If susan is either not strong or not wise then paul is funny and vice versa.
Everyone who is not patient or patient is either not calm or curious.
If someone is patient then mary is both funny and curious.
Everyone who is either not wise or brave is both patient and not patient.
If fred is not patient or not strong then someone is both not generous and not happy and vice versa.
Everyone who is creative is either rich or funny and vice versa.
Everyone who is not funny or wise is either not wise or not brave and vice versa.
Everyone who is not calm or happy is either not old or not patient.
Everyone who is either strong or old is both not humble and tall and vice versa.
Everyone who is both not kind and not quiet is not curious or not kind and vice versa.
Everyone who is either funny or brave is both happy and not brave.
Everyone who is either wise or not patient is not patient or curious and vice versa.
If someone is both quiet and not creative then someone is not curious or not old and vice versa.
If susan is either not curious or not patient then lucy is both not calm and not strong and vice versa.
Alice is either tall or not wise.
Susan is patient.
Alice is not humble.
Someone is either quiet or patient.
Someone is either not patient or not kind.
Someone is brave or not strong.
Paul is funny. | Lucy is not curious. | contradiction | (![X]:((tall(X)|~wise(X))=>tall(X)))&
(((~wise(paul)<~>~funny(paul)))<=>((~curious(fred)|~funny(fred))))&
(((~strong(susan)<~>~wise(susan)))<=>(funny(paul)))&
(![X]:((~patient(X)|patient(X))=>(~calm(X)<~>curious(X))))&
((?[X]:(patient(X)))=>((funny(mary)&curious(mary))))&
(![X]:((~wise(X)<~>brave(X))=>(patient(X)&~patient(X))))&
(((~patient(fred)|~strong(fred)))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(creative(X)<=>(rich(X)<~>funny(X))))&
(![X]:((~funny(X)|wise(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:((~calm(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(![X]:((strong(X)<~>old(X))<=>(~humble(X)&tall(X))))&
(![X]:((~kind(X)&~quiet(X))<=>(~curious(X)|~kind(X))))&
(![X]:((funny(X)<~>brave(X))=>(happy(X)&~brave(X))))&
(![X]:((wise(X)<~>~patient(X))<=>(~patient(X)|curious(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((~curious(X)|~old(X)))))&
(((~curious(susan)<~>~patient(susan)))<=>((~calm(lucy)&~strong(lucy))))&
((tall(alice)<~>~wise(alice)))&
(patient(susan))&
(~humble(alice))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:((brave(X)|~strong(X))))&
(funny(paul)) | ~curious(lucy) | [
"p5",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4364687956109416063155577
% SZS output start Proof for 4364687956109416063155577
6. ! [X0] : ((~wise(X0) <~> brave(X0)) => (~patient(X0) & patient(X0))) [input p5]
9. ! [X0] : ((wise(X0) | ~funny(X0)) <=> (~wise(X0) <~> ~brave(X0))) [input p8]
13. ! [X0] : ((funny(X0) <~> brave(X0)) => (~brave(X0) & happy(X0))) [input p12]
14. ! [X0] : ((wise(X0) <~> ~patient(X0)) <=> (curious(X0) | ~patient(X0))) [input p13]
24. ~curious(lucy) [input hypothesis]
29. ! [X0] : ((~patient(X0) & patient(X0)) | (~wise(X0) <=> brave(X0))) [ennf transformation 6]
31. ! [X0] : ((~brave(X0) & happy(X0)) | (funny(X0) <=> brave(X0))) [ennf transformation 13]
36. ! [X0] : ((~patient(X0) & patient(X0)) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) [nnf transformation 29]
43. ! [X0] : (((wise(X0) | ~funny(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~wise(X0) & funny(X0)))) [nnf transformation 9]
44. ! [X0] : ((wise(X0) | ~funny(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~wise(X0) & funny(X0)))) [flattening 43]
50. ! [X0] : ((~brave(X0) & happy(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) [nnf transformation 31]
51. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [nnf transformation 14]
52. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [flattening 51]
87. patient(X0) | brave(X0) | wise(X0) [cnf transformation 36]
88. patient(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 36]
89. ~patient(X0) | brave(X0) | wise(X0) [cnf transformation 36]
90. ~patient(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 36]
104. wise(X0) | ~funny(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
124. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 50]
125. curious(X0) | ~patient(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 52]
129. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 52]
152. ~curious(lucy) [cnf transformation 24]
153. curious(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 125]
154. ~wise(X0) | patient(X0) [duplicate literal removal 129]
155. ~brave(X0) | funny(X0) [duplicate literal removal 124]
157. wise(X0) | ~funny(X0) | ~brave(X0) [duplicate literal removal 104]
207. ~brave(X0) | ~wise(X0) [subsumption resolution 88,90]
208. brave(X0) | wise(X0) [subsumption resolution 87,89]
233. ~brave(X0) | ~funny(X0) [subsumption resolution 157,207]
234. ~brave(X0) [subsumption resolution 155,233]
236. ~wise(X0) | curious(X0) [subsumption resolution 153,154]
246. 17 <=> ! [X1] : curious(X1) [avatar definition]
247. curious(X1) <- (17) [avatar component clause 246]
314. $false <- (17) [resolution 247,152]
315. ~17 [avatar contradiction clause 314]
334. wise(X1) [resolution 208,234]
348. curious(X0) [resolution 236,334]
350. 17 [avatar split clause 348,246]
351. $false [avatar sat refutation 315,350]
% SZS output end Proof for 4364687956109416063155577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.