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 alice is old or not kind then someone is both happy and not brave.
Everyone who is rich is both tall and not humble and vice versa.
Everyone who is both strong and quiet is either not tall or generous.
If fred is either not strong or curious then alice is either curious or not strong and vice versa.
If someone is creative or quiet then lucy is not old or kind and vice versa.
Everyone who is curious or rich is not curious.
If someone is either wise or creative then susan is not funny and vice versa.
If someone is both not brave and not funny then susan is both not patient and not wise.
If paul is both not happy and calm then paul is both not wise and old and vice versa.
If someone is either creative or patient then someone is both not happy and not curious.
If someone is either not brave or not curious then alice is not rich.
Everyone who is either not generous or curious is both kind and not curious.
Everyone who is either not humble or not strong is either not wise or not kind.
If someone is curious then mary is both tall and not calm.
Everyone who is either strong or old is not kind or not strong.
Someone is not curious.
Someone is both funny and wise.
Someone is both not old and rich.
Paul is both not brave and old.
Someone is both not rich and not happy.
Someone is old or not happy.
Fred is either not curious or not patient.
Susan is both not curious and not rich. | Susan is not humble. | neutral | (((old(alice)|~kind(alice)))=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:(rich(X)<=>(tall(X)&~humble(X))))&
(![X]:((strong(X)&quiet(X))=>(~tall(X)<~>generous(X))))&
(((~strong(fred)<~>curious(fred)))<=>((curious(alice)<~>~strong(alice))))&
((?[X]:((creative(X)|quiet(X))))<=>((~old(lucy)|kind(lucy))))&
(![X]:((curious(X)|rich(X))=>~curious(X)))&
((?[X]:((wise(X)<~>creative(X))))<=>(~funny(susan)))&
((?[X]:((~brave(X)&~funny(X))))=>((~patient(susan)&~wise(susan))))&
(((~happy(paul)&calm(paul)))<=>((~wise(paul)&old(paul))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:((~happy(X)&~curious(X)))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(~rich(alice)))&
(![X]:((~generous(X)<~>curious(X))=>(kind(X)&~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~wise(X)<~>~kind(X))))&
((?[X]:(curious(X)))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|~strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((~old(X)&rich(X))))&
((~brave(paul)&old(paul)))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((old(X)|~happy(X))))&
((~curious(fred)<~>~patient(fred)))&
((~curious(susan)&~rich(susan))) | ~humble(susan) | [] | null | 0 |
If paul is both wise and not old then john is either funny or not patient and vice versa. Everyone who is old or not old is old or creative and vice versa. Everyone who is not funny or not patient is old. Everyone who is both not creative and not generous is not brave or wise and vice versa. Everyone who is either not rich or not brave is not strong and vice versa. If someone is both not calm and not curious then someone is not old or funny and vice versa. Everyone who is not humble is both not rich and humble and vice versa. If someone is not strong or funny then mary is wise and vice versa. If lucy is not generous then someone is not strong. Everyone who is not happy is either not calm or curious. Everyone who is not happy or not humble is both not creative and funny and vice versa. If fred is happy then john is either tall or not funny. If fred is quiet or not calm then john is quiet or patient and vice versa. If susan is either not generous or not curious then mary is both happy and not tall. Everyone who is humble is both funny and brave and vice versa. Everyone who is either tall or not calm is either not creative or calm and vice versa. Paul is both not curious and brave. Fred is old or not old. John is either not rich or not tall. Someone is both patient and not old. | Mary is tall. | contradiction | (((wise(paul)&~old(paul)))<=>((funny(john)<~>~patient(john))))&
(![X]:((old(X)|~old(X))<=>(old(X)|creative(X))))&
(![X]:((~funny(X)|~patient(X))=>old(X)))&
(![X]:((~creative(X)&~generous(X))<=>(~brave(X)|wise(X))))&
(![X]:((~rich(X)<~>~brave(X))<=>~strong(X)))&
((?[X]:((~calm(X)&~curious(X))))<=>(?[X]:((~old(X)|funny(X)))))&
(![X]:(~humble(X)<=>(~rich(X)&humble(X))))&
((?[X]:((~strong(X)|funny(X))))<=>(wise(mary)))&
((~generous(lucy))=>(?[X]:(~strong(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>curious(X))))&
(![X]:((~happy(X)|~humble(X))<=>(~creative(X)&funny(X))))&
((happy(fred))=>((tall(john)<~>~funny(john))))&
(((quiet(fred)|~calm(fred)))<=>((quiet(john)|patient(john))))&
(((~generous(susan)<~>~curious(susan)))=>((happy(mary)&~tall(mary))))&
(![X]:(humble(X)<=>(funny(X)&brave(X))))&
(![X]:((tall(X)<~>~calm(X))<=>(~creative(X)<~>calm(X))))&
((~curious(paul)&brave(paul)))&
((old(fred)|~old(fred)))&
((~rich(john)<~>~tall(john)))&
(?[X]:((patient(X)&~old(X)))) | tall(mary) | [
"p3",
"p6",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4291315157690923847964999
% SZS output start Proof for 4291315157690923847964999
4. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (wise(X0) | ~brave(X0))) [input p3]
7. ! [X0] : (~humble(X0) <=> (humble(X0) & ~rich(X0))) [input p6]
8. ? [X0] : (funny(X0) | ~strong(X0)) <=> wise(mary) [input p7]
15. ! [X0] : (humble(X0) <=> (brave(X0) & funny(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> ~calm(X0)) <=> (~creative(X0) <~> calm(X0))) [input p15]
21. tall(mary) [input hypothesis]
32. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 4]
33. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | generous(X0) | creative(X0))) [flattening 32]
40. ! [X0] : ((~humble(X0) | (~humble(X0) | rich(X0))) & ((humble(X0) & ~rich(X0)) | humble(X0))) [nnf transformation 7]
41. ! [X0] : ((~humble(X0) | ~humble(X0) | rich(X0)) & ((humble(X0) & ~rich(X0)) | humble(X0))) [flattening 40]
42. (? [X0] : (funny(X0) | ~strong(X0)) | ~wise(mary)) & (wise(mary) | ! [X0] : (~funny(X0) & strong(X0))) [nnf transformation 8]
43. (? [X0] : (funny(X0) | ~strong(X0)) | ~wise(mary)) & (wise(mary) | ! [X1] : (~funny(X1) & strong(X1))) [rectify 42]
44. ? [X0] : (funny(X0) | ~strong(X0)) => (funny(sK2) | ~strong(sK2)) [choice axiom]
45. ((funny(sK2) | ~strong(sK2)) | ~wise(mary)) & (wise(mary) | ! [X1] : (~funny(X1) & strong(X1))) [skolemisation 43,44]
55. ! [X0] : ((humble(X0) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | ~humble(X0))) [nnf transformation 15]
56. ! [X0] : ((humble(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | ~humble(X0))) [flattening 55]
57. ! [X0] : ((((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) & (((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))))) [nnf transformation 16]
75. ~creative(X0) | ~wise(X0) [cnf transformation 33]
88. humble(X0) | humble(X0) [cnf transformation 41]
91. wise(mary) | ~funny(X1) [cnf transformation 45]
111. funny(X0) | ~humble(X0) [cnf transformation 56]
116. ~calm(X0) | creative(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 57]
120. calm(X0) | ~tall(X0) | calm(X0) | creative(X0) [cnf transformation 57]
129. tall(mary) [cnf transformation 21]
131. ~calm(X0) | creative(X0) | ~tall(X0) [duplicate literal removal 116]
133. calm(X0) | ~tall(X0) | creative(X0) [duplicate literal removal 120]
134. humble(X0) [duplicate literal removal 88]
161. 5 <=> ! [X1] : ~funny(X1) [avatar definition]
162. ~funny(X1) <- (5) [avatar component clause 161]
188. 11 <=> wise(mary) [avatar definition]
189. wise(mary) <- (11) [avatar component clause 188]
200. 5 | 11 [avatar split clause 91,188,161]
250. 24 <=> tall(mary) [avatar definition]
251. tall(mary) <- (24) [avatar component clause 250]
262. funny(X0) [subsumption resolution 111,134]
263. ~tall(X0) | creative(X0) [subsumption resolution 131,133]
271. 24 [avatar split clause 129,250]
285. $false <- (5) [subsumption resolution 162,262]
286. ~5 [avatar contradiction clause 285]
289. creative(mary) <- (24) [resolution 263,251]
293. ~wise(mary) <- (24) [resolution 289,75]
296. $false <- (11, 24) [subsumption resolution 293,189]
297. ~11 | ~24 [avatar contradiction clause 296]
298. $false [avatar sat refutation 200,271,286,297]
% SZS output end Proof for 4291315157690923847964999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is happy or not happy and vice versa. Everyone who is rich or creative is either not generous or humble and vice versa. If someone is either creative or happy then fred is either curious or not patient and vice versa. Everyone who is old is either funny or not tall. Everyone who is calm or not funny is both not brave and not rich. If alice is either not quiet or kind then john is not funny or rich and vice versa. Everyone who is not rich is both funny and calm and vice versa. Everyone who is brave is not generous and vice versa. If someone is rich or not patient then someone is generous or not happy and vice versa. If fred is creative or not wise then lucy is tall. If someone is either not humble or not creative then mary is either funny or brave. Everyone who is not brave or calm is wise or not generous and vice versa. If alice is both rich and strong then susan is not curious. Everyone who is not old or not patient is both not patient and not old and vice versa. If paul is not kind or generous then someone is generous or quiet and vice versa. If susan is either calm or strong then someone is both not humble and not quiet and vice versa. Someone is curious or creative. Someone is either not tall or generous. Alice is not creative or creative. Someone is either patient or not creative. John is not curious. Alice is either patient or kind. | Alice is not creative. | neutral | ((?[X]:(funny(X)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)<~>humble(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>((curious(fred)<~>~patient(fred))))&
(![X]:(old(X)=>(funny(X)<~>~tall(X))))&
(![X]:((calm(X)|~funny(X))=>(~brave(X)&~rich(X))))&
(((~quiet(alice)<~>kind(alice)))<=>((~funny(john)|rich(john))))&
(![X]:(~rich(X)<=>(funny(X)&calm(X))))&
(![X]:(brave(X)<=>~generous(X)))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((generous(X)|~happy(X)))))&
(((creative(fred)|~wise(fred)))=>(tall(lucy)))&
((?[X]:((~humble(X)<~>~creative(X))))=>((funny(mary)<~>brave(mary))))&
(![X]:((~brave(X)|calm(X))<=>(wise(X)|~generous(X))))&
(((rich(alice)&strong(alice)))=>(~curious(susan)))&
(![X]:((~old(X)|~patient(X))<=>(~patient(X)&~old(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
(((calm(susan)<~>strong(susan)))<=>(?[X]:((~humble(X)&~quiet(X)))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
((~creative(alice)|creative(alice)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~curious(john))&
((patient(alice)<~>kind(alice))) | ~creative(alice) | [] | null | 0 |
If alice is both happy and not funny then lucy is either humble or not creative.
If someone is both tall and not kind then someone is not old and vice versa.
If fred is either not rich or not humble then mary is both calm and not kind and vice versa.
Everyone who is both brave and calm is both not rich and not brave and vice versa.
Everyone who is both not happy and not generous is either not wise or humble.
Everyone who is not calm is brave.
If someone is either quiet or not patient then john is rich and vice versa.
Everyone who is not patient or not rich is funny or quiet and vice versa.
If someone is funny then someone is either quiet or not tall.
Everyone who is not quiet or not brave is not kind or funny.
If someone is both not happy and quiet then fred is tall or brave.
Everyone who is not wise or patient is not tall.
Everyone who is not tall or funny is calm and vice versa.
If someone is either not funny or brave then someone is quiet and vice versa.
Everyone who is either patient or not rich is both not tall and not old.
Everyone who is either rich or not rich is funny or patient and vice versa.
Someone is both not tall and generous.
Mary is old or creative.
Someone is either not generous or not kind.
Someone is both not quiet and not old.
Someone is patient or not wise.
Someone is both not funny and not humble.
Someone is wise or happy. | Mary is rich. | entailment | (((happy(alice)&~funny(alice)))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((tall(X)&~kind(X))))<=>(?[X]:(~old(X))))&
(((~rich(fred)<~>~humble(fred)))<=>((calm(mary)&~kind(mary))))&
(![X]:((brave(X)&calm(X))<=>(~rich(X)&~brave(X))))&
(![X]:((~happy(X)&~generous(X))=>(~wise(X)<~>humble(X))))&
(![X]:(~calm(X)=>brave(X)))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(rich(john)))&
(![X]:((~patient(X)|~rich(X))<=>(funny(X)|quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~quiet(X)|~brave(X))=>(~kind(X)|funny(X))))&
((?[X]:((~happy(X)&quiet(X))))=>((tall(fred)|brave(fred))))&
(![X]:((~wise(X)|patient(X))=>~tall(X)))&
(![X]:((~tall(X)|funny(X))<=>calm(X)))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)&~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(funny(X)|patient(X))))&
(?[X]:((~tall(X)&generous(X))))&
((old(mary)|creative(mary)))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((wise(X)|happy(X)))) | rich(mary) | [
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4695855453288239140284283
% SZS output start Proof for 4695855453288239140284283
4. ! [X0] : ((calm(X0) & brave(X0)) <=> (~brave(X0) & ~rich(X0))) [input p3]
12. ! [X0] : ((patient(X0) | ~wise(X0)) => ~tall(X0)) [input p11]
13. ! [X0] : ((funny(X0) | ~tall(X0)) <=> calm(X0)) [input p12]
15. ! [X0] : ((patient(X0) <~> ~rich(X0)) => (~old(X0) & ~tall(X0))) [input p14]
24. ~rich(mary) [input hypothesis]
38. ! [X0] : (~tall(X0) | (~patient(X0) & wise(X0))) [ennf transformation 12]
39. ! [X0] : ((~old(X0) & ~tall(X0)) | (patient(X0) <=> ~rich(X0))) [ennf transformation 15]
48. ! [X0] : (((calm(X0) & brave(X0)) | (brave(X0) | rich(X0))) & ((~brave(X0) & ~rich(X0)) | (~calm(X0) | ~brave(X0)))) [nnf transformation 4]
49. ! [X0] : (((calm(X0) & brave(X0)) | brave(X0) | rich(X0)) & ((~brave(X0) & ~rich(X0)) | ~calm(X0) | ~brave(X0))) [flattening 48]
61. ! [X0] : (((funny(X0) | ~tall(X0)) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [nnf transformation 13]
62. ! [X0] : ((funny(X0) | ~tall(X0) | ~calm(X0)) & (calm(X0) | (~funny(X0) & tall(X0)))) [flattening 61]
68. ! [X0] : ((~old(X0) & ~tall(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) [nnf transformation 39]
96. ~brave(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 49]
97. brave(X0) | brave(X0) | rich(X0) [cnf transformation 49]
116. ~patient(X0) | ~tall(X0) [cnf transformation 38]
117. calm(X0) | tall(X0) [cnf transformation 62]
125. ~tall(X0) | patient(X0) | rich(X0) [cnf transformation 68]
145. ~rich(mary) [cnf transformation 24]
148. ~brave(X0) | ~calm(X0) [duplicate literal removal 96]
149. brave(X0) | rich(X0) [duplicate literal removal 97]
283. ~tall(X0) | rich(X0) [subsumption resolution 125,116]
330. ~calm(X0) | rich(X0) [resolution 149,148]
393. rich(X0) | tall(X0) [resolution 330,117]
396. rich(X0) [subsumption resolution 393,283]
398. $false [resolution 396,145]
% SZS output end Proof for 4695855453288239140284283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and not funny then someone is humble or calm. If someone is both happy and rich then someone is curious or not old and vice versa. Everyone who is calm or not old is rich. Everyone who is old or not rich is either not kind or kind and vice versa. Everyone who is happy is both not wise and not tall and vice versa. If alice is either not quiet or happy then someone is either generous or tall. If john is both creative and not happy then susan is calm and vice versa. Everyone who is either not kind or not happy is either not calm or not funny. Everyone who is not old is both not old and tall. Everyone who is both quiet and not strong is patient. Everyone who is calm or humble is both not rich and not curious. If someone is either wise or not curious then someone is either humble or not patient. If lucy is either humble or strong then someone is both not generous and not tall. Everyone who is both not humble and quiet is either patient or not quiet and vice versa. If someone is both tall and not rich then someone is both not brave and not old. Everyone who is either quiet or not quiet is both strong and patient. Someone is not generous. Lucy is funny or patient. Lucy is either old or not creative. Fred is not humble or tall. Lucy is not happy or strong. Susan is both humble and old. Someone is funny. | Lucy is not strong. | contradiction | ((?[X]:((rich(X)&~funny(X))))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((happy(X)&rich(X))))<=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((calm(X)|~old(X))=>rich(X)))&
(![X]:((old(X)|~rich(X))<=>(~kind(X)<~>kind(X))))&
(![X]:(happy(X)<=>(~wise(X)&~tall(X))))&
(((~quiet(alice)<~>happy(alice)))=>(?[X]:((generous(X)<~>tall(X)))))&
(((creative(john)&~happy(john)))<=>(calm(susan)))&
(![X]:((~kind(X)<~>~happy(X))=>(~calm(X)<~>~funny(X))))&
(![X]:(~old(X)=>(~old(X)&tall(X))))&
(![X]:((quiet(X)&~strong(X))=>patient(X)))&
(![X]:((calm(X)|humble(X))=>(~rich(X)&~curious(X))))&
((?[X]:((wise(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>~patient(X)))))&
(((humble(lucy)<~>strong(lucy)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((~humble(X)&quiet(X))<=>(patient(X)<~>~quiet(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(strong(X)&patient(X))))&
(?[X]:(~generous(X)))&
((funny(lucy)|patient(lucy)))&
((old(lucy)<~>~creative(lucy)))&
((~humble(fred)|tall(fred)))&
((~happy(lucy)|strong(lucy)))&
((humble(susan)&old(susan)))&
(?[X]:(funny(X))) | ~strong(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7136613851934094352526871
% SZS output start Proof for 7136613851934094352526871
16. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (patient(X0) & strong(X0))) [input p15]
24. ~strong(lucy) [input hypothesis]
41. ! [X0] : ((patient(X0) & strong(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 16]
72. ! [X0] : ((patient(X0) & strong(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 41]
128. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 72]
129. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 72]
141. ~strong(lucy) [cnf transformation 24]
142. strong(X0) | ~quiet(X0) [duplicate literal removal 128]
143. strong(X0) | quiet(X0) [duplicate literal removal 129]
280. strong(X0) [subsumption resolution 142,143]
300. $false [subsumption resolution 141,280]
% SZS output end Proof for 7136613851934094352526871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not funny or patient and vice versa.
Everyone who is not quiet or not patient is either curious or not brave and vice versa.
If someone is not funny or not wise then someone is brave or not patient.
If alice is not patient or tall then someone is either not rich or calm.
If someone is not brave then someone is both not generous and not humble.
Everyone who is not patient is either not patient or not curious and vice versa.
Everyone who is both quiet and not strong is either not humble or humble.
Everyone who is not brave is patient.
If someone is either not happy or brave then susan is not old and vice versa.
If john is both rich and creative then someone is curious and vice versa.
If alice is both not kind and creative then someone is both tall and not curious.
Everyone who is not patient or patient is not quiet and vice versa.
If susan is not creative then someone is either strong or not creative and vice versa.
Everyone who is either quiet or not humble is either kind or tall and vice versa.
If mary is not generous or not curious then someone is either quiet or not calm and vice versa.
Everyone who is funny is both happy and brave.
Paul is not tall or creative.
Paul is both strong and not generous.
Someone is funny.
Someone is both happy and not old.
Mary is both brave and humble.
Someone is either rich or creative.
Someone is both tall and not creative. | Paul is not funny. | contradiction | (![X]:(quiet(X)<=>(~funny(X)|patient(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(((~patient(alice)|tall(alice)))=>(?[X]:((~rich(X)<~>calm(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(~patient(X)<=>(~patient(X)<~>~curious(X))))&
(![X]:((quiet(X)&~strong(X))=>(~humble(X)<~>humble(X))))&
(![X]:(~brave(X)=>patient(X)))&
((?[X]:((~happy(X)<~>brave(X))))<=>(~old(susan)))&
(((rich(john)&creative(john)))<=>(?[X]:(curious(X))))&
(((~kind(alice)&creative(alice)))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((~patient(X)|patient(X))<=>~quiet(X)))&
((~creative(susan))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((quiet(X)<~>~humble(X))<=>(kind(X)<~>tall(X))))&
(((~generous(mary)|~curious(mary)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(funny(X)=>(happy(X)&brave(X))))&
((~tall(paul)|creative(paul)))&
((strong(paul)&~generous(paul)))&
(?[X]:(funny(X)))&
(?[X]:((happy(X)&~old(X))))&
((brave(mary)&humble(mary)))&
(?[X]:((rich(X)<~>creative(X))))&
(?[X]:((tall(X)&~creative(X)))) | ~funny(paul) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7335713131107108442295058
% SZS output start Proof for 7335713131107108442295058
1. ! [X0] : (quiet(X0) <=> (patient(X0) | ~funny(X0))) [input p0]
12. ! [X0] : ((patient(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p11]
24. ~funny(paul) [input hypothesis]
37. ! [X0] : ((quiet(X0) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | ~quiet(X0))) [nnf transformation 1]
38. ! [X0] : ((quiet(X0) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | ~quiet(X0))) [flattening 37]
63. ! [X0] : (((patient(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & patient(X0)))) [nnf transformation 12]
64. ! [X0] : ((patient(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~patient(X0) & patient(X0)))) [flattening 63]
85. funny(X0) | quiet(X0) [cnf transformation 38]
86. quiet(X0) | ~patient(X0) [cnf transformation 38]
116. ~quiet(X0) | patient(X0) [cnf transformation 64]
117. ~quiet(X0) | ~patient(X0) [cnf transformation 64]
151. ~funny(paul) [cnf transformation 24]
241. ~patient(X0) [subsumption resolution 117,86]
242. ~quiet(X0) [subsumption resolution 116,241]
304. quiet(paul) [resolution 85,151]
305. $false [subsumption resolution 304,242]
% SZS output end Proof for 7335713131107108442295058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is generous then someone is not humble and vice versa.
Everyone who is not calm or not strong is old or funny.
If someone is humble then paul is not funny or humble.
Everyone who is both curious and not patient is both not tall and quiet.
Everyone who is either old or not creative is either strong or not patient.
Everyone who is not happy is calm or not generous.
If lucy is old or not patient then alice is humble or quiet and vice versa.
Everyone who is either not old or calm is wise.
If someone is not funny then alice is either not quiet or generous.
Everyone who is both not patient and quiet is either rich or not humble and vice versa.
If lucy is both wise and not brave then someone is strong or not generous.
Everyone who is either happy or not generous is either tall or curious.
Everyone who is wise is either kind or happy and vice versa.
Everyone who is either not funny or not old is wise or old and vice versa.
Everyone who is both calm and not calm is happy or not humble and vice versa.
If someone is humble then mary is not happy and vice versa.
Someone is brave.
Susan is not curious or not generous.
Someone is not curious or happy.
Someone is not patient or funny.
Mary is both funny and generous.
Someone is either brave or not happy. | Alice is old. | neutral | ((generous(john))<=>(?[X]:(~humble(X))))&
(![X]:((~calm(X)|~strong(X))=>(old(X)|funny(X))))&
((?[X]:(humble(X)))=>((~funny(paul)|humble(paul))))&
(![X]:((curious(X)&~patient(X))=>(~tall(X)&quiet(X))))&
(![X]:((old(X)<~>~creative(X))=>(strong(X)<~>~patient(X))))&
(![X]:(~happy(X)=>(calm(X)|~generous(X))))&
(((old(lucy)|~patient(lucy)))<=>((humble(alice)|quiet(alice))))&
(![X]:((~old(X)<~>calm(X))=>wise(X)))&
((?[X]:(~funny(X)))=>((~quiet(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(rich(X)<~>~humble(X))))&
(((wise(lucy)&~brave(lucy)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((happy(X)<~>~generous(X))=>(tall(X)<~>curious(X))))&
(![X]:(wise(X)<=>(kind(X)<~>happy(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(wise(X)|old(X))))&
(![X]:((calm(X)&~calm(X))<=>(happy(X)|~humble(X))))&
((?[X]:(humble(X)))<=>(~happy(mary)))&
(?[X]:(brave(X)))&
((~curious(susan)|~generous(susan)))&
(?[X]:((~curious(X)|happy(X))))&
(?[X]:((~patient(X)|funny(X))))&
((funny(mary)&generous(mary)))&
(?[X]:((brave(X)<~>~happy(X)))) | old(alice) | [] | null | 0 |
Everyone who is humble or not humble is not strong and vice versa. Everyone who is old or generous is either creative or not calm. If someone is either creative or strong then mary is not brave. Everyone who is both humble and happy is either not kind or funny and vice versa. Everyone who is not quiet is not brave or not rich and vice versa. Everyone who is old is generous or not old and vice versa. Everyone who is not rich is both strong and quiet. Everyone who is both not rich and not tall is both patient and happy. Everyone who is quiet or not funny is curious or generous. If someone is humble or not kind then someone is not brave or not old and vice versa. If someone is either tall or not happy then susan is not happy or strong and vice versa. If someone is not quiet then someone is strong and vice versa. If someone is either not brave or curious then someone is both happy and not creative. If john is both tall and not patient then someone is either not funny or not generous. If someone is wise or not wise then someone is happy or not kind. If someone is both not quiet and not funny then someone is not happy or not humble. Someone is kind or not patient. Fred is both patient and not tall. Someone is not tall. Alice is not funny or creative. Someone is not happy or old. Fred is old. Someone is either not happy or old. Alice is kind. | Susan is not kind. | contradiction | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((old(X)|generous(X))=>(creative(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(((tall(john)&~patient(john)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((happy(X)|~kind(X)))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~happy(X)|~humble(X)))))&
(?[X]:((kind(X)|~patient(X))))&
((patient(fred)&~tall(fred)))&
(?[X]:(~tall(X)))&
((~funny(alice)|creative(alice)))&
(?[X]:((~happy(X)|old(X))))&
(old(fred))&
(?[X]:((~happy(X)<~>old(X))))&
(kind(alice)) | ~kind(susan) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2613607648099912663850256
% SZS output start Proof for 2613607648099912663850256
1. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~strong(X0)) [input p0]
5. ! [X0] : (~quiet(X0) <=> (~rich(X0) | ~brave(X0))) [input p4]
6. ! [X0] : (old(X0) <=> (~old(X0) | generous(X0))) [input p5]
10. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : (~old(X0) | ~brave(X0)) [input p9]
12. ? [X0] : ~quiet(X0) <=> ? [X0] : strong(X0) [input p11]
25. ~kind(susan) [input hypothesis]
26. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : (~old(X1) | ~brave(X1)) [rectify 10]
27. ? [X0] : ~quiet(X0) <=> ? [X1] : strong(X1) [rectify 12]
43. ! [X0] : (((~humble(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 1]
44. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [flattening 43]
49. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 5]
50. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | quiet(X0))) [flattening 49]
51. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | ~old(X0))) [nnf transformation 6]
52. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~old(X0))) [flattening 51]
53. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X1] : (~old(X1) | ~brave(X1)) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 26]
54. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X2] : (~old(X2) | ~brave(X2)) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 53]
55. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK0) | humble(sK0)) [choice axiom]
56. ? [X2] : (~old(X2) | ~brave(X2)) => (~old(sK1) | ~brave(sK1)) [choice axiom]
57. ((~kind(sK0) | humble(sK0)) | ! [X1] : (old(X1) & brave(X1))) & ((~old(sK1) | ~brave(sK1)) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 54,56,55]
63. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : quiet(X0)) [nnf transformation 27]
64. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : quiet(X3)) [rectify 63]
65. ? [X0] : ~quiet(X0) => ~quiet(sK3) [choice axiom]
66. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
67. (~quiet(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : quiet(X3)) [skolemisation 64,66,65]
90. ~strong(X0) | ~humble(X0) [cnf transformation 44]
91. ~strong(X0) | humble(X0) [cnf transformation 44]
106. ~quiet(X0) | brave(X0) [cnf transformation 50]
110. old(X0) | old(X0) [cnf transformation 52]
118. ~old(sK1) | ~brave(sK1) | kind(X3) [cnf transformation 57]
127. strong(sK4) | quiet(X3) [cnf transformation 67]
148. ~kind(susan) [cnf transformation 25]
150. old(X0) [duplicate literal removal 110]
151. ~strong(X0) [subsumption resolution 90,91]
164. 3 <=> ! [X1] : brave(X1) [avatar definition]
165. brave(X1) <- (3) [avatar component clause 164]
175. ~brave(sK1) | kind(X3) [subsumption resolution 118,150]
177. 6 <=> ! [X3] : kind(X3) [avatar definition]
178. kind(X3) <- (6) [avatar component clause 177]
180. 7 <=> brave(sK1) [avatar definition]
182. ~brave(sK1) <- (~7) [avatar component clause 180]
183. 6 | ~7 [avatar split clause 175,180,177]
213. quiet(X3) [subsumption resolution 127,151]
281. brave(X0) [resolution 106,213]
282. 3 [avatar split clause 281,164]
284. $false <- (3, ~7) [resolution 165,182]
285. ~3 | 7 [avatar contradiction clause 284]
287. $false <- (6) [resolution 178,148]
292. ~6 [avatar contradiction clause 287]
293. $false [avatar sat refutation 183,282,285,292]
% SZS output end Proof for 2613607648099912663850256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not rich.
Everyone who is patient or kind is humble or not tall.
Everyone who is either not humble or not wise is both calm and curious and vice versa.
Everyone who is both not tall and creative is creative or wise and vice versa.
Everyone who is calm or creative is not brave and vice versa.
Everyone who is not patient is funny.
Everyone who is either not patient or not generous is not funny or funny.
If someone is not funny then someone is both funny and brave.
Everyone who is old is wise.
If someone is either brave or kind then someone is not kind or patient.
If mary is either not quiet or humble then fred is wise.
Everyone who is not happy or happy is both brave and rich.
Everyone who is both not brave and patient is not tall and vice versa.
Everyone who is either brave or not humble is quiet or calm.
If someone is either not curious or generous then susan is either not strong or not generous and vice versa.
If someone is quiet or not happy then someone is not generous and vice versa.
Lucy is both not creative and not kind.
John is kind or not old.
Mary is not happy or happy.
Someone is not humble.
Susan is either not humble or not curious. | Fred is old. | contradiction | (![X]:(~strong(X)=>~rich(X)))&
(![X]:((patient(X)|kind(X))=>(humble(X)|~tall(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(calm(X)&curious(X))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)|wise(X))))&
(![X]:((calm(X)|creative(X))<=>~brave(X)))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:((~patient(X)<~>~generous(X))=>(~funny(X)|funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(old(X)=>wise(X)))&
((?[X]:((brave(X)<~>kind(X))))=>(?[X]:((~kind(X)|patient(X)))))&
(((~quiet(mary)<~>humble(mary)))=>(wise(fred)))&
(![X]:((~happy(X)|happy(X))=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~strong(susan)<~>~generous(susan))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(~generous(X))))&
((~creative(lucy)&~kind(lucy)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary)))&
(?[X]:(~humble(X)))&
((~humble(susan)<~>~curious(susan))) | old(fred) | [
"p3",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1965548464163464684283195
% SZS output start Proof for 1965548464163464684283195
4. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (wise(X0) | creative(X0))) [input p3]
9. ! [X0] : (old(X0) => wise(X0)) [input p8]
12. ! [X0] : ((happy(X0) | ~happy(X0)) => (rich(X0) & brave(X0))) [input p11]
13. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p12]
22. old(fred) [input hypothesis]
33. ! [X0] : (wise(X0) | ~old(X0)) [ennf transformation 9]
36. ! [X0] : ((rich(X0) & brave(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 12]
41. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~creative(X0) | tall(X0))) [flattening 41]
54. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 13]
55. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 54]
80. ~wise(X0) | ~tall(X0) [cnf transformation 42]
91. ~old(X0) | wise(X0) [cnf transformation 33]
96. brave(X0) | happy(X0) [cnf transformation 36]
97. brave(X0) | ~happy(X0) [cnf transformation 36]
101. ~brave(X0) | tall(X0) [cnf transformation 55]
123. old(fred) [cnf transformation 22]
162. 10 <=> wise(fred) [avatar definition]
164. wise(fred) <- (10) [avatar component clause 162]
168. brave(X0) [subsumption resolution 96,97]
169. tall(X0) [subsumption resolution 101,168]
249. wise(fred) [resolution 91,123]
250. 10 [avatar split clause 249,162]
252. ~tall(fred) <- (10) [resolution 164,80]
255. $false <- (10) [subsumption resolution 252,169]
256. ~10 [avatar contradiction clause 255]
257. $false [avatar sat refutation 250,256]
% SZS output end Proof for 1965548464163464684283195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is generous or patient then someone is kind or humble. If fred is happy then alice is both not humble and not kind. If john is either wise or not tall then alice is both not tall and not patient. Everyone who is not strong or funny is not quiet and vice versa. Everyone who is not kind or brave is not calm and vice versa. If mary is both not funny and not happy then fred is not quiet or curious. If someone is not quiet or humble then fred is both tall and funny. Everyone who is either brave or happy is not tall or kind. If someone is humble then susan is both strong and not strong. Everyone who is quiet is both generous and not strong. Everyone who is not creative is both wise and kind and vice versa. Everyone who is wise or calm is both happy and not happy and vice versa. If paul is both not funny and kind then mary is both humble and wise. If someone is happy or not rich then someone is either creative or not rich. If paul is not tall or curious then someone is either kind or curious and vice versa. Everyone who is not quiet or creative is creative. Lucy is either not humble or happy. Susan is both generous and not calm. John is either old or not rich. Alice is either not kind or not calm. Someone is not funny or not happy. John is both not rich and curious. Someone is wise or funny. | Susan is creative. | entailment | (((generous(mary)|patient(mary)))=>(?[X]:((kind(X)|humble(X)))))&
((happy(fred))=>((~humble(alice)&~kind(alice))))&
(((wise(john)<~>~tall(john)))=>((~tall(alice)&~patient(alice))))&
(![X]:((~strong(X)|funny(X))<=>~quiet(X)))&
(![X]:((~kind(X)|brave(X))<=>~calm(X)))&
(((~funny(mary)&~happy(mary)))=>((~quiet(fred)|curious(fred))))&
((?[X]:((~quiet(X)|humble(X))))=>((tall(fred)&funny(fred))))&
(![X]:((brave(X)<~>happy(X))=>(~tall(X)|kind(X))))&
((?[X]:(humble(X)))=>((strong(susan)&~strong(susan))))&
(![X]:(quiet(X)=>(generous(X)&~strong(X))))&
(![X]:(~creative(X)<=>(wise(X)&kind(X))))&
(![X]:((wise(X)|calm(X))<=>(happy(X)&~happy(X))))&
(((~funny(paul)&kind(paul)))=>((humble(mary)&wise(mary))))&
((?[X]:((happy(X)|~rich(X))))=>(?[X]:((creative(X)<~>~rich(X)))))&
(((~tall(paul)|curious(paul)))<=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((~quiet(X)|creative(X))=>creative(X)))&
((~humble(lucy)<~>happy(lucy)))&
((generous(susan)&~calm(susan)))&
((old(john)<~>~rich(john)))&
((~kind(alice)<~>~calm(alice)))&
(?[X]:((~funny(X)|~happy(X))))&
((~rich(john)&curious(john)))&
(?[X]:((wise(X)|funny(X)))) | creative(susan) | [
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 478123718345589384787018
% SZS output start Proof for 478123718345589384787018
4. ! [X0] : ((funny(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p3]
10. ! [X0] : (quiet(X0) => (~strong(X0) & generous(X0))) [input p9]
16. ! [X0] : ((creative(X0) | ~quiet(X0)) => creative(X0)) [input p15]
24. ~creative(susan) [input hypothesis]
37. ! [X0] : ((~strong(X0) & generous(X0)) | ~quiet(X0)) [ennf transformation 10]
41. ! [X0] : (creative(X0) | (~creative(X0) & quiet(X0))) [ennf transformation 16]
45. ! [X0] : (((funny(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & strong(X0)))) [nnf transformation 4]
46. ! [X0] : ((funny(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & strong(X0)))) [flattening 45]
75. ~quiet(X0) | strong(X0) [cnf transformation 46]
91. ~strong(X0) | ~quiet(X0) [cnf transformation 37]
112. creative(X0) | quiet(X0) [cnf transformation 41]
126. ~creative(susan) [cnf transformation 24]
209. ~quiet(X0) [subsumption resolution 91,75]
273. creative(X0) [subsumption resolution 112,209]
307. $false [subsumption resolution 126,273]
% SZS output end Proof for 478123718345589384787018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not rich then someone is kind or not funny and vice versa.
Everyone who is both not brave and not creative is both not quiet and curious.
Everyone who is patient or quiet is either generous or wise and vice versa.
Everyone who is both not strong and not funny is not brave.
Everyone who is both rich and strong is not old or not tall.
Everyone who is either not quiet or not strong is not strong and vice versa.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
If john is either wise or kind then someone is rich or not kind and vice versa.
Everyone who is either not wise or curious is not brave and vice versa.
Someone is both brave and not kind.
Someone is either creative or kind.
Susan is not kind or brave.
Fred is not funny or not tall.
Someone is either not curious or strong.
John is both not old and humble. | Susan is wise. | neutral | (((patient(susan)|~rich(susan)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~brave(X)&~creative(X))=>(~quiet(X)&curious(X))))&
(![X]:((patient(X)|quiet(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))=>~brave(X)))&
(![X]:((rich(X)&strong(X))=>(~old(X)|~tall(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
(((wise(john)<~>kind(john)))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>~brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((~kind(susan)|brave(susan)))&
((~funny(fred)|~tall(fred)))&
(?[X]:((~curious(X)<~>strong(X))))&
((~old(john)&humble(john))) | wise(susan) | [] | null | 0 |
If someone is wise then susan is either funny or brave and vice versa.
Everyone who is humble is old or funny and vice versa.
If someone is both not strong and not curious then susan is not happy.
Everyone who is either brave or not wise is humble.
Everyone who is both brave and funny is old and vice versa.
Everyone who is calm or curious is creative and vice versa.
Everyone who is rich or not patient is not wise.
If someone is not rich or not old then someone is not calm or not curious and vice versa.
If someone is either creative or not quiet then someone is quiet or creative.
If someone is not happy or not humble then susan is not brave or not strong and vice versa.
If someone is both not curious and wise then someone is funny and vice versa.
Everyone who is not wise or happy is brave or not kind.
Everyone who is not brave is not humble.
Everyone who is calm or not generous is not funny or not strong.
If alice is not happy then someone is kind or rich and vice versa.
Everyone who is either not tall or not brave is either not curious or not rich and vice versa.
Someone is not creative or humble.
Paul is not generous or not kind.
Mary is not patient.
Someone is either creative or rich.
Someone is calm or not patient.
Someone is both brave and calm.
Fred is brave.
Someone is humble. | Susan is old. | contradiction | ((?[X]:(wise(X)))<=>((funny(susan)<~>brave(susan))))&
(![X]:(humble(X)<=>(old(X)|funny(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(~happy(susan)))&
(![X]:((brave(X)<~>~wise(X))=>humble(X)))&
(![X]:((brave(X)&funny(X))<=>old(X)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(![X]:((rich(X)|~patient(X))=>~wise(X)))&
((?[X]:((~rich(X)|~old(X))))<=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((quiet(X)|creative(X)))))&
((?[X]:((~happy(X)|~humble(X))))<=>((~brave(susan)|~strong(susan))))&
((?[X]:((~curious(X)&wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|happy(X))=>(brave(X)|~kind(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((calm(X)|~generous(X))=>(~funny(X)|~strong(X))))&
((~happy(alice))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>(~curious(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
((~generous(paul)|~kind(paul)))&
(~patient(mary))&
(?[X]:((creative(X)<~>rich(X))))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((brave(X)&calm(X))))&
(brave(fred))&
(?[X]:(humble(X))) | old(susan) | [
"p0",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9151308651435659587470123
% SZS output start Proof for 9151308651435659587470123
1. ? [X0] : wise(X0) <=> (funny(susan) <~> brave(susan)) [input p0]
5. ! [X0] : ((funny(X0) & brave(X0)) <=> old(X0)) [input p4]
11. ? [X0] : (wise(X0) & ~curious(X0)) <=> ? [X0] : funny(X0) [input p10]
25. old(susan) [input hypothesis]
28. ? [X0] : (wise(X0) & ~curious(X0)) <=> ? [X1] : funny(X1) [rectify 11]
38. (? [X0] : wise(X0) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X0] : ~wise(X0)) [nnf transformation 1]
39. (? [X0] : wise(X0) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X1] : ~wise(X1)) [rectify 38]
40. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
41. (wise(sK0) | ((funny(susan) | ~brave(susan)) & (brave(susan) | ~funny(susan)))) & (((~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan))) | ! [X1] : ~wise(X1)) [skolemisation 39,40]
45. ! [X0] : (((funny(X0) & brave(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) | ~brave(X0)))) [nnf transformation 5]
46. ! [X0] : (((funny(X0) & brave(X0)) | ~old(X0)) & (old(X0) | ~funny(X0) | ~brave(X0))) [flattening 45]
63. (? [X0] : (wise(X0) & ~curious(X0)) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : (~wise(X0) | curious(X0))) [nnf transformation 28]
64. (? [X0] : (wise(X0) & ~curious(X0)) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : (~wise(X3) | curious(X3))) [rectify 63]
65. ? [X0] : (wise(X0) & ~curious(X0)) => (wise(sK5) & ~curious(sK5)) [choice axiom]
66. ? [X2] : funny(X2) => funny(sK6) [choice axiom]
67. ((wise(sK5) & ~curious(sK5)) | ! [X1] : ~funny(X1)) & (funny(sK6) | ! [X3] : (~wise(X3) | curious(X3))) [skolemisation 64,66,65]
85. ~brave(susan) | ~funny(susan) | ~wise(X1) [cnf transformation 41]
95. ~old(X0) | brave(X0) [cnf transformation 46]
96. ~old(X0) | funny(X0) [cnf transformation 46]
114. wise(sK5) | ~funny(X1) [cnf transformation 67]
141. old(susan) [cnf transformation 25]
143. 1 <=> brave(susan) [avatar definition]
147. 2 <=> funny(susan) [avatar definition]
148. ~funny(susan) <- (~2) [avatar component clause 147]
149. funny(susan) <- (2) [avatar component clause 147]
157. 4 <=> ! [X1] : ~wise(X1) [avatar definition]
158. ~wise(X1) <- (4) [avatar component clause 157]
159. 4 | ~2 | ~1 [avatar split clause 85,143,147,157]
240. 24 <=> ! [X1] : ~funny(X1) [avatar definition]
241. ~funny(X1) <- (24) [avatar component clause 240]
243. 25 <=> wise(sK5) [avatar definition]
245. wise(sK5) <- (25) [avatar component clause 243]
246. 24 | 25 [avatar split clause 114,243,240]
318. $false <- (2, 24) [subsumption resolution 149,241]
319. ~2 | ~24 [avatar contradiction clause 318]
324. brave(susan) [resolution 95,141]
327. 1 [avatar split clause 324,143]
328. $false <- (4, 25) [resolution 158,245]
329. ~4 | ~25 [avatar contradiction clause 328]
330. funny(susan) [resolution 96,141]
331. $false <- (~2) [subsumption resolution 330,148]
332. 2 [avatar contradiction clause 331]
333. $false [avatar sat refutation 159,246,319,327,329,332]
% SZS output end Proof for 9151308651435659587470123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and not funny and vice versa.
If paul is not humble or calm then someone is either not strong or not wise and vice versa.
If someone is funny or kind then someone is either generous or tall and vice versa.
Everyone who is both not funny and not quiet is either humble or strong and vice versa.
Everyone who is both not kind and brave is both calm and not calm and vice versa.
If someone is both funny and tall then someone is wise or calm.
If paul is not wise or not happy then mary is calm or curious and vice versa.
Everyone who is not brave or strong is old and vice versa.
If someone is creative or not curious then lucy is both not patient and patient.
If mary is both wise and not old then someone is kind or not tall and vice versa.
Everyone who is creative is both strong and not brave.
Everyone who is curious or happy is either not rich or brave.
If someone is both not patient and not humble then john is either not funny or quiet and vice versa.
If someone is either tall or not creative then mary is not creative.
Everyone who is not humble is both not kind and not brave.
If john is either old or tall then someone is not happy.
John is not quiet.
Paul is either curious or not happy.
Fred is humble or not kind.
Someone is either quiet or not curious.
Alice is either not old or not generous.
Someone is either not kind or creative.
Someone is either not humble or old. | Lucy is not rich. | entailment | (![X]:(~old(X)<=>(~curious(X)&~funny(X))))&
(((~humble(paul)|calm(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(humble(X)<~>strong(X))))&
(![X]:((~kind(X)&brave(X))<=>(calm(X)&~calm(X))))&
((?[X]:((funny(X)&tall(X))))=>(?[X]:((wise(X)|calm(X)))))&
(((~wise(paul)|~happy(paul)))<=>((calm(mary)|curious(mary))))&
(![X]:((~brave(X)|strong(X))<=>old(X)))&
((?[X]:((creative(X)|~curious(X))))=>((~patient(lucy)&patient(lucy))))&
(((wise(mary)&~old(mary)))<=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(creative(X)=>(strong(X)&~brave(X))))&
(![X]:((curious(X)|happy(X))=>(~rich(X)<~>brave(X))))&
((?[X]:((~patient(X)&~humble(X))))<=>((~funny(john)<~>quiet(john))))&
((?[X]:((tall(X)<~>~creative(X))))=>(~creative(mary)))&
(![X]:(~humble(X)=>(~kind(X)&~brave(X))))&
(((old(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
(~quiet(john))&
((curious(paul)<~>~happy(paul)))&
((humble(fred)|~kind(fred)))&
(?[X]:((quiet(X)<~>~curious(X))))&
((~old(alice)<~>~generous(alice)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((~humble(X)<~>old(X)))) | ~rich(lucy) | [
"p0",
"p4",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 339926810485562412054516
% SZS output start Proof for 339926810485562412054516
1. ! [X0] : (~old(X0) <=> (~funny(X0) & ~curious(X0))) [input p0]
5. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (~calm(X0) & calm(X0))) [input p4]
9. ? [X0] : (~curious(X0) | creative(X0)) => (patient(lucy) & ~patient(lucy)) [input p8]
10. (~old(mary) & wise(mary)) <=> ? [X0] : (~tall(X0) | kind(X0)) [input p9]
12. ! [X0] : ((happy(X0) | curious(X0)) => (~rich(X0) <~> brave(X0))) [input p11]
24. rich(lucy) [input hypothesis]
28. (patient(lucy) & ~patient(lucy)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 9]
30. ! [X0] : ((~rich(X0) <~> brave(X0)) | (~happy(X0) & ~curious(X0))) [ennf transformation 12]
34. ! [X0] : ((~old(X0) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | old(X0))) [nnf transformation 1]
35. ! [X0] : ((~old(X0) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | old(X0))) [flattening 34]
48. ! [X0] : (((brave(X0) & ~kind(X0)) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 5]
49. ! [X0] : (((brave(X0) & ~kind(X0)) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | ~brave(X0) | kind(X0))) [flattening 48]
57. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X0] : (~tall(X0) | kind(X0)) | (old(mary) | ~wise(mary))) [nnf transformation 10]
58. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X0] : (~tall(X0) | kind(X0)) | old(mary) | ~wise(mary)) [flattening 57]
59. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & (? [X1] : (~tall(X1) | kind(X1)) | old(mary) | ~wise(mary)) [rectify 58]
60. ? [X1] : (~tall(X1) | kind(X1)) => (~tall(sK4) | kind(sK4)) [choice axiom]
61. ((~old(mary) & wise(mary)) | ! [X0] : (tall(X0) & ~kind(X0))) & ((~tall(sK4) | kind(sK4)) | old(mary) | ~wise(mary)) [skolemisation 59,60]
62. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~happy(X0) & ~curious(X0))) [nnf transformation 30]
82. ~curious(X0) | old(X0) [cnf transformation 35]
103. calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 49]
104. ~brave(X0) | ~calm(X0) | kind(X0) [cnf transformation 49]
116. ~patient(lucy) | curious(X0) [cnf transformation 28]
118. patient(lucy) | curious(X0) [cnf transformation 28]
122. ~old(mary) | ~kind(X0) [cnf transformation 61]
126. ~rich(X0) | brave(X0) | ~curious(X0) [cnf transformation 62]
154. rich(lucy) [cnf transformation 24]
200. 11 <=> ! [X3] : ~kind(X3) [avatar definition]
201. ~kind(X3) <- (11) [avatar component clause 200]
217. ~brave(X0) | kind(X0) [subsumption resolution 103,104]
251. 22 <=> ! [X0] : curious(X0) [avatar definition]
252. curious(X0) <- (22) [avatar component clause 251]
254. 23 <=> patient(lucy) [avatar definition]
257. 22 | 23 [avatar split clause 118,254,251]
262. 22 | ~23 [avatar split clause 116,254,251]
268. 26 <=> old(mary) [avatar definition]
270. ~old(mary) <- (~26) [avatar component clause 268]
272. 11 | ~26 [avatar split clause 122,268,200]
403. old(X0) <- (22) [resolution 82,252]
459. brave(lucy) | ~curious(lucy) [resolution 126,154]
460. brave(lucy) <- (22) [subsumption resolution 459,252]
463. kind(lucy) <- (22) [resolution 460,217]
467. $false <- (11, 22) [subsumption resolution 463,201]
468. ~11 | ~22 [avatar contradiction clause 467]
469. $false <- (22, ~26) [subsumption resolution 270,403]
470. ~22 | 26 [avatar contradiction clause 469]
471. $false [avatar sat refutation 257,262,272,468,470]
% SZS output end Proof for 339926810485562412054516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or funny is not funny and vice versa.
Everyone who is calm or not humble is not quiet.
Everyone who is not curious or old is both creative and not funny.
If susan is kind then paul is generous or rich and vice versa.
Everyone who is humble is either not calm or happy and vice versa.
Everyone who is either not rich or not funny is not rich or not funny and vice versa.
Everyone who is old or not quiet is both curious and creative and vice versa.
Everyone who is either wise or quiet is either not creative or not humble.
Everyone who is not tall is not patient or rich.
Everyone who is generous is either not curious or not tall and vice versa.
Everyone who is strong is patient and vice versa.
If mary is both not old and not quiet then someone is wise or not creative.
Everyone who is not old or tall is rich or kind.
Everyone who is not kind is both happy and curious.
If someone is either kind or wise then lucy is either not strong or calm.
Fred is either strong or funny.
Paul is funny or rich.
John is funny or tall.
Someone is both not strong and tall.
Someone is not wise or not tall.
Fred is brave or not kind. | Susan is not strong. | neutral | (![X]:((~creative(X)|funny(X))<=>~funny(X)))&
(![X]:((calm(X)|~humble(X))=>~quiet(X)))&
(![X]:((~curious(X)|old(X))=>(creative(X)&~funny(X))))&
((kind(susan))<=>((generous(paul)|rich(paul))))&
(![X]:(humble(X)<=>(~calm(X)<~>happy(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~rich(X)|~funny(X))))&
(![X]:((old(X)|~quiet(X))<=>(curious(X)&creative(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(~patient(X)|rich(X))))&
(![X]:(generous(X)<=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>patient(X)))&
(((~old(mary)&~quiet(mary)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~old(X)|tall(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)=>(happy(X)&curious(X))))&
((?[X]:((kind(X)<~>wise(X))))=>((~strong(lucy)<~>calm(lucy))))&
((strong(fred)<~>funny(fred)))&
((funny(paul)|rich(paul)))&
((funny(john)|tall(john)))&
(?[X]:((~strong(X)&tall(X))))&
(?[X]:((~wise(X)|~tall(X))))&
((brave(fred)|~kind(fred))) | ~strong(susan) | [] | null | 0 |
Everyone who is both generous and old is not patient or rich. If someone is generous or not humble then someone is either curious or not humble and vice versa. If someone is either creative or not patient then someone is not brave or old and vice versa. If someone is both not curious and not happy then someone is both not strong and old and vice versa. Everyone who is not humble or funny is either not generous or not kind. Everyone who is not funny or wise is both calm and not generous. Everyone who is not calm is quiet and vice versa. Everyone who is not generous is both funny and rich and vice versa. Everyone who is both not strong and not kind is not humble and vice versa. Everyone who is quiet or not humble is both not kind and not calm. Everyone who is both not creative and not strong is both strong and not humble. If susan is creative then john is either old or rich. Everyone who is either not happy or generous is either not old or not humble and vice versa. Everyone who is not kind or wise is either humble or not calm and vice versa. If paul is tall or not wise then someone is both curious and not patient. If lucy is both creative and not quiet then someone is kind or old. Someone is both not happy and rich. Lucy is quiet or generous. Someone is either not strong or not calm. Paul is calm. Paul is not kind or humble. Someone is either not generous or not happy. John is not rich. | Lucy is wise. | contradiction | (![X]:((generous(X)&old(X))=>(~patient(X)|rich(X))))&
((?[X]:((generous(X)|~humble(X))))<=>(?[X]:((curious(X)<~>~humble(X)))))&
((?[X]:((creative(X)<~>~patient(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:((~curious(X)&~happy(X))))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~humble(X)|funny(X))=>(~generous(X)<~>~kind(X))))&
(![X]:((~funny(X)|wise(X))=>(calm(X)&~generous(X))))&
(![X]:(~calm(X)<=>quiet(X)))&
(![X]:(~generous(X)<=>(funny(X)&rich(X))))&
(![X]:((~strong(X)&~kind(X))<=>~humble(X)))&
(![X]:((quiet(X)|~humble(X))=>(~kind(X)&~calm(X))))&
(![X]:((~creative(X)&~strong(X))=>(strong(X)&~humble(X))))&
((creative(susan))=>((old(john)<~>rich(john))))&
(![X]:((~happy(X)<~>generous(X))<=>(~old(X)<~>~humble(X))))&
(![X]:((~kind(X)|wise(X))<=>(humble(X)<~>~calm(X))))&
(((tall(paul)|~wise(paul)))=>(?[X]:((curious(X)&~patient(X)))))&
(((creative(lucy)&~quiet(lucy)))=>(?[X]:((kind(X)|old(X)))))&
(?[X]:((~happy(X)&rich(X))))&
((quiet(lucy)|generous(lucy)))&
(?[X]:((~strong(X)<~>~calm(X))))&
(calm(paul))&
((~kind(paul)|humble(paul)))&
(?[X]:((~generous(X)<~>~happy(X))))&
(~rich(john)) | wise(lucy) | [
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7047269751310454958759400
% SZS output start Proof for 7047269751310454958759400
6. ! [X0] : ((wise(X0) | ~funny(X0)) => (~generous(X0) & calm(X0))) [input p5]
7. ! [X0] : (~calm(X0) <=> quiet(X0)) [input p6]
18. generous(lucy) | quiet(lucy) [input p17]
24. wise(lucy) [input hypothesis]
32. ! [X0] : ((~generous(X0) & calm(X0)) | (~wise(X0) & funny(X0))) [ennf transformation 6]
56. ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))) [nnf transformation 7]
99. ~wise(X0) | calm(X0) [cnf transformation 32]
101. ~wise(X0) | ~generous(X0) [cnf transformation 32]
103. ~quiet(X0) | ~calm(X0) [cnf transformation 56]
137. generous(lucy) | quiet(lucy) [cnf transformation 18]
145. wise(lucy) [cnf transformation 24]
277. 30 <=> quiet(lucy) [avatar definition]
279. quiet(lucy) <- (30) [avatar component clause 277]
290. 33 <=> generous(lucy) [avatar definition]
293. 30 | 33 [avatar split clause 137,290,277]
316. calm(lucy) [resolution 99,145]
319. ~generous(lucy) [resolution 101,145]
321. ~33 [avatar split clause 319,290]
322. ~calm(lucy) <- (30) [resolution 103,279]
324. $false <- (30) [subsumption resolution 322,316]
325. ~30 [avatar contradiction clause 324]
326. $false [avatar sat refutation 293,321,325]
% SZS output end Proof for 7047269751310454958759400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not calm or not humble and vice versa. Everyone who is not patient is both curious and not happy. Everyone who is not quiet is both not strong and not patient. Everyone who is not quiet or not happy is either not patient or not happy and vice versa. Everyone who is both strong and not happy is either brave or not strong. Everyone who is both not calm and strong is either happy or not calm and vice versa. Everyone who is both tall and calm is both not brave and not kind. If susan is strong then someone is both not strong and not curious and vice versa. Everyone who is not strong is humble and vice versa. If paul is both happy and not humble then alice is both quiet and curious. Everyone who is calm or brave is either calm or not happy. Everyone who is tall is both generous and not rich. If paul is both curious and not funny then someone is not strong and vice versa. Everyone who is not old is either not patient or funny. Everyone who is funny is not quiet. If fred is either rich or happy then someone is both kind and rich and vice versa. Someone is either old or wise. Someone is wise or not patient. Fred is not old or not brave. Mary is not curious or quiet. Someone is patient or not generous. Alice is not creative. | Susan is not funny. | entailment | (![X]:(~brave(X)<=>(~calm(X)|~humble(X))))&
(![X]:(~patient(X)=>(curious(X)&~happy(X))))&
(![X]:(~quiet(X)=>(~strong(X)&~patient(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((strong(X)&~happy(X))=>(brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&strong(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((tall(X)&calm(X))=>(~brave(X)&~kind(X))))&
((strong(susan))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:(~strong(X)<=>humble(X)))&
(((happy(paul)&~humble(paul)))=>((quiet(alice)&curious(alice))))&
(![X]:((calm(X)|brave(X))=>(calm(X)<~>~happy(X))))&
(![X]:(tall(X)=>(generous(X)&~rich(X))))&
(((curious(paul)&~funny(paul)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)=>(~patient(X)<~>funny(X))))&
(![X]:(funny(X)=>~quiet(X)))&
(((rich(fred)<~>happy(fred)))<=>(?[X]:((kind(X)&rich(X)))))&
(?[X]:((old(X)<~>wise(X))))&
(?[X]:((wise(X)|~patient(X))))&
((~old(fred)|~brave(fred)))&
((~curious(mary)|quiet(mary)))&
(?[X]:((patient(X)|~generous(X))))&
(~creative(alice)) | ~funny(susan) | [
"p1",
"p2",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3370913514275797285283067
% SZS output start Proof for 3370913514275797285283067
2. ! [X0] : (~patient(X0) => (~happy(X0) & curious(X0))) [input p1]
3. ! [X0] : (~quiet(X0) => (~patient(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (~patient(X0) <~> ~happy(X0))) [input p3]
15. ! [X0] : (funny(X0) => ~quiet(X0)) [input p14]
23. funny(susan) [input hypothesis]
28. ! [X0] : ((~happy(X0) & curious(X0)) | patient(X0)) [ennf transformation 2]
29. ! [X0] : ((~patient(X0) & ~strong(X0)) | quiet(X0)) [ennf transformation 3]
36. ! [X0] : (~quiet(X0) | ~funny(X0)) [ennf transformation 15]
39. ! [X0] : (((~happy(X0) | ~quiet(X0)) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (happy(X0) & quiet(X0)))) [nnf transformation 4]
40. ! [X0] : ((~happy(X0) | ~quiet(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (happy(X0) & quiet(X0)))) [flattening 39]
69. ~happy(X0) | patient(X0) [cnf transformation 28]
71. ~patient(X0) | quiet(X0) [cnf transformation 29]
75. happy(X0) | patient(X0) | happy(X0) [cnf transformation 40]
102. ~funny(X0) | ~quiet(X0) [cnf transformation 36]
114. funny(susan) [cnf transformation 23]
119. happy(X0) | patient(X0) [duplicate literal removal 75]
121. patient(X0) [subsumption resolution 119,69]
231. quiet(X0) [resolution 71,121]
237. ~quiet(susan) [resolution 102,114]
240. $false [subsumption resolution 237,231]
% SZS output end Proof for 3370913514275797285283067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not strong.
If lucy is strong then fred is both not strong and patient and vice versa.
If someone is both not brave and rich then alice is both not kind and wise and vice versa.
If mary is both brave and strong then susan is humble and vice versa.
Everyone who is both funny and curious is both not kind and not humble.
Everyone who is not humble is either not funny or not patient.
Everyone who is brave is not wise and vice versa.
Everyone who is tall is both not strong and not rich and vice versa.
Everyone who is both not old and patient is not strong or calm.
If someone is both curious and not humble then someone is both kind and happy and vice versa.
Everyone who is both curious and humble is both not wise and kind.
If john is both not kind and not calm then someone is either calm or strong.
Everyone who is both not creative and not quiet is generous or not calm and vice versa.
If susan is both brave and not creative then someone is quiet and vice versa.
If someone is wise or not happy then john is not wise.
If alice is not rich or tall then john is not creative.
John is brave or rich.
John is generous.
Someone is calm.
Paul is both happy and not quiet.
Mary is happy.
Someone is either not wise or not creative.
John is both not funny and not creative.
Someone is generous. | Mary is rich. | neutral | (![X]:(creative(X)=>~strong(X)))&
((strong(lucy))<=>((~strong(fred)&patient(fred))))&
((?[X]:((~brave(X)&rich(X))))<=>((~kind(alice)&wise(alice))))&
(((brave(mary)&strong(mary)))<=>(humble(susan)))&
(![X]:((funny(X)&curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>~patient(X))))&
(![X]:(brave(X)<=>~wise(X)))&
(![X]:(tall(X)<=>(~strong(X)&~rich(X))))&
(![X]:((~old(X)&patient(X))=>(~strong(X)|calm(X))))&
((?[X]:((curious(X)&~humble(X))))<=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((curious(X)&humble(X))=>(~wise(X)&kind(X))))&
(((~kind(john)&~calm(john)))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)|~calm(X))))&
(((brave(susan)&~creative(susan)))<=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)|~happy(X))))=>(~wise(john)))&
(((~rich(alice)|tall(alice)))=>(~creative(john)))&
((brave(john)|rich(john)))&
(generous(john))&
(?[X]:(calm(X)))&
((happy(paul)&~quiet(paul)))&
(happy(mary))&
(?[X]:((~wise(X)<~>~creative(X))))&
((~funny(john)&~creative(john)))&
(?[X]:(generous(X))) | rich(mary) | [] | null | 0 |
If someone is either curious or not humble then someone is both humble and not curious.
If someone is either not brave or calm then someone is either not rich or not kind and vice versa.
If susan is old then lucy is both not strong and brave and vice versa.
If someone is both creative and not generous then paul is not patient.
Everyone who is brave is not patient and vice versa.
Everyone who is both not creative and calm is either not quiet or tall and vice versa.
If someone is tall then alice is not quiet.
Everyone who is either wise or not strong is old.
If someone is either kind or humble then lucy is not humble or happy and vice versa.
If susan is both not generous and strong then mary is tall or not kind and vice versa.
Everyone who is either calm or not curious is not humble or not happy and vice versa.
Everyone who is either strong or not old is strong and vice versa.
If alice is not generous or not curious then someone is not patient or patient.
If paul is both not humble and not generous then someone is not quiet or generous and vice versa.
Everyone who is both not quiet and not funny is either brave or rich.
Everyone who is both not patient and not rich is either rich or not funny.
Someone is either not old or brave.
Someone is either not quiet or generous.
Someone is either calm or brave.
Alice is curious or rich.
Someone is quiet.
Someone is tall.
Someone is not generous. | Paul is not generous. | entailment | ((?[X]:((curious(X)<~>~humble(X))))=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
((old(susan))<=>((~strong(lucy)&brave(lucy))))&
((?[X]:((creative(X)&~generous(X))))=>(~patient(paul)))&
(![X]:(brave(X)<=>~patient(X)))&
(![X]:((~creative(X)&calm(X))<=>(~quiet(X)<~>tall(X))))&
((?[X]:(tall(X)))=>(~quiet(alice)))&
(![X]:((wise(X)<~>~strong(X))=>old(X)))&
((?[X]:((kind(X)<~>humble(X))))<=>((~humble(lucy)|happy(lucy))))&
(((~generous(susan)&strong(susan)))<=>((tall(mary)|~kind(mary))))&
(![X]:((calm(X)<~>~curious(X))<=>(~humble(X)|~happy(X))))&
(![X]:((strong(X)<~>~old(X))<=>strong(X)))&
(((~generous(alice)|~curious(alice)))=>(?[X]:((~patient(X)|patient(X)))))&
(((~humble(paul)&~generous(paul)))<=>(?[X]:((~quiet(X)|generous(X)))))&
(![X]:((~quiet(X)&~funny(X))=>(brave(X)<~>rich(X))))&
(![X]:((~patient(X)&~rich(X))=>(rich(X)<~>~funny(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((~quiet(X)<~>generous(X))))&
(?[X]:((calm(X)<~>brave(X))))&
((curious(alice)|rich(alice)))&
(?[X]:(quiet(X)))&
(?[X]:(tall(X)))&
(?[X]:(~generous(X))) | ~generous(paul) | [
"p6",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 629694786662668107654756
% SZS output start Proof for 629694786662668107654756
7. ? [X0] : tall(X0) => ~quiet(alice) [input p6]
14. (~generous(paul) & ~humble(paul)) <=> ? [X0] : (generous(X0) | ~quiet(X0)) [input p13]
22. ? [X0] : tall(X0) [input p21]
24. generous(paul) [input hypothesis]
29. ~quiet(alice) | ! [X0] : ~tall(X0) [ennf transformation 7]
63. ((~generous(paul) & ~humble(paul)) | ! [X0] : (~generous(X0) & quiet(X0))) & (? [X0] : (generous(X0) | ~quiet(X0)) | (generous(paul) | humble(paul))) [nnf transformation 14]
64. ((~generous(paul) & ~humble(paul)) | ! [X0] : (~generous(X0) & quiet(X0))) & (? [X0] : (generous(X0) | ~quiet(X0)) | generous(paul) | humble(paul)) [flattening 63]
65. ((~generous(paul) & ~humble(paul)) | ! [X0] : (~generous(X0) & quiet(X0))) & (? [X1] : (generous(X1) | ~quiet(X1)) | generous(paul) | humble(paul)) [rectify 64]
66. ? [X1] : (generous(X1) | ~quiet(X1)) => (generous(sK5) | ~quiet(sK5)) [choice axiom]
67. ((~generous(paul) & ~humble(paul)) | ! [X0] : (~generous(X0) & quiet(X0))) & ((generous(sK5) | ~quiet(sK5)) | generous(paul) | humble(paul)) [skolemisation 65,66]
81. ? [X0] : tall(X0) => tall(sK10) [choice axiom]
82. tall(sK10) [skolemisation 22,81]
109. ~quiet(alice) | ~tall(X0) [cnf transformation 29]
138. ~generous(paul) | quiet(X0) [cnf transformation 67]
152. tall(sK10) [cnf transformation 82]
154. generous(paul) [cnf transformation 24]
236. 18 <=> ! [X0] : ~tall(X0) [avatar definition]
237. ~tall(X0) <- (18) [avatar component clause 236]
239. 19 <=> quiet(alice) [avatar definition]
241. ~quiet(alice) <- (~19) [avatar component clause 239]
242. 18 | ~19 [avatar split clause 109,239,236]
297. 31 <=> generous(paul) [avatar definition]
302. 32 <=> ! [X0] : quiet(X0) [avatar definition]
303. quiet(X0) <- (32) [avatar component clause 302]
304. 32 | ~31 [avatar split clause 138,297,302]
350. 31 [avatar split clause 154,297]
351. $false <- (~19, 32) [subsumption resolution 241,303]
352. 19 | ~32 [avatar contradiction clause 351]
355. $false <- (18) [resolution 237,152]
356. ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 242,304,350,352,356]
% SZS output end Proof for 629694786662668107654756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both not funny and not tall.
Everyone who is both not creative and patient is generous or not quiet and vice versa.
If someone is brave then someone is both not calm and not brave.
Everyone who is both not rich and not humble is quiet or not generous and vice versa.
If someone is not wise then someone is not creative and vice versa.
Everyone who is either wise or calm is not curious or rich.
Everyone who is both not calm and not wise is kind or not kind and vice versa.
Everyone who is both creative and kind is both not rich and not calm.
If someone is either not brave or not kind then someone is rich or brave and vice versa.
If someone is old or not quiet then lucy is both wise and funny.
Everyone who is kind is not generous.
Everyone who is not funny is either strong or old and vice versa.
Everyone who is both not happy and patient is both tall and calm and vice versa.
If lucy is both calm and not calm then fred is either curious or funny.
Fred is not brave or quiet.
Someone is not wise.
Someone is not patient or not humble.
Someone is patient.
Someone is either happy or not quiet. | Fred is not happy. | neutral | (![X]:(~creative(X)=>(~funny(X)&~tall(X))))&
(![X]:((~creative(X)&patient(X))<=>(generous(X)|~quiet(X))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(quiet(X)|~generous(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~creative(X))))&
(![X]:((wise(X)<~>calm(X))=>(~curious(X)|rich(X))))&
(![X]:((~calm(X)&~wise(X))<=>(kind(X)|~kind(X))))&
(![X]:((creative(X)&kind(X))=>(~rich(X)&~calm(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((rich(X)|brave(X)))))&
((?[X]:((old(X)|~quiet(X))))=>((wise(lucy)&funny(lucy))))&
(![X]:(kind(X)=>~generous(X)))&
(![X]:(~funny(X)<=>(strong(X)<~>old(X))))&
(![X]:((~happy(X)&patient(X))<=>(tall(X)&calm(X))))&
(((calm(lucy)&~calm(lucy)))=>((curious(fred)<~>funny(fred))))&
((~brave(fred)|quiet(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((happy(X)<~>~quiet(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is either happy or not patient is not kind.
If susan is both kind and not kind then someone is happy and vice versa.
Everyone who is both not old and not wise is either rich or tall and vice versa.
Everyone who is curious is either quiet or wise and vice versa.
Everyone who is both old and not wise is humble or generous and vice versa.
Everyone who is either old or rich is either tall or generous and vice versa.
If someone is kind or patient then lucy is both not humble and creative and vice versa.
If susan is not quiet or patient then someone is wise and vice versa.
Everyone who is kind or not calm is both not patient and happy.
Everyone who is calm is brave.
If someone is not wise then lucy is either calm or not tall and vice versa.
Everyone who is not funny or brave is not happy or curious.
Everyone who is happy or tall is quiet or humble and vice versa.
If susan is both not calm and not happy then someone is either not funny or old and vice versa.
Everyone who is both not creative and not generous is curious or patient and vice versa.
Someone is both patient and not curious.
Mary is both generous and not creative.
Someone is either not humble or brave.
Paul is either funny or not creative.
Someone is both rich and creative.
Someone is wise or not brave.
Someone is old or calm. | Lucy is not rich. | contradiction | (![X]:((happy(X)<~>~patient(X))=>~kind(X)))&
(((kind(susan)&~kind(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)&~wise(X))<=>(rich(X)<~>tall(X))))&
(![X]:(curious(X)<=>(quiet(X)<~>wise(X))))&
(![X]:((old(X)&~wise(X))<=>(humble(X)|generous(X))))&
(![X]:((old(X)<~>rich(X))<=>(tall(X)<~>generous(X))))&
((?[X]:((kind(X)|patient(X))))<=>((~humble(lucy)&creative(lucy))))&
(((~quiet(susan)|patient(susan)))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~calm(X))=>(~patient(X)&happy(X))))&
(![X]:(calm(X)=>brave(X)))&
((?[X]:(~wise(X)))<=>((calm(lucy)<~>~tall(lucy))))&
(![X]:((~funny(X)|brave(X))=>(~happy(X)|curious(X))))&
(![X]:((happy(X)|tall(X))<=>(quiet(X)|humble(X))))&
(((~calm(susan)&~happy(susan)))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~creative(X)&~generous(X))<=>(curious(X)|patient(X))))&
(?[X]:((patient(X)&~curious(X))))&
((generous(mary)&~creative(mary)))&
(?[X]:((~humble(X)<~>brave(X))))&
((funny(paul)<~>~creative(paul)))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:((wise(X)|~brave(X))))&
(?[X]:((old(X)|calm(X)))) | ~rich(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p8",
"p10",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 253050597400898314430407
% SZS output start Proof for 253050597400898314430407
2. (~kind(susan) & kind(susan)) <=> ? [X0] : happy(X0) [input p1]
3. ! [X0] : ((~wise(X0) & ~old(X0)) <=> (rich(X0) <~> tall(X0))) [input p2]
4. ! [X0] : (curious(X0) <=> (quiet(X0) <~> wise(X0))) [input p3]
5. ! [X0] : ((~wise(X0) & old(X0)) <=> (generous(X0) | humble(X0))) [input p4]
7. ? [X0] : (patient(X0) | kind(X0)) <=> (creative(lucy) & ~humble(lucy)) [input p6]
9. ! [X0] : ((~calm(X0) | kind(X0)) => (happy(X0) & ~patient(X0))) [input p8]
11. ? [X0] : ~wise(X0) <=> (calm(lucy) <~> ~tall(lucy)) [input p10]
13. ! [X0] : ((tall(X0) | happy(X0)) <=> (humble(X0) | quiet(X0))) [input p12]
15. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (patient(X0) | curious(X0))) [input p14]
16. ? [X0] : (~curious(X0) & patient(X0)) [input p15]
17. ~creative(mary) & generous(mary) [input p16]
23. ~rich(lucy) [input hypothesis]
25. ! [X0] : ((happy(X0) & ~patient(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 9]
30. ((~kind(susan) & kind(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (kind(susan) | ~kind(susan))) [nnf transformation 2]
31. ((~kind(susan) & kind(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | kind(susan) | ~kind(susan)) [flattening 30]
32. ((~kind(susan) & kind(susan)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | kind(susan) | ~kind(susan)) [rectify 31]
33. ? [X1] : happy(X1) => happy(sK0) [choice axiom]
34. ((~kind(susan) & kind(susan)) | ! [X0] : ~happy(X0)) & (happy(sK0) | kind(susan) | ~kind(susan)) [skolemisation 32,33]
35. ! [X0] : (((~wise(X0) & ~old(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (wise(X0) | old(X0)))) [nnf transformation 3]
36. ! [X0] : (((~wise(X0) & ~old(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | wise(X0) | old(X0))) [flattening 35]
37. ! [X0] : ((curious(X0) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~curious(X0))) [nnf transformation 4]
38. ! [X0] : (((~wise(X0) & old(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 5]
39. ! [X0] : (((~wise(X0) & old(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | wise(X0) | ~old(X0))) [flattening 38]
41. (? [X0] : (patient(X0) | kind(X0)) | (~creative(lucy) | humble(lucy))) & ((creative(lucy) & ~humble(lucy)) | ! [X0] : (~patient(X0) & ~kind(X0))) [nnf transformation 7]
42. (? [X0] : (patient(X0) | kind(X0)) | ~creative(lucy) | humble(lucy)) & ((creative(lucy) & ~humble(lucy)) | ! [X0] : (~patient(X0) & ~kind(X0))) [flattening 41]
43. (? [X0] : (patient(X0) | kind(X0)) | ~creative(lucy) | humble(lucy)) & ((creative(lucy) & ~humble(lucy)) | ! [X1] : (~patient(X1) & ~kind(X1))) [rectify 42]
44. ? [X0] : (patient(X0) | kind(X0)) => (patient(sK1) | kind(sK1)) [choice axiom]
45. ((patient(sK1) | kind(sK1)) | ~creative(lucy) | humble(lucy)) & ((creative(lucy) & ~humble(lucy)) | ! [X1] : (~patient(X1) & ~kind(X1))) [skolemisation 43,44]
51. (? [X0] : ~wise(X0) | ((calm(lucy) | tall(lucy)) & (~tall(lucy) | ~calm(lucy)))) & (((tall(lucy) | ~calm(lucy)) & (~tall(lucy) | calm(lucy))) | ! [X0] : wise(X0)) [nnf transformation 11]
52. (? [X0] : ~wise(X0) | ((calm(lucy) | tall(lucy)) & (~tall(lucy) | ~calm(lucy)))) & (((tall(lucy) | ~calm(lucy)) & (~tall(lucy) | calm(lucy))) | ! [X1] : wise(X1)) [rectify 51]
53. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
54. (~wise(sK3) | ((calm(lucy) | tall(lucy)) & (~tall(lucy) | ~calm(lucy)))) & (((tall(lucy) | ~calm(lucy)) & (~tall(lucy) | calm(lucy))) | ! [X1] : wise(X1)) [skolemisation 52,53]
55. ! [X0] : (((tall(X0) | happy(X0)) | (~humble(X0) & ~quiet(X0))) & ((humble(X0) | quiet(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : ((tall(X0) | happy(X0) | (~humble(X0) & ~quiet(X0))) & (humble(X0) | quiet(X0) | (~tall(X0) & ~happy(X0)))) [flattening 55]
62. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~patient(X0) & ~curious(X0))) & ((patient(X0) | curious(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~patient(X0) & ~curious(X0))) & (patient(X0) | curious(X0) | generous(X0) | creative(X0))) [flattening 62]
64. ? [X0] : (~curious(X0) & patient(X0)) => (~curious(sK5) & patient(sK5)) [choice axiom]
65. ~curious(sK5) & patient(sK5) [skolemisation 16,64]
79. kind(susan) | ~happy(X0) [cnf transformation 34]
80. ~kind(susan) | ~happy(X0) [cnf transformation 34]
86. ~tall(X0) | rich(X0) | ~wise(X0) [cnf transformation 36]
89. ~quiet(X0) | wise(X0) | curious(X0) [cnf transformation 37]
95. ~generous(X0) | ~wise(X0) [cnf transformation 39]
105. ~humble(lucy) | ~patient(X1) [cnf transformation 45]
107. creative(lucy) | ~patient(X1) [cnf transformation 45]
115. calm(X0) | happy(X0) [cnf transformation 25]
118. tall(lucy) | ~calm(lucy) | wise(X1) [cnf transformation 54]
124. ~tall(X0) | quiet(X0) | humble(X0) [cnf transformation 56]
134. ~creative(X0) | ~curious(X0) [cnf transformation 63]
138. patient(sK5) [cnf transformation 65]
140. generous(mary) [cnf transformation 17]
150. ~rich(lucy) [cnf transformation 23]
152. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
153. ~happy(X0) <- (1) [avatar component clause 152]
155. 2 <=> kind(susan) [avatar definition]
158. 1 | ~2 [avatar split clause 80,155,152]
159. 1 | 2 [avatar split clause 79,155,152]
165. 3 <=> humble(lucy) [avatar definition]
166. ~humble(lucy) <- (~3) [avatar component clause 165]
169. 4 <=> creative(lucy) [avatar definition]
170. creative(lucy) <- (4) [avatar component clause 169]
182. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
183. ~patient(X1) <- (7) [avatar component clause 182]
184. 7 | 4 [avatar split clause 107,169,182]
189. 7 | ~3 [avatar split clause 105,165,182]
210. 13 <=> tall(lucy) [avatar definition]
212. tall(lucy) <- (13) [avatar component clause 210]
214. 14 <=> calm(lucy) [avatar definition]
215. ~calm(lucy) <- (~14) [avatar component clause 214]
224. 16 <=> ! [X1] : wise(X1) [avatar definition]
225. wise(X1) <- (16) [avatar component clause 224]
226. 16 | ~14 | 13 [avatar split clause 118,210,214,224]
285. ~wise(mary) [resolution 95,140]
293. happy(lucy) <- (~14) [resolution 115,215]
295. $false <- (1, ~14) [subsumption resolution 293,153]
296. ~1 | 14 [avatar contradiction clause 295]
311. ~curious(lucy) <- (4) [resolution 134,170]
345. rich(lucy) | ~wise(lucy) <- (13) [resolution 86,212]
346. ~wise(lucy) <- (13) [subsumption resolution 345,150]
384. quiet(lucy) | humble(lucy) <- (13) [resolution 124,212]
385. quiet(lucy) <- (~3, 13) [subsumption resolution 384,166]
386. wise(lucy) | curious(lucy) <- (~3, 13) [resolution 385,89]
388. curious(lucy) <- (~3, 13) [subsumption resolution 386,346]
389. $false <- (~3, 4, 13) [subsumption resolution 388,311]
390. 3 | ~4 | ~13 [avatar contradiction clause 389]
391. $false <- (7) [resolution 183,138]
396. ~7 [avatar contradiction clause 391]
400. $false <- (16) [resolution 225,285]
407. ~16 [avatar contradiction clause 400]
408. $false [avatar sat refutation 158,159,184,189,226,296,390,396,407]
% SZS output end Proof for 253050597400898314430407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or funny then mary is either brave or not curious and vice versa.
Everyone who is not curious or curious is both not humble and not funny and vice versa.
If someone is both happy and not calm then someone is calm or rich and vice versa.
Everyone who is either not brave or not happy is not old or not strong and vice versa.
Everyone who is both not wise and patient is either creative or not tall and vice versa.
If someone is not kind then john is both creative and kind.
If paul is not tall or not strong then fred is happy.
Everyone who is both not calm and not kind is either calm or quiet and vice versa.
Everyone who is either old or not tall is creative or humble and vice versa.
Everyone who is both wise and not kind is both wise and quiet.
Everyone who is not strong or calm is both not tall and tall.
If alice is not rich then someone is both not rich and not calm.
If someone is rich or strong then paul is not wise or not calm and vice versa.
If john is not tall then someone is not happy.
If someone is humble then someone is quiet or not creative and vice versa.
Everyone who is not calm or calm is not creative or curious.
Someone is rich or not tall.
Someone is either not curious or patient.
Alice is brave or strong.
Someone is either old or not happy.
Someone is generous or not brave. | Alice is not quiet. | entailment | (((~tall(alice)<~>funny(alice)))<=>((brave(mary)<~>~curious(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((happy(X)&~calm(X))))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~brave(X)<~>~happy(X))<=>(~old(X)|~strong(X))))&
(![X]:((~wise(X)&patient(X))<=>(creative(X)<~>~tall(X))))&
((?[X]:(~kind(X)))=>((creative(john)&kind(john))))&
(((~tall(paul)|~strong(paul)))=>(happy(fred)))&
(![X]:((~calm(X)&~kind(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(creative(X)|humble(X))))&
(![X]:((wise(X)&~kind(X))=>(wise(X)&quiet(X))))&
(![X]:((~strong(X)|calm(X))=>(~tall(X)&tall(X))))&
((~rich(alice))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((rich(X)|strong(X))))<=>((~wise(paul)|~calm(paul))))&
((~tall(john))=>(?[X]:(~happy(X))))&
((?[X]:(humble(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((brave(alice)|strong(alice)))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((generous(X)|~brave(X)))) | ~quiet(alice) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7068605433493581361287130
% SZS output start Proof for 7068605433493581361287130
2. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~funny(X0) & ~humble(X0))) [input p1]
15. ? [X0] : humble(X0) <=> ? [X0] : (~creative(X0) | quiet(X0)) [input p14]
22. quiet(alice) [input hypothesis]
24. ? [X0] : humble(X0) <=> ? [X1] : (~creative(X1) | quiet(X1)) [rectify 15]
36. ! [X0] : (((curious(X0) | ~curious(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 2]
37. ! [X0] : ((curious(X0) | ~curious(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~curious(X0) & curious(X0)))) [flattening 36]
60. (? [X0] : humble(X0) | ! [X1] : (creative(X1) & ~quiet(X1))) & (? [X1] : (~creative(X1) | quiet(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 24]
61. (? [X0] : humble(X0) | ! [X1] : (creative(X1) & ~quiet(X1))) & (? [X2] : (~creative(X2) | quiet(X2)) | ! [X3] : ~humble(X3)) [rectify 60]
62. ? [X0] : humble(X0) => humble(sK5) [choice axiom]
63. ? [X2] : (~creative(X2) | quiet(X2)) => (~creative(sK6) | quiet(sK6)) [choice axiom]
64. (humble(sK5) | ! [X1] : (creative(X1) & ~quiet(X1))) & ((~creative(sK6) | quiet(sK6)) | ! [X3] : ~humble(X3)) [skolemisation 61,63,62]
81. ~humble(X0) | curious(X0) [cnf transformation 37]
82. ~humble(X0) | ~curious(X0) [cnf transformation 37]
133. humble(sK5) | ~quiet(X1) [cnf transformation 64]
143. quiet(alice) [cnf transformation 22]
171. ~humble(X0) [subsumption resolution 81,82]
270. ~quiet(X1) [subsumption resolution 133,171]
294. $false [subsumption resolution 143,270]
% SZS output end Proof for 7068605433493581361287130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is both strong and not kind and vice versa. Everyone who is both kind and not wise is both generous and not generous and vice versa. Everyone who is either wise or not kind is not curious or happy. Everyone who is both rich and quiet is both curious and rich and vice versa. If paul is tall then someone is kind. Everyone who is both calm and happy is both not strong and not tall. If someone is not rich then fred is both old and curious and vice versa. If someone is either strong or calm then john is both humble and not humble and vice versa. If fred is not funny then someone is not generous. Everyone who is either not curious or funny is either brave or not tall. If john is not happy then someone is generous. Everyone who is both not generous and not wise is either happy or not patient. If someone is both rich and not wise then john is creative or quiet and vice versa. If someone is either not tall or rich then alice is not calm and vice versa. Everyone who is happy or patient is both not patient and happy and vice versa. If someone is both not happy and not old then someone is not brave or not happy and vice versa. Someone is not quiet or not creative. Fred is both brave and tall. Fred is not rich or not humble. Susan is both not creative and not strong. Lucy is both not rich and not old. Someone is either not old or rich. Someone is not brave or not wise. | John is creative. | neutral | ((?[X]:(~brave(X)))<=>(?[X]:((strong(X)&~kind(X)))))&
(![X]:((kind(X)&~wise(X))<=>(generous(X)&~generous(X))))&
(![X]:((wise(X)<~>~kind(X))=>(~curious(X)|happy(X))))&
(![X]:((rich(X)&quiet(X))<=>(curious(X)&rich(X))))&
((tall(paul))=>(?[X]:(kind(X))))&
(![X]:((calm(X)&happy(X))=>(~strong(X)&~tall(X))))&
((?[X]:(~rich(X)))<=>((old(fred)&curious(fred))))&
((?[X]:((strong(X)<~>calm(X))))<=>((humble(john)&~humble(john))))&
((~funny(fred))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>funny(X))=>(brave(X)<~>~tall(X))))&
((~happy(john))=>(?[X]:(generous(X))))&
(![X]:((~generous(X)&~wise(X))=>(happy(X)<~>~patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>((creative(john)|quiet(john))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(~calm(alice)))&
(![X]:((happy(X)|patient(X))<=>(~patient(X)&happy(X))))&
((?[X]:((~happy(X)&~old(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
(?[X]:((~quiet(X)|~creative(X))))&
((brave(fred)&tall(fred)))&
((~rich(fred)|~humble(fred)))&
((~creative(susan)&~strong(susan)))&
((~rich(lucy)&~old(lucy)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:((~brave(X)|~wise(X)))) | creative(john) | [] | null | 0 |
Everyone who is brave or rich is funny or strong and vice versa.
If mary is not generous then paul is both not rich and wise and vice versa.
If susan is both not curious and patient then someone is not strong or funny.
Everyone who is either not old or not creative is both wise and tall.
Everyone who is either not rich or not happy is both curious and generous and vice versa.
If someone is not happy or not kind then john is happy or generous and vice versa.
If someone is either not curious or old then john is both not patient and wise and vice versa.
Everyone who is old or not generous is brave.
Everyone who is both not kind and not tall is not tall or rich and vice versa.
Everyone who is both not calm and brave is not funny and vice versa.
Everyone who is not kind is not old or tall.
Everyone who is not rich or wise is either rich or not curious and vice versa.
Everyone who is kind is both patient and not funny and vice versa.
Everyone who is either not rich or quiet is tall or creative and vice versa.
If someone is both curious and strong then susan is either generous or kind.
If someone is curious then mary is not happy.
Someone is calm.
Susan is either happy or not rich.
Someone is both not curious and patient.
Fred is either generous or patient.
Paul is quiet.
Mary is not quiet.
Lucy is kind.
Someone is not brave or not patient. | John is not patient. | entailment | (![X]:((brave(X)|rich(X))<=>(funny(X)|strong(X))))&
((~generous(mary))<=>((~rich(paul)&wise(paul))))&
(((~curious(susan)&patient(susan)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~old(X)<~>~creative(X))=>(wise(X)&tall(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)&generous(X))))&
((?[X]:((~happy(X)|~kind(X))))<=>((happy(john)|generous(john))))&
((?[X]:((~curious(X)<~>old(X))))<=>((~patient(john)&wise(john))))&
(![X]:((old(X)|~generous(X))=>brave(X)))&
(![X]:((~kind(X)&~tall(X))<=>(~tall(X)|rich(X))))&
(![X]:((~calm(X)&brave(X))<=>~funny(X)))&
(![X]:(~kind(X)=>(~old(X)|tall(X))))&
(![X]:((~rich(X)|wise(X))<=>(rich(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(patient(X)&~funny(X))))&
(![X]:((~rich(X)<~>quiet(X))<=>(tall(X)|creative(X))))&
((?[X]:((curious(X)&strong(X))))=>((generous(susan)<~>kind(susan))))&
((?[X]:(curious(X)))=>(~happy(mary)))&
(?[X]:(calm(X)))&
((happy(susan)<~>~rich(susan)))&
(?[X]:((~curious(X)&patient(X))))&
((generous(fred)<~>patient(fred)))&
(quiet(paul))&
(~quiet(mary))&
(kind(lucy))&
(?[X]:((~brave(X)|~patient(X)))) | ~patient(john) | [
"p3",
"p6",
"p8",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3896455717937931575204847
% SZS output start Proof for 3896455717937931575204847
4. ! [X0] : ((~old(X0) <~> ~creative(X0)) => (tall(X0) & wise(X0))) [input p3]
7. ? [X0] : (~curious(X0) <~> old(X0)) <=> (wise(john) & ~patient(john)) [input p6]
9. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (rich(X0) | ~tall(X0))) [input p8]
11. ! [X0] : (~kind(X0) => (tall(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((wise(X0) | ~rich(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p11]
14. ! [X0] : ((~rich(X0) <~> quiet(X0)) <=> (creative(X0) | tall(X0))) [input p13]
21. quiet(paul) [input p20]
25. patient(john) [input hypothesis]
28. ! [X0] : ((tall(X0) & wise(X0)) | (~old(X0) <=> ~creative(X0))) [ennf transformation 4]
30. ! [X0] : ((tall(X0) | ~old(X0)) | kind(X0)) [ennf transformation 11]
31. ! [X0] : (tall(X0) | ~old(X0) | kind(X0)) [flattening 30]
40. ! [X0] : ((tall(X0) & wise(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) [nnf transformation 28]
48. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (~wise(john) | patient(john))) & ((wise(john) & ~patient(john)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [nnf transformation 7]
49. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) [flattening 48]
50. (? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [rectify 49]
51. ? [X0] : ((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) => ((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) [choice axiom]
52. (((~old(sK2) | curious(sK2)) & (old(sK2) | ~curious(sK2))) | ~wise(john) | patient(john)) & ((wise(john) & ~patient(john)) | ! [X1] : ((~curious(X1) | ~old(X1)) & (old(X1) | curious(X1)))) [skolemisation 50,51]
53. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 9]
54. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | tall(X0) | kind(X0))) [flattening 53]
57. ! [X0] : (((wise(X0) | ~rich(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) & rich(X0)))) [nnf transformation 12]
58. ! [X0] : ((wise(X0) | ~rich(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) & rich(X0)))) [flattening 57]
61. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [flattening 61]
82. ~creative(X0) | tall(X0) | old(X0) [cnf transformation 40]
94. ~patient(john) | old(X1) | curious(X1) [cnf transformation 52]
103. ~kind(X0) | tall(X0) [cnf transformation 54]
106. ~tall(X0) | ~rich(X0) [cnf transformation 54]
110. tall(X0) | ~old(X0) | kind(X0) [cnf transformation 31]
111. ~curious(X0) | rich(X0) | rich(X0) [cnf transformation 58]
121. creative(X0) | tall(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 62]
124. ~quiet(X0) | rich(X0) | ~tall(X0) [cnf transformation 62]
136. quiet(paul) [cnf transformation 21]
140. patient(john) [cnf transformation 25]
141. ~curious(X0) | rich(X0) [duplicate literal removal 111]
144. 1 <=> rich(paul) [avatar definition]
146. rich(paul) <- (1) [avatar component clause 144]
202. 14 <=> patient(john) [avatar definition]
224. 19 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
225. old(X1) | curious(X1) <- (19) [avatar component clause 224]
228. 19 | ~14 [avatar split clause 94,202,224]
229. ~old(X0) | tall(X0) [subsumption resolution 110,103]
230. ~quiet(X0) | ~tall(X0) [subsumption resolution 124,106]
231. ~quiet(X0) | ~rich(X0) | creative(X0) [subsumption resolution 121,230]
282. 14 [avatar split clause 140,202]
293. tall(X0) | curious(X0) <- (19) [resolution 229,225]
294. ~tall(paul) [resolution 230,136]
340. curious(paul) <- (19) [resolution 293,294]
342. rich(paul) <- (19) [resolution 340,141]
346. 1 | ~19 [avatar split clause 342,224,144]
426. ~rich(paul) | creative(paul) [resolution 231,136]
427. creative(paul) <- (1) [subsumption resolution 426,146]
429. tall(paul) | old(paul) <- (1) [resolution 427,82]
431. old(paul) <- (1) [subsumption resolution 429,294]
526. tall(paul) <- (1) [resolution 431,229]
529. $false <- (1) [subsumption resolution 526,294]
530. ~1 [avatar contradiction clause 529]
533. $false [avatar sat refutation 228,282,346,530]
% SZS output end Proof for 3896455717937931575204847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not strong is both not tall and not wise and vice versa. Everyone who is both tall and not generous is tall or curious. If someone is not happy then someone is either humble or not kind. Everyone who is both brave and not rich is not creative or rich and vice versa. If john is humble then mary is both not kind and patient. If someone is either not strong or not old then mary is generous or not humble. If someone is not creative or not funny then someone is either brave or not patient and vice versa. If mary is either not humble or not strong then someone is either rich or not humble and vice versa. Everyone who is both not brave and not generous is either not kind or tall. Everyone who is either not humble or not quiet is creative or not calm and vice versa. If someone is both not old and happy then mary is kind or not brave. Everyone who is both not happy and not patient is either generous or calm and vice versa. If susan is both not patient and not generous then lucy is either not patient or not wise. If john is tall then someone is either brave or not rich and vice versa. Everyone who is not creative is either not humble or tall. If someone is not brave then mary is either not rich or not creative and vice versa. Someone is either old or curious. John is not tall or old. Alice is not generous. Susan is strong or not creative. Susan is either not quiet or not creative. Fred is creative or patient. | Lucy is calm. | neutral | (![X]:((brave(X)|~strong(X))<=>(~tall(X)&~wise(X))))&
(![X]:((tall(X)&~generous(X))=>(tall(X)|curious(X))))&
((?[X]:(~happy(X)))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((brave(X)&~rich(X))<=>(~creative(X)|rich(X))))&
((humble(john))=>((~kind(mary)&patient(mary))))&
((?[X]:((~strong(X)<~>~old(X))))=>((generous(mary)|~humble(mary))))&
((?[X]:((~creative(X)|~funny(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
(((~humble(mary)<~>~strong(mary)))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((~brave(X)&~generous(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(creative(X)|~calm(X))))&
((?[X]:((~old(X)&happy(X))))=>((kind(mary)|~brave(mary))))&
(![X]:((~happy(X)&~patient(X))<=>(generous(X)<~>calm(X))))&
(((~patient(susan)&~generous(susan)))=>((~patient(lucy)<~>~wise(lucy))))&
((tall(john))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~creative(X)=>(~humble(X)<~>tall(X))))&
((?[X]:(~brave(X)))<=>((~rich(mary)<~>~creative(mary))))&
(?[X]:((old(X)<~>curious(X))))&
((~tall(john)|old(john)))&
(~generous(alice))&
((strong(susan)|~creative(susan)))&
((~quiet(susan)<~>~creative(susan)))&
((creative(fred)|patient(fred))) | calm(lucy) | [] | null | 0 |
If someone is both tall and kind then someone is both generous and funny. Everyone who is creative or not calm is not kind or not curious and vice versa. Everyone who is rich or not strong is not brave or not kind and vice versa. Everyone who is not kind or patient is both not brave and not tall. Everyone who is creative is rich and vice versa. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Everyone who is either not old or not funny is both kind and not strong and vice versa. Everyone who is quiet is generous and vice versa. If fred is either creative or not wise then someone is both brave and not patient. Susan is not humble. Someone is humble or brave. Mary is either funny or patient. Someone is wise. Someone is either not rich or rich. Paul is both strong and not kind. Someone is not brave or calm. | Mary is not wise. | entailment | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((humble(X)|brave(X))))&
((funny(mary)<~>patient(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | ~wise(mary) | [
"p3",
"p9",
"p10",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1991396571306672396783528
% SZS output start Proof for 1991396571306672396783528
4. ! [X0] : ((patient(X0) | ~kind(X0)) => (~tall(X0) & ~brave(X0))) [input p3]
10. ! [X0] : ((~tall(X0) & quiet(X0)) <=> (~wise(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p12]
15. ! [X0] : (quiet(X0) <=> generous(X0)) [input p14]
19. funny(mary) <~> patient(mary) [input p18]
24. wise(mary) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~brave(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 4]
31. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | (tall(X0) | ~quiet(X0)))) [nnf transformation 10]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | tall(X0) | ~quiet(X0))) [flattening 49]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 13]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 52]
56. ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))) [nnf transformation 15]
62. (~patient(mary) | ~funny(mary)) & (patient(mary) | funny(mary)) [nnf transformation 19]
83. ~patient(X0) | ~tall(X0) [cnf transformation 27]
99. ~wise(X0) | tall(X0) | ~quiet(X0) [cnf transformation 50]
103. generous(X0) | generous(X0) [cnf transformation 31]
109. ~funny(X0) | patient(X0) [cnf transformation 53]
118. quiet(X0) | ~generous(X0) [cnf transformation 56]
125. patient(mary) | funny(mary) [cnf transformation 62]
126. ~patient(mary) | ~funny(mary) [cnf transformation 62]
133. wise(mary) [cnf transformation 24]
135. generous(X0) [duplicate literal removal 103]
150. 4 <=> patient(mary) [avatar definition]
151. patient(mary) <- (4) [avatar component clause 150]
178. quiet(X0) [subsumption resolution 118,135]
208. ~funny(mary) [subsumption resolution 126,109]
209. patient(mary) [subsumption resolution 125,208]
210. 4 [avatar split clause 209,150]
221. ~tall(mary) <- (4) [resolution 83,151]
294. tall(mary) | ~quiet(mary) [resolution 99,133]
298. ~quiet(mary) <- (4) [subsumption resolution 294,221]
299. $false <- (4) [subsumption resolution 298,178]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 210,300]
% SZS output end Proof for 1991396571306672396783528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or curious is old and vice versa.
If alice is not calm or generous then paul is both calm and generous and vice versa.
If alice is not patient or not humble then someone is not old.
If alice is not patient then mary is both not rich and brave.
Everyone who is tall is both generous and strong and vice versa.
If fred is either strong or patient then someone is both creative and old and vice versa.
If paul is old then someone is not kind or calm and vice versa.
Everyone who is both happy and not old is both quiet and creative.
If susan is quiet or not kind then paul is either quiet or curious and vice versa.
If alice is not brave or wise then alice is both patient and not happy and vice versa.
If paul is either not old or generous then fred is either not old or not strong.
If someone is both old and not funny then fred is kind.
If someone is both generous and funny then fred is not wise and vice versa.
Everyone who is humble or strong is either not kind or not generous and vice versa.
If someone is not rich or humble then someone is calm or not curious and vice versa.
Everyone who is either tall or not rich is either creative or old.
Susan is strong.
Lucy is wise or not wise.
Someone is either not brave or not old.
Someone is quiet or patient.
Lucy is tall.
Lucy is either strong or brave.
John is both not patient and not strong. | Susan is quiet. | neutral | (![X]:((~patient(X)<~>curious(X))<=>old(X)))&
(((~calm(alice)|generous(alice)))<=>((calm(paul)&generous(paul))))&
(((~patient(alice)|~humble(alice)))=>(?[X]:(~old(X))))&
((~patient(alice))=>((~rich(mary)&brave(mary))))&
(![X]:(tall(X)<=>(generous(X)&strong(X))))&
(((strong(fred)<~>patient(fred)))<=>(?[X]:((creative(X)&old(X)))))&
((old(paul))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((happy(X)&~old(X))=>(quiet(X)&creative(X))))&
(((quiet(susan)|~kind(susan)))<=>((quiet(paul)<~>curious(paul))))&
(((~brave(alice)|wise(alice)))<=>((patient(alice)&~happy(alice))))&
(((~old(paul)<~>generous(paul)))=>((~old(fred)<~>~strong(fred))))&
((?[X]:((old(X)&~funny(X))))=>(kind(fred)))&
((?[X]:((generous(X)&funny(X))))<=>(~wise(fred)))&
(![X]:((humble(X)|strong(X))<=>(~kind(X)<~>~generous(X))))&
((?[X]:((~rich(X)|humble(X))))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((tall(X)<~>~rich(X))=>(creative(X)<~>old(X))))&
(strong(susan))&
((wise(lucy)|~wise(lucy)))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((quiet(X)|patient(X))))&
(tall(lucy))&
((strong(lucy)<~>brave(lucy)))&
((~patient(john)&~strong(john))) | quiet(susan) | [] | null | 0 |
Everyone who is both rich and patient is curious or not patient. Everyone who is tall or brave is brave and vice versa. Everyone who is both not quiet and calm is either patient or happy. Everyone who is not generous or not quiet is not kind. Everyone who is quiet is both not quiet and strong. Everyone who is not wise is both not wise and rich. If someone is tall or not wise then mary is either brave or curious and vice versa. Everyone who is both not wise and curious is both not curious and not rich. If fred is brave or kind then alice is both kind and old and vice versa. If someone is not humble then john is both kind and not patient and vice versa. Everyone who is not wise is strong or humble and vice versa. If someone is either creative or humble then someone is not curious or not happy. If john is not creative or kind then lucy is either humble or not old and vice versa. Everyone who is generous or humble is either not calm or happy and vice versa. Everyone who is either not curious or old is both not old and not humble and vice versa. Everyone who is not funny or creative is patient or kind and vice versa. Someone is not kind. Someone is tall. John is not creative or not wise. Susan is not tall. | Fred is not curious. | entailment | (![X]:((rich(X)&patient(X))=>(curious(X)|~patient(X))))&
(![X]:((tall(X)|brave(X))<=>brave(X)))&
(![X]:((~quiet(X)&calm(X))=>(patient(X)<~>happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>~kind(X)))&
(![X]:(quiet(X)=>(~quiet(X)&strong(X))))&
(![X]:(~wise(X)=>(~wise(X)&rich(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((brave(mary)<~>curious(mary))))&
(![X]:((~wise(X)&curious(X))=>(~curious(X)&~rich(X))))&
(((brave(fred)|kind(fred)))<=>((kind(alice)&old(alice))))&
((?[X]:(~humble(X)))<=>((kind(john)&~patient(john))))&
(![X]:(~wise(X)<=>(strong(X)|humble(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(((~creative(john)|kind(john)))<=>((humble(lucy)<~>~old(lucy))))&
(![X]:((generous(X)|humble(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)&~humble(X))))&
(![X]:((~funny(X)|creative(X))<=>(patient(X)|kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(tall(X)))&
((~creative(john)|~wise(john)))&
(~tall(susan)) | ~curious(fred) | [
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1634102358468193070456088
% SZS output start Proof for 1634102358468193070456088
4. ! [X0] : ((~quiet(X0) | ~generous(X0)) => ~kind(X0)) [input p3]
5. ! [X0] : (quiet(X0) => (strong(X0) & ~quiet(X0))) [input p4]
6. ! [X0] : (~wise(X0) => (rich(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((curious(X0) & ~wise(X0)) => (~rich(X0) & ~curious(X0))) [input p7]
10. ? [X0] : ~humble(X0) <=> (~patient(john) & kind(john)) [input p9]
11. ! [X0] : (~wise(X0) <=> (humble(X0) | strong(X0))) [input p10]
21. curious(fred) [input hypothesis]
27. ! [X0] : (~kind(X0) | (quiet(X0) & generous(X0))) [ennf transformation 4]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~quiet(X0)) [ennf transformation 5]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | wise(X0)) [ennf transformation 6]
30. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~curious(X0) | wise(X0))) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & ~curious(X0)) | ~curious(X0) | wise(X0)) [flattening 30]
42. (? [X0] : ~humble(X0) | (patient(john) | ~kind(john))) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [nnf transformation 10]
43. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [flattening 42]
44. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [rectify 43]
45. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
46. (~humble(sK1) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [skolemisation 44,45]
47. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | wise(X0))) [nnf transformation 11]
48. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | wise(X0))) [flattening 47]
72. ~kind(X0) | quiet(X0) [cnf transformation 27]
73. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
76. wise(X0) | rich(X0) [cnf transformation 29]
84. ~rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
90. kind(john) | humble(X1) [cnf transformation 46]
95. ~humble(X0) | ~wise(X0) [cnf transformation 48]
124. curious(fred) [cnf transformation 21]
128. ~quiet(X0) [duplicate literal removal 73]
158. ~curious(X0) | wise(X0) [subsumption resolution 84,76]
181. 11 <=> kind(john) [avatar definition]
182. kind(john) <- (11) [avatar component clause 181]
194. 14 <=> ! [X1] : humble(X1) [avatar definition]
195. humble(X1) <- (14) [avatar component clause 194]
197. 14 | 11 [avatar split clause 90,181,194]
239. quiet(john) <- (11) [resolution 72,182]
240. $false <- (11) [subsumption resolution 239,128]
241. ~11 [avatar contradiction clause 240]
249. ~wise(X0) <- (14) [resolution 95,195]
252. wise(fred) [resolution 158,124]
253. $false <- (14) [subsumption resolution 252,249]
254. ~14 [avatar contradiction clause 253]
255. $false [avatar sat refutation 197,241,254]
% SZS output end Proof for 1634102358468193070456088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is wise or not generous is not curious and vice versa. Everyone who is not tall is not quiet and vice versa. If paul is brave then someone is old. Everyone who is either old or humble is both funny and not quiet. Everyone who is not curious or generous is either generous or brave. If someone is either old or not brave then susan is not quiet or not tall and vice versa. Everyone who is patient is both not curious and funny. If fred is either not wise or not quiet then someone is not humble or happy and vice versa. If john is not humble or calm then someone is humble. If susan is tall then someone is not happy. Everyone who is humble is calm or generous and vice versa. If lucy is rich or funny then john is either not happy or not kind and vice versa. Everyone who is not wise is both generous and wise and vice versa. Everyone who is both rich and not humble is curious. If lucy is both funny and not funny then mary is both not old and not quiet. Everyone who is either not strong or wise is both strong and not calm. Alice is not creative or curious. Alice is either old or not strong. Lucy is not kind or not patient. Paul is not humble. Someone is kind or generous. Lucy is not creative or not humble. | Mary is not wise. | contradiction | (![X]:((wise(X)|~generous(X))<=>~curious(X)))&
(![X]:(~tall(X)<=>~quiet(X)))&
((brave(paul))=>(?[X]:(old(X))))&
(![X]:((old(X)<~>humble(X))=>(funny(X)&~quiet(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)<~>brave(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>((~quiet(susan)|~tall(susan))))&
(![X]:(patient(X)=>(~curious(X)&funny(X))))&
(((~wise(fred)<~>~quiet(fred)))<=>(?[X]:((~humble(X)|happy(X)))))&
(((~humble(john)|calm(john)))=>(?[X]:(humble(X))))&
((tall(susan))=>(?[X]:(~happy(X))))&
(![X]:(humble(X)<=>(calm(X)|generous(X))))&
(((rich(lucy)|funny(lucy)))<=>((~happy(john)<~>~kind(john))))&
(![X]:(~wise(X)<=>(generous(X)&wise(X))))&
(![X]:((rich(X)&~humble(X))=>curious(X)))&
(((funny(lucy)&~funny(lucy)))=>((~old(mary)&~quiet(mary))))&
(![X]:((~strong(X)<~>wise(X))=>(strong(X)&~calm(X))))&
((~creative(alice)|curious(alice)))&
((old(alice)<~>~strong(alice)))&
((~kind(lucy)|~patient(lucy)))&
(~humble(paul))&
(?[X]:((kind(X)|generous(X))))&
((~creative(lucy)|~humble(lucy))) | ~wise(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1294862000807256984958670
% SZS output start Proof for 1294862000807256984958670
13. ! [X0] : (~wise(X0) <=> (wise(X0) & generous(X0))) [input p12]
23. ~wise(mary) [input hypothesis]
62. ! [X0] : ((~wise(X0) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | wise(X0))) [nnf transformation 13]
63. ! [X0] : ((~wise(X0) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | wise(X0))) [flattening 62]
106. wise(X0) | wise(X0) [cnf transformation 63]
119. ~wise(mary) [cnf transformation 23]
121. wise(X0) [duplicate literal removal 106]
253. $false [subsumption resolution 119,121]
% SZS output end Proof for 1294862000807256984958670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either happy or not calm then someone is both happy and not tall. Everyone who is either not tall or not funny is not happy or not humble. If paul is not quiet then someone is humble or brave. Everyone who is funny is both happy and patient and vice versa. Everyone who is either wise or not creative is not curious. If alice is not strong or not rich then fred is not happy or patient. Everyone who is kind is not creative or not brave and vice versa. Everyone who is old is not kind or not humble and vice versa. If mary is either not strong or not quiet then someone is not strong or funny. Everyone who is either not rich or patient is funny or strong. Everyone who is not strong or strong is not old and vice versa. Everyone who is brave is either not old or rich and vice versa. If lucy is either funny or strong then someone is both rich and creative. Everyone who is not quiet is both patient and not brave and vice versa. Everyone who is either not kind or creative is both funny and not curious and vice versa. Everyone who is both not funny and tall is not humble or creative and vice versa. Someone is not strong. John is rich. Someone is not happy or generous. Someone is generous. Susan is kind. Someone is either not tall or creative. Someone is either quiet or not patient. | John is strong. | neutral | (((happy(paul)<~>~calm(paul)))=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~funny(X))=>(~happy(X)|~humble(X))))&
((~quiet(paul))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:(funny(X)<=>(happy(X)&patient(X))))&
(![X]:((wise(X)<~>~creative(X))=>~curious(X)))&
(((~strong(alice)|~rich(alice)))=>((~happy(fred)|patient(fred))))&
(![X]:(kind(X)<=>(~creative(X)|~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(![X]:(brave(X)<=>(~old(X)<~>rich(X))))&
(((funny(lucy)<~>strong(lucy)))=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~quiet(X)<=>(patient(X)&~brave(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(funny(X)&~curious(X))))&
(![X]:((~funny(X)&tall(X))<=>(~humble(X)|creative(X))))&
(?[X]:(~strong(X)))&
(rich(john))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:(generous(X)))&
(kind(susan))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | strong(john) | [] | null | 0 |
If lucy is patient then lucy is both not rich and kind.
If someone is not brave or tall then lucy is humble or not generous.
Everyone who is both not rich and not tall is not funny or old and vice versa.
If susan is both not funny and not humble then john is both happy and not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Mary is curious or not funny.
Someone is not quiet.
John is both wise and not patient.
Paul is either not creative or not kind.
Mary is both not patient and kind.
Someone is not happy or not generous.
Fred is both strong and humble. | Fred is happy. | contradiction | ((patient(lucy))=>((~rich(lucy)&kind(lucy))))&
((?[X]:((~brave(X)|tall(X))))=>((humble(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&~tall(X))<=>(~funny(X)|old(X))))&
(((~funny(susan)&~humble(susan)))<=>((happy(john)&~kind(john))))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
((curious(mary)|~funny(mary)))&
(?[X]:(~quiet(X)))&
((wise(john)&~patient(john)))&
((~creative(paul)<~>~kind(paul)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
((strong(fred)&humble(fred))) | happy(fred) | [
"p7",
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2472693103106528839994159
% SZS output start Proof for 2472693103106528839994159
8. ? [X0] : (generous(X0) | ~old(X0)) <=> (kind(paul) & brave(paul)) [input p7]
13. ! [X0] : ((~happy(X0) & generous(X0)) <=> (~funny(X0) | old(X0))) [input p12]
14. (~strong(fred) | old(fred)) <=> ? [X0] : (kind(X0) | happy(X0)) [input p13]
23. humble(fred) & strong(fred) [input p22]
24. happy(fred) [input hypothesis]
44. (? [X0] : (generous(X0) | ~old(X0)) | (~kind(paul) | ~brave(paul))) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [nnf transformation 8]
45. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X0] : (~generous(X0) & old(X0))) [flattening 44]
46. (? [X0] : (generous(X0) | ~old(X0)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [rectify 45]
47. ? [X0] : (generous(X0) | ~old(X0)) => (generous(sK1) | ~old(sK1)) [choice axiom]
48. ((generous(sK1) | ~old(sK1)) | ~kind(paul) | ~brave(paul)) & ((kind(paul) & brave(paul)) | ! [X1] : (~generous(X1) & old(X1))) [skolemisation 46,47]
61. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (happy(X0) | ~generous(X0)))) [nnf transformation 13]
62. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | happy(X0) | ~generous(X0))) [flattening 61]
63. ((~strong(fred) | old(fred)) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X0] : (kind(X0) | happy(X0)) | (strong(fred) & ~old(fred))) [nnf transformation 14]
64. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X0] : (kind(X0) | happy(X0)) | (strong(fred) & ~old(fred))) [flattening 63]
65. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & (? [X1] : (kind(X1) | happy(X1)) | (strong(fred) & ~old(fred))) [rectify 64]
66. ? [X1] : (kind(X1) | happy(X1)) => (kind(sK4) | happy(sK4)) [choice axiom]
67. (~strong(fred) | old(fred) | ! [X0] : (~kind(X0) & ~happy(X0))) & ((kind(sK4) | happy(sK4)) | (strong(fred) & ~old(fred))) [skolemisation 65,66]
110. kind(paul) | old(X1) [cnf transformation 48]
111. kind(paul) | ~generous(X1) [cnf transformation 48]
128. ~old(X0) | generous(X0) [cnf transformation 62]
130. ~happy(X0) | ~old(X0) [cnf transformation 62]
135. ~strong(fred) | old(fred) | ~kind(X0) [cnf transformation 67]
156. strong(fred) [cnf transformation 23]
158. happy(fred) [cnf transformation 24]
226. 16 <=> kind(paul) [avatar definition]
227. kind(paul) <- (16) [avatar component clause 226]
239. 19 <=> ! [X1] : ~generous(X1) [avatar definition]
240. ~generous(X1) <- (19) [avatar component clause 239]
241. 19 | 16 [avatar split clause 111,226,239]
243. 20 <=> ! [X1] : old(X1) [avatar definition]
244. old(X1) <- (20) [avatar component clause 243]
245. 20 | 16 [avatar split clause 110,226,243]
309. 34 <=> ! [X0] : ~kind(X0) [avatar definition]
310. ~kind(X0) <- (34) [avatar component clause 309]
312. 35 <=> old(fred) [avatar definition]
316. 36 <=> strong(fred) [avatar definition]
319. 34 | 35 | ~36 [avatar split clause 135,316,312,309]
404. 36 [avatar split clause 156,316]
405. $false <- (16, 34) [subsumption resolution 227,310]
406. ~16 | ~34 [avatar contradiction clause 405]
446. ~old(fred) [resolution 130,158]
451. ~35 [avatar split clause 446,312]
453. generous(X0) <- (20) [resolution 244,128]
456. $false <- (19, 20) [subsumption resolution 453,240]
457. ~19 | ~20 [avatar contradiction clause 456]
460. $false [avatar sat refutation 241,245,319,404,406,451,457]
% SZS output end Proof for 2472693103106528839994159
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or calm is both not brave and not tall. Everyone who is strong is both calm and generous. Everyone who is both calm and tall is not generous. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Everyone who is both happy and funny is not brave and vice versa. Everyone who is both wise and not wise is both not brave and not calm and vice versa. If paul is either wise or curious then someone is not humble or not kind. If someone is either not happy or not humble then someone is either not humble or not curious and vice versa. Everyone who is not curious or not tall is kind and vice versa. If lucy is both not happy and funny then alice is not kind and vice versa. Everyone who is both rich and strong is either kind or not quiet. Everyone who is either kind or happy is not wise. Everyone who is both not curious and not brave is humble or not curious and vice versa. Someone is quiet. John is either not happy or not rich. John is happy or old. Fred is not calm. Lucy is rich. Mary is not rich or generous. Someone is old or happy. | Alice is happy. | neutral | (![X]:((~patient(X)|calm(X))=>(~brave(X)&~tall(X))))&
(![X]:(strong(X)=>(calm(X)&generous(X))))&
(![X]:((calm(X)&tall(X))=>~generous(X)))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)|~curious(X))))&
(?[X]:(quiet(X)))&
((~happy(john)<~>~rich(john)))&
((happy(john)|old(john)))&
(~calm(fred))&
(rich(lucy))&
((~rich(mary)|generous(mary)))&
(?[X]:((old(X)|happy(X)))) | happy(alice) | [] | null | 0 |
Everyone who is not rich is either rich or strong and vice versa.
Everyone who is both not tall and not quiet is patient or not calm and vice versa.
If someone is either rich or not rich then mary is both tall and not old.
If someone is not calm or not generous then susan is not calm or rich.
Everyone who is not tall or not brave is either creative or funny and vice versa.
If someone is funny then paul is patient.
If lucy is not strong then mary is not rich and vice versa.
Everyone who is either not curious or not humble is not wise and vice versa.
If someone is either not generous or old then someone is calm or brave and vice versa.
If fred is not patient then someone is funny or curious.
Everyone who is not quiet is brave.
If someone is funny or tall then someone is both not funny and not humble.
If lucy is curious then someone is either not tall or not old and vice versa.
If paul is both not tall and not rich then lucy is either not strong or generous and vice versa.
If someone is not wise or generous then someone is not rich and vice versa.
Everyone who is either not rich or happy is curious or not patient.
Alice is old or rich.
John is not quiet.
Mary is both not kind and not old.
Alice is not old or quiet.
Paul is either not funny or not calm.
Fred is generous or not calm.
Someone is not wise.
Susan is not happy or not rich. | Susan is not creative. | neutral | (![X]:(~rich(X)<=>(rich(X)<~>strong(X))))&
(![X]:((~tall(X)&~quiet(X))<=>(patient(X)|~calm(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>((tall(mary)&~old(mary))))&
((?[X]:((~calm(X)|~generous(X))))=>((~calm(susan)|rich(susan))))&
(![X]:((~tall(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((?[X]:(funny(X)))=>(patient(paul)))&
((~strong(lucy))<=>(~rich(mary)))&
(![X]:((~curious(X)<~>~humble(X))<=>~wise(X)))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((calm(X)|brave(X)))))&
((~patient(fred))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:(~quiet(X)=>brave(X)))&
((?[X]:((funny(X)|tall(X))))=>(?[X]:((~funny(X)&~humble(X)))))&
((curious(lucy))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~tall(paul)&~rich(paul)))<=>((~strong(lucy)<~>generous(lucy))))&
((?[X]:((~wise(X)|generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)<~>happy(X))=>(curious(X)|~patient(X))))&
((old(alice)|rich(alice)))&
(~quiet(john))&
((~kind(mary)&~old(mary)))&
((~old(alice)|quiet(alice)))&
((~funny(paul)<~>~calm(paul)))&
((generous(fred)|~calm(fred)))&
(?[X]:(~wise(X)))&
((~happy(susan)|~rich(susan))) | ~creative(susan) | [] | null | 0 |
Everyone who is tall or not generous is either not calm or old and vice versa.
If alice is either curious or generous then someone is either calm or not quiet.
If someone is both funny and old then someone is both wise and happy.
If mary is kind or not tall then someone is both funny and not old and vice versa.
Everyone who is not kind is not patient or creative and vice versa.
Everyone who is creative is wise and vice versa.
If someone is not creative then fred is either calm or not generous.
If someone is not calm or tall then mary is not creative or quiet.
Everyone who is either not happy or calm is not creative and vice versa.
If john is generous or brave then someone is either not humble or happy.
Everyone who is both quiet and humble is not patient or curious.
Everyone who is both not strong and not quiet is generous and vice versa.
Everyone who is kind is not happy and vice versa.
If someone is not humble or not wise then paul is either funny or not rich and vice versa.
Everyone who is either wise or generous is both kind and tall.
Everyone who is kind or funny is not brave and vice versa.
Fred is patient or not strong.
Alice is not old.
Fred is not strong or humble.
Fred is rich.
Alice is either generous or rich.
Someone is not rich or happy.
Paul is both brave and patient.
Someone is calm. | Fred is calm. | contradiction | (![X]:((tall(X)|~generous(X))<=>(~calm(X)<~>old(X))))&
(((curious(alice)<~>generous(alice)))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((funny(X)&old(X))))=>(?[X]:((wise(X)&happy(X)))))&
(((kind(mary)|~tall(mary)))<=>(?[X]:((funny(X)&~old(X)))))&
(![X]:(~kind(X)<=>(~patient(X)|creative(X))))&
(![X]:(creative(X)<=>wise(X)))&
((?[X]:(~creative(X)))=>((calm(fred)<~>~generous(fred))))&
((?[X]:((~calm(X)|tall(X))))=>((~creative(mary)|quiet(mary))))&
(![X]:((~happy(X)<~>calm(X))<=>~creative(X)))&
(((generous(john)|brave(john)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:((quiet(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~strong(X)&~quiet(X))<=>generous(X)))&
(![X]:(kind(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>generous(X))=>(kind(X)&tall(X))))&
(![X]:((kind(X)|funny(X))<=>~brave(X)))&
((patient(fred)|~strong(fred)))&
(~old(alice))&
((~strong(fred)|humble(fred)))&
(rich(fred))&
((generous(alice)<~>rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((brave(paul)&patient(paul)))&
(?[X]:(calm(X))) | calm(fred) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p11",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 923812028253049753296340
% SZS output start Proof for 923812028253049753296340
5. ! [X0] : (~kind(X0) <=> (creative(X0) | ~patient(X0))) [input p4]
6. ! [X0] : (creative(X0) <=> wise(X0)) [input p5]
7. ? [X0] : ~creative(X0) => (calm(fred) <~> ~generous(fred)) [input p6]
8. ? [X0] : (tall(X0) | ~calm(X0)) => (quiet(mary) | ~creative(mary)) [input p7]
9. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> ~creative(X0)) [input p8]
12. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> generous(X0)) [input p11]
13. ! [X0] : (kind(X0) <=> ~happy(X0)) [input p12]
15. ! [X0] : ((wise(X0) <~> generous(X0)) => (tall(X0) & kind(X0))) [input p14]
16. ! [X0] : ((funny(X0) | kind(X0)) <=> ~brave(X0)) [input p15]
23. patient(paul) & brave(paul) [input p22]
25. calm(fred) [input hypothesis]
29. (calm(fred) <~> ~generous(fred)) | ! [X0] : creative(X0) [ennf transformation 7]
30. (quiet(mary) | ~creative(mary)) | ! [X0] : (~tall(X0) & calm(X0)) [ennf transformation 8]
31. quiet(mary) | ~creative(mary) | ! [X0] : (~tall(X0) & calm(X0)) [flattening 30]
35. ! [X0] : ((tall(X0) & kind(X0)) | (wise(X0) <=> generous(X0))) [ennf transformation 15]
49. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | kind(X0))) [nnf transformation 5]
50. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | kind(X0))) [flattening 49]
51. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 6]
52. ((generous(fred) | ~calm(fred)) & (~generous(fred) | calm(fred))) | ! [X0] : creative(X0) [nnf transformation 29]
53. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 9]
57. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 12]
58. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | quiet(X0) | strong(X0))) [flattening 57]
59. ! [X0] : ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))) [nnf transformation 13]
64. ! [X0] : ((tall(X0) & kind(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) [nnf transformation 35]
65. ! [X0] : (((funny(X0) | kind(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [nnf transformation 16]
66. ! [X0] : ((funny(X0) | kind(X0) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [flattening 65]
89. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 50]
91. ~creative(X0) | ~kind(X0) [cnf transformation 50]
92. ~creative(X0) | wise(X0) [cnf transformation 51]
93. ~wise(X0) | creative(X0) [cnf transformation 51]
95. generous(fred) | ~calm(fred) | creative(X0) [cnf transformation 52]
96. quiet(mary) | ~creative(mary) | calm(X0) [cnf transformation 31]
99. ~creative(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 53]
101. ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 53]
109. ~quiet(X0) | ~generous(X0) [cnf transformation 58]
110. ~kind(X0) | ~happy(X0) [cnf transformation 59]
111. kind(X0) | happy(X0) [cnf transformation 59]
118. ~wise(X0) | generous(X0) | kind(X0) [cnf transformation 64]
119. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 64]
122. ~brave(X0) | ~kind(X0) [cnf transformation 66]
132. brave(paul) [cnf transformation 23]
133. patient(paul) [cnf transformation 23]
135. calm(fred) [cnf transformation 25]
173. 9 <=> kind(mary) [avatar definition]
194. 13 <=> ! [X0] : creative(X0) [avatar definition]
195. creative(X0) <- (13) [avatar component clause 194]
197. 14 <=> calm(fred) [avatar definition]
198. calm(fred) <- (14) [avatar component clause 197]
201. 15 <=> generous(fred) [avatar definition]
203. generous(fred) <- (15) [avatar component clause 201]
204. 13 | ~14 | 15 [avatar split clause 95,201,197,194]
210. 17 <=> creative(mary) [avatar definition]
211. creative(mary) <- (17) [avatar component clause 210]
212. ~creative(mary) <- (~17) [avatar component clause 210]
214. 18 <=> quiet(mary) [avatar definition]
216. quiet(mary) <- (18) [avatar component clause 214]
219. 19 <=> ! [X0] : calm(X0) [avatar definition]
220. calm(X0) <- (19) [avatar component clause 219]
221. 19 | ~17 | 18 [avatar split clause 96,214,210,219]
299. 14 [avatar split clause 135,197]
301. $false <- (13, ~17) [resolution 212,195]
302. ~13 | 17 [avatar contradiction clause 301]
306. ~kind(paul) [resolution 122,132]
307. happy(paul) [resolution 306,111]
338. creative(paul) | kind(paul) [resolution 89,133]
340. creative(paul) [subsumption resolution 338,306]
344. ~happy(paul) | ~calm(paul) [resolution 99,340]
345. ~calm(paul) [subsumption resolution 344,307]
351. happy(fred) | creative(fred) <- (14) [resolution 101,198]
362. 43 <=> creative(fred) [avatar definition]
363. ~creative(fred) <- (~43) [avatar component clause 362]
364. creative(fred) <- (43) [avatar component clause 362]
366. 44 <=> happy(fred) [avatar definition]
367. ~happy(fred) <- (~44) [avatar component clause 366]
368. happy(fred) <- (44) [avatar component clause 366]
369. 43 | 44 | ~14 [avatar split clause 351,197,366,362]
380. ~happy(fred) | ~calm(fred) <- (43) [resolution 364,99]
383. ~kind(fred) <- (43) [resolution 364,91]
384. ~happy(fred) <- (14, 43) [subsumption resolution 380,198]
385. ~44 | ~14 | ~43 [avatar split clause 384,362,197,366]
386. wise(fred) | kind(fred) <- (15) [resolution 119,203]
392. 45 <=> generous(mary) [avatar definition]
407. wise(mary) <- (17) [resolution 211,92]
408. ~kind(mary) <- (17) [resolution 211,91]
410. ~generous(mary) <- (18) [resolution 216,109]
411. ~45 | ~18 [avatar split clause 410,214,392]
419. generous(mary) | kind(mary) <- (17) [resolution 407,118]
434. ~9 | ~17 [avatar split clause 408,210,173]
445. 9 | 45 | ~17 [avatar split clause 419,210,392,173]
460. $false <- (19) [resolution 220,345]
461. ~19 [avatar contradiction clause 460]
540. happy(fred) <- (43) [resolution 383,111]
541. $false <- (43, ~44) [subsumption resolution 540,367]
542. ~43 | 44 [avatar contradiction clause 541]
551. 55 <=> kind(fred) [avatar definition]
553. kind(fred) <- (55) [avatar component clause 551]
555. 56 <=> wise(fred) [avatar definition]
557. wise(fred) <- (56) [avatar component clause 555]
558. 55 | 56 | ~15 [avatar split clause 386,201,555,551]
563. ~happy(fred) <- (55) [resolution 553,110]
565. $false <- (44, 55) [subsumption resolution 563,368]
566. ~44 | ~55 [avatar contradiction clause 565]
571. creative(fred) <- (56) [resolution 557,93]
572. $false <- (~43, 56) [subsumption resolution 571,363]
573. 43 | ~56 [avatar contradiction clause 572]
574. $false [avatar sat refutation 204,221,299,302,369,385,411,434,445,461,542,558,566,573]
% SZS output end Proof for 923812028253049753296340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or brave is either not generous or rich.
Everyone who is both brave and not humble is both not rich and kind.
Everyone who is either not strong or humble is brave or not kind.
Everyone who is not strong is not creative.
Everyone who is either patient or brave is either patient or not kind and vice versa.
If mary is generous then someone is tall or strong.
Everyone who is not calm is not humble and vice versa.
If alice is not generous or not happy then someone is old.
If fred is curious or not humble then john is either strong or not generous and vice versa.
Everyone who is both happy and humble is both calm and not curious and vice versa.
Everyone who is brave or kind is either not funny or generous.
If someone is both not humble and humble then someone is humble or not tall and vice versa.
If someone is both not quiet and curious then someone is either calm or quiet and vice versa.
Everyone who is both old and curious is not brave or patient and vice versa.
If john is strong then someone is creative or not quiet and vice versa.
Everyone who is either not curious or not wise is not generous and vice versa.
Someone is both quiet and kind.
Mary is either creative or brave.
Someone is either not tall or not quiet.
Someone is both not patient and not funny.
Someone is either not wise or generous. | Mary is creative. | entailment | (![X]:((happy(X)|brave(X))=>(~generous(X)<~>rich(X))))&
(![X]:((brave(X)&~humble(X))=>(~rich(X)&kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)|~kind(X))))&
(![X]:(~strong(X)=>~creative(X)))&
(![X]:((patient(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
((generous(mary))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
(((~generous(alice)|~happy(alice)))=>(?[X]:(old(X))))&
(((curious(fred)|~humble(fred)))<=>((strong(john)<~>~generous(john))))&
(![X]:((happy(X)&humble(X))<=>(calm(X)&~curious(X))))&
(![X]:((brave(X)|kind(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((~humble(X)&humble(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)|patient(X))))&
((strong(john))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)&kind(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((~wise(X)<~>generous(X)))) | creative(mary) | [
"p1",
"p4",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2957023930771056305389985
% SZS output start Proof for 2957023930771056305389985
2. ! [X0] : ((~humble(X0) & brave(X0)) => (kind(X0) & ~rich(X0))) [input p1]
5. ! [X0] : ((patient(X0) <~> brave(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p4]
12. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X0] : (~tall(X0) | humble(X0)) [input p11]
18. creative(mary) <~> brave(mary) [input p17]
22. ~creative(mary) [input hypothesis]
23. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X1] : (~tall(X1) | humble(X1)) [rectify 12]
26. ! [X0] : ((kind(X0) & ~rich(X0)) | (humble(X0) | ~brave(X0))) [ennf transformation 2]
27. ! [X0] : ((kind(X0) & ~rich(X0)) | humble(X0) | ~brave(X0)) [flattening 26]
36. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 5]
47. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X1] : (~tall(X1) | humble(X1)) | ! [X0] : (~humble(X0) | humble(X0))) [nnf transformation 23]
48. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X2] : (~tall(X2) | humble(X2)) | ! [X3] : (~humble(X3) | humble(X3))) [rectify 47]
49. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
50. ? [X2] : (~tall(X2) | humble(X2)) => (~tall(sK3) | humble(sK3)) [choice axiom]
51. ((humble(sK2) & ~humble(sK2)) | ! [X1] : (tall(X1) & ~humble(X1))) & ((~tall(sK3) | humble(sK3)) | ! [X3] : (~humble(X3) | humble(X3))) [skolemisation 48,50,49]
66. (~brave(mary) | ~creative(mary)) & (brave(mary) | creative(mary)) [nnf transformation 18]
80. ~brave(X0) | humble(X0) | kind(X0) [cnf transformation 27]
85. ~kind(X0) | patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 36]
90. ~brave(X0) | ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 36]
112. ~humble(sK2) | ~humble(X1) [cnf transformation 51]
114. humble(sK2) | ~humble(X1) [cnf transformation 51]
136. brave(mary) | creative(mary) [cnf transformation 66]
144. ~creative(mary) [cnf transformation 22]
145. ~kind(X0) | patient(X0) | ~brave(X0) [duplicate literal removal 85]
148. ~brave(X0) | ~patient(X0) | ~kind(X0) [duplicate literal removal 90]
150. ~kind(X0) | ~brave(X0) [subsumption resolution 145,148]
204. 12 <=> humble(sK2) [avatar definition]
209. 13 <=> ! [X1] : ~humble(X1) [avatar definition]
210. ~humble(X1) <- (13) [avatar component clause 209]
211. 13 | 12 [avatar split clause 114,204,209]
213. 13 | ~12 [avatar split clause 112,204,209]
263. 25 <=> creative(mary) [avatar definition]
267. 26 <=> brave(mary) [avatar definition]
268. brave(mary) <- (26) [avatar component clause 267]
271. 25 | 26 [avatar split clause 136,267,263]
292. ~25 [avatar split clause 144,263]
327. humble(mary) | kind(mary) <- (26) [resolution 80,268]
328. kind(mary) <- (13, 26) [subsumption resolution 327,210]
331. ~brave(mary) <- (13, 26) [resolution 328,150]
332. $false <- (13, 26) [subsumption resolution 331,268]
333. ~13 | ~26 [avatar contradiction clause 332]
334. $false [avatar sat refutation 211,213,271,292,333]
% SZS output end Proof for 2957023930771056305389985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not wise is either not curious or generous and vice versa.
Everyone who is either curious or quiet is both brave and not happy.
Everyone who is not quiet is not curious.
Everyone who is wise or not strong is both brave and tall and vice versa.
If paul is old then someone is either strong or humble and vice versa.
If susan is either not calm or not quiet then alice is either quiet or calm.
If someone is either creative or funny then someone is either generous or creative.
Everyone who is either brave or not humble is either not old or humble.
If mary is both generous and not humble then susan is not calm and vice versa.
If mary is either tall or not wise then mary is either not generous or funny.
If someone is rich or not rich then someone is not calm and vice versa.
Everyone who is funny is both tall and not curious.
If susan is not curious or generous then someone is happy or not quiet.
Everyone who is either not rich or not wise is either not brave or generous.
If fred is happy or not old then fred is not brave or creative and vice versa.
If john is both tall and not tall then someone is rich or not happy.
Paul is not humble.
John is either not creative or creative.
Someone is tall or kind.
Alice is not wise or generous.
Susan is both not strong and patient.
Someone is either not happy or brave.
John is strong or calm.
John is brave or not kind. | Paul is not brave. | contradiction | (![X]:((~rich(X)<~>~wise(X))<=>(~curious(X)<~>generous(X))))&
(![X]:((curious(X)<~>quiet(X))=>(brave(X)&~happy(X))))&
(![X]:(~quiet(X)=>~curious(X)))&
(![X]:((wise(X)|~strong(X))<=>(brave(X)&tall(X))))&
((old(paul))<=>(?[X]:((strong(X)<~>humble(X)))))&
(((~calm(susan)<~>~quiet(susan)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((creative(X)<~>funny(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:((brave(X)<~>~humble(X))=>(~old(X)<~>humble(X))))&
(((generous(mary)&~humble(mary)))<=>(~calm(susan)))&
(((tall(mary)<~>~wise(mary)))=>((~generous(mary)<~>funny(mary))))&
((?[X]:((rich(X)|~rich(X))))<=>(?[X]:(~calm(X))))&
(![X]:(funny(X)=>(tall(X)&~curious(X))))&
(((~curious(susan)|generous(susan)))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~rich(X)<~>~wise(X))=>(~brave(X)<~>generous(X))))&
(((happy(fred)|~old(fred)))<=>((~brave(fred)|creative(fred))))&
(((tall(john)&~tall(john)))=>(?[X]:((rich(X)|~happy(X)))))&
(~humble(paul))&
((~creative(john)<~>creative(john)))&
(?[X]:((tall(X)|kind(X))))&
((~wise(alice)|generous(alice)))&
((~strong(susan)&patient(susan)))&
(?[X]:((~happy(X)<~>brave(X))))&
((strong(john)|calm(john)))&
((brave(john)|~kind(john))) | ~brave(paul) | [
"p3",
"p4",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2439558362531232662529
% SZS output start Proof for 2439558362531232662529
4. ! [X0] : ((~strong(X0) | wise(X0)) <=> (tall(X0) & brave(X0))) [input p3]
5. old(paul) <=> ? [X0] : (strong(X0) <~> humble(X0)) [input p4]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) => (~old(X0) <~> humble(X0))) [input p7]
17. ~humble(paul) [input p16]
25. ~brave(paul) [input hypothesis]
33. ! [X0] : ((~old(X0) <~> humble(X0)) | (brave(X0) <=> ~humble(X0))) [ennf transformation 8]
42. ! [X0] : (((~strong(X0) | wise(X0)) | (~tall(X0) | ~brave(X0))) & ((tall(X0) & brave(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((~strong(X0) | wise(X0) | ~tall(X0) | ~brave(X0)) & ((tall(X0) & brave(X0)) | (strong(X0) & ~wise(X0)))) [flattening 42]
44. (old(paul) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~old(paul)) [nnf transformation 5]
45. (old(paul) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) | ~old(paul)) [rectify 44]
46. ? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) => ((~humble(sK0) | ~strong(sK0)) & (humble(sK0) | strong(sK0))) [choice axiom]
47. (old(paul) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (((~humble(sK0) | ~strong(sK0)) & (humble(sK0) | strong(sK0))) | ~old(paul)) [skolemisation 45,46]
53. ! [X0] : (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 33]
89. strong(X0) | brave(X0) [cnf transformation 43]
95. old(paul) | humble(X0) | ~strong(X0) [cnf transformation 47]
106. humble(X0) | ~old(X0) | brave(X0) | humble(X0) [cnf transformation 53]
132. ~humble(paul) [cnf transformation 17]
142. ~brave(paul) [cnf transformation 25]
143. ~old(X0) | humble(X0) | brave(X0) [duplicate literal removal 106]
149. 2 <=> old(paul) [avatar definition]
151. old(paul) <- (2) [avatar component clause 149]
154. 3 <=> ! [X0] : (humble(X0) | ~strong(X0)) [avatar definition]
155. ~strong(X0) | humble(X0) <- (3) [avatar component clause 154]
156. 3 | 2 [avatar split clause 95,149,154]
336. humble(paul) | brave(paul) <- (2) [resolution 143,151]
337. brave(paul) <- (2) [subsumption resolution 336,132]
338. $false <- (2) [subsumption resolution 337,142]
339. ~2 [avatar contradiction clause 338]
342. humble(X0) | brave(X0) <- (3) [resolution 155,89]
374. brave(paul) <- (3) [resolution 342,132]
377. $false <- (3) [subsumption resolution 374,142]
378. ~3 [avatar contradiction clause 377]
379. $false [avatar sat refutation 156,339,378]
% SZS output end Proof for 2439558362531232662529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is not creative or not wise and vice versa.
If alice is not quiet or not rich then someone is not creative.
If someone is both not rich and rich then paul is not patient.
Everyone who is both not curious and not patient is not generous and vice versa.
If fred is not calm then someone is either creative or quiet.
Everyone who is both not happy and wise is not funny or not patient and vice versa.
If someone is patient or happy then mary is either not generous or not funny and vice versa.
Everyone who is either not funny or not humble is both not tall and not generous.
If susan is both brave and not creative then mary is brave and vice versa.
If someone is not old then susan is calm or patient.
Everyone who is both not humble and not kind is generous and vice versa.
Everyone who is either creative or tall is both not curious and not generous and vice versa.
Everyone who is both not happy and not tall is funny and vice versa.
If susan is not creative or strong then someone is not funny or humble.
If mary is both not generous and not kind then paul is not calm or curious and vice versa.
If john is both not strong and not creative then someone is either creative or not funny and vice versa.
Someone is either not old or not creative.
Someone is both not kind and not old.
Susan is happy or creative.
Someone is either kind or not creative.
Someone is generous.
Fred is both not patient and not generous.
Susan is humble.
Mary is either patient or not funny. | Susan is funny. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:((~creative(X)|~wise(X)))))&
(((~quiet(alice)|~rich(alice)))=>(?[X]:(~creative(X))))&
((?[X]:((~rich(X)&rich(X))))=>(~patient(paul)))&
(![X]:((~curious(X)&~patient(X))<=>~generous(X)))&
((~calm(fred))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:((~happy(X)&wise(X))<=>(~funny(X)|~patient(X))))&
((?[X]:((patient(X)|happy(X))))<=>((~generous(mary)<~>~funny(mary))))&
(![X]:((~funny(X)<~>~humble(X))=>(~tall(X)&~generous(X))))&
(((brave(susan)&~creative(susan)))<=>(brave(mary)))&
((?[X]:(~old(X)))=>((calm(susan)|patient(susan))))&
(![X]:((~humble(X)&~kind(X))<=>generous(X)))&
(![X]:((creative(X)<~>tall(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~happy(X)&~tall(X))<=>funny(X)))&
(((~creative(susan)|strong(susan)))=>(?[X]:((~funny(X)|humble(X)))))&
(((~generous(mary)&~kind(mary)))<=>((~calm(paul)|curious(paul))))&
(((~strong(john)&~creative(john)))<=>(?[X]:((creative(X)<~>~funny(X)))))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:((~kind(X)&~old(X))))&
((happy(susan)|creative(susan)))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:(generous(X)))&
((~patient(fred)&~generous(fred)))&
(humble(susan))&
((patient(mary)<~>~funny(mary))) | funny(susan) | [
"p5",
"p7",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6737331013871376694720084
% SZS output start Proof for 6737331013871376694720084
6. ! [X0] : ((wise(X0) & ~happy(X0)) <=> (~patient(X0) | ~funny(X0))) [input p5]
8. ! [X0] : ((~funny(X0) <~> ~humble(X0)) => (~generous(X0) & ~tall(X0))) [input p7]
13. ! [X0] : ((~tall(X0) & ~happy(X0)) <=> funny(X0)) [input p12]
23. humble(susan) [input p22]
25. ~funny(susan) [input hypothesis]
30. ! [X0] : ((~generous(X0) & ~tall(X0)) | (~funny(X0) <=> ~humble(X0))) [ennf transformation 8]
46. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & funny(X0))) & ((~patient(X0) | ~funny(X0)) | (~wise(X0) | happy(X0)))) [nnf transformation 6]
47. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & funny(X0))) & (~patient(X0) | ~funny(X0) | ~wise(X0) | happy(X0))) [flattening 46]
52. ! [X0] : ((~generous(X0) & ~tall(X0)) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) [nnf transformation 30]
59. ! [X0] : (((~tall(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | (tall(X0) | happy(X0)))) [nnf transformation 13]
60. ! [X0] : (((~tall(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | tall(X0) | happy(X0))) [flattening 59]
93. ~happy(X0) | funny(X0) [cnf transformation 47]
103. ~tall(X0) | ~humble(X0) | funny(X0) [cnf transformation 52]
120. funny(X0) | tall(X0) | happy(X0) [cnf transformation 60]
146. humble(susan) [cnf transformation 23]
149. ~funny(susan) [cnf transformation 25]
259. tall(X0) | funny(X0) [subsumption resolution 120,93]
377. ~humble(X0) | funny(X0) | funny(X0) [resolution 103,259]
378. ~humble(X0) | funny(X0) [duplicate literal removal 377]
385. funny(susan) [resolution 378,146]
386. $false [subsumption resolution 385,149]
% SZS output end Proof for 6737331013871376694720084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not creative is patient and vice versa.
Everyone who is not generous is either not strong or happy.
Everyone who is either quiet or not tall is not quiet or strong.
Everyone who is not rich or not old is both not funny and not rich.
Everyone who is brave is either not calm or not wise.
If lucy is both not happy and not kind then someone is patient and vice versa.
Everyone who is both brave and rich is both not quiet and strong and vice versa.
If john is both funny and wise then alice is both old and calm.
Everyone who is either old or calm is either curious or not quiet.
Everyone who is curious or brave is patient or humble and vice versa.
If alice is either not generous or not rich then someone is either calm or strong and vice versa.
If someone is calm then susan is funny and vice versa.
If someone is tall or not calm then someone is either old or not creative and vice versa.
If susan is rich or not humble then someone is either not creative or kind.
Everyone who is both not quiet and not patient is happy and vice versa.
Everyone who is either quiet or not quiet is both not creative and not old.
Someone is not happy.
Someone is both not kind and not strong.
Someone is not funny or rich.
Paul is not strong.
Fred is not tall or not patient.
Susan is both tall and not old.
Susan is not rich. | Susan is not creative. | entailment | (![X]:((creative(X)|~creative(X))<=>patient(X)))&
(![X]:(~generous(X)=>(~strong(X)<~>happy(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(~quiet(X)|strong(X))))&
(![X]:((~rich(X)|~old(X))=>(~funny(X)&~rich(X))))&
(![X]:(brave(X)=>(~calm(X)<~>~wise(X))))&
(((~happy(lucy)&~kind(lucy)))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)&rich(X))<=>(~quiet(X)&strong(X))))&
(((funny(john)&wise(john)))=>((old(alice)&calm(alice))))&
(![X]:((old(X)<~>calm(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((curious(X)|brave(X))<=>(patient(X)|humble(X))))&
(((~generous(alice)<~>~rich(alice)))<=>(?[X]:((calm(X)<~>strong(X)))))&
((?[X]:(calm(X)))<=>(funny(susan)))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:((old(X)<~>~creative(X)))))&
(((rich(susan)|~humble(susan)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:((~quiet(X)&~patient(X))<=>happy(X)))&
(![X]:((quiet(X)<~>~quiet(X))=>(~creative(X)&~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~funny(X)|rich(X))))&
(~strong(paul))&
((~tall(fred)|~patient(fred)))&
((tall(susan)&~old(susan)))&
(~rich(susan)) | ~creative(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6460650152688546019323438
% SZS output start Proof for 6460650152688546019323438
16. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (~old(X0) & ~creative(X0))) [input p15]
24. creative(susan) [input hypothesis]
35. ! [X0] : ((~old(X0) & ~creative(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 16]
69. ! [X0] : ((~old(X0) & ~creative(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 35]
129. ~creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 69]
130. ~creative(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
142. creative(susan) [cnf transformation 24]
143. ~creative(X0) | ~quiet(X0) [duplicate literal removal 129]
144. ~creative(X0) | quiet(X0) [duplicate literal removal 130]
269. ~creative(X0) [subsumption resolution 143,144]
272. $false [subsumption resolution 142,269]
% SZS output end Proof for 6460650152688546019323438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or tall is not kind or generous and vice versa.
If someone is both not humble and not funny then mary is both creative and not old.
If someone is either not happy or tall then lucy is both not quiet and calm.
Everyone who is either not happy or happy is both not kind and not happy.
Everyone who is both not creative and not brave is curious and vice versa.
If paul is either not creative or not old then someone is curious or creative.
Everyone who is not happy or happy is creative and vice versa.
Everyone who is both not generous and tall is either not rich or not quiet.
If lucy is either brave or not curious then alice is not curious.
If someone is both kind and wise then someone is both brave and not quiet and vice versa.
If alice is not humble then susan is either not curious or kind.
If susan is wise or calm then someone is either not tall or not rich.
Everyone who is either not tall or not wise is not strong or not curious and vice versa.
Everyone who is strong is not brave.
Everyone who is tall or quiet is generous or humble.
Mary is both rich and generous.
Someone is brave.
Mary is either not curious or tall.
Susan is old or not tall.
Someone is brave or not old.
Someone is not calm.
Someone is either rich or not curious.
Alice is not old or old. | Lucy is not happy. | entailment | (![X]:((~tall(X)<~>tall(X))<=>(~kind(X)|generous(X))))&
((?[X]:((~humble(X)&~funny(X))))=>((creative(mary)&~old(mary))))&
((?[X]:((~happy(X)<~>tall(X))))=>((~quiet(lucy)&calm(lucy))))&
(![X]:((~happy(X)<~>happy(X))=>(~kind(X)&~happy(X))))&
(![X]:((~creative(X)&~brave(X))<=>curious(X)))&
(((~creative(paul)<~>~old(paul)))=>(?[X]:((curious(X)|creative(X)))))&
(![X]:((~happy(X)|happy(X))<=>creative(X)))&
(![X]:((~generous(X)&tall(X))=>(~rich(X)<~>~quiet(X))))&
(((brave(lucy)<~>~curious(lucy)))=>(~curious(alice)))&
((?[X]:((kind(X)&wise(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
((~humble(alice))=>((~curious(susan)<~>kind(susan))))&
(((wise(susan)|calm(susan)))=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~strong(X)|~curious(X))))&
(![X]:(strong(X)=>~brave(X)))&
(![X]:((tall(X)|quiet(X))=>(generous(X)|humble(X))))&
((rich(mary)&generous(mary)))&
(?[X]:(brave(X)))&
((~curious(mary)<~>tall(mary)))&
((old(susan)|~tall(susan)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)<~>~curious(X))))&
((~old(alice)|old(alice))) | ~happy(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3996090289567447126503102
% SZS output start Proof for 3996090289567447126503102
4. ! [X0] : ((~happy(X0) <~> happy(X0)) => (~happy(X0) & ~kind(X0))) [input p3]
24. happy(lucy) [input hypothesis]
30. ! [X0] : ((~happy(X0) & ~kind(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 4]
40. ! [X0] : ((~happy(X0) & ~kind(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 30]
83. ~happy(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 40]
122. happy(lucy) [cnf transformation 24]
126. ~happy(X0) [duplicate literal removal 83]
249. $false [subsumption resolution 122,126]
% SZS output end Proof for 3996090289567447126503102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not old is not tall or not humble and vice versa. If mary is not funny or not rich then someone is patient and vice versa. Everyone who is not funny is calm or not tall. Everyone who is both not strong and not rich is not kind and vice versa. If someone is funny or not wise then fred is patient. If fred is not tall or old then fred is tall. If someone is both brave and not wise then lucy is both not quiet and quiet and vice versa. Everyone who is either not strong or not generous is not humble. Everyone who is both humble and not calm is calm and vice versa. Everyone who is either strong or not rich is both not rich and curious. If lucy is humble then fred is either not generous or not calm and vice versa. Everyone who is strong is both not patient and not kind and vice versa. Everyone who is not generous or not tall is not curious or patient. If lucy is old then someone is old and vice versa. Everyone who is both not rich and creative is not funny or not strong. Paul is not curious. Lucy is old or curious. Someone is creative. Someone is either not rich or not wise. Someone is rich or funny. Someone is either not quiet or not humble. Paul is both creative and not generous. Someone is kind or rich. | Mary is curious. | neutral | (![X]:((quiet(X)&~old(X))<=>(~tall(X)|~humble(X))))&
(((~funny(mary)|~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)=>(calm(X)|~tall(X))))&
(![X]:((~strong(X)&~rich(X))<=>~kind(X)))&
((?[X]:((funny(X)|~wise(X))))=>(patient(fred)))&
(((~tall(fred)|old(fred)))=>(tall(fred)))&
((?[X]:((brave(X)&~wise(X))))<=>((~quiet(lucy)&quiet(lucy))))&
(![X]:((~strong(X)<~>~generous(X))=>~humble(X)))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((strong(X)<~>~rich(X))=>(~rich(X)&curious(X))))&
((humble(lucy))<=>((~generous(fred)<~>~calm(fred))))&
(![X]:(strong(X)<=>(~patient(X)&~kind(X))))&
(![X]:((~generous(X)|~tall(X))=>(~curious(X)|patient(X))))&
((old(lucy))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&creative(X))=>(~funny(X)|~strong(X))))&
(~curious(paul))&
((old(lucy)|curious(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((creative(paul)&~generous(paul)))&
(?[X]:((kind(X)|rich(X)))) | curious(mary) | [] | null | 0 |
Everyone who is both not brave and not generous is either rich or not patient and vice versa. Everyone who is both not wise and kind is not humble. Everyone who is happy is patient or not happy. If alice is brave or not tall then someone is quiet. If lucy is both not quiet and creative then fred is tall and vice versa. If someone is not old or not funny then paul is calm and vice versa. Everyone who is not humble is rich or not calm and vice versa. Everyone who is either not rich or not generous is not wise and vice versa. If lucy is either not calm or not patient then john is not wise. Everyone who is not patient is not wise and vice versa. Everyone who is either not creative or not quiet is both not patient and rich. If alice is not quiet then someone is either not happy or generous. Everyone who is either quiet or patient is creative or not old and vice versa. Everyone who is both tall and not rich is not creative and vice versa. If someone is both not rich and strong then paul is creative and vice versa. Everyone who is not brave or strong is not calm and vice versa. John is not happy. Mary is not strong or not quiet. Someone is not generous. Someone is not quiet or not kind. John is either happy or wise. Mary is calm. Mary is either curious or strong. | Fred is not happy. | entailment | (![X]:((~brave(X)&~generous(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))=>~humble(X)))&
(![X]:(happy(X)=>(patient(X)|~happy(X))))&
(((brave(alice)|~tall(alice)))=>(?[X]:(quiet(X))))&
(((~quiet(lucy)&creative(lucy)))<=>(tall(fred)))&
((?[X]:((~old(X)|~funny(X))))<=>(calm(paul)))&
(![X]:(~humble(X)<=>(rich(X)|~calm(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>~wise(X)))&
(((~calm(lucy)<~>~patient(lucy)))=>(~wise(john)))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~patient(X)&rich(X))))&
((~quiet(alice))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>patient(X))<=>(creative(X)|~old(X))))&
(![X]:((tall(X)&~rich(X))<=>~creative(X)))&
((?[X]:((~rich(X)&strong(X))))<=>(creative(paul)))&
(![X]:((~brave(X)|strong(X))<=>~calm(X)))&
(~happy(john))&
((~strong(mary)|~quiet(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(john)<~>wise(john)))&
(calm(mary))&
((curious(mary)<~>strong(mary))) | ~happy(fred) | [
"p2",
"p4",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3572827619053487012232691
% SZS output start Proof for 3572827619053487012232691
3. ! [X0] : (happy(X0) => (~happy(X0) | patient(X0))) [input p2]
5. (creative(lucy) & ~quiet(lucy)) <=> tall(fred) [input p4]
11. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) => (rich(X0) & ~patient(X0))) [input p10]
13. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~old(X0) | creative(X0))) [input p12]
14. ! [X0] : ((~rich(X0) & tall(X0)) <=> ~creative(X0)) [input p13]
24. happy(fred) [input hypothesis]
29. ! [X0] : ((~happy(X0) | patient(X0)) | ~happy(X0)) [ennf transformation 3]
30. ! [X0] : (~happy(X0) | patient(X0) | ~happy(X0)) [flattening 29]
33. ! [X0] : ((rich(X0) & ~patient(X0)) | (~creative(X0) <=> ~quiet(X0))) [ennf transformation 11]
39. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | (~creative(lucy) | quiet(lucy))) [nnf transformation 5]
40. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | ~creative(lucy) | quiet(lucy)) [flattening 39]
48. ! [X0] : ((rich(X0) & ~patient(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) [nnf transformation 33]
52. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 13]
53. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 52]
54. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | (rich(X0) | ~tall(X0)))) [nnf transformation 14]
55. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | rich(X0) | ~tall(X0))) [flattening 54]
72. ~happy(X0) | patient(X0) | ~happy(X0) [cnf transformation 30]
76. ~quiet(lucy) | ~tall(fred) [cnf transformation 40]
77. creative(lucy) | ~tall(fred) [cnf transformation 40]
90. ~creative(X0) | ~patient(X0) | quiet(X0) [cnf transformation 48]
97. patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 53]
99. ~patient(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 53]
102. creative(X0) | tall(X0) [cnf transformation 55]
118. happy(fred) [cnf transformation 24]
119. ~happy(X0) | patient(X0) [duplicate literal removal 72]
135. 4 <=> tall(fred) [avatar definition]
139. 5 <=> creative(lucy) [avatar definition]
141. creative(lucy) <- (5) [avatar component clause 139]
142. ~4 | 5 [avatar split clause 77,139,135]
144. 6 <=> quiet(lucy) [avatar definition]
146. ~quiet(lucy) <- (~6) [avatar component clause 144]
147. ~4 | ~6 [avatar split clause 76,144,135]
198. ~creative(X0) | ~patient(X0) [subsumption resolution 99,90]
199. ~creative(X0) | quiet(X0) [subsumption resolution 97,90]
246. patient(fred) [resolution 119,118]
248. ~patient(X0) | tall(X0) [resolution 198,102]
365. tall(fred) [resolution 248,246]
369. 4 [avatar split clause 365,135]
373. quiet(lucy) <- (5) [resolution 141,199]
386. $false <- (5, ~6) [subsumption resolution 373,146]
387. ~5 | 6 [avatar contradiction clause 386]
388. $false [avatar sat refutation 142,147,369,387]
% SZS output end Proof for 3572827619053487012232691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is not funny or not brave. If alice is not wise or calm then someone is not quiet or old. Everyone who is both happy and curious is either not tall or not curious and vice versa. If mary is both wise and humble then someone is either old or generous. If someone is either humble or patient then someone is either not kind or not tall. If someone is both patient and not patient then lucy is not old or creative and vice versa. Everyone who is not curious or not kind is both not kind and not patient. If lucy is both creative and not calm then someone is wise and vice versa. If someone is both not old and not humble then fred is not patient or humble and vice versa. Everyone who is both not calm and funny is either kind or not tall. If alice is not calm then someone is either happy or funny and vice versa. If fred is old or quiet then someone is not brave and vice versa. If susan is generous or not funny then fred is tall. Everyone who is either not calm or calm is both not curious and happy and vice versa. If john is both calm and not humble then someone is both not happy and humble. If someone is not old then mary is not calm or not creative and vice versa. Someone is not brave. Someone is both strong and quiet. Paul is both creative and not strong. Someone is not wise. Alice is either not strong or not rich. Paul is curious or old. | Alice is not generous. | neutral | ((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)|~brave(X)))))&
(((~wise(alice)|calm(alice)))=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((happy(X)&curious(X))<=>(~tall(X)<~>~curious(X))))&
(((wise(mary)&humble(mary)))=>(?[X]:((old(X)<~>generous(X)))))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((patient(X)&~patient(X))))<=>((~old(lucy)|creative(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&~calm(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)&~humble(X))))<=>((~patient(fred)|humble(fred))))&
(![X]:((~calm(X)&funny(X))=>(kind(X)<~>~tall(X))))&
((~calm(alice))<=>(?[X]:((happy(X)<~>funny(X)))))&
(((old(fred)|quiet(fred)))<=>(?[X]:(~brave(X))))&
(((generous(susan)|~funny(susan)))=>(tall(fred)))&
(![X]:((~calm(X)<~>calm(X))<=>(~curious(X)&happy(X))))&
(((calm(john)&~humble(john)))=>(?[X]:((~happy(X)&humble(X)))))&
((?[X]:(~old(X)))<=>((~calm(mary)|~creative(mary))))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)&quiet(X))))&
((creative(paul)&~strong(paul)))&
(?[X]:(~wise(X)))&
((~strong(alice)<~>~rich(alice)))&
((curious(paul)|old(paul))) | ~generous(alice) | [] | null | 0 |
Everyone who is either brave or tall is not happy or calm and vice versa.
If john is either not creative or not calm then someone is both not creative and wise.
If someone is both not old and not strong then someone is kind and vice versa.
If someone is wise then someone is either not rich or patient.
If someone is not kind or not curious then someone is wise or not brave.
Everyone who is either not brave or old is both strong and not strong.
Everyone who is not brave is either not rich or generous and vice versa.
If someone is either not happy or calm then someone is not creative or generous.
If someone is both not strong and not patient then paul is not rich or generous.
Everyone who is both not creative and brave is both creative and brave and vice versa.
Everyone who is not quiet is both not tall and calm.
Everyone who is either not humble or not brave is either not old or humble and vice versa.
Everyone who is strong is quiet and vice versa.
If someone is rich then john is curious or humble.
Everyone who is both wise and not calm is both not tall and quiet.
Everyone who is both not creative and not generous is both wise and creative and vice versa.
Mary is not rich.
Someone is not humble or not calm.
Susan is not wise.
John is strong.
Someone is either not rich or not kind. | Paul is curious. | neutral | (![X]:((brave(X)<~>tall(X))<=>(~happy(X)|calm(X))))&
(((~creative(john)<~>~calm(john)))=>(?[X]:((~creative(X)&wise(X)))))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:(kind(X))))&
((?[X]:(wise(X)))=>(?[X]:((~rich(X)<~>patient(X)))))&
((?[X]:((~kind(X)|~curious(X))))=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:((~brave(X)<~>old(X))=>(strong(X)&~strong(X))))&
(![X]:(~brave(X)<=>(~rich(X)<~>generous(X))))&
((?[X]:((~happy(X)<~>calm(X))))=>(?[X]:((~creative(X)|generous(X)))))&
((?[X]:((~strong(X)&~patient(X))))=>((~rich(paul)|generous(paul))))&
(![X]:((~creative(X)&brave(X))<=>(creative(X)&brave(X))))&
(![X]:(~quiet(X)=>(~tall(X)&calm(X))))&
(![X]:((~humble(X)<~>~brave(X))<=>(~old(X)<~>humble(X))))&
(![X]:(strong(X)<=>quiet(X)))&
((?[X]:(rich(X)))=>((curious(john)|humble(john))))&
(![X]:((wise(X)&~calm(X))=>(~tall(X)&quiet(X))))&
(![X]:((~creative(X)&~generous(X))<=>(wise(X)&creative(X))))&
(~rich(mary))&
(?[X]:((~humble(X)|~calm(X))))&
(~wise(susan))&
(strong(john))&
(?[X]:((~rich(X)<~>~kind(X)))) | curious(paul) | [] | null | 0 |
If fred is not calm or rich then someone is tall. Everyone who is both not patient and not kind is patient. Everyone who is both not patient and happy is both not strong and not happy. If mary is both not kind and rich then someone is either not wise or generous and vice versa. Everyone who is both not old and quiet is strong and vice versa. Everyone who is tall or not creative is brave or creative. If someone is both not kind and not creative then john is both not patient and not happy and vice versa. Everyone who is both not creative and not strong is either calm or not rich and vice versa. Everyone who is brave or rich is not humble or rich. If susan is either old or kind then john is either wise or not old and vice versa. If someone is wise or not patient then someone is strong or not tall. If mary is either not happy or not kind then someone is not wise or not happy and vice versa. Everyone who is patient is tall or happy and vice versa. Everyone who is brave is kind or tall and vice versa. Everyone who is old is either curious or funny. Everyone who is either not patient or strong is not curious and vice versa. Susan is both funny and not happy. Mary is old or rich. Someone is both not tall and wise. John is both patient and strong. Susan is either wise or not wise. Mary is brave. Fred is both not tall and generous. John is not old or not rich. | Fred is not happy. | neutral | (((~calm(fred)|rich(fred)))=>(?[X]:(tall(X))))&
(![X]:((~patient(X)&~kind(X))=>patient(X)))&
(![X]:((~patient(X)&happy(X))=>(~strong(X)&~happy(X))))&
(((~kind(mary)&rich(mary)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((~old(X)&quiet(X))<=>strong(X)))&
(![X]:((tall(X)|~creative(X))=>(brave(X)|creative(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>((~patient(john)&~happy(john))))&
(![X]:((~creative(X)&~strong(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((brave(X)|rich(X))=>(~humble(X)|rich(X))))&
(((old(susan)<~>kind(susan)))<=>((wise(john)<~>~old(john))))&
((?[X]:((wise(X)|~patient(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(((~happy(mary)<~>~kind(mary)))<=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:(patient(X)<=>(tall(X)|happy(X))))&
(![X]:(brave(X)<=>(kind(X)|tall(X))))&
(![X]:(old(X)=>(curious(X)<~>funny(X))))&
(![X]:((~patient(X)<~>strong(X))<=>~curious(X)))&
((funny(susan)&~happy(susan)))&
((old(mary)|rich(mary)))&
(?[X]:((~tall(X)&wise(X))))&
((patient(john)&strong(john)))&
((wise(susan)<~>~wise(susan)))&
(brave(mary))&
((~tall(fred)&generous(fred)))&
((~old(john)|~rich(john))) | ~happy(fred) | [] | null | 0 |
If someone is both curious and kind then alice is both not wise and not calm.
If mary is either not calm or old then fred is both not kind and funny and vice versa.
Everyone who is not funny or not wise is both curious and not generous.
Everyone who is either not funny or creative is not tall and vice versa.
If someone is both not old and not kind then paul is either creative or wise and vice versa.
If someone is not old then mary is old or not humble and vice versa.
Everyone who is either patient or not happy is both not calm and not patient and vice versa.
Everyone who is both humble and not creative is strong and vice versa.
If susan is not kind or not brave then someone is both tall and not brave.
Everyone who is either patient or not tall is patient or creative and vice versa.
If someone is both not funny and not strong then paul is not rich or calm.
Everyone who is either calm or wise is not humble.
Everyone who is patient is not creative or not tall and vice versa.
If someone is both not curious and not brave then john is both not humble and not brave and vice versa.
Everyone who is both funny and wise is either not brave or strong.
If susan is both happy and not calm then paul is either old or quiet and vice versa.
Someone is both wise and strong.
Someone is not curious.
Someone is both not kind and humble.
Fred is wise or curious.
Paul is not tall or humble.
Paul is curious. | John is not patient. | contradiction | ((?[X]:((curious(X)&kind(X))))=>((~wise(alice)&~calm(alice))))&
(((~calm(mary)<~>old(mary)))<=>((~kind(fred)&funny(fred))))&
(![X]:((~funny(X)|~wise(X))=>(curious(X)&~generous(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~tall(X)))&
((?[X]:((~old(X)&~kind(X))))<=>((creative(paul)<~>wise(paul))))&
((?[X]:(~old(X)))<=>((old(mary)|~humble(mary))))&
(![X]:((patient(X)<~>~happy(X))<=>(~calm(X)&~patient(X))))&
(![X]:((humble(X)&~creative(X))<=>strong(X)))&
(((~kind(susan)|~brave(susan)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)<~>~tall(X))<=>(patient(X)|creative(X))))&
((?[X]:((~funny(X)&~strong(X))))=>((~rich(paul)|calm(paul))))&
(![X]:((calm(X)<~>wise(X))=>~humble(X)))&
(![X]:(patient(X)<=>(~creative(X)|~tall(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>((~humble(john)&~brave(john))))&
(![X]:((funny(X)&wise(X))=>(~brave(X)<~>strong(X))))&
(((happy(susan)&~calm(susan)))<=>((old(paul)<~>quiet(paul))))&
(?[X]:((wise(X)&strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~kind(X)&humble(X))))&
((wise(fred)|curious(fred)))&
((~tall(paul)|humble(paul)))&
(curious(paul)) | ~patient(john) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8491050945477653412109938
% SZS output start Proof for 8491050945477653412109938
10. ! [X0] : ((patient(X0) <~> ~tall(X0)) <=> (creative(X0) | patient(X0))) [input p9]
13. ! [X0] : (patient(X0) <=> (~tall(X0) | ~creative(X0))) [input p12]
23. ~patient(john) [input hypothesis]
50. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~creative(X0) & ~patient(X0))) & ((creative(X0) | patient(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [nnf transformation 10]
51. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~creative(X0) & ~patient(X0))) & (creative(X0) | patient(X0) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [flattening 50]
53. ! [X0] : ((patient(X0) | (tall(X0) & creative(X0))) & ((~tall(X0) | ~creative(X0)) | ~patient(X0))) [nnf transformation 13]
54. ! [X0] : ((patient(X0) | (tall(X0) & creative(X0))) & (~tall(X0) | ~creative(X0) | ~patient(X0))) [flattening 53]
108. ~tall(X0) | patient(X0) | ~creative(X0) [cnf transformation 51]
109. tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
113. ~tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 54]
114. patient(X0) | creative(X0) [cnf transformation 54]
115. patient(X0) | tall(X0) [cnf transformation 54]
136. ~patient(john) [cnf transformation 23]
138. ~patient(X0) | tall(X0) [duplicate literal removal 109]
236. tall(X0) [subsumption resolution 115,138]
237. ~patient(X0) | ~creative(X0) [subsumption resolution 113,236]
287. creative(john) [resolution 114,136]
324. patient(X1) | ~creative(X1) [resolution 108,236]
325. ~creative(X1) [subsumption resolution 324,237]
342. $false [resolution 325,287]
% SZS output end Proof for 8491050945477653412109938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or not kind then someone is curious or funny and vice versa.
Everyone who is either not quiet or not creative is both not strong and not kind and vice versa.
Everyone who is calm is not old or not calm and vice versa.
Everyone who is not generous is both not calm and curious and vice versa.
If someone is not humble then alice is old and vice versa.
Everyone who is either not generous or not strong is funny or rich and vice versa.
Everyone who is not wise is either old or not strong and vice versa.
If someone is both not creative and not strong then mary is not happy and vice versa.
If someone is both not old and wise then someone is both not curious and wise and vice versa.
If alice is both humble and tall then someone is not calm.
Everyone who is happy is calm or not generous and vice versa.
Everyone who is not old is either tall or not tall.
If lucy is kind or rich then lucy is either strong or not creative.
Everyone who is not patient or not humble is tall or not funny.
Everyone who is either brave or not strong is brave and vice versa.
Someone is both quiet and not patient.
John is either funny or kind.
Someone is both not old and not kind. | Lucy is not calm. | contradiction | ((?[X]:((~humble(X)<~>~kind(X))))<=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~strong(X)&~kind(X))))&
(![X]:(calm(X)<=>(~old(X)|~calm(X))))&
(![X]:(~generous(X)<=>(~calm(X)&curious(X))))&
((?[X]:(~humble(X)))<=>(old(alice)))&
(![X]:((~generous(X)<~>~strong(X))<=>(funny(X)|rich(X))))&
(![X]:(~wise(X)<=>(old(X)<~>~strong(X))))&
((?[X]:((~creative(X)&~strong(X))))<=>(~happy(mary)))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((~curious(X)&wise(X)))))&
(((humble(alice)&tall(alice)))=>(?[X]:(~calm(X))))&
(![X]:(happy(X)<=>(calm(X)|~generous(X))))&
(![X]:(~old(X)=>(tall(X)<~>~tall(X))))&
(((kind(lucy)|rich(lucy)))=>((strong(lucy)<~>~creative(lucy))))&
(![X]:((~patient(X)|~humble(X))=>(tall(X)|~funny(X))))&
(![X]:((brave(X)<~>~strong(X))<=>brave(X)))&
(?[X]:((quiet(X)&~patient(X))))&
((funny(john)<~>kind(john)))&
(?[X]:((~old(X)&~kind(X)))) | ~calm(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 99100450292447934717164
% SZS output start Proof for 99100450292447934717164
3. ! [X0] : (calm(X0) <=> (~calm(X0) | ~old(X0))) [input p2]
19. ~calm(lucy) [input hypothesis]
35. ! [X0] : ((calm(X0) | (calm(X0) & old(X0))) & ((~calm(X0) | ~old(X0)) | ~calm(X0))) [nnf transformation 3]
36. ! [X0] : ((calm(X0) | (calm(X0) & old(X0))) & (~calm(X0) | ~old(X0) | ~calm(X0))) [flattening 35]
81. calm(X0) | calm(X0) [cnf transformation 36]
126. ~calm(lucy) [cnf transformation 19]
130. calm(X0) [duplicate literal removal 81]
248. $false [subsumption resolution 126,130]
% SZS output end Proof for 99100450292447934717164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is old or not generous then paul is either funny or not quiet.
Everyone who is not funny is patient or tall.
Everyone who is either not creative or not quiet is either rich or not brave and vice versa.
If someone is generous then someone is both not creative and old.
Everyone who is generous or not funny is either not calm or not humble and vice versa.
Everyone who is happy or brave is both not creative and not rich and vice versa.
Everyone who is happy is not funny or kind.
Everyone who is both not brave and generous is strong or not rich.
If alice is both brave and quiet then someone is not humble or not happy and vice versa.
Everyone who is both not rich and not kind is both not happy and calm.
Everyone who is not patient is both quiet and not creative and vice versa.
Everyone who is both not wise and not curious is not happy or not rich.
If someone is happy then someone is either not curious or not generous and vice versa.
If someone is both not curious and humble then someone is both not kind and wise.
If someone is quiet or rich then someone is either happy or kind.
If fred is both not patient and not happy then someone is either not strong or tall.
John is wise.
Someone is either not quiet or quiet.
Someone is either not rich or not calm.
Someone is either generous or wise. | Paul is brave. | entailment | (((old(lucy)|~generous(lucy)))=>((funny(paul)<~>~quiet(paul))))&
(![X]:(~funny(X)=>(patient(X)|tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(rich(X)<~>~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((generous(X)|~funny(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((happy(X)|brave(X))<=>(~creative(X)&~rich(X))))&
(![X]:(happy(X)=>(~funny(X)|kind(X))))&
(![X]:((~brave(X)&generous(X))=>(strong(X)|~rich(X))))&
(((brave(alice)&quiet(alice)))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~rich(X)&~kind(X))=>(~happy(X)&calm(X))))&
(![X]:(~patient(X)<=>(quiet(X)&~creative(X))))&
(![X]:((~wise(X)&~curious(X))=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:((happy(X)<~>kind(X)))))&
(((~patient(fred)&~happy(fred)))=>(?[X]:((~strong(X)<~>tall(X)))))&
(wise(john))&
(?[X]:((~quiet(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>wise(X)))) | brave(paul) | [
"p2",
"p5",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1114909025155249026861675
% SZS output start Proof for 1114909025155249026861675
3. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p2]
6. ! [X0] : ((brave(X0) | happy(X0)) <=> (~rich(X0) & ~creative(X0))) [input p5]
9. (quiet(alice) & brave(alice)) <=> ? [X0] : (~happy(X0) | ~humble(X0)) [input p8]
10. ! [X0] : ((~kind(X0) & ~rich(X0)) => (calm(X0) & ~happy(X0))) [input p9]
15. ? [X0] : (rich(X0) | quiet(X0)) => ? [X0] : (happy(X0) <~> kind(X0)) [input p14]
21. ~brave(paul) [input hypothesis]
25. ? [X0] : (rich(X0) | quiet(X0)) => ? [X1] : (happy(X1) <~> kind(X1)) [rectify 15]
35. ! [X0] : ((calm(X0) & ~happy(X0)) | (kind(X0) | rich(X0))) [ennf transformation 10]
36. ! [X0] : ((calm(X0) & ~happy(X0)) | kind(X0) | rich(X0)) [flattening 35]
42. ? [X1] : (happy(X1) <~> kind(X1)) | ! [X0] : (~rich(X0) & ~quiet(X0)) [ennf transformation 25]
46. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 3]
52. ! [X0] : (((brave(X0) | happy(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 6]
53. ! [X0] : ((brave(X0) | happy(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 52]
54. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X0] : (~happy(X0) | ~humble(X0)) | (~quiet(alice) | ~brave(alice))) [nnf transformation 9]
55. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X0] : (~happy(X0) | ~humble(X0)) | ~quiet(alice) | ~brave(alice)) [flattening 54]
56. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & (? [X1] : (~happy(X1) | ~humble(X1)) | ~quiet(alice) | ~brave(alice)) [rectify 55]
57. ? [X1] : (~happy(X1) | ~humble(X1)) => (~happy(sK1) | ~humble(sK1)) [choice axiom]
58. ((quiet(alice) & brave(alice)) | ! [X0] : (happy(X0) & humble(X0))) & ((~happy(sK1) | ~humble(sK1)) | ~quiet(alice) | ~brave(alice)) [skolemisation 56,57]
67. ? [X1] : ((~kind(X1) | ~happy(X1)) & (kind(X1) | happy(X1))) | ! [X0] : (~rich(X0) & ~quiet(X0)) [nnf transformation 42]
68. ? [X0] : ((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | ! [X1] : (~rich(X1) & ~quiet(X1)) [rectify 67]
69. ? [X0] : ((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) => ((~kind(sK5) | ~happy(sK5)) & (kind(sK5) | happy(sK5))) [choice axiom]
70. ((~kind(sK5) | ~happy(sK5)) & (kind(sK5) | happy(sK5))) | ! [X1] : (~rich(X1) & ~quiet(X1)) [skolemisation 68,69]
88. ~brave(X0) | rich(X0) | ~quiet(X0) | creative(X0) [cnf transformation 46]
95. brave(X0) | creative(X0) | rich(X0) | quiet(X0) [cnf transformation 46]
104. ~happy(X0) | ~creative(X0) [cnf transformation 53]
105. ~brave(X0) | ~creative(X0) [cnf transformation 53]
106. ~happy(X0) | ~rich(X0) [cnf transformation 53]
107. ~brave(X0) | ~rich(X0) [cnf transformation 53]
113. brave(alice) | happy(X0) [cnf transformation 58]
115. quiet(alice) | happy(X0) [cnf transformation 58]
116. ~happy(X0) | kind(X0) | rich(X0) [cnf transformation 36]
128. ~kind(sK5) | ~happy(sK5) | ~quiet(X1) [cnf transformation 70]
129. ~kind(sK5) | ~happy(sK5) | ~rich(X1) [cnf transformation 70]
139. ~brave(paul) [cnf transformation 21]
175. 8 <=> ! [X0] : happy(X0) [avatar definition]
176. happy(X0) <- (8) [avatar component clause 175]
178. 9 <=> quiet(alice) [avatar definition]
181. 8 | 9 [avatar split clause 115,178,175]
187. 11 <=> brave(alice) [avatar definition]
189. brave(alice) <- (11) [avatar component clause 187]
190. 8 | 11 [avatar split clause 113,187,175]
201. ~happy(X0) | kind(X0) [subsumption resolution 116,106]
240. ~happy(sK5) | ~rich(X1) [subsumption resolution 129,201]
242. 23 <=> ! [X1] : ~rich(X1) [avatar definition]
243. ~rich(X1) <- (23) [avatar component clause 242]
245. 24 <=> happy(sK5) [avatar definition]
247. ~happy(sK5) <- (~24) [avatar component clause 245]
248. 23 | ~24 [avatar split clause 240,245,242]
249. ~happy(sK5) | ~quiet(X1) [subsumption resolution 128,201]
251. 25 <=> ! [X1] : ~quiet(X1) [avatar definition]
252. ~quiet(X1) <- (25) [avatar component clause 251]
253. 25 | ~24 [avatar split clause 249,245,251]
313. $false <- (8, ~24) [subsumption resolution 247,176]
314. ~8 | 24 [avatar contradiction clause 313]
318. ~creative(alice) <- (11) [resolution 105,189]
320. ~rich(alice) <- (11) [resolution 107,189]
351. rich(alice) | ~quiet(alice) | creative(alice) <- (11) [resolution 88,189]
352. ~quiet(alice) | creative(alice) <- (11) [subsumption resolution 351,320]
356. ~quiet(alice) <- (11) [subsumption resolution 352,318]
357. ~9 | ~11 [avatar split clause 356,187,178]
362. ~creative(X3) <- (8) [resolution 176,104]
373. creative(paul) | rich(paul) | quiet(paul) [resolution 95,139]
383. rich(paul) | quiet(paul) <- (8) [subsumption resolution 373,362]
384. quiet(paul) <- (8, 23) [subsumption resolution 383,243]
387. $false <- (8, 23, 25) [subsumption resolution 384,252]
388. ~8 | ~23 | ~25 [avatar contradiction clause 387]
393. $false [avatar sat refutation 181,190,248,253,314,357,388]
% SZS output end Proof for 1114909025155249026861675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not happy is either funny or not rich and vice versa. Everyone who is generous is curious or not creative and vice versa. Everyone who is either humble or old is both not humble and not patient and vice versa. If susan is quiet or not strong then someone is not kind or not old. Everyone who is not kind is rich or not calm and vice versa. If paul is both not happy and quiet then someone is happy. If paul is happy or calm then someone is either strong or not old and vice versa. If susan is either not tall or brave then someone is not strong or kind. Everyone who is either not happy or generous is not humble. Everyone who is strong or tall is funny and vice versa. Everyone who is both not brave and not calm is both creative and not patient and vice versa. Everyone who is not quiet is both not funny and not strong. Everyone who is both not wise and quiet is generous or not humble and vice versa. If lucy is generous or not tall then paul is either generous or wise. If fred is both not happy and funny then someone is both calm and patient and vice versa. If mary is rich or not happy then someone is either not rich or not patient and vice versa. Lucy is not strong or generous. Alice is both not strong and creative. Paul is both not wise and not happy. Someone is either humble or calm. Susan is either happy or strong. Someone is either curious or old. Someone is either funny or not brave. | Lucy is not tall. | neutral | (![X]:((~strong(X)<~>~happy(X))<=>(funny(X)<~>~rich(X))))&
(![X]:(generous(X)<=>(curious(X)|~creative(X))))&
(![X]:((humble(X)<~>old(X))<=>(~humble(X)&~patient(X))))&
(((quiet(susan)|~strong(susan)))=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:(~kind(X)<=>(rich(X)|~calm(X))))&
(((~happy(paul)&quiet(paul)))=>(?[X]:(happy(X))))&
(((happy(paul)|calm(paul)))<=>(?[X]:((strong(X)<~>~old(X)))))&
(((~tall(susan)<~>brave(susan)))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~happy(X)<~>generous(X))=>~humble(X)))&
(![X]:((strong(X)|tall(X))<=>funny(X)))&
(![X]:((~brave(X)&~calm(X))<=>(creative(X)&~patient(X))))&
(![X]:(~quiet(X)=>(~funny(X)&~strong(X))))&
(![X]:((~wise(X)&quiet(X))<=>(generous(X)|~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>((generous(paul)<~>wise(paul))))&
(((~happy(fred)&funny(fred)))<=>(?[X]:((calm(X)&patient(X)))))&
(((rich(mary)|~happy(mary)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
((~strong(lucy)|generous(lucy)))&
((~strong(alice)&creative(alice)))&
((~wise(paul)&~happy(paul)))&
(?[X]:((humble(X)<~>calm(X))))&
((happy(susan)<~>strong(susan)))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((funny(X)<~>~brave(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either not tall or calm is both tall and wise.
Everyone who is either strong or not patient is both creative and not brave and vice versa.
If paul is either curious or old then susan is happy and vice versa.
Everyone who is both tall and not happy is not old or not rich.
Everyone who is not funny or not generous is happy or not wise.
If lucy is not humble or wise then paul is either not rich or not generous and vice versa.
If someone is happy or humble then paul is both not wise and wise.
Everyone who is not creative is rich.
If someone is either creative or not generous then paul is not happy or wise and vice versa.
Everyone who is funny is both quiet and generous.
If paul is kind then someone is either not patient or not wise.
Everyone who is calm is either patient or humble.
If susan is either not funny or curious then mary is either wise or not kind and vice versa.
If paul is rich then fred is either tall or patient.
If someone is not quiet or creative then fred is strong.
If alice is not generous or calm then someone is not creative or funny and vice versa.
Alice is either not patient or not calm.
Fred is both brave and generous.
Susan is not calm.
Someone is not brave or curious.
Fred is tall.
Lucy is both not humble and not kind.
Susan is not tall or not happy.
Someone is not brave or not wise. | Alice is tall. | entailment | (![X]:((~tall(X)<~>calm(X))=>(tall(X)&wise(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(creative(X)&~brave(X))))&
(((curious(paul)<~>old(paul)))<=>(happy(susan)))&
(![X]:((tall(X)&~happy(X))=>(~old(X)|~rich(X))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)|~wise(X))))&
(((~humble(lucy)|wise(lucy)))<=>((~rich(paul)<~>~generous(paul))))&
((?[X]:((happy(X)|humble(X))))=>((~wise(paul)&wise(paul))))&
(![X]:(~creative(X)=>rich(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~happy(paul)|wise(paul))))&
(![X]:(funny(X)=>(quiet(X)&generous(X))))&
((kind(paul))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
(((~funny(susan)<~>curious(susan)))<=>((wise(mary)<~>~kind(mary))))&
((rich(paul))=>((tall(fred)<~>patient(fred))))&
((?[X]:((~quiet(X)|creative(X))))=>(strong(fred)))&
(((~generous(alice)|calm(alice)))<=>(?[X]:((~creative(X)|funny(X)))))&
((~patient(alice)<~>~calm(alice)))&
((brave(fred)&generous(fred)))&
(~calm(susan))&
(?[X]:((~brave(X)|curious(X))))&
(tall(fred))&
((~humble(lucy)&~kind(lucy)))&
((~tall(susan)|~happy(susan)))&
(?[X]:((~brave(X)|~wise(X)))) | tall(alice) | [
"p0",
"p6",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2600771253874689080472427
% SZS output start Proof for 2600771253874689080472427
1. ! [X0] : ((~tall(X0) <~> calm(X0)) => (wise(X0) & tall(X0))) [input p0]
7. ? [X0] : (humble(X0) | happy(X0)) => (wise(paul) & ~wise(paul)) [input p6]
12. ! [X0] : (calm(X0) => (patient(X0) <~> humble(X0))) [input p11]
17. ~patient(alice) <~> ~calm(alice) [input p16]
25. ~tall(alice) [input hypothesis]
28. ! [X0] : ((wise(X0) & tall(X0)) | (~tall(X0) <=> calm(X0))) [ennf transformation 1]
33. (wise(paul) & ~wise(paul)) | ! [X0] : (~humble(X0) & ~happy(X0)) [ennf transformation 7]
37. ! [X0] : ((patient(X0) <~> humble(X0)) | ~calm(X0)) [ennf transformation 12]
40. ! [X0] : ((wise(X0) & tall(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) [nnf transformation 28]
54. ! [X0] : (((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ~calm(X0)) [nnf transformation 37]
62. (calm(alice) | patient(alice)) & (~calm(alice) | ~patient(alice)) [nnf transformation 17]
67. tall(X0) | calm(X0) | tall(X0) [cnf transformation 40]
91. ~wise(paul) | ~humble(X0) [cnf transformation 33]
93. wise(paul) | ~humble(X0) [cnf transformation 33]
104. ~calm(X0) | patient(X0) | humble(X0) [cnf transformation 54]
121. ~calm(alice) | ~patient(alice) [cnf transformation 62]
132. ~tall(alice) [cnf transformation 25]
133. calm(X0) | tall(X0) [duplicate literal removal 67]
173. 8 <=> ! [X0] : ~humble(X0) [avatar definition]
174. ~humble(X0) <- (8) [avatar component clause 173]
176. 9 <=> wise(paul) [avatar definition]
179. 8 | 9 [avatar split clause 93,176,173]
184. 8 | ~9 [avatar split clause 91,176,173]
274. 29 <=> calm(alice) [avatar definition]
275. ~calm(alice) <- (~29) [avatar component clause 274]
276. calm(alice) <- (29) [avatar component clause 274]
293. 33 <=> patient(alice) [avatar definition]
294. ~patient(alice) <- (~33) [avatar component clause 293]
297. ~33 | ~29 [avatar split clause 121,274,293]
350. patient(alice) | humble(alice) <- (29) [resolution 104,276]
352. humble(alice) <- (29, ~33) [subsumption resolution 350,294]
353. $false <- (8, 29, ~33) [subsumption resolution 352,174]
354. ~8 | ~29 | 33 [avatar contradiction clause 353]
356. tall(alice) <- (~29) [resolution 275,133]
357. $false <- (~29) [subsumption resolution 356,132]
358. 29 [avatar contradiction clause 357]
359. $false [avatar sat refutation 179,184,297,354,358]
% SZS output end Proof for 2600771253874689080472427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.045 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich or not humble then mary is either happy or creative and vice versa.
If alice is either not old or not funny then paul is both wise and not creative.
Everyone who is not calm is either rich or not calm.
If someone is calm or not generous then fred is not brave or happy.
Everyone who is rich or not strong is either kind or generous and vice versa.
If someone is either old or wise then someone is either tall or not rich.
Everyone who is either happy or not kind is both not rich and not strong and vice versa.
Everyone who is not creative or not quiet is rich or not calm and vice versa.
If someone is generous or brave then someone is both not kind and happy.
Everyone who is not strong or not brave is both quiet and curious and vice versa.
If paul is both not creative and not humble then mary is either rich or calm.
If paul is not wise or creative then someone is both not wise and calm and vice versa.
Everyone who is quiet is both not quiet and not rich and vice versa.
Everyone who is not brave is not rich.
If someone is either brave or calm then someone is both not strong and not quiet and vice versa.
If mary is humble or patient then john is patient or humble and vice versa.
Lucy is either curious or tall.
Someone is both patient and humble.
Someone is humble.
Someone is not generous.
Mary is funny or not strong.
Someone is either not brave or not generous. | John is curious. | neutral | (((rich(john)|~humble(john)))<=>((happy(mary)<~>creative(mary))))&
(((~old(alice)<~>~funny(alice)))=>((wise(paul)&~creative(paul))))&
(![X]:(~calm(X)=>(rich(X)<~>~calm(X))))&
((?[X]:((calm(X)|~generous(X))))=>((~brave(fred)|happy(fred))))&
(![X]:((rich(X)|~strong(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((old(X)<~>wise(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((happy(X)<~>~kind(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(rich(X)|~calm(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((~strong(X)|~brave(X))<=>(quiet(X)&curious(X))))&
(((~creative(paul)&~humble(paul)))=>((rich(mary)<~>calm(mary))))&
(((~wise(paul)|creative(paul)))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)&~rich(X))))&
(![X]:(~brave(X)=>~rich(X)))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(((humble(mary)|patient(mary)))<=>((patient(john)|humble(john))))&
((curious(lucy)<~>tall(lucy)))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:(humble(X)))&
(?[X]:(~generous(X)))&
((funny(mary)|~strong(mary)))&
(?[X]:((~brave(X)<~>~generous(X)))) | curious(john) | [] | null | 0 |
Everyone who is both not kind and not generous is quiet or not calm and vice versa.
If someone is both not wise and rich then someone is both strong and rich.
If john is both generous and curious then alice is not kind or not creative.
Everyone who is both happy and wise is curious or not old and vice versa.
If fred is either not strong or not quiet then john is either curious or humble.
Everyone who is curious or calm is both not kind and not quiet.
If someone is patient then someone is both brave and curious and vice versa.
If someone is either not happy or wise then someone is funny or strong.
If paul is not wise or not calm then someone is either not old or old and vice versa.
If someone is both quiet and rich then fred is both not patient and kind and vice versa.
Everyone who is not calm is not wise.
If someone is not patient then someone is generous or happy.
Everyone who is both not creative and rich is calm and vice versa.
Everyone who is both not brave and not generous is rich or curious and vice versa.
If someone is brave or not humble then someone is not humble or not calm.
Everyone who is both not wise and happy is either not wise or not humble and vice versa.
Someone is both humble and not patient.
Paul is not strong.
Someone is not generous.
Someone is calm or not curious. | Alice is not curious. | entailment | (![X]:((~kind(X)&~generous(X))<=>(quiet(X)|~calm(X))))&
((?[X]:((~wise(X)&rich(X))))=>(?[X]:((strong(X)&rich(X)))))&
(((generous(john)&curious(john)))=>((~kind(alice)|~creative(alice))))&
(![X]:((happy(X)&wise(X))<=>(curious(X)|~old(X))))&
(((~strong(fred)<~>~quiet(fred)))=>((curious(john)<~>humble(john))))&
(![X]:((curious(X)|calm(X))=>(~kind(X)&~quiet(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((funny(X)|strong(X)))))&
(((~wise(paul)|~calm(paul)))<=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((quiet(X)&rich(X))))<=>((~patient(fred)&kind(fred))))&
(![X]:(~calm(X)=>~wise(X)))&
((?[X]:(~patient(X)))=>(?[X]:((generous(X)|happy(X)))))&
(![X]:((~creative(X)&rich(X))<=>calm(X)))&
(![X]:((~brave(X)&~generous(X))<=>(rich(X)|curious(X))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)<~>~humble(X))))&
(?[X]:((humble(X)&~patient(X))))&
(~strong(paul))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)|~curious(X)))) | ~curious(alice) | [
"p0",
"p3",
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2687765291288558969761063
% SZS output start Proof for 2687765291288558969761063
1. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (~calm(X0) | quiet(X0))) [input p0]
4. ! [X0] : ((wise(X0) & happy(X0)) <=> (~old(X0) | curious(X0))) [input p3]
6. ! [X0] : ((calm(X0) | curious(X0)) => (~quiet(X0) & ~kind(X0))) [input p5]
11. ! [X0] : (~calm(X0) => ~wise(X0)) [input p10]
14. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (curious(X0) | rich(X0))) [input p13]
21. curious(alice) [input hypothesis]
32. ! [X0] : ((~quiet(X0) & ~kind(X0)) | (~calm(X0) & ~curious(X0))) [ennf transformation 6]
33. ! [X0] : (~wise(X0) | calm(X0)) [ennf transformation 11]
36. ! [X0] : (((~generous(X0) & ~kind(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 1]
37. ! [X0] : (((~generous(X0) & ~kind(X0)) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | generous(X0) | kind(X0))) [flattening 36]
41. ! [X0] : (((wise(X0) & happy(X0)) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | (~wise(X0) | ~happy(X0)))) [nnf transformation 4]
42. ! [X0] : (((wise(X0) & happy(X0)) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ~wise(X0) | ~happy(X0))) [flattening 41]
64. ! [X0] : (((~generous(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | (generous(X0) | brave(X0)))) [nnf transformation 14]
65. ! [X0] : (((~generous(X0) & ~brave(X0)) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | generous(X0) | brave(X0))) [flattening 64]
77. ~calm(X0) | quiet(X0) | generous(X0) | kind(X0) [cnf transformation 37]
79. ~kind(X0) | calm(X0) [cnf transformation 37]
88. ~curious(X0) | wise(X0) [cnf transformation 42]
95. ~kind(X0) | ~calm(X0) [cnf transformation 32]
96. ~curious(X0) | ~quiet(X0) [cnf transformation 32]
111. ~wise(X0) | calm(X0) [cnf transformation 33]
120. ~curious(X0) | ~generous(X0) [cnf transformation 65]
134. curious(alice) [cnf transformation 21]
185. ~kind(X0) [subsumption resolution 95,79]
270. wise(alice) [resolution 88,134]
272. ~quiet(alice) [resolution 96,134]
275. calm(alice) [resolution 111,270]
286. ~generous(alice) [resolution 120,134]
327. quiet(alice) | generous(alice) | kind(alice) [resolution 77,275]
329. generous(alice) | kind(alice) [subsumption resolution 327,272]
330. kind(alice) [subsumption resolution 329,286]
331. $false [subsumption resolution 330,185]
% SZS output end Proof for 2687765291288558969761063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is brave or wise then alice is both generous and not happy.
If mary is either not generous or not old then alice is both not patient and not quiet and vice versa.
If alice is not strong then someone is creative.
Everyone who is not tall or not kind is not creative and vice versa.
If john is both wise and not brave then mary is both calm and humble.
Everyone who is humble or quiet is wise or happy.
If someone is both not humble and not wise then someone is not old or not tall and vice versa.
Everyone who is not strong or not creative is both not generous and creative and vice versa.
Everyone who is not quiet is both calm and not curious.
If john is both not happy and calm then mary is both happy and wise.
Everyone who is both generous and not rich is not kind or patient.
Everyone who is either wise or generous is kind.
Everyone who is either brave or patient is both not funny and funny and vice versa.
Everyone who is both not curious and old is not tall.
If fred is happy or not happy then mary is either not old or brave.
Everyone who is not funny is either not happy or not rich and vice versa.
Someone is both tall and not quiet.
Someone is not wise.
Someone is both not funny and not wise.
John is not tall or rich.
Someone is both not funny and rich.
Someone is both not brave and not rich.
Mary is patient or happy. | Mary is calm. | neutral | (((brave(lucy)|wise(lucy)))=>((generous(alice)&~happy(alice))))&
(((~generous(mary)<~>~old(mary)))<=>((~patient(alice)&~quiet(alice))))&
((~strong(alice))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|~kind(X))<=>~creative(X)))&
(((wise(john)&~brave(john)))=>((calm(mary)&humble(mary))))&
(![X]:((humble(X)|quiet(X))=>(wise(X)|happy(X))))&
((?[X]:((~humble(X)&~wise(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~strong(X)|~creative(X))<=>(~generous(X)&creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~curious(X))))&
(((~happy(john)&calm(john)))=>((happy(mary)&wise(mary))))&
(![X]:((generous(X)&~rich(X))=>(~kind(X)|patient(X))))&
(![X]:((wise(X)<~>generous(X))=>kind(X)))&
(![X]:((brave(X)<~>patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((~curious(X)&old(X))=>~tall(X)))&
(((happy(fred)|~happy(fred)))=>((~old(mary)<~>brave(mary))))&
(![X]:(~funny(X)<=>(~happy(X)<~>~rich(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~funny(X)&~wise(X))))&
((~tall(john)|rich(john)))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:((~brave(X)&~rich(X))))&
((patient(mary)|happy(mary))) | calm(mary) | [] | null | 0 |
If someone is calm then alice is both creative and tall and vice versa. Everyone who is both not patient and funny is either brave or funny. Everyone who is either tall or not generous is not calm or not happy. Everyone who is either not humble or strong is rich. Everyone who is quiet or not patient is creative. If john is not patient then someone is both wise and not kind and vice versa. If fred is not humble then someone is curious. If alice is not patient then fred is either not strong or not quiet and vice versa. Everyone who is strong or not rich is both creative and not patient. Everyone who is both not happy and quiet is either not old or not happy and vice versa. Everyone who is both funny and not creative is not quiet or not wise and vice versa. If someone is quiet or not wise then someone is both not old and not rich and vice versa. Everyone who is either strong or old is not kind or humble. Everyone who is quiet is old or not funny and vice versa. If someone is either not curious or kind then paul is both not calm and not creative and vice versa. Mary is not calm or not funny. Fred is either not old or humble. Someone is not happy. Someone is not creative or not patient. Fred is patient. | Fred is old. | contradiction | ((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
((~calm(mary)|~funny(mary)))&
((~old(fred)<~>humble(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)|~patient(X))))&
(patient(fred)) | old(fred) | [
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8453510385721498574791309
% SZS output start Proof for 8453510385721498574791309
9. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p10]
12. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p11]
14. ! [X0] : (quiet(X0) <=> (~funny(X0) | old(X0))) [input p13]
21. old(fred) [input hypothesis]
22. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 12]
30. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 9]
48. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 48]
50. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 11]
51. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 50]
52. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 22]
53. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 52]
54. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK3) | quiet(sK3)) [choice axiom]
55. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK4) & ~old(sK4)) [choice axiom]
56. ((~wise(sK3) | quiet(sK3)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK4) & ~old(sK4)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 53,55,54]
58. ! [X0] : ((quiet(X0) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ~quiet(X0))) [nnf transformation 14]
59. ! [X0] : ((quiet(X0) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ~quiet(X0))) [flattening 58]
90. rich(X0) | creative(X0) [cnf transformation 30]
94. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 49]
95. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
102. ~creative(X0) | quiet(X0) [cnf transformation 51]
104. ~old(sK4) | ~quiet(X3) [cnf transformation 56]
106. ~rich(sK4) | ~quiet(X3) [cnf transformation 56]
112. ~old(X0) | quiet(X0) [cnf transformation 59]
126. old(fred) [cnf transformation 21]
127. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 94]
128. ~happy(X0) | old(X0) [duplicate literal removal 95]
176. 11 <=> quiet(fred) [avatar definition]
178. quiet(fred) <- (11) [avatar component clause 176]
191. ~quiet(X0) | old(X0) [subsumption resolution 127,128]
208. 18 <=> rich(sK4) [avatar definition]
210. ~rich(sK4) <- (~18) [avatar component clause 208]
213. 19 <=> ! [X3] : ~quiet(X3) [avatar definition]
214. ~quiet(X3) <- (19) [avatar component clause 213]
215. 19 | ~18 [avatar split clause 106,208,213]
217. 20 <=> old(sK4) [avatar definition]
219. ~old(sK4) <- (~20) [avatar component clause 217]
221. 19 | ~20 [avatar split clause 104,217,213]
260. 29 <=> old(fred) [avatar definition]
262. old(fred) <- (29) [avatar component clause 260]
274. 29 [avatar split clause 126,260]
289. quiet(fred) <- (29) [resolution 112,262]
292. 11 | ~29 [avatar split clause 289,260,176]
323. $false <- (11, 19) [resolution 214,178]
326. ~11 | ~19 [avatar contradiction clause 323]
328. creative(sK4) <- (~18) [resolution 210,90]
339. quiet(sK4) <- (~18) [resolution 328,102]
378. old(sK4) <- (~18) [resolution 339,191]
380. $false <- (~18, ~20) [subsumption resolution 378,219]
381. 18 | 20 [avatar contradiction clause 380]
382. $false [avatar sat refutation 215,221,274,292,326,381]
% SZS output end Proof for 8453510385721498574791309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and brave is not tall and vice versa.
Everyone who is funny is both not curious and not quiet.
Everyone who is creative or rich is happy and vice versa.
Everyone who is not old or humble is not kind and vice versa.
Everyone who is not calm or humble is not creative or strong and vice versa.
If fred is both happy and patient then someone is humble or not wise and vice versa.
If john is either humble or happy then susan is both not brave and not rich.
Everyone who is either funny or rich is either not creative or not funny.
Everyone who is both patient and rich is both strong and humble.
Everyone who is not funny is not creative or tall and vice versa.
Everyone who is humble is both brave and not old.
Everyone who is both not brave and not wise is both rich and not quiet.
Everyone who is happy or patient is both not humble and humble and vice versa.
Everyone who is either tall or curious is calm or creative and vice versa.
If paul is not tall then someone is happy or brave.
If someone is not humble then lucy is brave or not humble and vice versa.
Someone is not calm.
Someone is both not funny and not rich.
Fred is kind or wise.
Someone is strong or not humble.
Fred is not funny or not old. | John is not brave. | neutral | (![X]:((rich(X)&brave(X))<=>~tall(X)))&
(![X]:(funny(X)=>(~curious(X)&~quiet(X))))&
(![X]:((creative(X)|rich(X))<=>happy(X)))&
(![X]:((~old(X)|humble(X))<=>~kind(X)))&
(![X]:((~calm(X)|humble(X))<=>(~creative(X)|strong(X))))&
(((happy(fred)&patient(fred)))<=>(?[X]:((humble(X)|~wise(X)))))&
(((humble(john)<~>happy(john)))=>((~brave(susan)&~rich(susan))))&
(![X]:((funny(X)<~>rich(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)&rich(X))=>(strong(X)&humble(X))))&
(![X]:(~funny(X)<=>(~creative(X)|tall(X))))&
(![X]:(humble(X)=>(brave(X)&~old(X))))&
(![X]:((~brave(X)&~wise(X))=>(rich(X)&~quiet(X))))&
(![X]:((happy(X)|patient(X))<=>(~humble(X)&humble(X))))&
(![X]:((tall(X)<~>curious(X))<=>(calm(X)|creative(X))))&
((~tall(paul))=>(?[X]:((happy(X)|brave(X)))))&
((?[X]:(~humble(X)))<=>((brave(lucy)|~humble(lucy))))&
(?[X]:(~calm(X)))&
(?[X]:((~funny(X)&~rich(X))))&
((kind(fred)|wise(fred)))&
(?[X]:((strong(X)|~humble(X))))&
((~funny(fred)|~old(fred))) | ~brave(john) | [] | null | 0 |
If alice is curious then susan is both not creative and creative.
Everyone who is either curious or not creative is both not tall and calm.
Everyone who is calm is funny or humble and vice versa.
Everyone who is kind is either humble or tall.
If someone is not kind then lucy is brave.
Everyone who is not patient is not strong or calm.
If alice is old then someone is not humble.
If fred is wise or not curious then someone is strong or not tall and vice versa.
If susan is quiet or tall then someone is not quiet or not generous.
If someone is either not strong or not generous then someone is both not wise and strong.
If someone is both not wise and calm then mary is both creative and kind.
Everyone who is old or curious is not strong or brave.
If susan is not old or not kind then fred is both happy and curious and vice versa.
If paul is both strong and not generous then susan is both brave and not strong.
If alice is either not patient or not quiet then fred is not happy.
If fred is not curious or old then lucy is both kind and not creative and vice versa.
Alice is either wise or creative.
Someone is patient or not strong.
Someone is brave or not kind.
Alice is both not funny and wise.
Someone is not generous.
Someone is either brave or generous.
Someone is both not rich and not humble. | Alice is wise. | entailment | ((curious(alice))=>((~creative(susan)&creative(susan))))&
(![X]:((curious(X)<~>~creative(X))=>(~tall(X)&calm(X))))&
(![X]:(calm(X)<=>(funny(X)|humble(X))))&
(![X]:(kind(X)=>(humble(X)<~>tall(X))))&
((?[X]:(~kind(X)))=>(brave(lucy)))&
(![X]:(~patient(X)=>(~strong(X)|calm(X))))&
((old(alice))=>(?[X]:(~humble(X))))&
(((wise(fred)|~curious(fred)))<=>(?[X]:((strong(X)|~tall(X)))))&
(((quiet(susan)|tall(susan)))=>(?[X]:((~quiet(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:((~wise(X)&calm(X))))=>((creative(mary)&kind(mary))))&
(![X]:((old(X)|curious(X))=>(~strong(X)|brave(X))))&
(((~old(susan)|~kind(susan)))<=>((happy(fred)&curious(fred))))&
(((strong(paul)&~generous(paul)))=>((brave(susan)&~strong(susan))))&
(((~patient(alice)<~>~quiet(alice)))=>(~happy(fred)))&
(((~curious(fred)|old(fred)))<=>((kind(lucy)&~creative(lucy))))&
((wise(alice)<~>creative(alice)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((brave(X)|~kind(X))))&
((~funny(alice)&wise(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~rich(X)&~humble(X)))) | wise(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1909038041467579212232349
% SZS output start Proof for 1909038041467579212232349
20. wise(alice) & ~funny(alice) [input p19]
24. ~wise(alice) [input hypothesis]
123. wise(alice) [cnf transformation 20]
128. ~wise(alice) [cnf transformation 24]
294. 36 <=> wise(alice) [avatar definition]
321. 36 [avatar split clause 123,294]
332. ~36 [avatar split clause 128,294]
333. $false [avatar sat refutation 321,332]
% SZS output end Proof for 1909038041467579212232349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either happy or curious.
Everyone who is not creative is both not brave and generous and vice versa.
If someone is not tall then someone is tall and vice versa.
Everyone who is either rich or happy is not brave.
If someone is not strong or calm then fred is both not creative and patient.
If john is not wise or not happy then someone is both not humble and humble and vice versa.
If fred is both not strong and not humble then susan is rich or curious.
Everyone who is not strong is both happy and not curious and vice versa.
If someone is both strong and not calm then someone is both creative and not wise.
If someone is either not rich or not strong then susan is either not kind or generous.
Everyone who is wise or kind is not calm or happy and vice versa.
Everyone who is either strong or brave is both not old and funny.
Everyone who is both strong and not old is either brave or not wise.
Everyone who is both curious and brave is not curious or not patient and vice versa.
Everyone who is either not happy or not brave is either not generous or calm.
If someone is both generous and not curious then lucy is either not humble or calm.
Someone is not strong or not rich.
Someone is not wise or happy.
Someone is both not funny and kind.
Someone is both quiet and not generous.
Someone is either not humble or not patient.
Fred is either old or funny.
Someone is not strong or not humble.
Alice is both not tall and not rich. | John is not creative. | contradiction | (![X]:(kind(X)=>(happy(X)<~>curious(X))))&
(![X]:(~creative(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(tall(X))))&
(![X]:((rich(X)<~>happy(X))=>~brave(X)))&
((?[X]:((~strong(X)|calm(X))))=>((~creative(fred)&patient(fred))))&
(((~wise(john)|~happy(john)))<=>(?[X]:((~humble(X)&humble(X)))))&
(((~strong(fred)&~humble(fred)))=>((rich(susan)|curious(susan))))&
(![X]:(~strong(X)<=>(happy(X)&~curious(X))))&
((?[X]:((strong(X)&~calm(X))))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((~kind(susan)<~>generous(susan))))&
(![X]:((wise(X)|kind(X))<=>(~calm(X)|happy(X))))&
(![X]:((strong(X)<~>brave(X))=>(~old(X)&funny(X))))&
(![X]:((strong(X)&~old(X))=>(brave(X)<~>~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~generous(X)<~>calm(X))))&
((?[X]:((generous(X)&~curious(X))))=>((~humble(lucy)<~>calm(lucy))))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~funny(X)&kind(X))))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~humble(X)<~>~patient(X))))&
((old(fred)<~>funny(fred)))&
(?[X]:((~strong(X)|~humble(X))))&
((~tall(alice)&~rich(alice))) | ~creative(john) | [
"p1",
"p5",
"p7",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 398658024395432684819863
% SZS output start Proof for 398658024395432684819863
2. ! [X0] : (~creative(X0) <=> (generous(X0) & ~brave(X0))) [input p1]
6. (~happy(john) | ~wise(john)) <=> ? [X0] : (humble(X0) & ~humble(X0)) [input p5]
8. ! [X0] : (~strong(X0) <=> (~curious(X0) & happy(X0))) [input p7]
12. ! [X0] : ((strong(X0) <~> brave(X0)) => (funny(X0) & ~old(X0))) [input p11]
13. ! [X0] : ((~old(X0) & strong(X0)) => (brave(X0) <~> ~wise(X0))) [input p12]
14. ! [X0] : ((brave(X0) & curious(X0)) <=> (~patient(X0) | ~curious(X0))) [input p13]
25. ~creative(john) [input hypothesis]
36. ! [X0] : ((funny(X0) & ~old(X0)) | (strong(X0) <=> brave(X0))) [ennf transformation 12]
37. ! [X0] : ((brave(X0) <~> ~wise(X0)) | (old(X0) | ~strong(X0))) [ennf transformation 13]
38. ! [X0] : ((brave(X0) <~> ~wise(X0)) | old(X0) | ~strong(X0)) [flattening 37]
42. ! [X0] : ((~creative(X0) | (~generous(X0) | brave(X0))) & ((generous(X0) & ~brave(X0)) | creative(X0))) [nnf transformation 2]
43. ! [X0] : ((~creative(X0) | ~generous(X0) | brave(X0)) & ((generous(X0) & ~brave(X0)) | creative(X0))) [flattening 42]
50. ((~happy(john) | ~wise(john)) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [nnf transformation 6]
51. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [flattening 50]
52. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X1] : (humble(X1) & ~humble(X1)) | (happy(john) & wise(john))) [rectify 51]
53. ? [X1] : (humble(X1) & ~humble(X1)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
54. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & ((humble(sK2) & ~humble(sK2)) | (happy(john) & wise(john))) [skolemisation 52,53]
55. ! [X0] : ((~strong(X0) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | strong(X0))) [nnf transformation 8]
56. ! [X0] : ((~strong(X0) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | strong(X0))) [flattening 55]
63. ! [X0] : ((funny(X0) & ~old(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) [nnf transformation 36]
64. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | old(X0) | ~strong(X0)) [nnf transformation 38]
65. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | (~brave(X0) | ~curious(X0)))) [nnf transformation 14]
66. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | ~brave(X0) | ~curious(X0))) [flattening 65]
85. ~brave(X0) | creative(X0) [cnf transformation 43]
96. ~humble(sK2) | wise(john) [cnf transformation 54]
98. humble(sK2) | wise(john) [cnf transformation 54]
103. ~curious(X0) | strong(X0) [cnf transformation 56]
115. ~old(X0) | brave(X0) | ~strong(X0) [cnf transformation 63]
119. ~wise(X0) | brave(X0) | old(X0) | ~strong(X0) [cnf transformation 64]
122. curious(X0) | curious(X0) [cnf transformation 66]
144. ~creative(john) [cnf transformation 25]
146. curious(X0) [duplicate literal removal 122]
172. 7 <=> ! [X0] : strong(X0) [avatar definition]
173. strong(X0) <- (7) [avatar component clause 172]
186. 10 <=> humble(sK2) [avatar definition]
191. 11 <=> wise(john) [avatar definition]
193. wise(john) <- (11) [avatar component clause 191]
194. 11 | 10 [avatar split clause 98,186,191]
196. 11 | ~10 [avatar split clause 96,186,191]
245. ~wise(X0) | brave(X0) | ~strong(X0) [subsumption resolution 119,115]
299. strong(X0) [resolution 103,146]
300. 7 [avatar split clause 299,172]
399. brave(john) | ~strong(john) <- (11) [resolution 245,193]
402. brave(john) <- (7, 11) [subsumption resolution 399,173]
407. creative(john) <- (7, 11) [resolution 402,85]
409. $false <- (7, 11) [subsumption resolution 407,144]
410. ~7 | ~11 [avatar contradiction clause 409]
411. $false [avatar sat refutation 194,196,300,410]
% SZS output end Proof for 398658024395432684819863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not old then someone is old or not kind. If fred is both not brave and rich then fred is strong or not curious. Everyone who is either quiet or not rich is either calm or patient and vice versa. If paul is not old then lucy is either patient or not calm and vice versa. If someone is either not humble or not tall then mary is either brave or not patient and vice versa. If someone is both humble and not creative then someone is either not tall or kind. Everyone who is either not funny or not tall is both patient and not happy. If fred is either rich or old then fred is brave or not brave and vice versa. Everyone who is either not strong or not rich is not strong or patient and vice versa. Everyone who is either funny or not curious is either generous or happy. Everyone who is either not happy or not funny is both wise and rich and vice versa. If fred is either rich or funny then someone is calm. Everyone who is not generous or not creative is both creative and not humble and vice versa. Everyone who is tall is old or not funny and vice versa. If someone is either not curious or brave then john is patient and vice versa. If someone is humble then someone is funny. Someone is tall or calm. Someone is both patient and not humble. Someone is calm or curious. Someone is either brave or not happy. Fred is not funny or not happy. Someone is not generous. Someone is generous or not wise. | Fred is patient. | entailment | ((~old(john))=>(?[X]:((old(X)|~kind(X)))))&
(((~brave(fred)&rich(fred)))=>((strong(fred)|~curious(fred))))&
(![X]:((quiet(X)<~>~rich(X))<=>(calm(X)<~>patient(X))))&
((~old(paul))<=>((patient(lucy)<~>~calm(lucy))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>((brave(mary)<~>~patient(mary))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:((~funny(X)<~>~tall(X))=>(patient(X)&~happy(X))))&
(((rich(fred)<~>old(fred)))<=>((brave(fred)|~brave(fred))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(wise(X)&rich(X))))&
(((rich(fred)<~>funny(fred)))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(creative(X)&~humble(X))))&
(![X]:(tall(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(patient(john)))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((patient(X)&~humble(X))))&
(?[X]:((calm(X)|curious(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((~funny(fred)|~happy(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)|~wise(X)))) | patient(fred) | [
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5012670552166228802501293
% SZS output start Proof for 5012670552166228802501293
7. ! [X0] : ((~funny(X0) <~> ~tall(X0)) => (~happy(X0) & patient(X0))) [input p6]
8. (rich(fred) <~> old(fred)) <=> (~brave(fred) | brave(fred)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~rich(X0)) <=> (patient(X0) | ~strong(X0))) [input p8]
14. ! [X0] : (tall(X0) <=> (~funny(X0) | old(X0))) [input p13]
24. ~patient(fred) [input hypothesis]
31. ! [X0] : ((~happy(X0) & patient(X0)) | (~funny(X0) <=> ~tall(X0))) [ennf transformation 7]
47. ! [X0] : ((~happy(X0) & patient(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) [nnf transformation 31]
48. (((~old(fred) | ~rich(fred)) & (old(fred) | rich(fred))) | (brave(fred) & ~brave(fred))) & ((~brave(fred) | brave(fred)) | ((rich(fred) | ~old(fred)) & (old(fred) | ~rich(fred)))) [nnf transformation 8]
49. (((~old(fred) | ~rich(fred)) & (old(fred) | rich(fred))) | (brave(fred) & ~brave(fred))) & (~brave(fred) | brave(fred) | ((rich(fred) | ~old(fred)) & (old(fred) | ~rich(fred)))) [flattening 48]
50. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [nnf transformation 9]
51. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [flattening 50]
60. ! [X0] : ((tall(X0) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ~tall(X0))) [nnf transformation 14]
61. ! [X0] : ((tall(X0) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ~tall(X0))) [flattening 60]
106. ~tall(X0) | patient(X0) | funny(X0) [cnf transformation 47]
107. ~funny(X0) | patient(X0) | tall(X0) [cnf transformation 47]
114. ~old(fred) | ~rich(fred) | ~brave(fred) [cnf transformation 49]
115. ~old(fred) | ~rich(fred) | brave(fred) [cnf transformation 49]
117. patient(X0) | ~strong(X0) | ~strong(X0) | rich(X0) [cnf transformation 51]
120. rich(X0) | strong(X0) | strong(X0) [cnf transformation 51]
139. ~funny(X0) | old(X0) | ~tall(X0) [cnf transformation 61]
141. funny(X0) | tall(X0) [cnf transformation 61]
156. ~patient(fred) [cnf transformation 24]
159. patient(X0) | ~strong(X0) | rich(X0) [duplicate literal removal 117]
160. strong(X0) | rich(X0) [duplicate literal removal 120]
175. 4 <=> brave(fred) [avatar definition]
179. 5 <=> rich(fred) [avatar definition]
251. 20 <=> old(fred) [avatar definition]
253. ~old(fred) <- (~20) [avatar component clause 251]
254. 4 | ~5 | ~20 [avatar split clause 115,251,179,175]
255. ~4 | ~5 | ~20 [avatar split clause 114,251,179,175]
258. patient(X0) | rich(X0) [subsumption resolution 159,160]
260. 21 <=> funny(fred) [avatar definition]
261. funny(fred) <- (21) [avatar component clause 260]
262. ~funny(fred) <- (~21) [avatar component clause 260]
347. rich(fred) [resolution 258,156]
352. 5 [avatar split clause 347,179]
364. patient(X0) | tall(X0) | tall(X0) [resolution 107,141]
366. tall(X0) | patient(X0) [duplicate literal removal 364]
442. old(fred) | ~tall(fred) <- (21) [resolution 139,261]
445. ~tall(fred) <- (~20, 21) [subsumption resolution 442,253]
510. patient(X0) | patient(X0) | funny(X0) [resolution 366,106]
511. patient(fred) <- (~20, 21) [resolution 366,445]
512. funny(X0) | patient(X0) [duplicate literal removal 510]
513. $false <- (~20, 21) [subsumption resolution 511,156]
514. 20 | ~21 [avatar contradiction clause 513]
768. patient(fred) <- (~21) [resolution 512,262]
771. $false <- (~21) [subsumption resolution 768,156]
772. 21 [avatar contradiction clause 771]
773. $false [avatar sat refutation 254,255,352,514,772]
% SZS output end Proof for 5012670552166228802501293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not wise is not wise and vice versa. Everyone who is not happy or not strong is either not kind or curious. If fred is not rich then fred is not calm and vice versa. Everyone who is either not creative or quiet is both not curious and kind. Everyone who is not happy is both funny and old. Everyone who is strong is not calm or not creative. Everyone who is both not curious and happy is either rich or not rich. Everyone who is either not humble or humble is both quiet and not kind. Everyone who is both strong and not funny is both creative and not calm and vice versa. If paul is either not kind or humble then someone is both brave and old and vice versa. Everyone who is not kind is wise or not wise and vice versa. Everyone who is curious is either not kind or strong and vice versa. If paul is either quiet or old then paul is not strong and vice versa. Everyone who is creative or not generous is not tall or creative and vice versa. Paul is not kind or not strong. Fred is either not brave or not tall. Paul is not brave or not funny. Someone is rich. Paul is either not old or not rich. Alice is calm or not kind. Someone is either not curious or not tall. Fred is not rich or patient. | Alice is not strong. | contradiction | (![X]:((brave(X)<~>~wise(X))<=>~wise(X)))&
(![X]:((~happy(X)|~strong(X))=>(~kind(X)<~>curious(X))))&
((~rich(fred))<=>(~calm(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(~curious(X)&kind(X))))&
(![X]:(~happy(X)=>(funny(X)&old(X))))&
(![X]:(strong(X)=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)&happy(X))=>(rich(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>humble(X))=>(quiet(X)&~kind(X))))&
(![X]:((strong(X)&~funny(X))<=>(creative(X)&~calm(X))))&
(((~kind(paul)<~>humble(paul)))<=>(?[X]:((brave(X)&old(X)))))&
(![X]:(~kind(X)<=>(wise(X)|~wise(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>strong(X))))&
(((quiet(paul)<~>old(paul)))<=>(~strong(paul)))&
(![X]:((creative(X)|~generous(X))<=>(~tall(X)|creative(X))))&
((~kind(paul)|~strong(paul)))&
((~brave(fred)<~>~tall(fred)))&
((~brave(paul)|~funny(paul)))&
(?[X]:(rich(X)))&
((~old(paul)<~>~rich(paul)))&
((calm(alice)|~kind(alice)))&
(?[X]:((~curious(X)<~>~tall(X))))&
((~rich(fred)|patient(fred))) | ~strong(alice) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2624268850989793531158685
% SZS output start Proof for 2624268850989793531158685
2. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~kind(X0) <~> curious(X0))) [input p1]
8. ! [X0] : ((~humble(X0) <~> humble(X0)) => (~kind(X0) & quiet(X0))) [input p7]
12. ! [X0] : (curious(X0) <=> (~kind(X0) <~> strong(X0))) [input p11]
23. ~strong(alice) [input hypothesis]
25. ! [X0] : ((~kind(X0) <~> curious(X0)) | (strong(X0) & happy(X0))) [ennf transformation 2]
32. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 8]
34. ! [X0] : (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | (strong(X0) & happy(X0))) [nnf transformation 25]
38. ! [X0] : ((~kind(X0) & quiet(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 32]
47. ! [X0] : ((curious(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ~curious(X0))) [nnf transformation 12]
65. ~curious(X0) | kind(X0) | strong(X0) [cnf transformation 34]
79. ~kind(X0) | humble(X0) | humble(X0) [cnf transformation 38]
80. ~kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38]
96. curious(X0) | strong(X0) | kind(X0) [cnf transformation 47]
116. ~strong(alice) [cnf transformation 23]
119. ~kind(X0) | humble(X0) [duplicate literal removal 79]
120. ~humble(X0) | ~kind(X0) [duplicate literal removal 80]
134. ~kind(X0) [subsumption resolution 119,120]
149. curious(X0) | strong(X0) [subsumption resolution 96,134]
189. kind(X0) | strong(X0) | strong(X0) [resolution 65,149]
190. kind(X0) | strong(X0) [duplicate literal removal 189]
194. strong(X0) [subsumption resolution 190,134]
196. $false [resolution 194,116]
% SZS output end Proof for 2624268850989793531158685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either creative or wise is either not quiet or old and vice versa. Everyone who is both quiet and generous is both not funny and generous and vice versa. If someone is either rich or humble then someone is wise. Everyone who is strong is both tall and not strong and vice versa. Everyone who is both humble and rich is tall. If susan is either old or not generous then susan is calm. If john is patient then paul is both not strong and curious and vice versa. Everyone who is either curious or not patient is both not rich and humble. If someone is either not strong or not kind then someone is both not patient and not humble and vice versa. If susan is not curious or not wise then john is both kind and rich. If john is both not funny and kind then john is quiet or not brave. Everyone who is both not humble and not funny is both not rich and quiet and vice versa. If fred is both rich and strong then someone is either not humble or kind. If someone is both not patient and strong then someone is tall or rich. Everyone who is both creative and not humble is both humble and funny and vice versa. If susan is not creative or not curious then someone is both not calm and not creative and vice versa. Fred is happy or calm. Someone is generous. Someone is either not tall or funny. Someone is not quiet. Someone is either patient or brave. Fred is old or not tall. Someone is both not brave and not generous. | John is strong. | contradiction | (![X]:((creative(X)<~>wise(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((quiet(X)&generous(X))<=>(~funny(X)&generous(X))))&
((?[X]:((rich(X)<~>humble(X))))=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(tall(X)&~strong(X))))&
(![X]:((humble(X)&rich(X))=>tall(X)))&
(((old(susan)<~>~generous(susan)))=>(calm(susan)))&
((patient(john))<=>((~strong(paul)&curious(paul))))&
(![X]:((curious(X)<~>~patient(X))=>(~rich(X)&humble(X))))&
((?[X]:((~strong(X)<~>~kind(X))))<=>(?[X]:((~patient(X)&~humble(X)))))&
(((~curious(susan)|~wise(susan)))=>((kind(john)&rich(john))))&
(((~funny(john)&kind(john)))=>((quiet(john)|~brave(john))))&
(![X]:((~humble(X)&~funny(X))<=>(~rich(X)&quiet(X))))&
(((rich(fred)&strong(fred)))=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~patient(X)&strong(X))))=>(?[X]:((tall(X)|rich(X)))))&
(![X]:((creative(X)&~humble(X))<=>(humble(X)&funny(X))))&
(((~creative(susan)|~curious(susan)))<=>(?[X]:((~calm(X)&~creative(X)))))&
((happy(fred)|calm(fred)))&
(?[X]:(generous(X)))&
(?[X]:((~tall(X)<~>funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)<~>brave(X))))&
((old(fred)|~tall(fred)))&
(?[X]:((~brave(X)&~generous(X)))) | strong(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1605103184947658967415167
% SZS output start Proof for 1605103184947658967415167
4. ! [X0] : (strong(X0) <=> (~strong(X0) & tall(X0))) [input p3]
24. strong(john) [input hypothesis]
47. ! [X0] : ((strong(X0) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | ~strong(X0))) [nnf transformation 4]
48. ! [X0] : ((strong(X0) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | ~strong(X0))) [flattening 47]
100. ~strong(X0) | ~strong(X0) [cnf transformation 48]
148. strong(john) [cnf transformation 24]
151. ~strong(X0) [duplicate literal removal 100]
296. $false [subsumption resolution 148,151]
% SZS output end Proof for 1605103184947658967415167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or humble is either not patient or quiet and vice versa.
If paul is both humble and rich then someone is both not patient and not generous.
If someone is both not generous and funny then someone is wise.
If someone is both kind and not curious then john is not funny.
Everyone who is generous is either curious or wise.
If someone is either not wise or generous then paul is not kind.
Everyone who is creative or rich is both not old and happy.
If someone is either not rich or creative then paul is not generous and vice versa.
Everyone who is not calm is calm or humble.
Everyone who is either not rich or not strong is not strong.
If someone is kind then someone is either wise or rich.
If someone is generous then someone is wise or humble and vice versa.
Everyone who is both happy and not rich is either old or not happy and vice versa.
Everyone who is quiet is creative and vice versa.
If fred is happy or not quiet then someone is either strong or patient and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Someone is both not generous and tall.
Someone is patient or not generous.
Someone is either wise or humble.
Fred is both not brave and not rich.
Lucy is either funny or not curious.
Someone is both humble and not creative.
Someone is not curious.
Someone is old or not quiet. | Fred is not quiet. | entailment | (![X]:((rich(X)<~>humble(X))<=>(~patient(X)<~>quiet(X))))&
(((humble(paul)&rich(paul)))=>(?[X]:((~patient(X)&~generous(X)))))&
((?[X]:((~generous(X)&funny(X))))=>(?[X]:(wise(X))))&
((?[X]:((kind(X)&~curious(X))))=>(~funny(john)))&
(![X]:(generous(X)=>(curious(X)<~>wise(X))))&
((?[X]:((~wise(X)<~>generous(X))))=>(~kind(paul)))&
(![X]:((creative(X)|rich(X))=>(~old(X)&happy(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>(~generous(paul)))&
(![X]:(~calm(X)=>(calm(X)|humble(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~strong(X)))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(((happy(fred)|~quiet(fred)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:((wise(X)<~>humble(X))))&
((~brave(fred)&~rich(fred)))&
((funny(lucy)<~>~curious(lucy)))&
(?[X]:((humble(X)&~creative(X))))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)|~quiet(X)))) | ~quiet(fred) | [
"p6",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6469501860764461259843306
% SZS output start Proof for 6469501860764461259843306
7. ! [X0] : ((rich(X0) | creative(X0)) => (happy(X0) & ~old(X0))) [input p6]
13. ! [X0] : ((~rich(X0) & happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p12]
14. ! [X0] : (quiet(X0) <=> creative(X0)) [input p13]
20. ~rich(fred) & ~brave(fred) [input p19]
25. quiet(fred) [input hypothesis]
29. ~rich(fred) [pure predicate removal 20]
39. ! [X0] : ((happy(X0) & ~old(X0)) | (~rich(X0) & ~creative(X0))) [ennf transformation 7]
58. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (rich(X0) | ~happy(X0)))) [nnf transformation 13]
59. ! [X0] : (((~rich(X0) & happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | rich(X0) | ~happy(X0))) [flattening 58]
60. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 14]
94. ~old(X0) | ~creative(X0) [cnf transformation 39]
107. ~happy(X0) | old(X0) | rich(X0) | ~happy(X0) [cnf transformation 59]
110. happy(X0) | old(X0) | happy(X0) [cnf transformation 59]
113. ~quiet(X0) | creative(X0) [cnf transformation 60]
129. ~rich(fred) [cnf transformation 29]
136. quiet(fred) [cnf transformation 25]
137. ~happy(X0) | old(X0) | rich(X0) [duplicate literal removal 107]
138. happy(X0) | old(X0) [duplicate literal removal 110]
212. old(X0) | rich(X0) [subsumption resolution 137,138]
221. 20 <=> quiet(fred) [avatar definition]
222. quiet(fred) <- (20) [avatar component clause 221]
279. 20 [avatar split clause 136,221]
287. creative(fred) <- (20) [resolution 113,222]
296. ~creative(X1) | rich(X1) [resolution 212,94]
300. rich(fred) <- (20) [resolution 296,287]
301. $false <- (20) [subsumption resolution 300,129]
302. ~20 [avatar contradiction clause 301]
303. $false [avatar sat refutation 279,302]
% SZS output end Proof for 6469501860764461259843306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and quiet then someone is not kind. If mary is either quiet or patient then someone is not strong. Everyone who is both not rich and not quiet is kind or creative. Everyone who is both old and kind is not humble or wise. If someone is not curious or generous then someone is not generous and vice versa. If someone is patient then someone is either curious or strong and vice versa. If someone is not curious then mary is not humble. Everyone who is both creative and not calm is both calm and kind and vice versa. If susan is either creative or happy then someone is either not quiet or generous and vice versa. Everyone who is either quiet or not strong is not tall and vice versa. Everyone who is strong or not creative is not humble or funny and vice versa. Everyone who is tall or wise is either patient or calm and vice versa. Everyone who is quiet is not patient and vice versa. Everyone who is not wise is both not funny and not tall. If someone is either not happy or not funny then someone is both not curious and not old. Everyone who is not quiet or creative is funny and vice versa. Someone is not old or brave. Mary is either not calm or not creative. Susan is not tall. Someone is not humble or patient. Susan is either not curious or not strong. Someone is generous or strong. | Susan is not old. | neutral | ((?[X]:((kind(X)&quiet(X))))=>(?[X]:(~kind(X))))&
(((quiet(mary)<~>patient(mary)))=>(?[X]:(~strong(X))))&
(![X]:((~rich(X)&~quiet(X))=>(kind(X)|creative(X))))&
(![X]:((old(X)&kind(X))=>(~humble(X)|wise(X))))&
((?[X]:((~curious(X)|generous(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(patient(X)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((?[X]:(~curious(X)))=>(~humble(mary)))&
(![X]:((creative(X)&~calm(X))<=>(calm(X)&kind(X))))&
(((creative(susan)<~>happy(susan)))<=>(?[X]:((~quiet(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>~strong(X))<=>~tall(X)))&
(![X]:((strong(X)|~creative(X))<=>(~humble(X)|funny(X))))&
(![X]:((tall(X)|wise(X))<=>(patient(X)<~>calm(X))))&
(![X]:(quiet(X)<=>~patient(X)))&
(![X]:(~wise(X)=>(~funny(X)&~tall(X))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((~quiet(X)|creative(X))<=>funny(X)))&
(?[X]:((~old(X)|brave(X))))&
((~calm(mary)<~>~creative(mary)))&
(~tall(susan))&
(?[X]:((~humble(X)|patient(X))))&
((~curious(susan)<~>~strong(susan)))&
(?[X]:((generous(X)|strong(X)))) | ~old(susan) | [] | null | 0 |
If mary is not wise or patient then someone is either not quiet or not patient.
If someone is not curious or not kind then someone is both not kind and not brave and vice versa.
Everyone who is not strong or generous is calm or generous and vice versa.
If john is both not quiet and funny then someone is either not kind or not tall and vice versa.
If lucy is both not humble and not old then someone is wise and vice versa.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Susan is both generous and not wise.
Someone is either tall or creative. | Mary is not funny. | entailment | (((~wise(mary)|patient(mary)))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)|generous(X))))&
(((~quiet(john)&funny(john)))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~humble(lucy)&~old(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | ~funny(mary) | [
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3755923038129697336275576
% SZS output start Proof for 3755923038129697336275576
6. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p7]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
24. funny(mary) [input hypothesis]
30. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 8]
56. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 6]
64. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 64]
110. ~happy(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
116. strong(X0) | happy(X0) [cnf transformation 30]
117. ~happy(X0) | strong(X0) [cnf transformation 30]
129. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
130. happy(X0) | happy(X0) [cnf transformation 65]
131. happy(X0) | kind(X0) [cnf transformation 65]
156. funny(mary) [cnf transformation 24]
157. ~kind(X0) | ~happy(X0) [duplicate literal removal 129]
158. happy(X0) [duplicate literal removal 130]
257. strong(X0) [subsumption resolution 116,117]
271. ~kind(X0) [subsumption resolution 157,158]
367. ~strong(X0) | ~funny(X0) | kind(X0) [resolution 110,131]
369. ~funny(X0) | kind(X0) [subsumption resolution 367,257]
370. ~funny(X0) [subsumption resolution 369,271]
373. $false [resolution 370,156]
% SZS output end Proof for 3755923038129697336275576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not strong then paul is not calm or not happy and vice versa.
If susan is either not old or not rich then paul is both not strong and not generous.
Everyone who is either curious or creative is humble or creative.
Everyone who is both not calm and quiet is both humble and rich.
Everyone who is both funny and rich is either funny or not curious.
If lucy is either calm or creative then lucy is happy or kind.
If someone is brave or generous then alice is quiet or calm and vice versa.
If someone is either not happy or not kind then someone is both not strong and humble.
Everyone who is both not humble and wise is both not creative and tall and vice versa.
Everyone who is not humble is either rich or old and vice versa.
Everyone who is curious is either curious or not patient and vice versa.
If someone is not kind or not strong then paul is curious.
Everyone who is either kind or not funny is quiet or happy and vice versa.
Everyone who is not quiet is not curious and vice versa.
If someone is happy then john is calm or humble and vice versa.
Everyone who is either not curious or not patient is not creative or not strong.
Someone is both not quiet and tall.
Someone is either not strong or patient.
Someone is generous or rich.
Paul is happy.
Paul is either old or quiet.
Someone is not humble or not wise.
Someone is either not old or strong.
Someone is both not calm and brave. | Lucy is patient. | entailment | ((?[X]:((~humble(X)&~strong(X))))<=>((~calm(paul)|~happy(paul))))&
(((~old(susan)<~>~rich(susan)))=>((~strong(paul)&~generous(paul))))&
(![X]:((curious(X)<~>creative(X))=>(humble(X)|creative(X))))&
(![X]:((~calm(X)&quiet(X))=>(humble(X)&rich(X))))&
(![X]:((funny(X)&rich(X))=>(funny(X)<~>~curious(X))))&
(((calm(lucy)<~>creative(lucy)))=>((happy(lucy)|kind(lucy))))&
((?[X]:((brave(X)|generous(X))))<=>((quiet(alice)|calm(alice))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:((~humble(X)&wise(X))<=>(~creative(X)&tall(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>old(X))))&
(![X]:(curious(X)<=>(curious(X)<~>~patient(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(curious(paul)))&
(![X]:((kind(X)<~>~funny(X))<=>(quiet(X)|happy(X))))&
(![X]:(~quiet(X)<=>~curious(X)))&
((?[X]:(happy(X)))<=>((calm(john)|humble(john))))&
(![X]:((~curious(X)<~>~patient(X))=>(~creative(X)|~strong(X))))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((generous(X)|rich(X))))&
(happy(paul))&
((old(paul)<~>quiet(paul)))&
(?[X]:((~humble(X)|~wise(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:((~calm(X)&brave(X)))) | patient(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3640133133820677996326769
% SZS output start Proof for 3640133133820677996326769
11. ! [X0] : (curious(X0) <=> (curious(X0) <~> ~patient(X0))) [input p10]
25. ~patient(lucy) [input hypothesis]
61. ! [X0] : ((curious(X0) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) & (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 11]
120. patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 61]
122. curious(X0) | curious(X0) | patient(X0) [cnf transformation 61]
151. ~patient(lucy) [cnf transformation 25]
152. patient(X0) | ~curious(X0) [duplicate literal removal 120]
153. curious(X0) | patient(X0) [duplicate literal removal 122]
262. patient(X0) [subsumption resolution 152,153]
334. $false [subsumption resolution 151,262]
% SZS output end Proof for 3640133133820677996326769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is quiet or not creative then alice is rich or not old. Everyone who is both not humble and generous is either not creative or calm. Everyone who is not humble is either not quiet or wise and vice versa. Everyone who is generous is both not generous and funny and vice versa. Everyone who is humble or calm is wise or not humble. If someone is curious or not strong then someone is both humble and strong. If susan is not patient or humble then mary is not creative or creative. Everyone who is both wise and not old is not tall or kind and vice versa. Everyone who is old or not humble is rich or not creative and vice versa. Everyone who is either not curious or funny is not patient or curious and vice versa. Everyone who is either rich or funny is both not strong and tall. Everyone who is both not quiet and funny is humble or happy and vice versa. If someone is both not funny and not curious then someone is not humble and vice versa. If alice is not tall or humble then susan is not patient or not creative. Everyone who is either creative or not quiet is not kind or not old. If someone is funny or not patient then fred is not patient or generous and vice versa. Someone is not kind or not calm. Someone is either not humble or old. John is not tall. Someone is tall or funny. | Alice is curious. | contradiction | (((quiet(mary)|~creative(mary)))=>((rich(alice)|~old(alice))))&
(![X]:((~humble(X)&generous(X))=>(~creative(X)<~>calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:(generous(X)<=>(~generous(X)&funny(X))))&
(![X]:((humble(X)|calm(X))=>(wise(X)|~humble(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((~patient(susan)|humble(susan)))=>((~creative(mary)|creative(mary))))&
(![X]:((wise(X)&~old(X))<=>(~tall(X)|kind(X))))&
(![X]:((old(X)|~humble(X))<=>(rich(X)|~creative(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(![X]:((~quiet(X)&funny(X))<=>(humble(X)|happy(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(((~tall(alice)|humble(alice)))=>((~patient(susan)|~creative(susan))))&
(![X]:((creative(X)<~>~quiet(X))=>(~kind(X)|~old(X))))&
((?[X]:((funny(X)|~patient(X))))<=>((~patient(fred)|generous(fred))))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:((~humble(X)<~>old(X))))&
(~tall(john))&
(?[X]:((tall(X)|funny(X)))) | curious(alice) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4411830691674430594497057
% SZS output start Proof for 4411830691674430594497057
4. ! [X0] : (generous(X0) <=> (funny(X0) & ~generous(X0))) [input p3]
10. ! [X0] : ((~curious(X0) <~> funny(X0)) <=> (curious(X0) | ~patient(X0))) [input p9]
21. curious(alice) [input hypothesis]
40. ! [X0] : ((generous(X0) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | ~generous(X0))) [nnf transformation 4]
41. ! [X0] : ((generous(X0) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | ~generous(X0))) [flattening 40]
49. ! [X0] : ((((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))))) [nnf transformation 10]
50. ! [X0] : ((((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))))) [flattening 49]
80. ~generous(X0) | ~generous(X0) [cnf transformation 41]
82. generous(X0) | ~funny(X0) | generous(X0) [cnf transformation 41]
103. funny(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 50]
131. curious(alice) [cnf transformation 21]
133. ~curious(X0) | funny(X0) [duplicate literal removal 103]
135. ~generous(X0) [duplicate literal removal 80]
136. ~funny(X0) | generous(X0) [duplicate literal removal 82]
261. funny(alice) [resolution 133,131]
264. generous(alice) [resolution 136,261]
267. $false [subsumption resolution 264,135]
% SZS output end Proof for 4411830691674430594497057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or patient is rich or patient.
If fred is either happy or strong then someone is creative or not old and vice versa.
If someone is either not funny or not strong then lucy is both creative and quiet.
Everyone who is both not happy and happy is not humble or not generous.
Everyone who is either calm or not brave is not creative and vice versa.
If someone is not creative or wise then someone is both brave and funny and vice versa.
If susan is old then alice is not kind.
Everyone who is either not kind or not creative is both not calm and wise and vice versa.
Everyone who is either brave or creative is either brave or old.
If someone is strong then mary is both not calm and quiet and vice versa.
Everyone who is either brave or patient is both creative and quiet.
If paul is both kind and not curious then someone is curious or funny and vice versa.
Everyone who is either not creative or not wise is not kind and vice versa.
Everyone who is not rich or happy is either not funny or not strong and vice versa.
Everyone who is both wise and curious is both not quiet and curious.
Everyone who is kind is both not rich and kind.
John is both not patient and not happy.
Susan is brave.
Someone is either curious or strong.
Mary is old or calm.
John is brave or quiet.
Someone is not quiet.
John is either not strong or tall.
Susan is both not tall and curious. | Lucy is funny. | entailment | (![X]:((~calm(X)|patient(X))=>(rich(X)|patient(X))))&
(((happy(fred)<~>strong(fred)))<=>(?[X]:((creative(X)|~old(X)))))&
((?[X]:((~funny(X)<~>~strong(X))))=>((creative(lucy)&quiet(lucy))))&
(![X]:((~happy(X)&happy(X))=>(~humble(X)|~generous(X))))&
(![X]:((calm(X)<~>~brave(X))<=>~creative(X)))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((brave(X)&funny(X)))))&
((old(susan))=>(~kind(alice)))&
(![X]:((~kind(X)<~>~creative(X))<=>(~calm(X)&wise(X))))&
(![X]:((brave(X)<~>creative(X))=>(brave(X)<~>old(X))))&
((?[X]:(strong(X)))<=>((~calm(mary)&quiet(mary))))&
(![X]:((brave(X)<~>patient(X))=>(creative(X)&quiet(X))))&
(((kind(paul)&~curious(paul)))<=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~creative(X)<~>~wise(X))<=>~kind(X)))&
(![X]:((~rich(X)|happy(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)&curious(X))=>(~quiet(X)&curious(X))))&
(![X]:(kind(X)=>(~rich(X)&kind(X))))&
((~patient(john)&~happy(john)))&
(brave(susan))&
(?[X]:((curious(X)<~>strong(X))))&
((old(mary)|calm(mary)))&
((brave(john)|quiet(john)))&
(?[X]:(~quiet(X)))&
((~strong(john)<~>tall(john)))&
((~tall(susan)&curious(susan))) | funny(lucy) | [
"p2",
"p5",
"p7",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 107649563896051830957715
% SZS output start Proof for 107649563896051830957715
3. ? [X0] : (~funny(X0) <~> ~strong(X0)) => (quiet(lucy) & creative(lucy)) [input p2]
6. ? [X0] : (wise(X0) | ~creative(X0)) <=> ? [X0] : (funny(X0) & brave(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> ~creative(X0)) <=> (wise(X0) & ~calm(X0))) [input p7]
10. ? [X0] : strong(X0) <=> (quiet(mary) & ~calm(mary)) [input p9]
13. ! [X0] : ((~creative(X0) <~> ~wise(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((happy(X0) | ~rich(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p13]
16. ! [X0] : (kind(X0) => (kind(X0) & ~rich(X0))) [input p15]
25. ~funny(lucy) [input hypothesis]
26. ? [X0] : (wise(X0) | ~creative(X0)) <=> ? [X1] : (funny(X1) & brave(X1)) [rectify 6]
30. (quiet(lucy) & creative(lucy)) | ! [X0] : (~funny(X0) <=> ~strong(X0)) [ennf transformation 3]
36. ! [X0] : ((kind(X0) & ~rich(X0)) | ~kind(X0)) [ennf transformation 16]
41. (quiet(lucy) & creative(lucy)) | ! [X0] : ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0))) [nnf transformation 30]
43. (? [X0] : (wise(X0) | ~creative(X0)) | ! [X1] : (~funny(X1) | ~brave(X1))) & (? [X1] : (funny(X1) & brave(X1)) | ! [X0] : (~wise(X0) & creative(X0))) [nnf transformation 26]
44. (? [X0] : (wise(X0) | ~creative(X0)) | ! [X1] : (~funny(X1) | ~brave(X1))) & (? [X2] : (funny(X2) & brave(X2)) | ! [X3] : (~wise(X3) & creative(X3))) [rectify 43]
45. ? [X0] : (wise(X0) | ~creative(X0)) => (wise(sK1) | ~creative(sK1)) [choice axiom]
46. ? [X2] : (funny(X2) & brave(X2)) => (funny(sK2) & brave(sK2)) [choice axiom]
47. ((wise(sK1) | ~creative(sK1)) | ! [X1] : (~funny(X1) | ~brave(X1))) & ((funny(sK2) & brave(sK2)) | ! [X3] : (~wise(X3) & creative(X3))) [skolemisation 44,46,45]
48. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [nnf transformation 8]
49. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [flattening 48]
51. (? [X0] : strong(X0) | (~quiet(mary) | calm(mary))) & ((quiet(mary) & ~calm(mary)) | ! [X0] : ~strong(X0)) [nnf transformation 10]
52. (? [X0] : strong(X0) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X0] : ~strong(X0)) [flattening 51]
53. (? [X0] : strong(X0) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X1] : ~strong(X1)) [rectify 52]
54. ? [X0] : strong(X0) => strong(sK3) [choice axiom]
55. (strong(sK3) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X1] : ~strong(X1)) [skolemisation 53,54]
62. ! [X0] : ((((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | kind(X0)) & (~kind(X0) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0))))) [nnf transformation 13]
63. ! [X0] : (((happy(X0) | ~rich(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [nnf transformation 14]
64. ! [X0] : ((happy(X0) | ~rich(X0) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [flattening 63]
80. creative(lucy) | ~funny(X0) | strong(X0) [cnf transformation 41]
90. funny(sK2) | ~wise(X3) [cnf transformation 47]
93. ~creative(X0) | ~calm(X0) | kind(X0) [cnf transformation 49]
95. ~creative(X0) | wise(X0) | kind(X0) [cnf transformation 49]
96. ~kind(X0) | wise(X0) | creative(X0) [cnf transformation 49]
97. ~kind(X0) | ~creative(X0) | ~wise(X0) | calm(X0) [cnf transformation 49]
98. ~wise(X0) | kind(X0) | creative(X0) | calm(X0) [cnf transformation 49]
103. ~calm(mary) | ~strong(X1) [cnf transformation 55]
115. ~kind(X0) | ~wise(X0) | creative(X0) [cnf transformation 62]
116. ~kind(X0) | ~creative(X0) | wise(X0) [cnf transformation 62]
117. ~wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 62]
118. wise(X0) | creative(X0) | kind(X0) [cnf transformation 62]
121. funny(X0) | strong(X0) | rich(X0) [cnf transformation 64]
127. ~kind(X0) | ~rich(X0) [cnf transformation 36]
141. ~funny(lucy) [cnf transformation 25]
173. 7 <=> ! [X0] : (~funny(X0) | strong(X0)) [avatar definition]
174. ~funny(X0) | strong(X0) <- (7) [avatar component clause 173]
185. 10 <=> creative(lucy) [avatar definition]
187. creative(lucy) <- (10) [avatar component clause 185]
188. 7 | 10 [avatar split clause 80,185,173]
203. 14 <=> ! [X3] : ~wise(X3) [avatar definition]
204. ~wise(X3) <- (14) [avatar component clause 203]
206. 15 <=> funny(sK2) [avatar definition]
208. funny(sK2) <- (15) [avatar component clause 206]
209. 14 | 15 [avatar split clause 90,206,203]
230. 20 <=> calm(mary) [avatar definition]
231. ~calm(mary) <- (~20) [avatar component clause 230]
243. 23 <=> ! [X1] : ~strong(X1) [avatar definition]
244. ~strong(X1) <- (23) [avatar component clause 243]
246. 23 | ~20 [avatar split clause 103,230,243]
248. 24 <=> ! [X0] : ~funny(X0) [avatar definition]
249. ~funny(X0) <- (24) [avatar component clause 248]
274. kind(X0) | wise(X0) [subsumption resolution 118,95]
275. ~creative(X0) | kind(X0) [subsumption resolution 117,95]
276. ~kind(X0) | wise(X0) [subsumption resolution 116,96]
277. wise(X0) [subsumption resolution 276,274]
278. ~kind(X0) | creative(X0) [subsumption resolution 115,277]
314. $false <- (14) [subsumption resolution 204,277]
315. ~14 [avatar contradiction clause 314]
318. $false <- (15, 24) [subsumption resolution 208,249]
319. ~15 | ~24 [avatar contradiction clause 318]
320. ~funny(X0) <- (7, 23) [subsumption resolution 174,244]
321. 24 | ~7 | ~23 [avatar split clause 320,243,173,248]
451. strong(lucy) | rich(lucy) [resolution 121,141]
458. 49 <=> rich(lucy) [avatar definition]
462. 50 <=> strong(lucy) [avatar definition]
464. strong(lucy) <- (50) [avatar component clause 462]
465. 49 | 50 [avatar split clause 451,462,458]
495. kind(X0) | creative(X0) | calm(X0) [resolution 98,277]
496. kind(X0) | calm(X0) [subsumption resolution 495,275]
510. calm(X0) | ~creative(X0) | ~wise(X0) | calm(X0) [resolution 496,97]
513. calm(X3) | creative(X3) [resolution 496,278]
515. calm(X0) | ~creative(X0) | ~wise(X0) [duplicate literal removal 510]
516. calm(X0) | ~creative(X0) [subsumption resolution 515,277]
517. calm(X3) [subsumption resolution 513,516]
528. $false <- (~20) [resolution 517,231]
530. 20 [avatar contradiction clause 528]
548. ~calm(lucy) | kind(lucy) <- (10) [resolution 187,93]
551. kind(lucy) <- (10) [subsumption resolution 548,517]
618. ~rich(lucy) <- (10) [resolution 551,127]
621. ~49 | ~10 [avatar split clause 618,185,458]
622. $false <- (23, 50) [subsumption resolution 464,244]
623. ~23 | ~50 [avatar contradiction clause 622]
624. $false [avatar sat refutation 188,209,246,315,319,321,465,530,621,623]
% SZS output end Proof for 107649563896051830957715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or creative then susan is curious or not rich.
If someone is not rich or not humble then someone is not funny or not brave and vice versa.
If paul is curious then john is both not strong and not generous.
If someone is both not creative and not funny then fred is both not generous and wise and vice versa.
If someone is either not generous or not rich then john is quiet.
If lucy is both not rich and happy then someone is not patient or strong and vice versa.
Everyone who is not quiet is either not wise or rich and vice versa.
Everyone who is either not brave or not tall is both not funny and not brave and vice versa.
If someone is not curious then john is creative or not old.
Everyone who is both wise and not tall is both tall and not funny and vice versa.
Everyone who is not brave is both tall and happy and vice versa.
If someone is not quiet or quiet then someone is not happy and vice versa.
If someone is either funny or rich then mary is either not old or humble.
If paul is either happy or not curious then someone is both not brave and strong.
Everyone who is not wise is either generous or curious and vice versa.
Everyone who is not strong is either not rich or tall.
Susan is either creative or not tall.
Alice is either humble or kind.
Someone is creative.
Someone is humble or quiet.
Someone is not funny or kind.
Someone is old. | Lucy is funny. | entailment | ((?[X]:((~tall(X)|creative(X))))=>((curious(susan)|~rich(susan))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
((curious(paul))=>((~strong(john)&~generous(john))))&
((?[X]:((~creative(X)&~funny(X))))<=>((~generous(fred)&wise(fred))))&
((?[X]:((~generous(X)<~>~rich(X))))=>(quiet(john)))&
(((~rich(lucy)&happy(lucy)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>rich(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>(~funny(X)&~brave(X))))&
((?[X]:(~curious(X)))=>((creative(john)|~old(john))))&
(![X]:((wise(X)&~tall(X))<=>(tall(X)&~funny(X))))&
(![X]:(~brave(X)<=>(tall(X)&happy(X))))&
((?[X]:((~quiet(X)|quiet(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((funny(X)<~>rich(X))))=>((~old(mary)<~>humble(mary))))&
(((happy(paul)<~>~curious(paul)))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:(~wise(X)<=>(generous(X)<~>curious(X))))&
(![X]:(~strong(X)=>(~rich(X)<~>tall(X))))&
((creative(susan)<~>~tall(susan)))&
((humble(alice)<~>kind(alice)))&
(?[X]:(creative(X)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((~funny(X)|kind(X))))&
(?[X]:(old(X))) | funny(lucy) | [
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4258809177433470037384664
% SZS output start Proof for 4258809177433470037384664
8. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (~brave(X0) & ~funny(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & wise(X0)) <=> (~funny(X0) & tall(X0))) [input p9]
11. ! [X0] : (~brave(X0) <=> (happy(X0) & tall(X0))) [input p10]
23. ~funny(lucy) [input hypothesis]
52. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (brave(X0) | funny(X0))) & ((~brave(X0) & ~funny(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 8]
53. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | brave(X0) | funny(X0)) & ((~brave(X0) & ~funny(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 52]
54. ! [X0] : (((~tall(X0) & wise(X0)) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 10]
55. ! [X0] : (((~tall(X0) & wise(X0)) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | tall(X0) | ~wise(X0))) [flattening 54]
56. ! [X0] : ((~brave(X0) | (~happy(X0) | ~tall(X0))) & ((happy(X0) & tall(X0)) | brave(X0))) [nnf transformation 11]
57. ! [X0] : ((~brave(X0) | ~happy(X0) | ~tall(X0)) & ((happy(X0) & tall(X0)) | brave(X0))) [flattening 56]
105. ~brave(X0) | ~brave(X0) | tall(X0) [cnf transformation 53]
112. ~tall(X0) | funny(X0) | ~tall(X0) [cnf transformation 55]
113. tall(X0) | brave(X0) [cnf transformation 57]
141. ~funny(lucy) [cnf transformation 23]
143. ~tall(X0) | funny(X0) [duplicate literal removal 112]
144. ~brave(X0) | tall(X0) [duplicate literal removal 105]
159. 4 <=> ! [X0] : tall(X0) [avatar definition]
160. tall(X0) <- (4) [avatar component clause 159]
175. 8 <=> ! [X1] : funny(X1) [avatar definition]
176. funny(X1) <- (8) [avatar component clause 175]
283. tall(X0) [subsumption resolution 113,144]
284. 4 [avatar split clause 283,159]
374. funny(X0) <- (4) [resolution 143,160]
375. 8 | ~4 [avatar split clause 374,159,175]
376. $false <- (8) [resolution 176,141]
383. ~8 [avatar contradiction clause 376]
384. $false [avatar sat refutation 284,375,383]
% SZS output end Proof for 4258809177433470037384664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is patient or not rich then lucy is kind and vice versa.
Everyone who is not funny is both not wise and not quiet and vice versa.
If someone is either calm or happy then someone is not curious.
Everyone who is both not happy and not curious is either not calm or not wise and vice versa.
Everyone who is both calm and not happy is either not wise or kind and vice versa.
If fred is both generous and quiet then someone is not tall and vice versa.
If lucy is not happy then mary is happy or not funny.
If lucy is either rich or not kind then fred is not patient.
If mary is generous or patient then fred is either not tall or humble.
If mary is not curious then someone is either not generous or not curious.
Everyone who is either tall or not rich is both brave and not creative and vice versa.
If lucy is not patient or brave then someone is not generous or quiet.
If someone is both curious and not strong then john is both not calm and calm and vice versa.
Everyone who is tall is both not patient and not tall.
Everyone who is either curious or tall is not quiet or strong.
Everyone who is not rich or tall is either not creative or not wise and vice versa.
Someone is curious.
Lucy is not kind or not rich.
Someone is not tall.
Someone is either not calm or brave.
John is either curious or not rich.
Someone is both not funny and not humble.
John is not quiet or not brave.
Lucy is funny or strong. | Mary is not funny. | neutral | (((patient(susan)|~rich(susan)))<=>(kind(lucy)))&
(![X]:(~funny(X)<=>(~wise(X)&~quiet(X))))&
((?[X]:((calm(X)<~>happy(X))))=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((calm(X)&~happy(X))<=>(~wise(X)<~>kind(X))))&
(((generous(fred)&quiet(fred)))<=>(?[X]:(~tall(X))))&
((~happy(lucy))=>((happy(mary)|~funny(mary))))&
(((rich(lucy)<~>~kind(lucy)))=>(~patient(fred)))&
(((generous(mary)|patient(mary)))=>((~tall(fred)<~>humble(fred))))&
((~curious(mary))=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>~rich(X))<=>(brave(X)&~creative(X))))&
(((~patient(lucy)|brave(lucy)))=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:((curious(X)&~strong(X))))<=>((~calm(john)&calm(john))))&
(![X]:(tall(X)=>(~patient(X)&~tall(X))))&
(![X]:((curious(X)<~>tall(X))=>(~quiet(X)|strong(X))))&
(![X]:((~rich(X)|tall(X))<=>(~creative(X)<~>~wise(X))))&
(?[X]:(curious(X)))&
((~kind(lucy)|~rich(lucy)))&
(?[X]:(~tall(X)))&
(?[X]:((~calm(X)<~>brave(X))))&
((curious(john)<~>~rich(john)))&
(?[X]:((~funny(X)&~humble(X))))&
((~quiet(john)|~brave(john)))&
((funny(lucy)|strong(lucy))) | ~funny(mary) | [] | null | 0 |
If someone is both creative and happy then susan is not generous.
Everyone who is not brave or humble is humble.
If paul is funny then fred is both brave and not patient and vice versa.
Everyone who is either not old or not humble is both not curious and rich and vice versa.
Everyone who is both not tall and generous is not patient or not humble.
If paul is not old or not curious then mary is not happy and vice versa.
Everyone who is both not humble and quiet is both not strong and not kind and vice versa.
Everyone who is happy is either not quiet or not patient and vice versa.
Everyone who is not rich or creative is creative or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
Someone is either not happy or not kind.
Someone is both not calm and old.
Alice is either not creative or not patient.
John is strong or curious. | Mary is calm. | contradiction | ((?[X]:((creative(X)&happy(X))))=>(~generous(susan)))&
(![X]:((~brave(X)|humble(X))=>humble(X)))&
((funny(paul))<=>((brave(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~humble(X))<=>(~curious(X)&rich(X))))&
(![X]:((~tall(X)&generous(X))=>(~patient(X)|~humble(X))))&
(((~old(paul)|~curious(paul)))<=>(~happy(mary)))&
(![X]:((~humble(X)&quiet(X))<=>(~strong(X)&~kind(X))))&
(![X]:(happy(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((~rich(X)|creative(X))=>(creative(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~calm(X)&old(X))))&
((~creative(alice)<~>~patient(alice)))&
((strong(john)|curious(john))) | calm(mary) | [
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 739158686599196481970800
% SZS output start Proof for 739158686599196481970800
9. ! [X0] : ((creative(X0) | ~rich(X0)) => (rich(X0) | creative(X0))) [input p8]
10. ! [X0] : ((rich(X0) | curious(X0)) <=> (~calm(X0) | ~rich(X0))) [input p9]
11. ! [X0] : ((~curious(X0) & happy(X0)) <=> (kind(X0) | wise(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> curious(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p12]
21. calm(mary) [input hypothesis]
25. ! [X0] : ((rich(X0) | creative(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 9]
26. ! [X0] : (rich(X0) | creative(X0) | (~creative(X0) & rich(X0))) [flattening 25]
37. ! [X0] : (((rich(X0) | curious(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (~rich(X0) & ~curious(X0)))) [nnf transformation 10]
38. ! [X0] : ((rich(X0) | curious(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (~rich(X0) & ~curious(X0)))) [flattening 37]
39. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (curious(X0) | ~happy(X0)))) [nnf transformation 11]
40. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | curious(X0) | ~happy(X0))) [flattening 39]
42. ! [X0] : ((((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0))))) [nnf transformation 13]
79. rich(X0) | creative(X0) | rich(X0) [cnf transformation 26]
82. ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 38]
83. rich(X0) | curious(X0) | rich(X0) [cnf transformation 38]
89. ~kind(X0) | ~curious(X0) [cnf transformation 40]
98. ~curious(X0) | kind(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 42]
121. calm(mary) [cnf transformation 21]
122. ~calm(X0) | ~rich(X0) [duplicate literal removal 82]
123. rich(X0) | curious(X0) [duplicate literal removal 83]
124. rich(X0) | creative(X0) [duplicate literal removal 79]
170. ~calm(X0) | ~creative(X0) | ~curious(X0) [subsumption resolution 98,89]
242. ~rich(mary) [resolution 122,121]
246. curious(mary) [resolution 242,123]
247. creative(mary) [resolution 124,242]
357. ~creative(mary) | ~curious(mary) [resolution 170,121]
360. ~curious(mary) [subsumption resolution 357,247]
361. $false [subsumption resolution 360,246]
% SZS output end Proof for 739158686599196481970800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is either quiet or not creative.
Everyone who is brave is either not curious or creative and vice versa.
Everyone who is not patient is rich or not creative and vice versa.
If fred is either quiet or not brave then someone is either not strong or not brave.
Everyone who is quiet or old is either curious or not old.
Everyone who is both not funny and humble is not brave or not happy.
Everyone who is strong or patient is generous.
Everyone who is not strong is both not humble and not generous.
If someone is either generous or tall then mary is either not generous or patient.
Everyone who is both creative and calm is not generous or happy and vice versa.
If someone is patient then lucy is tall.
If john is either not funny or not curious then someone is brave or patient.
Everyone who is either tall or not brave is curious or not happy and vice versa.
If mary is not wise or not humble then someone is both strong and brave and vice versa.
If someone is not kind then fred is both rich and not funny.
Everyone who is rich or not old is both patient and not creative.
Alice is both generous and not wise.
Someone is either calm or strong.
Someone is either not generous or happy.
Susan is generous.
Alice is both generous and funny.
Alice is not tall. | Fred is not strong. | contradiction | (![X]:(~wise(X)=>(quiet(X)<~>~creative(X))))&
(![X]:(brave(X)<=>(~curious(X)<~>creative(X))))&
(![X]:(~patient(X)<=>(rich(X)|~creative(X))))&
(((quiet(fred)<~>~brave(fred)))=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:((quiet(X)|old(X))=>(curious(X)<~>~old(X))))&
(![X]:((~funny(X)&humble(X))=>(~brave(X)|~happy(X))))&
(![X]:((strong(X)|patient(X))=>generous(X)))&
(![X]:(~strong(X)=>(~humble(X)&~generous(X))))&
((?[X]:((generous(X)<~>tall(X))))=>((~generous(mary)<~>patient(mary))))&
(![X]:((creative(X)&calm(X))<=>(~generous(X)|happy(X))))&
((?[X]:(patient(X)))=>(tall(lucy)))&
(((~funny(john)<~>~curious(john)))=>(?[X]:((brave(X)|patient(X)))))&
(![X]:((tall(X)<~>~brave(X))<=>(curious(X)|~happy(X))))&
(((~wise(mary)|~humble(mary)))<=>(?[X]:((strong(X)&brave(X)))))&
((?[X]:(~kind(X)))=>((rich(fred)&~funny(fred))))&
(![X]:((rich(X)|~old(X))=>(patient(X)&~creative(X))))&
((generous(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>strong(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
(generous(susan))&
((generous(alice)&funny(alice)))&
(~tall(alice)) | ~strong(fred) | [
"p2",
"p6",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9217327258243917455858182
% SZS output start Proof for 9217327258243917455858182
3. ! [X0] : (~patient(X0) <=> (~creative(X0) | rich(X0))) [input p2]
7. ! [X0] : ((patient(X0) | strong(X0)) => generous(X0)) [input p6]
8. ! [X0] : (~strong(X0) => (~generous(X0) & ~humble(X0))) [input p7]
10. ! [X0] : ((calm(X0) & creative(X0)) <=> (happy(X0) | ~generous(X0))) [input p9]
16. ! [X0] : ((~old(X0) | rich(X0)) => (~creative(X0) & patient(X0))) [input p15]
23. ~strong(fred) [input hypothesis]
30. ! [X0] : (generous(X0) | (~patient(X0) & ~strong(X0))) [ennf transformation 7]
31. ! [X0] : ((~generous(X0) & ~humble(X0)) | strong(X0)) [ennf transformation 8]
35. ! [X0] : ((~creative(X0) & patient(X0)) | (old(X0) & ~rich(X0))) [ennf transformation 16]
38. ! [X0] : ((~patient(X0) | (creative(X0) & ~rich(X0))) & ((~creative(X0) | rich(X0)) | patient(X0))) [nnf transformation 3]
39. ! [X0] : ((~patient(X0) | (creative(X0) & ~rich(X0))) & (~creative(X0) | rich(X0) | patient(X0))) [flattening 38]
45. ! [X0] : (((calm(X0) & creative(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~calm(X0) | ~creative(X0)))) [nnf transformation 10]
46. ! [X0] : (((calm(X0) & creative(X0)) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ~calm(X0) | ~creative(X0))) [flattening 45]
69. ~creative(X0) | rich(X0) | patient(X0) [cnf transformation 39]
70. ~rich(X0) | ~patient(X0) [cnf transformation 39]
82. ~patient(X0) | generous(X0) [cnf transformation 30]
84. ~generous(X0) | strong(X0) [cnf transformation 31]
90. generous(X0) | creative(X0) [cnf transformation 46]
108. patient(X0) | ~rich(X0) [cnf transformation 35]
122. ~strong(fred) [cnf transformation 23]
210. ~rich(X0) [subsumption resolution 108,70]
242. strong(X0) | creative(X0) [resolution 90,84]
287. 27 <=> creative(fred) [avatar definition]
289. creative(fred) <- (27) [avatar component clause 287]
466. creative(fred) [resolution 242,122]
469. 27 [avatar split clause 466,287]
507. rich(fred) | patient(fred) <- (27) [resolution 289,69]
510. patient(fred) <- (27) [subsumption resolution 507,210]
608. generous(fred) <- (27) [resolution 510,82]
677. strong(fred) <- (27) [resolution 608,84]
678. $false <- (27) [subsumption resolution 677,122]
679. ~27 [avatar contradiction clause 678]
680. $false [avatar sat refutation 469,679]
% SZS output end Proof for 9217327258243917455858182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not funny is not rich or rich and vice versa.
Everyone who is both creative and rich is tall and vice versa.
Everyone who is curious or brave is generous.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
Someone is both happy and not tall.
Someone is generous.
Someone is either brave or not curious.
Paul is either not calm or not kind. | Paul is tall. | contradiction | (![X]:((patient(X)&~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((creative(X)&rich(X))<=>tall(X)))&
(![X]:((curious(X)|brave(X))=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:(generous(X)))&
(?[X]:((brave(X)<~>~curious(X))))&
((~calm(paul)<~>~kind(paul))) | tall(paul) | [
"p0",
"p1",
"p4",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2669638977501956096176300
% SZS output start Proof for 2669638977501956096176300
1. ! [X0] : ((~funny(X0) & patient(X0)) <=> (rich(X0) | ~rich(X0))) [input p0]
2. ! [X0] : ((rich(X0) & creative(X0)) <=> tall(X0)) [input p1]
5. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p4]
10. (~quiet(lucy) & ~brave(lucy)) <=> ? [X0] : rich(X0) [input p9]
11. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (~old(X0) | wise(X0))) [input p10]
20. tall(paul) [input hypothesis]
23. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 5]
28. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 1]
29. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | funny(X0) | ~patient(X0))) [flattening 28]
30. ! [X0] : (((rich(X0) & creative(X0)) | ~tall(X0)) & (tall(X0) | (~rich(X0) | ~creative(X0)))) [nnf transformation 2]
31. ! [X0] : (((rich(X0) & creative(X0)) | ~tall(X0)) & (tall(X0) | ~rich(X0) | ~creative(X0))) [flattening 30]
45. ((~quiet(lucy) & ~brave(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | (quiet(lucy) | brave(lucy))) [nnf transformation 10]
46. ((~quiet(lucy) & ~brave(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | quiet(lucy) | brave(lucy)) [flattening 45]
47. ((~quiet(lucy) & ~brave(lucy)) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | quiet(lucy) | brave(lucy)) [rectify 46]
48. ? [X1] : rich(X1) => rich(sK2) [choice axiom]
49. ((~quiet(lucy) & ~brave(lucy)) | ! [X0] : ~rich(X0)) & (rich(sK2) | quiet(lucy) | brave(lucy)) [skolemisation 47,48]
50. ! [X0] : (((wise(X0) & ~patient(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 11]
51. ! [X0] : (((wise(X0) & ~patient(X0)) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | ~wise(X0) | patient(X0))) [flattening 50]
66. patient(X0) | rich(X0) [cnf transformation 29]
67. ~rich(X0) | patient(X0) [cnf transformation 29]
72. ~tall(X0) | rich(X0) [cnf transformation 31]
78. wise(X0) | quiet(X0) [cnf transformation 23]
97. ~quiet(lucy) | ~rich(X0) [cnf transformation 49]
99. ~patient(X0) | ~wise(X0) [cnf transformation 51]
126. tall(paul) [cnf transformation 20]
128. patient(X0) [subsumption resolution 66,67]
168. 9 <=> ! [X0] : ~rich(X0) [avatar definition]
169. ~rich(X0) <- (9) [avatar component clause 168]
171. 10 <=> quiet(lucy) [avatar definition]
173. ~quiet(lucy) <- (~10) [avatar component clause 171]
174. 9 | ~10 [avatar split clause 97,171,168]
186. ~wise(X0) [subsumption resolution 99,128]
216. rich(paul) [resolution 72,126]
217. $false <- (9) [subsumption resolution 216,169]
218. ~9 [avatar contradiction clause 217]
225. quiet(X0) [resolution 78,186]
226. $false <- (~10) [resolution 225,173]
227. 10 [avatar contradiction clause 226]
228. $false [avatar sat refutation 174,218,227]
% SZS output end Proof for 2669638977501956096176300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and kind is not generous and vice versa.
If john is both not curious and tall then someone is either not tall or kind and vice versa.
Everyone who is not brave is both kind and creative and vice versa.
If someone is either strong or humble then someone is both strong and wise and vice versa.
Everyone who is quiet is not patient or not generous.
If fred is either patient or not strong then susan is not rich and vice versa.
Everyone who is not wise is both not curious and old.
If fred is not humble then alice is not funny or not curious and vice versa.
Everyone who is either not rich or not happy is not creative and vice versa.
Everyone who is happy or patient is either patient or not rich and vice versa.
If paul is happy then lucy is strong or not kind.
If someone is not patient or not quiet then alice is both not kind and not creative.
If paul is not happy then someone is humble or not creative and vice versa.
Everyone who is both patient and not happy is funny and vice versa.
If someone is either not calm or not kind then someone is not generous and vice versa.
Everyone who is not quiet or not funny is either not happy or not quiet.
Lucy is not happy or kind.
Fred is either quiet or kind.
John is rich or not tall.
Fred is both not brave and not calm.
Fred is generous.
Someone is not patient or strong.
Fred is rich or not humble.
John is not kind. | Fred is quiet. | contradiction | (![X]:((funny(X)&kind(X))<=>~generous(X)))&
(((~curious(john)&tall(john)))<=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:(~brave(X)<=>(kind(X)&creative(X))))&
((?[X]:((strong(X)<~>humble(X))))<=>(?[X]:((strong(X)&wise(X)))))&
(![X]:(quiet(X)=>(~patient(X)|~generous(X))))&
(((patient(fred)<~>~strong(fred)))<=>(~rich(susan)))&
(![X]:(~wise(X)=>(~curious(X)&old(X))))&
((~humble(fred))<=>((~funny(alice)|~curious(alice))))&
(![X]:((~rich(X)<~>~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|patient(X))<=>(patient(X)<~>~rich(X))))&
((happy(paul))=>((strong(lucy)|~kind(lucy))))&
((?[X]:((~patient(X)|~quiet(X))))=>((~kind(alice)&~creative(alice))))&
((~happy(paul))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((patient(X)&~happy(X))<=>funny(X)))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~happy(X)<~>~quiet(X))))&
((~happy(lucy)|kind(lucy)))&
((quiet(fred)<~>kind(fred)))&
((rich(john)|~tall(john)))&
((~brave(fred)&~calm(fred)))&
(generous(fred))&
(?[X]:((~patient(X)|strong(X))))&
((rich(fred)|~humble(fred)))&
(~kind(john)) | quiet(fred) | [
"p2",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5590299746527293517481675
% SZS output start Proof for 5590299746527293517481675
3. ! [X0] : (~brave(X0) <=> (creative(X0) & kind(X0))) [input p2]
18. quiet(fred) <~> kind(fred) [input p17]
20. ~calm(fred) & ~brave(fred) [input p19]
25. quiet(fred) [input hypothesis]
28. ! [X0] : (~brave(X0) => (creative(X0) & kind(X0))) [unused predicate definition removal 3]
30. ! [X0] : ((creative(X0) & kind(X0)) | brave(X0)) [ennf transformation 28]
68. (~kind(fred) | ~quiet(fred)) & (kind(fred) | quiet(fred)) [nnf transformation 18]
80. brave(X0) | kind(X0) [cnf transformation 30]
128. ~kind(fred) | ~quiet(fred) [cnf transformation 68]
130. ~brave(fred) [cnf transformation 20]
136. quiet(fred) [cnf transformation 25]
310. 38 <=> quiet(fred) [avatar definition]
314. 39 <=> kind(fred) [avatar definition]
316. ~kind(fred) <- (~39) [avatar component clause 314]
317. ~38 | ~39 [avatar split clause 128,314,310]
338. 38 [avatar split clause 136,310]
343. kind(fred) [resolution 80,130]
344. $false <- (~39) [subsumption resolution 343,316]
345. 39 [avatar contradiction clause 344]
346. $false [avatar sat refutation 317,338,345]
% SZS output end Proof for 5590299746527293517481675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not generous is generous or patient.
Everyone who is not old or brave is either not old or not kind.
If alice is curious or creative then alice is either not rich or old and vice versa.
Everyone who is either not rich or not curious is funny.
Everyone who is patient is not calm or kind and vice versa.
Everyone who is creative or not old is old or quiet and vice versa.
If paul is quiet or not kind then someone is not calm and vice versa.
Everyone who is not calm or not quiet is kind and vice versa.
Everyone who is humble or tall is not old.
If fred is both not calm and not humble then someone is tall or not old.
Everyone who is both not curious and not wise is not strong and vice versa.
Everyone who is tall or happy is either not creative or happy and vice versa.
If someone is not patient then someone is both not kind and not creative.
If fred is old then john is both wise and not old.
Everyone who is generous is not curious and vice versa.
If mary is not rich then someone is not strong or not quiet and vice versa.
Someone is either brave or not rich.
Someone is old.
John is either creative or calm.
John is either not quiet or old.
Paul is not brave.
Someone is either not funny or creative.
Someone is not old or not tall. | John is kind. | entailment | (![X]:((~humble(X)&~generous(X))=>(generous(X)|patient(X))))&
(![X]:((~old(X)|brave(X))=>(~old(X)<~>~kind(X))))&
(((curious(alice)|creative(alice)))<=>((~rich(alice)<~>old(alice))))&
(![X]:((~rich(X)<~>~curious(X))=>funny(X)))&
(![X]:(patient(X)<=>(~calm(X)|kind(X))))&
(![X]:((creative(X)|~old(X))<=>(old(X)|quiet(X))))&
(((quiet(paul)|~kind(paul)))<=>(?[X]:(~calm(X))))&
(![X]:((~calm(X)|~quiet(X))<=>kind(X)))&
(![X]:((humble(X)|tall(X))=>~old(X)))&
(((~calm(fred)&~humble(fred)))=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~curious(X)&~wise(X))<=>~strong(X)))&
(![X]:((tall(X)|happy(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~kind(X)&~creative(X)))))&
((old(fred))=>((wise(john)&~old(john))))&
(![X]:(generous(X)<=>~curious(X)))&
((~rich(mary))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:(old(X)))&
((creative(john)<~>calm(john)))&
((~quiet(john)<~>old(john)))&
(~brave(paul))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((~old(X)|~tall(X)))) | kind(john) | [
"p5",
"p7",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5678729358298086883858920
% SZS output start Proof for 5678729358298086883858920
6. ! [X0] : ((~old(X0) | creative(X0)) <=> (quiet(X0) | old(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) | ~calm(X0)) <=> kind(X0)) [input p7]
19. creative(john) <~> calm(john) [input p18]
20. ~quiet(john) <~> old(john) [input p19]
24. ~kind(john) [input hypothesis]
44. ! [X0] : (((~old(X0) | creative(X0)) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | (old(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((~old(X0) | creative(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | (old(X0) & ~creative(X0)))) [flattening 44]
51. ! [X0] : (((~quiet(X0) | ~calm(X0)) | ~kind(X0)) & (kind(X0) | (quiet(X0) & calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((~quiet(X0) | ~calm(X0) | ~kind(X0)) & (kind(X0) | (quiet(X0) & calm(X0)))) [flattening 51]
71. (~calm(john) | ~creative(john)) & (calm(john) | creative(john)) [nnf transformation 19]
72. (~old(john) | quiet(john)) & (old(john) | ~quiet(john)) [nnf transformation 20]
93. quiet(X0) | old(X0) | old(X0) [cnf transformation 45]
94. ~old(X0) | creative(X0) | ~old(X0) [cnf transformation 45]
99. calm(X0) | kind(X0) [cnf transformation 52]
126. ~calm(john) | ~creative(john) [cnf transformation 71]
127. old(john) | ~quiet(john) [cnf transformation 72]
128. ~old(john) | quiet(john) [cnf transformation 72]
133. ~kind(john) [cnf transformation 24]
136. quiet(X0) | old(X0) [duplicate literal removal 93]
137. ~old(X0) | creative(X0) [duplicate literal removal 94]
212. 16 <=> old(john) [avatar definition]
213. old(john) <- (16) [avatar component clause 212]
253. 25 <=> creative(john) [avatar definition]
255. ~creative(john) <- (~25) [avatar component clause 253]
257. 26 <=> calm(john) [avatar definition]
259. ~calm(john) <- (~26) [avatar component clause 257]
260. ~25 | ~26 [avatar split clause 126,257,253]
262. quiet(john) [subsumption resolution 128,136]
263. old(john) [subsumption resolution 127,262]
264. 16 [avatar split clause 263,212]
276. kind(john) <- (~26) [resolution 99,259]
277. $false <- (~26) [subsumption resolution 276,133]
278. 26 [avatar contradiction clause 277]
285. creative(john) <- (16) [resolution 137,213]
287. $false <- (16, ~25) [subsumption resolution 285,255]
288. ~16 | 25 [avatar contradiction clause 287]
289. $false [avatar sat refutation 260,264,278,288]
% SZS output end Proof for 5678729358298086883858920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or happy is not funny or humble and vice versa. If someone is both not curious and humble then someone is either not old or patient and vice versa. Everyone who is creative or patient is not kind. If someone is not funny then someone is either kind or strong. Everyone who is either kind or calm is patient or curious and vice versa. If someone is either calm or not humble then someone is either rich or not humble. If fred is not brave or generous then john is either not strong or not old and vice versa. If someone is wise or not curious then susan is quiet. Everyone who is not quiet or quiet is both quiet and not happy and vice versa. If someone is creative then someone is not tall and vice versa. If someone is not generous or not strong then someone is either not calm or calm. If john is tall or not quiet then someone is either creative or not happy and vice versa. Everyone who is both tall and generous is rich and vice versa. Everyone who is wise or not old is generous. Everyone who is either not tall or calm is both happy and not wise and vice versa. Everyone who is not kind or not patient is both generous and rich. Someone is funny or not generous. Alice is both not happy and not old. Paul is either not happy or not strong. Someone is not happy or not wise. Someone is generous or brave. Alice is both wise and rich. Someone is both not old and not wise. | John is patient. | contradiction | (![X]:((funny(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((creative(X)|patient(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(?[X]:((kind(X)<~>strong(X)))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)|curious(X))))&
((?[X]:((calm(X)<~>~humble(X))))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~brave(fred)|generous(fred)))<=>((~strong(john)<~>~old(john))))&
((?[X]:((wise(X)|~curious(X))))=>(quiet(susan)))&
(![X]:((~quiet(X)|quiet(X))<=>(quiet(X)&~happy(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(((tall(john)|~quiet(john)))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((tall(X)&generous(X))<=>rich(X)))&
(![X]:((wise(X)|~old(X))=>generous(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(happy(X)&~wise(X))))&
(![X]:((~kind(X)|~patient(X))=>(generous(X)&rich(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~happy(alice)&~old(alice)))&
((~happy(paul)<~>~strong(paul)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((generous(X)|brave(X))))&
((wise(alice)&rich(alice)))&
(?[X]:((~old(X)&~wise(X)))) | patient(john) | [
"p2",
"p4",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 141384766539966629864840
% SZS output start Proof for 141384766539966629864840
3. ! [X0] : ((patient(X0) | creative(X0)) => ~kind(X0)) [input p2]
5. ! [X0] : ((kind(X0) <~> calm(X0)) <=> (curious(X0) | patient(X0))) [input p4]
9. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~happy(X0) & quiet(X0))) [input p8]
10. ? [X0] : creative(X0) <=> ? [X0] : ~tall(X0) [input p9]
12. (~quiet(john) | tall(john)) <=> ? [X0] : (creative(X0) <~> ~happy(X0)) [input p11]
13. ! [X0] : ((generous(X0) & tall(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> (~wise(X0) & happy(X0))) [input p14]
16. ! [X0] : ((~patient(X0) | ~kind(X0)) => (rich(X0) & generous(X0))) [input p15]
24. patient(john) [input hypothesis]
28. ? [X0] : creative(X0) <=> ? [X1] : ~tall(X1) [rectify 10]
30. ! [X0] : (~kind(X0) | (~patient(X0) & ~creative(X0))) [ennf transformation 3]
36. ! [X0] : ((rich(X0) & generous(X0)) | (patient(X0) & kind(X0))) [ennf transformation 16]
48. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [nnf transformation 5]
49. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [flattening 48]
56. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (happy(X0) | ~quiet(X0))) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 9]
57. ! [X0] : ((quiet(X0) | ~quiet(X0) | happy(X0) | ~quiet(X0)) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 56]
58. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : ~creative(X0)) [nnf transformation 28]
59. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : ~creative(X3)) [rectify 58]
60. ? [X0] : creative(X0) => creative(sK4) [choice axiom]
61. ? [X2] : ~tall(X2) => ~tall(sK5) [choice axiom]
62. (creative(sK4) | ! [X1] : tall(X1)) & (~tall(sK5) | ! [X3] : ~creative(X3)) [skolemisation 59,61,60]
67. ((~quiet(john) | tall(john)) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [nnf transformation 12]
68. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [flattening 67]
69. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) | (quiet(john) & ~tall(john))) [rectify 68]
70. ? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) => ((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) [choice axiom]
71. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) | (quiet(john) & ~tall(john))) [skolemisation 69,70]
72. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | (~generous(X0) | ~tall(X0)))) [nnf transformation 13]
73. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | ~generous(X0) | ~tall(X0))) [flattening 72]
74. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 15]
75. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [flattening 74]
97. ~kind(X0) | ~creative(X0) [cnf transformation 30]
98. ~kind(X0) | ~patient(X0) [cnf transformation 30]
103. calm(X0) | kind(X0) | ~patient(X0) [cnf transformation 49]
119. quiet(X0) | quiet(X0) [cnf transformation 57]
121. ~happy(X0) | quiet(X0) [cnf transformation 57]
122. ~quiet(X0) | ~happy(X0) [cnf transformation 57]
124. ~tall(sK5) | ~creative(X3) [cnf transformation 62]
135. ~quiet(john) | tall(john) | creative(X0) | happy(X0) [cnf transformation 71]
137. ~rich(X0) | tall(X0) [cnf transformation 73]
142. happy(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 75]
149. rich(X0) | kind(X0) [cnf transformation 36]
162. patient(john) [cnf transformation 24]
163. quiet(X0) [duplicate literal removal 119]
212. ~patient(X0) | calm(X0) [subsumption resolution 103,98]
266. ~happy(X0) [subsumption resolution 121,122]
276. 24 <=> ! [X3] : ~creative(X3) [avatar definition]
277. ~creative(X3) <- (24) [avatar component clause 276]
279. 25 <=> tall(sK5) [avatar definition]
281. ~tall(sK5) <- (~25) [avatar component clause 279]
282. 24 | ~25 [avatar split clause 124,279,276]
283. tall(john) | creative(X0) | happy(X0) [subsumption resolution 135,163]
284. tall(john) | creative(X0) [subsumption resolution 283,266]
286. 26 <=> ! [X0] : creative(X0) [avatar definition]
287. creative(X0) <- (26) [avatar component clause 286]
289. 27 <=> tall(john) [avatar definition]
291. tall(john) <- (27) [avatar component clause 289]
292. 26 | 27 [avatar split clause 284,289,286]
299. ~tall(X0) | ~calm(X0) [subsumption resolution 142,266]
337. tall(X1) | kind(X1) [resolution 149,137]
348. calm(john) [resolution 212,162]
350. ~calm(john) <- (27) [resolution 299,291]
352. $false <- (27) [subsumption resolution 350,348]
353. ~27 [avatar contradiction clause 352]
366. kind(sK5) <- (~25) [resolution 337,281]
374. ~creative(sK5) <- (~25) [resolution 366,97]
375. $false <- (~25, 26) [subsumption resolution 374,287]
376. 25 | ~26 [avatar contradiction clause 375]
377. $false <- (24, 26) [subsumption resolution 277,287]
378. ~24 | ~26 [avatar contradiction clause 377]
379. $false [avatar sat refutation 282,292,353,376,378]
% SZS output end Proof for 141384766539966629864840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and quiet is not humble or patient and vice versa.
If someone is not quiet or old then someone is not brave or wise and vice versa.
Everyone who is either not happy or not wise is both kind and happy and vice versa.
If someone is funny then someone is not kind or wise and vice versa.
If mary is rich then john is not funny and vice versa.
Everyone who is creative is strong.
If someone is not kind or generous then someone is both not patient and not old and vice versa.
Everyone who is happy or not brave is both happy and funny and vice versa.
Everyone who is both not curious and patient is not tall or tall.
If someone is calm or not generous then someone is generous and vice versa.
Everyone who is generous or not old is either not strong or old.
Everyone who is not happy or humble is patient.
If fred is quiet then john is quiet or not funny.
If alice is both not calm and kind then alice is strong or not creative and vice versa.
If someone is humble or creative then susan is not calm or not wise and vice versa.
If paul is tall or creative then paul is old or not humble.
Fred is both not patient and not calm.
Someone is both not generous and creative.
Someone is not generous.
John is creative.
Lucy is wise.
Alice is not brave or strong. | Mary is not curious. | neutral | (![X]:((~brave(X)&quiet(X))<=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)|old(X))))<=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~happy(X)<~>~wise(X))<=>(kind(X)&happy(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~kind(X)|wise(X)))))&
((rich(mary))<=>(~funny(john)))&
(![X]:(creative(X)=>strong(X)))&
((?[X]:((~kind(X)|generous(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((happy(X)|~brave(X))<=>(happy(X)&funny(X))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)|tall(X))))&
((?[X]:((calm(X)|~generous(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|~old(X))=>(~strong(X)<~>old(X))))&
(![X]:((~happy(X)|humble(X))=>patient(X)))&
((quiet(fred))=>((quiet(john)|~funny(john))))&
(((~calm(alice)&kind(alice)))<=>((strong(alice)|~creative(alice))))&
((?[X]:((humble(X)|creative(X))))<=>((~calm(susan)|~wise(susan))))&
(((tall(paul)|creative(paul)))=>((old(paul)|~humble(paul))))&
((~patient(fred)&~calm(fred)))&
(?[X]:((~generous(X)&creative(X))))&
(?[X]:(~generous(X)))&
(creative(john))&
(wise(lucy))&
((~brave(alice)|strong(alice))) | ~curious(mary) | [] | null | 0 |
Everyone who is strong is not patient. If susan is not humble or not old then paul is old or curious and vice versa. Everyone who is not humble is strong. If alice is patient then paul is humble or not humble and vice versa. If alice is both not patient and not kind then someone is both old and generous and vice versa. Everyone who is either not kind or not strong is both patient and not tall and vice versa. Everyone who is either not happy or tall is not kind or tall and vice versa. If someone is either not wise or not happy then lucy is not creative or not kind and vice versa. Everyone who is humble is either kind or curious. If someone is both not happy and not generous then paul is either curious or quiet. If someone is both curious and not generous then someone is not quiet. If mary is either calm or generous then alice is both not wise and not quiet and vice versa. Everyone who is calm is patient or quiet and vice versa. If alice is not brave then someone is rich. If lucy is both not calm and not creative then someone is either not happy or not generous and vice versa. If lucy is either generous or not happy then someone is not old or not rich. Someone is not humble or quiet. Mary is not rich. Susan is both not humble and calm. Paul is not old. Susan is not creative or strong. Susan is both not rich and quiet. Someone is both not strong and not happy. Alice is either not tall or not funny. | Lucy is creative. | neutral | (![X]:(strong(X)=>~patient(X)))&
(((~humble(susan)|~old(susan)))<=>((old(paul)|curious(paul))))&
(![X]:(~humble(X)=>strong(X)))&
((patient(alice))<=>((humble(paul)|~humble(paul))))&
(((~patient(alice)&~kind(alice)))<=>(?[X]:((old(X)&generous(X)))))&
(![X]:((~kind(X)<~>~strong(X))<=>(patient(X)&~tall(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~kind(X)|tall(X))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~creative(lucy)|~kind(lucy))))&
(![X]:(humble(X)=>(kind(X)<~>curious(X))))&
((?[X]:((~happy(X)&~generous(X))))=>((curious(paul)<~>quiet(paul))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:(~quiet(X))))&
(((calm(mary)<~>generous(mary)))<=>((~wise(alice)&~quiet(alice))))&
(![X]:(calm(X)<=>(patient(X)|quiet(X))))&
((~brave(alice))=>(?[X]:(rich(X))))&
(((~calm(lucy)&~creative(lucy)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(((generous(lucy)<~>~happy(lucy)))=>(?[X]:((~old(X)|~rich(X)))))&
(?[X]:((~humble(X)|quiet(X))))&
(~rich(mary))&
((~humble(susan)&calm(susan)))&
(~old(paul))&
((~creative(susan)|strong(susan)))&
((~rich(susan)&quiet(susan)))&
(?[X]:((~strong(X)&~happy(X))))&
((~tall(alice)<~>~funny(alice))) | creative(lucy) | [] | null | 0 |
Everyone who is both strong and creative is both not kind and humble and vice versa. Everyone who is not curious or strong is both not curious and wise. Everyone who is not curious is funny and vice versa. Everyone who is quiet is either funny or old and vice versa. Everyone who is either not generous or wise is both not patient and brave. If someone is either patient or wise then someone is both not happy and curious and vice versa. If susan is either strong or kind then someone is either not tall or rich. Everyone who is both not curious and quiet is both patient and not tall. Everyone who is wise is either kind or not creative. Everyone who is both not brave and kind is either kind or quiet and vice versa. Everyone who is not patient or not kind is calm or strong and vice versa. If someone is funny or not funny then susan is both generous and not tall. Everyone who is funny is both not old and not funny and vice versa. If someone is both not creative and not brave then someone is both old and not creative and vice versa. If john is not generous then someone is either not curious or kind and vice versa. Everyone who is both not calm and not patient is funny and vice versa. John is either not happy or not funny. Fred is not funny. John is either calm or tall. Someone is creative or not brave. Someone is not wise. Paul is both not tall and quiet. | Fred is not calm. | neutral | (![X]:((strong(X)&creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~curious(X)|strong(X))=>(~curious(X)&wise(X))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:(quiet(X)<=>(funny(X)<~>old(X))))&
(![X]:((~generous(X)<~>wise(X))=>(~patient(X)&brave(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((~happy(X)&curious(X)))))&
(((strong(susan)<~>kind(susan)))=>(?[X]:((~tall(X)<~>rich(X)))))&
(![X]:((~curious(X)&quiet(X))=>(patient(X)&~tall(X))))&
(![X]:(wise(X)=>(kind(X)<~>~creative(X))))&
(![X]:((~brave(X)&kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:((~patient(X)|~kind(X))<=>(calm(X)|strong(X))))&
((?[X]:((funny(X)|~funny(X))))=>((generous(susan)&~tall(susan))))&
(![X]:(funny(X)<=>(~old(X)&~funny(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:((old(X)&~creative(X)))))&
((~generous(john))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~calm(X)&~patient(X))<=>funny(X)))&
((~happy(john)<~>~funny(john)))&
(~funny(fred))&
((calm(john)<~>tall(john)))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(~wise(X)))&
((~tall(paul)&quiet(paul))) | ~calm(fred) | [] | null | 0 |
If someone is both curious and not creative then paul is both not tall and patient. Everyone who is both not generous and not old is funny and vice versa. If fred is both not brave and humble then fred is either calm or not wise. Everyone who is not strong is happy or tall. If someone is happy then someone is both not patient and brave. Everyone who is wise is not wise or not patient. Everyone who is calm or not generous is either quiet or strong and vice versa. Everyone who is either tall or funny is funny. If someone is both not old and strong then someone is not curious or creative. Everyone who is both not strong and not curious is tall or not strong. If susan is calm or curious then paul is both not creative and not old. If john is not humble then paul is either tall or not rich. Everyone who is either tall or not rich is either happy or tall. Everyone who is either not funny or not old is either rich or quiet. Everyone who is patient is curious and vice versa. If someone is both not rich and not strong then john is either not wise or humble. Someone is either not quiet or quiet. Mary is tall or not brave. Someone is either not tall or brave. Alice is not happy. Someone is strong or wise. Susan is curious. John is both not kind and curious. Mary is strong. | Susan is patient. | entailment | ((?[X]:((curious(X)&~creative(X))))=>((~tall(paul)&patient(paul))))&
(![X]:((~generous(X)&~old(X))<=>funny(X)))&
(((~brave(fred)&humble(fred)))=>((calm(fred)<~>~wise(fred))))&
(![X]:(~strong(X)=>(happy(X)|tall(X))))&
((?[X]:(happy(X)))=>(?[X]:((~patient(X)&brave(X)))))&
(![X]:(wise(X)=>(~wise(X)|~patient(X))))&
(![X]:((calm(X)|~generous(X))<=>(quiet(X)<~>strong(X))))&
(![X]:((tall(X)<~>funny(X))=>funny(X)))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~curious(X)|creative(X)))))&
(![X]:((~strong(X)&~curious(X))=>(tall(X)|~strong(X))))&
(((calm(susan)|curious(susan)))=>((~creative(paul)&~old(paul))))&
((~humble(john))=>((tall(paul)<~>~rich(paul))))&
(![X]:((tall(X)<~>~rich(X))=>(happy(X)<~>tall(X))))&
(![X]:((~funny(X)<~>~old(X))=>(rich(X)<~>quiet(X))))&
(![X]:(patient(X)<=>curious(X)))&
((?[X]:((~rich(X)&~strong(X))))=>((~wise(john)<~>humble(john))))&
(?[X]:((~quiet(X)<~>quiet(X))))&
((tall(mary)|~brave(mary)))&
(?[X]:((~tall(X)<~>brave(X))))&
(~happy(alice))&
(?[X]:((strong(X)|wise(X))))&
(curious(susan))&
((~kind(john)&curious(john)))&
(strong(mary)) | patient(susan) | [
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8691610264703158093122205
% SZS output start Proof for 8691610264703158093122205
15. ! [X0] : (patient(X0) <=> curious(X0)) [input p14]
22. curious(susan) [input p21]
25. ~patient(susan) [input hypothesis]
61. ! [X0] : ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))) [nnf transformation 15]
107. ~curious(X0) | patient(X0) [cnf transformation 61]
117. curious(susan) [cnf transformation 22]
120. ~patient(susan) [cnf transformation 25]
182. 14 <=> curious(susan) [avatar definition]
183. curious(susan) <- (14) [avatar component clause 182]
252. 14 [avatar split clause 117,182]
255. patient(susan) <- (14) [resolution 107,183]
257. $false <- (14) [subsumption resolution 255,120]
258. ~14 [avatar contradiction clause 257]
259. $false [avatar sat refutation 252,258]
% SZS output end Proof for 8691610264703158093122205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is tall.
If someone is both not tall and patient then someone is both not humble and creative.
If someone is not quiet or kind then someone is not creative.
If john is both wise and humble then susan is both wise and not quiet.
Everyone who is not patient or funny is funny or tall.
Everyone who is both calm and not creative is either curious or not quiet.
Everyone who is happy is not quiet or tall.
If someone is old or calm then lucy is both brave and not calm.
If someone is calm or quiet then mary is old or strong and vice versa.
Everyone who is both old and not happy is both quiet and not brave.
If someone is strong or not strong then alice is creative and vice versa.
If paul is both old and not patient then someone is either generous or creative.
Everyone who is not brave is both not calm and generous and vice versa.
Everyone who is either strong or patient is both not calm and not funny.
Everyone who is either funny or patient is happy and vice versa.
If fred is either curious or not kind then john is both quiet and not old.
Someone is happy.
John is both not strong and not wise.
Someone is both not humble and not tall.
Someone is calm.
Lucy is not happy.
Lucy is both not calm and strong.
Someone is quiet or humble.
Mary is both curious and not quiet. | Mary is curious. | entailment | ((?[X]:(~happy(X)))=>(tall(fred)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
((?[X]:((~quiet(X)|kind(X))))=>(?[X]:(~creative(X))))&
(((wise(john)&humble(john)))=>((wise(susan)&~quiet(susan))))&
(![X]:((~patient(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&~creative(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>((brave(lucy)&~calm(lucy))))&
((?[X]:((calm(X)|quiet(X))))<=>((old(mary)|strong(mary))))&
(![X]:((old(X)&~happy(X))=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(creative(alice)))&
(((old(paul)&~patient(paul)))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~brave(X)<=>(~calm(X)&generous(X))))&
(![X]:((strong(X)<~>patient(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)<~>patient(X))<=>happy(X)))&
(((curious(fred)<~>~kind(fred)))=>((quiet(john)&~old(john))))&
(?[X]:(happy(X)))&
((~strong(john)&~wise(john)))&
(?[X]:((~humble(X)&~tall(X))))&
(?[X]:(calm(X)))&
(~happy(lucy))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
((curious(mary)&~quiet(mary))) | curious(mary) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8469782629883959367850720
% SZS output start Proof for 8469782629883959367850720
24. ~quiet(mary) & curious(mary) [input p23]
25. ~curious(mary) [input hypothesis]
130. curious(mary) [cnf transformation 24]
132. ~curious(mary) [cnf transformation 25]
286. $false [subsumption resolution 132,130]
% SZS output end Proof for 8469782629883959367850720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not brave and kind then susan is rich or quiet.
Everyone who is either rich or not funny is either rich or creative.
Everyone who is strong is either not patient or calm and vice versa.
Everyone who is both kind and generous is both generous and not curious.
Everyone who is both quiet and funny is both not creative and not quiet.
Everyone who is either not curious or rich is curious and vice versa.
Everyone who is calm is both not strong and not curious and vice versa.
If lucy is brave then john is both not strong and not curious and vice versa.
Everyone who is creative or not tall is either not curious or not funny and vice versa.
Everyone who is both curious and not rich is wise.
If fred is old then someone is both strong and not humble and vice versa.
Everyone who is not generous is wise or humble and vice versa.
If someone is both calm and humble then someone is both not old and not brave.
If someone is old or quiet then someone is not rich.
Everyone who is both wise and not rich is both not brave and humble and vice versa.
Everyone who is both calm and not brave is either not patient or not strong and vice versa.
Lucy is both happy and not tall.
Someone is not curious.
Someone is either not brave or calm.
John is either wise or brave.
Someone is generous or not patient.
John is tall or patient.
Someone is not funny. | John is strong. | contradiction | (((~brave(mary)&kind(mary)))=>((rich(susan)|quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(rich(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)&~curious(X))))&
(![X]:((quiet(X)&funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)<~>rich(X))<=>curious(X)))&
(![X]:(calm(X)<=>(~strong(X)&~curious(X))))&
((brave(lucy))<=>((~strong(john)&~curious(john))))&
(![X]:((creative(X)|~tall(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((curious(X)&~rich(X))=>wise(X)))&
((old(fred))<=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:(~generous(X)<=>(wise(X)|humble(X))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((calm(X)&~brave(X))<=>(~patient(X)<~>~strong(X))))&
((happy(lucy)&~tall(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((wise(john)<~>brave(john)))&
(?[X]:((generous(X)|~patient(X))))&
((tall(john)|patient(john)))&
(?[X]:(~funny(X))) | strong(john) | [
"p2",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2234456676626206708466146
% SZS output start Proof for 2234456676626206708466146
3. ! [X0] : (strong(X0) <=> (~patient(X0) <~> calm(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> (~curious(X0) & ~strong(X0))) [input p6]
16. ! [X0] : ((~brave(X0) & calm(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p15]
24. strong(john) [input hypothesis]
40. ! [X0] : ((strong(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ~strong(X0))) [nnf transformation 3]
42. ! [X0] : ((calm(X0) | (curious(X0) | strong(X0))) & ((~curious(X0) & ~strong(X0)) | ~calm(X0))) [nnf transformation 7]
43. ! [X0] : ((calm(X0) | curious(X0) | strong(X0)) & ((~curious(X0) & ~strong(X0)) | ~calm(X0))) [flattening 42]
60. ! [X0] : (((~brave(X0) & calm(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | (brave(X0) | ~calm(X0)))) [nnf transformation 16]
61. ! [X0] : (((~brave(X0) & calm(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | brave(X0) | ~calm(X0))) [flattening 60]
76. calm(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 40]
78. strong(X0) | calm(X0) | patient(X0) [cnf transformation 40]
84. ~calm(X0) | ~strong(X0) [cnf transformation 43]
111. calm(X0) | ~strong(X0) | patient(X0) [cnf transformation 61]
112. calm(X0) | ~patient(X0) | strong(X0) [cnf transformation 61]
124. strong(john) [cnf transformation 24]
131. 1 <=> strong(john) [avatar definition]
133. strong(john) <- (1) [avatar component clause 131]
178. calm(X0) | strong(X0) [subsumption resolution 112,78]
179. calm(X0) | ~strong(X0) [subsumption resolution 111,76]
180. calm(X0) [subsumption resolution 179,178]
211. 1 [avatar split clause 124,131]
212. ~strong(X0) [resolution 84,180]
213. $false <- (1) [resolution 212,133]
214. ~1 [avatar contradiction clause 213]
215. $false [avatar sat refutation 211,214]
% SZS output end Proof for 2234456676626206708466146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and happy is both humble and not humble and vice versa.
Everyone who is humble or creative is both not humble and not funny and vice versa.
If john is not funny then paul is not curious or funny and vice versa.
If fred is generous or humble then lucy is both generous and not tall and vice versa.
If susan is not humble then someone is curious or kind.
If someone is not humble or funny then alice is either kind or not strong and vice versa.
Everyone who is tall or not tall is not quiet or creative and vice versa.
If someone is both not generous and humble then someone is both humble and strong.
If mary is both patient and brave then paul is either calm or not curious.
Everyone who is not generous or not wise is either not quiet or not creative and vice versa.
Everyone who is old or calm is both not strong and not creative.
Everyone who is either rich or creative is both curious and not tall.
If mary is both generous and not patient then someone is not happy and vice versa.
If someone is kind then someone is both generous and brave and vice versa.
Everyone who is both patient and not happy is either generous or calm.
If someone is either not humble or kind then paul is both not funny and brave and vice versa.
Paul is either brave or strong.
Someone is not quiet.
Someone is not curious or not brave.
Someone is not kind.
Someone is happy or kind.
Mary is old or not funny.
Someone is either calm or rich. | John is brave. | neutral | (![X]:((~curious(X)&happy(X))<=>(humble(X)&~humble(X))))&
(![X]:((humble(X)|creative(X))<=>(~humble(X)&~funny(X))))&
((~funny(john))<=>((~curious(paul)|funny(paul))))&
(((generous(fred)|humble(fred)))<=>((generous(lucy)&~tall(lucy))))&
((~humble(susan))=>(?[X]:((curious(X)|kind(X)))))&
((?[X]:((~humble(X)|funny(X))))<=>((kind(alice)<~>~strong(alice))))&
(![X]:((tall(X)|~tall(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((~generous(X)&humble(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((patient(mary)&brave(mary)))=>((calm(paul)<~>~curious(paul))))&
(![X]:((~generous(X)|~wise(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((old(X)|calm(X))=>(~strong(X)&~creative(X))))&
(![X]:((rich(X)<~>creative(X))=>(curious(X)&~tall(X))))&
(((generous(mary)&~patient(mary)))<=>(?[X]:(~happy(X))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((patient(X)&~happy(X))=>(generous(X)<~>calm(X))))&
((?[X]:((~humble(X)<~>kind(X))))<=>((~funny(paul)&brave(paul))))&
((brave(paul)<~>strong(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)|kind(X))))&
((old(mary)|~funny(mary)))&
(?[X]:((calm(X)<~>rich(X)))) | brave(john) | [] | null | 0 |
If someone is not brave then mary is both not wise and strong and vice versa.
If alice is both calm and not quiet then someone is both quiet and creative.
Everyone who is tall or not calm is not tall and vice versa.
Everyone who is both humble and not funny is rich or quiet.
Everyone who is happy is not rich or not quiet.
Everyone who is not funny is either happy or patient.
If someone is both not calm and not strong then lucy is both not wise and kind and vice versa.
Everyone who is happy is both not wise and not rich and vice versa.
If alice is not humble then someone is kind or not quiet.
Everyone who is both generous and not curious is funny and vice versa.
Everyone who is either not strong or calm is not curious and vice versa.
If mary is both not humble and patient then someone is not quiet or old and vice versa.
Everyone who is both not creative and not humble is either calm or tall and vice versa.
If susan is not happy then lucy is either not happy or not wise and vice versa.
Everyone who is not tall or not wise is not generous and vice versa.
Everyone who is not creative or brave is rich or curious.
John is old or rich.
Someone is not wise or happy.
Someone is either brave or funny.
Someone is either strong or humble.
Fred is not patient.
Alice is both not old and patient.
Fred is not curious. | Mary is not wise. | entailment | ((?[X]:(~brave(X)))<=>((~wise(mary)&strong(mary))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((tall(X)|~calm(X))<=>~tall(X)))&
(![X]:((humble(X)&~funny(X))=>(rich(X)|quiet(X))))&
(![X]:(happy(X)=>(~rich(X)|~quiet(X))))&
(![X]:(~funny(X)=>(happy(X)<~>patient(X))))&
((?[X]:((~calm(X)&~strong(X))))<=>((~wise(lucy)&kind(lucy))))&
(![X]:(happy(X)<=>(~wise(X)&~rich(X))))&
((~humble(alice))=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((generous(X)&~curious(X))<=>funny(X)))&
(![X]:((~strong(X)<~>calm(X))<=>~curious(X)))&
(((~humble(mary)&patient(mary)))<=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((~creative(X)&~humble(X))<=>(calm(X)<~>tall(X))))&
((~happy(susan))<=>((~happy(lucy)<~>~wise(lucy))))&
(![X]:((~tall(X)|~wise(X))<=>~generous(X)))&
(![X]:((~creative(X)|brave(X))=>(rich(X)|curious(X))))&
((old(john)|rich(john)))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(~patient(fred))&
((~old(alice)&patient(alice)))&
(~curious(fred)) | ~wise(mary) | [
"p0",
"p2",
"p5",
"p7",
"p9",
"p14",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2084832288005076081671651
% SZS output start Proof for 2084832288005076081671651
1. ? [X0] : ~brave(X0) <=> (strong(mary) & ~wise(mary)) [input p0]
3. ! [X0] : ((~calm(X0) | tall(X0)) <=> ~tall(X0)) [input p2]
6. ! [X0] : (~funny(X0) => (happy(X0) <~> patient(X0))) [input p5]
8. ! [X0] : (happy(X0) <=> (~rich(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~curious(X0) & generous(X0)) <=> funny(X0)) [input p9]
15. ! [X0] : ((~wise(X0) | ~tall(X0)) <=> ~generous(X0)) [input p14]
16. ! [X0] : ((brave(X0) | ~creative(X0)) => (curious(X0) | rich(X0))) [input p15]
21. ~patient(fred) [input p20]
23. ~curious(fred) [input p22]
24. wise(mary) [input hypothesis]
31. ! [X0] : ((happy(X0) <~> patient(X0)) | funny(X0)) [ennf transformation 6]
33. ! [X0] : ((curious(X0) | rich(X0)) | (~brave(X0) & creative(X0))) [ennf transformation 16]
34. ! [X0] : (curious(X0) | rich(X0) | (~brave(X0) & creative(X0))) [flattening 33]
35. (? [X0] : ~brave(X0) | (~strong(mary) | wise(mary))) & ((strong(mary) & ~wise(mary)) | ! [X0] : brave(X0)) [nnf transformation 1]
36. (? [X0] : ~brave(X0) | ~strong(mary) | wise(mary)) & ((strong(mary) & ~wise(mary)) | ! [X0] : brave(X0)) [flattening 35]
37. (? [X0] : ~brave(X0) | ~strong(mary) | wise(mary)) & ((strong(mary) & ~wise(mary)) | ! [X1] : brave(X1)) [rectify 36]
38. ? [X0] : ~brave(X0) => ~brave(sK0) [choice axiom]
39. (~brave(sK0) | ~strong(mary) | wise(mary)) & ((strong(mary) & ~wise(mary)) | ! [X1] : brave(X1)) [skolemisation 37,38]
42. ! [X0] : (((~calm(X0) | tall(X0)) | tall(X0)) & (~tall(X0) | (calm(X0) & ~tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((~calm(X0) | tall(X0) | tall(X0)) & (~tall(X0) | (calm(X0) & ~tall(X0)))) [flattening 42]
44. ! [X0] : (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | funny(X0)) [nnf transformation 31]
50. ! [X0] : ((happy(X0) | (rich(X0) | wise(X0))) & ((~rich(X0) & ~wise(X0)) | ~happy(X0))) [nnf transformation 8]
51. ! [X0] : ((happy(X0) | rich(X0) | wise(X0)) & ((~rich(X0) & ~wise(X0)) | ~happy(X0))) [flattening 50]
54. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 10]
55. ! [X0] : (((~curious(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~generous(X0))) [flattening 54]
65. ! [X0] : (((~wise(X0) | ~tall(X0)) | generous(X0)) & (~generous(X0) | (wise(X0) & tall(X0)))) [nnf transformation 15]
66. ! [X0] : ((~wise(X0) | ~tall(X0) | generous(X0)) & (~generous(X0) | (wise(X0) & tall(X0)))) [flattening 65]
75. ~wise(mary) | brave(X1) [cnf transformation 39]
80. ~tall(X0) | ~tall(X0) [cnf transformation 43]
85. patient(X0) | happy(X0) | funny(X0) [cnf transformation 44]
92. ~happy(X0) | ~rich(X0) [cnf transformation 51]
96. ~funny(X0) | generous(X0) [cnf transformation 55]
117. ~generous(X0) | tall(X0) [cnf transformation 66]
121. ~brave(X0) | rich(X0) | curious(X0) [cnf transformation 34]
128. ~patient(fred) [cnf transformation 21]
131. ~curious(fred) [cnf transformation 23]
132. wise(mary) [cnf transformation 24]
133. ~tall(X0) [duplicate literal removal 80]
136. 1 <=> wise(mary) [avatar definition]
149. 4 <=> ! [X1] : brave(X1) [avatar definition]
150. brave(X1) <- (4) [avatar component clause 149]
152. 4 | ~1 [avatar split clause 75,136,149]
248. ~generous(X0) [subsumption resolution 117,133]
279. 1 [avatar split clause 132,136]
283. happy(fred) | funny(fred) [resolution 85,128]
285. 31 <=> funny(fred) [avatar definition]
287. funny(fred) <- (31) [avatar component clause 285]
289. 32 <=> happy(fred) [avatar definition]
291. happy(fred) <- (32) [avatar component clause 289]
292. 31 | 32 [avatar split clause 283,289,285]
315. generous(fred) <- (31) [resolution 287,96]
316. $false <- (31) [subsumption resolution 315,248]
317. ~31 [avatar contradiction clause 316]
344. ~rich(fred) <- (32) [resolution 291,92]
351. 41 <=> rich(fred) [avatar definition]
353. ~rich(fred) <- (~41) [avatar component clause 351]
355. ~41 | ~32 [avatar split clause 344,289,351]
390. curious(X0) | rich(X0) <- (4) [resolution 121,150]
413. rich(fred) <- (4) [resolution 390,131]
417. $false <- (4, ~41) [subsumption resolution 413,353]
418. ~4 | 41 [avatar contradiction clause 417]
419. $false [avatar sat refutation 152,279,292,317,355,418]
% SZS output end Proof for 2084832288005076081671651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or happy then lucy is happy and vice versa. Everyone who is not old or strong is not calm. Everyone who is old or patient is both not brave and patient. Everyone who is happy is both not old and humble. Everyone who is both calm and not patient is old or not brave and vice versa. If someone is both wise and not happy then lucy is either wise or creative. If john is not generous then fred is not humble or kind and vice versa. Everyone who is both generous and not tall is both curious and tall and vice versa. If someone is both generous and not strong then mary is either funny or not calm. Everyone who is either not generous or humble is creative and vice versa. If susan is both not tall and not humble then fred is either not humble or not patient. Everyone who is old is not brave and vice versa. Everyone who is tall or not wise is both calm and generous. Everyone who is happy or not calm is either wise or not curious. If someone is either not rich or not funny then someone is not old and vice versa. Someone is either not humble or not creative. Someone is either not creative or not rich. Paul is not strong or old. Someone is either quiet or not calm. Susan is not quiet or not curious. Someone is either not brave or not creative. | Lucy is tall. | contradiction | ((?[X]:((~kind(X)<~>happy(X))))<=>(happy(lucy)))&
(![X]:((~old(X)|strong(X))=>~calm(X)))&
(![X]:((old(X)|patient(X))=>(~brave(X)&patient(X))))&
(![X]:(happy(X)=>(~old(X)&humble(X))))&
(![X]:((calm(X)&~patient(X))<=>(old(X)|~brave(X))))&
((?[X]:((wise(X)&~happy(X))))=>((wise(lucy)<~>creative(lucy))))&
((~generous(john))<=>((~humble(fred)|kind(fred))))&
(![X]:((generous(X)&~tall(X))<=>(curious(X)&tall(X))))&
((?[X]:((generous(X)&~strong(X))))=>((funny(mary)<~>~calm(mary))))&
(![X]:((~generous(X)<~>humble(X))<=>creative(X)))&
(((~tall(susan)&~humble(susan)))=>((~humble(fred)<~>~patient(fred))))&
(![X]:(old(X)<=>~brave(X)))&
(![X]:((tall(X)|~wise(X))=>(calm(X)&generous(X))))&
(![X]:((happy(X)|~calm(X))=>(wise(X)<~>~curious(X))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>(?[X]:(~old(X))))&
(?[X]:((~humble(X)<~>~creative(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
((~strong(paul)|old(paul)))&
(?[X]:((quiet(X)<~>~calm(X))))&
((~quiet(susan)|~curious(susan)))&
(?[X]:((~brave(X)<~>~creative(X)))) | tall(lucy) | [
"p1",
"p2",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1621821716310773539915312
% SZS output start Proof for 1621821716310773539915312
2. ! [X0] : ((strong(X0) | ~old(X0)) => ~calm(X0)) [input p1]
3. ! [X0] : ((patient(X0) | old(X0)) => (patient(X0) & ~brave(X0))) [input p2]
5. ! [X0] : ((~patient(X0) & calm(X0)) <=> (~brave(X0) | old(X0))) [input p4]
13. ! [X0] : ((~wise(X0) | tall(X0)) => (generous(X0) & calm(X0))) [input p12]
22. tall(lucy) [input hypothesis]
24. ! [X0] : (~calm(X0) | (~strong(X0) & old(X0))) [ennf transformation 2]
25. ! [X0] : ((patient(X0) & ~brave(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 3]
31. ! [X0] : ((generous(X0) & calm(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 13]
37. ! [X0] : (((~patient(X0) & calm(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 5]
38. ! [X0] : (((~patient(X0) & calm(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | patient(X0) | ~calm(X0))) [flattening 37]
70. ~calm(X0) | old(X0) [cnf transformation 24]
73. ~brave(X0) | ~patient(X0) [cnf transformation 25]
74. ~old(X0) | patient(X0) [cnf transformation 25]
82. ~patient(X0) | brave(X0) [cnf transformation 38]
102. ~tall(X0) | calm(X0) [cnf transformation 31]
124. tall(lucy) [cnf transformation 22]
149. ~patient(X0) [subsumption resolution 82,73]
293. calm(lucy) [resolution 102,124]
295. old(lucy) [resolution 293,70]
302. patient(lucy) [resolution 295,74]
303. $false [subsumption resolution 302,149]
% SZS output end Proof for 1621821716310773539915312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not wise is not wise. Everyone who is either not old or not quiet is either curious or not strong and vice versa. If someone is both tall and generous then lucy is not wise. Everyone who is creative or strong is strong or patient and vice versa. Everyone who is both not kind and kind is either patient or creative. Everyone who is not kind is not rich. Everyone who is both happy and not old is not calm and vice versa. Everyone who is happy is both not creative and brave and vice versa. If john is either not kind or calm then someone is rich and vice versa. Everyone who is creative or not calm is funny or brave and vice versa. Everyone who is not happy is either not calm or not humble. Everyone who is brave or quiet is not quiet or curious and vice versa. If fred is not wise then someone is both humble and not brave. If someone is not creative or strong then mary is either kind or tall. Everyone who is calm is both curious and humble. If someone is brave then paul is not patient and vice versa. Fred is wise. Someone is not humble. Someone is either wise or curious. Mary is not funny or creative. John is both not rich and kind. Fred is either not patient or not tall. Susan is either funny or quiet. Someone is not curious. | John is brave. | entailment | (![X]:((~curious(X)|~wise(X))=>~wise(X)))&
(![X]:((~old(X)<~>~quiet(X))<=>(curious(X)<~>~strong(X))))&
((?[X]:((tall(X)&generous(X))))=>(~wise(lucy)))&
(![X]:((creative(X)|strong(X))<=>(strong(X)|patient(X))))&
(![X]:((~kind(X)&kind(X))=>(patient(X)<~>creative(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
(![X]:(calm(X)=>(curious(X)&humble(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
(wise(fred))&
(?[X]:(~humble(X)))&
(?[X]:((wise(X)<~>curious(X))))&
((~funny(mary)|creative(mary)))&
((~rich(john)&kind(john)))&
((~patient(fred)<~>~tall(fred)))&
((funny(susan)<~>quiet(susan)))&
(?[X]:(~curious(X))) | brave(john) | [
"p6",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5529228240106097774249410
% SZS output start Proof for 5529228240106097774249410
7. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : (happy(X0) <=> (brave(X0) & ~creative(X0))) [input p7]
11. ! [X0] : (~happy(X0) => (~calm(X0) <~> ~humble(X0))) [input p10]
15. ! [X0] : (calm(X0) => (humble(X0) & curious(X0))) [input p14]
25. ~brave(john) [input hypothesis]
31. ! [X0] : ((~calm(X0) <~> ~humble(X0)) | happy(X0)) [ennf transformation 11]
34. ! [X0] : ((humble(X0) & curious(X0)) | ~calm(X0)) [ennf transformation 15]
39. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 7]
40. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 39]
41. ! [X0] : ((happy(X0) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 8]
42. ! [X0] : ((happy(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [flattening 41]
49. ! [X0] : (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | happy(X0)) [nnf transformation 31]
86. calm(X0) | happy(X0) [cnf transformation 40]
89. ~happy(X0) | brave(X0) [cnf transformation 42]
99. ~humble(X0) | ~calm(X0) | happy(X0) [cnf transformation 49]
112. ~calm(X0) | humble(X0) [cnf transformation 34]
127. ~brave(john) [cnf transformation 25]
149. ~humble(X0) | happy(X0) [subsumption resolution 99,86]
233. humble(X0) | happy(X0) [resolution 112,86]
234. happy(X0) [subsumption resolution 233,149]
235. brave(X0) [resolution 234,89]
240. $false [resolution 235,127]
% SZS output end Proof for 5529228240106097774249410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not kind is happy and vice versa.
If alice is not strong or old then john is both not brave and not wise and vice versa.
If someone is not old then susan is not curious or funny.
Everyone who is both curious and not happy is either not calm or not strong and vice versa.
If paul is kind then mary is humble and vice versa.
Everyone who is both funny and not kind is either not rich or creative and vice versa.
Everyone who is not curious is strong or funny and vice versa.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
If someone is strong or not funny then someone is not happy or not brave and vice versa.
Everyone who is either curious or not funny is either kind or not brave and vice versa.
Everyone who is both patient and not old is both not patient and funny and vice versa.
Everyone who is both not happy and not generous is either not creative or not funny.
If john is not brave or old then fred is rich and vice versa.
Everyone who is strong is either not patient or not strong and vice versa.
Everyone who is not rich is either not calm or not brave.
Someone is either calm or rich.
Someone is not old.
Someone is strong.
Someone is quiet or not strong.
John is either humble or not wise.
Fred is both old and not patient.
Paul is not wise or not kind. | Paul is not strong. | entailment | (![X]:((tall(X)&~kind(X))<=>happy(X)))&
(((~strong(alice)|old(alice)))<=>((~brave(john)&~wise(john))))&
((?[X]:(~old(X)))=>((~curious(susan)|funny(susan))))&
(![X]:((curious(X)&~happy(X))<=>(~calm(X)<~>~strong(X))))&
((kind(paul))<=>(humble(mary)))&
(![X]:((funny(X)&~kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:(~curious(X)<=>(strong(X)|funny(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)|~strong(X))))&
((humble(john)<~>~wise(john)))&
((old(fred)&~patient(fred)))&
((~wise(paul)|~kind(paul))) | ~strong(paul) | [
"p4",
"p7",
"p8",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2987439805963982337672977
% SZS output start Proof for 2987439805963982337672977
5. kind(paul) <=> humble(mary) [input p4]
8. ! [X0] : ((strong(X0) | ~curious(X0)) <=> wise(X0)) [input p7]
9. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p8]
15. ! [X0] : (strong(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p14]
23. ~kind(paul) | ~wise(paul) [input p22]
24. strong(paul) [input hypothesis]
37. (kind(paul) | ~humble(mary)) & (humble(mary) | ~kind(paul)) [nnf transformation 5]
42. ! [X0] : (((strong(X0) | ~curious(X0)) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [nnf transformation 8]
43. ! [X0] : ((strong(X0) | ~curious(X0) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [flattening 42]
44. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 9]
45. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 44]
56. ! [X0] : ((strong(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~strong(X0))) [nnf transformation 15]
82. kind(paul) | ~humble(mary) [cnf transformation 37]
93. ~strong(X0) | wise(X0) [cnf transformation 43]
95. humble(X0) | brave(X0) | patient(X0) | brave(X0) [cnf transformation 45]
96. ~brave(X0) | ~brave(X0) [cnf transformation 45]
119. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 56]
122. strong(X0) | ~patient(X0) | strong(X0) [cnf transformation 56]
133. ~kind(paul) | ~wise(paul) [cnf transformation 23]
134. strong(paul) [cnf transformation 24]
135. ~strong(X0) | ~patient(X0) [duplicate literal removal 119]
136. ~patient(X0) | strong(X0) [duplicate literal removal 122]
139. humble(X0) | brave(X0) | patient(X0) [duplicate literal removal 95]
140. ~brave(X0) [duplicate literal removal 96]
175. 8 <=> humble(mary) [avatar definition]
177. ~humble(mary) <- (~8) [avatar component clause 175]
179. 9 <=> kind(paul) [avatar definition]
182. ~8 | 9 [avatar split clause 82,179,175]
185. patient(X0) | humble(X0) [subsumption resolution 139,140]
216. ~patient(X0) [subsumption resolution 135,136]
234. 18 <=> wise(paul) [avatar definition]
237. ~18 | ~9 [avatar split clause 133,179,234]
241. wise(paul) [resolution 93,134]
242. 18 [avatar split clause 241,234]
248. humble(X4) [resolution 185,216]
249. $false <- (~8) [resolution 248,177]
253. 8 [avatar contradiction clause 249]
254. $false [avatar sat refutation 182,237,242,253]
% SZS output end Proof for 2987439805963982337672977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is both not tall and tall. If lucy is calm then paul is not generous. Everyone who is either not curious or rich is calm. Everyone who is rich is either not creative or not funny. If someone is either not brave or quiet then someone is curious. Everyone who is not wise or not patient is both funny and not funny and vice versa. If someone is kind then someone is rich or curious and vice versa. If fred is either not brave or rich then susan is both not kind and calm. If john is both strong and not calm then paul is either generous or not humble and vice versa. Everyone who is both not quiet and not happy is not curious and vice versa. Everyone who is both rich and not rich is either patient or not rich. If someone is both not rich and kind then someone is generous and vice versa. Everyone who is humble or not rich is creative or not rich and vice versa. Everyone who is patient is not calm or not generous and vice versa. If susan is both not kind and not quiet then susan is brave or strong and vice versa. Mary is not generous or humble. Mary is both funny and not kind. Someone is either tall or wise. Someone is not kind. Fred is brave or not happy. | Mary is calm. | entailment | (![X]:(kind(X)=>(~tall(X)&tall(X))))&
((calm(lucy))=>(~generous(paul)))&
(![X]:((~curious(X)<~>rich(X))=>calm(X)))&
(![X]:(rich(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|curious(X)))))&
(((~brave(fred)<~>rich(fred)))=>((~kind(susan)&calm(susan))))&
(((strong(john)&~calm(john)))<=>((generous(paul)<~>~humble(paul))))&
(![X]:((~quiet(X)&~happy(X))<=>~curious(X)))&
(![X]:((rich(X)&~rich(X))=>(patient(X)<~>~rich(X))))&
((?[X]:((~rich(X)&kind(X))))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|~rich(X))<=>(creative(X)|~rich(X))))&
(![X]:(patient(X)<=>(~calm(X)|~generous(X))))&
(((~kind(susan)&~quiet(susan)))<=>((brave(susan)|strong(susan))))&
((~generous(mary)|humble(mary)))&
((funny(mary)&~kind(mary)))&
(?[X]:((tall(X)<~>wise(X))))&
(?[X]:(~kind(X)))&
((brave(fred)|~happy(fred))) | calm(mary) | [
"p0",
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6257708669611540445270467
% SZS output start Proof for 6257708669611540445270467
1. ! [X0] : (kind(X0) => (tall(X0) & ~tall(X0))) [input p0]
3. ! [X0] : ((~curious(X0) <~> rich(X0)) => calm(X0)) [input p2]
7. ? [X0] : kind(X0) <=> ? [X0] : (curious(X0) | rich(X0)) [input p6]
21. ~calm(mary) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : (curious(X1) | rich(X1)) [rectify 7]
25. ! [X0] : ((tall(X0) & ~tall(X0)) | ~kind(X0)) [ennf transformation 1]
27. ! [X0] : (calm(X0) | (~curious(X0) <=> rich(X0))) [ennf transformation 3]
33. ! [X0] : (calm(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) [nnf transformation 27]
41. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X1] : (curious(X1) | rich(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 23]
42. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X2] : (curious(X2) | rich(X2)) | ! [X3] : ~kind(X3)) [rectify 41]
43. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
44. ? [X2] : (curious(X2) | rich(X2)) => (curious(sK2) | rich(sK2)) [choice axiom]
45. (kind(sK1) | ! [X1] : (~curious(X1) & ~rich(X1))) & ((curious(sK2) | rich(sK2)) | ! [X3] : ~kind(X3)) [skolemisation 42,44,43]
68. ~tall(X0) | ~kind(X0) [cnf transformation 25]
69. ~kind(X0) | tall(X0) [cnf transformation 25]
71. rich(X0) | calm(X0) | curious(X0) [cnf transformation 33]
83. kind(sK1) | ~rich(X1) [cnf transformation 45]
84. kind(sK1) | ~curious(X1) [cnf transformation 45]
122. ~calm(mary) [cnf transformation 21]
125. ~kind(X0) [subsumption resolution 68,69]
149. ~curious(X1) [subsumption resolution 84,125]
150. ~rich(X1) [subsumption resolution 83,125]
201. calm(X0) | curious(X0) [resolution 71,150]
202. calm(X0) [subsumption resolution 201,149]
205. $false [resolution 202,122]
% SZS output end Proof for 6257708669611540445270467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either brave or not patient then someone is not patient and vice versa.
If paul is calm or not kind then john is both not generous and tall.
Everyone who is both kind and not quiet is not creative or generous and vice versa.
If someone is not humble then someone is either not happy or generous.
If fred is humble or not kind then paul is both funny and happy and vice versa.
If alice is both not calm and not strong then john is creative or not calm.
Everyone who is both not patient and not brave is old or not calm.
Everyone who is both not humble and tall is both not quiet and not strong.
Everyone who is either not curious or old is kind and vice versa.
If john is either not funny or not calm then mary is quiet and vice versa.
Everyone who is both rich and brave is both not old and not tall.
Everyone who is tall is both brave and patient.
Everyone who is not curious is not rich or not generous and vice versa.
Everyone who is patient is not wise and vice versa.
Everyone who is not happy or strong is either not quiet or patient and vice versa.
If fred is either happy or brave then mary is not calm or not strong.
John is generous.
Someone is either calm or not creative.
Someone is rich.
Fred is not funny.
Mary is quiet.
Someone is curious.
Fred is both not brave and curious.
Lucy is either quiet or not calm. | John is kind. | entailment | (((brave(fred)<~>~patient(fred)))<=>(?[X]:(~patient(X))))&
(((calm(paul)|~kind(paul)))=>((~generous(john)&tall(john))))&
(![X]:((kind(X)&~quiet(X))<=>(~creative(X)|generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~happy(X)<~>generous(X)))))&
(((humble(fred)|~kind(fred)))<=>((funny(paul)&happy(paul))))&
(((~calm(alice)&~strong(alice)))=>((creative(john)|~calm(john))))&
(![X]:((~patient(X)&~brave(X))=>(old(X)|~calm(X))))&
(![X]:((~humble(X)&tall(X))=>(~quiet(X)&~strong(X))))&
(![X]:((~curious(X)<~>old(X))<=>kind(X)))&
(((~funny(john)<~>~calm(john)))<=>(quiet(mary)))&
(![X]:((rich(X)&brave(X))=>(~old(X)&~tall(X))))&
(![X]:(tall(X)=>(brave(X)&patient(X))))&
(![X]:(~curious(X)<=>(~rich(X)|~generous(X))))&
(![X]:(patient(X)<=>~wise(X)))&
(![X]:((~happy(X)|strong(X))<=>(~quiet(X)<~>patient(X))))&
(((happy(fred)<~>brave(fred)))=>((~calm(mary)|~strong(mary))))&
(generous(john))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:(rich(X)))&
(~funny(fred))&
(quiet(mary))&
(?[X]:(curious(X)))&
((~brave(fred)&curious(fred)))&
((quiet(lucy)<~>~calm(lucy))) | kind(john) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 240534025842830718244782
% SZS output start Proof for 240534025842830718244782
3. ! [X0] : ((~quiet(X0) & kind(X0)) <=> (generous(X0) | ~creative(X0))) [input p2]
17. generous(john) [input p16]
25. ~kind(john) [input hypothesis]
44. ! [X0] : (((~quiet(X0) & kind(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (quiet(X0) | ~kind(X0)))) [nnf transformation 3]
45. ! [X0] : (((~quiet(X0) & kind(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | quiet(X0) | ~kind(X0))) [flattening 44]
78. ~generous(X0) | kind(X0) [cnf transformation 45]
117. generous(john) [cnf transformation 17]
128. ~kind(john) [cnf transformation 25]
163. 8 <=> generous(john) [avatar definition]
164. generous(john) <- (8) [avatar component clause 163]
245. 8 [avatar split clause 117,163]
269. kind(john) <- (8) [resolution 78,164]
270. $false <- (8) [subsumption resolution 269,128]
271. ~8 [avatar contradiction clause 270]
272. $false [avatar sat refutation 245,271]
% SZS output end Proof for 240534025842830718244782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is tall or rich.
If mary is not tall or creative then someone is both brave and wise.
If susan is both not funny and creative then john is either humble or not curious and vice versa.
If someone is either calm or humble then someone is either not wise or rich and vice versa.
If paul is not kind or calm then mary is either not strong or not generous.
Everyone who is not generous or wise is either creative or not strong.
Everyone who is either rich or curious is not rich and vice versa.
If someone is brave or funny then fred is not rich or funny.
Everyone who is both generous and not tall is either not humble or generous and vice versa.
Everyone who is either old or not generous is patient or rich.
If paul is either rich or not patient then someone is either funny or not quiet and vice versa.
If alice is strong then lucy is not creative or calm and vice versa.
Everyone who is not strong is either not old or not kind.
If susan is not tall then susan is humble or not generous and vice versa.
Everyone who is both old and not tall is not strong or not curious.
If fred is not patient or not creative then someone is not happy or humble.
Alice is not brave or not kind.
Someone is either not happy or not generous.
Someone is not generous or not rich.
Lucy is not tall.
Someone is not humble or not patient.
Someone is either not patient or not calm.
Someone is both not brave and not creative. | Mary is not tall. | neutral | (![X]:((brave(X)|~generous(X))=>(tall(X)|rich(X))))&
(((~tall(mary)|creative(mary)))=>(?[X]:((brave(X)&wise(X)))))&
(((~funny(susan)&creative(susan)))<=>((humble(john)<~>~curious(john))))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((~wise(X)<~>rich(X)))))&
(((~kind(paul)|calm(paul)))=>((~strong(mary)<~>~generous(mary))))&
(![X]:((~generous(X)|wise(X))=>(creative(X)<~>~strong(X))))&
(![X]:((rich(X)<~>curious(X))<=>~rich(X)))&
((?[X]:((brave(X)|funny(X))))=>((~rich(fred)|funny(fred))))&
(![X]:((generous(X)&~tall(X))<=>(~humble(X)<~>generous(X))))&
(![X]:((old(X)<~>~generous(X))=>(patient(X)|rich(X))))&
(((rich(paul)<~>~patient(paul)))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
((strong(alice))<=>((~creative(lucy)|calm(lucy))))&
(![X]:(~strong(X)=>(~old(X)<~>~kind(X))))&
((~tall(susan))<=>((humble(susan)|~generous(susan))))&
(![X]:((old(X)&~tall(X))=>(~strong(X)|~curious(X))))&
(((~patient(fred)|~creative(fred)))=>(?[X]:((~happy(X)|humble(X)))))&
((~brave(alice)|~kind(alice)))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~generous(X)|~rich(X))))&
(~tall(lucy))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((~brave(X)&~creative(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is humble is not brave or happy and vice versa.
Everyone who is not strong is either calm or kind.
If alice is not curious or rich then someone is either generous or not brave and vice versa.
If someone is both not brave and not funny then someone is not kind and vice versa.
Everyone who is not wise or brave is quiet or not funny.
Everyone who is both not curious and brave is not patient or not calm and vice versa.
If alice is both funny and curious then alice is either not calm or funny.
Everyone who is not happy or not strong is quiet or not calm.
Everyone who is strong or calm is both humble and funny.
If someone is both not curious and calm then alice is not tall or rich and vice versa.
If someone is either wise or not strong then someone is kind or curious and vice versa.
Everyone who is both humble and quiet is both not old and not humble and vice versa.
Everyone who is either not brave or rich is both not curious and not generous.
Everyone who is wise or curious is both not tall and not funny.
If someone is either not kind or not wise then someone is both brave and not curious and vice versa.
Lucy is either happy or not patient.
Someone is either not happy or not wise.
Someone is rich.
Susan is not creative.
Someone is both not strong and not rich.
Someone is not strong or strong.
Alice is either old or not humble. | Alice is strong. | contradiction | (![X]:(humble(X)<=>(~brave(X)|happy(X))))&
(![X]:(~strong(X)=>(calm(X)<~>kind(X))))&
(((~curious(alice)|rich(alice)))<=>(?[X]:((generous(X)<~>~brave(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)|~funny(X))))&
(![X]:((~curious(X)&brave(X))<=>(~patient(X)|~calm(X))))&
(((funny(alice)&curious(alice)))=>((~calm(alice)<~>funny(alice))))&
(![X]:((~happy(X)|~strong(X))=>(quiet(X)|~calm(X))))&
(![X]:((strong(X)|calm(X))=>(humble(X)&funny(X))))&
((?[X]:((~curious(X)&calm(X))))<=>((~tall(alice)|rich(alice))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((humble(X)&quiet(X))<=>(~old(X)&~humble(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~curious(X)&~generous(X))))&
(![X]:((wise(X)|curious(X))=>(~tall(X)&~funny(X))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:((brave(X)&~curious(X)))))&
((happy(lucy)<~>~patient(lucy)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:(rich(X)))&
(~creative(susan))&
(?[X]:((~strong(X)&~rich(X))))&
(?[X]:((~strong(X)|strong(X))))&
((old(alice)<~>~humble(alice))) | strong(alice) | [
"p4",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 415332264124450381764608
% SZS output start Proof for 415332264124450381764608
5. ! [X0] : ((brave(X0) | ~wise(X0)) => (~funny(X0) | quiet(X0))) [input p4]
9. ! [X0] : ((calm(X0) | strong(X0)) => (funny(X0) & humble(X0))) [input p8]
12. ! [X0] : ((quiet(X0) & humble(X0)) <=> (~humble(X0) & ~old(X0))) [input p11]
14. ! [X0] : ((curious(X0) | wise(X0)) => (~funny(X0) & ~tall(X0))) [input p13]
22. old(alice) <~> ~humble(alice) [input p21]
23. strong(alice) [input hypothesis]
29. ! [X0] : ((~funny(X0) | quiet(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 5]
30. ! [X0] : (~funny(X0) | quiet(X0) | (~brave(X0) & wise(X0))) [flattening 29]
35. ! [X0] : ((funny(X0) & humble(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 9]
37. ! [X0] : ((~funny(X0) & ~tall(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 14]
64. ! [X0] : (((quiet(X0) & humble(X0)) | (humble(X0) | old(X0))) & ((~humble(X0) & ~old(X0)) | (~quiet(X0) | ~humble(X0)))) [nnf transformation 12]
65. ! [X0] : (((quiet(X0) & humble(X0)) | humble(X0) | old(X0)) & ((~humble(X0) & ~old(X0)) | ~quiet(X0) | ~humble(X0))) [flattening 64]
82. (humble(alice) | ~old(alice)) & (~humble(alice) | old(alice)) [nnf transformation 22]
97. ~funny(X0) | quiet(X0) | wise(X0) [cnf transformation 30]
110. ~strong(X0) | funny(X0) [cnf transformation 35]
124. ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 65]
125. humble(X0) | humble(X0) | old(X0) [cnf transformation 65]
133. ~wise(X0) | ~funny(X0) [cnf transformation 37]
150. humble(alice) | ~old(alice) [cnf transformation 82]
151. strong(alice) [cnf transformation 23]
152. ~quiet(X0) | ~humble(X0) [duplicate literal removal 124]
153. old(X0) | humble(X0) [duplicate literal removal 125]
309. humble(alice) [subsumption resolution 150,153]
318. funny(alice) [resolution 110,151]
374. quiet(alice) | wise(alice) [resolution 97,318]
378. 39 <=> wise(alice) [avatar definition]
380. wise(alice) <- (39) [avatar component clause 378]
382. 40 <=> quiet(alice) [avatar definition]
384. quiet(alice) <- (40) [avatar component clause 382]
385. 39 | 40 [avatar split clause 374,382,378]
436. ~funny(alice) <- (39) [resolution 380,133]
437. $false <- (39) [subsumption resolution 436,318]
438. ~39 [avatar contradiction clause 437]
439. ~humble(alice) <- (40) [resolution 384,152]
440. $false <- (40) [subsumption resolution 439,309]
441. ~40 [avatar contradiction clause 440]
442. $false [avatar sat refutation 385,438,441]
% SZS output end Proof for 415332264124450381764608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is not humble or not brave and vice versa.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
If fred is either not quiet or quiet then alice is not tall and vice versa.
Everyone who is both not wise and curious is both not quiet and not old.
If susan is both not brave and curious then lucy is both calm and not strong.
Someone is not happy.
Fred is creative.
John is both creative and not generous.
Mary is both brave and funny.
Alice is rich or not curious. | Fred is patient. | neutral | (![X]:((~brave(X)<~>~strong(X))<=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
(((~quiet(fred)<~>quiet(fred)))<=>(~tall(alice)))&
(![X]:((~wise(X)&curious(X))=>(~quiet(X)&~old(X))))&
(((~brave(susan)&curious(susan)))=>((calm(lucy)&~strong(lucy))))&
(?[X]:(~happy(X)))&
(creative(fred))&
((creative(john)&~generous(john)))&
((brave(mary)&funny(mary)))&
((rich(alice)|~curious(alice))) | patient(fred) | [] | null | 0 |
If paul is not brave or humble then someone is either tall or curious.
If paul is old or wise then paul is kind.
Everyone who is happy is both calm and not wise.
Everyone who is either not generous or brave is both not patient and happy.
If fred is either quiet or not humble then someone is either humble or not patient and vice versa.
Everyone who is either not humble or not quiet is either funny or not curious and vice versa.
If someone is both funny and not old then someone is either curious or not generous and vice versa.
Everyone who is not old is humble and vice versa.
Everyone who is either not quiet or creative is strong or rich.
If someone is not wise or wise then fred is tall and vice versa.
If someone is both kind and not wise then alice is either calm or old and vice versa.
Everyone who is both not old and not patient is either not creative or calm.
Everyone who is either calm or not creative is not brave or not funny.
If fred is brave then fred is funny and vice versa.
Everyone who is not funny is either not creative or not wise and vice versa.
Everyone who is creative is not wise and vice versa.
Paul is not humble.
John is both not happy and not generous.
Someone is tall.
Someone is not patient or not old.
Fred is both not happy and generous.
Someone is either curious or creative.
Mary is not happy. | John is not brave. | contradiction | (((~brave(paul)|humble(paul)))=>(?[X]:((tall(X)<~>curious(X)))))&
(((old(paul)|wise(paul)))=>(kind(paul)))&
(![X]:(happy(X)=>(calm(X)&~wise(X))))&
(![X]:((~generous(X)<~>brave(X))=>(~patient(X)&happy(X))))&
(((quiet(fred)<~>~humble(fred)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(funny(X)<~>~curious(X))))&
((?[X]:((funny(X)&~old(X))))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~old(X)<=>humble(X)))&
(![X]:((~quiet(X)<~>creative(X))=>(strong(X)|rich(X))))&
((?[X]:((~wise(X)|wise(X))))<=>(tall(fred)))&
((?[X]:((kind(X)&~wise(X))))<=>((calm(alice)<~>old(alice))))&
(![X]:((~old(X)&~patient(X))=>(~creative(X)<~>calm(X))))&
(![X]:((calm(X)<~>~creative(X))=>(~brave(X)|~funny(X))))&
((brave(fred))<=>(funny(fred)))&
(![X]:(~funny(X)<=>(~creative(X)<~>~wise(X))))&
(![X]:(creative(X)<=>~wise(X)))&
(~humble(paul))&
((~happy(john)&~generous(john)))&
(?[X]:(tall(X)))&
(?[X]:((~patient(X)|~old(X))))&
((~happy(fred)&generous(fred)))&
(?[X]:((curious(X)<~>creative(X))))&
(~happy(mary)) | ~brave(john) | [
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3279751591093609433917797
% SZS output start Proof for 3279751591093609433917797
4. ! [X0] : ((~generous(X0) <~> brave(X0)) => (happy(X0) & ~patient(X0))) [input p3]
18. ~generous(john) & ~happy(john) [input p17]
24. ~brave(john) [input hypothesis]
30. ! [X0] : ((happy(X0) & ~patient(X0)) | (~generous(X0) <=> brave(X0))) [ennf transformation 4]
38. ! [X0] : ((happy(X0) & ~patient(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0)))) [nnf transformation 30]
80. generous(X0) | brave(X0) | happy(X0) [cnf transformation 38]
128. ~happy(john) [cnf transformation 18]
129. ~generous(john) [cnf transformation 18]
137. ~brave(john) [cnf transformation 24]
316. brave(john) | happy(john) [resolution 80,129]
318. happy(john) [subsumption resolution 316,137]
319. $false [subsumption resolution 318,128]
% SZS output end Proof for 3279751591093609433917797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise is not funny. If fred is either not funny or strong then someone is not happy or quiet. Everyone who is quiet is not calm or not kind and vice versa. If someone is either not brave or strong then someone is not old. If someone is not patient or patient then lucy is both wise and old and vice versa. If susan is both not creative and quiet then someone is patient and vice versa. Everyone who is not funny is not wise and vice versa. Everyone who is either not curious or not generous is not brave or brave. If someone is either not old or humble then alice is not funny and vice versa. If someone is patient then someone is not patient and vice versa. Everyone who is happy is either not brave or not patient. Everyone who is not old or old is either not quiet or patient. Everyone who is either kind or curious is kind and vice versa. Everyone who is both not funny and not patient is either not rich or calm and vice versa. Everyone who is either curious or humble is patient or not wise. If paul is funny or tall then someone is not kind. John is wise. Alice is not creative or not quiet. Someone is both quiet and happy. Someone is both funny and calm. Susan is either old or not brave. Fred is strong or happy. Paul is either tall or not humble. | Paul is brave. | neutral | (![X]:((creative(X)<~>wise(X))=>~funny(X)))&
(((~funny(fred)<~>strong(fred)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:(quiet(X)<=>(~calm(X)|~kind(X))))&
((?[X]:((~brave(X)<~>strong(X))))=>(?[X]:(~old(X))))&
((?[X]:((~patient(X)|patient(X))))<=>((wise(lucy)&old(lucy))))&
(((~creative(susan)&quiet(susan)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)<=>~wise(X)))&
(![X]:((~curious(X)<~>~generous(X))=>(~brave(X)|brave(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>(~funny(alice)))&
((?[X]:(patient(X)))<=>(?[X]:(~patient(X))))&
(![X]:(happy(X)=>(~brave(X)<~>~patient(X))))&
(![X]:((~old(X)|old(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((kind(X)<~>curious(X))<=>kind(X)))&
(![X]:((~funny(X)&~patient(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((curious(X)<~>humble(X))=>(patient(X)|~wise(X))))&
(((funny(paul)|tall(paul)))=>(?[X]:(~kind(X))))&
(wise(john))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((quiet(X)&happy(X))))&
(?[X]:((funny(X)&calm(X))))&
((old(susan)<~>~brave(susan)))&
((strong(fred)|happy(fred)))&
((tall(paul)<~>~humble(paul))) | brave(paul) | [] | null | 0 |
If someone is both tall and not calm then someone is wise. If john is both not kind and not old then paul is either not rich or not patient. If susan is wise then someone is either not calm or quiet. Everyone who is generous is both not creative and not quiet and vice versa. Everyone who is not rich or not funny is not kind or not old. Everyone who is not kind or not generous is both rich and not tall and vice versa. If alice is both not funny and not strong then paul is creative. If mary is both not strong and not quiet then someone is not old. If someone is either not tall or not humble then someone is not creative and vice versa. If john is either kind or not calm then someone is either strong or quiet. Everyone who is both funny and calm is generous and vice versa. If fred is wise or funny then someone is either not creative or humble. Everyone who is both strong and humble is either not happy or generous and vice versa. Susan is either calm or wise. Mary is not kind or generous. Alice is both not humble and old. Someone is either not funny or patient. Someone is not humble or wise. Susan is not tall. | Mary is wise. | neutral | ((?[X]:((tall(X)&~calm(X))))=>(?[X]:(wise(X))))&
(((~kind(john)&~old(john)))=>((~rich(paul)<~>~patient(paul))))&
((wise(susan))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(generous(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((~rich(X)|~funny(X))=>(~kind(X)|~old(X))))&
(![X]:((~kind(X)|~generous(X))<=>(rich(X)&~tall(X))))&
(((~funny(alice)&~strong(alice)))=>(creative(paul)))&
(((~strong(mary)&~quiet(mary)))=>(?[X]:(~old(X))))&
((?[X]:((~tall(X)<~>~humble(X))))<=>(?[X]:(~creative(X))))&
(((kind(john)<~>~calm(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((funny(X)&calm(X))<=>generous(X)))&
(((wise(fred)|funny(fred)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((strong(X)&humble(X))<=>(~happy(X)<~>generous(X))))&
((calm(susan)<~>wise(susan)))&
((~kind(mary)|generous(mary)))&
((~humble(alice)&old(alice)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~humble(X)|wise(X))))&
(~tall(susan)) | wise(mary) | [] | null | 0 |
Everyone who is calm is tall and vice versa. Everyone who is either not creative or strong is both kind and funny. If someone is both humble and not curious then someone is either not humble or rich. Everyone who is either humble or not tall is curious. If someone is not kind or happy then someone is both curious and rich. Everyone who is either rich or quiet is both not brave and not tall. If someone is either not tall or not calm then alice is both calm and patient. Everyone who is either not creative or tall is calm. Everyone who is not kind or not quiet is patient. Everyone who is patient or not humble is not rich and vice versa. Everyone who is generous is either not happy or patient. Everyone who is not curious or not quiet is either not wise or not strong and vice versa. Everyone who is happy is both old and happy. Everyone who is not tall or not strong is not strong or not quiet and vice versa. If someone is both patient and generous then someone is not rich. Someone is kind or tall. Someone is not calm or kind. Fred is either not calm or funny. Someone is not brave or not old. Alice is both not wise and curious. Alice is creative or not funny. | Fred is calm. | neutral | (![X]:(calm(X)<=>tall(X)))&
(![X]:((~creative(X)<~>strong(X))=>(kind(X)&funny(X))))&
((?[X]:((humble(X)&~curious(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((humble(X)<~>~tall(X))=>curious(X)))&
((?[X]:((~kind(X)|happy(X))))=>(?[X]:((curious(X)&rich(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(~brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~calm(X))))=>((calm(alice)&patient(alice))))&
(![X]:((~creative(X)<~>tall(X))=>calm(X)))&
(![X]:((~kind(X)|~quiet(X))=>patient(X)))&
(![X]:((patient(X)|~humble(X))<=>~rich(X)))&
(![X]:(generous(X)=>(~happy(X)<~>patient(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:(happy(X)=>(old(X)&happy(X))))&
(![X]:((~tall(X)|~strong(X))<=>(~strong(X)|~quiet(X))))&
((?[X]:((patient(X)&generous(X))))=>(?[X]:(~rich(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((~calm(X)|kind(X))))&
((~calm(fred)<~>funny(fred)))&
(?[X]:((~brave(X)|~old(X))))&
((~wise(alice)&curious(alice)))&
((creative(alice)|~funny(alice))) | calm(fred) | [] | null | 0 |
Everyone who is either wise or generous is both not wise and wise and vice versa.
If fred is either not wise or generous then alice is either not quiet or calm and vice versa.
Everyone who is either not kind or calm is both calm and happy and vice versa.
Everyone who is either not kind or patient is both not happy and generous.
If someone is not old then lucy is not generous or kind and vice versa.
Everyone who is either tall or old is either not generous or old.
Everyone who is both not calm and not strong is not generous or strong.
Everyone who is both generous and happy is both not strong and curious.
Everyone who is funny or wise is both strong and not calm and vice versa.
If someone is either strong or rich then someone is either not calm or creative and vice versa.
Everyone who is both not funny and humble is funny or rich and vice versa.
Everyone who is not curious or not tall is funny or not quiet and vice versa.
Everyone who is wise is both not old and not kind and vice versa.
If someone is either not humble or not wise then alice is not rich.
If someone is rich or not old then someone is both not happy and not tall.
Everyone who is either kind or brave is both old and not calm and vice versa.
Someone is both brave and calm.
Someone is not kind or not brave.
Alice is not happy or creative.
Someone is tall.
Someone is both old and not curious.
Alice is both not calm and brave.
Someone is either not happy or not tall. | Lucy is strong. | neutral | (![X]:((wise(X)<~>generous(X))<=>(~wise(X)&wise(X))))&
(((~wise(fred)<~>generous(fred)))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:((~kind(X)<~>calm(X))<=>(calm(X)&happy(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~happy(X)&generous(X))))&
((?[X]:(~old(X)))<=>((~generous(lucy)|kind(lucy))))&
(![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(~rich(alice)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
(![X]:((kind(X)<~>brave(X))<=>(old(X)&~calm(X))))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~kind(X)|~brave(X))))&
((~happy(alice)|creative(alice)))&
(?[X]:(tall(X)))&
(?[X]:((old(X)&~curious(X))))&
((~calm(alice)&brave(alice)))&
(?[X]:((~happy(X)<~>~tall(X)))) | strong(lucy) | [] | null | 0 |
If someone is not funny then lucy is both creative and not curious and vice versa.
Everyone who is either kind or not humble is either not humble or calm.
If someone is either not old or not calm then lucy is not kind and vice versa.
If someone is not brave then someone is not brave or wise.
Everyone who is wise or not humble is not rich.
Everyone who is either not rich or rich is either creative or brave.
Everyone who is not creative is either not creative or wise.
Everyone who is both not creative and creative is creative and vice versa.
If paul is patient then someone is either happy or not curious.
If someone is not creative or not kind then someone is not tall.
If someone is both old and not calm then someone is not strong and vice versa.
If susan is old then lucy is either rich or happy.
Everyone who is not tall or patient is not calm.
Everyone who is not rich or not calm is either wise or not rich.
If alice is not humble or not quiet then lucy is tall or not humble and vice versa.
Everyone who is not calm or generous is not funny or not calm and vice versa.
Lucy is quiet or curious.
Lucy is not humble.
Someone is not happy or generous.
Someone is quiet.
Lucy is either not tall or curious.
John is either not funny or not humble.
Someone is not strong.
Susan is old or brave. | Paul is not creative. | entailment | ((?[X]:(~funny(X)))<=>((creative(lucy)&~curious(lucy))))&
(![X]:((kind(X)<~>~humble(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(~kind(lucy)))&
((?[X]:(~brave(X)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((wise(X)|~humble(X))=>~rich(X)))&
(![X]:((~rich(X)<~>rich(X))=>(creative(X)<~>brave(X))))&
(![X]:(~creative(X)=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)&creative(X))<=>creative(X)))&
((patient(paul))=>(?[X]:((happy(X)<~>~curious(X)))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
((old(susan))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~tall(X)|patient(X))=>~calm(X)))&
(![X]:((~rich(X)|~calm(X))=>(wise(X)<~>~rich(X))))&
(((~humble(alice)|~quiet(alice)))<=>((tall(lucy)|~humble(lucy))))&
(![X]:((~calm(X)|generous(X))<=>(~funny(X)|~calm(X))))&
((quiet(lucy)|curious(lucy)))&
(~humble(lucy))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:(quiet(X)))&
((~tall(lucy)<~>curious(lucy)))&
((~funny(john)<~>~humble(john)))&
(?[X]:(~strong(X)))&
((old(susan)|brave(susan))) | ~creative(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7667743462365143270976572
% SZS output start Proof for 7667743462365143270976572
8. ! [X0] : ((creative(X0) & ~creative(X0)) <=> creative(X0)) [input p7]
25. creative(paul) [input hypothesis]
55. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 8]
56. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | ~creative(X0) | creative(X0))) [flattening 55]
100. ~creative(X0) | ~creative(X0) [cnf transformation 56]
132. creative(paul) [cnf transformation 25]
135. ~creative(X0) [duplicate literal removal 100]
294. $false [subsumption resolution 132,135]
% SZS output end Proof for 7667743462365143270976572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and generous is creative or patient and vice versa.
If mary is not funny then someone is either funny or happy.
If someone is both old and calm then someone is both not quiet and not humble.
Everyone who is funny is not wise and vice versa.
If someone is tall then alice is either strong or humble.
Everyone who is both not quiet and patient is either happy or generous and vice versa.
If someone is both creative and quiet then someone is either not kind or not quiet.
If someone is patient then lucy is both tall and calm.
If fred is either calm or not brave then john is both strong and not happy.
If someone is not calm or kind then susan is both not happy and not generous.
Everyone who is either not tall or patient is not curious or not generous.
Everyone who is old or quiet is both tall and patient and vice versa.
Everyone who is quiet or rich is either brave or not funny.
Everyone who is funny or not generous is not quiet and vice versa.
Everyone who is patient or not wise is not strong or old and vice versa.
If mary is both not quiet and calm then john is not brave or funny.
Alice is not strong or not creative.
John is both not patient and not rich.
Lucy is both not tall and not old.
Someone is tall.
Paul is not calm.
Someone is either happy or creative.
Alice is either not creative or not old.
Fred is brave. | Alice is curious. | contradiction | (![X]:((~tall(X)&generous(X))<=>(creative(X)|patient(X))))&
((~funny(mary))=>(?[X]:((funny(X)<~>happy(X)))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:(tall(X)))=>((strong(alice)<~>humble(alice))))&
(![X]:((~quiet(X)&patient(X))<=>(happy(X)<~>generous(X))))&
((?[X]:((creative(X)&quiet(X))))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:(patient(X)))=>((tall(lucy)&calm(lucy))))&
(((calm(fred)<~>~brave(fred)))=>((strong(john)&~happy(john))))&
((?[X]:((~calm(X)|kind(X))))=>((~happy(susan)&~generous(susan))))&
(![X]:((~tall(X)<~>patient(X))=>(~curious(X)|~generous(X))))&
(![X]:((old(X)|quiet(X))<=>(tall(X)&patient(X))))&
(![X]:((quiet(X)|rich(X))=>(brave(X)<~>~funny(X))))&
(![X]:((funny(X)|~generous(X))<=>~quiet(X)))&
(![X]:((patient(X)|~wise(X))<=>(~strong(X)|old(X))))&
(((~quiet(mary)&calm(mary)))=>((~brave(john)|funny(john))))&
((~strong(alice)|~creative(alice)))&
((~patient(john)&~rich(john)))&
((~tall(lucy)&~old(lucy)))&
(?[X]:(tall(X)))&
(~calm(paul))&
(?[X]:((happy(X)<~>creative(X))))&
((~creative(alice)<~>~old(alice)))&
(brave(fred)) | curious(alice) | [
"p0",
"p7",
"p10",
"p11",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2597668566020411434469883
% SZS output start Proof for 2597668566020411434469883
1. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (patient(X0) | creative(X0))) [input p0]
8. ? [X0] : patient(X0) => (calm(lucy) & tall(lucy)) [input p7]
11. ! [X0] : ((~tall(X0) <~> patient(X0)) => (~generous(X0) | ~curious(X0))) [input p10]
12. ! [X0] : ((quiet(X0) | old(X0)) <=> (patient(X0) & tall(X0))) [input p11]
19. ~old(lucy) & ~tall(lucy) [input p18]
23. ~creative(alice) <~> ~old(alice) [input p22]
25. curious(alice) [input hypothesis]
34. (calm(lucy) & tall(lucy)) | ! [X0] : ~patient(X0) [ennf transformation 8]
37. ! [X0] : ((~generous(X0) | ~curious(X0)) | (~tall(X0) <=> patient(X0))) [ennf transformation 11]
38. ! [X0] : (~generous(X0) | ~curious(X0) | (~tall(X0) <=> patient(X0))) [flattening 37]
42. ! [X0] : (((generous(X0) & ~tall(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 1]
43. ! [X0] : (((generous(X0) & ~tall(X0)) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | ~generous(X0) | tall(X0))) [flattening 42]
59. ! [X0] : (~generous(X0) | ~curious(X0) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) [nnf transformation 38]
60. ! [X0] : (((quiet(X0) | old(X0)) | (~patient(X0) | ~tall(X0))) & ((patient(X0) & tall(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 12]
61. ! [X0] : ((quiet(X0) | old(X0) | ~patient(X0) | ~tall(X0)) & ((patient(X0) & tall(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 60]
72. (old(alice) | creative(alice)) & (~old(alice) | ~creative(alice)) [nnf transformation 23]
74. ~creative(X0) | ~tall(X0) [cnf transformation 43]
76. ~creative(X0) | generous(X0) [cnf transformation 43]
94. tall(lucy) | ~patient(X0) [cnf transformation 34]
104. ~curious(X0) | ~generous(X0) | patient(X0) | tall(X0) [cnf transformation 59]
108. ~old(X0) | patient(X0) [cnf transformation 61]
123. ~tall(lucy) [cnf transformation 19]
130. old(alice) | creative(alice) [cnf transformation 72]
132. curious(alice) [cnf transformation 25]
189. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
190. ~patient(X0) <- (13) [avatar component clause 189]
197. 15 <=> tall(lucy) [avatar definition]
200. 13 | 15 [avatar split clause 94,197,189]
257. 28 <=> creative(alice) [avatar definition]
258. creative(alice) <- (28) [avatar component clause 257]
261. ~15 [avatar split clause 123,197]
273. 31 <=> old(alice) [avatar definition]
275. old(alice) <- (31) [avatar component clause 273]
276. 28 | 31 [avatar split clause 130,273,257]
313. patient(alice) <- (31) [resolution 275,108]
315. $false <- (13, 31) [subsumption resolution 313,190]
316. ~13 | ~31 [avatar contradiction clause 315]
317. generous(alice) <- (28) [resolution 258,76]
318. ~tall(alice) <- (28) [resolution 258,74]
358. ~generous(alice) | patient(alice) | tall(alice) [resolution 104,132]
359. patient(alice) | tall(alice) <- (28) [subsumption resolution 358,317]
360. tall(alice) <- (13, 28) [subsumption resolution 359,190]
361. $false <- (13, 28) [subsumption resolution 360,318]
362. ~13 | ~28 [avatar contradiction clause 361]
363. $false [avatar sat refutation 200,261,276,316,362]
% SZS output end Proof for 2597668566020411434469883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not generous is creative or not strong and vice versa.
If someone is not calm or kind then alice is not wise or not creative and vice versa.
Everyone who is either not brave or happy is not calm and vice versa.
Everyone who is happy or not creative is not calm or not old and vice versa.
If someone is funny or not happy then someone is either not quiet or tall.
If someone is both humble and creative then susan is either patient or not generous.
Everyone who is both not happy and not quiet is both not strong and not kind.
Everyone who is both not quiet and not kind is generous or creative.
If someone is quiet or not patient then fred is either patient or wise and vice versa.
Everyone who is not old or creative is both old and not funny and vice versa.
If someone is either calm or not quiet then someone is wise and vice versa.
Everyone who is either not quiet or humble is kind and vice versa.
If someone is quiet then someone is either funny or not tall.
Everyone who is funny or not calm is either not humble or not funny.
Everyone who is either curious or brave is both funny and wise and vice versa.
If fred is either quiet or brave then someone is either not strong or not creative and vice versa.
Someone is patient.
Mary is either not quiet or not creative.
Someone is both creative and humble.
Someone is both old and calm.
Susan is not funny or not patient.
Mary is not brave.
Susan is both not tall and not generous.
Paul is either old or curious. | Paul is strong. | entailment | (![X]:((humble(X)&~generous(X))<=>(creative(X)|~strong(X))))&
((?[X]:((~calm(X)|kind(X))))<=>((~wise(alice)|~creative(alice))))&
(![X]:((~brave(X)<~>happy(X))<=>~calm(X)))&
(![X]:((happy(X)|~creative(X))<=>(~calm(X)|~old(X))))&
((?[X]:((funny(X)|~happy(X))))=>(?[X]:((~quiet(X)<~>tall(X)))))&
((?[X]:((humble(X)&creative(X))))=>((patient(susan)<~>~generous(susan))))&
(![X]:((~happy(X)&~quiet(X))=>(~strong(X)&~kind(X))))&
(![X]:((~quiet(X)&~kind(X))=>(generous(X)|creative(X))))&
((?[X]:((quiet(X)|~patient(X))))<=>((patient(fred)<~>wise(fred))))&
(![X]:((~old(X)|creative(X))<=>(old(X)&~funny(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>kind(X)))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((funny(X)|~calm(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((curious(X)<~>brave(X))<=>(funny(X)&wise(X))))&
(((quiet(fred)<~>brave(fred)))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(?[X]:(patient(X)))&
((~quiet(mary)<~>~creative(mary)))&
(?[X]:((creative(X)&humble(X))))&
(?[X]:((old(X)&calm(X))))&
((~funny(susan)|~patient(susan)))&
(~brave(mary))&
((~tall(susan)&~generous(susan)))&
((old(paul)<~>curious(paul))) | strong(paul) | [
"p0",
"p2",
"p3",
"p9",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 23849071159146804076150
% SZS output start Proof for 23849071159146804076150
1. ! [X0] : ((~generous(X0) & humble(X0)) <=> (~strong(X0) | creative(X0))) [input p0]
3. ! [X0] : ((~brave(X0) <~> happy(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((~creative(X0) | happy(X0)) <=> (~old(X0) | ~calm(X0))) [input p3]
10. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~funny(X0) & old(X0))) [input p9]
14. ! [X0] : ((~calm(X0) | funny(X0)) => (~humble(X0) <~> ~funny(X0))) [input p13]
15. ! [X0] : ((curious(X0) <~> brave(X0)) <=> (wise(X0) & funny(X0))) [input p14]
24. old(paul) <~> curious(paul) [input p23]
25. ~strong(paul) [input hypothesis]
36. ! [X0] : ((~humble(X0) <~> ~funny(X0)) | (calm(X0) & ~funny(X0))) [ennf transformation 14]
37. ! [X0] : (((~generous(X0) & humble(X0)) | (strong(X0) & ~creative(X0))) & ((~strong(X0) | creative(X0)) | (generous(X0) | ~humble(X0)))) [nnf transformation 1]
38. ! [X0] : (((~generous(X0) & humble(X0)) | (strong(X0) & ~creative(X0))) & (~strong(X0) | creative(X0) | generous(X0) | ~humble(X0))) [flattening 37]
44. ! [X0] : ((((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | calm(X0)) & (~calm(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0))))) [nnf transformation 3]
45. ! [X0] : (((~creative(X0) | happy(X0)) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | (creative(X0) & ~happy(X0)))) [nnf transformation 4]
46. ! [X0] : ((~creative(X0) | happy(X0) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | (creative(X0) & ~happy(X0)))) [flattening 45]
56. ! [X0] : (((creative(X0) | ~old(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 10]
57. ! [X0] : ((creative(X0) | ~old(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~creative(X0) & old(X0)))) [flattening 56]
68. ! [X0] : (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | (calm(X0) & ~funny(X0))) [nnf transformation 36]
69. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 15]
70. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [flattening 69]
82. (~curious(paul) | ~old(paul)) & (curious(paul) | old(paul)) [nnf transformation 24]
85. strong(X0) | humble(X0) [cnf transformation 38]
92. ~calm(X0) | happy(X0) | brave(X0) [cnf transformation 44]
95. ~happy(X0) | brave(X0) | calm(X0) [cnf transformation 44]
96. ~old(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 46]
98. ~creative(X0) | happy(X0) | calm(X0) [cnf transformation 46]
115. old(X0) | old(X0) [cnf transformation 57]
119. creative(X0) | ~old(X0) | funny(X0) | ~old(X0) [cnf transformation 57]
130. ~funny(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 68]
135. ~brave(X0) | curious(X0) | funny(X0) [cnf transformation 70]
160. ~curious(paul) | ~old(paul) [cnf transformation 82]
161. ~strong(paul) [cnf transformation 25]
162. ~funny(X0) | ~humble(X0) [duplicate literal removal 130]
163. old(X0) [duplicate literal removal 115]
164. ~old(X0) | creative(X0) | funny(X0) [duplicate literal removal 119]
333. ~curious(paul) [subsumption resolution 160,163]
335. humble(paul) [resolution 85,161]
353. ~happy(X0) | ~calm(X0) [resolution 96,163]
448. funny(X0) | creative(X0) [resolution 164,163]
454. ~humble(X1) | creative(X1) [resolution 448,162]
714. 78 <=> creative(paul) [avatar definition]
716. creative(paul) <- (78) [avatar component clause 714]
768. creative(paul) [resolution 454,335]
771. 78 [avatar split clause 768,714]
774. happy(paul) | calm(paul) <- (78) [resolution 716,98]
780. 87 <=> calm(paul) [avatar definition]
782. calm(paul) <- (87) [avatar component clause 780]
784. 88 <=> happy(paul) [avatar definition]
786. happy(paul) <- (88) [avatar component clause 784]
787. 87 | 88 | ~78 [avatar split clause 774,714,784,780]
956. happy(paul) | brave(paul) <- (87) [resolution 782,92]
958. 103 <=> brave(paul) [avatar definition]
959. ~brave(paul) <- (~103) [avatar component clause 958]
960. brave(paul) <- (103) [avatar component clause 958]
961. 103 | 88 | ~87 [avatar split clause 956,780,784,958]
1153. ~calm(paul) <- (88) [resolution 786,353]
1154. brave(paul) | calm(paul) <- (88) [resolution 786,95]
1158. calm(paul) <- (88, ~103) [subsumption resolution 1154,959]
1159. 87 | ~88 | 103 [avatar split clause 1158,958,784,780]
1160. ~87 | ~88 [avatar split clause 1153,784,780]
1187. curious(paul) | funny(paul) <- (103) [resolution 960,135]
1190. funny(paul) <- (103) [subsumption resolution 1187,333]
1215. ~humble(paul) <- (103) [resolution 1190,162]
1218. $false <- (103) [subsumption resolution 1215,335]
1219. ~103 [avatar contradiction clause 1218]
1222. $false [avatar sat refutation 771,787,961,1159,1160,1219]
% SZS output end Proof for 23849071159146804076150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is either not curious or not humble and vice versa.
If mary is not rich then someone is curious or not humble.
Everyone who is both not rich and old is both wise and patient.
Everyone who is not happy or old is both not calm and curious and vice versa.
Everyone who is either humble or not generous is old.
If someone is both not calm and not quiet then someone is either not wise or not funny.
If someone is old or wise then someone is both not curious and not funny and vice versa.
Everyone who is not strong is not kind or old.
If alice is tall then john is not funny or curious and vice versa.
Everyone who is not brave or patient is either not calm or tall.
Everyone who is both not happy and not curious is not kind or not funny and vice versa.
If fred is not humble then mary is both kind and not old.
Everyone who is funny or not wise is not tall and vice versa.
If someone is not humble then someone is not old and vice versa.
Everyone who is either not calm or generous is both not patient and not creative.
If someone is either patient or not quiet then someone is either not strong or creative and vice versa.
Lucy is not curious.
John is not creative or humble.
Alice is both brave and not patient.
Someone is creative.
Someone is not calm or happy.
Alice is calm. | Mary is old. | contradiction | (![X]:(~calm(X)<=>(~curious(X)<~>~humble(X))))&
((~rich(mary))=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~rich(X)&old(X))=>(wise(X)&patient(X))))&
(![X]:((~happy(X)|old(X))<=>(~calm(X)&curious(X))))&
(![X]:((humble(X)<~>~generous(X))=>old(X)))&
((?[X]:((~calm(X)&~quiet(X))))=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:(~strong(X)=>(~kind(X)|old(X))))&
((tall(alice))<=>((~funny(john)|curious(john))))&
(![X]:((~brave(X)|patient(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)|~funny(X))))&
((~humble(fred))=>((kind(mary)&~old(mary))))&
(![X]:((funny(X)|~wise(X))<=>~tall(X)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~patient(X)&~creative(X))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(~curious(lucy))&
((~creative(john)|humble(john)))&
((brave(alice)&~patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)|happy(X))))&
(calm(alice)) | old(mary) | [
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8496936479668710044198622
% SZS output start Proof for 8496936479668710044198622
4. ! [X0] : ((old(X0) | ~happy(X0)) <=> (curious(X0) & ~calm(X0))) [input p3]
7. ? [X0] : (wise(X0) | old(X0)) <=> ? [X0] : (~funny(X0) & ~curious(X0)) [input p6]
11. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (~funny(X0) | ~kind(X0))) [input p10]
23. old(mary) [input hypothesis]
25. ? [X0] : (wise(X0) | old(X0)) <=> ? [X1] : (~funny(X1) & ~curious(X1)) [rectify 7]
40. ! [X0] : (((old(X0) | ~happy(X0)) | (~curious(X0) | calm(X0))) & ((curious(X0) & ~calm(X0)) | (~old(X0) & happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((old(X0) | ~happy(X0) | ~curious(X0) | calm(X0)) & ((curious(X0) & ~calm(X0)) | (~old(X0) & happy(X0)))) [flattening 40]
47. (? [X0] : (wise(X0) | old(X0)) | ! [X1] : (funny(X1) | curious(X1))) & (? [X1] : (~funny(X1) & ~curious(X1)) | ! [X0] : (~wise(X0) & ~old(X0))) [nnf transformation 25]
48. (? [X0] : (wise(X0) | old(X0)) | ! [X1] : (funny(X1) | curious(X1))) & (? [X2] : (~funny(X2) & ~curious(X2)) | ! [X3] : (~wise(X3) & ~old(X3))) [rectify 47]
49. ? [X0] : (wise(X0) | old(X0)) => (wise(sK1) | old(sK1)) [choice axiom]
50. ? [X2] : (~funny(X2) & ~curious(X2)) => (~funny(sK2) & ~curious(sK2)) [choice axiom]
51. ((wise(sK1) | old(sK1)) | ! [X1] : (funny(X1) | curious(X1))) & ((~funny(sK2) & ~curious(sK2)) | ! [X3] : (~wise(X3) & ~old(X3))) [skolemisation 48,50,49]
55. ! [X0] : (((~curious(X0) & ~happy(X0)) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 11]
56. ! [X0] : (((~curious(X0) & ~happy(X0)) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | curious(X0) | happy(X0))) [flattening 55]
80. happy(X0) | curious(X0) [cnf transformation 41]
89. ~funny(sK2) | ~old(X3) [cnf transformation 51]
100. ~happy(X0) | funny(X0) [cnf transformation 56]
102. ~curious(X0) | funny(X0) [cnf transformation 56]
128. old(mary) [cnf transformation 23]
158. 8 <=> funny(sK2) [avatar definition]
160. ~funny(sK2) <- (~8) [avatar component clause 158]
163. 9 <=> ! [X3] : ~old(X3) [avatar definition]
164. ~old(X3) <- (9) [avatar component clause 163]
165. 9 | ~8 [avatar split clause 89,158,163]
192. 15 <=> old(mary) [avatar definition]
193. old(mary) <- (15) [avatar component clause 192]
262. 15 [avatar split clause 128,192]
275. funny(X0) | curious(X0) [resolution 100,80]
276. funny(X0) [subsumption resolution 275,102]
282. $false <- (~8) [resolution 276,160]
285. 8 [avatar contradiction clause 282]
288. $false <- (9, 15) [resolution 164,193]
289. ~9 | ~15 [avatar contradiction clause 288]
291. $false [avatar sat refutation 165,262,285,289]
% SZS output end Proof for 8496936479668710044198622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not humble is creative or happy.
Everyone who is either not curious or not strong is curious or happy and vice versa.
If someone is both tall and not curious then lucy is both rich and curious and vice versa.
Everyone who is not calm or brave is both not quiet and generous and vice versa.
Everyone who is not strong or rich is creative.
If someone is not calm then someone is not humble.
Everyone who is creative is both not tall and old.
Everyone who is either not kind or not humble is both rich and not funny and vice versa.
Everyone who is either not curious or quiet is either funny or strong.
Everyone who is not patient or not happy is either not calm or not happy.
Everyone who is strong is not old.
If someone is either creative or not happy then lucy is not humble and vice versa.
If john is either strong or calm then fred is both calm and not rich and vice versa.
If fred is either calm or patient then someone is not rich or not strong.
If fred is not curious or not calm then someone is generous or not old.
If lucy is not curious or not humble then fred is not creative.
Susan is not creative or not humble.
Someone is either not creative or not funny.
Fred is both old and patient.
John is not calm.
Susan is brave.
Susan is not humble.
John is happy or patient. | Fred is not happy. | entailment | (![X]:((curious(X)<~>~humble(X))=>(creative(X)|happy(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(curious(X)|happy(X))))&
((?[X]:((tall(X)&~curious(X))))<=>((rich(lucy)&curious(lucy))))&
(![X]:((~calm(X)|brave(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:(creative(X)=>(~tall(X)&old(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(funny(X)<~>strong(X))))&
(![X]:((~patient(X)|~happy(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((creative(X)<~>~happy(X))))<=>(~humble(lucy)))&
(((strong(john)<~>calm(john)))<=>((calm(fred)&~rich(fred))))&
(((calm(fred)<~>patient(fred)))=>(?[X]:((~rich(X)|~strong(X)))))&
(((~curious(fred)|~calm(fred)))=>(?[X]:((generous(X)|~old(X)))))&
(((~curious(lucy)|~humble(lucy)))=>(~creative(fred)))&
((~creative(susan)|~humble(susan)))&
(?[X]:((~creative(X)<~>~funny(X))))&
((old(fred)&patient(fred)))&
(~calm(john))&
(brave(susan))&
(~humble(susan))&
((happy(john)|patient(john))) | ~happy(fred) | [
"p4",
"p10",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 975435185918911525995057
% SZS output start Proof for 975435185918911525995057
5. ! [X0] : ((rich(X0) | ~strong(X0)) => creative(X0)) [input p4]
11. ! [X0] : (strong(X0) => ~old(X0)) [input p10]
12. ? [X0] : (creative(X0) <~> ~happy(X0)) <=> ~humble(lucy) [input p11]
16. (~humble(lucy) | ~curious(lucy)) => ~creative(fred) [input p15]
19. patient(fred) & old(fred) [input p18]
24. happy(fred) [input hypothesis]
28. ! [X0] : (creative(X0) | (~rich(X0) & strong(X0))) [ennf transformation 5]
33. ! [X0] : (~old(X0) | ~strong(X0)) [ennf transformation 11]
36. ~creative(fred) | (humble(lucy) & curious(lucy)) [ennf transformation 16]
54. (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | humble(lucy)) & (~humble(lucy) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) [nnf transformation 12]
55. (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((creative(X1) | happy(X1)) & (~happy(X1) | ~creative(X1)))) [rectify 54]
56. ? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) => ((happy(sK2) | ~creative(sK2)) & (~happy(sK2) | creative(sK2))) [choice axiom]
57. (((happy(sK2) | ~creative(sK2)) & (~happy(sK2) | creative(sK2))) | humble(lucy)) & (~humble(lucy) | ! [X1] : ((creative(X1) | happy(X1)) & (~happy(X1) | ~creative(X1)))) [skolemisation 55,56]
85. strong(X0) | creative(X0) [cnf transformation 28]
104. ~old(X0) | ~strong(X0) [cnf transformation 33]
105. ~humble(lucy) | ~happy(X1) | ~creative(X1) [cnf transformation 57]
120. ~creative(fred) | humble(lucy) [cnf transformation 36]
124. old(fred) [cnf transformation 19]
130. happy(fred) [cnf transformation 24]
169. 8 <=> humble(lucy) [avatar definition]
187. 12 <=> ! [X1] : (~happy(X1) | ~creative(X1)) [avatar definition]
188. ~happy(X1) | ~creative(X1) <- (12) [avatar component clause 187]
189. 12 | ~8 [avatar split clause 105,169,187]
241. 23 <=> creative(fred) [avatar definition]
242. creative(fred) <- (23) [avatar component clause 241]
244. 8 | ~23 [avatar split clause 120,241,169]
283. ~strong(fred) [resolution 104,124]
285. creative(fred) [resolution 283,85]
288. 23 [avatar split clause 285,241]
302. ~creative(fred) <- (12) [resolution 188,130]
305. $false <- (12, 23) [subsumption resolution 302,242]
306. ~12 | ~23 [avatar contradiction clause 305]
309. $false [avatar sat refutation 189,244,288,306]
% SZS output end Proof for 975435185918911525995057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then paul is not wise or humble and vice versa.
If fred is not generous or not quiet then john is either strong or funny and vice versa.
Everyone who is either kind or humble is both not creative and not strong and vice versa.
If fred is not brave then lucy is both not old and patient and vice versa.
If john is creative or not strong then john is happy or not strong and vice versa.
Everyone who is not creative or not humble is either not funny or not wise and vice versa.
If alice is both not strong and brave then lucy is either not kind or patient.
If fred is both wise and not generous then someone is both brave and rich and vice versa.
Everyone who is both not happy and not quiet is both not curious and not calm and vice versa.
Everyone who is not humble is generous or not curious.
Everyone who is not strong is either not funny or wise.
Everyone who is rich or brave is either not creative or rich and vice versa.
If lucy is not curious then lucy is wise and vice versa.
If john is not curious then someone is not kind or not humble.
If someone is either not generous or not funny then someone is both not creative and not tall.
Everyone who is either not kind or not humble is not old.
Someone is not generous or funny.
Someone is kind or funny.
Someone is either rich or strong.
Someone is either not happy or not calm.
Paul is not generous or funny.
Someone is not wise or not quiet.
Susan is either not calm or patient.
Alice is both strong and not old. | John is happy. | neutral | ((~old(alice))<=>((~wise(paul)|humble(paul))))&
(((~generous(fred)|~quiet(fred)))<=>((strong(john)<~>funny(john))))&
(![X]:((kind(X)<~>humble(X))<=>(~creative(X)&~strong(X))))&
((~brave(fred))<=>((~old(lucy)&patient(lucy))))&
(((creative(john)|~strong(john)))<=>((happy(john)|~strong(john))))&
(![X]:((~creative(X)|~humble(X))<=>(~funny(X)<~>~wise(X))))&
(((~strong(alice)&brave(alice)))=>((~kind(lucy)<~>patient(lucy))))&
(((wise(fred)&~generous(fred)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(~curious(X)&~calm(X))))&
(![X]:(~humble(X)=>(generous(X)|~curious(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>wise(X))))&
(![X]:((rich(X)|brave(X))<=>(~creative(X)<~>rich(X))))&
((~curious(lucy))<=>(wise(lucy)))&
((~curious(john))=>(?[X]:((~kind(X)|~humble(X)))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~kind(X)<~>~humble(X))=>~old(X)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~happy(X)<~>~calm(X))))&
((~generous(paul)|funny(paul)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~calm(susan)<~>patient(susan)))&
((strong(alice)&~old(alice))) | happy(john) | [] | null | 0 |
Everyone who is old is both not kind and not old and vice versa.
If someone is not generous then someone is not quiet.
If someone is not patient then alice is both wise and not generous and vice versa.
Everyone who is not brave is either not rich or not curious.
Everyone who is both not tall and quiet is not funny or wise and vice versa.
If someone is either happy or patient then someone is old.
If someone is either humble or strong then lucy is both happy and strong.
Everyone who is either happy or tall is either humble or old.
If lucy is both calm and not funny then someone is either not tall or not quiet and vice versa.
Everyone who is either not rich or curious is either not rich or not humble.
If someone is both not creative and wise then alice is either not tall or calm and vice versa.
If someone is both patient and strong then someone is creative.
If someone is either not old or not brave then alice is not wise or not quiet and vice versa.
If someone is not wise then someone is either funny or not creative.
If lucy is creative or not quiet then lucy is not humble or calm.
If someone is curious or not old then paul is either calm or not rich.
Someone is both happy and not curious.
Someone is either rich or patient.
Paul is both strong and rich.
Someone is both tall and not wise.
Someone is not funny or strong.
Someone is not funny or humble.
Someone is not strong.
Someone is calm or not patient. | Lucy is not kind. | contradiction | (![X]:(old(X)<=>(~kind(X)&~old(X))))&
((?[X]:(~generous(X)))=>(?[X]:(~quiet(X))))&
((?[X]:(~patient(X)))<=>((wise(alice)&~generous(alice))))&
(![X]:(~brave(X)=>(~rich(X)<~>~curious(X))))&
(![X]:((~tall(X)&quiet(X))<=>(~funny(X)|wise(X))))&
((?[X]:((happy(X)<~>patient(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)<~>strong(X))))=>((happy(lucy)&strong(lucy))))&
(![X]:((happy(X)<~>tall(X))=>(humble(X)<~>old(X))))&
(((calm(lucy)&~funny(lucy)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~rich(X)<~>curious(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:((~creative(X)&wise(X))))<=>((~tall(alice)<~>calm(alice))))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(alice)|~quiet(alice))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~creative(X)))))&
(((creative(lucy)|~quiet(lucy)))=>((~humble(lucy)|calm(lucy))))&
((?[X]:((curious(X)|~old(X))))=>((calm(paul)<~>~rich(paul))))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:((rich(X)<~>patient(X))))&
((strong(paul)&rich(paul)))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)|~patient(X)))) | ~kind(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1955638686367022390412072
% SZS output start Proof for 1955638686367022390412072
1. ! [X0] : (old(X0) <=> (~old(X0) & ~kind(X0))) [input p0]
25. ~kind(lucy) [input hypothesis]
41. ! [X0] : ((old(X0) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | ~old(X0))) [nnf transformation 1]
42. ! [X0] : ((old(X0) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | ~old(X0))) [flattening 41]
99. ~old(X0) | ~old(X0) [cnf transformation 42]
100. old(X0) | old(X0) | kind(X0) [cnf transformation 42]
165. ~kind(lucy) [cnf transformation 25]
168. ~old(X0) [duplicate literal removal 99]
169. kind(X0) | old(X0) [duplicate literal removal 100]
390. old(lucy) [resolution 169,165]
391. $false [subsumption resolution 390,168]
% SZS output end Proof for 1955638686367022390412072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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