premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is funny then paul is both not happy and not humble and vice versa.
If someone is generous then someone is either not strong or not calm.
If john is either not kind or tall then someone is not curious.
Everyone who is generous is either calm or wise and vice versa.
Everyone who is both not creative and not tall is not creative and vice versa.
If someone is funny then paul is not humble or quiet.
Everyone who is calm or curious is funny or not calm and vice versa.
If paul is both quiet and calm then paul is not generous or not wise.
Everyone who is both not brave and not old is both creative and not patient.
Everyone who is not quiet or funny is humble or not funny.
If someone is not rich or humble then someone is both not generous and not kind.
If someone is not funny or kind then fred is either calm or not tall.
Everyone who is either strong or generous is not happy and vice versa.
Everyone who is generous is brave and vice versa.
If someone is quiet or not tall then john is either happy or not rich and vice versa.
Everyone who is happy is not calm and vice versa.
John is not funny.
Someone is either not strong or not happy.
Alice is either patient or not brave.
Paul is curious.
John is not rich or not funny.
Someone is patient.
Alice is not patient.
Fred is either old or not old. | Alice is not tall. | neutral | ((?[X]:(funny(X)))<=>((~happy(paul)&~humble(paul))))&
((?[X]:(generous(X)))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(((~kind(john)<~>tall(john)))=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(calm(X)<~>wise(X))))&
(![X]:((~creative(X)&~tall(X))<=>~creative(X)))&
((?[X]:(funny(X)))=>((~humble(paul)|quiet(paul))))&
(![X]:((calm(X)|curious(X))<=>(funny(X)|~calm(X))))&
(((quiet(paul)&calm(paul)))=>((~generous(paul)|~wise(paul))))&
(![X]:((~brave(X)&~old(X))=>(creative(X)&~patient(X))))&
(![X]:((~quiet(X)|funny(X))=>(humble(X)|~funny(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~funny(X)|kind(X))))=>((calm(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>generous(X))<=>~happy(X)))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((quiet(X)|~tall(X))))<=>((happy(john)<~>~rich(john))))&
(![X]:(happy(X)<=>~calm(X)))&
(~funny(john))&
(?[X]:((~strong(X)<~>~happy(X))))&
((patient(alice)<~>~brave(alice)))&
(curious(paul))&
((~rich(john)|~funny(john)))&
(?[X]:(patient(X)))&
(~patient(alice))&
((old(fred)<~>~old(fred))) | ~tall(alice) | [] | null | 0 |
Everyone who is both calm and quiet is both not happy and curious and vice versa. Everyone who is not wise is quiet and vice versa. If someone is not generous or not calm then someone is curious. If someone is old then lucy is both old and not tall. Everyone who is either not patient or brave is both humble and not happy and vice versa. Everyone who is tall or not creative is either not brave or not creative. Everyone who is not quiet or not curious is happy and vice versa. If paul is both funny and rich then fred is not rich. Everyone who is both not strong and happy is both not creative and not kind and vice versa. Everyone who is funny or creative is not wise and vice versa. Everyone who is brave or funny is rich or not tall and vice versa. Everyone who is either not creative or not quiet is either happy or not kind and vice versa. Everyone who is not funny is either not humble or not strong and vice versa. If paul is calm then mary is humble or kind. Everyone who is funny or not humble is either happy or not brave and vice versa. Everyone who is both quiet and wise is both old and not quiet and vice versa. Mary is not calm. Alice is not brave. John is not humble. Someone is curious. Someone is both not old and not strong. Someone is either generous or not kind. Fred is not happy or not creative. | John is not kind. | neutral | (![X]:((calm(X)&quiet(X))<=>(~happy(X)&curious(X))))&
(![X]:(~wise(X)<=>quiet(X)))&
((?[X]:((~generous(X)|~calm(X))))=>(?[X]:(curious(X))))&
((?[X]:(old(X)))=>((old(lucy)&~tall(lucy))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)|~creative(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~curious(X))<=>happy(X)))&
(((funny(paul)&rich(paul)))=>(~rich(fred)))&
(![X]:((~strong(X)&happy(X))<=>(~creative(X)&~kind(X))))&
(![X]:((funny(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
(![X]:((quiet(X)&wise(X))<=>(old(X)&~quiet(X))))&
(~calm(mary))&
(~brave(alice))&
(~humble(john))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred))) | ~kind(john) | [] | null | 0 |
If someone is either not funny or creative then someone is either not curious or quiet and vice versa.
If john is not wise or tall then paul is strong or funny.
If someone is not funny or not happy then john is both humble and strong and vice versa.
If someone is not funny then john is not curious.
Everyone who is not old or not funny is not rich.
If susan is both calm and not patient then paul is both old and wise.
Everyone who is not quiet is happy or funny and vice versa.
If someone is either brave or not quiet then someone is wise.
If someone is creative or not quiet then mary is either not wise or not brave.
If susan is generous then someone is not happy or not wise and vice versa.
Everyone who is both not brave and creative is old or patient.
If someone is both not funny and not humble then susan is both not patient and not happy and vice versa.
If someone is not happy then someone is either old or not kind and vice versa.
Everyone who is brave or not happy is both not tall and funny and vice versa.
Everyone who is not patient is not quiet or not happy and vice versa.
If paul is either not curious or old then someone is both strong and not curious and vice versa.
Lucy is both happy and funny.
Lucy is humble or not wise.
Someone is both curious and not calm.
Alice is both not brave and funny.
Someone is kind or not old.
Someone is either not kind or not brave.
Fred is either old or not happy. | Lucy is patient. | contradiction | ((?[X]:((~funny(X)<~>creative(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((~wise(john)|tall(john)))=>((strong(paul)|funny(paul))))&
((?[X]:((~funny(X)|~happy(X))))<=>((humble(john)&strong(john))))&
((?[X]:(~funny(X)))=>(~curious(john)))&
(![X]:((~old(X)|~funny(X))=>~rich(X)))&
(((calm(susan)&~patient(susan)))=>((old(paul)&wise(paul))))&
(![X]:(~quiet(X)<=>(happy(X)|funny(X))))&
((?[X]:((brave(X)<~>~quiet(X))))=>(?[X]:(wise(X))))&
((?[X]:((creative(X)|~quiet(X))))=>((~wise(mary)<~>~brave(mary))))&
((generous(susan))<=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:((~brave(X)&creative(X))=>(old(X)|patient(X))))&
((?[X]:((~funny(X)&~humble(X))))<=>((~patient(susan)&~happy(susan))))&
((?[X]:(~happy(X)))<=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((brave(X)|~happy(X))<=>(~tall(X)&funny(X))))&
(![X]:(~patient(X)<=>(~quiet(X)|~happy(X))))&
(((~curious(paul)<~>old(paul)))<=>(?[X]:((strong(X)&~curious(X)))))&
((happy(lucy)&funny(lucy)))&
((humble(lucy)|~wise(lucy)))&
(?[X]:((curious(X)&~calm(X))))&
((~brave(alice)&funny(alice)))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((old(fred)<~>~happy(fred))) | patient(lucy) | [
"p6",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 173306408692600968588396
% SZS output start Proof for 173306408692600968588396
7. ! [X0] : (~quiet(X0) <=> (funny(X0) | happy(X0))) [input p6]
15. ! [X0] : (~patient(X0) <=> (~happy(X0) | ~quiet(X0))) [input p14]
17. funny(lucy) & happy(lucy) [input p16]
24. patient(lucy) [input hypothesis]
48. ! [X0] : ((~quiet(X0) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | quiet(X0))) [nnf transformation 7]
49. ! [X0] : ((~quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | quiet(X0))) [flattening 48]
71. ! [X0] : ((~patient(X0) | (happy(X0) & quiet(X0))) & ((~happy(X0) | ~quiet(X0)) | patient(X0))) [nnf transformation 15]
72. ! [X0] : ((~patient(X0) | (happy(X0) & quiet(X0))) & (~happy(X0) | ~quiet(X0) | patient(X0))) [flattening 71]
102. ~happy(X0) | ~quiet(X0) [cnf transformation 49]
128. ~patient(X0) | quiet(X0) [cnf transformation 72]
136. happy(lucy) [cnf transformation 17]
147. patient(lucy) [cnf transformation 24]
394. ~quiet(lucy) [resolution 102,136]
400. quiet(lucy) [resolution 128,147]
401. $false [subsumption resolution 400,394]
% SZS output end Proof for 173306408692600968588396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is either not strong or rich and vice versa. Everyone who is both not curious and not calm is either creative or not humble and vice versa. If someone is wise or rich then alice is tall or creative and vice versa. If alice is not humble or not creative then someone is either quiet or not strong. Everyone who is happy is not humble or not old and vice versa. Everyone who is either curious or tall is calm or happy. If fred is not generous then alice is brave or not humble and vice versa. Everyone who is not humble is both not creative and not curious. If someone is both tall and brave then someone is generous or wise. Everyone who is either not humble or kind is both kind and not humble and vice versa. If someone is not curious or happy then someone is kind and vice versa. If someone is not calm then someone is not brave or kind and vice versa. Everyone who is rich or wise is either not rich or not tall. If john is not quiet or funny then someone is curious or not old. Everyone who is both not wise and happy is both tall and not rich and vice versa. Someone is either patient or happy. Paul is not quiet or strong. Lucy is both humble and not happy. Fred is both not strong and not creative. Someone is both strong and not happy. Someone is calm or creative. Someone is either quiet or not strong. | John is not wise. | entailment | (![X]:((~creative(X)&patient(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|rich(X))))<=>((tall(alice)|creative(alice))))&
(((~humble(alice)|~creative(alice)))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(happy(X)<=>(~humble(X)|~old(X))))&
(![X]:((curious(X)<~>tall(X))=>(calm(X)|happy(X))))&
((~generous(fred))<=>((brave(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&~humble(X))))&
((?[X]:((~curious(X)|happy(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((rich(X)|wise(X))=>(~rich(X)<~>~tall(X))))&
(((~quiet(john)|funny(john)))=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((~wise(X)&happy(X))<=>(tall(X)&~rich(X))))&
(?[X]:((patient(X)<~>happy(X))))&
((~quiet(paul)|strong(paul)))&
((humble(lucy)&~happy(lucy)))&
((~strong(fred)&~creative(fred)))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((quiet(X)<~>~strong(X)))) | ~wise(john) | [
"p1",
"p2",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1370621382364080696352951
% SZS output start Proof for 1370621382364080696352951
2. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p1]
3. ? [X0] : (rich(X0) | wise(X0)) <=> (creative(alice) | tall(alice)) [input p2]
10. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~humble(X0) & kind(X0))) [input p9]
11. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X0] : kind(X0) [input p10]
13. ! [X0] : ((wise(X0) | rich(X0)) => (~rich(X0) <~> ~tall(X0))) [input p12]
15. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~rich(X0) & tall(X0))) [input p14]
23. wise(john) [input hypothesis]
25. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X1] : kind(X1) [rectify 11]
33. ! [X0] : ((~rich(X0) <~> ~tall(X0)) | (~wise(X0) & ~rich(X0))) [ennf transformation 13]
37. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (calm(X0) | curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | calm(X0) | curious(X0))) [flattening 37]
39. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & ((creative(alice) | tall(alice)) | ! [X0] : (~rich(X0) & ~wise(X0))) [nnf transformation 3]
40. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X0] : (~rich(X0) & ~wise(X0))) [flattening 39]
41. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [rectify 40]
42. ? [X0] : (rich(X0) | wise(X0)) => (rich(sK0) | wise(sK0)) [choice axiom]
43. ((rich(sK0) | wise(sK0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [skolemisation 41,42]
55. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 55]
57. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~happy(X0) & curious(X0))) [nnf transformation 25]
58. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~happy(X3) & curious(X3))) [rectify 57]
59. ? [X0] : (happy(X0) | ~curious(X0)) => (happy(sK3) | ~curious(sK3)) [choice axiom]
60. ? [X2] : kind(X2) => kind(sK4) [choice axiom]
61. ((happy(sK3) | ~curious(sK3)) | ! [X1] : ~kind(X1)) & (kind(sK4) | ! [X3] : (~happy(X3) & curious(X3))) [skolemisation 58,60,59]
67. ! [X0] : (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~wise(X0) & ~rich(X0))) [nnf transformation 33]
70. ! [X0] : (((happy(X0) & ~wise(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 15]
71. ! [X0] : (((happy(X0) & ~wise(X0)) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | ~happy(X0) | wise(X0))) [flattening 70]
90. ~humble(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 38]
94. creative(alice) | tall(alice) | ~wise(X1) [cnf transformation 43]
113. kind(X0) | kind(X0) | humble(X0) [cnf transformation 56]
116. ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 56]
118. ~kind(X0) | humble(X0) | humble(X0) | ~kind(X0) [cnf transformation 56]
119. kind(sK4) | curious(X3) [cnf transformation 61]
120. kind(sK4) | ~happy(X3) [cnf transformation 61]
125. ~tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 67]
133. happy(X0) | rich(X0) | ~tall(X0) [cnf transformation 71]
146. wise(john) [cnf transformation 23]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 125]
148. kind(X0) | humble(X0) [duplicate literal removal 113]
149. ~humble(X0) | ~kind(X0) [duplicate literal removal 116]
150. ~kind(X0) | humble(X0) [duplicate literal removal 118]
152. 1 <=> creative(alice) [avatar definition]
153. creative(alice) <- (1) [avatar component clause 152]
165. 4 <=> tall(alice) [avatar definition]
166. tall(alice) <- (4) [avatar component clause 165]
174. 6 <=> ! [X1] : ~wise(X1) [avatar definition]
175. ~wise(X1) <- (6) [avatar component clause 174]
176. 6 | 4 | 1 [avatar split clause 94,152,165,174]
216. ~kind(X0) [subsumption resolution 149,150]
217. humble(X0) [subsumption resolution 148,216]
218. ~happy(X3) [subsumption resolution 120,216]
219. curious(X3) [subsumption resolution 119,216]
237. rich(X0) | ~tall(X0) [subsumption resolution 133,218]
238. ~tall(X0) [subsumption resolution 237,147]
270. $false <- (4) [subsumption resolution 166,238]
271. ~4 [avatar contradiction clause 270]
272. $false <- (6) [resolution 175,146]
275. ~6 [avatar contradiction clause 272]
288. ~curious(X0) | ~creative(X0) [resolution 90,217]
289. ~creative(X0) [subsumption resolution 288,219]
290. $false <- (1) [resolution 289,153]
291. ~1 [avatar contradiction clause 290]
292. $false [avatar sat refutation 176,271,275,291]
% SZS output end Proof for 1370621382364080696352951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not humble is kind.
If someone is not creative then john is either funny or not wise and vice versa.
If someone is both not quiet and brave then fred is wise or not curious.
If someone is curious then alice is both not humble and not kind.
Everyone who is humble is creative and vice versa.
If mary is either generous or brave then someone is curious or quiet.
Everyone who is both wise and quiet is either not patient or strong and vice versa.
Everyone who is tall or not wise is tall or not curious.
If john is both strong and not strong then someone is both curious and quiet and vice versa.
Everyone who is either tall or funny is both not calm and not curious and vice versa.
Everyone who is either quiet or strong is calm or not wise.
If someone is not wise or not humble then alice is both funny and quiet.
Everyone who is not rich is either tall or creative and vice versa.
If someone is not kind or generous then alice is brave or not quiet.
If paul is not creative then lucy is brave or quiet and vice versa.
If john is curious or not curious then someone is both happy and curious and vice versa.
Someone is quiet.
Paul is old.
Someone is both not calm and not strong.
Someone is old or not funny.
Someone is brave or wise.
Paul is rich or patient. | Alice is strong. | neutral | (![X]:((quiet(X)<~>~humble(X))=>kind(X)))&
((?[X]:(~creative(X)))<=>((funny(john)<~>~wise(john))))&
((?[X]:((~quiet(X)&brave(X))))=>((wise(fred)|~curious(fred))))&
((?[X]:(curious(X)))=>((~humble(alice)&~kind(alice))))&
(![X]:(humble(X)<=>creative(X)))&
(((generous(mary)<~>brave(mary)))=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~patient(X)<~>strong(X))))&
(![X]:((tall(X)|~wise(X))=>(tall(X)|~curious(X))))&
(((strong(john)&~strong(john)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(calm(X)|~wise(X))))&
((?[X]:((~wise(X)|~humble(X))))=>((funny(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((~kind(X)|generous(X))))=>((brave(alice)|~quiet(alice))))&
((~creative(paul))<=>((brave(lucy)|quiet(lucy))))&
(((curious(john)|~curious(john)))<=>(?[X]:((happy(X)&curious(X)))))&
(?[X]:(quiet(X)))&
(old(paul))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul))) | strong(alice) | [] | null | 0 |
Everyone who is either not kind or not wise is not funny.
If alice is not quiet then susan is not brave and vice versa.
Everyone who is not funny or not brave is not rich or not calm and vice versa.
Everyone who is not generous or not creative is not wise or not tall and vice versa.
Everyone who is happy or brave is either not calm or tall.
If susan is not funny then john is not quiet and vice versa.
If someone is both creative and funny then someone is both not creative and not quiet.
Everyone who is not kind or not tall is not curious or creative and vice versa.
Everyone who is both not humble and not happy is old or not strong.
Everyone who is both not happy and humble is both funny and not happy.
Everyone who is either not calm or not wise is old or not generous and vice versa.
If someone is either not rich or kind then someone is not funny or tall and vice versa.
If someone is both kind and not kind then someone is either wise or kind and vice versa.
Everyone who is not rich is both not generous and generous and vice versa.
If someone is both kind and humble then someone is both not rich and not quiet and vice versa.
Everyone who is not creative or not old is both not creative and creative.
Paul is not generous.
Someone is generous or quiet.
Mary is not curious.
Someone is not happy or not brave.
Someone is either strong or not humble.
Someone is strong or quiet.
Someone is either old or generous. | Alice is not wise. | contradiction | (![X]:((~kind(X)<~>~wise(X))=>~funny(X)))&
((~quiet(alice))<=>(~brave(susan)))&
(![X]:((~funny(X)|~brave(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(~wise(X)|~tall(X))))&
(![X]:((happy(X)|brave(X))=>(~calm(X)<~>tall(X))))&
((~funny(susan))<=>(~quiet(john)))&
((?[X]:((creative(X)&funny(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~kind(X)|~tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((~humble(X)&~happy(X))=>(old(X)|~strong(X))))&
(![X]:((~happy(X)&humble(X))=>(funny(X)&~happy(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(old(X)|~generous(X))))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
((?[X]:((kind(X)&~kind(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(~rich(X)<=>(~generous(X)&generous(X))))&
((?[X]:((kind(X)&humble(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)|~old(X))=>(~creative(X)&creative(X))))&
(~generous(paul))&
(?[X]:((generous(X)|quiet(X))))&
(~curious(mary))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:((old(X)<~>generous(X)))) | ~wise(alice) | [
"p2",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9136649764502337611756556
% SZS output start Proof for 9136649764502337611756556
3. ! [X0] : ((~brave(X0) | ~funny(X0)) <=> (~calm(X0) | ~rich(X0))) [input p2]
7. ? [X0] : (funny(X0) & creative(X0)) => ? [X0] : (~quiet(X0) & ~creative(X0)) [input p6]
11. ! [X0] : ((~calm(X0) <~> ~wise(X0)) <=> (~generous(X0) | old(X0))) [input p10]
14. ! [X0] : (~rich(X0) <=> (generous(X0) & ~generous(X0))) [input p13]
16. ! [X0] : ((~old(X0) | ~creative(X0)) => (creative(X0) & ~creative(X0))) [input p15]
24. ~wise(alice) [input hypothesis]
25. ? [X0] : (funny(X0) & creative(X0)) => ? [X1] : (~quiet(X1) & ~creative(X1)) [rectify 7]
31. ? [X1] : (~quiet(X1) & ~creative(X1)) | ! [X0] : (~funny(X0) | ~creative(X0)) [ennf transformation 25]
36. ! [X0] : ((creative(X0) & ~creative(X0)) | (old(X0) & creative(X0))) [ennf transformation 16]
39. ! [X0] : (((~brave(X0) | ~funny(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (brave(X0) & funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~brave(X0) | ~funny(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (brave(X0) & funny(X0)))) [flattening 39]
45. ? [X0] : (~quiet(X0) & ~creative(X0)) | ! [X1] : (~funny(X1) | ~creative(X1)) [rectify 31]
46. ? [X0] : (~quiet(X0) & ~creative(X0)) => (~quiet(sK0) & ~creative(sK0)) [choice axiom]
47. (~quiet(sK0) & ~creative(sK0)) | ! [X1] : (~funny(X1) | ~creative(X1)) [skolemisation 45,46]
50. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [nnf transformation 11]
51. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [flattening 50]
62. ! [X0] : ((~rich(X0) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | rich(X0))) [nnf transformation 14]
63. ! [X0] : ((~rich(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | rich(X0))) [flattening 62]
85. ~calm(X0) | ~rich(X0) | funny(X0) [cnf transformation 40]
99. ~creative(sK0) | ~funny(X1) | ~creative(X1) [cnf transformation 47]
112. ~old(X0) | calm(X0) | wise(X0) [cnf transformation 51]
126. ~generous(X0) | rich(X0) [cnf transformation 63]
127. generous(X0) | rich(X0) [cnf transformation 63]
134. ~creative(X0) | old(X0) [cnf transformation 36]
135. creative(X0) | creative(X0) [cnf transformation 36]
146. ~wise(alice) [cnf transformation 24]
147. creative(X0) [duplicate literal removal 135]
169. 5 <=> ! [X1] : (~funny(X1) | ~creative(X1)) [avatar definition]
170. ~funny(X1) | ~creative(X1) <- (5) [avatar component clause 169]
177. 7 <=> creative(sK0) [avatar definition]
179. ~creative(sK0) <- (~7) [avatar component clause 177]
180. 5 | ~7 [avatar split clause 99,177,169]
229. rich(X0) [subsumption resolution 126,127]
240. old(X0) [subsumption resolution 134,147]
281. $false <- (~7) [subsumption resolution 179,147]
282. 7 [avatar contradiction clause 281]
283. ~funny(X1) <- (5) [subsumption resolution 170,147]
318. calm(X1) | wise(X1) [resolution 112,240]
329. wise(X4) | ~rich(X4) | funny(X4) [resolution 318,85]
331. wise(X4) | funny(X4) [subsumption resolution 329,229]
332. wise(X4) <- (5) [subsumption resolution 331,283]
334. $false <- (5) [resolution 332,146]
336. ~5 [avatar contradiction clause 334]
337. $false [avatar sat refutation 180,282,336]
% SZS output end Proof for 9136649764502337611756556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not funny or not old then someone is not curious and vice versa.
Everyone who is funny or patient is creative and vice versa.
Everyone who is both not funny and not kind is either brave or wise.
If someone is not brave then alice is not happy and vice versa.
Everyone who is not strong or not old is not creative.
Everyone who is either curious or creative is either not old or rich and vice versa.
Everyone who is both not creative and not tall is creative or patient.
Everyone who is calm or not calm is curious or happy.
Everyone who is kind is both happy and not calm.
If someone is both old and calm then mary is quiet and vice versa.
If someone is not old then alice is either kind or strong.
Everyone who is either not creative or not brave is wise and vice versa.
Everyone who is not humble is both happy and not brave and vice versa.
Everyone who is either not curious or humble is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Someone is not quiet or strong.
Alice is both wise and not quiet.
Someone is both rich and not patient.
Someone is either calm or not wise.
John is both not calm and generous.
Alice is not rich or not old. | John is curious. | neutral | (((~funny(john)|~old(john)))<=>(?[X]:(~curious(X))))&
(![X]:((funny(X)|patient(X))<=>creative(X)))&
(![X]:((~funny(X)&~kind(X))=>(brave(X)<~>wise(X))))&
((?[X]:(~brave(X)))<=>(~happy(alice)))&
(![X]:((~strong(X)|~old(X))=>~creative(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|patient(X))))&
(![X]:((calm(X)|~calm(X))=>(curious(X)|happy(X))))&
(![X]:(kind(X)=>(happy(X)&~calm(X))))&
((?[X]:((old(X)&calm(X))))<=>(quiet(mary)))&
((?[X]:(~old(X)))=>((kind(alice)<~>strong(alice))))&
(![X]:((~creative(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~humble(X)<=>(happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>humble(X))=>(quiet(X)|kind(X))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
((~calm(john)&generous(john)))&
((~rich(alice)|~old(alice))) | curious(john) | [] | null | 0 |
Everyone who is not brave or not generous is either not brave or not generous.
Everyone who is not kind or rich is either not patient or creative.
Everyone who is not kind or not curious is either not generous or not happy.
Everyone who is not old or funny is not calm and vice versa.
If someone is both rich and not curious then someone is either not kind or brave and vice versa.
If someone is humble then someone is funny.
If alice is kind then alice is either creative or kind and vice versa.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
If paul is patient or funny then alice is not happy or not patient and vice versa.
Everyone who is funny is either not old or not humble.
Everyone who is both not tall and not humble is old.
John is generous.
Someone is patient or tall.
Paul is not rich or generous.
Someone is strong or quiet.
Someone is patient.
Someone is not tall.
Someone is humble.
Mary is not creative or quiet. | Paul is not old. | neutral | (![X]:((~brave(X)|~generous(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~kind(X)|rich(X))=>(~patient(X)<~>creative(X))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|funny(X))<=>~calm(X)))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((kind(alice))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(((patient(paul)|funny(paul)))<=>((~happy(alice)|~patient(alice))))&
(![X]:(funny(X)=>(~old(X)<~>~humble(X))))&
(![X]:((~tall(X)&~humble(X))=>old(X)))&
(generous(john))&
(?[X]:((patient(X)|tall(X))))&
((~rich(paul)|generous(paul)))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X)))&
((~creative(mary)|quiet(mary))) | ~old(paul) | [] | null | 0 |
Everyone who is not patient or wise is both not generous and kind and vice versa. If someone is not patient then lucy is wise. Everyone who is both kind and creative is either not tall or not creative and vice versa. Everyone who is both not humble and not funny is humble. Everyone who is either not strong or not happy is not rich and vice versa. If lucy is not generous then someone is both rich and calm and vice versa. If someone is quiet or humble then fred is either not happy or not patient. Everyone who is happy or quiet is both not old and not kind. If lucy is both not patient and curious then lucy is both not quiet and happy. Everyone who is either happy or patient is either not wise or not happy. If mary is not happy or calm then john is both not wise and not tall and vice versa. Everyone who is either humble or not creative is not creative or tall. If someone is both quiet and rich then someone is either not humble or not happy. Everyone who is both quiet and not creative is both quiet and wise and vice versa. If someone is both not brave and wise then mary is strong. If someone is happy or wise then someone is not humble. Someone is tall or not generous. Fred is either not quiet or generous. Mary is kind. Lucy is either not funny or kind. Someone is either not wise or tall. Fred is both brave and patient. Fred is brave. | Fred is not quiet. | entailment | (![X]:((~patient(X)|wise(X))<=>(~generous(X)&kind(X))))&
((?[X]:(~patient(X)))=>(wise(lucy)))&
(![X]:((kind(X)&creative(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((~humble(X)&~funny(X))=>humble(X)))&
(![X]:((~strong(X)<~>~happy(X))<=>~rich(X)))&
((~generous(lucy))<=>(?[X]:((rich(X)&calm(X)))))&
((?[X]:((quiet(X)|humble(X))))=>((~happy(fred)<~>~patient(fred))))&
(![X]:((happy(X)|quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)&curious(lucy)))=>((~quiet(lucy)&happy(lucy))))&
(![X]:((happy(X)<~>patient(X))=>(~wise(X)<~>~happy(X))))&
(((~happy(mary)|calm(mary)))<=>((~wise(john)&~tall(john))))&
(![X]:((humble(X)<~>~creative(X))=>(~creative(X)|tall(X))))&
((?[X]:((quiet(X)&rich(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
(![X]:((quiet(X)&~creative(X))<=>(quiet(X)&wise(X))))&
((?[X]:((~brave(X)&wise(X))))=>(strong(mary)))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:(~humble(X))))&
(?[X]:((tall(X)|~generous(X))))&
((~quiet(fred)<~>generous(fred)))&
(kind(mary))&
((~funny(lucy)<~>kind(lucy)))&
(?[X]:((~wise(X)<~>tall(X))))&
((brave(fred)&patient(fred)))&
(brave(fred)) | ~quiet(fred) | [
"p0",
"p6",
"p9",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7653092077207506636123547
% SZS output start Proof for 7653092077207506636123547
1. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (kind(X0) & ~generous(X0))) [input p0]
7. ? [X0] : (humble(X0) | quiet(X0)) => (~happy(fred) <~> ~patient(fred)) [input p6]
10. ! [X0] : ((happy(X0) <~> patient(X0)) => (~wise(X0) <~> ~happy(X0))) [input p9]
18. ~quiet(fred) <~> generous(fred) [input p17]
22. patient(fred) & brave(fred) [input p21]
24. quiet(fred) [input hypothesis]
28. patient(fred) [pure predicate removal 22]
35. (~happy(fred) <~> ~patient(fred)) | ! [X0] : (~humble(X0) & ~quiet(X0)) [ennf transformation 7]
37. ! [X0] : ((~wise(X0) <~> ~happy(X0)) | (happy(X0) <=> patient(X0))) [ennf transformation 10]
42. ! [X0] : (((wise(X0) | ~patient(X0)) | (~kind(X0) | generous(X0))) & ((kind(X0) & ~generous(X0)) | (~wise(X0) & patient(X0)))) [nnf transformation 1]
43. ! [X0] : ((wise(X0) | ~patient(X0) | ~kind(X0) | generous(X0)) & ((kind(X0) & ~generous(X0)) | (~wise(X0) & patient(X0)))) [flattening 42]
51. ((patient(fred) | happy(fred)) & (~patient(fred) | ~happy(fred))) | ! [X0] : (~humble(X0) & ~quiet(X0)) [nnf transformation 35]
52. ! [X0] : (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0)))) [nnf transformation 37]
67. (~generous(fred) | quiet(fred)) & (generous(fred) | ~quiet(fred)) [nnf transformation 18]
73. ~generous(X0) | ~wise(X0) [cnf transformation 43]
92. ~patient(fred) | ~happy(fred) | ~quiet(X0) [cnf transformation 51]
101. happy(X0) | wise(X0) | happy(X0) | ~patient(X0) [cnf transformation 52]
118. generous(fred) | ~quiet(fred) [cnf transformation 67]
125. patient(fred) [cnf transformation 28]
126. quiet(fred) [cnf transformation 24]
129. ~patient(X0) | wise(X0) | happy(X0) [duplicate literal removal 101]
164. 8 <=> happy(fred) [avatar definition]
168. 9 <=> patient(fred) [avatar definition]
170. patient(fred) <- (9) [avatar component clause 168]
173. 10 <=> ! [X0] : ~quiet(X0) [avatar definition]
174. ~quiet(X0) <- (10) [avatar component clause 173]
177. 10 | ~8 | ~9 [avatar split clause 92,168,164,173]
234. 23 <=> quiet(fred) [avatar definition]
236. quiet(fred) <- (23) [avatar component clause 234]
238. 24 <=> generous(fred) [avatar definition]
239. generous(fred) <- (24) [avatar component clause 238]
242. ~23 | 24 [avatar split clause 118,238,234]
263. 9 [avatar split clause 125,168]
264. 23 [avatar split clause 126,234]
268. ~wise(fred) <- (24) [resolution 73,239]
300. wise(fred) | happy(fred) <- (9) [resolution 129,170]
303. happy(fred) <- (9, 24) [subsumption resolution 300,268]
307. 8 | ~9 | ~24 [avatar split clause 303,238,168,164]
320. $false <- (10, 23) [resolution 174,236]
321. ~10 | ~23 [avatar contradiction clause 320]
322. $false [avatar sat refutation 177,242,263,264,307,321]
% SZS output end Proof for 7653092077207506636123547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is humble. If john is either creative or not wise then mary is calm or not curious and vice versa. If someone is not kind or not rich then susan is both not happy and not generous. Everyone who is calm is both not happy and humble. Everyone who is tall is brave or not curious and vice versa. If someone is either strong or not patient then someone is either kind or not quiet and vice versa. If john is not creative or not curious then mary is both not funny and not strong and vice versa. If someone is not old then someone is not rich. If someone is not creative then paul is both not humble and not strong and vice versa. If john is either patient or old then someone is not humble or funny and vice versa. If someone is either not kind or creative then fred is either funny or not humble. Everyone who is not old or not strong is not humble or rich. If john is wise or creative then lucy is strong or not curious. If mary is kind then lucy is either not funny or not generous. If someone is both not funny and not curious then someone is either not strong or not brave. Someone is not old. Mary is quiet or not calm. Fred is either not happy or creative. Susan is not funny. Mary is funny. Lucy is curious or not strong. Someone is both quiet and curious. Someone is either curious or not humble. | John is creative. | entailment | (![X]:(calm(X)=>humble(X)))&
(((creative(john)<~>~wise(john)))<=>((calm(mary)|~curious(mary))))&
((?[X]:((~kind(X)|~rich(X))))=>((~happy(susan)&~generous(susan))))&
(![X]:(calm(X)=>(~happy(X)&humble(X))))&
(![X]:(tall(X)<=>(brave(X)|~curious(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(((~creative(john)|~curious(john)))<=>((~funny(mary)&~strong(mary))))&
((?[X]:(~old(X)))=>(?[X]:(~rich(X))))&
((?[X]:(~creative(X)))<=>((~humble(paul)&~strong(paul))))&
(((patient(john)<~>old(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
((?[X]:((~kind(X)<~>creative(X))))=>((funny(fred)<~>~humble(fred))))&
(![X]:((~old(X)|~strong(X))=>(~humble(X)|rich(X))))&
(((wise(john)|creative(john)))=>((strong(lucy)|~curious(lucy))))&
((kind(mary))=>((~funny(lucy)<~>~generous(lucy))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:((~strong(X)<~>~brave(X)))))&
(?[X]:(~old(X)))&
((quiet(mary)|~calm(mary)))&
((~happy(fred)<~>creative(fred)))&
(~funny(susan))&
(funny(mary))&
((curious(lucy)|~strong(lucy)))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((curious(X)<~>~humble(X)))) | creative(john) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8195045546601909026253608
% SZS output start Proof for 8195045546601909026253608
7. (~curious(john) | ~creative(john)) <=> (~strong(mary) & ~funny(mary)) [input p6]
20. funny(mary) [input p19]
24. ~creative(john) [input hypothesis]
46. ((~curious(john) | ~creative(john)) | (strong(mary) | funny(mary))) & ((~strong(mary) & ~funny(mary)) | (curious(john) & creative(john))) [nnf transformation 7]
47. (~curious(john) | ~creative(john) | strong(mary) | funny(mary)) & ((~strong(mary) & ~funny(mary)) | (curious(john) & creative(john))) [flattening 46]
95. ~funny(mary) | creative(john) [cnf transformation 47]
127. funny(mary) [cnf transformation 20]
133. ~creative(john) [cnf transformation 24]
139. 2 <=> creative(john) [avatar definition]
211. 17 <=> funny(mary) [avatar definition]
226. 2 | ~17 [avatar split clause 95,211,139]
351. 17 [avatar split clause 127,211]
363. ~2 [avatar split clause 133,139]
364. $false [avatar sat refutation 226,351,363]
% SZS output end Proof for 8195045546601909026253608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both not brave and rich and vice versa.
If lucy is both creative and not creative then someone is not wise or quiet and vice versa.
If susan is both not happy and not curious then susan is both wise and funny and vice versa.
If someone is both not quiet and not old then someone is old or generous and vice versa.
Everyone who is both not patient and not calm is calm or not creative.
If someone is either strong or funny then someone is happy or not old and vice versa.
Everyone who is not creative is both calm and not rich.
Everyone who is kind or not funny is either creative or not quiet.
If someone is creative or kind then alice is either not humble or old.
Everyone who is not humble is tall.
If someone is either humble or not creative then someone is both not rich and funny and vice versa.
If fred is both old and happy then someone is either not funny or not strong and vice versa.
Everyone who is not funny is not generous and vice versa.
If fred is either not wise or patient then lucy is either not kind or old and vice versa.
If fred is humble then someone is not kind or not rich.
Everyone who is both calm and not tall is not humble or generous and vice versa.
Alice is either humble or rich.
Someone is calm or generous.
Someone is either not patient or tall.
Mary is either quiet or not happy. | Lucy is creative. | contradiction | (![X]:(~tall(X)<=>(~brave(X)&rich(X))))&
(((creative(lucy)&~creative(lucy)))<=>(?[X]:((~wise(X)|quiet(X)))))&
(((~happy(susan)&~curious(susan)))<=>((wise(susan)&funny(susan))))&
((?[X]:((~quiet(X)&~old(X))))<=>(?[X]:((old(X)|generous(X)))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~creative(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:(~creative(X)=>(calm(X)&~rich(X))))&
(![X]:((kind(X)|~funny(X))=>(creative(X)<~>~quiet(X))))&
((?[X]:((creative(X)|kind(X))))=>((~humble(alice)<~>old(alice))))&
(![X]:(~humble(X)=>tall(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
(((old(fred)&happy(fred)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~funny(X)<=>~generous(X)))&
(((~wise(fred)<~>patient(fred)))<=>((~kind(lucy)<~>old(lucy))))&
((humble(fred))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((calm(X)&~tall(X))<=>(~humble(X)|generous(X))))&
((humble(alice)<~>rich(alice)))&
(?[X]:((calm(X)|generous(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((quiet(mary)<~>~happy(mary))) | creative(lucy) | [
"p0",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 663095858864691723888318
% SZS output start Proof for 663095858864691723888318
1. ! [X0] : (~tall(X0) <=> (rich(X0) & ~brave(X0))) [input p0]
10. ! [X0] : (~humble(X0) => tall(X0)) [input p9]
11. ? [X0] : (humble(X0) <~> ~creative(X0)) <=> ? [X0] : (funny(X0) & ~rich(X0)) [input p10]
13. ! [X0] : (~funny(X0) <=> ~generous(X0)) [input p12]
16. ! [X0] : ((~tall(X0) & calm(X0)) <=> (generous(X0) | ~humble(X0))) [input p15]
21. creative(lucy) [input hypothesis]
24. ? [X0] : (humble(X0) <~> ~creative(X0)) <=> ? [X1] : (funny(X1) & ~rich(X1)) [rectify 11]
30. ! [X0] : (tall(X0) | humble(X0)) [ennf transformation 10]
32. ! [X0] : ((~tall(X0) | (~rich(X0) | brave(X0))) & ((rich(X0) & ~brave(X0)) | tall(X0))) [nnf transformation 1]
33. ! [X0] : ((~tall(X0) | ~rich(X0) | brave(X0)) & ((rich(X0) & ~brave(X0)) | tall(X0))) [flattening 32]
53. (? [X0] : ((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | ! [X1] : (~funny(X1) | rich(X1))) & (? [X1] : (funny(X1) & ~rich(X1)) | ! [X0] : ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) [nnf transformation 24]
54. (? [X0] : ((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | ! [X1] : (~funny(X1) | rich(X1))) & (? [X2] : (funny(X2) & ~rich(X2)) | ! [X3] : ((humble(X3) | creative(X3)) & (~creative(X3) | ~humble(X3)))) [rectify 53]
55. ? [X0] : ((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) => ((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) [choice axiom]
56. ? [X2] : (funny(X2) & ~rich(X2)) => (funny(sK6) & ~rich(sK6)) [choice axiom]
57. (((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) | ! [X1] : (~funny(X1) | rich(X1))) & ((funny(sK6) & ~rich(sK6)) | ! [X3] : ((humble(X3) | creative(X3)) & (~creative(X3) | ~humble(X3)))) [skolemisation 54,56,55]
63. ! [X0] : ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0))) [nnf transformation 13]
67. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 16]
68. ! [X0] : (((~tall(X0) & calm(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | tall(X0) | ~calm(X0))) [flattening 67]
77. rich(X0) | tall(X0) [cnf transformation 33]
110. humble(X0) | tall(X0) [cnf transformation 30]
111. ~rich(sK6) | ~creative(X3) | ~humble(X3) [cnf transformation 57]
113. funny(sK6) | ~creative(X3) | ~humble(X3) [cnf transformation 57]
124. ~funny(X0) | generous(X0) [cnf transformation 63]
137. ~tall(X0) | humble(X0) [cnf transformation 68]
138. ~generous(X0) | ~tall(X0) [cnf transformation 68]
146. creative(lucy) [cnf transformation 21]
152. 2 <=> creative(lucy) [avatar definition]
153. creative(lucy) <- (2) [avatar component clause 152]
259. 26 <=> ! [X0] : ~creative(X0) [avatar definition]
260. ~creative(X0) <- (26) [avatar component clause 259]
281. 31 <=> funny(sK6) [avatar definition]
283. funny(sK6) <- (31) [avatar component clause 281]
286. 32 <=> ! [X3] : (~creative(X3) | ~humble(X3)) [avatar definition]
287. ~creative(X3) | ~humble(X3) <- (32) [avatar component clause 286]
288. 32 | 31 [avatar split clause 113,281,286]
290. 33 <=> rich(sK6) [avatar definition]
292. ~rich(sK6) <- (~33) [avatar component clause 290]
294. 32 | ~33 [avatar split clause 111,290,286]
354. humble(X0) [subsumption resolution 137,110]
378. 2 [avatar split clause 146,152]
387. tall(sK6) <- (~33) [resolution 77,292]
391. generous(sK6) <- (31) [resolution 124,283]
394. ~tall(sK6) <- (31) [resolution 138,391]
395. $false <- (31, ~33) [subsumption resolution 394,387]
396. ~31 | 33 [avatar contradiction clause 395]
397. ~creative(X3) <- (32) [subsumption resolution 287,354]
398. 26 | ~32 [avatar split clause 397,286,259]
399. $false <- (2, 26) [resolution 260,153]
400. ~2 | ~26 [avatar contradiction clause 399]
401. $false [avatar sat refutation 288,294,378,396,398,400]
% SZS output end Proof for 663095858864691723888318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not happy or not quiet is both patient and not wise and vice versa.
Everyone who is not funny or not generous is funny or not old and vice versa.
If mary is not curious then someone is not creative or rich and vice versa.
If susan is wise then someone is rich.
Everyone who is calm is either curious or humble.
Everyone who is not generous or not kind is not calm or creative and vice versa.
If alice is not rich or old then someone is happy or not humble.
If someone is not patient then someone is either curious or not patient and vice versa.
Everyone who is both not strong and funny is calm or not creative and vice versa.
Everyone who is either not old or quiet is generous.
Everyone who is not old or quiet is old.
Everyone who is kind is either generous or not strong and vice versa.
Everyone who is both not quiet and not kind is not kind or old.
Everyone who is either old or not calm is wise or not humble.
Everyone who is not happy or kind is not brave or quiet and vice versa.
Alice is rich.
Fred is either not tall or generous.
Someone is not curious or not rich.
Mary is happy or kind. | Susan is patient. | entailment | (![X]:((~happy(X)|~quiet(X))<=>(patient(X)&~wise(X))))&
(![X]:((~funny(X)|~generous(X))<=>(funny(X)|~old(X))))&
((~curious(mary))<=>(?[X]:((~creative(X)|rich(X)))))&
((wise(susan))=>(?[X]:(rich(X))))&
(![X]:(calm(X)=>(curious(X)<~>humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>(~calm(X)|creative(X))))&
(((~rich(alice)|old(alice)))=>(?[X]:((happy(X)|~humble(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((~strong(X)&funny(X))<=>(calm(X)|~creative(X))))&
(![X]:((~old(X)<~>quiet(X))=>generous(X)))&
(![X]:((~old(X)|quiet(X))=>old(X)))&
(![X]:(kind(X)<=>(generous(X)<~>~strong(X))))&
(![X]:((~quiet(X)&~kind(X))=>(~kind(X)|old(X))))&
(![X]:((old(X)<~>~calm(X))=>(wise(X)|~humble(X))))&
(![X]:((~happy(X)|kind(X))<=>(~brave(X)|quiet(X))))&
(rich(alice))&
((~tall(fred)<~>generous(fred)))&
(?[X]:((~curious(X)|~rich(X))))&
((happy(mary)|kind(mary))) | patient(susan) | [
"p0",
"p1",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7484093127553156019158194
% SZS output start Proof for 7484093127553156019158194
1. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~wise(X0) & patient(X0))) [input p0]
2. ! [X0] : ((~generous(X0) | ~funny(X0)) <=> (~old(X0) | funny(X0))) [input p1]
10. ! [X0] : ((~old(X0) <~> quiet(X0)) => generous(X0)) [input p9]
11. ! [X0] : ((quiet(X0) | ~old(X0)) => old(X0)) [input p10]
20. ~patient(susan) [input hypothesis]
25. ! [X0] : (generous(X0) | (~old(X0) <=> quiet(X0))) [ennf transformation 10]
26. ! [X0] : (old(X0) | (~quiet(X0) & old(X0))) [ennf transformation 11]
31. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (wise(X0) | ~patient(X0))) & ((~wise(X0) & patient(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 1]
32. ! [X0] : ((~quiet(X0) | ~happy(X0) | wise(X0) | ~patient(X0)) & ((~wise(X0) & patient(X0)) | (quiet(X0) & happy(X0)))) [flattening 31]
33. ! [X0] : (((~generous(X0) | ~funny(X0)) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | (generous(X0) & funny(X0)))) [nnf transformation 2]
34. ! [X0] : ((~generous(X0) | ~funny(X0) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | (generous(X0) & funny(X0)))) [flattening 33]
53. ! [X0] : (generous(X0) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) [nnf transformation 25]
62. patient(X0) | quiet(X0) [cnf transformation 32]
66. ~old(X0) | funny(X0) | funny(X0) [cnf transformation 34]
68. ~generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 34]
92. ~old(X0) | generous(X0) | ~quiet(X0) [cnf transformation 53]
93. old(X0) | old(X0) [cnf transformation 26]
111. ~patient(susan) [cnf transformation 20]
112. old(X0) [duplicate literal removal 93]
113. ~old(X0) | funny(X0) [duplicate literal removal 66]
114. ~generous(X0) | ~funny(X0) [duplicate literal removal 68]
223. quiet(susan) [resolution 62,111]
230. funny(X0) [resolution 113,112]
236. ~quiet(X1) | generous(X1) [resolution 92,112]
238. generous(susan) [resolution 236,223]
242. ~funny(susan) [resolution 238,114]
243. $false [subsumption resolution 242,230]
% SZS output end Proof for 7484093127553156019158194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both kind and not strong then alice is not generous.
Everyone who is generous or old is either funny or not patient.
If alice is not kind then someone is calm or not tall and vice versa.
If someone is either not generous or happy then john is either creative or quiet.
Everyone who is either humble or quiet is funny.
Everyone who is both old and happy is humble or not strong and vice versa.
Everyone who is rich is either not humble or not tall.
If susan is strong then someone is calm.
If mary is calm or not generous then someone is both not rich and tall.
If john is both curious and not generous then someone is not happy or kind.
If fred is rich then someone is both not generous and not happy.
Everyone who is not strong is both not patient and not generous and vice versa.
If someone is not wise then alice is not happy and vice versa.
Everyone who is both funny and not happy is both old and happy and vice versa.
Everyone who is brave is not happy.
Everyone who is happy is either wise or rich.
Paul is both not kind and tall.
Someone is either not generous or quiet.
Mary is both not generous and not quiet.
Someone is either old or not humble.
John is either not creative or happy.
Susan is either not rich or not kind. | Paul is not humble. | entailment | (((kind(john)&~strong(john)))=>(~generous(alice)))&
(![X]:((generous(X)|old(X))=>(funny(X)<~>~patient(X))))&
((~kind(alice))<=>(?[X]:((calm(X)|~tall(X)))))&
((?[X]:((~generous(X)<~>happy(X))))=>((creative(john)<~>quiet(john))))&
(![X]:((humble(X)<~>quiet(X))=>funny(X)))&
(![X]:((old(X)&happy(X))<=>(humble(X)|~strong(X))))&
(![X]:(rich(X)=>(~humble(X)<~>~tall(X))))&
((strong(susan))=>(?[X]:(calm(X))))&
(((calm(mary)|~generous(mary)))=>(?[X]:((~rich(X)&tall(X)))))&
(((curious(john)&~generous(john)))=>(?[X]:((~happy(X)|kind(X)))))&
((rich(fred))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(~strong(X)<=>(~patient(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~happy(alice)))&
(![X]:((funny(X)&~happy(X))<=>(old(X)&happy(X))))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(happy(X)=>(wise(X)<~>rich(X))))&
((~kind(paul)&tall(paul)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~generous(mary)&~quiet(mary)))&
(?[X]:((old(X)<~>~humble(X))))&
((~creative(john)<~>happy(john)))&
((~rich(susan)<~>~kind(susan))) | ~humble(paul) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3127014844231616118137475
% SZS output start Proof for 3127014844231616118137475
6. ! [X0] : ((happy(X0) & old(X0)) <=> (~strong(X0) | humble(X0))) [input p5]
14. ! [X0] : ((~happy(X0) & funny(X0)) <=> (happy(X0) & old(X0))) [input p13]
23. humble(paul) [input hypothesis]
43. ! [X0] : (((happy(X0) & old(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 6]
44. ! [X0] : (((happy(X0) & old(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~happy(X0) | ~old(X0))) [flattening 43]
58. ! [X0] : (((~happy(X0) & funny(X0)) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 14]
59. ! [X0] : (((~happy(X0) & funny(X0)) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | happy(X0) | ~funny(X0))) [flattening 58]
84. ~humble(X0) | old(X0) [cnf transformation 44]
86. ~humble(X0) | happy(X0) [cnf transformation 44]
105. ~happy(X0) | ~happy(X0) | ~old(X0) [cnf transformation 59]
120. humble(paul) [cnf transformation 23]
122. ~happy(X0) | ~old(X0) [duplicate literal removal 105]
267. old(paul) [resolution 84,120]
269. happy(paul) [resolution 86,120]
275. ~old(paul) [resolution 122,269]
277. $false [subsumption resolution 275,267]
% SZS output end Proof for 3127014844231616118137475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not old is both not strong and not patient. Everyone who is both not tall and not strong is both tall and not kind and vice versa. If someone is both not funny and old then paul is both tall and kind. Everyone who is both not rich and creative is curious and vice versa. Everyone who is strong or not kind is both strong and generous and vice versa. If someone is either not humble or not creative then someone is either not curious or not quiet. If someone is both not funny and not quiet then lucy is patient and vice versa. If someone is strong or tall then lucy is both tall and humble. If someone is both not wise and not patient then lucy is both creative and not old. Everyone who is either old or not rich is not quiet or funny and vice versa. Everyone who is brave or calm is funny. If someone is old or happy then fred is both rich and not generous. Everyone who is either not happy or not brave is not humble or wise and vice versa. Everyone who is strong is not patient. If alice is either generous or not strong then someone is not calm. If someone is either creative or not kind then mary is both wise and calm. Someone is either rich or calm. Someone is both not quiet and calm. John is funny. Alice is funny. Someone is either old or generous. John is not calm or wise. Someone is generous or not happy. Susan is both not rich and not brave. | Lucy is kind. | entailment | (![X]:((funny(X)&~old(X))=>(~strong(X)&~patient(X))))&
(![X]:((~tall(X)&~strong(X))<=>(tall(X)&~kind(X))))&
((?[X]:((~funny(X)&old(X))))=>((tall(paul)&kind(paul))))&
(![X]:((~rich(X)&creative(X))<=>curious(X)))&
(![X]:((strong(X)|~kind(X))<=>(strong(X)&generous(X))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(patient(lucy)))&
((?[X]:((strong(X)|tall(X))))=>((tall(lucy)&humble(lucy))))&
((?[X]:((~wise(X)&~patient(X))))=>((creative(lucy)&~old(lucy))))&
(![X]:((old(X)<~>~rich(X))<=>(~quiet(X)|funny(X))))&
(![X]:((brave(X)|calm(X))=>funny(X)))&
((?[X]:((old(X)|happy(X))))=>((rich(fred)&~generous(fred))))&
(![X]:((~happy(X)<~>~brave(X))<=>(~humble(X)|wise(X))))&
(![X]:(strong(X)=>~patient(X)))&
(((generous(alice)<~>~strong(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((creative(X)<~>~kind(X))))=>((wise(mary)&calm(mary))))&
(?[X]:((rich(X)<~>calm(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(funny(john))&
(funny(alice))&
(?[X]:((old(X)<~>generous(X))))&
((~calm(john)|wise(john)))&
(?[X]:((generous(X)|~happy(X))))&
((~rich(susan)&~brave(susan))) | kind(lucy) | [
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3504489439128251917944826
% SZS output start Proof for 3504489439128251917944826
2. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (~kind(X0) & tall(X0))) [input p1]
5. ! [X0] : ((~kind(X0) | strong(X0)) <=> (generous(X0) & strong(X0))) [input p4]
8. ? [X0] : (tall(X0) | strong(X0)) => (humble(lucy) & tall(lucy)) [input p7]
25. ~kind(lucy) [input hypothesis]
31. (humble(lucy) & tall(lucy)) | ! [X0] : (~tall(X0) & ~strong(X0)) [ennf transformation 8]
38. ! [X0] : (((~strong(X0) & ~tall(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (strong(X0) | tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((~strong(X0) & ~tall(X0)) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | strong(X0) | tall(X0))) [flattening 38]
42. ! [X0] : (((~kind(X0) | strong(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (kind(X0) & ~strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((~kind(X0) | strong(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (kind(X0) & ~strong(X0)))) [flattening 42]
74. ~tall(X0) | kind(X0) | ~tall(X0) [cnf transformation 39]
82. kind(X0) | strong(X0) [cnf transformation 43]
93. tall(lucy) | ~strong(X0) [cnf transformation 31]
136. ~kind(lucy) [cnf transformation 25]
138. ~tall(X0) | kind(X0) [duplicate literal removal 74]
197. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
198. ~strong(X0) <- (14) [avatar component clause 197]
201. 15 <=> tall(lucy) [avatar definition]
203. tall(lucy) <- (15) [avatar component clause 201]
205. 14 | 15 [avatar split clause 93,201,197]
315. strong(lucy) [resolution 82,136]
316. $false <- (14) [subsumption resolution 315,198]
317. ~14 [avatar contradiction clause 316]
326. kind(lucy) <- (15) [resolution 138,203]
328. $false <- (15) [subsumption resolution 326,136]
329. ~15 [avatar contradiction clause 328]
330. $false [avatar sat refutation 205,317,329]
% SZS output end Proof for 3504489439128251917944826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not humble is not creative.
Everyone who is not patient or not old is brave.
If mary is calm then someone is both not humble and not kind.
Everyone who is not humble or humble is either not brave or not calm.
Everyone who is not quiet is both funny and not kind and vice versa.
Everyone who is creative or old is either not kind or patient and vice versa.
If someone is wise or not generous then alice is kind or not quiet and vice versa.
Everyone who is not funny is humble and vice versa.
If someone is old or not funny then someone is not old and vice versa.
If someone is both not kind and wise then someone is either brave or not rich.
Everyone who is not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Someone is either creative or not kind.
Lucy is humble or not curious.
Someone is both not rich and not curious.
Alice is patient or not kind.
Someone is strong.
Someone is either not happy or quiet.
Someone is not curious.
Paul is quiet or not happy. | Mary is brave. | entailment | (![X]:((funny(X)&~humble(X))=>~creative(X)))&
(![X]:((~patient(X)|~old(X))=>brave(X)))&
((calm(mary))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((~humble(X)|humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:(~quiet(X)<=>(funny(X)&~kind(X))))&
(![X]:((creative(X)|old(X))<=>(~kind(X)<~>patient(X))))&
((?[X]:((wise(X)|~generous(X))))<=>((kind(alice)|~quiet(alice))))&
(![X]:(~funny(X)<=>humble(X)))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(?[X]:((creative(X)<~>~kind(X))))&
((humble(lucy)|~curious(lucy)))&
(?[X]:((~rich(X)&~curious(X))))&
((patient(alice)|~kind(alice)))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:(~curious(X)))&
((quiet(paul)|~happy(paul))) | brave(mary) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3493083914648153300620354
% SZS output start Proof for 3493083914648153300620354
2. ! [X0] : ((~old(X0) | ~patient(X0)) => brave(X0)) [input p1]
3. calm(mary) => ? [X0] : (~kind(X0) & ~humble(X0)) [input p2]
4. ! [X0] : ((humble(X0) | ~humble(X0)) => (~brave(X0) <~> ~calm(X0))) [input p3]
5. ! [X0] : (~quiet(X0) <=> (~kind(X0) & funny(X0))) [input p4]
6. ! [X0] : ((old(X0) | creative(X0)) <=> (~kind(X0) <~> patient(X0))) [input p5]
8. ! [X0] : (~funny(X0) <=> humble(X0)) [input p7]
11. ! [X0] : (~quiet(X0) => (curious(X0) & ~brave(X0))) [input p10]
24. ~brave(mary) [input hypothesis]
32. ! [X0] : (brave(X0) | (old(X0) & patient(X0))) [ennf transformation 2]
33. ? [X0] : (~kind(X0) & ~humble(X0)) | ~calm(mary) [ennf transformation 3]
34. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 4]
36. ! [X0] : ((curious(X0) & ~brave(X0)) | quiet(X0)) [ennf transformation 11]
38. ? [X0] : (~kind(X0) & ~humble(X0)) => (~kind(sK0) & ~humble(sK0)) [choice axiom]
39. (~kind(sK0) & ~humble(sK0)) | ~calm(mary) [skolemisation 33,38]
40. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~humble(X0) & humble(X0))) [nnf transformation 34]
41. ! [X0] : ((~quiet(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | quiet(X0))) [nnf transformation 5]
42. ! [X0] : ((~quiet(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | quiet(X0))) [flattening 41]
43. ! [X0] : (((old(X0) | creative(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~old(X0) & ~creative(X0)))) [nnf transformation 6]
44. ! [X0] : ((old(X0) | creative(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~old(X0) & ~creative(X0)))) [flattening 43]
50. ! [X0] : ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0))) [nnf transformation 8]
87. brave(X0) | patient(X0) [cnf transformation 32]
88. brave(X0) | old(X0) [cnf transformation 32]
89. ~humble(sK0) | ~calm(mary) [cnf transformation 39]
90. ~kind(sK0) | ~calm(mary) [cnf transformation 39]
93. calm(X0) | brave(X0) | humble(X0) [cnf transformation 40]
94. ~humble(X0) | brave(X0) | calm(X0) [cnf transformation 40]
97. ~quiet(X0) | kind(X0) | ~funny(X0) [cnf transformation 42]
101. ~old(X0) | kind(X0) | ~patient(X0) [cnf transformation 44]
108. humble(X0) | funny(X0) [cnf transformation 50]
115. ~brave(X0) | quiet(X0) [cnf transformation 36]
145. ~brave(mary) [cnf transformation 24]
147. 1 <=> calm(mary) [avatar definition]
149. ~calm(mary) <- (~1) [avatar component clause 147]
151. 2 <=> kind(sK0) [avatar definition]
153. ~kind(sK0) <- (~2) [avatar component clause 151]
154. ~1 | ~2 [avatar split clause 90,151,147]
156. 3 <=> humble(sK0) [avatar definition]
158. ~humble(sK0) <- (~3) [avatar component clause 156]
159. ~1 | ~3 [avatar split clause 89,156,147]
160. calm(X0) | brave(X0) [subsumption resolution 93,94]
407. quiet(X0) | old(X0) [resolution 115,88]
408. quiet(X1) | patient(X1) [resolution 115,87]
413. brave(mary) <- (~1) [resolution 160,149]
415. $false <- (~1) [subsumption resolution 413,145]
416. 1 [avatar contradiction clause 415]
417. funny(sK0) <- (~3) [resolution 158,108]
537. 66 <=> old(sK0) [avatar definition]
539. old(sK0) <- (66) [avatar component clause 537]
541. 67 <=> patient(sK0) [avatar definition]
562. kind(sK0) | ~patient(sK0) <- (66) [resolution 539,101]
563. ~patient(sK0) <- (~2, 66) [subsumption resolution 562,153]
564. ~67 | 2 | ~66 [avatar split clause 563,537,151,541]
579. ~funny(X0) | kind(X0) | old(X0) [resolution 407,97]
581. ~funny(X0) | kind(X0) | patient(X0) [resolution 408,97]
598. kind(sK0) | old(sK0) <- (~3) [resolution 579,417]
605. kind(sK0) | patient(sK0) <- (~3) [resolution 581,417]
608. patient(sK0) <- (~2, ~3) [subsumption resolution 605,153]
611. old(sK0) <- (~2, ~3) [subsumption resolution 598,153]
612. 66 | 2 | 3 [avatar split clause 611,156,151,537]
613. 67 | 2 | 3 [avatar split clause 608,156,151,541]
614. $false [avatar sat refutation 154,159,416,564,612,613]
% SZS output end Proof for 3493083914648153300620354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then paul is funny or not strong. If paul is generous or kind then someone is wise and vice versa. Everyone who is either generous or not happy is not strong and vice versa. If alice is funny then mary is not humble or brave. Everyone who is either not tall or not humble is both not old and not tall. Everyone who is both curious and wise is not strong or rich. Everyone who is humble is happy. If someone is either wise or not old then someone is both generous and not tall and vice versa. Everyone who is calm or not quiet is not old and vice versa. If paul is brave or generous then someone is either calm or not patient and vice versa. If someone is either not old or not strong then someone is both generous and kind. Everyone who is either not quiet or not tall is happy or rich. Everyone who is both wise and not calm is quiet or not wise and vice versa. Everyone who is not humble is either generous or not kind and vice versa. If someone is not patient or not curious then paul is calm or creative and vice versa. Everyone who is both funny and not humble is both happy and not tall and vice versa. Someone is wise or brave. Someone is both not creative and kind. Someone is both wise and not funny. Lucy is both not funny and patient. Someone is patient. Someone is either not kind or tall. Someone is not generous. | Lucy is humble. | neutral | ((~old(alice))=>((funny(paul)|~strong(paul))))&
(((generous(paul)|kind(paul)))<=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~strong(X)))&
((funny(alice))=>((~humble(mary)|brave(mary))))&
(![X]:((~tall(X)<~>~humble(X))=>(~old(X)&~tall(X))))&
(![X]:((curious(X)&wise(X))=>(~strong(X)|rich(X))))&
(![X]:(humble(X)=>happy(X)))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((calm(X)|~quiet(X))<=>~old(X)))&
(((brave(paul)|generous(paul)))<=>(?[X]:((calm(X)<~>~patient(X)))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((~quiet(X)<~>~tall(X))=>(happy(X)|rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(quiet(X)|~wise(X))))&
(![X]:(~humble(X)<=>(generous(X)<~>~kind(X))))&
((?[X]:((~patient(X)|~curious(X))))<=>((calm(paul)|creative(paul))))&
(![X]:((funny(X)&~humble(X))<=>(happy(X)&~tall(X))))&
(?[X]:((wise(X)|brave(X))))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((wise(X)&~funny(X))))&
((~funny(lucy)&patient(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:(~generous(X))) | humble(lucy) | [] | null | 0 |
If someone is both not tall and not patient then someone is not rich.
Everyone who is either kind or rich is old and vice versa.
If john is kind then susan is both not patient and creative and vice versa.
If someone is not happy or not generous then mary is both old and creative and vice versa.
Everyone who is old is both wise and old and vice versa.
If lucy is either not brave or tall then paul is both wise and not generous.
If fred is humble or generous then mary is tall and vice versa.
Everyone who is either brave or not patient is either not rich or not calm and vice versa.
Everyone who is either strong or not patient is either not happy or not patient and vice versa.
Everyone who is generous is humble and vice versa.
If mary is creative or not kind then susan is both curious and not brave.
If mary is both kind and quiet then someone is either not kind or funny.
Everyone who is both not kind and happy is kind or quiet and vice versa.
If john is both kind and not curious then paul is generous.
If alice is not patient then john is generous.
Everyone who is both rich and humble is not funny.
Someone is either not strong or not wise.
Paul is quiet.
Someone is both not wise and humble.
Someone is rich or patient.
Someone is both patient and rich.
Mary is strong.
Paul is both not humble and old.
Someone is wise. | Alice is kind. | contradiction | ((?[X]:((~tall(X)&~patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((kind(X)<~>rich(X))<=>old(X)))&
((kind(john))<=>((~patient(susan)&creative(susan))))&
((?[X]:((~happy(X)|~generous(X))))<=>((old(mary)&creative(mary))))&
(![X]:(old(X)<=>(wise(X)&old(X))))&
(((~brave(lucy)<~>tall(lucy)))=>((wise(paul)&~generous(paul))))&
(((humble(fred)|generous(fred)))<=>(tall(mary)))&
(![X]:((brave(X)<~>~patient(X))<=>(~rich(X)<~>~calm(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(~happy(X)<~>~patient(X))))&
(![X]:(generous(X)<=>humble(X)))&
(((creative(mary)|~kind(mary)))=>((curious(susan)&~brave(susan))))&
(((kind(mary)&quiet(mary)))=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:((~kind(X)&happy(X))<=>(kind(X)|quiet(X))))&
(((kind(john)&~curious(john)))=>(generous(paul)))&
((~patient(alice))=>(generous(john)))&
(![X]:((rich(X)&humble(X))=>~funny(X)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(quiet(paul))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((patient(X)&rich(X))))&
(strong(mary))&
((~humble(paul)&old(paul)))&
(?[X]:(wise(X))) | kind(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 832406841321827944196327
% SZS output start Proof for 832406841321827944196327
13. ! [X0] : ((happy(X0) & ~kind(X0)) <=> (quiet(X0) | kind(X0))) [input p12]
25. kind(alice) [input hypothesis]
59. ! [X0] : (((happy(X0) & ~kind(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (~happy(X0) | kind(X0)))) [nnf transformation 13]
60. ! [X0] : (((happy(X0) & ~kind(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | ~happy(X0) | kind(X0))) [flattening 59]
118. ~kind(X0) | ~kind(X0) [cnf transformation 60]
136. kind(alice) [cnf transformation 25]
138. ~kind(X0) [duplicate literal removal 118]
283. $false [subsumption resolution 136,138]
% SZS output end Proof for 832406841321827944196327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and calm then someone is funny or brave and vice versa.
If someone is both not old and not wise then someone is not humble and vice versa.
Everyone who is either not wise or not patient is old.
Everyone who is patient is kind and vice versa.
Everyone who is both not old and kind is happy or quiet and vice versa.
If lucy is either humble or not tall then john is either not humble or not curious.
Everyone who is both creative and not calm is strong.
If someone is generous or tall then someone is patient or not generous.
Everyone who is either happy or brave is not calm or generous and vice versa.
Everyone who is both not kind and not generous is humble or not calm.
If mary is both not brave and quiet then john is not kind.
Everyone who is not rich is not brave or not wise and vice versa.
If mary is either not generous or not patient then someone is both quiet and not rich and vice versa.
Everyone who is happy or patient is humble or not funny and vice versa.
If someone is not tall or creative then someone is either brave or not old and vice versa.
Everyone who is curious is kind and vice versa.
Someone is not rich or not funny.
Someone is strong or not tall.
Someone is both not calm and not creative.
Lucy is wise or kind.
Someone is either not wise or not tall.
Alice is either not kind or patient.
Someone is either humble or calm.
Mary is both not old and generous. | Mary is patient. | neutral | ((?[X]:((wise(X)&calm(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)<~>~patient(X))=>old(X)))&
(![X]:(patient(X)<=>kind(X)))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|quiet(X))))&
(((humble(lucy)<~>~tall(lucy)))=>((~humble(john)<~>~curious(john))))&
(![X]:((creative(X)&~calm(X))=>strong(X)))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~calm(X)|generous(X))))&
(![X]:((~kind(X)&~generous(X))=>(humble(X)|~calm(X))))&
(((~brave(mary)&quiet(mary)))=>(~kind(john)))&
(![X]:(~rich(X)<=>(~brave(X)|~wise(X))))&
(((~generous(mary)<~>~patient(mary)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)|~funny(X))))&
((?[X]:((~tall(X)|creative(X))))<=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(curious(X)<=>kind(X)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~calm(X)&~creative(X))))&
((wise(lucy)|kind(lucy)))&
(?[X]:((~wise(X)<~>~tall(X))))&
((~kind(alice)<~>patient(alice)))&
(?[X]:((humble(X)<~>calm(X))))&
((~old(mary)&generous(mary))) | patient(mary) | [] | null | 0 |
Everyone who is either not calm or not funny is either calm or not rich.
Everyone who is not calm or not funny is both curious and tall and vice versa.
Everyone who is both brave and funny is both not happy and not tall.
Everyone who is both not creative and not tall is both not patient and wise.
Everyone who is humble or not generous is either brave or rich and vice versa.
If mary is both not brave and not tall then lucy is either brave or not quiet and vice versa.
If fred is funny or calm then susan is not brave or not curious and vice versa.
If john is tall then susan is not happy and vice versa.
Everyone who is either not creative or curious is quiet or not tall and vice versa.
Everyone who is both not curious and wise is wise.
If someone is either not quiet or wise then someone is either tall or patient.
Everyone who is either not calm or strong is patient.
Everyone who is either creative or patient is strong or not quiet and vice versa.
Everyone who is not brave is wise.
If someone is rich then john is not curious or not patient.
If mary is tall or not patient then mary is not rich.
John is both not quiet and funny.
John is not quiet or not humble.
John is either kind or wise.
John is both humble and not brave.
Alice is curious.
Alice is quiet.
Alice is patient or calm.
Lucy is both funny and not humble. | John is not quiet. | entailment | (![X]:((~calm(X)<~>~funny(X))=>(calm(X)<~>~rich(X))))&
(![X]:((~calm(X)|~funny(X))<=>(curious(X)&tall(X))))&
(![X]:((brave(X)&funny(X))=>(~happy(X)&~tall(X))))&
(![X]:((~creative(X)&~tall(X))=>(~patient(X)&wise(X))))&
(![X]:((humble(X)|~generous(X))<=>(brave(X)<~>rich(X))))&
(((~brave(mary)&~tall(mary)))<=>((brave(lucy)<~>~quiet(lucy))))&
(((funny(fred)|calm(fred)))<=>((~brave(susan)|~curious(susan))))&
((tall(john))<=>(~happy(susan)))&
(![X]:((~creative(X)<~>curious(X))<=>(quiet(X)|~tall(X))))&
(![X]:((~curious(X)&wise(X))=>wise(X)))&
((?[X]:((~quiet(X)<~>wise(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((~calm(X)<~>strong(X))=>patient(X)))&
(![X]:((creative(X)<~>patient(X))<=>(strong(X)|~quiet(X))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:(rich(X)))=>((~curious(john)|~patient(john))))&
(((tall(mary)|~patient(mary)))=>(~rich(mary)))&
((~quiet(john)&funny(john)))&
((~quiet(john)|~humble(john)))&
((kind(john)<~>wise(john)))&
((humble(john)&~brave(john)))&
(curious(alice))&
(quiet(alice))&
((patient(alice)|calm(alice)))&
((funny(lucy)&~humble(lucy))) | ~quiet(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3557961632722878219223527
% SZS output start Proof for 3557961632722878219223527
17. funny(john) & ~quiet(john) [input p16]
25. quiet(john) [input hypothesis]
114. ~quiet(john) [cnf transformation 17]
126. quiet(john) [cnf transformation 25]
240. $false [subsumption resolution 126,114]
% SZS output end Proof for 3557961632722878219223527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not creative and humble then someone is funny and vice versa. Everyone who is either not funny or patient is both not kind and not generous. Everyone who is both not funny and creative is humble. Everyone who is not kind is not strong or happy and vice versa. If someone is either not funny or not generous then someone is both rich and patient and vice versa. If fred is happy then someone is both creative and not rich. Everyone who is either not strong or not funny is both funny and kind. If someone is not humble then someone is either brave or curious. If someone is not rich or not calm then paul is not calm or not happy and vice versa. Everyone who is either not kind or strong is both kind and not humble. If someone is both brave and calm then lucy is both old and not kind and vice versa. Everyone who is calm is either not patient or patient and vice versa. Everyone who is kind or not brave is either curious or patient and vice versa. If someone is curious or not strong then someone is either not quiet or not patient. Everyone who is not strong is both not old and not creative and vice versa. Everyone who is either funny or calm is both rich and not quiet and vice versa. Susan is both quiet and humble. Susan is not wise. Someone is either patient or not strong. Someone is not kind. Lucy is both curious and not happy. Fred is either rich or not funny. Someone is both not curious and quiet. Someone is both tall and patient. | Paul is not humble. | entailment | (((~creative(fred)&humble(fred)))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~kind(X)&~generous(X))))&
(![X]:((~funny(X)&creative(X))=>humble(X)))&
(![X]:(~kind(X)<=>(~strong(X)|happy(X))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:((rich(X)&patient(X)))))&
((happy(fred))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~strong(X)<~>~funny(X))=>(funny(X)&kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:((brave(X)<~>curious(X)))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~calm(paul)|~happy(paul))))&
(![X]:((~kind(X)<~>strong(X))=>(kind(X)&~humble(X))))&
((?[X]:((brave(X)&calm(X))))<=>((old(lucy)&~kind(lucy))))&
(![X]:(calm(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((kind(X)|~brave(X))<=>(curious(X)<~>patient(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:(~strong(X)<=>(~old(X)&~creative(X))))&
(![X]:((funny(X)<~>calm(X))<=>(rich(X)&~quiet(X))))&
((quiet(susan)&humble(susan)))&
(~wise(susan))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:(~kind(X)))&
((curious(lucy)&~happy(lucy)))&
((rich(fred)<~>~funny(fred)))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:((tall(X)&patient(X)))) | ~humble(paul) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7046320036645878809785477
% SZS output start Proof for 7046320036645878809785477
1. (humble(fred) & ~creative(fred)) <=> ? [X0] : funny(X0) [input p0]
4. ! [X0] : (~kind(X0) <=> (happy(X0) | ~strong(X0))) [input p3]
6. happy(fred) => ? [X0] : (~rich(X0) & creative(X0)) [input p5]
7. ! [X0] : ((~strong(X0) <~> ~funny(X0)) => (kind(X0) & funny(X0))) [input p6]
9. ? [X0] : (~calm(X0) | ~rich(X0)) <=> (~happy(paul) | ~calm(paul)) [input p8]
10. ! [X0] : ((~kind(X0) <~> strong(X0)) => (~humble(X0) & kind(X0))) [input p9]
12. ! [X0] : (calm(X0) <=> (~patient(X0) <~> patient(X0))) [input p11]
25. humble(paul) [input hypothesis]
34. ? [X0] : (~rich(X0) & creative(X0)) | ~happy(fred) [ennf transformation 6]
35. ! [X0] : ((kind(X0) & funny(X0)) | (~strong(X0) <=> ~funny(X0))) [ennf transformation 7]
37. ! [X0] : ((~humble(X0) & kind(X0)) | (~kind(X0) <=> strong(X0))) [ennf transformation 10]
39. ((humble(fred) & ~creative(fred)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (~humble(fred) | creative(fred))) [nnf transformation 1]
40. ((humble(fred) & ~creative(fred)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ~humble(fred) | creative(fred)) [flattening 39]
41. ((humble(fred) & ~creative(fred)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ~humble(fred) | creative(fred)) [rectify 40]
42. ? [X1] : funny(X1) => funny(sK0) [choice axiom]
43. ((humble(fred) & ~creative(fred)) | ! [X0] : ~funny(X0)) & (funny(sK0) | ~humble(fred) | creative(fred)) [skolemisation 41,42]
45. ! [X0] : ((~kind(X0) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | kind(X0))) [nnf transformation 4]
46. ! [X0] : ((~kind(X0) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | kind(X0))) [flattening 45]
52. ? [X0] : (~rich(X0) & creative(X0)) => (~rich(sK3) & creative(sK3)) [choice axiom]
53. (~rich(sK3) & creative(sK3)) | ~happy(fred) [skolemisation 34,52]
54. ! [X0] : ((kind(X0) & funny(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) [nnf transformation 35]
59. (? [X0] : (~calm(X0) | ~rich(X0)) | (happy(paul) & calm(paul))) & ((~happy(paul) | ~calm(paul)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 9]
60. (? [X0] : (~calm(X0) | ~rich(X0)) | (happy(paul) & calm(paul))) & (~happy(paul) | ~calm(paul) | ! [X0] : (calm(X0) & rich(X0))) [flattening 59]
61. (? [X0] : (~calm(X0) | ~rich(X0)) | (happy(paul) & calm(paul))) & (~happy(paul) | ~calm(paul) | ! [X1] : (calm(X1) & rich(X1))) [rectify 60]
62. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK5) | ~rich(sK5)) [choice axiom]
63. ((~calm(sK5) | ~rich(sK5)) | (happy(paul) & calm(paul))) & (~happy(paul) | ~calm(paul) | ! [X1] : (calm(X1) & rich(X1))) [skolemisation 61,62]
64. ! [X0] : ((~humble(X0) & kind(X0)) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) [nnf transformation 37]
70. ! [X0] : ((calm(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ~calm(X0))) [nnf transformation 12]
93. humble(fred) | ~funny(X0) [cnf transformation 43]
99. ~strong(X0) | happy(X0) | kind(X0) [cnf transformation 46]
100. ~kind(X0) | strong(X0) [cnf transformation 46]
109. ~rich(sK3) | ~happy(fred) [cnf transformation 53]
111. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 54]
116. ~happy(paul) | ~calm(paul) | rich(X1) [cnf transformation 63]
120. kind(X0) | strong(X0) | kind(X0) [cnf transformation 64]
123. ~humble(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 64]
130. calm(X0) | patient(X0) | patient(X0) [cnf transformation 70]
131. calm(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 70]
163. humble(paul) [cnf transformation 25]
164. calm(X0) | patient(X0) [duplicate literal removal 130]
165. ~patient(X0) | calm(X0) [duplicate literal removal 131]
166. kind(X0) | strong(X0) [duplicate literal removal 120]
167. ~strong(X0) | funny(X0) [duplicate literal removal 111]
169. 1 <=> ! [X0] : ~funny(X0) [avatar definition]
170. ~funny(X0) <- (1) [avatar component clause 169]
172. 2 <=> humble(fred) [avatar definition]
174. humble(fred) <- (2) [avatar component clause 172]
175. 1 | 2 [avatar split clause 93,172,169]
218. 12 <=> happy(fred) [avatar definition]
220. ~happy(fred) <- (~12) [avatar component clause 218]
222. 13 <=> rich(sK3) [avatar definition]
224. ~rich(sK3) <- (~13) [avatar component clause 222]
225. ~12 | ~13 [avatar split clause 109,222,218]
246. 18 <=> happy(paul) [avatar definition]
247. ~happy(paul) <- (~18) [avatar component clause 246]
259. 21 <=> calm(paul) [avatar definition]
260. ~calm(paul) <- (~21) [avatar component clause 259]
264. 22 <=> ! [X1] : calm(X1) [avatar definition]
265. calm(X1) <- (22) [avatar component clause 264]
268. 23 <=> ! [X1] : rich(X1) [avatar definition]
269. rich(X1) <- (23) [avatar component clause 268]
270. 23 | ~21 | ~18 [avatar split clause 116,246,259,268]
271. ~kind(X0) | ~humble(X0) [subsumption resolution 123,100]
273. strong(X0) [subsumption resolution 166,100]
297. calm(X0) [subsumption resolution 164,165]
298. 22 [avatar split clause 297,264]
324. $false <- (~21, 22) [subsumption resolution 260,265]
325. 21 | ~22 [avatar contradiction clause 324]
332. funny(X0) [resolution 167,273]
351. happy(X0) | kind(X0) [resolution 99,273]
361. kind(fred) <- (~12) [resolution 351,220]
362. kind(paul) <- (~18) [resolution 351,247]
408. ~humble(fred) <- (~12) [resolution 361,271]
421. $false <- (2, ~12) [subsumption resolution 408,174]
422. ~2 | 12 [avatar contradiction clause 421]
430. ~humble(paul) <- (~18) [resolution 362,271]
443. $false <- (~18) [subsumption resolution 430,163]
444. 18 [avatar contradiction clause 443]
447. $false <- (~13, 23) [resolution 269,224]
448. 13 | ~23 [avatar contradiction clause 447]
450. $false <- (1) [subsumption resolution 170,332]
451. ~1 [avatar contradiction clause 450]
452. $false [avatar sat refutation 175,225,270,298,325,422,444,448,451]
% SZS output end Proof for 7046320036645878809785477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not generous then someone is both not humble and brave and vice versa.
Everyone who is either rich or not happy is both not patient and generous and vice versa.
Everyone who is either patient or funny is either not generous or rich and vice versa.
Everyone who is both not strong and not happy is both not quiet and tall.
Everyone who is rich is calm.
If someone is both not kind and curious then someone is strong or not old and vice versa.
Everyone who is either kind or not happy is not strong or patient and vice versa.
If fred is either happy or not kind then someone is both not quiet and not creative and vice versa.
If someone is both humble and funny then fred is not kind or not rich.
Everyone who is not calm or happy is not curious and vice versa.
Everyone who is either not tall or not generous is both not quiet and brave.
Everyone who is not funny is kind or strong and vice versa.
Everyone who is either creative or not curious is both wise and not calm.
Everyone who is both not happy and tall is old or not rich.
Everyone who is tall or not generous is generous and vice versa.
If someone is both not rich and not curious then someone is not tall.
Someone is rich.
Someone is not happy.
Someone is not generous or kind.
Susan is both old and not creative.
Alice is not generous or old.
Someone is not wise or not funny. | Alice is not calm. | contradiction | (((~happy(fred)|~generous(fred)))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((rich(X)<~>~happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((patient(X)<~>funny(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~strong(X)&~happy(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>calm(X)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(((happy(fred)<~>~kind(fred)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((humble(X)&funny(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~calm(X)|happy(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>~generous(X))=>(~quiet(X)&brave(X))))&
(![X]:(~funny(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)<~>~curious(X))=>(wise(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))=>(old(X)|~rich(X))))&
(![X]:((tall(X)|~generous(X))<=>generous(X)))&
((?[X]:((~rich(X)&~curious(X))))=>(?[X]:(~tall(X))))&
(?[X]:(rich(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)|kind(X))))&
((old(susan)&~creative(susan)))&
((~generous(alice)|old(alice)))&
(?[X]:((~wise(X)|~funny(X)))) | ~calm(alice) | [
"p4",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3345657167576844716118426
% SZS output start Proof for 3345657167576844716118426
5. ! [X0] : (rich(X0) => calm(X0)) [input p4]
10. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~curious(X0)) [input p9]
15. ! [X0] : ((~generous(X0) | tall(X0)) <=> generous(X0)) [input p14]
16. ? [X0] : (~curious(X0) & ~rich(X0)) => ? [X0] : ~tall(X0) [input p15]
23. ~calm(alice) [input hypothesis]
25. ? [X0] : (~curious(X0) & ~rich(X0)) => ? [X1] : ~tall(X1) [rectify 16]
28. ! [X0] : (calm(X0) | ~rich(X0)) [ennf transformation 5]
35. ? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | rich(X0)) [ennf transformation 25]
55. ! [X0] : (((happy(X0) | ~calm(X0)) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 10]
56. ! [X0] : ((happy(X0) | ~calm(X0) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [flattening 55]
61. ! [X0] : (((~generous(X0) | tall(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 15]
62. ! [X0] : ((~generous(X0) | tall(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [flattening 61]
63. ? [X0] : ~tall(X0) | ! [X1] : (curious(X1) | rich(X1)) [rectify 35]
64. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
65. ~tall(sK4) | ! [X1] : (curious(X1) | rich(X1)) [skolemisation 63,64]
95. ~rich(X0) | calm(X0) [cnf transformation 28]
114. ~curious(X0) | calm(X0) [cnf transformation 56]
130. generous(X0) | generous(X0) [cnf transformation 62]
131. ~generous(X0) | tall(X0) | ~generous(X0) [cnf transformation 62]
132. ~tall(sK4) | curious(X1) | rich(X1) [cnf transformation 65]
140. ~calm(alice) [cnf transformation 23]
141. generous(X0) [duplicate literal removal 130]
142. ~generous(X0) | tall(X0) [duplicate literal removal 131]
228. 19 <=> ! [X1] : (curious(X1) | rich(X1)) [avatar definition]
229. curious(X1) | rich(X1) <- (19) [avatar component clause 228]
231. 20 <=> tall(sK4) [avatar definition]
233. ~tall(sK4) <- (~20) [avatar component clause 231]
234. 19 | ~20 [avatar split clause 132,231,228]
250. tall(X0) [resolution 142,141]
251. $false <- (~20) [resolution 250,233]
252. 20 [avatar contradiction clause 251]
254. rich(X1) | calm(X1) <- (19) [resolution 229,114]
255. calm(X1) <- (19) [subsumption resolution 254,95]
256. $false <- (19) [resolution 255,140]
257. ~19 [avatar contradiction clause 256]
258. $false [avatar sat refutation 234,252,257]
% SZS output end Proof for 3345657167576844716118426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both wise and generous and vice versa.
Everyone who is generous is both calm and creative.
Everyone who is either not kind or not quiet is both kind and not brave.
If john is either not quiet or rich then fred is quiet and vice versa.
If paul is either not generous or tall then mary is brave or curious.
If mary is both not funny and not wise then alice is generous or calm and vice versa.
Everyone who is kind or generous is either happy or kind and vice versa.
Everyone who is not patient or quiet is either old or funny and vice versa.
Everyone who is both generous and not kind is either not funny or funny.
Everyone who is both happy and curious is humble.
If lucy is both kind and generous then alice is not rich.
Everyone who is either old or not calm is quiet and vice versa.
If lucy is calm or kind then paul is both old and not old.
If susan is calm or wise then someone is either not quiet or not tall.
Everyone who is wise or creative is either wise or not humble.
If someone is either humble or not kind then mary is both not calm and happy and vice versa.
Someone is both not humble and not creative.
Someone is generous.
Someone is both not generous and not kind.
Mary is tall.
John is both not happy and not quiet.
Mary is both not creative and not old.
Mary is both humble and not old.
Fred is both curious and not funny. | Mary is curious. | neutral | (![X]:(rich(X)<=>(wise(X)&generous(X))))&
(![X]:(generous(X)=>(calm(X)&creative(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>(kind(X)&~brave(X))))&
(((~quiet(john)<~>rich(john)))<=>(quiet(fred)))&
(((~generous(paul)<~>tall(paul)))=>((brave(mary)|curious(mary))))&
(((~funny(mary)&~wise(mary)))<=>((generous(alice)|calm(alice))))&
(![X]:((kind(X)|generous(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)|quiet(X))<=>(old(X)<~>funny(X))))&
(![X]:((generous(X)&~kind(X))=>(~funny(X)<~>funny(X))))&
(![X]:((happy(X)&curious(X))=>humble(X)))&
(((kind(lucy)&generous(lucy)))=>(~rich(alice)))&
(![X]:((old(X)<~>~calm(X))<=>quiet(X)))&
(((calm(lucy)|kind(lucy)))=>((old(paul)&~old(paul))))&
(((calm(susan)|wise(susan)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((wise(X)|creative(X))=>(wise(X)<~>~humble(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~calm(mary)&happy(mary))))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)&~kind(X))))&
(tall(mary))&
((~happy(john)&~quiet(john)))&
((~creative(mary)&~old(mary)))&
((humble(mary)&~old(mary)))&
((curious(fred)&~funny(fred))) | curious(mary) | [] | null | 0 |
Everyone who is generous is not rich and vice versa. If someone is either not kind or strong then paul is not generous. If susan is rich or not calm then fred is either calm or wise. Everyone who is not funny or rich is either not rich or not funny. Everyone who is either strong or not funny is both quiet and happy. If susan is both curious and kind then fred is either curious or not patient. Everyone who is both kind and not rich is either kind or not rich. If someone is old or generous then someone is creative or not funny. Everyone who is not wise is not rich and vice versa. If someone is both wise and old then someone is quiet or strong. Everyone who is both curious and not wise is either calm or patient and vice versa. If susan is not calm then someone is curious or rich. If john is happy or not humble then someone is not happy or not tall and vice versa. If someone is quiet or happy then someone is not wise or not quiet and vice versa. Everyone who is both not humble and old is generous. If someone is wise or calm then paul is humble or happy and vice versa. Someone is not humble. Fred is both old and quiet. John is both not happy and curious. Someone is either wise or happy. Someone is both tall and not brave. Fred is not generous or not quiet. Someone is not rich. Paul is curious or kind. | John is not funny. | neutral | (![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~kind(X)<~>strong(X))))=>(~generous(paul)))&
(((rich(susan)|~calm(susan)))=>((calm(fred)<~>wise(fred))))&
(![X]:((~funny(X)|rich(X))=>(~rich(X)<~>~funny(X))))&
(![X]:((strong(X)<~>~funny(X))=>(quiet(X)&happy(X))))&
(((curious(susan)&kind(susan)))=>((curious(fred)<~>~patient(fred))))&
(![X]:((kind(X)&~rich(X))=>(kind(X)<~>~rich(X))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:(~wise(X)<=>~rich(X)))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
(![X]:((curious(X)&~wise(X))<=>(calm(X)<~>patient(X))))&
((~calm(susan))=>(?[X]:((curious(X)|rich(X)))))&
(((happy(john)|~humble(john)))<=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((quiet(X)|happy(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&old(X))=>generous(X)))&
((?[X]:((wise(X)|calm(X))))<=>((humble(paul)|happy(paul))))&
(?[X]:(~humble(X)))&
((old(fred)&quiet(fred)))&
((~happy(john)&curious(john)))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((tall(X)&~brave(X))))&
((~generous(fred)|~quiet(fred)))&
(?[X]:(~rich(X)))&
((curious(paul)|kind(paul))) | ~funny(john) | [] | null | 0 |
Everyone who is either not tall or old is not creative or not happy and vice versa. If someone is either strong or wise then alice is curious. Everyone who is both old and quiet is wise or not old and vice versa. Everyone who is kind or not old is not happy and vice versa. If someone is kind then someone is both not humble and not old. Everyone who is either not strong or rich is not curious or not calm and vice versa. Everyone who is both kind and wise is wise. Everyone who is either funny or not happy is not happy and vice versa. If john is either creative or not humble then someone is tall. Everyone who is tall is funny. Everyone who is either not calm or not old is generous. If fred is kind or not rich then someone is curious. If alice is either not patient or not funny then someone is both not curious and not creative and vice versa. Everyone who is happy is generous or quiet and vice versa. Everyone who is not brave or not strong is either not wise or quiet. Everyone who is either not humble or patient is both generous and not happy and vice versa. Lucy is either rich or happy. Someone is calm or not creative. Someone is not tall or patient. John is not calm. Someone is quiet. Someone is not rich or not brave. | Lucy is not strong. | neutral | (![X]:((~tall(X)<~>old(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((strong(X)<~>wise(X))))=>(curious(alice)))&
(![X]:((old(X)&quiet(X))<=>(wise(X)|~old(X))))&
(![X]:((kind(X)|~old(X))<=>~happy(X)))&
((?[X]:(kind(X)))=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~strong(X)<~>rich(X))<=>(~curious(X)|~calm(X))))&
(![X]:((kind(X)&wise(X))=>wise(X)))&
(![X]:((funny(X)<~>~happy(X))<=>~happy(X)))&
(((creative(john)<~>~humble(john)))=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>funny(X)))&
(![X]:((~calm(X)<~>~old(X))=>generous(X)))&
(((kind(fred)|~rich(fred)))=>(?[X]:(curious(X))))&
(((~patient(alice)<~>~funny(alice)))<=>(?[X]:((~curious(X)&~creative(X)))))&
(![X]:(happy(X)<=>(generous(X)|quiet(X))))&
(![X]:((~brave(X)|~strong(X))=>(~wise(X)<~>quiet(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(generous(X)&~happy(X))))&
((rich(lucy)<~>happy(lucy)))&
(?[X]:((calm(X)|~creative(X))))&
(?[X]:((~tall(X)|patient(X))))&
(~calm(john))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|~brave(X)))) | ~strong(lucy) | [] | null | 0 |
If alice is both not creative and kind then someone is both not funny and patient. Everyone who is strong is not calm or wise and vice versa. If lucy is either not funny or not old then paul is not funny. Everyone who is either not old or not wise is generous and vice versa. If someone is not tall or not patient then fred is not brave or generous and vice versa. Everyone who is either happy or not patient is brave and vice versa. Everyone who is either funny or not generous is old or not brave and vice versa. Everyone who is kind is either not rich or quiet and vice versa. Everyone who is not humble or wise is strong and vice versa. Everyone who is both humble and brave is not strong. If lucy is both humble and curious then mary is patient or tall and vice versa. Everyone who is not tall is quiet or patient. If paul is not kind then john is not tall or calm and vice versa. Everyone who is not happy or brave is patient or not strong and vice versa. If mary is funny then susan is tall or not rich and vice versa. Everyone who is both not brave and not creative is rich and vice versa. Someone is strong or patient. Someone is either not strong or strong. Lucy is both generous and humble. Paul is not wise. Mary is not curious or not generous. Someone is both brave and not humble. Someone is old. | Fred is not wise. | neutral | (((~creative(alice)&kind(alice)))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:(strong(X)<=>(~calm(X)|wise(X))))&
(((~funny(lucy)<~>~old(lucy)))=>(~funny(paul)))&
(![X]:((~old(X)<~>~wise(X))<=>generous(X)))&
((?[X]:((~tall(X)|~patient(X))))<=>((~brave(fred)|generous(fred))))&
(![X]:((happy(X)<~>~patient(X))<=>brave(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(old(X)|~brave(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>quiet(X))))&
(![X]:((~humble(X)|wise(X))<=>strong(X)))&
(![X]:((humble(X)&brave(X))=>~strong(X)))&
(((humble(lucy)&curious(lucy)))<=>((patient(mary)|tall(mary))))&
(![X]:(~tall(X)=>(quiet(X)|patient(X))))&
((~kind(paul))<=>((~tall(john)|calm(john))))&
(![X]:((~happy(X)|brave(X))<=>(patient(X)|~strong(X))))&
((funny(mary))<=>((tall(susan)|~rich(susan))))&
(![X]:((~brave(X)&~creative(X))<=>rich(X)))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
((generous(lucy)&humble(lucy)))&
(~wise(paul))&
((~curious(mary)|~generous(mary)))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:(old(X))) | ~wise(fred) | [] | null | 0 |
Everyone who is both strong and creative is both brave and not happy and vice versa. Everyone who is patient is both curious and calm. If someone is both not strong and not brave then alice is either not happy or calm. If fred is either rich or calm then mary is either not brave or calm. Everyone who is both curious and creative is not generous and vice versa. Everyone who is both tall and wise is both not happy and not creative. Everyone who is generous is creative or brave and vice versa. Everyone who is calm is either calm or not kind and vice versa. If alice is not old or not happy then someone is not old. Everyone who is either kind or not humble is either humble or rich and vice versa. If someone is curious or not quiet then someone is both brave and not quiet and vice versa. If alice is not funny then mary is not calm or wise and vice versa. Everyone who is not generous or rich is both not quiet and curious and vice versa. If someone is either not strong or generous then someone is either brave or not funny. Everyone who is not brave is quiet or wise and vice versa. Everyone who is not curious or rich is curious or not curious. Someone is funny or not creative. Paul is kind. Paul is not tall. Someone is either happy or generous. Someone is both tall and not funny. | Paul is humble. | neutral | (![X]:((strong(X)&creative(X))<=>(brave(X)&~happy(X))))&
(![X]:(patient(X)=>(curious(X)&calm(X))))&
((?[X]:((~strong(X)&~brave(X))))=>((~happy(alice)<~>calm(alice))))&
(((rich(fred)<~>calm(fred)))=>((~brave(mary)<~>calm(mary))))&
(![X]:((curious(X)&creative(X))<=>~generous(X)))&
(![X]:((tall(X)&wise(X))=>(~happy(X)&~creative(X))))&
(![X]:(generous(X)<=>(creative(X)|brave(X))))&
(![X]:(calm(X)<=>(calm(X)<~>~kind(X))))&
(((~old(alice)|~happy(alice)))=>(?[X]:(~old(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
((~funny(alice))<=>((~calm(mary)|wise(mary))))&
(![X]:((~generous(X)|rich(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((~strong(X)<~>generous(X))))=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:(~brave(X)<=>(quiet(X)|wise(X))))&
(![X]:((~curious(X)|rich(X))=>(curious(X)|~curious(X))))&
(?[X]:((funny(X)|~creative(X))))&
(kind(paul))&
(~tall(paul))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((tall(X)&~funny(X)))) | humble(paul) | [] | null | 0 |
If someone is both wise and not wise then someone is humble or not rich.
Everyone who is both tall and strong is either creative or not old.
Everyone who is not humble or not strong is creative or calm and vice versa.
Everyone who is either not brave or not funny is either old or not kind.
Everyone who is either wise or not generous is not generous or curious.
If paul is either not rich or funny then paul is creative and vice versa.
If alice is happy or humble then susan is both not patient and kind.
If paul is both rich and funny then lucy is either funny or patient and vice versa.
If mary is either not humble or rich then someone is both patient and not happy and vice versa.
Everyone who is strong is both not humble and kind and vice versa.
If paul is funny then alice is either not quiet or kind.
Everyone who is not tall is both kind and not old and vice versa.
Everyone who is either not old or curious is patient.
If susan is not happy or not patient then someone is either not old or not creative and vice versa.
Everyone who is not calm or not happy is both wise and not patient.
Everyone who is not generous or strong is both not creative and not rich and vice versa.
Someone is both rich and curious.
Someone is humble or patient.
Someone is both happy and strong.
Lucy is both strong and generous.
Mary is both tall and rich.
Susan is quiet.
Someone is either not brave or not rich.
Someone is either not strong or strong. | Mary is humble. | contradiction | ((?[X]:((wise(X)&~wise(X))))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((tall(X)&strong(X))=>(creative(X)<~>~old(X))))&
(![X]:((~humble(X)|~strong(X))<=>(creative(X)|calm(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(old(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~generous(X))=>(~generous(X)|curious(X))))&
(((~rich(paul)<~>funny(paul)))<=>(creative(paul)))&
(((happy(alice)|humble(alice)))=>((~patient(susan)&kind(susan))))&
(((rich(paul)&funny(paul)))<=>((funny(lucy)<~>patient(lucy))))&
(((~humble(mary)<~>rich(mary)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:(strong(X)<=>(~humble(X)&kind(X))))&
((funny(paul))=>((~quiet(alice)<~>kind(alice))))&
(![X]:(~tall(X)<=>(kind(X)&~old(X))))&
(![X]:((~old(X)<~>curious(X))=>patient(X)))&
(((~happy(susan)|~patient(susan)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)&~patient(X))))&
(![X]:((~generous(X)|strong(X))<=>(~creative(X)&~rich(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((happy(X)&strong(X))))&
((strong(lucy)&generous(lucy)))&
((tall(mary)&rich(mary)))&
(quiet(susan))&
(?[X]:((~brave(X)<~>~rich(X))))&
(?[X]:((~strong(X)<~>strong(X)))) | humble(mary) | [
"p8",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6853820820398260078418644
% SZS output start Proof for 6853820820398260078418644
9. (~humble(mary) <~> rich(mary)) <=> ? [X0] : (~happy(X0) & patient(X0)) [input p8]
15. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~patient(X0) & wise(X0))) [input p14]
21. rich(mary) & tall(mary) [input p20]
25. humble(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) & wise(X0)) | (happy(X0) & calm(X0))) [ennf transformation 15]
48. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X0] : (~happy(X0) & patient(X0)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [nnf transformation 9]
49. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X1] : (~happy(X1) & patient(X1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [rectify 48]
50. ? [X1] : (~happy(X1) & patient(X1)) => (~happy(sK1) & patient(sK1)) [choice axiom]
51. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & ((~happy(sK1) & patient(sK1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [skolemisation 49,50]
105. patient(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
107. ~happy(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
129. ~patient(X0) | happy(X0) [cnf transformation 36]
143. rich(mary) [cnf transformation 21]
149. humble(mary) [cnf transformation 25]
202. 10 <=> ! [X0] : (happy(X0) | ~patient(X0)) [avatar definition]
203. ~patient(X0) | happy(X0) <- (10) [avatar component clause 202]
205. 11 <=> humble(mary) [avatar definition]
209. 12 <=> rich(mary) [avatar definition]
215. 13 <=> happy(sK1) [avatar definition]
217. ~happy(sK1) <- (~13) [avatar component clause 215]
218. ~12 | ~11 | ~13 [avatar split clause 107,215,205,209]
221. 14 <=> patient(sK1) [avatar definition]
223. patient(sK1) <- (14) [avatar component clause 221]
224. ~12 | ~11 | 14 [avatar split clause 105,221,205,209]
260. 10 [avatar split clause 129,202]
270. 12 [avatar split clause 143,209]
281. 11 [avatar split clause 149,205]
296. happy(sK1) <- (10, 14) [resolution 203,223]
297. $false <- (10, ~13, 14) [subsumption resolution 296,217]
298. ~10 | 13 | ~14 [avatar contradiction clause 297]
299. $false [avatar sat refutation 218,224,260,270,281,298]
% SZS output end Proof for 6853820820398260078418644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not funny is both not strong and humble and vice versa.
Everyone who is not tall or not old is both kind and generous and vice versa.
If susan is either not generous or 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.
If susan is not rich then someone is both creative and tall and vice versa.
Everyone who is not generous is not tall and vice versa.
Everyone who is happy or not calm is not creative and vice versa.
Everyone who is brave or not curious is both funny and rich.
If someone is both not rich and not humble then alice is both not tall and generous.
If someone is not curious or humble then someone is both wise and funny and vice versa.
If someone is both not wise and calm then someone is kind or not happy.
Someone is quiet or not creative.
Mary is either tall or not creative.
Someone is generous.
Lucy is either patient or tall.
Someone is both generous and kind.
Someone is patient.
John is either wise or not humble. | Fred is generous. | entailment | (![X]:((funny(X)|~funny(X))<=>(~strong(X)&humble(X))))&
(![X]:((~tall(X)|~old(X))<=>(kind(X)&generous(X))))&
(((~generous(susan)<~>calm(susan)))=>((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))))&
((~rich(susan))<=>(?[X]:((creative(X)&tall(X)))))&
(![X]:(~generous(X)<=>~tall(X)))&
(![X]:((happy(X)|~calm(X))<=>~creative(X)))&
(![X]:((brave(X)|~curious(X))=>(funny(X)&rich(X))))&
((?[X]:((~rich(X)&~humble(X))))=>((~tall(alice)&generous(alice))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((~wise(X)&calm(X))))=>(?[X]:((kind(X)|~happy(X)))))&
(?[X]:((quiet(X)|~creative(X))))&
((tall(mary)<~>~creative(mary)))&
(?[X]:(generous(X)))&
((patient(lucy)<~>tall(lucy)))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:(patient(X)))&
((wise(john)<~>~humble(john))) | generous(fred) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5926074978176470725347072
% SZS output start Proof for 5926074978176470725347072
2. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (generous(X0) & kind(X0))) [input p1]
10. ! [X0] : (~generous(X0) <=> ~tall(X0)) [input p9]
23. ~generous(fred) [input hypothesis]
37. ! [X0] : (((~old(X0) | ~tall(X0)) | (~generous(X0) | ~kind(X0))) & ((generous(X0) & kind(X0)) | (old(X0) & tall(X0)))) [nnf transformation 2]
38. ! [X0] : ((~old(X0) | ~tall(X0) | ~generous(X0) | ~kind(X0)) & ((generous(X0) & kind(X0)) | (old(X0) & tall(X0)))) [flattening 37]
49. ! [X0] : ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))) [nnf transformation 10]
78. generous(X0) | tall(X0) [cnf transformation 38]
104. ~tall(X0) | generous(X0) [cnf transformation 49]
105. ~generous(X0) | tall(X0) [cnf transformation 49]
132. ~generous(fred) [cnf transformation 23]
221. tall(X0) [subsumption resolution 105,78]
222. generous(X0) [subsumption resolution 104,221]
250. $false [subsumption resolution 132,222]
% SZS output end Proof for 5926074978176470725347072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not wise is curious or not funny and vice versa.
If someone is either happy or creative then someone is rich or strong and vice versa.
Everyone who is strong or patient is not humble.
Everyone who is patient or not old is creative or curious.
If someone is funny or strong then lucy is humble.
If john is either not creative or calm then someone is not funny or not generous and vice versa.
Everyone who is either not strong or not tall is both not generous and rich and vice versa.
Everyone who is not kind or not curious is curious and vice versa.
If someone is tall then fred is not rich or not humble and vice versa.
Everyone who is not creative is both not strong and generous.
Everyone who is not creative or not happy is not strong.
If lucy is creative then someone is both wise and happy and vice versa.
Everyone who is not tall is not kind or curious.
If paul is both not quiet and rich then someone is either happy or not generous.
If paul is both humble and brave then someone is either brave or creative and vice versa.
If john is both not quiet and not kind then susan is curious or not rich and vice versa.
Someone is both not strong and not tall.
Mary is not quiet or funny.
Susan is not calm or tall.
Someone is not old or patient.
Susan is strong or not creative.
Someone is not old.
Someone is not creative or curious. | Mary is kind. | contradiction | (![X]:((~strong(X)|~wise(X))<=>(curious(X)|~funny(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((strong(X)|patient(X))=>~humble(X)))&
(![X]:((patient(X)|~old(X))=>(creative(X)|curious(X))))&
((?[X]:((funny(X)|strong(X))))=>(humble(lucy)))&
(((~creative(john)<~>calm(john)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~generous(X)&rich(X))))&
(![X]:((~kind(X)|~curious(X))<=>curious(X)))&
((?[X]:(tall(X)))<=>((~rich(fred)|~humble(fred))))&
(![X]:(~creative(X)=>(~strong(X)&generous(X))))&
(![X]:((~creative(X)|~happy(X))=>~strong(X)))&
((creative(lucy))<=>(?[X]:((wise(X)&happy(X)))))&
(![X]:(~tall(X)=>(~kind(X)|curious(X))))&
(((~quiet(paul)&rich(paul)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(((humble(paul)&brave(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(((~quiet(john)&~kind(john)))<=>((curious(susan)|~rich(susan))))&
(?[X]:((~strong(X)&~tall(X))))&
((~quiet(mary)|funny(mary)))&
((~calm(susan)|tall(susan)))&
(?[X]:((~old(X)|patient(X))))&
((strong(susan)|~creative(susan)))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)|curious(X)))) | kind(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6085088720246132907902099
% SZS output start Proof for 6085088720246132907902099
8. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> curious(X0)) [input p7]
24. kind(mary) [input hypothesis]
49. ! [X0] : (((~curious(X0) | ~kind(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) & kind(X0)))) [nnf transformation 8]
50. ! [X0] : ((~curious(X0) | ~kind(X0) | ~curious(X0)) & (curious(X0) | (curious(X0) & kind(X0)))) [flattening 49]
107. curious(X0) | curious(X0) [cnf transformation 50]
108. ~curious(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 50]
141. kind(mary) [cnf transformation 24]
142. curious(X0) [duplicate literal removal 107]
143. ~kind(X0) | ~curious(X0) [duplicate literal removal 108]
353. ~curious(mary) [resolution 143,141]
354. $false [subsumption resolution 353,142]
% SZS output end Proof for 6085088720246132907902099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is either patient or not happy. Everyone who is either calm or brave is kind or curious. Everyone who is strong or not quiet is either curious or funny and vice versa. If paul is either generous or not generous then alice is either humble or wise and vice versa. If someone is both not tall and not generous then alice is both brave and not creative and vice versa. Everyone who is not quiet is not humble or creative and vice versa. Everyone who is not happy or creative is not calm. Everyone who is quiet or old is not happy. Everyone who is either old or not generous is patient or not creative. Everyone who is either not brave or not happy is humble. Everyone who is either not patient or not funny is not patient or wise. Everyone who is either not happy or strong is not generous and vice versa. If susan is generous or not creative then someone is both not patient and calm and vice versa. If someone is not strong or happy then someone is either wise or funny. If someone is either generous or curious then paul is not generous or not patient. Everyone who is either not patient or not brave is not funny or not brave and vice versa. Susan is both kind and funny. Someone is brave or not creative. Someone is tall. Someone is either not brave or rich. Alice is both not kind and not humble. Mary is either not strong or happy. Someone is strong. Fred is both not wise and not happy. | Susan is happy. | entailment | (![X]:(~quiet(X)=>(patient(X)<~>~happy(X))))&
(![X]:((calm(X)<~>brave(X))=>(kind(X)|curious(X))))&
(![X]:((strong(X)|~quiet(X))<=>(curious(X)<~>funny(X))))&
(((generous(paul)<~>~generous(paul)))<=>((humble(alice)<~>wise(alice))))&
((?[X]:((~tall(X)&~generous(X))))<=>((brave(alice)&~creative(alice))))&
(![X]:(~quiet(X)<=>(~humble(X)|creative(X))))&
(![X]:((~happy(X)|creative(X))=>~calm(X)))&
(![X]:((quiet(X)|old(X))=>~happy(X)))&
(![X]:((old(X)<~>~generous(X))=>(patient(X)|~creative(X))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(~patient(X)|wise(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~generous(X)))&
(((generous(susan)|~creative(susan)))<=>(?[X]:((~patient(X)&calm(X)))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((generous(X)<~>curious(X))))=>((~generous(paul)|~patient(paul))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~funny(X)|~brave(X))))&
((kind(susan)&funny(susan)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~brave(X)<~>rich(X))))&
((~kind(alice)&~humble(alice)))&
((~strong(mary)<~>happy(mary)))&
(?[X]:(strong(X)))&
((~wise(fred)&~happy(fred))) | happy(susan) | [
"p0",
"p5",
"p6",
"p7",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 71615091478434798489549
% SZS output start Proof for 71615091478434798489549
1. ! [X0] : (~quiet(X0) => (patient(X0) <~> ~happy(X0))) [input p0]
6. ! [X0] : (~quiet(X0) <=> (creative(X0) | ~humble(X0))) [input p5]
7. ! [X0] : ((creative(X0) | ~happy(X0)) => ~calm(X0)) [input p6]
8. ! [X0] : ((old(X0) | quiet(X0)) => ~happy(X0)) [input p7]
13. (~creative(susan) | generous(susan)) <=> ? [X0] : (calm(X0) & ~patient(X0)) [input p12]
16. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~brave(X0) | ~funny(X0))) [input p15]
17. funny(susan) & kind(susan) [input p16]
25. ~happy(susan) [input hypothesis]
27. ! [X0] : ((patient(X0) <~> ~happy(X0)) | quiet(X0)) [ennf transformation 1]
30. ! [X0] : (~calm(X0) | (~creative(X0) & happy(X0))) [ennf transformation 7]
31. ! [X0] : (~happy(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 8]
40. ! [X0] : (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | quiet(X0)) [nnf transformation 27]
50. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & ((creative(X0) | ~humble(X0)) | quiet(X0))) [nnf transformation 6]
51. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & (creative(X0) | ~humble(X0) | quiet(X0))) [flattening 50]
56. ((~creative(susan) | generous(susan)) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [nnf transformation 13]
57. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [flattening 56]
58. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X1] : (calm(X1) & ~patient(X1)) | (creative(susan) & ~generous(susan))) [rectify 57]
59. ? [X1] : (calm(X1) & ~patient(X1)) => (calm(sK1) & ~patient(sK1)) [choice axiom]
60. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & ((calm(sK1) & ~patient(sK1)) | (creative(susan) & ~generous(susan))) [skolemisation 58,59]
66. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 16]
67. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 66]
78. ~happy(X0) | patient(X0) | quiet(X0) [cnf transformation 40]
79. ~patient(X0) | happy(X0) | quiet(X0) [cnf transformation 40]
102. ~creative(X0) | ~quiet(X0) [cnf transformation 51]
103. ~calm(X0) | happy(X0) [cnf transformation 30]
105. ~happy(X0) | ~quiet(X0) [cnf transformation 31]
118. ~patient(sK1) | creative(susan) [cnf transformation 60]
120. calm(sK1) | creative(susan) [cnf transformation 60]
128. ~brave(X0) | ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 67]
133. brave(X0) | patient(X0) | brave(X0) [cnf transformation 67]
135. funny(susan) [cnf transformation 17]
147. ~happy(susan) [cnf transformation 25]
148. ~brave(X0) | ~funny(X0) | patient(X0) [duplicate literal removal 128]
149. brave(X0) | patient(X0) [duplicate literal removal 133]
202. 11 <=> creative(susan) [avatar definition]
203. creative(susan) <- (11) [avatar component clause 202]
207. 12 <=> calm(sK1) [avatar definition]
209. calm(sK1) <- (12) [avatar component clause 207]
210. 11 | 12 [avatar split clause 120,207,202]
213. 13 <=> patient(sK1) [avatar definition]
215. ~patient(sK1) <- (~13) [avatar component clause 213]
216. 11 | ~13 [avatar split clause 118,213,202]
248. ~funny(X0) | patient(X0) [subsumption resolution 148,149]
279. ~quiet(susan) <- (11) [resolution 102,203]
282. patient(susan) [resolution 248,135]
284. happy(susan) | quiet(susan) [resolution 79,282]
294. quiet(susan) [subsumption resolution 284,147]
295. $false <- (11) [subsumption resolution 294,279]
296. ~11 [avatar contradiction clause 295]
298. happy(sK1) <- (12) [resolution 209,103]
301. patient(sK1) | quiet(sK1) <- (12) [resolution 298,78]
302. ~quiet(sK1) <- (12) [resolution 298,105]
303. quiet(sK1) <- (12, ~13) [subsumption resolution 301,215]
304. $false <- (12, ~13) [subsumption resolution 302,303]
305. ~12 | 13 [avatar contradiction clause 304]
306. $false [avatar sat refutation 210,216,296,305]
% SZS output end Proof for 71615091478434798489549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not old then someone is either not brave or not rich and vice versa.
If susan is either funny or not strong then john is either not happy or calm and vice versa.
If fred is either brave or not patient then john is either curious or not calm and vice versa.
Everyone who is not wise or quiet is both not quiet and patient and vice versa.
If john is either happy or kind then someone is either not rich or not funny.
If someone is either brave or creative then someone is quiet and vice versa.
If someone is either not quiet or calm then alice is not generous.
Everyone who is not humble is not tall or not calm.
If someone is not kind or funny then someone is either quiet or not tall.
If susan is both not curious and humble then someone is old and vice versa.
If paul is both not creative and not rich then john is strong or not tall and vice versa.
If someone is either not strong or not calm then paul is happy.
Everyone who is both generous and not happy is either creative or not old and vice versa.
If paul is not strong then someone is not generous and vice versa.
Everyone who is not patient or not creative is happy and vice versa.
Everyone who is both not calm and not quiet is either not creative or creative and vice versa.
Someone is either not wise or quiet.
Someone is brave or not generous.
Someone is not generous.
John is not quiet or funny.
John is old or quiet.
Alice is not calm or creative.
Fred is both not brave and not rich.
Someone is either not tall or calm. | John is old. | entailment | (((~happy(mary)<~>~old(mary)))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
(((funny(susan)<~>~strong(susan)))<=>((~happy(john)<~>calm(john))))&
(((brave(fred)<~>~patient(fred)))<=>((curious(john)<~>~calm(john))))&
(![X]:((~wise(X)|quiet(X))<=>(~quiet(X)&patient(X))))&
(((happy(john)<~>kind(john)))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((~quiet(X)<~>calm(X))))=>(~generous(alice)))&
(![X]:(~humble(X)=>(~tall(X)|~calm(X))))&
((?[X]:((~kind(X)|funny(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(((~curious(susan)&humble(susan)))<=>(?[X]:(old(X))))&
(((~creative(paul)&~rich(paul)))<=>((strong(john)|~tall(john))))&
((?[X]:((~strong(X)<~>~calm(X))))=>(happy(paul)))&
(![X]:((generous(X)&~happy(X))<=>(creative(X)<~>~old(X))))&
((~strong(paul))<=>(?[X]:(~generous(X))))&
(![X]:((~patient(X)|~creative(X))<=>happy(X)))&
(![X]:((~calm(X)&~quiet(X))<=>(~creative(X)<~>creative(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:(~generous(X)))&
((~quiet(john)|funny(john)))&
((old(john)|quiet(john)))&
((~calm(alice)|creative(alice)))&
((~brave(fred)&~rich(fred)))&
(?[X]:((~tall(X)<~>calm(X)))) | old(john) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9162873462655527184485342
% SZS output start Proof for 9162873462655527184485342
4. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (patient(X0) & ~quiet(X0))) [input p3]
21. quiet(john) | old(john) [input p20]
25. ~old(john) [input hypothesis]
40. ! [X0] : (((quiet(X0) | ~wise(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | ~wise(X0) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | (~quiet(X0) & wise(X0)))) [flattening 40]
108. ~quiet(X0) | ~quiet(X0) [cnf transformation 41]
159. quiet(john) | old(john) [cnf transformation 21]
165. ~old(john) [cnf transformation 25]
170. ~quiet(X0) [duplicate literal removal 108]
362. old(john) [subsumption resolution 159,170]
365. $false [subsumption resolution 165,362]
% SZS output end Proof for 9162873462655527184485342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and creative is happy or generous. If alice is not brave or not tall then someone is both not generous and not creative and vice versa. If john is not humble or old then alice is not creative or wise and vice versa. If john is rich or not creative then susan is generous or funny. Everyone who is not old is not curious. If someone is both not funny and not happy then someone is quiet and vice versa. If mary is both not funny and calm then john is rich. Everyone who is brave is not calm and vice versa. Everyone who is rich is not generous or not humble and vice versa. Everyone who is kind is not old. If someone is both strong and happy then someone is either creative or not quiet. Everyone who is either calm or not generous is generous or not humble. Everyone who is rich is not patient and vice versa. Everyone who is strong or wise is either not generous or not quiet and vice versa. Everyone who is both brave and curious is both quiet and not kind and vice versa. Everyone who is patient or not rich is not brave or quiet and vice versa. Mary is tall. Alice is both not kind and strong. Fred is old. Fred is either not rich or not happy. Paul is not strong or patient. Fred is humble. Lucy is not patient or patient. Someone is wise or not calm. | Lucy is wise. | neutral | (![X]:((~creative(X)&creative(X))=>(happy(X)|generous(X))))&
(((~brave(alice)|~tall(alice)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~humble(john)|old(john)))<=>((~creative(alice)|wise(alice))))&
(((rich(john)|~creative(john)))=>((generous(susan)|funny(susan))))&
(![X]:(~old(X)=>~curious(X)))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:(quiet(X))))&
(((~funny(mary)&calm(mary)))=>(rich(john)))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:(rich(X)<=>(~generous(X)|~humble(X))))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:((strong(X)&happy(X))))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((calm(X)<~>~generous(X))=>(generous(X)|~humble(X))))&
(![X]:(rich(X)<=>~patient(X)))&
(![X]:((strong(X)|wise(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)&~kind(X))))&
(![X]:((patient(X)|~rich(X))<=>(~brave(X)|quiet(X))))&
(tall(mary))&
((~kind(alice)&strong(alice)))&
(old(fred))&
((~rich(fred)<~>~happy(fred)))&
((~strong(paul)|patient(paul)))&
(humble(fred))&
((~patient(lucy)|patient(lucy)))&
(?[X]:((wise(X)|~calm(X)))) | wise(lucy) | [] | null | 0 |
If someone is both funny and not quiet then someone is both not curious and not old and vice versa. If susan is both not generous and rich then someone is not happy or old. If someone is not tall then someone is creative or not rich. Everyone who is either generous or not funny is both not quiet and curious. Everyone who is either not old or not curious is patient and vice versa. If someone is patient then someone is not old or not patient and vice versa. Everyone who is curious or strong is patient and vice versa. Everyone who is either not tall or not calm is both not calm and not tall. Everyone who is either not funny or not patient is wise or not humble. If alice is not wise or not strong then someone is both not strong and not quiet. Everyone who is not calm or not kind is not funny and vice versa. Everyone who is happy is wise. If someone is not kind or not patient then someone is either not generous or not brave and vice versa. Everyone who is either not rich or creative is humble or not calm and vice versa. Everyone who is both generous and funny is generous or quiet. Everyone who is either kind or not funny is either not tall or not calm and vice versa. Someone is not rich or funny. Someone is either brave or curious. John is both not rich and humble. Susan is rich. Someone is not curious or not patient. Someone is either humble or generous. | John is patient. | entailment | ((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((~curious(X)&~old(X)))))&
(((~generous(susan)&rich(susan)))=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:((generous(X)<~>~funny(X))=>(~quiet(X)&curious(X))))&
(![X]:((~old(X)<~>~curious(X))<=>patient(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((curious(X)|strong(X))<=>patient(X)))&
(![X]:((~tall(X)<~>~calm(X))=>(~calm(X)&~tall(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(wise(X)|~humble(X))))&
(((~wise(alice)|~strong(alice)))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~funny(X)))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((generous(X)&funny(X))=>(generous(X)|quiet(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~tall(X)<~>~calm(X))))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:((brave(X)<~>curious(X))))&
((~rich(john)&humble(john)))&
(rich(susan))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((humble(X)<~>generous(X)))) | patient(john) | [
"p0",
"p4",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 262579901311555737994835
% SZS output start Proof for 262579901311555737994835
1. ? [X0] : (~quiet(X0) & funny(X0)) <=> ? [X0] : (~old(X0) & ~curious(X0)) [input p0]
5. ! [X0] : ((~old(X0) <~> ~curious(X0)) <=> patient(X0)) [input p4]
7. ! [X0] : ((strong(X0) | curious(X0)) <=> patient(X0)) [input p6]
8. ! [X0] : ((~tall(X0) <~> ~calm(X0)) => (~tall(X0) & ~calm(X0))) [input p7]
11. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> ~funny(X0)) [input p10]
16. ! [X0] : ((kind(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> ~calm(X0))) [input p15]
23. ~patient(john) [input hypothesis]
24. ? [X0] : (~quiet(X0) & funny(X0)) <=> ? [X1] : (~old(X1) & ~curious(X1)) [rectify 1]
34. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~tall(X0) <=> ~calm(X0))) [ennf transformation 8]
38. (? [X0] : (~quiet(X0) & funny(X0)) | ! [X1] : (old(X1) | curious(X1))) & (? [X1] : (~old(X1) & ~curious(X1)) | ! [X0] : (quiet(X0) | ~funny(X0))) [nnf transformation 24]
39. (? [X0] : (~quiet(X0) & funny(X0)) | ! [X1] : (old(X1) | curious(X1))) & (? [X2] : (~old(X2) & ~curious(X2)) | ! [X3] : (quiet(X3) | ~funny(X3))) [rectify 38]
40. ? [X0] : (~quiet(X0) & funny(X0)) => (~quiet(sK0) & funny(sK0)) [choice axiom]
41. ? [X2] : (~old(X2) & ~curious(X2)) => (~old(sK1) & ~curious(sK1)) [choice axiom]
42. ((~quiet(sK0) & funny(sK0)) | ! [X1] : (old(X1) | curious(X1))) & ((~old(sK1) & ~curious(sK1)) | ! [X3] : (quiet(X3) | ~funny(X3))) [skolemisation 39,41,40]
47. ! [X0] : ((((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | ~patient(X0)) & (patient(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0))))) [nnf transformation 5]
53. ! [X0] : (((strong(X0) | curious(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~curious(X0)))) [nnf transformation 7]
54. ! [X0] : ((strong(X0) | curious(X0) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~curious(X0)))) [flattening 53]
55. ! [X0] : ((~tall(X0) & ~calm(X0)) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) [nnf transformation 34]
58. ! [X0] : (((~kind(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) & calm(X0)))) [nnf transformation 11]
59. ! [X0] : ((~kind(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (kind(X0) & calm(X0)))) [flattening 58]
67. ! [X0] : ((((funny(X0) | ~kind(X0)) & (~funny(X0) | kind(X0))) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) & (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))))) [nnf transformation 16]
80. funny(sK0) | old(X1) | curious(X1) [cnf transformation 42]
88. ~old(X0) | patient(X0) | curious(X0) [cnf transformation 47]
94. ~curious(X0) | patient(X0) [cnf transformation 54]
97. ~calm(X0) | ~calm(X0) | tall(X0) [cnf transformation 55]
103. ~funny(X0) | calm(X0) [cnf transformation 59]
104. ~funny(X0) | kind(X0) [cnf transformation 59]
105. ~kind(X0) | ~calm(X0) | funny(X0) [cnf transformation 59]
119. ~calm(X0) | ~tall(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 67]
136. ~patient(john) [cnf transformation 23]
137. ~calm(X0) | tall(X0) [duplicate literal removal 97]
140. 1 <=> ! [X1] : (old(X1) | curious(X1)) [avatar definition]
141. old(X1) | curious(X1) <- (1) [avatar component clause 140]
148. 3 <=> funny(sK0) [avatar definition]
150. funny(sK0) <- (3) [avatar component clause 148]
151. 1 | 3 [avatar split clause 80,148,140]
178. 10 <=> ! [X1] : patient(X1) [avatar definition]
179. patient(X1) <- (10) [avatar component clause 178]
250. ~calm(X0) | ~tall(X0) | ~kind(X0) [subsumption resolution 119,105]
251. ~kind(X0) | ~calm(X0) [subsumption resolution 250,137]
282. calm(sK0) <- (3) [resolution 103,150]
283. kind(sK0) <- (3) [resolution 104,150]
293. ~calm(sK0) <- (3) [resolution 251,283]
296. $false <- (3) [subsumption resolution 293,282]
297. ~3 [avatar contradiction clause 296]
332. patient(X0) | curious(X0) | curious(X0) <- (1) [resolution 88,141]
335. patient(X0) | curious(X0) <- (1) [duplicate literal removal 332]
336. patient(X0) <- (1) [subsumption resolution 335,94]
337. 10 | ~1 [avatar split clause 336,140,178]
340. $false <- (10) [resolution 179,136]
345. ~10 [avatar contradiction clause 340]
346. $false [avatar sat refutation 151,297,337,345]
% SZS output end Proof for 262579901311555737994835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not kind is both kind and wise and vice versa.
Everyone who is not strong is not calm and vice versa.
Everyone who is not wise or not old is strong and vice versa.
If lucy is either not curious or not creative then someone is calm or not generous and vice versa.
If susan is either not kind or wise then someone is both happy and not tall and vice versa.
If lucy is both not generous and not calm then someone is strong.
Everyone who is both tall and not happy is both kind and not wise.
If someone is tall or rich then fred is either happy or not wise and vice versa.
If someone is brave then susan is both old and not wise and vice versa.
If lucy is either creative or not patient then susan is wise.
If someone is either not rich or not curious then someone is either not quiet or creative and vice versa.
Everyone who is both creative and not tall is not kind or not brave and vice versa.
Everyone who is not humble is either funny or generous.
Everyone who is patient or tall is both not quiet and old and vice versa.
Everyone who is both patient and not calm is funny or kind and vice versa.
Everyone who is not humble is calm or not happy.
Someone is not curious.
Fred is kind or creative.
Someone is funny or not quiet.
Mary is wise.
Someone is strong or not brave.
Someone is either patient or brave.
Someone is generous. | Mary is quiet. | contradiction | (![X]:((~funny(X)&~kind(X))<=>(kind(X)&wise(X))))&
(![X]:(~strong(X)<=>~calm(X)))&
(![X]:((~wise(X)|~old(X))<=>strong(X)))&
(((~curious(lucy)<~>~creative(lucy)))<=>(?[X]:((calm(X)|~generous(X)))))&
(((~kind(susan)<~>wise(susan)))<=>(?[X]:((happy(X)&~tall(X)))))&
(((~generous(lucy)&~calm(lucy)))=>(?[X]:(strong(X))))&
(![X]:((tall(X)&~happy(X))=>(kind(X)&~wise(X))))&
((?[X]:((tall(X)|rich(X))))<=>((happy(fred)<~>~wise(fred))))&
((?[X]:(brave(X)))<=>((old(susan)&~wise(susan))))&
(((creative(lucy)<~>~patient(lucy)))=>(wise(susan)))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((creative(X)&~tall(X))<=>(~kind(X)|~brave(X))))&
(![X]:(~humble(X)=>(funny(X)<~>generous(X))))&
(![X]:((patient(X)|tall(X))<=>(~quiet(X)&old(X))))&
(![X]:((patient(X)&~calm(X))<=>(funny(X)|kind(X))))&
(![X]:(~humble(X)=>(calm(X)|~happy(X))))&
(?[X]:(~curious(X)))&
((kind(fred)|creative(fred)))&
(?[X]:((funny(X)|~quiet(X))))&
(wise(mary))&
(?[X]:((strong(X)|~brave(X))))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:(generous(X))) | quiet(mary) | [
"p0",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8023495995113951529112792
% SZS output start Proof for 8023495995113951529112792
1. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (wise(X0) & kind(X0))) [input p0]
14. ! [X0] : ((tall(X0) | patient(X0)) <=> (old(X0) & ~quiet(X0))) [input p13]
15. ! [X0] : ((~calm(X0) & patient(X0)) <=> (kind(X0) | funny(X0))) [input p14]
24. quiet(mary) [input hypothesis]
33. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 1]
34. ! [X0] : (((~kind(X0) & ~funny(X0)) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | kind(X0) | funny(X0))) [flattening 33]
65. ! [X0] : (((tall(X0) | patient(X0)) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | (~tall(X0) & ~patient(X0)))) [nnf transformation 14]
66. ! [X0] : ((tall(X0) | patient(X0) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | (~tall(X0) & ~patient(X0)))) [flattening 65]
67. ! [X0] : (((~calm(X0) & patient(X0)) | (~kind(X0) & ~funny(X0))) & ((kind(X0) | funny(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 15]
68. ! [X0] : (((~calm(X0) & patient(X0)) | (~kind(X0) & ~funny(X0))) & (kind(X0) | funny(X0) | calm(X0) | ~patient(X0))) [flattening 67]
80. kind(X0) | kind(X0) | funny(X0) [cnf transformation 34]
128. ~quiet(X0) | ~patient(X0) [cnf transformation 66]
134. ~funny(X0) | patient(X0) [cnf transformation 68]
135. ~kind(X0) | patient(X0) [cnf transformation 68]
146. quiet(mary) [cnf transformation 24]
147. kind(X0) | funny(X0) [duplicate literal removal 80]
333. ~patient(mary) [resolution 128,146]
342. funny(X0) | patient(X0) [resolution 147,135]
343. patient(X0) [subsumption resolution 342,134]
346. $false [resolution 343,333]
% SZS output end Proof for 8023495995113951529112792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not rich is rich or humble and vice versa. If someone is both not tall and not rich then susan is both humble and strong and vice versa. Everyone who is both kind and happy is both strong and not strong. If someone is humble or quiet then someone is generous or not kind. Everyone who is not creative or not happy is rich. If susan is either not curious or not patient then someone is either not creative or creative and vice versa. Everyone who is not generous is either not curious or generous. If mary is not humble then someone is either not creative or kind. Everyone who is either kind or not wise is both not happy and quiet and vice versa. If someone is either not curious or not kind then john is not curious or not kind and vice versa. If someone is both not calm and not tall then someone is either not quiet or not strong and vice versa. Everyone who is both patient and not brave is not curious and vice versa. If someone is not happy then lucy is either not patient or wise and vice versa. Everyone who is both quiet and not strong is either strong or happy. If someone is patient then mary is not strong. Everyone who is not wise is either not humble or not kind. Alice is either patient or not kind. Lucy is either not happy or calm. Someone is both wise and strong. Someone is either humble or rich. Fred is both wise and brave. Someone is both not quiet and not old. Fred is not patient or brave. | Fred is not wise. | contradiction | (![X]:((~kind(X)|~rich(X))<=>(rich(X)|humble(X))))&
((?[X]:((~tall(X)&~rich(X))))<=>((humble(susan)&strong(susan))))&
(![X]:((kind(X)&happy(X))=>(strong(X)&~strong(X))))&
((?[X]:((humble(X)|quiet(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:((~creative(X)|~happy(X))=>rich(X)))&
(((~curious(susan)<~>~patient(susan)))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~generous(X)=>(~curious(X)<~>generous(X))))&
((~humble(mary))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:((kind(X)<~>~wise(X))<=>(~happy(X)&quiet(X))))&
((?[X]:((~curious(X)<~>~kind(X))))<=>((~curious(john)|~kind(john))))&
((?[X]:((~calm(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:((patient(X)&~brave(X))<=>~curious(X)))&
((?[X]:(~happy(X)))<=>((~patient(lucy)<~>wise(lucy))))&
(![X]:((quiet(X)&~strong(X))=>(strong(X)<~>happy(X))))&
((?[X]:(patient(X)))=>(~strong(mary)))&
(![X]:(~wise(X)=>(~humble(X)<~>~kind(X))))&
((patient(alice)<~>~kind(alice)))&
((~happy(lucy)<~>calm(lucy)))&
(?[X]:((wise(X)&strong(X))))&
(?[X]:((humble(X)<~>rich(X))))&
((wise(fred)&brave(fred)))&
(?[X]:((~quiet(X)&~old(X))))&
((~patient(fred)|brave(fred))) | ~wise(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1201939286293621567519017
% SZS output start Proof for 1201939286293621567519017
21. brave(fred) & wise(fred) [input p20]
24. ~wise(fred) [input hypothesis]
149. wise(fred) [cnf transformation 21]
153. ~wise(fred) [cnf transformation 24]
351. $false [subsumption resolution 153,149]
% SZS output end Proof for 1201939286293621567519017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not brave is both not strong and strong and vice versa. Everyone who is creative is not strong and vice versa. If someone is either humble or not calm then lucy is both not creative and not rich. If someone is not old or not happy then susan is not calm or happy. Everyone who is brave is not creative. Everyone who is either not brave or not tall is humble. Everyone who is quiet is not happy or not creative and vice versa. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. If john is not strong then someone is either quiet or humble and vice versa. Paul is either humble or generous. John is either curious or rich. Someone is not humble or tall. Someone is funny. Someone is strong. Susan is both humble and calm. Someone is not old or not curious. | John is old. | neutral | (![X]:((~calm(X)|~brave(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((humble(X)<~>~calm(X))))=>((~creative(lucy)&~rich(lucy))))&
((?[X]:((~old(X)|~happy(X))))=>((~calm(susan)|happy(susan))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:((~brave(X)<~>~tall(X))=>humble(X)))&
(![X]:(quiet(X)<=>(~happy(X)|~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((humble(paul)<~>generous(paul)))&
((curious(john)<~>rich(john)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(funny(X)))&
(?[X]:(strong(X)))&
((humble(susan)&calm(susan)))&
(?[X]:((~old(X)|~curious(X)))) | old(john) | [] | null | 0 |
If someone is not happy or happy then someone is happy. Everyone who is happy or calm is not old and vice versa. Everyone who is both curious and not patient is not kind or not generous and vice versa. If lucy is both not rich and not old then john is either not quiet or generous and vice versa. If someone is not curious or not brave then alice is both not brave and not quiet and vice versa. Everyone who is not kind is both wise and not happy. If alice is brave or not strong then john is either not tall or curious and vice versa. If someone is either humble or wise then someone is strong or not kind and vice versa. Everyone who is either not funny or not creative is both not patient and calm. If paul is not funny or rich then lucy is quiet or not kind. If someone is either not humble or not generous then someone is both rich and not creative and vice versa. Everyone who is not rich is both not calm and not generous and vice versa. Everyone who is not generous is both old and funny. Everyone who is either kind or calm is either not happy or strong. If someone is either not quiet or patient then someone is both old and not creative and vice versa. Everyone who is both rich and not brave is either not rich or not funny and vice versa. Paul is not calm or quiet. Someone is either kind or not old. Someone is not quiet. Someone is not calm or not quiet. Lucy is both patient and rich. Someone is not funny or generous. | Alice is brave. | contradiction | ((?[X]:((~happy(X)|happy(X))))=>(?[X]:(happy(X))))&
(![X]:((happy(X)|calm(X))<=>~old(X)))&
(![X]:((curious(X)&~patient(X))<=>(~kind(X)|~generous(X))))&
(((~rich(lucy)&~old(lucy)))<=>((~quiet(john)<~>generous(john))))&
((?[X]:((~curious(X)|~brave(X))))<=>((~brave(alice)&~quiet(alice))))&
(![X]:(~kind(X)=>(wise(X)&~happy(X))))&
(((brave(alice)|~strong(alice)))<=>((~tall(john)<~>curious(john))))&
((?[X]:((humble(X)<~>wise(X))))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~patient(X)&calm(X))))&
(((~funny(paul)|rich(paul)))=>((quiet(lucy)|~kind(lucy))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(~rich(X)<=>(~calm(X)&~generous(X))))&
(![X]:(~generous(X)=>(old(X)&funny(X))))&
(![X]:((kind(X)<~>calm(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((~calm(paul)|quiet(paul)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
((patient(lucy)&rich(lucy)))&
(?[X]:((~funny(X)|generous(X)))) | brave(alice) | [
"p1",
"p2",
"p4",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 368154565895619949059157
% SZS output start Proof for 368154565895619949059157
2. ! [X0] : ((calm(X0) | happy(X0)) <=> ~old(X0)) [input p1]
3. ! [X0] : ((~patient(X0) & curious(X0)) <=> (~generous(X0) | ~kind(X0))) [input p2]
5. ? [X0] : (~brave(X0) | ~curious(X0)) <=> (~quiet(alice) & ~brave(alice)) [input p4]
9. ! [X0] : ((~funny(X0) <~> ~creative(X0)) => (calm(X0) & ~patient(X0))) [input p8]
10. (rich(paul) | ~funny(paul)) => (~kind(lucy) | quiet(lucy)) [input p9]
12. ! [X0] : (~rich(X0) <=> (~generous(X0) & ~calm(X0))) [input p11]
13. ! [X0] : (~generous(X0) => (funny(X0) & old(X0))) [input p12]
15. ? [X0] : (~quiet(X0) <~> patient(X0)) <=> ? [X0] : (~creative(X0) & old(X0)) [input p14]
16. ! [X0] : ((~brave(X0) & rich(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p15]
21. rich(lucy) & patient(lucy) [input p20]
23. brave(alice) [input hypothesis]
27. ? [X0] : (~quiet(X0) <~> patient(X0)) <=> ? [X1] : (~creative(X1) & old(X1)) [rectify 15]
30. ! [X0] : ((calm(X0) & ~patient(X0)) | (~funny(X0) <=> ~creative(X0))) [ennf transformation 9]
31. (~kind(lucy) | quiet(lucy)) | (~rich(paul) & funny(paul)) [ennf transformation 10]
32. ~kind(lucy) | quiet(lucy) | (~rich(paul) & funny(paul)) [flattening 31]
33. ! [X0] : ((funny(X0) & old(X0)) | generous(X0)) [ennf transformation 13]
38. ! [X0] : (((calm(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~calm(X0) & ~happy(X0)))) [nnf transformation 2]
39. ! [X0] : ((calm(X0) | happy(X0) | old(X0)) & (~old(X0) | (~calm(X0) & ~happy(X0)))) [flattening 38]
40. ! [X0] : (((~patient(X0) & curious(X0)) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | (patient(X0) | ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : (((~patient(X0) & curious(X0)) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | patient(X0) | ~curious(X0))) [flattening 40]
44. (? [X0] : (~brave(X0) | ~curious(X0)) | (quiet(alice) | brave(alice))) & ((~quiet(alice) & ~brave(alice)) | ! [X0] : (brave(X0) & curious(X0))) [nnf transformation 5]
45. (? [X0] : (~brave(X0) | ~curious(X0)) | quiet(alice) | brave(alice)) & ((~quiet(alice) & ~brave(alice)) | ! [X0] : (brave(X0) & curious(X0))) [flattening 44]
46. (? [X0] : (~brave(X0) | ~curious(X0)) | quiet(alice) | brave(alice)) & ((~quiet(alice) & ~brave(alice)) | ! [X1] : (brave(X1) & curious(X1))) [rectify 45]
47. ? [X0] : (~brave(X0) | ~curious(X0)) => (~brave(sK1) | ~curious(sK1)) [choice axiom]
48. ((~brave(sK1) | ~curious(sK1)) | quiet(alice) | brave(alice)) & ((~quiet(alice) & ~brave(alice)) | ! [X1] : (brave(X1) & curious(X1))) [skolemisation 46,47]
56. ! [X0] : ((calm(X0) & ~patient(X0)) | ((~funny(X0) | creative(X0)) & (~creative(X0) | funny(X0)))) [nnf transformation 30]
62. ! [X0] : ((~rich(X0) | (generous(X0) | calm(X0))) & ((~generous(X0) & ~calm(X0)) | rich(X0))) [nnf transformation 12]
63. ! [X0] : ((~rich(X0) | generous(X0) | calm(X0)) & ((~generous(X0) & ~calm(X0)) | rich(X0))) [flattening 62]
65. (? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | ! [X1] : (creative(X1) | ~old(X1))) & (? [X1] : (~creative(X1) & old(X1)) | ! [X0] : ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) [nnf transformation 27]
66. (? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | ! [X1] : (creative(X1) | ~old(X1))) & (? [X2] : (~creative(X2) & old(X2)) | ! [X3] : ((~quiet(X3) | ~patient(X3)) & (patient(X3) | quiet(X3)))) [rectify 65]
67. ? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) => ((~patient(sK6) | quiet(sK6)) & (patient(sK6) | ~quiet(sK6))) [choice axiom]
68. ? [X2] : (~creative(X2) & old(X2)) => (~creative(sK7) & old(sK7)) [choice axiom]
69. (((~patient(sK6) | quiet(sK6)) & (patient(sK6) | ~quiet(sK6))) | ! [X1] : (creative(X1) | ~old(X1))) & ((~creative(sK7) & old(sK7)) | ! [X3] : ((~quiet(X3) | ~patient(X3)) & (patient(X3) | quiet(X3)))) [skolemisation 66,68,67]
70. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (brave(X0) | ~rich(X0)))) [nnf transformation 16]
71. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | brave(X0) | ~rich(X0))) [flattening 70]
84. ~old(X0) | ~calm(X0) [cnf transformation 39]
89. ~patient(X0) | kind(X0) [cnf transformation 41]
98. ~brave(alice) | brave(X1) [cnf transformation 48]
119. ~funny(X0) | calm(X0) | creative(X0) [cnf transformation 56]
121. ~kind(lucy) | quiet(lucy) | ~rich(paul) [cnf transformation 32]
129. ~generous(X0) | rich(X0) [cnf transformation 63]
132. funny(X0) | generous(X0) [cnf transformation 33]
138. old(sK7) | ~quiet(X3) | ~patient(X3) [cnf transformation 69]
140. ~creative(sK7) | ~quiet(X3) | ~patient(X3) [cnf transformation 69]
145. rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 71]
148. ~brave(X0) | ~rich(X0) | funny(X0) [cnf transformation 71]
154. patient(lucy) [cnf transformation 21]
157. brave(alice) [cnf transformation 23]
159. ~funny(X0) | rich(X0) [duplicate literal removal 145]
195. 8 <=> brave(alice) [avatar definition]
212. 12 <=> ! [X1] : brave(X1) [avatar definition]
213. brave(X1) <- (12) [avatar component clause 212]
219. 12 | ~8 [avatar split clause 98,195,212]
274. 25 <=> rich(paul) [avatar definition]
276. ~rich(paul) <- (~25) [avatar component clause 274]
278. 26 <=> quiet(lucy) [avatar definition]
280. quiet(lucy) <- (26) [avatar component clause 278]
282. 27 <=> kind(lucy) [avatar definition]
285. ~25 | 26 | ~27 [avatar split clause 121,282,278,274]
338. 39 <=> ! [X3] : (~quiet(X3) | ~patient(X3)) [avatar definition]
339. ~quiet(X3) | ~patient(X3) <- (39) [avatar component clause 338]
341. 40 <=> creative(sK7) [avatar definition]
343. ~creative(sK7) <- (~40) [avatar component clause 341]
344. 39 | ~40 [avatar split clause 140,341,338]
350. 42 <=> old(sK7) [avatar definition]
352. old(sK7) <- (42) [avatar component clause 350]
353. 39 | 42 [avatar split clause 138,350,338]
386. 8 [avatar split clause 157,195]
392. kind(lucy) [resolution 89,154]
395. 27 [avatar split clause 392,282]
404. rich(X0) | generous(X0) [resolution 159,132]
405. rich(X0) [subsumption resolution 404,129]
429. ~patient(lucy) <- (26, 39) [resolution 339,280]
430. $false <- (26, 39) [subsumption resolution 429,154]
431. ~26 | ~39 [avatar contradiction clause 430]
432. $false <- (~25) [subsumption resolution 276,405]
433. 25 [avatar contradiction clause 432]
435. ~calm(sK7) <- (42) [resolution 352,84]
491. ~rich(X0) | funny(X0) <- (12) [resolution 148,213]
492. funny(X0) <- (12) [subsumption resolution 491,405]
517. creative(X1) | calm(X1) <- (12) [resolution 492,119]
599. calm(sK7) <- (12, ~40) [resolution 517,343]
603. $false <- (12, ~40, 42) [subsumption resolution 599,435]
604. ~12 | 40 | ~42 [avatar contradiction clause 603]
605. $false [avatar sat refutation 219,285,344,353,386,395,431,433,604]
% SZS output end Proof for 368154565895619949059157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or kind is either not quiet or wise and vice versa. Everyone who is wise is either old or wise. Everyone who is both not strong and not funny is both not quiet and not wise and vice versa. Everyone who is both not old and quiet is curious. If paul is generous or not brave then lucy is both generous and happy and vice versa. Everyone who is tall or creative is both kind and not funny. Everyone who is happy is either not calm or rich and vice versa. Everyone who is both not brave and not generous is either not patient or tall. Everyone who is not humble or tall is not tall. Everyone who is not brave or creative is funny and vice versa. Everyone who is not tall or not humble is either not generous or strong and vice versa. Everyone who is either creative or rich is not brave and vice versa. If fred is either creative or curious then lucy is curious and vice versa. If someone is happy then someone is either not patient or calm and vice versa. Everyone who is patient is not humble. Everyone who is not kind is both creative and humble and vice versa. Paul is either not generous or calm. Paul is wise. Paul is both brave and not funny. Someone is both not quiet and not strong. Someone is either not creative or patient. Someone is generous or old. John is either not wise or wise. | John is wise. | neutral | (![X]:((patient(X)|kind(X))<=>(~quiet(X)<~>wise(X))))&
(![X]:(wise(X)=>(old(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))<=>(~quiet(X)&~wise(X))))&
(![X]:((~old(X)&quiet(X))=>curious(X)))&
(((generous(paul)|~brave(paul)))<=>((generous(lucy)&happy(lucy))))&
(![X]:((tall(X)|creative(X))=>(kind(X)&~funny(X))))&
(![X]:(happy(X)<=>(~calm(X)<~>rich(X))))&
(![X]:((~brave(X)&~generous(X))=>(~patient(X)<~>tall(X))))&
(![X]:((~humble(X)|tall(X))=>~tall(X)))&
(![X]:((~brave(X)|creative(X))<=>funny(X)))&
(![X]:((~tall(X)|~humble(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((creative(X)<~>rich(X))<=>~brave(X)))&
(((creative(fred)<~>curious(fred)))<=>(curious(lucy)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(patient(X)=>~humble(X)))&
(![X]:(~kind(X)<=>(creative(X)&humble(X))))&
((~generous(paul)<~>calm(paul)))&
(wise(paul))&
((brave(paul)&~funny(paul)))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(?[X]:((generous(X)|old(X))))&
((~wise(john)<~>wise(john))) | wise(john) | [] | null | 0 |
If someone is both creative and not humble then someone is both not old and not wise. Everyone who is both generous and not tall is not humble or wise and vice versa. Everyone who is both not curious and not creative is humble or not generous and vice versa. If paul is not kind then fred is both curious and not happy. If someone is quiet or not generous then someone is both not old and not tall and vice versa. Everyone who is curious or strong is both not wise and not humble and vice versa. If someone is both not generous and not humble then susan is not generous. If paul is creative or wise then lucy is rich or happy and vice versa. Everyone who is both calm and not quiet is not rich or not wise. Everyone who is patient or wise is quiet and vice versa. Everyone who is both tall and generous is not tall or not creative and vice versa. If john is either kind or not humble then someone is not curious and vice versa. Everyone who is both not curious and happy is quiet or curious. If john is strong then susan is rich and vice versa. If someone is not brave or not rich then susan is either not funny or old and vice versa. Someone is either strong or not kind. Someone is not creative or patient. John is both not rich and not strong. Lucy is not patient or quiet. Lucy is generous. John is both not brave and not strong. | Paul is not tall. | contradiction | ((?[X]:((creative(X)&~humble(X))))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((generous(X)&~tall(X))<=>(~humble(X)|wise(X))))&
(![X]:((~curious(X)&~creative(X))<=>(humble(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
(((kind(john)<~>~humble(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)&happy(X))=>(quiet(X)|curious(X))))&
((strong(john))<=>(rich(susan)))&
((?[X]:((~brave(X)|~rich(X))))<=>((~funny(susan)<~>old(susan))))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:((~creative(X)|patient(X))))&
((~rich(john)&~strong(john)))&
((~patient(lucy)|quiet(lucy)))&
(generous(lucy))&
((~brave(john)&~strong(john))) | ~tall(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7629256628629525054727913
% SZS output start Proof for 7629256628629525054727913
11. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p10]
22. ~tall(paul) [input hypothesis]
49. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 11]
50. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 49]
98. tall(X0) | tall(X0) [cnf transformation 50]
124. ~tall(paul) [cnf transformation 22]
127. tall(X0) [duplicate literal removal 98]
279. $false [subsumption resolution 124,127]
% SZS output end Proof for 7629256628629525054727913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not calm then someone is quiet or not curious and vice versa.
Everyone who is not calm is rich or strong.
Everyone who is quiet or not wise is not wise or not funny.
If john is not creative or not generous then someone is not rich or not quiet and vice versa.
If someone is strong then paul is not quiet or not curious and vice versa.
If someone is old or kind then someone is both brave and not brave.
If alice is not kind then someone is not generous or humble and vice versa.
If john is curious then someone is not brave or not kind.
Everyone who is kind is generous or not patient and vice versa.
Everyone who is strong is either curious or rich and vice versa.
If lucy is generous then paul is either curious or not patient.
If mary is not brave or strong then lucy is not quiet and vice versa.
If susan is not strong then john is both curious and not patient and vice versa.
If susan is not strong or creative then someone is either strong or old.
Everyone who is both wise and not happy is curious or not curious and vice versa.
Everyone who is either not brave or generous is not wise and vice versa.
Someone is either not tall or humble.
Lucy is curious.
Someone is both strong and not tall.
Fred is both not kind and not humble.
Alice is either not brave or calm.
Lucy is rich or not strong. | Susan is not generous. | entailment | ((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:(~calm(X)=>(rich(X)|strong(X))))&
(![X]:((quiet(X)|~wise(X))=>(~wise(X)|~funny(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((?[X]:(strong(X)))<=>((~quiet(paul)|~curious(paul))))&
((?[X]:((old(X)|kind(X))))=>(?[X]:((brave(X)&~brave(X)))))&
((~kind(alice))<=>(?[X]:((~generous(X)|humble(X)))))&
((curious(john))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(kind(X)<=>(generous(X)|~patient(X))))&
(![X]:(strong(X)<=>(curious(X)<~>rich(X))))&
((generous(lucy))=>((curious(paul)<~>~patient(paul))))&
(((~brave(mary)|strong(mary)))<=>(~quiet(lucy)))&
((~strong(susan))<=>((curious(john)&~patient(john))))&
(((~strong(susan)|creative(susan)))=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:((wise(X)&~happy(X))<=>(curious(X)|~curious(X))))&
(![X]:((~brave(X)<~>generous(X))<=>~wise(X)))&
(?[X]:((~tall(X)<~>humble(X))))&
(curious(lucy))&
(?[X]:((strong(X)&~tall(X))))&
((~kind(fred)&~humble(fred)))&
((~brave(alice)<~>calm(alice)))&
((rich(lucy)|~strong(lucy))) | ~generous(susan) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8542042167860902367880026
% SZS output start Proof for 8542042167860902367880026
6. ? [X0] : (kind(X0) | old(X0)) => ? [X0] : (~brave(X0) & brave(X0)) [input p5]
9. ! [X0] : (kind(X0) <=> (~patient(X0) | generous(X0))) [input p8]
23. generous(susan) [input hypothesis]
25. ? [X0] : (kind(X0) | old(X0)) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 6]
29. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : (~kind(X0) & ~old(X0)) [ennf transformation 25]
48. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : (~kind(X1) & ~old(X1)) [rectify 29]
49. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK4) & brave(sK4)) [choice axiom]
50. (~brave(sK4) & brave(sK4)) | ! [X1] : (~kind(X1) & ~old(X1)) [skolemisation 48,49]
57. ! [X0] : ((kind(X0) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | ~kind(X0))) [nnf transformation 9]
58. ! [X0] : ((kind(X0) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | ~kind(X0))) [flattening 57]
91. brave(sK4) | ~kind(X1) [cnf transformation 50]
93. ~brave(sK4) | ~kind(X1) [cnf transformation 50]
99. ~generous(X0) | kind(X0) [cnf transformation 58]
136. generous(susan) [cnf transformation 23]
212. 18 <=> ! [X1] : ~kind(X1) [avatar definition]
213. ~kind(X1) <- (18) [avatar component clause 212]
215. 19 <=> brave(sK4) [avatar definition]
218. 18 | ~19 [avatar split clause 93,215,212]
223. 18 | 19 [avatar split clause 91,215,212]
344. kind(susan) [resolution 99,136]
345. $false <- (18) [subsumption resolution 344,213]
346. ~18 [avatar contradiction clause 345]
347. $false [avatar sat refutation 218,223,346]
% SZS output end Proof for 8542042167860902367880026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not kind is either not tall or patient and vice versa.
If mary is either not patient or tall then lucy is either not generous or not creative.
If someone is either not generous or wise then someone is strong.
Everyone who is curious is not kind.
Everyone who is curious or not curious is both not quiet and kind.
Everyone who is strong or not happy is both wise and funny.
Everyone who is both not kind and generous is not old or calm.
If someone is not creative or wise then lucy is both funny and rich.
If someone is not calm or not patient then someone is quiet or not tall and vice versa.
Everyone who is old is quiet or funny and vice versa.
Everyone who is either strong or not calm is either patient or not strong.
If susan is both strong and not brave then lucy is either not tall or not kind.
Everyone who is not brave is not generous and vice versa.
If someone is not generous or not happy then fred is strong or not tall and vice versa.
Everyone who is both wise and not curious is rich or not old and vice versa.
Lucy is generous.
Someone is both patient and not rich.
Someone is not strong. | Fred is tall. | neutral | (![X]:((happy(X)<~>~kind(X))<=>(~tall(X)<~>patient(X))))&
(((~patient(mary)<~>tall(mary)))=>((~generous(lucy)<~>~creative(lucy))))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:(strong(X))))&
(![X]:(curious(X)=>~kind(X)))&
(![X]:((curious(X)|~curious(X))=>(~quiet(X)&kind(X))))&
(![X]:((strong(X)|~happy(X))=>(wise(X)&funny(X))))&
(![X]:((~kind(X)&generous(X))=>(~old(X)|calm(X))))&
((?[X]:((~creative(X)|wise(X))))=>((funny(lucy)&rich(lucy))))&
((?[X]:((~calm(X)|~patient(X))))<=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:(old(X)<=>(quiet(X)|funny(X))))&
(![X]:((strong(X)<~>~calm(X))=>(patient(X)<~>~strong(X))))&
(((strong(susan)&~brave(susan)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~brave(X)<=>~generous(X)))&
((?[X]:((~generous(X)|~happy(X))))<=>((strong(fred)|~tall(fred))))&
(![X]:((wise(X)&~curious(X))<=>(rich(X)|~old(X))))&
(generous(lucy))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:(~strong(X))) | tall(fred) | [] | null | 0 |
Everyone who is creative is generous and vice versa.
If someone is not wise then someone is quiet.
Everyone who is strong or rich is not patient and vice versa.
If alice is not calm then alice is not curious.
Everyone who is kind or happy is not wise or not strong and vice versa.
If susan is either funny or calm then someone is happy or not patient and vice versa.
Everyone who is not quiet is either tall or not wise and vice versa.
If someone is either creative or not quiet then fred is humble or not wise.
Everyone who is either tall or not curious is not creative or not kind.
Everyone who is kind is either not happy or calm.
Everyone who is happy or not quiet is rich or not wise.
If lucy is not patient then someone is both patient and not calm.
Everyone who is not brave is not funny or not patient and vice versa.
If susan is either not quiet or not calm then john is both rich and not funny.
If someone is not brave then paul is funny and vice versa.
If mary is not wise or old then someone is both funny and rich and vice versa.
Mary is both not humble and not curious.
Someone is not kind or generous.
Paul is either not humble or creative.
Someone is not creative or curious.
Mary is both not brave and not old.
Mary is either not wise or not brave.
Someone is happy. | Lucy is not quiet. | neutral | (![X]:(creative(X)<=>generous(X)))&
((?[X]:(~wise(X)))=>(?[X]:(quiet(X))))&
(![X]:((strong(X)|rich(X))<=>~patient(X)))&
((~calm(alice))=>(~curious(alice)))&
(![X]:((kind(X)|happy(X))<=>(~wise(X)|~strong(X))))&
(((funny(susan)<~>calm(susan)))<=>(?[X]:((happy(X)|~patient(X)))))&
(![X]:(~quiet(X)<=>(tall(X)<~>~wise(X))))&
((?[X]:((creative(X)<~>~quiet(X))))=>((humble(fred)|~wise(fred))))&
(![X]:((tall(X)<~>~curious(X))=>(~creative(X)|~kind(X))))&
(![X]:(kind(X)=>(~happy(X)<~>calm(X))))&
(![X]:((happy(X)|~quiet(X))=>(rich(X)|~wise(X))))&
((~patient(lucy))=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:(~brave(X)<=>(~funny(X)|~patient(X))))&
(((~quiet(susan)<~>~calm(susan)))=>((rich(john)&~funny(john))))&
((?[X]:(~brave(X)))<=>(funny(paul)))&
(((~wise(mary)|old(mary)))<=>(?[X]:((funny(X)&rich(X)))))&
((~humble(mary)&~curious(mary)))&
(?[X]:((~kind(X)|generous(X))))&
((~humble(paul)<~>creative(paul)))&
(?[X]:((~creative(X)|curious(X))))&
((~brave(mary)&~old(mary)))&
((~wise(mary)<~>~brave(mary)))&
(?[X]:(happy(X))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is funny is both not kind and wise.
Everyone who is happy or not quiet is not quiet and vice versa.
Everyone who is either not brave or not old is calm and vice versa.
If someone is both old and not generous then someone is brave and vice versa.
If someone is both not wise and not quiet then someone is humble or brave.
Everyone who is either curious or wise is both funny and strong.
Everyone who is not generous is both creative and patient and vice versa.
If someone is creative or not old then paul is calm.
If someone is both calm and old then lucy is either rich or not quiet and vice versa.
If someone is both quiet and old then someone is either not wise or happy and vice versa.
Everyone who is both not funny and kind is both curious and not happy and vice versa.
Everyone who is both brave and generous is both not creative and funny and vice versa.
If paul is both not patient and creative then someone is funny and vice versa.
Everyone who is either happy or calm is either not kind or calm and vice versa.
If someone is either old or tall then someone is tall and vice versa.
If susan is both not humble and kind then fred is both not calm and old.
Susan is both tall and not generous.
Someone is not wise or tall.
John is both not quiet and not creative.
Someone is curious.
Someone is not calm.
Someone is either not humble or happy.
Fred is either wise or calm.
Mary is not creative. | Fred is not old. | neutral | (![X]:(funny(X)=>(~kind(X)&wise(X))))&
(![X]:((happy(X)|~quiet(X))<=>~quiet(X)))&
(![X]:((~brave(X)<~>~old(X))<=>calm(X)))&
((?[X]:((old(X)&~generous(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~wise(X)&~quiet(X))))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:((curious(X)<~>wise(X))=>(funny(X)&strong(X))))&
(![X]:(~generous(X)<=>(creative(X)&patient(X))))&
((?[X]:((creative(X)|~old(X))))=>(calm(paul)))&
((?[X]:((calm(X)&old(X))))<=>((rich(lucy)<~>~quiet(lucy))))&
((?[X]:((quiet(X)&old(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
(![X]:((~funny(X)&kind(X))<=>(curious(X)&~happy(X))))&
(![X]:((brave(X)&generous(X))<=>(~creative(X)&funny(X))))&
(((~patient(paul)&creative(paul)))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)<~>calm(X))<=>(~kind(X)<~>calm(X))))&
((?[X]:((old(X)<~>tall(X))))<=>(?[X]:(tall(X))))&
(((~humble(susan)&kind(susan)))=>((~calm(fred)&old(fred))))&
((tall(susan)&~generous(susan)))&
(?[X]:((~wise(X)|tall(X))))&
((~quiet(john)&~creative(john)))&
(?[X]:(curious(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~humble(X)<~>happy(X))))&
((wise(fred)<~>calm(fred)))&
(~creative(mary)) | ~old(fred) | [] | null | 0 |
If someone is happy then alice is patient and vice versa.
If alice is both not happy and creative then lucy is both curious and not kind and vice versa.
Everyone who is not old is tall.
Everyone who is both not old and not happy is creative or humble and vice versa.
Everyone who is either happy or not funny is not tall or humble and vice versa.
Everyone who is either not creative or tall is not humble.
Everyone who is curious or brave is both humble and quiet and vice versa.
Everyone who is both not brave and not rich is not brave.
Everyone who is not brave or wise is either tall or funny.
Everyone who is either funny or not curious is generous.
If someone is patient or quiet then susan is both funny and not quiet.
Everyone who is kind is either not generous or not kind and vice versa.
Everyone who is not strong is both humble and not brave and vice versa.
Everyone who is rich or calm is not funny.
Everyone who is either wise or quiet is either quiet or funny and vice versa.
If someone is generous then lucy is either calm or not creative.
Someone is not generous.
Lucy is either tall or not brave.
Someone is curious.
Susan is not generous.
Lucy is either not brave or not calm.
Someone is both not funny and not generous.
Mary is patient or brave. | Susan is wise. | entailment | ((?[X]:(happy(X)))<=>(patient(alice)))&
(((~happy(alice)&creative(alice)))<=>((curious(lucy)&~kind(lucy))))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((~old(X)&~happy(X))<=>(creative(X)|humble(X))))&
(![X]:((happy(X)<~>~funny(X))<=>(~tall(X)|humble(X))))&
(![X]:((~creative(X)<~>tall(X))=>~humble(X)))&
(![X]:((curious(X)|brave(X))<=>(humble(X)&quiet(X))))&
(![X]:((~brave(X)&~rich(X))=>~brave(X)))&
(![X]:((~brave(X)|wise(X))=>(tall(X)<~>funny(X))))&
(![X]:((funny(X)<~>~curious(X))=>generous(X)))&
((?[X]:((patient(X)|quiet(X))))=>((funny(susan)&~quiet(susan))))&
(![X]:(kind(X)<=>(~generous(X)<~>~kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~brave(X))))&
(![X]:((rich(X)|calm(X))=>~funny(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(quiet(X)<~>funny(X))))&
((?[X]:(generous(X)))=>((calm(lucy)<~>~creative(lucy))))&
(?[X]:(~generous(X)))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:(curious(X)))&
(~generous(susan))&
((~brave(lucy)<~>~calm(lucy)))&
(?[X]:((~funny(X)&~generous(X))))&
((patient(mary)|brave(mary))) | wise(susan) | [
"p6",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8204232343232923080834299
% SZS output start Proof for 8204232343232923080834299
7. ! [X0] : ((brave(X0) | curious(X0)) <=> (quiet(X0) & humble(X0))) [input p6]
11. ? [X0] : (quiet(X0) | patient(X0)) => (~quiet(susan) & funny(susan)) [input p10]
15. ! [X0] : ((wise(X0) <~> quiet(X0)) <=> (quiet(X0) <~> funny(X0))) [input p14]
19. ? [X0] : curious(X0) [input p18]
24. ~wise(susan) [input hypothesis]
31. (~quiet(susan) & funny(susan)) | ! [X0] : (~quiet(X0) & ~patient(X0)) [ennf transformation 11]
45. ! [X0] : (((brave(X0) | curious(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 7]
46. ! [X0] : ((brave(X0) | curious(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 45]
50. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [nnf transformation 15]
55. ? [X0] : curious(X0) => curious(sK2) [choice axiom]
56. curious(sK2) [skolemisation 19,55]
82. ~curious(X0) | quiet(X0) [cnf transformation 46]
93. funny(susan) | ~quiet(X0) [cnf transformation 31]
105. ~funny(X0) | ~quiet(X0) | wise(X0) | ~quiet(X0) [cnf transformation 50]
107. quiet(X0) | wise(X0) | quiet(X0) | ~funny(X0) [cnf transformation 50]
115. curious(sK2) [cnf transformation 56]
122. ~wise(susan) [cnf transformation 24]
124. ~funny(X0) | ~quiet(X0) | wise(X0) [duplicate literal removal 105]
125. quiet(X0) | wise(X0) | ~funny(X0) [duplicate literal removal 107]
165. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
166. ~quiet(X0) <- (8) [avatar component clause 165]
177. 11 <=> funny(susan) [avatar definition]
179. funny(susan) <- (11) [avatar component clause 177]
180. 8 | 11 [avatar split clause 93,177,165]
183. ~funny(X0) | wise(X0) [subsumption resolution 124,125]
218. quiet(sK2) [resolution 82,115]
219. $false <- (8) [subsumption resolution 218,166]
220. ~8 [avatar contradiction clause 219]
223. wise(susan) <- (11) [resolution 183,179]
224. $false <- (11) [subsumption resolution 223,122]
225. ~11 [avatar contradiction clause 224]
226. $false [avatar sat refutation 180,220,225]
% SZS output end Proof for 8204232343232923080834299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either brave or kind then someone is both not creative and rich and vice versa.
Everyone who is both not generous and not kind is not creative.
Everyone who is funny or not old is either not strong or not kind and vice versa.
Everyone who is both not old and not quiet is wise or old and vice versa.
Everyone who is both creative and rich is either old or not rich and vice versa.
If someone is humble then someone is old and vice versa.
If john is both not strong and not creative then mary is either kind or strong.
If fred is either generous or not brave then alice is generous.
Everyone who is not funny or not kind is either not quiet or brave.
If mary is patient or calm then susan is old or humble and vice versa.
If john is tall then someone is kind and vice versa.
Everyone who is quiet or not wise is brave or rich and vice versa.
If paul is wise or not strong then someone is not wise or rich and vice versa.
If mary is either not generous or not patient then someone is both generous and calm and vice versa.
Everyone who is both not calm and humble is both funny and wise.
If susan is either rich or patient then someone is not creative and vice versa.
Lucy is not tall or curious.
Someone is either curious or not generous.
Lucy is generous or quiet.
Someone is not old.
Someone is both not patient and not tall.
Fred is both not tall and quiet.
Someone is either not funny or not kind.
Paul is either quiet or not brave. | Lucy is not humble. | entailment | (((brave(alice)<~>kind(alice)))<=>(?[X]:((~creative(X)&rich(X)))))&
(![X]:((~generous(X)&~kind(X))=>~creative(X)))&
(![X]:((funny(X)|~old(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:((~old(X)&~quiet(X))<=>(wise(X)|old(X))))&
(![X]:((creative(X)&rich(X))<=>(old(X)<~>~rich(X))))&
((?[X]:(humble(X)))<=>(?[X]:(old(X))))&
(((~strong(john)&~creative(john)))=>((kind(mary)<~>strong(mary))))&
(((generous(fred)<~>~brave(fred)))=>(generous(alice)))&
(![X]:((~funny(X)|~kind(X))=>(~quiet(X)<~>brave(X))))&
(((patient(mary)|calm(mary)))<=>((old(susan)|humble(susan))))&
((tall(john))<=>(?[X]:(kind(X))))&
(![X]:((quiet(X)|~wise(X))<=>(brave(X)|rich(X))))&
(((wise(paul)|~strong(paul)))<=>(?[X]:((~wise(X)|rich(X)))))&
(((~generous(mary)<~>~patient(mary)))<=>(?[X]:((generous(X)&calm(X)))))&
(![X]:((~calm(X)&humble(X))=>(funny(X)&wise(X))))&
(((rich(susan)<~>patient(susan)))<=>(?[X]:(~creative(X))))&
((~tall(lucy)|curious(lucy)))&
(?[X]:((curious(X)<~>~generous(X))))&
((generous(lucy)|quiet(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((~patient(X)&~tall(X))))&
((~tall(fred)&quiet(fred)))&
(?[X]:((~funny(X)<~>~kind(X))))&
((quiet(paul)<~>~brave(paul))) | ~humble(lucy) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6143073079994017090331656
% SZS output start Proof for 6143073079994017090331656
4. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (old(X0) | wise(X0))) [input p3]
6. ? [X0] : humble(X0) <=> ? [X0] : old(X0) [input p5]
25. humble(lucy) [input hypothesis]
26. ? [X0] : humble(X0) <=> ? [X1] : old(X1) [rectify 6]
41. ! [X0] : (((~quiet(X0) & ~old(X0)) | (~old(X0) & ~wise(X0))) & ((old(X0) | wise(X0)) | (quiet(X0) | old(X0)))) [nnf transformation 4]
42. ! [X0] : (((~quiet(X0) & ~old(X0)) | (~old(X0) & ~wise(X0))) & (old(X0) | wise(X0) | quiet(X0) | old(X0))) [flattening 41]
45. (? [X0] : humble(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : ~humble(X0)) [nnf transformation 26]
46. (? [X0] : humble(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : ~humble(X3)) [rectify 45]
47. ? [X0] : humble(X0) => humble(sK1) [choice axiom]
48. ? [X2] : old(X2) => old(sK2) [choice axiom]
49. (humble(sK1) | ! [X1] : ~old(X1)) & (old(sK2) | ! [X3] : ~humble(X3)) [skolemisation 46,48,47]
100. ~old(X0) | ~old(X0) [cnf transformation 42]
109. old(sK2) | ~humble(X3) [cnf transformation 49]
158. humble(lucy) [cnf transformation 25]
162. ~old(X0) [duplicate literal removal 100]
192. ~humble(X3) [subsumption resolution 109,162]
315. $false [subsumption resolution 158,192]
% SZS output end Proof for 6143073079994017090331656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or generous is quiet or not tall. Everyone who is either happy or kind is either not quiet or not happy and vice versa. If alice is not generous then someone is either old or not happy. Everyone who is either brave or not generous is either not curious or rich. Everyone who is both strong and brave is brave and vice versa. If someone is either not wise or strong then someone is not calm and vice versa. If susan is either not old or kind then paul is either not calm or rich and vice versa. Everyone who is kind or old is humble or quiet and vice versa. If someone is either not generous or funny then someone is strong or not creative and vice versa. Everyone who is old or not kind is either not rich or not generous and vice versa. If fred is not rich then someone is both humble and not strong and vice versa. If susan is not quiet then someone is kind or not funny and vice versa. If someone is either tall or generous then mary is both tall and brave. Everyone who is calm or not humble is either tall or not humble. Everyone who is not kind is not wise. Everyone who is not brave or not generous is both patient and strong. Someone is either tall or not wise. Someone is kind or not humble. Someone is creative or funny. Lucy is not tall. Someone is brave or not humble. Someone is tall. Paul is brave or tall. | Alice is not quiet. | neutral | (![X]:((rich(X)|generous(X))=>(quiet(X)|~tall(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~quiet(X)<~>~happy(X))))&
((~generous(alice))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
(((~old(susan)<~>kind(susan)))<=>((~calm(paul)<~>rich(paul))))&
(![X]:((kind(X)|old(X))<=>(humble(X)|quiet(X))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((old(X)|~kind(X))<=>(~rich(X)<~>~generous(X))))&
((~rich(fred))<=>(?[X]:((humble(X)&~strong(X)))))&
((~quiet(susan))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((tall(mary)&brave(mary))))&
(![X]:((calm(X)|~humble(X))=>(tall(X)<~>~humble(X))))&
(![X]:(~kind(X)=>~wise(X)))&
(![X]:((~brave(X)|~generous(X))=>(patient(X)&strong(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:((creative(X)|funny(X))))&
(~tall(lucy))&
(?[X]:((brave(X)|~humble(X))))&
(?[X]:(tall(X)))&
((brave(paul)|tall(paul))) | ~quiet(alice) | [] | null | 0 |
If someone is either not humble or not patient then someone is calm and vice versa.
If someone is either not strong or not patient then paul is both generous and rich and vice versa.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Susan is not kind or curious.
Someone is old. | Lucy is not creative. | entailment | ((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((generous(paul)&rich(paul))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X))) | ~creative(lucy) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 410560466285005589395993
% SZS output start Proof for 410560466285005589395993
1. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X0] : calm(X0) [input p0]
2. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> (rich(paul) & generous(paul)) [input p1]
5. ! [X0] : (brave(X0) <=> (~generous(X0) <~> humble(X0))) [input p4]
6. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | creative(X0)) => brave(X0)) [input p7]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p8]
12. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p11]
21. creative(lucy) [input hypothesis]
22. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X1] : calm(X1) [rectify 1]
24. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 12]
25. ! [X0] : (brave(X0) => (~generous(X0) <~> humble(X0))) [unused predicate definition removal 5]
28. ! [X0] : ((~generous(X0) <~> humble(X0)) | ~brave(X0)) [ennf transformation 25]
29. ! [X0] : (brave(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 8]
37. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 22]
38. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) => ((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) [choice axiom]
40. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
41. (((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [skolemisation 38,40,39]
42. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~rich(paul) | ~generous(paul))) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 2]
43. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [flattening 42]
44. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [rectify 43]
45. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) [choice axiom]
46. (((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [skolemisation 44,45]
47. ! [X0] : (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~brave(X0)) [nnf transformation 28]
48. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 6]
49. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 48]
52. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 9]
53. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 52]
58. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 24]
59. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 58]
60. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK4) & generous(sK4)) [choice axiom]
61. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
62. ((~funny(sK4) & generous(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 59,61,60]
69. calm(sK1) | ~patient(X3) | humble(X3) [cnf transformation 41]
74. generous(paul) | ~strong(X1) | patient(X1) [cnf transformation 46]
80. ~brave(X0) | generous(X0) | ~humble(X0) [cnf transformation 47]
82. ~strong(X0) | generous(X0) | ~calm(X0) | curious(X0) [cnf transformation 49]
93. ~creative(X0) | brave(X0) [cnf transformation 29]
95. strong(X0) | strong(X0) [cnf transformation 53]
97. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
106. generous(sK4) | ~curious(X1) [cnf transformation 62]
125. creative(lucy) [cnf transformation 21]
126. strong(X0) [duplicate literal removal 95]
127. ~generous(X0) | ~strong(X0) [duplicate literal removal 97]
147. 5 <=> calm(sK1) [avatar definition]
149. calm(sK1) <- (5) [avatar component clause 147]
152. 6 <=> ! [X3] : (~patient(X3) | humble(X3)) [avatar definition]
153. ~patient(X3) | humble(X3) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 69,147,152]
156. 7 <=> generous(paul) [avatar definition]
157. generous(paul) <- (7) [avatar component clause 156]
174. 11 <=> ! [X1] : (~strong(X1) | patient(X1)) [avatar definition]
175. ~strong(X1) | patient(X1) <- (11) [avatar component clause 174]
181. 11 | 7 [avatar split clause 74,156,174]
209. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
210. ~curious(X1) <- (18) [avatar component clause 209]
217. 20 <=> generous(sK4) [avatar definition]
219. generous(sK4) <- (20) [avatar component clause 217]
220. 18 | 20 [avatar split clause 106,217,209]
274. brave(lucy) [resolution 93,125]
278. ~strong(paul) <- (7) [resolution 127,157]
280. $false <- (7) [subsumption resolution 278,126]
281. ~7 [avatar contradiction clause 280]
282. patient(X1) <- (11) [subsumption resolution 175,126]
296. 34 <=> generous(lucy) [avatar definition]
297. generous(lucy) <- (34) [avatar component clause 296]
300. generous(lucy) | ~humble(lucy) [resolution 80,274]
318. generous(X0) | ~calm(X0) | curious(X0) [resolution 82,126]
319. ~calm(X0) | generous(X0) <- (18) [subsumption resolution 318,210]
320. generous(sK1) <- (5, 18) [resolution 319,149]
343. ~strong(sK1) <- (5, 18) [resolution 320,127]
344. $false <- (5, 18) [subsumption resolution 343,126]
345. ~5 | ~18 [avatar contradiction clause 344]
349. ~strong(sK4) <- (20) [resolution 219,127]
361. $false <- (20) [subsumption resolution 349,126]
362. ~20 [avatar contradiction clause 361]
363. humble(X3) <- (6, 11) [subsumption resolution 153,282]
376. generous(lucy) <- (6, 11) [subsumption resolution 300,363]
377. 34 | ~6 | ~11 [avatar split clause 376,174,152,296]
404. ~strong(lucy) <- (34) [resolution 297,127]
418. $false <- (34) [subsumption resolution 404,126]
419. ~34 [avatar contradiction clause 418]
420. $false [avatar sat refutation 154,181,220,281,345,362,377,419]
% SZS output end Proof for 410560466285005589395993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not wise then someone is not calm or not humble.
If someone is either not creative or not happy then someone is either tall or not old and vice versa.
Everyone who is not generous or not calm is not curious.
If someone is curious or not strong then paul is not patient.
If someone is either tall or brave then alice is not tall or patient and vice versa.
Everyone who is rich or tall is funny or not quiet and vice versa.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
Someone is generous.
Someone is either humble or generous.
Someone is calm.
Someone is not tall.
Paul is both curious and old.
Someone is not humble or not rich. | Paul is happy. | contradiction | ((~wise(paul))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((~generous(X)|~calm(X))=>~curious(X)))&
((?[X]:((curious(X)|~strong(X))))=>(~patient(paul)))&
((?[X]:((tall(X)<~>brave(X))))<=>((~tall(alice)|patient(alice))))&
(![X]:((rich(X)|tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(?[X]:(generous(X)))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
((curious(paul)&old(paul)))&
(?[X]:((~humble(X)|~rich(X)))) | happy(paul) | [
"p2",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 265762869120399827886791
% SZS output start Proof for 265762869120399827886791
3. ! [X0] : ((~calm(X0) | ~generous(X0)) => ~curious(X0)) [input p2]
13. ? [X0] : (happy(X0) <~> creative(X0)) => (creative(fred) <~> ~calm(fred)) [input p12]
15. ! [X0] : (patient(X0) <=> (creative(X0) & ~patient(X0))) [input p14]
16. ! [X0] : (creative(X0) <=> (~curious(X0) | creative(X0))) [input p15]
23. happy(paul) [input hypothesis]
27. ! [X0] : (~curious(X0) | (calm(X0) & generous(X0))) [ennf transformation 3]
33. (creative(fred) <~> ~calm(fred)) | ! [X0] : (happy(X0) <=> creative(X0)) [ennf transformation 13]
63. ((calm(fred) | ~creative(fred)) & (~calm(fred) | creative(fred))) | ! [X0] : ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0))) [nnf transformation 33]
65. ! [X0] : ((patient(X0) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 15]
66. ! [X0] : ((patient(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [flattening 65]
67. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 16]
68. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~creative(X0))) [flattening 67]
90. ~curious(X0) | calm(X0) [cnf transformation 27]
125. ~calm(fred) | creative(fred) | creative(X0) | ~happy(X0) [cnf transformation 63]
133. ~patient(X0) | ~patient(X0) [cnf transformation 66]
135. patient(X0) | ~creative(X0) | patient(X0) [cnf transformation 66]
138. curious(X0) | creative(X0) [cnf transformation 68]
147. happy(paul) [cnf transformation 23]
148. ~patient(X0) [duplicate literal removal 133]
149. ~creative(X0) | patient(X0) [duplicate literal removal 135]
194. 11 <=> ! [X3] : (~happy(X3) | creative(X3)) [avatar definition]
195. ~happy(X3) | creative(X3) <- (11) [avatar component clause 194]
301. 34 <=> creative(fred) [avatar definition]
302. creative(fred) <- (34) [avatar component clause 301]
303. ~creative(fred) <- (~34) [avatar component clause 301]
305. 35 <=> calm(fred) [avatar definition]
306. ~calm(fred) <- (~35) [avatar component clause 305]
311. 11 | 34 | ~35 [avatar split clause 125,305,301,194]
337. creative(X1) | calm(X1) [resolution 138,90]
367. calm(fred) <- (~34) [resolution 337,303]
370. $false <- (~34, ~35) [subsumption resolution 367,306]
371. 34 | 35 [avatar contradiction clause 370]
373. patient(fred) <- (34) [resolution 302,149]
374. $false <- (34) [subsumption resolution 373,148]
375. ~34 [avatar contradiction clause 374]
382. creative(paul) <- (11) [resolution 195,147]
394. patient(paul) <- (11) [resolution 382,149]
395. $false <- (11) [subsumption resolution 394,148]
396. ~11 [avatar contradiction clause 395]
397. $false [avatar sat refutation 311,371,375,396]
% SZS output end Proof for 265762869120399827886791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or brave is not quiet or not humble.
If paul is both not generous and rich then john is either not kind or calm.
Everyone who is not calm is wise or creative and vice versa.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.
Everyone who is both old and not old is both rich and funny and vice versa.
If someone is either not wise or not funny then mary is both not humble and not happy.
If someone is kind or tall then susan is either not patient or not happy and vice versa.
Everyone who is brave is both kind and not kind and vice versa.
Everyone who is both generous and not creative is quiet or not happy and vice versa.
If susan is not creative then mary is both not strong and patient and vice versa.
If mary is not strong or kind then paul is not tall and vice versa.
Everyone who is either not generous or patient is not brave and vice versa.
Everyone who is both not rich and not patient is either calm or not old and vice versa.
Everyone who is not happy or rich is not patient or rich and vice versa.
Everyone who is happy or not strong is either not curious or not patient.
Lucy is kind or brave.
Someone is not brave.
Someone is both not happy and old.
Alice is either not creative or not curious.
John is either not kind or not patient.
Susan is either not brave or not strong.
John is either old or not humble. | Susan is not generous. | neutral | (![X]:((~humble(X)|brave(X))=>(~quiet(X)|~humble(X))))&
(((~generous(paul)&rich(paul)))=>((~kind(john)<~>calm(john))))&
(![X]:(~calm(X)<=>(wise(X)|creative(X))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~humble(mary)&~happy(mary))))&
((?[X]:((kind(X)|tall(X))))<=>((~patient(susan)<~>~happy(susan))))&
(![X]:(brave(X)<=>(kind(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(quiet(X)|~happy(X))))&
((~creative(susan))<=>((~strong(mary)&patient(mary))))&
(((~strong(mary)|kind(mary)))<=>(~tall(paul)))&
(![X]:((~generous(X)<~>patient(X))<=>~brave(X)))&
(![X]:((~rich(X)&~patient(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((kind(lucy)|brave(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)&old(X))))&
((~creative(alice)<~>~curious(alice)))&
((~kind(john)<~>~patient(john)))&
((~brave(susan)<~>~strong(susan)))&
((old(john)<~>~humble(john))) | ~generous(susan) | [] | null | 0 |
Everyone who is curious or wise is either creative or not rich and vice versa.
If someone is either wise or happy then alice is both not happy and quiet and vice versa.
Everyone who is both brave and creative is both not quiet and not patient.
Everyone who is not rich or curious is quiet.
Everyone who is creative is either calm or strong.
If someone is both not generous and not quiet then alice is both not rich and curious and vice versa.
Everyone who is brave is not quiet or rich and vice versa.
If john is not curious or not brave then someone is brave or humble.
If paul is not generous or kind then someone is both generous and quiet.
Everyone who is either not tall or happy is not funny and vice versa.
Everyone who is not old or not funny is both wise and quiet and vice versa.
Everyone who is not strong is not quiet.
Everyone who is both patient and happy is either not quiet or not happy.
Everyone who is not curious or tall is not strong or not quiet.
Everyone who is old is brave or quiet.
If lucy is not old then fred is not creative.
John is old or wise.
Alice is both calm and not humble.
Paul is either not tall or quiet.
John is not humble or not kind.
John is curious or patient.
Someone is funny.
Susan is either quiet or not generous.
Paul is either funny or curious. | John is not curious. | neutral | (![X]:((curious(X)|wise(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((wise(X)<~>happy(X))))<=>((~happy(alice)&quiet(alice))))&
(![X]:((brave(X)&creative(X))=>(~quiet(X)&~patient(X))))&
(![X]:((~rich(X)|curious(X))=>quiet(X)))&
(![X]:(creative(X)=>(calm(X)<~>strong(X))))&
((?[X]:((~generous(X)&~quiet(X))))<=>((~rich(alice)&curious(alice))))&
(![X]:(brave(X)<=>(~quiet(X)|rich(X))))&
(((~curious(john)|~brave(john)))=>(?[X]:((brave(X)|humble(X)))))&
(((~generous(paul)|kind(paul)))=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((~tall(X)<~>happy(X))<=>~funny(X)))&
(![X]:((~old(X)|~funny(X))<=>(wise(X)&quiet(X))))&
(![X]:(~strong(X)=>~quiet(X)))&
(![X]:((patient(X)&happy(X))=>(~quiet(X)<~>~happy(X))))&
(![X]:((~curious(X)|tall(X))=>(~strong(X)|~quiet(X))))&
(![X]:(old(X)=>(brave(X)|quiet(X))))&
((~old(lucy))=>(~creative(fred)))&
((old(john)|wise(john)))&
((calm(alice)&~humble(alice)))&
((~tall(paul)<~>quiet(paul)))&
((~humble(john)|~kind(john)))&
((curious(john)|patient(john)))&
(?[X]:(funny(X)))&
((quiet(susan)<~>~generous(susan)))&
((funny(paul)<~>curious(paul))) | ~curious(john) | [] | null | 0 |
Everyone who is generous or not curious is either not happy or humble. Everyone who is not curious is either not calm or creative. Everyone who is both patient and funny is not tall or old and vice versa. Everyone who is either funny or not old is not patient. Everyone who is not calm is either not old or humble and vice versa. If alice is both not funny and not wise then someone is generous. Everyone who is strong or humble is not funny and vice versa. If susan is happy or not creative then someone is patient and vice versa. Everyone who is either not tall or curious is not generous or not happy. If someone is patient or calm then alice is not strong or not creative and vice versa. If john is not creative or patient then susan is not happy and vice versa. If lucy is old then paul is kind. If someone is not quiet or not curious then someone is not kind or not old and vice versa. If lucy is either generous or not curious then someone is not tall or not curious and vice versa. Everyone who is both rich and not happy is not curious or not generous. Everyone who is both not strong and curious is not rich or not brave. Someone is not old or old. Someone is not curious. Someone is curious or calm. Mary is either quiet or not quiet. Mary is wise or quiet. Someone is either creative or not curious. Susan is either not brave or not generous. Someone is tall or not humble. | Mary is not quiet. | neutral | (![X]:((generous(X)|~curious(X))=>(~happy(X)<~>humble(X))))&
(![X]:(~curious(X)=>(~calm(X)<~>creative(X))))&
(![X]:((patient(X)&funny(X))<=>(~tall(X)|old(X))))&
(![X]:((funny(X)<~>~old(X))=>~patient(X)))&
(![X]:(~calm(X)<=>(~old(X)<~>humble(X))))&
(((~funny(alice)&~wise(alice)))=>(?[X]:(generous(X))))&
(![X]:((strong(X)|humble(X))<=>~funny(X)))&
(((happy(susan)|~creative(susan)))<=>(?[X]:(patient(X))))&
(![X]:((~tall(X)<~>curious(X))=>(~generous(X)|~happy(X))))&
((?[X]:((patient(X)|calm(X))))<=>((~strong(alice)|~creative(alice))))&
(((~creative(john)|patient(john)))<=>(~happy(susan)))&
((old(lucy))=>(kind(paul)))&
((?[X]:((~quiet(X)|~curious(X))))<=>(?[X]:((~kind(X)|~old(X)))))&
(((generous(lucy)<~>~curious(lucy)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((rich(X)&~happy(X))=>(~curious(X)|~generous(X))))&
(![X]:((~strong(X)&curious(X))=>(~rich(X)|~brave(X))))&
(?[X]:((~old(X)|old(X))))&
(?[X]:(~curious(X)))&
(?[X]:((curious(X)|calm(X))))&
((quiet(mary)<~>~quiet(mary)))&
((wise(mary)|quiet(mary)))&
(?[X]:((creative(X)<~>~curious(X))))&
((~brave(susan)<~>~generous(susan)))&
(?[X]:((tall(X)|~humble(X)))) | ~quiet(mary) | [] | null | 0 |
Everyone who is both brave and not calm is kind or not strong and vice versa. Everyone who is either brave or not rich is either old or creative and vice versa. If susan is either not generous or strong then susan is both not rich and not patient and vice versa. If someone is both old and patient then lucy is either not happy or not quiet and vice versa. If fred is both wise and not curious then someone is not calm and vice versa. If mary is either quiet or not tall then someone is not happy. If someone is either old or not old then fred is not calm and vice versa. If someone is tall or not quiet then someone is kind. Everyone who is brave or quiet is both not humble and rich and vice versa. If someone is not brave or not tall then someone is both tall and not brave. If mary is either wise or not generous then fred is not happy or not rich. If someone is either not quiet or not rich then fred is not wise and vice versa. If someone is wise then fred is both patient and not strong. Everyone who is not patient is not happy or not patient and vice versa. If someone is either not wise or brave then someone is both rich and quiet. Everyone who is either happy or funny is either not rich or not wise and vice versa. Someone is both kind and curious. Someone is both tall and humble. Someone is either funny or not humble. Someone is not generous. Mary is either not tall or not old. Mary is both old and not wise. Susan is either funny or not wise. John is either not rich or kind. | Fred is wise. | entailment | (![X]:((brave(X)&~calm(X))<=>(kind(X)|~strong(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(old(X)<~>creative(X))))&
(((~generous(susan)<~>strong(susan)))<=>((~rich(susan)&~patient(susan))))&
((?[X]:((old(X)&patient(X))))<=>((~happy(lucy)<~>~quiet(lucy))))&
(((wise(fred)&~curious(fred)))<=>(?[X]:(~calm(X))))&
(((quiet(mary)<~>~tall(mary)))=>(?[X]:(~happy(X))))&
((?[X]:((old(X)<~>~old(X))))<=>(~calm(fred)))&
((?[X]:((tall(X)|~quiet(X))))=>(?[X]:(kind(X))))&
(![X]:((brave(X)|quiet(X))<=>(~humble(X)&rich(X))))&
((?[X]:((~brave(X)|~tall(X))))=>(?[X]:((tall(X)&~brave(X)))))&
(((wise(mary)<~>~generous(mary)))=>((~happy(fred)|~rich(fred))))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>(~wise(fred)))&
((?[X]:(wise(X)))=>((patient(fred)&~strong(fred))))&
(![X]:(~patient(X)<=>(~happy(X)|~patient(X))))&
((?[X]:((~wise(X)<~>brave(X))))=>(?[X]:((rich(X)&quiet(X)))))&
(![X]:((happy(X)<~>funny(X))<=>(~rich(X)<~>~wise(X))))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:((tall(X)&humble(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:(~generous(X)))&
((~tall(mary)<~>~old(mary)))&
((old(mary)&~wise(mary)))&
((funny(susan)<~>~wise(susan)))&
((~rich(john)<~>kind(john))) | wise(fred) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 823554299667836880522185
% SZS output start Proof for 823554299667836880522185
5. (~curious(fred) & wise(fred)) <=> ? [X0] : ~calm(X0) [input p4]
7. ? [X0] : (old(X0) <~> ~old(X0)) <=> ~calm(fred) [input p6]
25. ~wise(fred) [input hypothesis]
45. ((~curious(fred) & wise(fred)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | (curious(fred) | ~wise(fred))) [nnf transformation 5]
46. ((~curious(fred) & wise(fred)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | curious(fred) | ~wise(fred)) [flattening 45]
47. ((~curious(fred) & wise(fred)) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | curious(fred) | ~wise(fred)) [rectify 46]
48. ? [X1] : ~calm(X1) => ~calm(sK1) [choice axiom]
49. ((~curious(fred) & wise(fred)) | ! [X0] : calm(X0)) & (~calm(sK1) | curious(fred) | ~wise(fred)) [skolemisation 47,48]
53. (? [X0] : ((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | calm(fred)) & (~calm(fred) | ! [X0] : ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 7]
54. (? [X0] : ((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | calm(fred)) & (~calm(fred) | ! [X1] : ((old(X1) | old(X1)) & (~old(X1) | ~old(X1)))) [rectify 53]
55. ? [X0] : ((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) => ((old(sK3) | ~old(sK3)) & (~old(sK3) | old(sK3))) [choice axiom]
56. (((old(sK3) | ~old(sK3)) & (~old(sK3) | old(sK3))) | calm(fred)) & (~calm(fred) | ! [X1] : ((old(X1) | old(X1)) & (~old(X1) | ~old(X1)))) [skolemisation 54,55]
115. wise(fred) | calm(X0) [cnf transformation 49]
119. ~calm(fred) | ~old(X1) | ~old(X1) [cnf transformation 56]
120. ~calm(fred) | old(X1) | old(X1) [cnf transformation 56]
172. ~wise(fred) [cnf transformation 25]
173. ~calm(fred) | ~old(X1) [duplicate literal removal 119]
174. ~calm(fred) | old(X1) [duplicate literal removal 120]
223. 10 <=> ! [X0] : calm(X0) [avatar definition]
224. calm(X0) <- (10) [avatar component clause 223]
231. 12 <=> wise(fred) [avatar definition]
234. 10 | 12 [avatar split clause 115,231,223]
255. 17 <=> ! [X1] : old(X1) [avatar definition]
256. old(X1) <- (17) [avatar component clause 255]
258. 18 <=> calm(fred) [avatar definition]
260. ~calm(fred) <- (~18) [avatar component clause 258]
261. 17 | ~18 [avatar split clause 174,258,255]
263. 19 <=> ! [X1] : ~old(X1) [avatar definition]
264. ~old(X1) <- (19) [avatar component clause 263]
265. 19 | ~18 [avatar split clause 173,258,263]
399. ~12 [avatar split clause 172,231]
404. $false <- (10, ~18) [resolution 260,224]
405. ~10 | 18 [avatar contradiction clause 404]
406. $false <- (17, 19) [subsumption resolution 256,264]
407. ~17 | ~19 [avatar contradiction clause 406]
408. $false [avatar sat refutation 234,261,265,399,405,407]
% SZS output end Proof for 823554299667836880522185
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not creative is kind and vice versa.
If mary is both curious and not kind then fred is not patient and vice versa.
Everyone who is not tall or not humble is both not generous and creative.
If someone is not funny then alice is either not brave or kind and vice versa.
Everyone who is not patient or not old is not kind or strong and vice versa.
Everyone who is either brave or patient is both kind and patient.
If fred is either generous or humble then someone is creative or not old and vice versa.
Everyone who is either not patient or tall is quiet or brave and vice versa.
If john is either funny or not happy then someone is kind and vice versa.
If someone is either not kind or tall then alice is not wise or wise.
Everyone who is both funny and rich is either not quiet or not patient and vice versa.
Everyone who is tall or not generous is not calm or creative.
Everyone who is not strong is not quiet and vice versa.
If someone is either generous or not humble then susan is not old and vice versa.
Everyone who is either happy or funny is curious or happy and vice versa.
Everyone who is either not calm or patient is generous.
Lucy is old.
Lucy is both creative and not generous.
Someone is both not rich and not curious.
Fred is both not curious and patient.
Someone is funny. | Susan is rich. | neutral | (![X]:((~humble(X)&~creative(X))<=>kind(X)))&
(((curious(mary)&~kind(mary)))<=>(~patient(fred)))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&creative(X))))&
((?[X]:(~funny(X)))<=>((~brave(alice)<~>kind(alice))))&
(![X]:((~patient(X)|~old(X))<=>(~kind(X)|strong(X))))&
(![X]:((brave(X)<~>patient(X))=>(kind(X)&patient(X))))&
(((generous(fred)<~>humble(fred)))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>(quiet(X)|brave(X))))&
(((funny(john)<~>~happy(john)))<=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(![X]:((~calm(X)<~>patient(X))=>generous(X)))&
(old(lucy))&
((creative(lucy)&~generous(lucy)))&
(?[X]:((~rich(X)&~curious(X))))&
((~curious(fred)&patient(fred)))&
(?[X]:(funny(X))) | rich(susan) | [] | null | 0 |
If someone is curious then susan is not brave or quiet and vice versa.
Everyone who is not generous or not brave is humble or creative and vice versa.
Everyone who is both quiet and funny is not kind.
If someone is either funny or not humble then mary is curious or not creative.
Everyone who is either not strong or rich is either humble or not generous and vice versa.
If someone is generous or humble then someone is either rich or not strong.
If someone is not patient then susan is not humble or quiet.
Everyone who is rich is not generous or strong.
If someone is both not wise and not old then someone is both not humble and old.
If someone is both not quiet and not patient then susan is both kind and not patient.
If lucy is not old or not humble then someone is either not rich or not generous.
If someone is either quiet or not rich then susan is either not humble or not kind.
If someone is not brave then lucy is either tall or creative and vice versa.
Everyone who is either rich or quiet is quiet and vice versa.
If fred is either old or generous then someone is not generous or happy.
If someone is not rich then alice is patient.
Someone is not strong or not old.
Someone is both curious and happy.
Someone is not creative.
John is not calm or not curious.
Someone is either not patient or not quiet.
Someone is both calm and not brave.
Someone is either not generous or not creative.
Someone is either not curious or patient. | Lucy is rich. | contradiction | ((?[X]:(curious(X)))<=>((~brave(susan)|quiet(susan))))&
(![X]:((~generous(X)|~brave(X))<=>(humble(X)|creative(X))))&
(![X]:((quiet(X)&funny(X))=>~kind(X)))&
((?[X]:((funny(X)<~>~humble(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~strong(X)<~>rich(X))<=>(humble(X)<~>~generous(X))))&
((?[X]:((generous(X)|humble(X))))=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(~patient(X)))=>((~humble(susan)|quiet(susan))))&
(![X]:(rich(X)=>(~generous(X)|strong(X))))&
((?[X]:((~wise(X)&~old(X))))=>(?[X]:((~humble(X)&old(X)))))&
((?[X]:((~quiet(X)&~patient(X))))=>((kind(susan)&~patient(susan))))&
(((~old(lucy)|~humble(lucy)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((~humble(susan)<~>~kind(susan))))&
((?[X]:(~brave(X)))<=>((tall(lucy)<~>creative(lucy))))&
(![X]:((rich(X)<~>quiet(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((~generous(X)|happy(X)))))&
((?[X]:(~rich(X)))=>(patient(alice)))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((curious(X)&happy(X))))&
(?[X]:(~creative(X)))&
((~calm(john)|~curious(john)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((calm(X)&~brave(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((~curious(X)<~>patient(X)))) | rich(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7702290510500113984725266
% SZS output start Proof for 7702290510500113984725266
14. ! [X0] : ((rich(X0) <~> quiet(X0)) <=> quiet(X0)) [input p13]
25. rich(lucy) [input hypothesis]
65. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~quiet(X0)) & (quiet(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [nnf transformation 14]
121. quiet(X0) | quiet(X0) | ~rich(X0) [cnf transformation 65]
124. ~quiet(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 65]
138. rich(lucy) [cnf transformation 25]
139. ~rich(X0) | quiet(X0) [duplicate literal removal 121]
140. ~quiet(X0) | ~rich(X0) [duplicate literal removal 124]
239. 23 <=> ! [X0] : (~rich(X0) | ~quiet(X0)) [avatar definition]
240. ~rich(X0) | ~quiet(X0) <- (23) [avatar component clause 239]
263. 23 [avatar split clause 140,239]
333. ~rich(X0) <- (23) [subsumption resolution 240,139]
336. $false <- (23) [resolution 333,138]
341. ~23 [avatar contradiction clause 336]
342. $false [avatar sat refutation 263,341]
% SZS output end Proof for 7702290510500113984725266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not curious then lucy is not happy and vice versa. Everyone who is both curious and not curious is both creative and strong. If paul is either rich or not humble then someone is not rich or not strong. Everyone who is strong is wise or not rich and vice versa. If someone is either calm or not generous then someone is both patient and kind. Everyone who is either not funny or patient is not strong. Everyone who is either not rich or not old is not happy and vice versa. Everyone who is kind or not old is both not curious and not calm and vice versa. If john is wise or humble then someone is patient and vice versa. Everyone who is either old or happy is strong. If someone is either not quiet or not rich then mary is both not humble and humble. Everyone who is kind or brave is brave or not kind. Everyone who is both not curious and not creative is happy and vice versa. If someone is creative or calm then someone is both wise and not calm and vice versa. Everyone who is kind or not humble is either not old or not curious and vice versa. If paul is not old then lucy is either creative or not rich. Someone is patient or creative. Someone is both not quiet and not funny. Mary is brave or not calm. Mary is either not creative or not tall. Someone is creative or quiet. Paul is both humble and calm. John is both not calm and not tall. Someone is not generous. | Paul is not strong. | contradiction | ((?[X]:((wise(X)|~curious(X))))<=>(~happy(lucy)))&
(![X]:((curious(X)&~curious(X))=>(creative(X)&strong(X))))&
(((rich(paul)<~>~humble(paul)))=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:(strong(X)<=>(wise(X)|~rich(X))))&
((?[X]:((calm(X)<~>~generous(X))))=>(?[X]:((patient(X)&kind(X)))))&
(![X]:((~funny(X)<~>patient(X))=>~strong(X)))&
(![X]:((~rich(X)<~>~old(X))<=>~happy(X)))&
(![X]:((kind(X)|~old(X))<=>(~curious(X)&~calm(X))))&
(((wise(john)|humble(john)))<=>(?[X]:(patient(X))))&
(![X]:((old(X)<~>happy(X))=>strong(X)))&
((?[X]:((~quiet(X)<~>~rich(X))))=>((~humble(mary)&humble(mary))))&
(![X]:((kind(X)|brave(X))=>(brave(X)|~kind(X))))&
(![X]:((~curious(X)&~creative(X))<=>happy(X)))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((kind(X)|~humble(X))<=>(~old(X)<~>~curious(X))))&
((~old(paul))=>((creative(lucy)<~>~rich(lucy))))&
(?[X]:((patient(X)|creative(X))))&
(?[X]:((~quiet(X)&~funny(X))))&
((brave(mary)|~calm(mary)))&
((~creative(mary)<~>~tall(mary)))&
(?[X]:((creative(X)|quiet(X))))&
((humble(paul)&calm(paul)))&
((~calm(john)&~tall(john)))&
(?[X]:(~generous(X))) | ~strong(paul) | [
"p3",
"p6",
"p7",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7013164063772409624503826
% SZS output start Proof for 7013164063772409624503826
4. ! [X0] : (strong(X0) <=> (~rich(X0) | wise(X0))) [input p3]
7. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> ~happy(X0)) [input p6]
8. ! [X0] : ((~old(X0) | kind(X0)) <=> (~calm(X0) & ~curious(X0))) [input p7]
13. ! [X0] : ((~creative(X0) & ~curious(X0)) <=> happy(X0)) [input p12]
15. ! [X0] : ((~humble(X0) | kind(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p14]
22. calm(paul) & humble(paul) [input p21]
25. ~strong(paul) [input hypothesis]
45. ! [X0] : ((strong(X0) | (rich(X0) & ~wise(X0))) & ((~rich(X0) | wise(X0)) | ~strong(X0))) [nnf transformation 4]
46. ! [X0] : ((strong(X0) | (rich(X0) & ~wise(X0))) & (~rich(X0) | wise(X0) | ~strong(X0))) [flattening 45]
52. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | happy(X0)) & (~happy(X0) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 7]
53. ! [X0] : (((~old(X0) | kind(X0)) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 8]
54. ! [X0] : ((~old(X0) | kind(X0) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | (old(X0) & ~kind(X0)))) [flattening 53]
62. ! [X0] : (((~creative(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | curious(X0)))) [nnf transformation 13]
63. ! [X0] : (((~creative(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | curious(X0))) [flattening 62]
69. ! [X0] : (((~humble(X0) | kind(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [nnf transformation 15]
70. ! [X0] : ((~humble(X0) | kind(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (humble(X0) & ~kind(X0)))) [flattening 69]
90. rich(X0) | strong(X0) [cnf transformation 46]
99. ~old(X0) | ~rich(X0) | happy(X0) [cnf transformation 52]
103. ~kind(X0) | ~calm(X0) [cnf transformation 54]
104. ~calm(X0) | old(X0) [cnf transformation 54]
118. ~happy(X0) | ~curious(X0) [cnf transformation 63]
130. ~old(X0) | kind(X0) | ~humble(X0) | curious(X0) [cnf transformation 70]
140. humble(paul) [cnf transformation 22]
141. calm(paul) [cnf transformation 22]
145. ~strong(paul) [cnf transformation 25]
169. 6 <=> humble(paul) [avatar definition]
171. humble(paul) <- (6) [avatar component clause 169]
173. 7 <=> rich(paul) [avatar definition]
174. ~rich(paul) <- (~7) [avatar component clause 173]
270. 28 <=> old(paul) [avatar definition]
272. old(paul) <- (28) [avatar component clause 270]
320. 6 [avatar split clause 140,169]
337. old(paul) [resolution 104,141]
338. 28 [avatar split clause 337,270]
393. 45 <=> happy(paul) [avatar definition]
394. happy(paul) <- (45) [avatar component clause 393]
427. ~rich(paul) | happy(paul) <- (28) [resolution 99,272]
436. strong(paul) <- (~7) [resolution 174,90]
437. $false <- (~7) [subsumption resolution 436,145]
438. 7 [avatar contradiction clause 437]
439. 45 | ~7 | ~28 [avatar split clause 427,270,173,393]
443. ~curious(paul) <- (45) [resolution 394,118]
473. kind(paul) | ~humble(paul) | curious(paul) <- (28) [resolution 130,272]
476. kind(paul) | curious(paul) <- (6, 28) [subsumption resolution 473,171]
477. kind(paul) <- (6, 28, 45) [subsumption resolution 476,443]
493. ~calm(paul) <- (6, 28, 45) [resolution 477,103]
495. $false <- (6, 28, 45) [subsumption resolution 493,141]
496. ~6 | ~28 | ~45 [avatar contradiction clause 495]
497. $false [avatar sat refutation 320,338,438,439,496]
% SZS output end Proof for 7013164063772409624503826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not kind is both not happy and not curious and vice versa.
Everyone who is not generous is not rich or not humble and vice versa.
Everyone who is both tall and not happy is either old or generous and vice versa.
If someone is not creative or calm then paul is not brave or curious and vice versa.
Everyone who is both not kind and curious is not humble.
Everyone who is both not curious and not wise is tall or quiet.
If someone is both not funny and happy then susan is not happy or curious and vice versa.
If lucy is brave or strong then alice is calm.
Everyone who is both not creative and creative is either not patient or happy.
If susan is both curious and not creative then susan is not curious.
If someone is both not happy and not calm then lucy is not curious or not rich and vice versa.
Everyone who is wise or tall is rich and vice versa.
Everyone who is tall or not tall is not kind.
If someone is either not generous or not rich then john is not humble or not creative and vice versa.
If paul is either not wise or not quiet then someone is wise.
Everyone who is not creative is wise and vice versa.
John is both rich and not strong.
Someone is either not quiet or not brave.
Someone is both not quiet and not humble.
Lucy is funny.
Someone is not humble.
Someone is not kind.
Someone is either not curious or patient. | Lucy is curious. | neutral | (![X]:((~brave(X)&~kind(X))<=>(~happy(X)&~curious(X))))&
(![X]:(~generous(X)<=>(~rich(X)|~humble(X))))&
(![X]:((tall(X)&~happy(X))<=>(old(X)<~>generous(X))))&
((?[X]:((~creative(X)|calm(X))))<=>((~brave(paul)|curious(paul))))&
(![X]:((~kind(X)&curious(X))=>~humble(X)))&
(![X]:((~curious(X)&~wise(X))=>(tall(X)|quiet(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(susan)|curious(susan))))&
(((brave(lucy)|strong(lucy)))=>(calm(alice)))&
(![X]:((~creative(X)&creative(X))=>(~patient(X)<~>happy(X))))&
(((curious(susan)&~creative(susan)))=>(~curious(susan)))&
((?[X]:((~happy(X)&~calm(X))))<=>((~curious(lucy)|~rich(lucy))))&
(![X]:((wise(X)|tall(X))<=>rich(X)))&
(![X]:((tall(X)|~tall(X))=>~kind(X)))&
((?[X]:((~generous(X)<~>~rich(X))))<=>((~humble(john)|~creative(john))))&
(((~wise(paul)<~>~quiet(paul)))=>(?[X]:(wise(X))))&
(![X]:(~creative(X)<=>wise(X)))&
((rich(john)&~strong(john)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:((~quiet(X)&~humble(X))))&
(funny(lucy))&
(?[X]:(~humble(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~curious(X)<~>patient(X)))) | curious(lucy) | [] | null | 0 |
Everyone who is creative is not tall or not old. Everyone who is both not humble and not patient is either not calm or not brave and vice versa. If fred is not tall or not rich then someone is happy or creative. Everyone who is not humble or brave is not wise or not curious. If lucy is either not wise or rich then someone is either not happy or old and vice versa. Everyone who is both not patient and not creative is either curious or not brave and vice versa. Everyone who is not kind is not funny. Everyone who is rich or calm is both not humble and generous. If alice is not humble then someone is not patient and vice versa. Everyone who is both not tall and calm is either not patient or patient and vice versa. Everyone who is either strong or not funny is not kind and vice versa. If paul is both not rich and wise then lucy is kind or curious. Everyone who is happy is either not rich or old. Everyone who is not tall is both rich and not brave. Everyone who is either tall or not generous is either not old or not tall. If someone is patient or not kind then someone is either kind or happy and vice versa. Mary is kind or calm. Someone is curious. Someone is either rich or kind. Alice is either wise or funny. Susan is either humble or funny. | Susan is funny. | entailment | (![X]:(creative(X)=>(~tall(X)|~old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~calm(X)<~>~brave(X))))&
(((~tall(fred)|~rich(fred)))=>(?[X]:((happy(X)|creative(X)))))&
(![X]:((~humble(X)|brave(X))=>(~wise(X)|~curious(X))))&
(((~wise(lucy)<~>rich(lucy)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((~patient(X)&~creative(X))<=>(curious(X)<~>~brave(X))))&
(![X]:(~kind(X)=>~funny(X)))&
(![X]:((rich(X)|calm(X))=>(~humble(X)&generous(X))))&
((~humble(alice))<=>(?[X]:(~patient(X))))&
(![X]:((~tall(X)&calm(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~kind(X)))&
(((~rich(paul)&wise(paul)))=>((kind(lucy)|curious(lucy))))&
(![X]:(happy(X)=>(~rich(X)<~>old(X))))&
(![X]:(~tall(X)=>(rich(X)&~brave(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
((kind(mary)|calm(mary)))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)<~>kind(X))))&
((wise(alice)<~>funny(alice)))&
((humble(susan)<~>funny(susan))) | funny(susan) | [
"p7",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 560331310816424651546129
% SZS output start Proof for 560331310816424651546129
8. ! [X0] : ((calm(X0) | rich(X0)) => (generous(X0) & ~humble(X0))) [input p7]
10. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~patient(X0) <~> patient(X0))) [input p9]
14. ! [X0] : (~tall(X0) => (~brave(X0) & rich(X0))) [input p13]
21. humble(susan) <~> funny(susan) [input p20]
22. ~funny(susan) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~humble(X0)) | (~calm(X0) & ~rich(X0))) [ennf transformation 8]
34. ! [X0] : ((~brave(X0) & rich(X0)) | tall(X0)) [ennf transformation 14]
50. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (~calm(X0) | tall(X0)))) [nnf transformation 10]
51. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ~calm(X0) | tall(X0))) [flattening 50]
66. (~funny(susan) | ~humble(susan)) & (funny(susan) | humble(susan)) [nnf transformation 21]
93. ~rich(X0) | ~humble(X0) [cnf transformation 30]
101. ~tall(X0) | patient(X0) | patient(X0) [cnf transformation 51]
102. ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
112. rich(X0) | tall(X0) [cnf transformation 34]
130. funny(susan) | humble(susan) [cnf transformation 66]
132. ~funny(susan) [cnf transformation 22]
135. ~tall(X0) | patient(X0) [duplicate literal removal 101]
136. ~tall(X0) | ~patient(X0) [duplicate literal removal 102]
201. ~tall(X0) [subsumption resolution 135,136]
222. rich(X0) [subsumption resolution 112,201]
270. 28 <=> humble(susan) [avatar definition]
271. humble(susan) <- (28) [avatar component clause 270]
274. 29 <=> funny(susan) [avatar definition]
278. 28 | 29 [avatar split clause 130,274,270]
279. ~29 [avatar split clause 132,274]
282. ~humble(X0) [resolution 93,222]
283. $false <- (28) [resolution 282,271]
284. ~28 [avatar contradiction clause 283]
285. $false [avatar sat refutation 278,279,284]
% SZS output end Proof for 560331310816424651546129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or funny is brave or quiet. Everyone who is not wise or happy is both creative and wise. If someone is rich or not creative then someone is not curious or old. If susan is both not curious and happy then someone is both not rich and not tall and vice versa. If someone is either wise or quiet then paul is both creative and not creative and vice versa. If susan is both not humble and not old then mary is curious or not old. If someone is both not humble and not patient then susan is not quiet and vice versa. Everyone who is not rich is brave and vice versa. Everyone who is both old and kind is not funny. If someone is either not quiet or not strong then john is wise. If someone is either generous or not quiet then mary is both funny and not rich. Everyone who is either quiet or curious is either creative or rich and vice versa. If someone is not patient then alice is not funny. Everyone who is not curious or strong is both not kind and not brave and vice versa. If mary is either not rich or strong then fred is kind or happy and vice versa. If lucy is both patient and kind then someone is both not old and tall and vice versa. Mary is generous or not wise. Lucy is either not tall or not patient. Lucy is not funny or calm. Someone is either not funny or not creative. Fred is kind. Someone is either wise or not kind. Mary is kind. | Mary is creative. | contradiction | (![X]:((~old(X)<~>funny(X))=>(brave(X)|quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(creative(X)&wise(X))))&
((?[X]:((rich(X)|~creative(X))))=>(?[X]:((~curious(X)|old(X)))))&
(((~curious(susan)&happy(susan)))<=>(?[X]:((~rich(X)&~tall(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>((creative(paul)&~creative(paul))))&
(((~humble(susan)&~old(susan)))=>((curious(mary)|~old(mary))))&
((?[X]:((~humble(X)&~patient(X))))<=>(~quiet(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((old(X)&kind(X))=>~funny(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))=>(wise(john)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((funny(mary)&~rich(mary))))&
(![X]:((quiet(X)<~>curious(X))<=>(creative(X)<~>rich(X))))&
((?[X]:(~patient(X)))=>(~funny(alice)))&
(![X]:((~curious(X)|strong(X))<=>(~kind(X)&~brave(X))))&
(((~rich(mary)<~>strong(mary)))<=>((kind(fred)|happy(fred))))&
(((patient(lucy)&kind(lucy)))<=>(?[X]:((~old(X)&tall(X)))))&
((generous(mary)|~wise(mary)))&
((~tall(lucy)<~>~patient(lucy)))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(kind(fred))&
(?[X]:((wise(X)<~>~kind(X))))&
(kind(mary)) | creative(mary) | [
"p1",
"p4",
"p10",
"p11",
"p13",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4491192503369669271362285
% SZS output start Proof for 4491192503369669271362285
2. ! [X0] : ((happy(X0) | ~wise(X0)) => (wise(X0) & creative(X0))) [input p1]
5. ? [X0] : (wise(X0) <~> quiet(X0)) <=> (~creative(paul) & creative(paul)) [input p4]
11. ? [X0] : (generous(X0) <~> ~quiet(X0)) => (~rich(mary) & funny(mary)) [input p10]
12. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (creative(X0) <~> rich(X0))) [input p11]
14. ! [X0] : ((strong(X0) | ~curious(X0)) <=> (~brave(X0) & ~kind(X0))) [input p13]
17. ~wise(mary) | generous(mary) [input p16]
23. kind(mary) [input p22]
24. creative(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & creative(X0)) | (~happy(X0) & wise(X0))) [ennf transformation 2]
36. (~rich(mary) & funny(mary)) | ! [X0] : (generous(X0) <=> ~quiet(X0)) [ennf transformation 11]
47. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | (creative(paul) | ~creative(paul))) & ((~creative(paul) & creative(paul)) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [nnf transformation 5]
48. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [flattening 47]
49. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X1] : ((wise(X1) | ~quiet(X1)) & (quiet(X1) | ~wise(X1)))) [rectify 48]
50. ? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) => ((~quiet(sK2) | ~wise(sK2)) & (quiet(sK2) | wise(sK2))) [choice axiom]
51. (((~quiet(sK2) | ~wise(sK2)) & (quiet(sK2) | wise(sK2))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X1] : ((wise(X1) | ~quiet(X1)) & (quiet(X1) | ~wise(X1)))) [skolemisation 49,50]
58. (~rich(mary) & funny(mary)) | ! [X0] : ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0))) [nnf transformation 36]
59. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 12]
60. ! [X0] : (((strong(X0) | ~curious(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (~strong(X0) & curious(X0)))) [nnf transformation 14]
61. ! [X0] : ((strong(X0) | ~curious(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (~strong(X0) & curious(X0)))) [flattening 60]
80. wise(X0) | wise(X0) [cnf transformation 29]
88. creative(paul) | quiet(X1) | ~wise(X1) [cnf transformation 51]
90. ~creative(paul) | quiet(X1) | ~wise(X1) [cnf transformation 51]
105. ~rich(mary) | ~quiet(X0) | ~generous(X0) [cnf transformation 58]
113. ~curious(X0) | ~quiet(X0) | rich(X0) | ~creative(X0) [cnf transformation 59]
116. ~kind(X0) | curious(X0) [cnf transformation 61]
131. ~wise(mary) | generous(mary) [cnf transformation 17]
139. kind(mary) [cnf transformation 23]
140. creative(mary) [cnf transformation 24]
141. wise(X0) [duplicate literal removal 80]
181. ~creative(paul) | quiet(X1) [subsumption resolution 90,141]
183. 10 <=> ! [X1] : quiet(X1) [avatar definition]
184. quiet(X1) <- (10) [avatar component clause 183]
186. 11 <=> creative(paul) [avatar definition]
189. 10 | ~11 [avatar split clause 181,186,183]
190. creative(paul) | quiet(X1) [subsumption resolution 88,141]
191. 10 | 11 [avatar split clause 190,186,183]
201. 14 <=> curious(mary) [avatar definition]
203. curious(mary) <- (14) [avatar component clause 201]
231. 21 <=> rich(mary) [avatar definition]
233. ~rich(mary) <- (~21) [avatar component clause 231]
236. 22 <=> ! [X0] : (~quiet(X0) | ~generous(X0)) [avatar definition]
237. ~generous(X0) | ~quiet(X0) <- (22) [avatar component clause 236]
238. 22 | ~21 [avatar split clause 105,231,236]
294. generous(mary) [subsumption resolution 131,141]
317. curious(mary) [resolution 116,139]
320. 14 [avatar split clause 317,201]
327. ~quiet(mary) <- (22) [resolution 237,294]
329. $false <- (10, 22) [subsumption resolution 327,184]
330. ~10 | ~22 [avatar contradiction clause 329]
404. ~quiet(mary) | rich(mary) | ~creative(mary) <- (14) [resolution 113,203]
409. rich(mary) | ~creative(mary) <- (10, 14) [subsumption resolution 404,184]
410. ~creative(mary) <- (10, 14, ~21) [subsumption resolution 409,233]
411. $false <- (10, 14, ~21) [subsumption resolution 410,140]
412. ~10 | ~14 | 21 [avatar contradiction clause 411]
435. $false [avatar sat refutation 189,191,238,320,330,412]
% SZS output end Proof for 4491192503369669271362285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not kind and not quiet.
Everyone who is not strong is either not patient or not quiet and vice versa.
If someone is both brave and humble then mary is wise or creative and vice versa.
Everyone who is quiet is either creative or tall and vice versa.
Everyone who is old is both kind and calm.
If someone is not creative then susan is either not curious or generous.
Everyone who is both strong and old is patient or not funny.
Everyone who is curious or not curious is either rich or not creative and vice versa.
If fred is not happy then alice is either happy or humble and vice versa.
Everyone who is kind or tall is either rich or not kind and vice versa.
If susan is patient or funny then someone is not strong and vice versa.
Everyone who is both not calm and funny is calm.
Everyone who is not kind or curious is both strong and not rich.
If someone is not old then someone is either rich or brave and vice versa.
If alice is both not humble and humble then john is not funny or not creative and vice versa.
Everyone who is either not happy or not kind is not old or quiet.
Mary is not rich.
Someone is either not humble or not rich.
Mary is either tall or not calm.
Someone is tall or generous.
Susan is either not patient or brave.
Paul is both happy and tall.
Alice is funny.
Someone is kind or curious. | Mary is not patient. | contradiction | (![X]:(wise(X)=>(~kind(X)&~quiet(X))))&
(![X]:(~strong(X)<=>(~patient(X)<~>~quiet(X))))&
((?[X]:((brave(X)&humble(X))))<=>((wise(mary)|creative(mary))))&
(![X]:(quiet(X)<=>(creative(X)<~>tall(X))))&
(![X]:(old(X)=>(kind(X)&calm(X))))&
((?[X]:(~creative(X)))=>((~curious(susan)<~>generous(susan))))&
(![X]:((strong(X)&old(X))=>(patient(X)|~funny(X))))&
(![X]:((curious(X)|~curious(X))<=>(rich(X)<~>~creative(X))))&
((~happy(fred))<=>((happy(alice)<~>humble(alice))))&
(![X]:((kind(X)|tall(X))<=>(rich(X)<~>~kind(X))))&
(((patient(susan)|funny(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&funny(X))=>calm(X)))&
(![X]:((~kind(X)|curious(X))=>(strong(X)&~rich(X))))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>brave(X)))))&
(((~humble(alice)&humble(alice)))<=>((~funny(john)|~creative(john))))&
(![X]:((~happy(X)<~>~kind(X))=>(~old(X)|quiet(X))))&
(~rich(mary))&
(?[X]:((~humble(X)<~>~rich(X))))&
((tall(mary)<~>~calm(mary)))&
(?[X]:((tall(X)|generous(X))))&
((~patient(susan)<~>brave(susan)))&
((happy(paul)&tall(paul)))&
(funny(alice))&
(?[X]:((kind(X)|curious(X)))) | ~patient(mary) | [
"p1",
"p3",
"p7",
"p9",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4298185027381370686645776
% SZS output start Proof for 4298185027381370686645776
2. ! [X0] : (~strong(X0) <=> (~patient(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : (quiet(X0) <=> (creative(X0) <~> tall(X0))) [input p3]
8. ! [X0] : ((~curious(X0) | curious(X0)) <=> (rich(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : ((tall(X0) | kind(X0)) <=> (rich(X0) <~> ~kind(X0))) [input p9]
13. ! [X0] : ((curious(X0) | ~kind(X0)) => (~rich(X0) & strong(X0))) [input p12]
17. ~rich(mary) [input p16]
25. ~patient(mary) [input hypothesis]
34. ! [X0] : ((~rich(X0) & strong(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
37. ! [X0] : ((~strong(X0) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | strong(X0))) [nnf transformation 2]
43. ! [X0] : ((quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~quiet(X0))) [nnf transformation 4]
45. ! [X0] : (((~curious(X0) | curious(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | curious(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [flattening 45]
48. ! [X0] : (((tall(X0) | kind(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | kind(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [flattening 48]
76. ~strong(X0) | ~quiet(X0) | patient(X0) [cnf transformation 37]
86. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 43]
92. ~creative(X0) | rich(X0) | ~curious(X0) [cnf transformation 46]
93. ~creative(X0) | rich(X0) | curious(X0) [cnf transformation 46]
102. ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 49]
107. tall(X0) | kind(X0) | rich(X0) | kind(X0) [cnf transformation 49]
112. strong(X0) | kind(X0) [cnf transformation 34]
127. ~rich(mary) [cnf transformation 17]
139. ~patient(mary) [cnf transformation 25]
141. ~kind(X0) | rich(X0) [duplicate literal removal 102]
142. rich(X0) | kind(X0) | tall(X0) [duplicate literal removal 107]
144. 1 <=> creative(mary) [avatar definition]
145. creative(mary) <- (1) [avatar component clause 144]
146. ~creative(mary) <- (~1) [avatar component clause 144]
181. ~creative(X0) | rich(X0) [subsumption resolution 92,93]
265. 26 <=> tall(mary) [avatar definition]
266. tall(mary) <- (26) [avatar component clause 265]
267. ~tall(mary) <- (~26) [avatar component clause 265]
322. rich(mary) <- (1) [resolution 181,145]
325. $false <- (1) [subsumption resolution 322,127]
326. ~1 [avatar contradiction clause 325]
345. ~quiet(X0) | patient(X0) | kind(X0) [resolution 76,112]
441. kind(mary) | tall(mary) [resolution 142,127]
450. kind(mary) <- (~26) [subsumption resolution 441,267]
460. rich(mary) <- (~26) [resolution 450,141]
462. $false <- (~26) [subsumption resolution 460,127]
463. 26 [avatar contradiction clause 462]
467. creative(mary) | quiet(mary) <- (26) [resolution 266,86]
469. quiet(mary) <- (~1, 26) [subsumption resolution 467,146]
557. patient(mary) | kind(mary) <- (~1, 26) [resolution 345,469]
562. kind(mary) <- (~1, 26) [subsumption resolution 557,139]
634. rich(mary) <- (~1, 26) [resolution 562,141]
636. $false <- (~1, 26) [subsumption resolution 634,127]
637. 1 | ~26 [avatar contradiction clause 636]
638. $false [avatar sat refutation 326,463,637]
% SZS output end Proof for 4298185027381370686645776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Susan is not calm. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~calm(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8455003724894895689986372
% SZS output start Proof for 8455003724894895689986372
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p1]
3. ? [X0] : ~old(X0) <=> ~calm(susan) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) => ~curious(X0)) [input p3]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
8. ? [X0] : brave(X0) <=> (~rich(fred) & kind(fred)) [input p7]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> old(X0)) => (humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (~strong(X0) => brave(X0)) [input p11]
21. ~calm(susan) [input hypothesis]
22. ! [X0] : (~curious(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> generous(X0)) | (~creative(X0) <=> old(X0))) [ennf transformation 10]
24. ! [X0] : (brave(X0) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
30. ! [X0] : (((~humble(X0) | ~curious(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | ~curious(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [flattening 30]
32. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X0] : old(X0)) [nnf transformation 3]
33. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [rectify 32]
34. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
35. (~old(sK0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [skolemisation 33,34]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
45. (? [X0] : brave(X0) | (rich(fred) | ~kind(fred))) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
46. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
49. (brave(sK2) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 23]
66. brave(X0) | generous(X0) | rich(X0) [cnf transformation 29]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
68. brave(X0) | calm(X0) | rich(X0) [cnf transformation 29]
70. ~creative(X0) | ~calm(X0) | curious(X0) [cnf transformation 31]
77. ~old(sK0) | calm(susan) [cnf transformation 35]
78. ~strong(X0) | ~curious(X0) [cnf transformation 22]
80. old(X0) | humble(X0) | brave(X0) | rich(X0) [cnf transformation 37]
85. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
97. kind(fred) | ~brave(X1) [cnf transformation 49]
98. ~rich(fred) | ~brave(X1) [cnf transformation 49]
99. brave(sK2) | rich(fred) | ~kind(fred) [cnf transformation 49]
101. ~funny(X0) | old(X0) [cnf transformation 51]
102. ~brave(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~generous(X0) | old(X0) | creative(X0) [cnf transformation 52]
113. strong(X0) | brave(X0) [cnf transformation 24]
132. ~calm(susan) [cnf transformation 21]
134. 1 <=> calm(susan) [avatar definition]
138. 2 <=> old(sK0) [avatar definition]
140. ~old(sK0) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 77,138,134]
175. 10 <=> kind(fred) [avatar definition]
179. 11 <=> rich(fred) [avatar definition]
183. 12 <=> brave(sK2) [avatar definition]
185. brave(sK2) <- (12) [avatar component clause 183]
186. ~10 | 11 | 12 [avatar split clause 99,183,179,175]
188. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (13) [avatar component clause 188]
190. 13 | ~11 [avatar split clause 98,179,188]
191. 13 | 10 [avatar split clause 97,175,188]
265. ~1 [avatar split clause 132,134]
273. old(sK2) <- (12) [resolution 102,185]
274. ~curious(X0) | brave(X0) [resolution 113,78]
288. ~rich(sK2) | generous(sK2) <- (12) [resolution 67,185]
292. ~rich(sK2) <- (12) [subsumption resolution 288,87]
343. rich(sK2) | ~brave(sK2) <- (12) [resolution 85,273]
350. ~brave(sK2) <- (12) [subsumption resolution 343,292]
351. $false <- (12) [subsumption resolution 350,185]
352. ~12 [avatar contradiction clause 351]
367. rich(X0) | calm(X0) <- (13) [resolution 189,68]
368. rich(X1) | generous(X1) <- (13) [resolution 189,66]
407. humble(sK0) | brave(sK0) | rich(sK0) <- (~2) [resolution 80,140]
415. humble(sK0) | rich(sK0) <- (~2, 13) [subsumption resolution 407,189]
417. 37 <=> rich(sK0) [avatar definition]
418. ~rich(sK0) <- (~37) [avatar component clause 417]
419. rich(sK0) <- (37) [avatar component clause 417]
421. 38 <=> humble(sK0) [avatar definition]
423. humble(sK0) <- (38) [avatar component clause 421]
424. 37 | 38 | 2 | ~13 [avatar split clause 415,188,138,421,417]
442. funny(sK0) <- (37) [resolution 419,88]
446. 39 <=> generous(sK0) [avatar definition]
447. generous(sK0) <- (39) [avatar component clause 446]
450. 40 <=> calm(sK0) [avatar definition]
462. 41 <=> creative(sK0) [avatar definition]
464. creative(sK0) <- (41) [avatar component clause 462]
498. ~calm(sK0) | curious(sK0) <- (41) [resolution 464,70]
500. 46 <=> curious(sK0) [avatar definition]
501. curious(sK0) <- (46) [avatar component clause 500]
505. 46 | ~40 | ~41 [avatar split clause 498,462,450,500]
592. old(sK0) <- (37) [resolution 442,101]
593. $false <- (~2, 37) [subsumption resolution 592,140]
594. 2 | ~37 [avatar contradiction clause 593]
599. ~generous(sK0) | old(sK0) | creative(sK0) <- (38) [resolution 423,105]
621. calm(sK0) <- (13, ~37) [resolution 367,418]
627. 40 | ~13 | 37 [avatar split clause 621,417,188,450]
636. generous(sK0) <- (13, ~37) [resolution 368,418]
642. 39 | ~13 | 37 [avatar split clause 636,417,188,446]
643. ~generous(sK0) | creative(sK0) <- (~2, 38) [subsumption resolution 599,140]
646. creative(sK0) <- (~2, 38, 39) [subsumption resolution 643,447]
647. 41 | 2 | ~38 | ~39 [avatar split clause 646,446,421,138,462]
715. brave(sK0) <- (46) [resolution 501,274]
717. $false <- (13, 46) [subsumption resolution 715,189]
718. ~13 | ~46 [avatar contradiction clause 717]
719. $false [avatar sat refutation 141,186,190,191,265,352,424,505,594,627,642,647,718]
% SZS output end Proof for 8455003724894895689986372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and humble is not happy or not wise and vice versa. Everyone who is humble is not humble or not curious. Everyone who is not wise is not funny. If susan is either not patient or creative then someone is not generous and vice versa. Everyone who is not strong or not rich is curious and vice versa. Everyone who is either wise or not funny is both not rich and curious. Everyone who is either rich or not curious is happy and vice versa. Everyone who is both generous and patient is either curious or creative. Everyone who is not strong is not calm or strong and vice versa. Everyone who is both strong and humble is creative. If susan is wise or not funny then someone is either quiet or not rich and vice versa. If john is either quiet or not patient then someone is both not quiet and not humble. If someone is either not strong or patient then someone is either not rich or wise and vice versa. If lucy is not creative or brave then someone is calm or not brave and vice versa. If lucy is either not funny or generous then someone is tall or not happy and vice versa. If someone is patient or old then someone is wise and vice versa. Fred is quiet or happy. Alice is creative or not tall. Someone is either curious or old. Someone is either not humble or not brave. Someone is either not curious or not calm. Someone is not funny or tall. Lucy is both wise and not generous. | Alice is not humble. | entailment | (![X]:((rich(X)&humble(X))<=>(~happy(X)|~wise(X))))&
(![X]:(humble(X)=>(~humble(X)|~curious(X))))&
(![X]:(~wise(X)=>~funny(X)))&
(((~patient(susan)<~>creative(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)|~rich(X))<=>curious(X)))&
(![X]:((wise(X)<~>~funny(X))=>(~rich(X)&curious(X))))&
(![X]:((rich(X)<~>~curious(X))<=>happy(X)))&
(![X]:((generous(X)&patient(X))=>(curious(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(~calm(X)|strong(X))))&
(![X]:((strong(X)&humble(X))=>creative(X)))&
(((wise(susan)|~funny(susan)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((quiet(john)<~>~patient(john)))=>(?[X]:((~quiet(X)&~humble(X)))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((~rich(X)<~>wise(X)))))&
(((~creative(lucy)|brave(lucy)))<=>(?[X]:((calm(X)|~brave(X)))))&
(((~funny(lucy)<~>generous(lucy)))<=>(?[X]:((tall(X)|~happy(X)))))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:(wise(X))))&
((quiet(fred)|happy(fred)))&
((creative(alice)|~tall(alice)))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((~funny(X)|tall(X))))&
((wise(lucy)&~generous(lucy))) | ~humble(alice) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4678724949828268249837601
% SZS output start Proof for 4678724949828268249837601
2. ! [X0] : (humble(X0) => (~curious(X0) | ~humble(X0))) [input p1]
5. ! [X0] : ((~rich(X0) | ~strong(X0)) <=> curious(X0)) [input p4]
9. ! [X0] : (~strong(X0) <=> (strong(X0) | ~calm(X0))) [input p8]
24. humble(alice) [input hypothesis]
27. ! [X0] : ((~curious(X0) | ~humble(X0)) | ~humble(X0)) [ennf transformation 2]
28. ! [X0] : (~curious(X0) | ~humble(X0) | ~humble(X0)) [flattening 27]
42. ! [X0] : (((~rich(X0) | ~strong(X0)) | ~curious(X0)) & (curious(X0) | (rich(X0) & strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((~rich(X0) | ~strong(X0) | ~curious(X0)) & (curious(X0) | (rich(X0) & strong(X0)))) [flattening 42]
47. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | strong(X0))) [nnf transformation 9]
48. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | strong(X0))) [flattening 47]
92. ~curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 28]
98. strong(X0) | curious(X0) [cnf transformation 43]
113. ~strong(X0) | ~strong(X0) [cnf transformation 48]
157. humble(alice) [cnf transformation 24]
159. ~strong(X0) [duplicate literal removal 113]
160. ~curious(X0) | ~humble(X0) [duplicate literal removal 92]
335. curious(X0) [resolution 98,159]
339. ~humble(X1) [resolution 160,335]
341. $false [resolution 339,157]
% SZS output end Proof for 4678724949828268249837601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either strong or wise then someone is not brave. If susan is not happy or not wise then lucy is either kind or not old. If someone is curious then someone is both happy and not happy. Everyone who is old is humble and vice versa. If someone is not strong or strong then someone is either not generous or not humble. Everyone who is either humble or happy is both not tall and brave and vice versa. Everyone who is not tall is not humble and vice versa. Everyone who is creative or quiet is both not wise and generous. If mary is either generous or not rich then someone is patient and vice versa. Everyone who is both patient and not generous is both not tall and not curious. Everyone who is not quiet or not old is not patient or tall. Everyone who is not strong is both strong and tall and vice versa. Everyone who is either not rich or not quiet is not brave or humble and vice versa. Everyone who is either strong or generous is rich or not happy and vice versa. Everyone who is strong or not strong is both not creative and not tall. If someone is not happy or quiet then alice is strong or quiet and vice versa. John is either creative or not kind. Alice is brave or not generous. Someone is either not curious or generous. Someone is old or not generous. Susan is both not old and not humble. John is either wise or not old. Someone is both not generous and not old. | Lucy is not curious. | entailment | (((strong(susan)<~>wise(susan)))=>(?[X]:(~brave(X))))&
(((~happy(susan)|~wise(susan)))=>((kind(lucy)<~>~old(lucy))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:(old(X)<=>humble(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~tall(X)&brave(X))))&
(![X]:(~tall(X)<=>~humble(X)))&
(![X]:((creative(X)|quiet(X))=>(~wise(X)&generous(X))))&
(((generous(mary)<~>~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~tall(X)&~curious(X))))&
(![X]:((~quiet(X)|~old(X))=>(~patient(X)|tall(X))))&
(![X]:(~strong(X)<=>(strong(X)&tall(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(~brave(X)|humble(X))))&
(![X]:((strong(X)<~>generous(X))<=>(rich(X)|~happy(X))))&
(![X]:((strong(X)|~strong(X))=>(~creative(X)&~tall(X))))&
((?[X]:((~happy(X)|quiet(X))))<=>((strong(alice)|quiet(alice))))&
((creative(john)<~>~kind(john)))&
((brave(alice)|~generous(alice)))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((old(X)|~generous(X))))&
((~old(susan)&~humble(susan)))&
((wise(john)<~>~old(john)))&
(?[X]:((~generous(X)&~old(X)))) | ~curious(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 868196261486238449950735
% SZS output start Proof for 868196261486238449950735
3. ? [X0] : curious(X0) => ? [X0] : (~happy(X0) & happy(X0)) [input p2]
24. curious(lucy) [input hypothesis]
25. ? [X0] : curious(X0) => ? [X1] : (~happy(X1) & happy(X1)) [rectify 3]
29. ? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ~curious(X0) [ennf transformation 25]
41. ? [X0] : (~happy(X0) & happy(X0)) | ! [X1] : ~curious(X1) [rectify 29]
42. ? [X0] : (~happy(X0) & happy(X0)) => (~happy(sK1) & happy(sK1)) [choice axiom]
43. (~happy(sK1) & happy(sK1)) | ! [X1] : ~curious(X1) [skolemisation 41,42]
82. happy(sK1) | ~curious(X1) [cnf transformation 43]
83. ~happy(sK1) | ~curious(X1) [cnf transformation 43]
145. curious(lucy) [cnf transformation 24]
179. 7 <=> ! [X1] : ~curious(X1) [avatar definition]
180. ~curious(X1) <- (7) [avatar component clause 179]
182. 8 <=> happy(sK1) [avatar definition]
185. 7 | ~8 [avatar split clause 83,182,179]
186. 7 | 8 [avatar split clause 82,182,179]
294. $false <- (7) [resolution 180,145]
295. ~7 [avatar contradiction clause 294]
296. $false [avatar sat refutation 185,186,295]
% SZS output end Proof for 868196261486238449950735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not quiet and rich.
Everyone who is old is either not tall or not old and vice versa.
Everyone who is both not wise and curious is both not creative and old and vice versa.
Everyone who is both not happy and calm is both funny and not generous.
Everyone who is either not quiet or not strong is tall.
Everyone who is both wise and not patient is not humble or not quiet.
If susan is both brave and not quiet then lucy is both not creative and quiet and vice versa.
If someone is not wise then someone is creative.
Everyone who is either not strong or not patient is either not creative or not rich and vice versa.
Everyone who is not brave is funny and vice versa.
If someone is creative or not strong then susan is both curious and happy and vice versa.
Everyone who is both curious and patient is either not quiet or not generous and vice versa.
Everyone who is not quiet or strong is either not kind or not calm and vice versa.
Everyone who is calm is either not happy or funny.
If someone is humble then someone is funny or humble and vice versa.
If mary is both curious and funny then fred is generous.
Susan is wise.
Someone is not curious or not calm.
Alice is quiet.
Someone is not funny or not quiet.
Paul is not patient.
Someone is calm or brave. | Paul is not quiet. | entailment | (![X]:(generous(X)=>(~quiet(X)&rich(X))))&
(![X]:(old(X)<=>(~tall(X)<~>~old(X))))&
(![X]:((~wise(X)&curious(X))<=>(~creative(X)&old(X))))&
(![X]:((~happy(X)&calm(X))=>(funny(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>tall(X)))&
(![X]:((wise(X)&~patient(X))=>(~humble(X)|~quiet(X))))&
(((brave(susan)&~quiet(susan)))<=>((~creative(lucy)&quiet(lucy))))&
((?[X]:(~wise(X)))=>(?[X]:(creative(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>funny(X)))&
((?[X]:((creative(X)|~strong(X))))<=>((curious(susan)&happy(susan))))&
(![X]:((curious(X)&patient(X))<=>(~quiet(X)<~>~generous(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~kind(X)<~>~calm(X))))&
(![X]:(calm(X)=>(~happy(X)<~>funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:((funny(X)|humble(X)))))&
(((curious(mary)&funny(mary)))=>(generous(fred)))&
(wise(susan))&
(?[X]:((~curious(X)|~calm(X))))&
(quiet(alice))&
(?[X]:((~funny(X)|~quiet(X))))&
(~patient(paul))&
(?[X]:((calm(X)|brave(X)))) | ~quiet(paul) | [
"p0",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4198971645971504258606784
% SZS output start Proof for 4198971645971504258606784
1. ! [X0] : (generous(X0) => (rich(X0) & ~quiet(X0))) [input p0]
12. ! [X0] : ((patient(X0) & curious(X0)) <=> (~quiet(X0) <~> ~generous(X0))) [input p11]
21. ~patient(paul) [input p20]
23. quiet(paul) [input hypothesis]
26. ! [X0] : ((rich(X0) & ~quiet(X0)) | ~generous(X0)) [ennf transformation 1]
52. ! [X0] : (((patient(X0) & curious(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (~patient(X0) | ~curious(X0)))) [nnf transformation 12]
53. ! [X0] : (((patient(X0) & curious(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | ~patient(X0) | ~curious(X0))) [flattening 52]
68. ~quiet(X0) | ~generous(X0) [cnf transformation 26]
108. patient(X0) | ~quiet(X0) | generous(X0) [cnf transformation 53]
125. ~patient(paul) [cnf transformation 21]
127. quiet(paul) [cnf transformation 23]
188. ~quiet(X0) | patient(X0) [subsumption resolution 108,68]
267. patient(paul) [resolution 188,127]
268. $false [subsumption resolution 267,125]
% SZS output end Proof for 4198971645971504258606784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or patient then paul is both kind and old. Everyone who is both not tall and not patient is rich. If someone is humble then susan is both kind and quiet and vice versa. If mary is rich or not rich then alice is quiet. Everyone who is rich or wise is humble and vice versa. Everyone who is either patient or strong is both generous and not creative and vice versa. Everyone who is wise or not calm is either rich or not humble and vice versa. Everyone who is either quiet or not creative is not rich or not quiet and vice versa. Everyone who is either brave or curious is either not quiet or rich. If lucy is not humble then someone is not tall and vice versa. If mary is brave or funny then someone is not old or not brave and vice versa. If alice is both strong and tall then john is quiet or tall. Everyone who is not humble or kind is either not rich or not strong. If someone is both rich and strong then mary is either not old or not humble. Everyone who is kind is both not tall and not old and vice versa. If alice is either happy or not generous then someone is not strong and vice versa. Someone is either not quiet or not humble. Mary is either tall or not wise. Mary is old or not creative. Lucy is curious. Susan is old or generous. Someone is not creative or old. | Mary is not tall. | neutral | (((calm(susan)<~>patient(susan)))=>((kind(paul)&old(paul))))&
(![X]:((~tall(X)&~patient(X))=>rich(X)))&
((?[X]:(humble(X)))<=>((kind(susan)&quiet(susan))))&
(((rich(mary)|~rich(mary)))=>(quiet(alice)))&
(![X]:((rich(X)|wise(X))<=>humble(X)))&
(![X]:((patient(X)<~>strong(X))<=>(generous(X)&~creative(X))))&
(![X]:((wise(X)|~calm(X))<=>(rich(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~rich(X)|~quiet(X))))&
(![X]:((brave(X)<~>curious(X))=>(~quiet(X)<~>rich(X))))&
((~humble(lucy))<=>(?[X]:(~tall(X))))&
(((brave(mary)|funny(mary)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((strong(alice)&tall(alice)))=>((quiet(john)|tall(john))))&
(![X]:((~humble(X)|kind(X))=>(~rich(X)<~>~strong(X))))&
((?[X]:((rich(X)&strong(X))))=>((~old(mary)<~>~humble(mary))))&
(![X]:(kind(X)<=>(~tall(X)&~old(X))))&
(((happy(alice)<~>~generous(alice)))<=>(?[X]:(~strong(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((tall(mary)<~>~wise(mary)))&
((old(mary)|~creative(mary)))&
(curious(lucy))&
((old(susan)|generous(susan)))&
(?[X]:((~creative(X)|old(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is both not quiet and generous is old or not creative and vice versa. Everyone who is both not old and not generous is either not happy or not generous. Everyone who is either brave or not tall is either not old or not rich and vice versa. Everyone who is creative is not strong or kind. If alice is not funny or rich then fred is patient. If alice is both old and not creative then someone is happy or not kind and vice versa. Everyone who is either not calm or generous is not old and vice versa. If alice is both not calm and creative then someone is not rich or strong and vice versa. Everyone who is both not kind and not creative is curious or kind and vice versa. If paul is not strong or not brave then alice is not quiet or happy and vice versa. If lucy is both kind and not curious then susan is brave or not curious. If someone is not wise then someone is both brave and quiet and vice versa. If susan is not wise then someone is both kind and not generous and vice versa. If john is either calm or not funny then mary is kind and vice versa. Someone is both not old and wise. Mary is both quiet and creative. Someone is either funny or not wise. Someone is either humble or not creative. | Paul is not creative. | neutral | (![X]:((~quiet(X)&generous(X))<=>(old(X)|~creative(X))))&
(![X]:((~old(X)&~generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(creative(X)=>(~strong(X)|kind(X))))&
(((~funny(alice)|rich(alice)))=>(patient(fred)))&
(((old(alice)&~creative(alice)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>~old(X)))&
(((~calm(alice)&creative(alice)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)|kind(X))))&
(((~strong(paul)|~brave(paul)))<=>((~quiet(alice)|happy(alice))))&
(((kind(lucy)&~curious(lucy)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)&quiet(X)))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(?[X]:((~old(X)&wise(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>~creative(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is quiet or not happy is either patient or happy and vice versa.
If someone is either tall or strong then someone is not curious and vice versa.
Everyone who is either generous or not curious is either not rich or kind.
Everyone who is both not patient and happy is tall or not wise.
Everyone who is humble is both not funny and not curious and vice versa.
Everyone who is not brave is both not funny and tall and vice versa.
If someone is both not generous and brave then paul is kind.
If lucy is not wise then someone is not quiet and vice versa.
Everyone who is not generous or wise is either curious or happy.
Everyone who is not rich or not funny is wise.
Everyone who is both not curious and patient is not calm and vice versa.
If paul is either not humble or old then someone is either tall or not humble and vice versa.
If alice is either not quiet or not creative then lucy is both not funny and not calm and vice versa.
If someone is either not creative or not happy then someone is brave or kind.
If lucy is not calm then someone is not brave and vice versa.
Everyone who is old is either generous or wise and vice versa.
Lucy is not funny.
Someone is calm.
Alice is not rich or wise.
Someone is rich.
Someone is not creative or not brave.
Alice is brave or humble.
John is either not quiet or kind.
Someone is either tall or not wise. | Lucy is not curious. | contradiction | (![X]:((quiet(X)|~happy(X))<=>(patient(X)<~>happy(X))))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>~curious(X))=>(~rich(X)<~>kind(X))))&
(![X]:((~patient(X)&happy(X))=>(tall(X)|~wise(X))))&
(![X]:(humble(X)<=>(~funny(X)&~curious(X))))&
(![X]:(~brave(X)<=>(~funny(X)&tall(X))))&
((?[X]:((~generous(X)&brave(X))))=>(kind(paul)))&
((~wise(lucy))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)|wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))=>wise(X)))&
(![X]:((~curious(X)&patient(X))<=>~calm(X)))&
(((~humble(paul)<~>old(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~quiet(alice)<~>~creative(alice)))<=>((~funny(lucy)&~calm(lucy))))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:((brave(X)|kind(X)))))&
((~calm(lucy))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(generous(X)<~>wise(X))))&
(~funny(lucy))&
(?[X]:(calm(X)))&
((~rich(alice)|wise(alice)))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)|~brave(X))))&
((brave(alice)|humble(alice)))&
((~quiet(john)<~>kind(john)))&
(?[X]:((tall(X)<~>~wise(X)))) | ~curious(lucy) | [
"p0",
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2985916878594817670914371
% SZS output start Proof for 2985916878594817670914371
1. ! [X0] : ((~happy(X0) | quiet(X0)) <=> (patient(X0) <~> happy(X0))) [input p0]
4. ! [X0] : ((happy(X0) & ~patient(X0)) => (~wise(X0) | tall(X0))) [input p3]
6. ! [X0] : (~brave(X0) <=> (tall(X0) & ~funny(X0))) [input p5]
8. ~wise(lucy) <=> ? [X0] : ~quiet(X0) [input p7]
9. ! [X0] : ((wise(X0) | ~generous(X0)) => (curious(X0) <~> happy(X0))) [input p8]
10. ! [X0] : ((~funny(X0) | ~rich(X0)) => wise(X0)) [input p9]
11. ! [X0] : ((patient(X0) & ~curious(X0)) <=> ~calm(X0)) [input p10]
15. ~calm(lucy) <=> ? [X0] : ~brave(X0) [input p14]
17. ~funny(lucy) [input p16]
25. ~curious(lucy) [input hypothesis]
29. ! [X0] : ((~wise(X0) | tall(X0)) | (~happy(X0) | patient(X0))) [ennf transformation 4]
30. ! [X0] : (~wise(X0) | tall(X0) | ~happy(X0) | patient(X0)) [flattening 29]
32. ! [X0] : ((curious(X0) <~> happy(X0)) | (~wise(X0) & generous(X0))) [ennf transformation 9]
33. ! [X0] : (wise(X0) | (funny(X0) & rich(X0))) [ennf transformation 10]
35. ! [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 1]
36. ! [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 35]
45. ! [X0] : ((~brave(X0) | (~tall(X0) | funny(X0))) & ((tall(X0) & ~funny(X0)) | brave(X0))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | ~tall(X0) | funny(X0)) & ((tall(X0) & ~funny(X0)) | brave(X0))) [flattening 45]
47. (~wise(lucy) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | wise(lucy)) [nnf transformation 8]
48. (~wise(lucy) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | wise(lucy)) [rectify 47]
49. ? [X1] : ~quiet(X1) => ~quiet(sK2) [choice axiom]
50. (~wise(lucy) | ! [X0] : quiet(X0)) & (~quiet(sK2) | wise(lucy)) [skolemisation 48,49]
51. ! [X0] : (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (~wise(X0) & generous(X0))) [nnf transformation 32]
52. ! [X0] : (((patient(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~patient(X0) | curious(X0)))) [nnf transformation 11]
53. ! [X0] : (((patient(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~patient(X0) | curious(X0))) [flattening 52]
64. (~calm(lucy) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | calm(lucy)) [nnf transformation 15]
65. (~calm(lucy) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | calm(lucy)) [rectify 64]
66. ? [X1] : ~brave(X1) => ~brave(sK5) [choice axiom]
67. (~calm(lucy) | ! [X0] : brave(X0)) & (~brave(sK5) | calm(lucy)) [skolemisation 65,66]
80. happy(X0) | patient(X0) | happy(X0) [cnf transformation 36]
81. ~patient(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 36]
93. ~wise(X0) | tall(X0) | ~happy(X0) | patient(X0) [cnf transformation 30]
99. ~brave(X0) | ~tall(X0) | funny(X0) [cnf transformation 46]
102. ~wise(lucy) | quiet(X0) [cnf transformation 50]
104. ~wise(X0) | curious(X0) | happy(X0) [cnf transformation 51]
108. funny(X0) | wise(X0) [cnf transformation 33]
109. ~calm(X0) | ~patient(X0) | curious(X0) [cnf transformation 53]
111. calm(X0) | patient(X0) [cnf transformation 53]
129. ~calm(lucy) | brave(X0) [cnf transformation 67]
134. ~funny(lucy) [cnf transformation 17]
144. ~curious(lucy) [cnf transformation 25]
145. patient(X0) | happy(X0) [duplicate literal removal 80]
172. ~wise(X0) | tall(X0) | patient(X0) [subsumption resolution 93,145]
182. 9 <=> ! [X0] : quiet(X0) [avatar definition]
183. quiet(X0) <- (9) [avatar component clause 182]
185. 10 <=> wise(lucy) [avatar definition]
186. wise(lucy) <- (10) [avatar component clause 185]
188. 9 | ~10 [avatar split clause 102,185,182]
225. 18 <=> funny(lucy) [avatar definition]
226. ~funny(lucy) <- (~18) [avatar component clause 225]
229. 19 <=> calm(lucy) [avatar definition]
230. ~calm(lucy) <- (~19) [avatar component clause 229]
231. calm(lucy) <- (19) [avatar component clause 229]
263. 26 <=> ! [X0] : brave(X0) [avatar definition]
264. brave(X0) <- (26) [avatar component clause 263]
265. 26 | ~19 [avatar split clause 129,229,263]
271. ~18 [avatar split clause 134,225]
315. wise(lucy) <- (~18) [resolution 108,226]
320. 10 | 18 [avatar split clause 315,225,185]
325. patient(lucy) <- (~19) [resolution 111,230]
330. ~happy(lucy) | ~quiet(lucy) <- (~19) [resolution 81,325]
331. ~happy(lucy) <- (9, ~19) [subsumption resolution 330,183]
360. curious(lucy) | happy(lucy) <- (10) [resolution 104,186]
370. happy(lucy) <- (10) [subsumption resolution 360,144]
371. $false <- (9, 10, ~19) [subsumption resolution 370,331]
372. ~9 | ~10 | 19 [avatar contradiction clause 371]
377. ~tall(X0) | funny(X0) <- (26) [resolution 264,99]
388. ~patient(lucy) | curious(lucy) <- (19) [resolution 109,231]
398. ~patient(lucy) <- (19) [subsumption resolution 388,144]
445. tall(lucy) | patient(lucy) <- (10) [resolution 172,186]
447. tall(lucy) <- (10, 19) [subsumption resolution 445,398]
574. funny(lucy) <- (10, 19, 26) [resolution 377,447]
578. $false <- (10, ~18, 19, 26) [subsumption resolution 574,226]
579. ~10 | 18 | ~19 | ~26 [avatar contradiction clause 578]
580. $false [avatar sat refutation 188,265,271,320,372,579]
% SZS output end Proof for 2985916878594817670914371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either not humble or creative then fred is patient or not quiet and vice versa.
If susan is not patient or not brave then susan is not creative.
Everyone who is either not rich or kind is not tall and vice versa.
Everyone who is both not curious and humble is both curious and old and vice versa.
If someone is both tall and curious then paul is either kind or wise and vice versa.
If alice is humble then someone is humble or not happy and vice versa.
If paul is both not wise and not rich then alice is tall.
If someone is both strong and not calm then fred is not generous or happy.
If someone is both not creative and not patient then someone is either not strong or not old.
Everyone who is kind is both not creative and not rich and vice versa.
If someone is not happy then lucy is both not humble and curious.
Everyone who is creative or not happy is not happy and vice versa.
Everyone who is both humble and creative is creative.
Everyone who is not funny is either happy or not happy.
If someone is not wise or not tall then someone is both happy and brave.
If fred is calm then someone is both not kind and not curious.
Lucy is not kind or not curious.
Lucy is generous.
Someone is both not strong and not funny.
Someone is both not wise and not old.
Someone is either not tall or curious.
Lucy is both not patient and happy.
Someone is not old or calm.
Someone is either not kind or not strong. | Lucy is curious. | neutral | ((?[X]:((~humble(X)<~>creative(X))))<=>((patient(fred)|~quiet(fred))))&
(((~patient(susan)|~brave(susan)))=>(~creative(susan)))&
(![X]:((~rich(X)<~>kind(X))<=>~tall(X)))&
(![X]:((~curious(X)&humble(X))<=>(curious(X)&old(X))))&
((?[X]:((tall(X)&curious(X))))<=>((kind(paul)<~>wise(paul))))&
((humble(alice))<=>(?[X]:((humble(X)|~happy(X)))))&
(((~wise(paul)&~rich(paul)))=>(tall(alice)))&
((?[X]:((strong(X)&~calm(X))))=>((~generous(fred)|happy(fred))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:(kind(X)<=>(~creative(X)&~rich(X))))&
((?[X]:(~happy(X)))=>((~humble(lucy)&curious(lucy))))&
(![X]:((creative(X)|~happy(X))<=>~happy(X)))&
(![X]:((humble(X)&creative(X))=>creative(X)))&
(![X]:(~funny(X)=>(happy(X)<~>~happy(X))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((happy(X)&brave(X)))))&
((calm(fred))=>(?[X]:((~kind(X)&~curious(X)))))&
((~kind(lucy)|~curious(lucy)))&
(generous(lucy))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((~wise(X)&~old(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
((~patient(lucy)&happy(lucy)))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:((~kind(X)<~>~strong(X)))) | curious(lucy) | [] | null | 0 |
Everyone who is both not quiet and funny is not wise or funny and vice versa.
If someone is both rich and not patient then someone is generous or not strong and vice versa.
If fred is brave or not kind then someone is both not strong and strong and vice versa.
Everyone who is not happy is both not wise and not creative.
Everyone who is both not humble and quiet is tall or quiet.
Everyone who is not wise is not calm or not patient.
Everyone who is either not generous or quiet is humble and vice versa.
If someone is either patient or not happy then john is not brave and vice versa.
Everyone who is patient or not generous is both strong and old and vice versa.
If someone is both brave and happy then someone is both not patient and not old.
If someone is brave then someone is both not rich and rich and vice versa.
If fred is not quiet or wise then john is not rich or funny and vice versa.
Everyone who is either rich or happy is strong or humble.
Everyone who is both curious and not quiet is not old or wise.
Everyone who is creative or not calm is brave or happy.
Everyone who is quiet or not wise is both funny and not humble and vice versa.
Mary is either not kind or calm.
Someone is brave or not wise.
Someone is either tall or not happy.
Someone is either patient or kind.
Susan is not old.
Susan is both kind and calm. | John is not generous. | neutral | (![X]:((~quiet(X)&funny(X))<=>(~wise(X)|funny(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((generous(X)|~strong(X)))))&
(((brave(fred)|~kind(fred)))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:(~happy(X)=>(~wise(X)&~creative(X))))&
(![X]:((~humble(X)&quiet(X))=>(tall(X)|quiet(X))))&
(![X]:(~wise(X)=>(~calm(X)|~patient(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~happy(X))))<=>(~brave(john)))&
(![X]:((patient(X)|~generous(X))<=>(strong(X)&old(X))))&
((?[X]:((brave(X)&happy(X))))=>(?[X]:((~patient(X)&~old(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~rich(X)&rich(X)))))&
(((~quiet(fred)|wise(fred)))<=>((~rich(john)|funny(john))))&
(![X]:((rich(X)<~>happy(X))=>(strong(X)|humble(X))))&
(![X]:((curious(X)&~quiet(X))=>(~old(X)|wise(X))))&
(![X]:((creative(X)|~calm(X))=>(brave(X)|happy(X))))&
(![X]:((quiet(X)|~wise(X))<=>(funny(X)&~humble(X))))&
((~kind(mary)<~>calm(mary)))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((patient(X)<~>kind(X))))&
(~old(susan))&
((kind(susan)&calm(susan))) | ~generous(john) | [] | null | 0 |
Everyone who is happy or not happy is rich or strong and vice versa. If lucy is both quiet and generous then someone is both not kind and not quiet and vice versa. If mary is generous then someone is patient and vice versa. Everyone who is not generous or not calm is both not old and not calm. Everyone who is rich is not old or wise and vice versa. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is either not strong or not wise is either not generous or not humble. Everyone who is not curious is both quiet and tall and vice versa. If someone is either not tall or curious then someone is not happy or funny. If someone is not generous or wise then lucy is not brave. If someone is wise then someone is not happy or funny and vice versa. Everyone who is calm or tall is not funny and vice versa. Everyone who is either not tall or brave is tall and vice versa. Everyone who is not calm is both brave and not quiet. If someone is not quiet or not old then someone is humble and vice versa. If john is both kind and creative then someone is both not funny and not curious and vice versa. Someone is happy or humble. Alice is generous or happy. Someone is calm or not happy. Paul is not generous or quiet. Someone is both not kind and brave. Paul is not calm or curious. | John is not calm. | contradiction | (![X]:((happy(X)|~happy(X))<=>(rich(X)|strong(X))))&
(((quiet(lucy)&generous(lucy)))<=>(?[X]:((~kind(X)&~quiet(X)))))&
((generous(mary))<=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|~calm(X))=>(~old(X)&~calm(X))))&
(![X]:(rich(X)<=>(~old(X)|wise(X))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(~generous(X)<~>~humble(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>(?[X]:((~happy(X)|funny(X)))))&
((?[X]:((~generous(X)|wise(X))))=>(~brave(lucy)))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:((calm(X)|tall(X))<=>~funny(X)))&
(![X]:((~tall(X)<~>brave(X))<=>tall(X)))&
(![X]:(~calm(X)=>(brave(X)&~quiet(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:(humble(X))))&
(((kind(john)&creative(john)))<=>(?[X]:((~funny(X)&~curious(X)))))&
(?[X]:((happy(X)|humble(X))))&
((generous(alice)|happy(alice)))&
(?[X]:((calm(X)|~happy(X))))&
((~generous(paul)|quiet(paul)))&
(?[X]:((~kind(X)&brave(X))))&
((~calm(paul)|curious(paul))) | ~calm(john) | [
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2817805092005011892649373
% SZS output start Proof for 2817805092005011892649373
8. ! [X0] : (~curious(X0) <=> (tall(X0) & quiet(X0))) [input p7]
9. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X0] : (funny(X0) | ~happy(X0)) [input p8]
10. ? [X0] : (wise(X0) | ~generous(X0)) => ~brave(lucy) [input p9]
11. ? [X0] : wise(X0) <=> ? [X0] : (funny(X0) | ~happy(X0)) [input p10]
12. ! [X0] : ((tall(X0) | calm(X0)) <=> ~funny(X0)) [input p11]
13. ! [X0] : ((~tall(X0) <~> brave(X0)) <=> tall(X0)) [input p12]
14. ! [X0] : (~calm(X0) => (~quiet(X0) & brave(X0))) [input p13]
23. ~calm(john) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> curious(X0)) => ? [X1] : (funny(X1) | ~happy(X1)) [rectify 9]
25. ? [X0] : wise(X0) <=> ? [X1] : (funny(X1) | ~happy(X1)) [rectify 11]
29. ? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : (~tall(X0) <=> curious(X0)) [ennf transformation 24]
30. ~brave(lucy) | ! [X0] : (~wise(X0) & generous(X0)) [ennf transformation 10]
31. ! [X0] : ((~quiet(X0) & brave(X0)) | calm(X0)) [ennf transformation 14]
47. ! [X0] : ((~curious(X0) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | curious(X0))) [nnf transformation 8]
48. ! [X0] : ((~curious(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | curious(X0))) [flattening 47]
49. ? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 29]
50. ? [X0] : (funny(X0) | ~happy(X0)) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [rectify 49]
51. ? [X0] : (funny(X0) | ~happy(X0)) => (funny(sK2) | ~happy(sK2)) [choice axiom]
52. (funny(sK2) | ~happy(sK2)) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1))) [skolemisation 50,51]
53. (? [X0] : wise(X0) | ! [X1] : (~funny(X1) & happy(X1))) & (? [X1] : (funny(X1) | ~happy(X1)) | ! [X0] : ~wise(X0)) [nnf transformation 25]
54. (? [X0] : wise(X0) | ! [X1] : (~funny(X1) & happy(X1))) & (? [X2] : (funny(X2) | ~happy(X2)) | ! [X3] : ~wise(X3)) [rectify 53]
55. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
56. ? [X2] : (funny(X2) | ~happy(X2)) => (funny(sK4) | ~happy(sK4)) [choice axiom]
57. (wise(sK3) | ! [X1] : (~funny(X1) & happy(X1))) & ((funny(sK4) | ~happy(sK4)) | ! [X3] : ~wise(X3)) [skolemisation 54,56,55]
58. ! [X0] : (((tall(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~calm(X0)))) [nnf transformation 12]
59. ! [X0] : ((tall(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~calm(X0)))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0))))) [nnf transformation 13]
102. curious(X0) | quiet(X0) [cnf transformation 48]
106. funny(sK2) | ~happy(sK2) | ~tall(X1) | ~curious(X1) [cnf transformation 52]
108. ~brave(lucy) | ~wise(X0) [cnf transformation 30]
110. wise(sK3) | happy(X1) [cnf transformation 57]
111. wise(sK3) | ~funny(X1) [cnf transformation 57]
114. funny(X0) | calm(X0) | tall(X0) [cnf transformation 59]
115. tall(X0) | brave(X0) | tall(X0) [cnf transformation 60]
117. brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 60]
120. ~quiet(X0) | calm(X0) [cnf transformation 31]
135. ~calm(john) [cnf transformation 23]
136. tall(X0) | brave(X0) [duplicate literal removal 115]
137. ~tall(X0) | brave(X0) [duplicate literal removal 117]
176. 9 <=> ! [X1] : (~tall(X1) | ~curious(X1)) [avatar definition]
177. ~tall(X1) | ~curious(X1) <- (9) [avatar component clause 176]
179. 10 <=> happy(sK2) [avatar definition]
181. ~happy(sK2) <- (~10) [avatar component clause 179]
183. 11 <=> funny(sK2) [avatar definition]
185. funny(sK2) <- (11) [avatar component clause 183]
186. 9 | ~10 | 11 [avatar split clause 106,183,179,176]
188. 12 <=> ! [X0] : ~wise(X0) [avatar definition]
189. ~wise(X0) <- (12) [avatar component clause 188]
191. 13 <=> brave(lucy) [avatar definition]
193. ~brave(lucy) <- (~13) [avatar component clause 191]
194. 12 | ~13 [avatar split clause 108,191,188]
200. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
201. ~funny(X1) <- (15) [avatar component clause 200]
203. 16 <=> wise(sK3) [avatar definition]
205. wise(sK3) <- (16) [avatar component clause 203]
206. 15 | 16 [avatar split clause 111,203,200]
208. 17 <=> ! [X1] : happy(X1) [avatar definition]
209. happy(X1) <- (17) [avatar component clause 208]
210. 17 | 16 [avatar split clause 110,203,208]
220. brave(X0) [subsumption resolution 136,137]
313. $false <- (~13) [subsumption resolution 193,220]
314. 13 [avatar contradiction clause 313]
319. $false <- (12, 16) [resolution 205,189]
320. ~12 | ~16 [avatar contradiction clause 319]
321. $false <- (~10, 17) [resolution 209,181]
322. 10 | ~17 [avatar contradiction clause 321]
323. $false <- (11, 15) [subsumption resolution 185,201]
324. ~11 | ~15 [avatar contradiction clause 323]
396. tall(X2) | calm(X2) <- (15) [resolution 114,201]
427. ~curious(X1) | calm(X1) <- (9, 15) [resolution 396,177]
429. calm(X0) | quiet(X0) <- (9, 15) [resolution 427,102]
431. calm(X0) <- (9, 15) [subsumption resolution 429,120]
432. $false <- (9, 15) [resolution 431,135]
434. ~9 | ~15 [avatar contradiction clause 432]
435. $false [avatar sat refutation 186,194,206,210,314,320,322,324,434]
% SZS output end Proof for 2817805092005011892649373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or kind is patient and vice versa.
If someone is not calm then someone is either wise or not tall and vice versa.
Everyone who is either funny or not tall is quiet or not happy.
If someone is either generous or not funny then fred is either humble or rich.
Everyone who is either creative or kind is curious or not brave.
Everyone who is not humble is either quiet or not quiet and vice versa.
If lucy is both not calm and curious then someone is patient.
Everyone who is not happy or not quiet is either generous or not patient.
Everyone who is either strong or not humble is calm or brave.
If lucy is either curious or not generous then susan is both brave and not brave.
Everyone who is not brave is both not curious and happy.
If someone is not patient then someone is strong and vice versa.
Everyone who is both not strong and not humble is strong or quiet and vice versa.
If mary is both funny and not calm then susan is calm.
Everyone who is either not wise or kind is either calm or rich.
If lucy is not patient or not wise then alice is not brave.
Susan is not strong or wise.
Someone is either quiet or not tall.
Susan is calm.
John is not wise or quiet.
Someone is not funny or not old.
Someone is both generous and not funny.
Someone is not kind or generous.
Someone is both creative and not humble. | Fred is patient. | entailment | (![X]:((~humble(X)<~>kind(X))<=>patient(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((funny(X)<~>~tall(X))=>(quiet(X)|~happy(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>((humble(fred)<~>rich(fred))))&
(![X]:((creative(X)<~>kind(X))=>(curious(X)|~brave(X))))&
(![X]:(~humble(X)<=>(quiet(X)<~>~quiet(X))))&
(((~calm(lucy)&curious(lucy)))=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|~quiet(X))=>(generous(X)<~>~patient(X))))&
(![X]:((strong(X)<~>~humble(X))=>(calm(X)|brave(X))))&
(((curious(lucy)<~>~generous(lucy)))=>((brave(susan)&~brave(susan))))&
(![X]:(~brave(X)=>(~curious(X)&happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~humble(X))<=>(strong(X)|quiet(X))))&
(((funny(mary)&~calm(mary)))=>(calm(susan)))&
(![X]:((~wise(X)<~>kind(X))=>(calm(X)<~>rich(X))))&
(((~patient(lucy)|~wise(lucy)))=>(~brave(alice)))&
((~strong(susan)|wise(susan)))&
(?[X]:((quiet(X)<~>~tall(X))))&
(calm(susan))&
((~wise(john)|quiet(john)))&
(?[X]:((~funny(X)|~old(X))))&
(?[X]:((generous(X)&~funny(X))))&
(?[X]:((~kind(X)|generous(X))))&
(?[X]:((creative(X)&~humble(X)))) | patient(fred) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6321058600665976460795709
% SZS output start Proof for 6321058600665976460795709
12. ? [X0] : ~patient(X0) <=> ? [X0] : strong(X0) [input p11]
13. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (quiet(X0) | strong(X0))) [input p12]
25. ~patient(fred) [input hypothesis]
27. ? [X0] : ~patient(X0) <=> ? [X1] : strong(X1) [rectify 12]
60. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : patient(X0)) [nnf transformation 27]
61. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : patient(X3)) [rectify 60]
62. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
63. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
64. (~patient(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : patient(X3)) [skolemisation 61,63,62]
65. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 13]
66. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | humble(X0) | strong(X0))) [flattening 65]
110. strong(sK4) | patient(X3) [cnf transformation 64]
113. ~strong(X0) | ~strong(X0) [cnf transformation 66]
134. ~patient(fred) [cnf transformation 25]
136. ~strong(X0) [duplicate literal removal 113]
210. 16 <=> ! [X1] : ~strong(X1) [avatar definition]
211. ~strong(X1) <- (16) [avatar component clause 210]
218. 18 <=> ! [X3] : patient(X3) [avatar definition]
219. patient(X3) <- (18) [avatar component clause 218]
221. 19 <=> strong(sK4) [avatar definition]
223. strong(sK4) <- (19) [avatar component clause 221]
224. 18 | 19 [avatar split clause 110,221,218]
225. 16 [avatar split clause 136,210]
294. $false <- (18) [resolution 219,134]
295. ~18 [avatar contradiction clause 294]
296. $false <- (16, 19) [subsumption resolution 223,211]
297. ~16 | ~19 [avatar contradiction clause 296]
298. $false [avatar sat refutation 224,225,295,297]
% SZS output end Proof for 6321058600665976460795709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then mary is kind or old and vice versa.
Everyone who is not old is both patient and not tall.
Everyone who is not happy is both wise and not funny.
Everyone who is brave is wise or patient and vice versa.
If someone is either humble or funny then someone is patient or not brave.
If susan is brave or not rich then someone is not brave or not kind.
Everyone who is not strong or funny is not wise or happy and vice versa.
Everyone who is either not patient or not quiet is either quiet or happy and vice versa.
If susan is either not generous or not humble then someone is not wise and vice versa.
If someone is both patient and not tall then someone is not strong and vice versa.
If someone is either not tall or curious then someone is not old or strong and vice versa.
If paul is brave or generous then alice is either not curious or not humble.
Everyone who is both brave and strong is either funny or not creative and vice versa.
Everyone who is creative or not quiet is both old and not creative and vice versa.
If someone is not curious then someone is generous and vice versa.
Someone is both brave and not patient.
Lucy is either not humble or kind.
Someone is not brave or generous.
Someone is not kind.
Someone is not generous.
Alice is not creative. | Susan is brave. | entailment | ((?[X]:(~kind(X)))<=>((kind(mary)|old(mary))))&
(![X]:(~old(X)=>(patient(X)&~tall(X))))&
(![X]:(~happy(X)=>(wise(X)&~funny(X))))&
(![X]:(brave(X)<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((brave(susan)|~rich(susan)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)|funny(X))<=>(~wise(X)|happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(quiet(X)<~>happy(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((brave(paul)|generous(paul)))=>((~curious(alice)<~>~humble(alice))))&
(![X]:((brave(X)&strong(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~quiet(X))<=>(old(X)&~creative(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(generous(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~humble(lucy)<~>kind(lucy)))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~generous(X)))&
(~creative(alice)) | brave(susan) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8951839792146294681222316
% SZS output start Proof for 8951839792146294681222316
3. ! [X0] : (~happy(X0) => (~funny(X0) & wise(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (patient(X0) | wise(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (quiet(X0) <~> happy(X0))) [input p7]
22. ~brave(susan) [input hypothesis]
29. ! [X0] : ((~funny(X0) & wise(X0)) | happy(X0)) [ennf transformation 3]
38. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ~brave(X0))) [nnf transformation 4]
39. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~brave(X0))) [flattening 38]
48. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 8]
87. wise(X0) | happy(X0) [cnf transformation 29]
90. ~wise(X0) | brave(X0) [cnf transformation 39]
91. ~patient(X0) | brave(X0) [cnf transformation 39]
101. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 48]
106. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 48]
145. ~brave(susan) [cnf transformation 22]
149. ~happy(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 101]
151. ~happy(X0) | patient(X0) | quiet(X0) [duplicate literal removal 106]
187. 9 <=> brave(susan) [avatar definition]
189. ~brave(susan) <- (~9) [avatar component clause 187]
200. ~happy(X0) | patient(X0) [subsumption resolution 149,151]
331. ~9 [avatar split clause 145,187]
347. brave(X0) | happy(X0) [resolution 90,87]
373. happy(susan) <- (~9) [resolution 347,189]
378. patient(susan) <- (~9) [resolution 373,200]
410. brave(susan) <- (~9) [resolution 378,91]
411. $false <- (~9) [subsumption resolution 410,189]
412. 9 [avatar contradiction clause 411]
413. $false [avatar sat refutation 331,412]
% SZS output end Proof for 8951839792146294681222316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or funny then someone is both patient and happy and vice versa.
If lucy is both not curious and curious then mary is not wise and vice versa.
Everyone who is both not generous and old is not rich or creative and vice versa.
Everyone who is not happy is not old.
Everyone who is patient or calm is either not strong or wise.
If lucy is both kind and tall then mary is both calm and not happy.
Everyone who is both creative and not quiet is both not wise and not strong and vice versa.
Everyone who is either calm or not happy is tall or wise.
If mary is both not curious and strong then someone is either not strong or humble.
If lucy is rich then someone is old or not wise.
If lucy is both old and generous then paul is not funny and vice versa.
If paul is both not calm and strong then susan is creative and vice versa.
If someone is both quiet and calm then someone is not curious or strong and vice versa.
Everyone who is either humble or curious is humble.
Everyone who is curious is either kind or not quiet and vice versa.
If someone is not calm then someone is both happy and not old and vice versa.
Someone is not quiet.
Mary is either not old or not happy.
Someone is either not happy or not old.
Lucy is happy.
Alice is strong.
Mary is both not strong and brave.
Susan is rich.
Someone is both not funny and not curious. | Mary is patient. | contradiction | ((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(((~curious(lucy)&curious(lucy)))<=>(~wise(mary)))&
(![X]:((~generous(X)&old(X))<=>(~rich(X)|creative(X))))&
(![X]:(~happy(X)=>~old(X)))&
(![X]:((patient(X)|calm(X))=>(~strong(X)<~>wise(X))))&
(((kind(lucy)&tall(lucy)))=>((calm(mary)&~happy(mary))))&
(![X]:((creative(X)&~quiet(X))<=>(~wise(X)&~strong(X))))&
(![X]:((calm(X)<~>~happy(X))=>(tall(X)|wise(X))))&
(((~curious(mary)&strong(mary)))=>(?[X]:((~strong(X)<~>humble(X)))))&
((rich(lucy))=>(?[X]:((old(X)|~wise(X)))))&
(((old(lucy)&generous(lucy)))<=>(~funny(paul)))&
(((~calm(paul)&strong(paul)))<=>(creative(susan)))&
((?[X]:((quiet(X)&calm(X))))<=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((humble(X)<~>curious(X))=>humble(X)))&
(![X]:(curious(X)<=>(kind(X)<~>~quiet(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((happy(X)&~old(X)))))&
(?[X]:(~quiet(X)))&
((~old(mary)<~>~happy(mary)))&
(?[X]:((~happy(X)<~>~old(X))))&
(happy(lucy))&
(strong(alice))&
((~strong(mary)&brave(mary)))&
(rich(susan))&
(?[X]:((~funny(X)&~curious(X)))) | patient(mary) | [
"p1",
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9136473454389861221913782
% SZS output start Proof for 9136473454389861221913782
2. (curious(lucy) & ~curious(lucy)) <=> ~wise(mary) [input p1]
5. ! [X0] : ((calm(X0) | patient(X0)) => (~strong(X0) <~> wise(X0))) [input p4]
22. brave(mary) & ~strong(mary) [input p21]
25. patient(mary) [input hypothesis]
29. ~strong(mary) [pure predicate removal 22]
31. ! [X0] : ((~strong(X0) <~> wise(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 5]
45. ((curious(lucy) & ~curious(lucy)) | wise(mary)) & (~wise(mary) | (~curious(lucy) | curious(lucy))) [nnf transformation 2]
46. ((curious(lucy) & ~curious(lucy)) | wise(mary)) & (~wise(mary) | ~curious(lucy) | curious(lucy)) [flattening 45]
49. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (~calm(X0) & ~patient(X0))) [nnf transformation 31]
89. ~curious(lucy) | wise(mary) [cnf transformation 46]
90. curious(lucy) | wise(mary) [cnf transformation 46]
99. ~wise(X0) | strong(X0) | ~patient(X0) [cnf transformation 49]
139. ~strong(mary) [cnf transformation 29]
143. patient(mary) [cnf transformation 25]
177. 8 <=> wise(mary) [avatar definition]
179. wise(mary) <- (8) [avatar component clause 177]
181. 9 <=> curious(lucy) [avatar definition]
184. 8 | 9 [avatar split clause 90,181,177]
185. 8 | ~9 [avatar split clause 89,181,177]
209. 15 <=> strong(mary) [avatar definition]
211. ~strong(mary) <- (~15) [avatar component clause 209]
321. ~15 [avatar split clause 139,209]
359. strong(mary) | ~patient(mary) <- (8) [resolution 99,179]
360. ~patient(mary) <- (8, ~15) [subsumption resolution 359,211]
361. $false <- (8, ~15) [subsumption resolution 360,143]
362. ~8 | 15 [avatar contradiction clause 361]
363. $false [avatar sat refutation 184,185,321,362]
% SZS output end Proof for 9136473454389861221913782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not kind is both kind and wise and vice versa.
Everyone who is not strong is not calm and vice versa.
Everyone who is not wise or not old is strong and vice versa.
If lucy is either not curious or not creative then someone is calm or not generous and vice versa.
If susan is either not kind or wise then someone is both happy and not tall and vice versa.
If lucy is both not generous and not calm then someone is strong.
Everyone who is both tall and not happy is both kind and not wise.
If someone is tall or rich then fred is either happy or not wise and vice versa.
If someone is brave then susan is both old and not wise and vice versa.
If lucy is either creative or not patient then susan is wise.
If someone is either not rich or not curious then someone is either not quiet or creative and vice versa.
Everyone who is both creative and not tall is not kind or not brave and vice versa.
Everyone who is not humble is either funny or generous.
Everyone who is patient or tall is both not quiet and old and vice versa.
Everyone who is both patient and not calm is funny or kind and vice versa.
Everyone who is not humble is calm or not happy.
Someone is not curious.
Fred is kind or creative.
Someone is funny or not quiet.
Mary is wise.
Someone is strong or not brave.
Someone is either patient or brave.
Someone is generous. | Lucy is rich. | contradiction | (![X]:((~funny(X)&~kind(X))<=>(kind(X)&wise(X))))&
(![X]:(~strong(X)<=>~calm(X)))&
(![X]:((~wise(X)|~old(X))<=>strong(X)))&
(((~curious(lucy)<~>~creative(lucy)))<=>(?[X]:((calm(X)|~generous(X)))))&
(((~kind(susan)<~>wise(susan)))<=>(?[X]:((happy(X)&~tall(X)))))&
(((~generous(lucy)&~calm(lucy)))=>(?[X]:(strong(X))))&
(![X]:((tall(X)&~happy(X))=>(kind(X)&~wise(X))))&
((?[X]:((tall(X)|rich(X))))<=>((happy(fred)<~>~wise(fred))))&
((?[X]:(brave(X)))<=>((old(susan)&~wise(susan))))&
(((creative(lucy)<~>~patient(lucy)))=>(wise(susan)))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((creative(X)&~tall(X))<=>(~kind(X)|~brave(X))))&
(![X]:(~humble(X)=>(funny(X)<~>generous(X))))&
(![X]:((patient(X)|tall(X))<=>(~quiet(X)&old(X))))&
(![X]:((patient(X)&~calm(X))<=>(funny(X)|kind(X))))&
(![X]:(~humble(X)=>(calm(X)|~happy(X))))&
(?[X]:(~curious(X)))&
((kind(fred)|creative(fred)))&
(?[X]:((funny(X)|~quiet(X))))&
(wise(mary))&
(?[X]:((strong(X)|~brave(X))))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:(generous(X))) | rich(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3565149787788569575715380
% SZS output start Proof for 3565149787788569575715380
1. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (wise(X0) & kind(X0))) [input p0]
2. ! [X0] : (~strong(X0) <=> ~calm(X0)) [input p1]
3. ! [X0] : ((~old(X0) | ~wise(X0)) <=> strong(X0)) [input p2]
4. (~curious(lucy) <~> ~creative(lucy)) <=> ? [X0] : (~generous(X0) | calm(X0)) [input p3]
5. (~kind(susan) <~> wise(susan)) <=> ? [X0] : (~tall(X0) & happy(X0)) [input p4]
8. ? [X0] : (rich(X0) | tall(X0)) <=> (happy(fred) <~> ~wise(fred)) [input p7]
10. (creative(lucy) <~> ~patient(lucy)) => wise(susan) [input p9]
11. ? [X0] : (~rich(X0) <~> ~curious(X0)) <=> ? [X0] : (~quiet(X0) <~> creative(X0)) [input p10]
12. ! [X0] : ((~tall(X0) & creative(X0)) <=> (~brave(X0) | ~kind(X0))) [input p11]
14. ! [X0] : ((tall(X0) | patient(X0)) <=> (old(X0) & ~quiet(X0))) [input p13]
15. ! [X0] : ((~calm(X0) & patient(X0)) <=> (kind(X0) | funny(X0))) [input p14]
24. rich(lucy) [input hypothesis]
25. ? [X0] : (~rich(X0) <~> ~curious(X0)) <=> ? [X1] : (~quiet(X1) <~> creative(X1)) [rectify 11]
32. wise(susan) | (creative(lucy) <=> ~patient(lucy)) [ennf transformation 10]
33. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 1]
34. ! [X0] : (((~kind(X0) & ~funny(X0)) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | kind(X0) | funny(X0))) [flattening 33]
35. ! [X0] : ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0))) [nnf transformation 2]
36. ! [X0] : (((~old(X0) | ~wise(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) & wise(X0)))) [nnf transformation 3]
37. ! [X0] : ((~old(X0) | ~wise(X0) | ~strong(X0)) & (strong(X0) | (old(X0) & wise(X0)))) [flattening 36]
38. (((creative(lucy) | curious(lucy)) & (~creative(lucy) | ~curious(lucy))) | ! [X0] : (generous(X0) & ~calm(X0))) & (? [X0] : (~generous(X0) | calm(X0)) | ((~curious(lucy) | creative(lucy)) & (~creative(lucy) | curious(lucy)))) [nnf transformation 4]
39. (((creative(lucy) | curious(lucy)) & (~creative(lucy) | ~curious(lucy))) | ! [X0] : (generous(X0) & ~calm(X0))) & (? [X1] : (~generous(X1) | calm(X1)) | ((~curious(lucy) | creative(lucy)) & (~creative(lucy) | curious(lucy)))) [rectify 38]
40. ? [X1] : (~generous(X1) | calm(X1)) => (~generous(sK0) | calm(sK0)) [choice axiom]
41. (((creative(lucy) | curious(lucy)) & (~creative(lucy) | ~curious(lucy))) | ! [X0] : (generous(X0) & ~calm(X0))) & ((~generous(sK0) | calm(sK0)) | ((~curious(lucy) | creative(lucy)) & (~creative(lucy) | curious(lucy)))) [skolemisation 39,40]
42. (((~wise(susan) | kind(susan)) & (wise(susan) | ~kind(susan))) | ! [X0] : (tall(X0) | ~happy(X0))) & (? [X0] : (~tall(X0) & happy(X0)) | ((~kind(susan) | ~wise(susan)) & (wise(susan) | kind(susan)))) [nnf transformation 5]
43. (((~wise(susan) | kind(susan)) & (wise(susan) | ~kind(susan))) | ! [X0] : (tall(X0) | ~happy(X0))) & (? [X1] : (~tall(X1) & happy(X1)) | ((~kind(susan) | ~wise(susan)) & (wise(susan) | kind(susan)))) [rectify 42]
44. ? [X1] : (~tall(X1) & happy(X1)) => (~tall(sK1) & happy(sK1)) [choice axiom]
45. (((~wise(susan) | kind(susan)) & (wise(susan) | ~kind(susan))) | ! [X0] : (tall(X0) | ~happy(X0))) & ((~tall(sK1) & happy(sK1)) | ((~kind(susan) | ~wise(susan)) & (wise(susan) | kind(susan)))) [skolemisation 43,44]
48. (? [X0] : (rich(X0) | tall(X0)) | ((happy(fred) | wise(fred)) & (~wise(fred) | ~happy(fred)))) & (((wise(fred) | ~happy(fred)) & (~wise(fred) | happy(fred))) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 8]
49. (? [X0] : (rich(X0) | tall(X0)) | ((happy(fred) | wise(fred)) & (~wise(fred) | ~happy(fred)))) & (((wise(fred) | ~happy(fred)) & (~wise(fred) | happy(fred))) | ! [X1] : (~rich(X1) & ~tall(X1))) [rectify 48]
50. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom]
51. ((rich(sK3) | tall(sK3)) | ((happy(fred) | wise(fred)) & (~wise(fred) | ~happy(fred)))) & (((wise(fred) | ~happy(fred)) & (~wise(fred) | happy(fred))) | ! [X1] : (~rich(X1) & ~tall(X1))) [skolemisation 49,50]
57. wise(susan) | ((creative(lucy) | patient(lucy)) & (~patient(lucy) | ~creative(lucy))) [nnf transformation 32]
58. (? [X0] : ((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | ! [X1] : ((~quiet(X1) | ~creative(X1)) & (creative(X1) | quiet(X1)))) & (? [X1] : ((~creative(X1) | quiet(X1)) & (creative(X1) | ~quiet(X1))) | ! [X0] : ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) [nnf transformation 25]
59. (? [X0] : ((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | ! [X1] : ((~quiet(X1) | ~creative(X1)) & (creative(X1) | quiet(X1)))) & (? [X2] : ((~creative(X2) | quiet(X2)) & (creative(X2) | ~quiet(X2))) | ! [X3] : ((~rich(X3) | curious(X3)) & (~curious(X3) | rich(X3)))) [rectify 58]
60. ? [X0] : ((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) => ((curious(sK5) | rich(sK5)) & (~curious(sK5) | ~rich(sK5))) [choice axiom]
61. ? [X2] : ((~creative(X2) | quiet(X2)) & (creative(X2) | ~quiet(X2))) => ((~creative(sK6) | quiet(sK6)) & (creative(sK6) | ~quiet(sK6))) [choice axiom]
62. (((curious(sK5) | rich(sK5)) & (~curious(sK5) | ~rich(sK5))) | ! [X1] : ((~quiet(X1) | ~creative(X1)) & (creative(X1) | quiet(X1)))) & (((~creative(sK6) | quiet(sK6)) & (creative(sK6) | ~quiet(sK6))) | ! [X3] : ((~rich(X3) | curious(X3)) & (~curious(X3) | rich(X3)))) [skolemisation 59,61,60]
63. ! [X0] : (((~tall(X0) & creative(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (tall(X0) | ~creative(X0)))) [nnf transformation 12]
64. ! [X0] : (((~tall(X0) & creative(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | tall(X0) | ~creative(X0))) [flattening 63]
65. ! [X0] : (((tall(X0) | patient(X0)) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | (~tall(X0) & ~patient(X0)))) [nnf transformation 14]
66. ! [X0] : ((tall(X0) | patient(X0) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | (~tall(X0) & ~patient(X0)))) [flattening 65]
67. ! [X0] : (((~calm(X0) & patient(X0)) | (~kind(X0) & ~funny(X0))) & ((kind(X0) | funny(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 15]
68. ! [X0] : (((~calm(X0) & patient(X0)) | (~kind(X0) & ~funny(X0))) & (kind(X0) | funny(X0) | calm(X0) | ~patient(X0))) [flattening 67]
80. kind(X0) | kind(X0) | funny(X0) [cnf transformation 34]
83. ~kind(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 34]
85. ~strong(X0) | calm(X0) [cnf transformation 35]
86. strong(X0) | wise(X0) [cnf transformation 37]
91. ~creative(lucy) | ~curious(lucy) | ~calm(X0) [cnf transformation 41]
100. ~wise(susan) | kind(susan) | tall(X0) | ~happy(X0) [cnf transformation 45]
105. ~wise(fred) | happy(fred) | ~rich(X1) [cnf transformation 51]
113. wise(susan) | ~patient(lucy) | ~creative(lucy) [cnf transformation 57]
118. ~creative(sK6) | quiet(sK6) | ~rich(X3) | curious(X3) [cnf transformation 62]
124. creative(X0) | kind(X0) [cnf transformation 64]
126. ~tall(X0) | kind(X0) [cnf transformation 64]
128. ~quiet(X0) | ~patient(X0) [cnf transformation 66]
134. ~funny(X0) | patient(X0) [cnf transformation 68]
135. ~kind(X0) | patient(X0) [cnf transformation 68]
137. ~calm(X0) | ~kind(X0) [cnf transformation 68]
146. rich(lucy) [cnf transformation 24]
147. kind(X0) | funny(X0) [duplicate literal removal 80]
148. ~wise(X0) | ~kind(X0) [duplicate literal removal 83]
153. 2 <=> curious(lucy) [avatar definition]
157. 3 <=> creative(lucy) [avatar definition]
158. ~creative(lucy) <- (~3) [avatar component clause 157]
162. 4 <=> ! [X0] : ~calm(X0) [avatar definition]
163. ~calm(X0) <- (4) [avatar component clause 162]
166. 4 | ~2 | ~3 [avatar split clause 91,157,153,162]
177. ~wise(susan) | tall(X0) | ~happy(X0) [subsumption resolution 100,148]
179. 7 <=> ! [X0] : (tall(X0) | ~happy(X0)) [avatar definition]
180. ~happy(X0) | tall(X0) <- (7) [avatar component clause 179]
182. 8 <=> wise(susan) [avatar definition]
185. 7 | ~8 [avatar split clause 177,182,179]
216. 15 <=> wise(fred) [avatar definition]
217. ~wise(fred) <- (~15) [avatar component clause 216]
220. 16 <=> happy(fred) [avatar definition]
222. happy(fred) <- (16) [avatar component clause 220]
234. 19 <=> ! [X1] : ~rich(X1) [avatar definition]
235. ~rich(X1) <- (19) [avatar component clause 234]
241. 19 | 16 | ~15 [avatar split clause 105,216,220,234]
258. 24 <=> patient(lucy) [avatar definition]
259. ~patient(lucy) <- (~24) [avatar component clause 258]
262. ~3 | ~24 | 8 [avatar split clause 113,182,258,157]
282. 29 <=> ! [X3] : (~rich(X3) | curious(X3)) [avatar definition]
283. ~rich(X3) | curious(X3) <- (29) [avatar component clause 282]
285. 30 <=> quiet(sK6) [avatar definition]
287. quiet(sK6) <- (30) [avatar component clause 285]
289. 31 <=> creative(sK6) [avatar definition]
291. ~creative(sK6) <- (~31) [avatar component clause 289]
292. 29 | 30 | ~31 [avatar split clause 118,289,285,282]
327. calm(X0) | wise(X0) [resolution 86,85]
328. kind(sK6) <- (~31) [resolution 124,291]
340. funny(X0) | patient(X0) [resolution 147,135]
341. patient(X0) [subsumption resolution 340,134]
342. $false <- (~24) [resolution 341,259]
344. 24 [avatar contradiction clause 342]
347. kind(lucy) <- (~3) [resolution 158,124]
400. wise(X0) <- (4) [resolution 327,163]
401. wise(X1) | ~kind(X1) [resolution 327,137]
406. $false <- (4, ~15) [resolution 400,217]
409. ~4 | 15 [avatar contradiction clause 406]
411. ~kind(X1) [subsumption resolution 401,148]
413. $false <- (~3) [resolution 411,347]
416. $false <- (~31) [resolution 411,328]
417. 31 [avatar contradiction clause 416]
420. 3 [avatar contradiction clause 413]
426. ~patient(sK6) <- (30) [resolution 287,128]
427. $false <- (30) [subsumption resolution 426,341]
428. ~30 [avatar contradiction clause 427]
429. curious(lucy) <- (29) [resolution 283,146]
436. 2 | ~29 [avatar split clause 429,282,153]
439. tall(fred) <- (7, 16) [resolution 222,180]
451. kind(fred) <- (7, 16) [resolution 439,126]
454. $false <- (7, 16) [subsumption resolution 451,411]
455. ~7 | ~16 [avatar contradiction clause 454]
456. $false <- (19) [resolution 235,146]
459. ~19 [avatar contradiction clause 456]
460. $false [avatar sat refutation 166,185,241,262,292,344,409,417,420,428,436,455,459]
% SZS output end Proof for 3565149787788569575715380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is not wise. Everyone who is both not humble and kind is both not wise and strong and vice versa. Everyone who is both not tall and calm is not happy or patient and vice versa. If someone is not strong or humble then someone is either not happy or not humble. Everyone who is not humble is happy or not generous. If john is either strong or not kind then someone is either not quiet or not brave and vice versa. If someone is not curious then fred is happy or not rich and vice versa. Everyone who is both not happy and strong is not funny and vice versa. If mary is not strong then someone is wise or quiet. Everyone who is both not happy and not tall is either tall or happy. If someone is not patient then fred is either not creative or generous. Everyone who is either not strong or quiet is both not humble and not happy and vice versa. If mary is either humble or wise then someone is either rich or happy and vice versa. If paul is either not quiet or strong then someone is calm or not rich and vice versa. Everyone who is not old is wise and vice versa. Everyone who is not old or not rich is creative and vice versa. Someone is both not wise and kind. Someone is either not strong or not brave. Fred is not wise. Lucy is both funny and not wise. Susan is not wise. Someone is either not rich or curious. Susan is either kind or not funny. | Susan is not kind. | contradiction | (![X]:((quiet(X)&~funny(X))=>~wise(X)))&
(![X]:((~humble(X)&kind(X))<=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:(~humble(X)=>(happy(X)|~generous(X))))&
(((strong(john)<~>~kind(john)))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:(~curious(X)))<=>((happy(fred)|~rich(fred))))&
(![X]:((~happy(X)&strong(X))<=>~funny(X)))&
((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~strong(X)<~>~brave(X))))&
(~wise(fred))&
((funny(lucy)&~wise(lucy)))&
(~wise(susan))&
(?[X]:((~rich(X)<~>curious(X))))&
((kind(susan)<~>~funny(susan))) | ~kind(susan) | [
"p2",
"p7",
"p9",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7919784357510801941155918
% SZS output start Proof for 7919784357510801941155918
3. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (patient(X0) | ~happy(X0))) [input p2]
8. ! [X0] : ((strong(X0) & ~happy(X0)) <=> ~funny(X0)) [input p7]
10. ! [X0] : ((~tall(X0) & ~happy(X0)) => (tall(X0) <~> happy(X0))) [input p9]
12. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p11]
14. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p13]
23. kind(susan) <~> ~funny(susan) [input p22]
24. ~kind(susan) [input hypothesis]
32. ! [X0] : ((tall(X0) <~> happy(X0)) | (tall(X0) | happy(X0))) [ennf transformation 10]
33. ! [X0] : ((tall(X0) <~> happy(X0)) | tall(X0) | happy(X0)) [flattening 32]
37. ! [X0] : (((calm(X0) & ~tall(X0)) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | (~calm(X0) | tall(X0)))) [nnf transformation 3]
38. ! [X0] : (((calm(X0) & ~tall(X0)) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ~calm(X0) | tall(X0))) [flattening 37]
52. ! [X0] : (((strong(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | (~strong(X0) | happy(X0)))) [nnf transformation 8]
53. ! [X0] : (((strong(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | ~strong(X0) | happy(X0))) [flattening 52]
56. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | tall(X0) | happy(X0)) [nnf transformation 33]
58. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 58]
64. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 14]
65. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 64]
66. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK5) | calm(sK5)) [choice axiom]
67. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK5) | calm(sK5)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 65,66]
79. (funny(susan) | ~kind(susan)) & (~funny(susan) | kind(susan)) [nnf transformation 23]
86. ~tall(X0) | happy(X0) [cnf transformation 38]
88. happy(X0) | calm(X0) [cnf transformation 38]
107. ~happy(X0) | funny(X0) [cnf transformation 53]
110. happy(X0) | tall(X0) | tall(X0) | happy(X0) [cnf transformation 56]
116. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 59]
117. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 59]
130. strong(paul) | ~quiet(paul) | ~calm(X0) [cnf transformation 67]
132. ~strong(paul) | quiet(paul) | ~calm(X0) [cnf transformation 67]
149. ~funny(susan) | kind(susan) [cnf transformation 79]
151. ~kind(susan) [cnf transformation 24]
152. happy(X0) | tall(X0) [duplicate literal removal 110]
232. happy(X0) [subsumption resolution 152,86]
246. ~strong(X0) | ~quiet(X0) [subsumption resolution 117,232]
247. quiet(X0) | strong(X0) [subsumption resolution 116,232]
273. 25 <=> quiet(paul) [avatar definition]
277. quiet(paul) | ~calm(X0) [subsumption resolution 132,247]
279. 26 <=> ! [X0] : ~calm(X0) [avatar definition]
280. ~calm(X0) <- (26) [avatar component clause 279]
281. 26 | 25 [avatar split clause 277,273,279]
284. ~quiet(paul) | ~calm(X0) [subsumption resolution 130,246]
285. 26 | ~25 [avatar split clause 284,273,279]
307. 31 <=> kind(susan) [avatar definition]
311. 32 <=> funny(susan) [avatar definition]
312. ~funny(susan) <- (~32) [avatar component clause 311]
315. 31 | ~32 [avatar split clause 149,311,307]
316. ~31 [avatar split clause 151,307]
323. funny(X0) | calm(X0) [resolution 107,88]
325. funny(X0) <- (26) [subsumption resolution 323,280]
326. $false <- (26, ~32) [resolution 325,312]
327. ~26 | 32 [avatar contradiction clause 326]
328. $false [avatar sat refutation 281,285,315,316,327]
% SZS output end Proof for 7919784357510801941155918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not kind and vice versa.
If alice is not creative then someone is old or patient.
If john is both not curious and not humble then someone is either creative or not kind and vice versa.
Everyone who is not patient or quiet is both not patient and creative and vice versa.
If mary is either not quiet or creative then john is not quiet and vice versa.
Everyone who is either not curious or not tall is not curious and vice versa.
Everyone who is not wise or funny is rich or generous.
If fred is either not strong or quiet then someone is either wise or tall.
Everyone who is either not generous or kind is either not funny or strong.
If someone is both happy and wise then paul is not curious.
If john is creative or tall then lucy is not rich.
If someone is quiet or not rich then paul is both humble and patient.
If susan is curious or not quiet then lucy is not funny and vice versa.
Everyone who is curious or not happy is tall.
Everyone who is either calm or not generous is both not curious and not generous.
Fred is patient or not humble.
Someone is wise.
Someone is both old and not funny.
Susan is not creative.
Mary is either generous or not humble.
Someone is patient.
Someone is both old and tall.
Someone is humble. | Fred is tall. | entailment | (![X]:((creative(X)<~>happy(X))<=>~kind(X)))&
((~creative(alice))=>(?[X]:((old(X)|patient(X)))))&
(((~curious(john)&~humble(john)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~patient(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(((~quiet(mary)<~>creative(mary)))<=>(~quiet(john)))&
(![X]:((~curious(X)<~>~tall(X))<=>~curious(X)))&
(![X]:((~wise(X)|funny(X))=>(rich(X)|generous(X))))&
(((~strong(fred)<~>quiet(fred)))=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((~generous(X)<~>kind(X))=>(~funny(X)<~>strong(X))))&
((?[X]:((happy(X)&wise(X))))=>(~curious(paul)))&
(((creative(john)|tall(john)))=>(~rich(lucy)))&
((?[X]:((quiet(X)|~rich(X))))=>((humble(paul)&patient(paul))))&
(((curious(susan)|~quiet(susan)))<=>(~funny(lucy)))&
(![X]:((curious(X)|~happy(X))=>tall(X)))&
(![X]:((calm(X)<~>~generous(X))=>(~curious(X)&~generous(X))))&
((patient(fred)|~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((old(X)&~funny(X))))&
(~creative(susan))&
((generous(mary)<~>~humble(mary)))&
(?[X]:(patient(X)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:(humble(X))) | tall(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6236793048216305029986333
% SZS output start Proof for 6236793048216305029986333
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> ~curious(X0)) [input p5]
24. ~tall(fred) [input hypothesis]
46. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | curious(X0)) & (~curious(X0) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
85. ~curious(X0) | ~curious(X0) | tall(X0) [cnf transformation 46]
87. tall(X0) | curious(X0) | curious(X0) [cnf transformation 46]
123. ~tall(fred) [cnf transformation 24]
125. ~curious(X0) | tall(X0) [duplicate literal removal 85]
126. tall(X0) | curious(X0) [duplicate literal removal 87]
172. tall(X0) [subsumption resolution 125,126]
250. $false [subsumption resolution 123,172]
% SZS output end Proof for 6236793048216305029986333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not kind then someone is both happy and calm and vice versa. Everyone who is strong or rich is not kind or not rich. Everyone who is not rich or funny is either not curious or kind. If alice is both patient and not happy then someone is either not curious or not old. Everyone who is not wise or not old is both rich and not wise and vice versa. If john is not brave or not kind then alice is either not humble or not kind. Everyone who is humble or creative is either not humble or brave. Everyone who is not creative or creative is funny. If someone is patient then someone is both not curious and not generous and vice versa. If someone is both brave and not old then someone is kind or not strong. If someone is both old and not funny then someone is rich and vice versa. Everyone who is both not strong and not wise is both not wise and not calm. Everyone who is not calm is not quiet or old and vice versa. Everyone who is patient is either not old or not wise and vice versa. If lucy is both old and not tall then alice is either not curious or curious and vice versa. Everyone who is rich or quiet is not generous. Someone is rich or not happy. Someone is not happy. Alice is not wise or tall. Lucy is either not kind or not tall. Alice is both tall and not happy. | Lucy is not brave. | neutral | ((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~curious(X)<~>kind(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~happy(X)))&
((~wise(alice)|tall(alice)))&
((~kind(lucy)<~>~tall(lucy)))&
((tall(alice)&~happy(alice))) | ~brave(lucy) | [] | null | 0 |
If someone is funny then lucy is kind or not patient.
If someone is either wise or tall then someone is not quiet and vice versa.
If someone is both funny and calm then someone is brave or not kind and vice versa.
Everyone who is both not patient and not generous is either humble or not kind.
Everyone who is either creative or not old is both old and not kind.
If john is both not kind and funny then susan is either wise or not old.
If john is either rich or not strong then someone is either not creative or not quiet and vice versa.
Everyone who is either old or tall is not quiet or not wise and vice versa.
Everyone who is not tall is not creative and vice versa.
If someone is either old or humble then fred is not funny and vice versa.
Everyone who is both calm and not quiet is either not generous or not creative and vice versa.
If paul is either calm or rich then someone is either tall or not humble and vice versa.
If john is not tall or calm then paul is both calm and old and vice versa.
If lucy is not tall then someone is brave and vice versa.
Everyone who is both not funny and quiet is not strong.
Everyone who is not creative or not curious is tall.
Someone is rich.
Susan is both not humble and happy.
Someone is both patient and not brave.
Someone is strong or tall.
Mary is not curious.
John is not rich or not brave.
Someone is either humble or funny. | Susan is brave. | contradiction | ((?[X]:(funny(X)))=>((kind(lucy)|~patient(lucy))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((funny(X)&calm(X))))<=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((~patient(X)&~generous(X))=>(humble(X)<~>~kind(X))))&
(![X]:((creative(X)<~>~old(X))=>(old(X)&~kind(X))))&
(((~kind(john)&funny(john)))=>((wise(susan)<~>~old(susan))))&
(((rich(john)<~>~strong(john)))<=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((old(X)<~>tall(X))<=>(~quiet(X)|~wise(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
((?[X]:((old(X)<~>humble(X))))<=>(~funny(fred)))&
(![X]:((calm(X)&~quiet(X))<=>(~generous(X)<~>~creative(X))))&
(((calm(paul)<~>rich(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(((~tall(john)|calm(john)))<=>((calm(paul)&old(paul))))&
((~tall(lucy))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)&quiet(X))=>~strong(X)))&
(![X]:((~creative(X)|~curious(X))=>tall(X)))&
(?[X]:(rich(X)))&
((~humble(susan)&happy(susan)))&
(?[X]:((patient(X)&~brave(X))))&
(?[X]:((strong(X)|tall(X))))&
(~curious(mary))&
((~rich(john)|~brave(john)))&
(?[X]:((humble(X)<~>funny(X)))) | brave(susan) | [
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6233139407983091479603275
% SZS output start Proof for 6233139407983091479603275
9. ! [X0] : (~tall(X0) <=> ~creative(X0)) [input p8]
14. ~tall(lucy) <=> ? [X0] : brave(X0) [input p13]
16. ! [X0] : ((~curious(X0) | ~creative(X0)) => tall(X0)) [input p15]
24. brave(susan) [input hypothesis]
37. ! [X0] : (tall(X0) | (curious(X0) & creative(X0))) [ennf transformation 16]
57. ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 9]
70. (~tall(lucy) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | tall(lucy)) [nnf transformation 14]
71. (~tall(lucy) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | tall(lucy)) [rectify 70]
72. ? [X1] : brave(X1) => brave(sK7) [choice axiom]
73. (~tall(lucy) | ! [X0] : ~brave(X0)) & (brave(sK7) | tall(lucy)) [skolemisation 71,72]
115. ~creative(X0) | tall(X0) [cnf transformation 57]
116. ~tall(X0) | creative(X0) [cnf transformation 57]
141. ~tall(lucy) | ~brave(X0) [cnf transformation 73]
143. tall(X0) | creative(X0) [cnf transformation 37]
154. brave(susan) [cnf transformation 24]
202. 12 <=> ! [X1] : ~brave(X1) [avatar definition]
203. ~brave(X1) <- (12) [avatar component clause 202]
341. 41 <=> tall(lucy) [avatar definition]
343. ~tall(lucy) <- (~41) [avatar component clause 341]
344. 12 | ~41 [avatar split clause 141,341,202]
350. creative(X0) [subsumption resolution 143,116]
379. $false <- (12) [resolution 203,154]
380. ~12 [avatar contradiction clause 379]
383. tall(X0) [resolution 115,350]
385. $false <- (~41) [resolution 383,343]
390. 41 [avatar contradiction clause 385]
391. $false [avatar sat refutation 344,380,390]
% SZS output end Proof for 6233139407983091479603275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not humble is both not brave and quiet and vice versa.
If paul is curious or not brave then alice is not kind or not humble.
If someone is both not calm and rich then someone is either patient or wise.
If susan is not wise then fred is not humble or funny and vice versa.
If lucy is both curious and old then someone is not brave or not funny and vice versa.
If susan is not calm then susan is both not tall and not old and vice versa.
If paul is both not kind and not funny then lucy is either not generous or not creative and vice versa.
Everyone who is not tall is not calm.
If someone is curious or strong then john is curious or tall.
If someone is kind then someone is either not curious or rich and vice versa.
Everyone who is not wise or creative is both humble and patient.
If someone is humble then alice is either old or humble.
Everyone who is either not kind or not funny is not rich or strong and vice versa.
Everyone who is kind or not tall is not wise or brave and vice versa.
Everyone who is both not calm and patient is both calm and creative.
If lucy is generous then susan is not humble or not happy and vice versa.
Someone is not old or not humble.
Someone is not generous or generous.
Susan is not patient or not happy.
Susan is rich.
Someone is not rich or not creative.
Someone is strong.
Fred is both funny and not creative. | Lucy is old. | entailment | (![X]:((wise(X)|~humble(X))<=>(~brave(X)&quiet(X))))&
(((curious(paul)|~brave(paul)))=>((~kind(alice)|~humble(alice))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((patient(X)<~>wise(X)))))&
((~wise(susan))<=>((~humble(fred)|funny(fred))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:((~brave(X)|~funny(X)))))&
((~calm(susan))<=>((~tall(susan)&~old(susan))))&
(((~kind(paul)&~funny(paul)))<=>((~generous(lucy)<~>~creative(lucy))))&
(![X]:(~tall(X)=>~calm(X)))&
((?[X]:((curious(X)|strong(X))))=>((curious(john)|tall(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((~wise(X)|creative(X))=>(humble(X)&patient(X))))&
((?[X]:(humble(X)))=>((old(alice)<~>humble(alice))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~rich(X)|strong(X))))&
(![X]:((kind(X)|~tall(X))<=>(~wise(X)|brave(X))))&
(![X]:((~calm(X)&patient(X))=>(calm(X)&creative(X))))&
((generous(lucy))<=>((~humble(susan)|~happy(susan))))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~generous(X)|generous(X))))&
((~patient(susan)|~happy(susan)))&
(rich(susan))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(strong(X)))&
((funny(fred)&~creative(fred))) | old(lucy) | [
"p0",
"p4",
"p7",
"p10",
"p12",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 816097376701809934793255
% SZS output start Proof for 816097376701809934793255
1. ! [X0] : ((~humble(X0) | wise(X0)) <=> (quiet(X0) & ~brave(X0))) [input p0]
5. (old(lucy) & curious(lucy)) <=> ? [X0] : (~funny(X0) | ~brave(X0)) [input p4]
8. ! [X0] : (~tall(X0) => ~calm(X0)) [input p7]
11. ! [X0] : ((creative(X0) | ~wise(X0)) => (patient(X0) & humble(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> (strong(X0) | ~rich(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | kind(X0)) <=> (brave(X0) | ~wise(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~calm(X0)) => (creative(X0) & calm(X0))) [input p14]
22. ? [X0] : strong(X0) [input p21]
24. ~old(lucy) [input hypothesis]
30. ! [X0] : (~calm(X0) | tall(X0)) [ennf transformation 8]
33. ! [X0] : ((patient(X0) & humble(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 11]
35. ! [X0] : ((creative(X0) & calm(X0)) | (~patient(X0) | calm(X0))) [ennf transformation 15]
36. ! [X0] : ((creative(X0) & calm(X0)) | ~patient(X0) | calm(X0)) [flattening 35]
37. ! [X0] : (((~humble(X0) | wise(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [nnf transformation 1]
38. ! [X0] : ((~humble(X0) | wise(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [flattening 37]
45. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X0] : (~funny(X0) | ~brave(X0)) | (~old(lucy) | ~curious(lucy))) [nnf transformation 5]
46. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X0] : (~funny(X0) | ~brave(X0)) | ~old(lucy) | ~curious(lucy)) [flattening 45]
47. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X1] : (~funny(X1) | ~brave(X1)) | ~old(lucy) | ~curious(lucy)) [rectify 46]
48. ? [X1] : (~funny(X1) | ~brave(X1)) => (~funny(sK1) | ~brave(sK1)) [choice axiom]
49. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & ((~funny(sK1) | ~brave(sK1)) | ~old(lucy) | ~curious(lucy)) [skolemisation 47,48]
60. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 13]
61. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [flattening 60]
62. ! [X0] : (((~tall(X0) | kind(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (tall(X0) & ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((~tall(X0) | kind(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | (tall(X0) & ~kind(X0)))) [flattening 62]
72. ? [X0] : strong(X0) => strong(sK7) [choice axiom]
73. strong(sK7) [skolemisation 22,72]
74. ~brave(X0) | ~wise(X0) [cnf transformation 38]
89. old(lucy) | brave(X0) [cnf transformation 49]
90. old(lucy) | funny(X0) [cnf transformation 49]
100. ~calm(X0) | tall(X0) [cnf transformation 30]
109. patient(X0) | wise(X0) [cnf transformation 33]
116. ~strong(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 61]
121. ~tall(X0) | kind(X0) | wise(X0) [cnf transformation 63]
123. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 36]
133. strong(sK7) [cnf transformation 73]
136. ~old(lucy) [cnf transformation 24]
137. ~patient(X0) | calm(X0) [duplicate literal removal 123]
185. 11 <=> ! [X0] : funny(X0) [avatar definition]
186. funny(X0) <- (11) [avatar component clause 185]
188. 12 <=> old(lucy) [avatar definition]
191. 11 | 12 [avatar split clause 90,188,185]
193. 13 <=> ! [X0] : brave(X0) [avatar definition]
194. brave(X0) <- (13) [avatar component clause 193]
195. 13 | 12 [avatar split clause 89,188,193]
335. ~12 [avatar split clause 136,188]
338. ~wise(X0) <- (13) [resolution 74,194]
344. calm(X0) | wise(X0) [resolution 137,109]
345. calm(X0) <- (13) [subsumption resolution 344,338]
349. tall(X0) <- (13) [resolution 345,100]
353. ~kind(sK7) | ~funny(sK7) [resolution 116,133]
354. ~kind(sK7) <- (11) [subsumption resolution 353,186]
360. kind(X0) | wise(X0) <- (13) [resolution 121,349]
361. kind(X0) <- (13) [subsumption resolution 360,338]
366. $false <- (11, 13) [resolution 361,354]
367. ~11 | ~13 [avatar contradiction clause 366]
370. $false [avatar sat refutation 191,195,335,367]
% SZS output end Proof for 816097376701809934793255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and not brave then someone is both not tall and old.
If someone is not quiet or rich then susan is tall.
If someone is either not old or not creative then mary is either not happy or not quiet.
If susan is both not happy and funny then john is patient and vice versa.
If someone is not curious then someone is not wise.
Everyone who is either strong or not calm is either rich or not wise.
Everyone who is humble or rich is both wise and not quiet and vice versa.
If someone is either humble or generous then susan is not humble.
Everyone who is either not brave or patient is not old.
Everyone who is not creative or generous is not patient or patient and vice versa.
If john is not curious then someone is not creative or not generous.
If lucy is either not generous or not tall then susan is either funny or not humble and vice versa.
If someone is either not wise or tall then susan is not wise.
Everyone who is patient or not wise is both curious and rich.
If someone is both not patient and not wise then susan is both not generous and not kind and vice versa.
Everyone who is not old or not quiet is not generous and vice versa.
Someone is not old or curious.
Alice is funny.
Alice is both generous and old.
Someone is either not calm or not curious.
John is humble or curious.
Someone is not tall. | Lucy is not humble. | entailment | ((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(tall(susan)))&
((?[X]:((~old(X)<~>~creative(X))))=>((~happy(mary)<~>~quiet(mary))))&
(((~happy(susan)&funny(susan)))<=>(patient(john)))&
((?[X]:(~curious(X)))=>(?[X]:(~wise(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>~wise(X))))&
(![X]:((humble(X)|rich(X))<=>(wise(X)&~quiet(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(~humble(susan)))&
(![X]:((~brave(X)<~>patient(X))=>~old(X)))&
(![X]:((~creative(X)|generous(X))<=>(~patient(X)|patient(X))))&
((~curious(john))=>(?[X]:((~creative(X)|~generous(X)))))&
(((~generous(lucy)<~>~tall(lucy)))<=>((funny(susan)<~>~humble(susan))))&
((?[X]:((~wise(X)<~>tall(X))))=>(~wise(susan)))&
(![X]:((patient(X)|~wise(X))=>(curious(X)&rich(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((~generous(susan)&~kind(susan))))&
(![X]:((~old(X)|~quiet(X))<=>~generous(X)))&
(?[X]:((~old(X)|curious(X))))&
(funny(alice))&
((generous(alice)&old(alice)))&
(?[X]:((~calm(X)<~>~curious(X))))&
((humble(john)|curious(john)))&
(?[X]:(~tall(X))) | ~humble(lucy) | [
"p1",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2880276589028481584527760
% SZS output start Proof for 2880276589028481584527760
2. ? [X0] : (rich(X0) | ~quiet(X0)) => tall(susan) [input p1]
7. ! [X0] : ((rich(X0) | humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p6]
13. ? [X0] : (~wise(X0) <~> tall(X0)) => ~wise(susan) [input p12]
14. ! [X0] : ((~wise(X0) | patient(X0)) => (rich(X0) & curious(X0))) [input p13]
23. humble(lucy) [input hypothesis]
27. tall(susan) | ! [X0] : (~rich(X0) & quiet(X0)) [ennf transformation 2]
34. ~wise(susan) | ! [X0] : (~wise(X0) <=> tall(X0)) [ennf transformation 13]
35. ! [X0] : ((rich(X0) & curious(X0)) | (wise(X0) & ~patient(X0))) [ennf transformation 14]
46. ! [X0] : (((rich(X0) | humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | humble(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [flattening 46]
55. ~wise(susan) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))) [nnf transformation 34]
72. tall(susan) | quiet(X0) [cnf transformation 27]
87. ~rich(X0) | wise(X0) [cnf transformation 47]
88. ~humble(X0) | ~quiet(X0) [cnf transformation 47]
109. ~wise(susan) | ~wise(X0) | ~tall(X0) [cnf transformation 55]
113. rich(X0) | wise(X0) [cnf transformation 35]
129. humble(lucy) [cnf transformation 23]
147. 5 <=> tall(susan) [avatar definition]
149. tall(susan) <- (5) [avatar component clause 147]
152. 6 <=> ! [X0] : quiet(X0) [avatar definition]
153. quiet(X0) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 72,147,152]
236. 23 <=> ! [X0] : (~wise(X0) | ~tall(X0)) [avatar definition]
237. ~wise(X0) | ~tall(X0) <- (23) [avatar component clause 236]
239. 24 <=> wise(susan) [avatar definition]
241. ~wise(susan) <- (~24) [avatar component clause 239]
242. 23 | ~24 [avatar split clause 109,239,236]
247. wise(X0) [subsumption resolution 113,87]
287. $false <- (~24) [subsumption resolution 241,247]
288. 24 [avatar contradiction clause 287]
291. ~tall(X0) <- (23) [subsumption resolution 237,247]
294. $false <- (5, 23) [resolution 291,149]
295. ~5 | ~23 [avatar contradiction clause 294]
299. ~quiet(lucy) [resolution 88,129]
300. $false <- (6) [subsumption resolution 299,153]
301. ~6 [avatar contradiction clause 300]
302. $false [avatar sat refutation 154,242,288,295,301]
% SZS output end Proof for 2880276589028481584527760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or kind is curious. If someone is humble or strong then lucy is either not patient or not strong and vice versa. Everyone who is either brave or old is either happy or old and vice versa. If susan is both funny and patient then someone is not brave or not quiet and vice versa. Everyone who is creative or wise is either not patient or strong. Everyone who is creative is not creative or calm. Everyone who is not curious or patient is not creative or not quiet and vice versa. If someone is funny then someone is not strong. If someone is not tall then someone is curious or not calm and vice versa. If john is patient then mary is not creative and vice versa. If someone is both rich and not brave then someone is both wise and humble. Everyone who is not curious is generous or creative and vice versa. If mary is either funny or not creative then someone is both happy and not generous. Everyone who is both brave and humble is not rich or not generous and vice versa. If someone is quiet or wise then someone is generous or strong. Mary is either strong or not humble. Someone is curious or not patient. | Susan is patient. | entailment | (![X]:((~creative(X)|kind(X))=>curious(X)))&
((?[X]:((humble(X)|strong(X))))<=>((~patient(lucy)<~>~strong(lucy))))&
(![X]:((brave(X)<~>old(X))<=>(happy(X)<~>old(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((creative(X)|wise(X))=>(~patient(X)<~>strong(X))))&
(![X]:(creative(X)=>(~creative(X)|calm(X))))&
(![X]:((~curious(X)|patient(X))<=>(~creative(X)|~quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~strong(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((curious(X)|~calm(X)))))&
((patient(john))<=>(~creative(mary)))&
((?[X]:((rich(X)&~brave(X))))=>(?[X]:((wise(X)&humble(X)))))&
(![X]:(~curious(X)<=>(generous(X)|creative(X))))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((generous(X)|strong(X)))))&
((strong(mary)<~>~humble(mary)))&
(?[X]:((curious(X)|~patient(X)))) | patient(susan) | [
"p0",
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 208004823241026625672795
% SZS output start Proof for 208004823241026625672795
1. ! [X0] : ((kind(X0) | ~creative(X0)) => curious(X0)) [input p0]
4. (patient(susan) & funny(susan)) <=> ? [X0] : (~quiet(X0) | ~brave(X0)) [input p3]
7. ! [X0] : ((patient(X0) | ~curious(X0)) <=> (~quiet(X0) | ~creative(X0))) [input p6]
12. ! [X0] : (~curious(X0) <=> (creative(X0) | generous(X0))) [input p11]
18. ~patient(susan) [input hypothesis]
23. ! [X0] : (~creative(X0) => curious(X0)) [pure predicate removal 1]
24. ! [X0] : (curious(X0) | creative(X0)) [ennf transformation 23]
37. ((patient(susan) & funny(susan)) | ! [X0] : (quiet(X0) & brave(X0))) & (? [X0] : (~quiet(X0) | ~brave(X0)) | (~patient(susan) | ~funny(susan))) [nnf transformation 4]
38. ((patient(susan) & funny(susan)) | ! [X0] : (quiet(X0) & brave(X0))) & (? [X0] : (~quiet(X0) | ~brave(X0)) | ~patient(susan) | ~funny(susan)) [flattening 37]
39. ((patient(susan) & funny(susan)) | ! [X0] : (quiet(X0) & brave(X0))) & (? [X1] : (~quiet(X1) | ~brave(X1)) | ~patient(susan) | ~funny(susan)) [rectify 38]
40. ? [X1] : (~quiet(X1) | ~brave(X1)) => (~quiet(sK1) | ~brave(sK1)) [choice axiom]
41. ((patient(susan) & funny(susan)) | ! [X0] : (quiet(X0) & brave(X0))) & ((~quiet(sK1) | ~brave(sK1)) | ~patient(susan) | ~funny(susan)) [skolemisation 39,40]
43. ! [X0] : (((patient(X0) | ~curious(X0)) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | (~patient(X0) & curious(X0)))) [nnf transformation 7]
44. ! [X0] : ((patient(X0) | ~curious(X0) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | (~patient(X0) & curious(X0)))) [flattening 43]
57. ! [X0] : ((~curious(X0) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | curious(X0))) [nnf transformation 12]
58. ! [X0] : ((~curious(X0) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | curious(X0))) [flattening 57]
70. curious(X0) | creative(X0) [cnf transformation 24]
89. patient(susan) | quiet(X0) [cnf transformation 41]
95. ~quiet(X0) | ~creative(X0) | curious(X0) [cnf transformation 44]
97. patient(X0) | ~curious(X0) | creative(X0) [cnf transformation 44]
109. ~curious(X0) | ~creative(X0) [cnf transformation 58]
124. ~patient(susan) [cnf transformation 18]
161. 7 <=> ! [X0] : quiet(X0) [avatar definition]
162. quiet(X0) <- (7) [avatar component clause 161]
164. 8 <=> patient(susan) [avatar definition]
165. ~patient(susan) <- (~8) [avatar component clause 164]
167. 7 | 8 [avatar split clause 89,164,161]
187. patient(X0) | creative(X0) [subsumption resolution 97,70]
188. ~quiet(X0) | curious(X0) [subsumption resolution 95,70]
295. ~8 [avatar split clause 124,164]
307. creative(susan) <- (~8) [resolution 187,165]
311. curious(X0) <- (7) [resolution 188,162]
318. ~creative(X0) <- (7) [resolution 311,109]
327. $false <- (7, ~8) [resolution 318,307]
334. ~7 | 8 [avatar contradiction clause 327]
335. $false [avatar sat refutation 167,295,334]
% SZS output end Proof for 208004823241026625672795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or kind then someone is both old and not quiet.
Everyone who is not creative is not happy and vice versa.
Everyone who is either brave or tall is patient or not calm and vice versa.
Everyone who is creative is old.
If paul is curious then someone is generous.
Everyone who is not old is curious or not kind and vice versa.
If someone is curious or not generous then someone is both humble and rich and vice versa.
If someone is both not tall and tall then someone is strong or funny.
If someone is either wise or not quiet then susan is not old or not creative and vice versa.
Everyone who is both not happy and not curious is both funny and not calm and vice versa.
If someone is not funny then paul is not tall or not curious and vice versa.
If someone is funny then paul is not kind or curious and vice versa.
Everyone who is brave or not kind is either not wise or not quiet and vice versa.
Everyone who is not funny or not calm is either wise or not kind and vice versa.
Everyone who is both not rich and not kind is not calm.
If someone is both not rich and tall then someone is either kind or not happy and vice versa.
Susan is both not generous and quiet.
Someone is not funny.
Susan is patient or wise.
John is not happy.
Someone is both curious and rich.
Susan is either quiet or not old.
John is either not wise or not calm.
Someone is not happy or not funny. | Paul is not old. | entailment | ((?[X]:((calm(X)<~>kind(X))))=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:(~creative(X)<=>~happy(X)))&
(![X]:((brave(X)<~>tall(X))<=>(patient(X)|~calm(X))))&
(![X]:(creative(X)=>old(X)))&
((curious(paul))=>(?[X]:(generous(X))))&
(![X]:(~old(X)<=>(curious(X)|~kind(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((strong(X)|funny(X)))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~old(susan)|~creative(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((?[X]:(~funny(X)))<=>((~tall(paul)|~curious(paul))))&
((?[X]:(funny(X)))<=>((~kind(paul)|curious(paul))))&
(![X]:((brave(X)|~kind(X))<=>(~wise(X)<~>~quiet(X))))&
(![X]:((~funny(X)|~calm(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~rich(X)&~kind(X))=>~calm(X)))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
((~generous(susan)&quiet(susan)))&
(?[X]:(~funny(X)))&
((patient(susan)|wise(susan)))&
(~happy(john))&
(?[X]:((curious(X)&rich(X))))&
((quiet(susan)<~>~old(susan)))&
((~wise(john)<~>~calm(john)))&
(?[X]:((~happy(X)|~funny(X)))) | ~old(paul) | [
"p1",
"p3",
"p5",
"p8",
"p9",
"p11",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3186675413731564776466652
% SZS output start Proof for 3186675413731564776466652
2. ! [X0] : (~creative(X0) <=> ~happy(X0)) [input p1]
4. ! [X0] : (creative(X0) => old(X0)) [input p3]
6. ! [X0] : (~old(X0) <=> (~kind(X0) | curious(X0))) [input p5]
9. ? [X0] : (wise(X0) <~> ~quiet(X0)) <=> (~creative(susan) | ~old(susan)) [input p8]
10. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (~calm(X0) & funny(X0))) [input p9]
12. ? [X0] : funny(X0) <=> (curious(paul) | ~kind(paul)) [input p11]
14. ! [X0] : ((~calm(X0) | ~funny(X0)) <=> (wise(X0) <~> ~kind(X0))) [input p13]
17. quiet(susan) & ~generous(susan) [input p16]
22. quiet(susan) <~> ~old(susan) [input p21]
25. old(paul) [input hypothesis]
32. ! [X0] : (old(X0) | ~creative(X0)) [ennf transformation 4]
40. ! [X0] : ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))) [nnf transformation 2]
45. ! [X0] : ((~old(X0) | (kind(X0) & ~curious(X0))) & ((~kind(X0) | curious(X0)) | old(X0))) [nnf transformation 6]
46. ! [X0] : ((~old(X0) | (kind(X0) & ~curious(X0))) & (~kind(X0) | curious(X0) | old(X0))) [flattening 45]
52. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (creative(susan) & old(susan))) & ((~creative(susan) | ~old(susan)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 9]
53. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (creative(susan) & old(susan))) & (~creative(susan) | ~old(susan) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [flattening 52]
54. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (creative(susan) & old(susan))) & (~creative(susan) | ~old(susan) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [rectify 53]
55. ? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) => ((quiet(sK4) | ~wise(sK4)) & (~quiet(sK4) | wise(sK4))) [choice axiom]
56. (((quiet(sK4) | ~wise(sK4)) & (~quiet(sK4) | wise(sK4))) | (creative(susan) & old(susan))) & (~creative(susan) | ~old(susan) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [skolemisation 54,55]
57. ! [X0] : (((~curious(X0) & ~happy(X0)) | (calm(X0) | ~funny(X0))) & ((~calm(X0) & funny(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 10]
58. ! [X0] : (((~curious(X0) & ~happy(X0)) | calm(X0) | ~funny(X0)) & ((~calm(X0) & funny(X0)) | curious(X0) | happy(X0))) [flattening 57]
64. (? [X0] : funny(X0) | (~curious(paul) & kind(paul))) & ((curious(paul) | ~kind(paul)) | ! [X0] : ~funny(X0)) [nnf transformation 12]
65. (? [X0] : funny(X0) | (~curious(paul) & kind(paul))) & (curious(paul) | ~kind(paul) | ! [X0] : ~funny(X0)) [flattening 64]
66. (? [X0] : funny(X0) | (~curious(paul) & kind(paul))) & (curious(paul) | ~kind(paul) | ! [X1] : ~funny(X1)) [rectify 65]
67. ? [X0] : funny(X0) => funny(sK6) [choice axiom]
68. (funny(sK6) | (~curious(paul) & kind(paul))) & (curious(paul) | ~kind(paul) | ! [X1] : ~funny(X1)) [skolemisation 66,67]
71. ! [X0] : (((~calm(X0) | ~funny(X0)) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0)))) & (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | (calm(X0) & funny(X0)))) [nnf transformation 14]
72. ! [X0] : ((~calm(X0) | ~funny(X0) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0)))) & (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | (calm(X0) & funny(X0)))) [flattening 71]
82. (old(susan) | ~quiet(susan)) & (~old(susan) | quiet(susan)) [nnf transformation 22]
90. ~happy(X0) | creative(X0) [cnf transformation 40]
98. ~creative(X0) | old(X0) [cnf transformation 32]
101. ~curious(X0) | ~old(X0) [cnf transformation 46]
102. ~old(X0) | kind(X0) [cnf transformation 46]
108. ~creative(susan) | ~old(susan) | ~quiet(X1) | ~wise(X1) [cnf transformation 56]
114. funny(X0) | curious(X0) | happy(X0) [cnf transformation 58]
121. curious(paul) | ~kind(paul) | ~funny(X1) [cnf transformation 68]
130. ~kind(X0) | wise(X0) | funny(X0) [cnf transformation 72]
144. quiet(susan) [cnf transformation 17]
151. old(susan) | ~quiet(susan) [cnf transformation 82]
155. old(paul) [cnf transformation 25]
175. 5 <=> curious(paul) [avatar definition]
176. curious(paul) <- (5) [avatar component clause 175]
214. 14 <=> creative(susan) [avatar definition]
227. 17 <=> old(susan) [avatar definition]
229. old(susan) <- (17) [avatar component clause 227]
238. ~creative(susan) | ~quiet(X1) | ~wise(X1) [subsumption resolution 108,98]
240. 19 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
241. ~wise(X1) | ~quiet(X1) <- (19) [avatar component clause 240]
242. 19 | ~14 [avatar split clause 238,214,240]
263. 24 <=> kind(paul) [avatar definition]
268. 25 <=> ! [X1] : ~funny(X1) [avatar definition]
269. ~funny(X1) <- (25) [avatar component clause 268]
270. 25 | ~24 | 5 [avatar split clause 121,175,263,268]
307. 34 <=> wise(susan) [avatar definition]
309. wise(susan) <- (34) [avatar component clause 307]
311. old(susan) [subsumption resolution 151,144]
312. 17 [avatar split clause 311,227]
339. kind(paul) [resolution 102,155]
341. kind(susan) <- (17) [resolution 102,229]
344. 24 [avatar split clause 339,263]
345. ~old(paul) <- (5) [resolution 176,101]
346. $false <- (5) [subsumption resolution 345,155]
347. ~5 [avatar contradiction clause 346]
392. curious(X0) | happy(X0) <- (25) [resolution 114,269]
396. ~old(X0) | happy(X0) <- (25) [resolution 392,101]
405. happy(susan) <- (17, 25) [resolution 396,229]
447. creative(susan) <- (17, 25) [resolution 405,90]
449. ~quiet(susan) <- (19, 34) [resolution 241,309]
452. $false <- (19, 34) [subsumption resolution 449,144]
453. ~19 | ~34 [avatar contradiction clause 452]
460. wise(susan) | funny(susan) <- (17) [resolution 130,341]
467. 14 | ~17 | ~25 [avatar split clause 447,268,227,214]
468. wise(susan) <- (17, 25) [subsumption resolution 460,269]
469. 34 | ~17 | ~25 [avatar split clause 468,268,227,307]
470. $false [avatar sat refutation 242,270,312,344,347,453,467,469]
% SZS output end Proof for 3186675413731564776466652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not happy is either not generous or brave. If someone is curious then someone is both brave and generous and vice versa. If paul is funny then someone is either not humble or calm. If someone is both rich and wise then john is old and vice versa. Everyone who is not old is not wise or not funny and vice versa. Everyone who is not wise or strong is brave. If someone is both not wise and rich then john is brave or not brave. If paul is quiet then someone is either curious or not rich and vice versa. If someone is either not generous or kind then paul is both rich and kind. Everyone who is rich or kind is not wise or rich. If someone is wise then someone is not happy or not humble. If paul is strong or not brave then someone is either not funny or wise and vice versa. If someone is not funny then lucy is old and vice versa. Everyone who is quiet or rich is both not rich and funny and vice versa. If someone is strong or curious then mary is not kind. Everyone who is not generous or patient is not quiet or rich and vice versa. John is both not old and quiet. Susan is both funny and not brave. Fred is either not funny or not old. Someone is either humble or brave. Someone is not strong. Mary is either wise or generous. Someone is both not strong and happy. | Mary is not old. | entailment | (![X]:((patient(X)&~happy(X))=>(~generous(X)<~>brave(X))))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)&generous(X)))))&
((funny(paul))=>(?[X]:((~humble(X)<~>calm(X)))))&
((?[X]:((rich(X)&wise(X))))<=>(old(john)))&
(![X]:(~old(X)<=>(~wise(X)|~funny(X))))&
(![X]:((~wise(X)|strong(X))=>brave(X)))&
((?[X]:((~wise(X)&rich(X))))=>((brave(john)|~brave(john))))&
((quiet(paul))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~generous(X)<~>kind(X))))=>((rich(paul)&kind(paul))))&
(![X]:((rich(X)|kind(X))=>(~wise(X)|rich(X))))&
((?[X]:(wise(X)))=>(?[X]:((~happy(X)|~humble(X)))))&
(((strong(paul)|~brave(paul)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:(~funny(X)))<=>(old(lucy)))&
(![X]:((quiet(X)|rich(X))<=>(~rich(X)&funny(X))))&
((?[X]:((strong(X)|curious(X))))=>(~kind(mary)))&
(![X]:((~generous(X)|patient(X))<=>(~quiet(X)|rich(X))))&
((~old(john)&quiet(john)))&
((funny(susan)&~brave(susan)))&
((~funny(fred)<~>~old(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~strong(X)))&
((wise(mary)<~>generous(mary)))&
(?[X]:((~strong(X)&happy(X)))) | ~old(mary) | [
"p4",
"p8",
"p9",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3091479180094227394518046
% SZS output start Proof for 3091479180094227394518046
5. ! [X0] : (~old(X0) <=> (~funny(X0) | ~wise(X0))) [input p4]
9. ? [X0] : (~generous(X0) <~> kind(X0)) => (kind(paul) & rich(paul)) [input p8]
10. ! [X0] : ((kind(X0) | rich(X0)) => (rich(X0) | ~wise(X0))) [input p9]
14. ! [X0] : ((rich(X0) | quiet(X0)) <=> (funny(X0) & ~rich(X0))) [input p13]
22. wise(mary) <~> generous(mary) [input p21]
24. old(mary) [input hypothesis]
33. (kind(paul) & rich(paul)) | ! [X0] : (~generous(X0) <=> kind(X0)) [ennf transformation 9]
34. ! [X0] : ((rich(X0) | ~wise(X0)) | (~kind(X0) & ~rich(X0))) [ennf transformation 10]
35. ! [X0] : (rich(X0) | ~wise(X0) | (~kind(X0) & ~rich(X0))) [flattening 34]
51. ! [X0] : ((~old(X0) | (funny(X0) & wise(X0))) & ((~funny(X0) | ~wise(X0)) | old(X0))) [nnf transformation 5]
52. ! [X0] : ((~old(X0) | (funny(X0) & wise(X0))) & (~funny(X0) | ~wise(X0) | old(X0))) [flattening 51]
57. (kind(paul) & rich(paul)) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))) [nnf transformation 33]
70. ! [X0] : (((rich(X0) | quiet(X0)) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | (~rich(X0) & ~quiet(X0)))) [nnf transformation 14]
71. ! [X0] : ((rich(X0) | quiet(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | (~rich(X0) & ~quiet(X0)))) [flattening 70]
80. (~generous(mary) | ~wise(mary)) & (generous(mary) | wise(mary)) [nnf transformation 22]
94. ~old(X0) | wise(X0) [cnf transformation 52]
103. rich(paul) | kind(X0) | generous(X0) [cnf transformation 57]
108. ~kind(X0) | ~wise(X0) | rich(X0) [cnf transformation 35]
119. ~rich(X0) | ~rich(X0) [cnf transformation 71]
139. ~generous(mary) | ~wise(mary) [cnf transformation 80]
142. old(mary) [cnf transformation 24]
143. ~rich(X0) [duplicate literal removal 119]
229. 20 <=> ! [X0] : (kind(X0) | generous(X0)) [avatar definition]
230. kind(X0) | generous(X0) <- (20) [avatar component clause 229]
233. 21 <=> rich(paul) [avatar definition]
235. rich(paul) <- (21) [avatar component clause 233]
237. 20 | 21 [avatar split clause 103,233,229]
292. 34 <=> kind(mary) [avatar definition]
293. kind(mary) <- (34) [avatar component clause 292]
294. ~kind(mary) <- (~34) [avatar component clause 292]
316. 38 <=> wise(mary) [avatar definition]
320. 39 <=> generous(mary) [avatar definition]
322. ~generous(mary) <- (~39) [avatar component clause 320]
323. ~38 | ~39 [avatar split clause 139,320,316]
327. wise(mary) [resolution 94,142]
338. generous(mary) <- (20, ~34) [resolution 230,294]
340. $false <- (20, ~34, ~39) [subsumption resolution 338,322]
341. ~20 | 34 | 39 [avatar contradiction clause 340]
342. $false <- (21) [subsumption resolution 235,143]
343. ~21 [avatar contradiction clause 342]
364. ~wise(mary) | rich(mary) <- (34) [resolution 108,293]
369. ~wise(mary) <- (34) [subsumption resolution 364,143]
370. ~38 | ~34 [avatar split clause 369,292,316]
371. 38 [avatar split clause 327,316]
373. $false [avatar sat refutation 237,323,341,343,370,371]
% SZS output end Proof for 3091479180094227394518046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is either calm or not kind. Everyone who is either not kind or not funny is not generous or patient. If someone is both tall and not curious then someone is both quiet and not funny and vice versa. Everyone who is either not funny or not kind is both not generous and generous and vice versa. If someone is not patient or kind then someone is not quiet and vice versa. Everyone who is humble is not wise and vice versa. Everyone who is patient is both not brave and not generous and vice versa. Everyone who is both wise and tall is not patient. If someone is not happy or tall then someone is both curious and strong and vice versa. Everyone who is not kind or not generous is either not curious or not funny and vice versa. Everyone who is both creative and tall is not generous and vice versa. Everyone who is funny is either not tall or not rich and vice versa. Everyone who is generous is both not happy and not quiet and vice versa. If someone is not generous then john is both curious and patient and vice versa. Everyone who is not happy is both not strong and patient and vice versa. If someone is wise or patient then someone is kind or happy and vice versa. Someone is calm. Someone is not patient. Someone is either creative or not wise. Someone is either humble or not brave. Someone is not patient or tall. Someone is old or wise. Alice is not curious. | John is funny. | contradiction | ((?[X]:(~wise(X)))=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~kind(X)<~>~funny(X))=>(~generous(X)|patient(X))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:((quiet(X)&~funny(X)))))&
(![X]:((~funny(X)<~>~kind(X))<=>(~generous(X)&generous(X))))&
((?[X]:((~patient(X)|kind(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:(patient(X)<=>(~brave(X)&~generous(X))))&
(![X]:((wise(X)&tall(X))=>~patient(X)))&
((?[X]:((~happy(X)|tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((~kind(X)|~generous(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((creative(X)&tall(X))<=>~generous(X)))&
(![X]:(funny(X)<=>(~tall(X)<~>~rich(X))))&
(![X]:(generous(X)<=>(~happy(X)&~quiet(X))))&
((?[X]:(~generous(X)))<=>((curious(john)&patient(john))))&
(![X]:(~happy(X)<=>(~strong(X)&patient(X))))&
((?[X]:((wise(X)|patient(X))))<=>(?[X]:((kind(X)|happy(X)))))&
(?[X]:(calm(X)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((old(X)|wise(X))))&
(~curious(alice)) | funny(john) | [
"p6",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7321095769235260340513521
% SZS output start Proof for 7321095769235260340513521
7. ! [X0] : (patient(X0) <=> (~generous(X0) & ~brave(X0))) [input p6]
10. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (~curious(X0) <~> ~funny(X0))) [input p9]
13. ! [X0] : (generous(X0) <=> (~quiet(X0) & ~happy(X0))) [input p12]
14. ? [X0] : ~generous(X0) <=> (patient(john) & curious(john)) [input p13]
15. ! [X0] : (~happy(X0) <=> (patient(X0) & ~strong(X0))) [input p14]
24. funny(john) [input hypothesis]
54. ! [X0] : ((patient(X0) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | ~patient(X0))) [nnf transformation 7]
55. ! [X0] : ((patient(X0) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | ~patient(X0))) [flattening 54]
61. ! [X0] : (((~generous(X0) | ~kind(X0)) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0)))) & (((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | (generous(X0) & kind(X0)))) [nnf transformation 10]
62. ! [X0] : ((~generous(X0) | ~kind(X0) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0)))) & (((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | (generous(X0) & kind(X0)))) [flattening 61]
66. ! [X0] : ((generous(X0) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | ~generous(X0))) [nnf transformation 13]
67. ! [X0] : ((generous(X0) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | ~generous(X0))) [flattening 66]
68. (? [X0] : ~generous(X0) | (~patient(john) | ~curious(john))) & ((patient(john) & curious(john)) | ! [X0] : generous(X0)) [nnf transformation 14]
69. (? [X0] : ~generous(X0) | ~patient(john) | ~curious(john)) & ((patient(john) & curious(john)) | ! [X0] : generous(X0)) [flattening 68]
70. (? [X0] : ~generous(X0) | ~patient(john) | ~curious(john)) & ((patient(john) & curious(john)) | ! [X1] : generous(X1)) [rectify 69]
71. ? [X0] : ~generous(X0) => ~generous(sK7) [choice axiom]
72. (~generous(sK7) | ~patient(john) | ~curious(john)) & ((patient(john) & curious(john)) | ! [X1] : generous(X1)) [skolemisation 70,71]
73. ! [X0] : ((~happy(X0) | (~patient(X0) | strong(X0))) & ((patient(X0) & ~strong(X0)) | happy(X0))) [nnf transformation 15]
74. ! [X0] : ((~happy(X0) | ~patient(X0) | strong(X0)) & ((patient(X0) & ~strong(X0)) | happy(X0))) [flattening 73]
112. ~patient(X0) | ~generous(X0) [cnf transformation 55]
121. ~curious(X0) | ~funny(X0) | generous(X0) [cnf transformation 62]
133. ~happy(X0) | ~generous(X0) [cnf transformation 67]
136. curious(john) | generous(X1) [cnf transformation 72]
140. happy(X0) | patient(X0) [cnf transformation 74]
154. funny(john) [cnf transformation 24]
253. 23 <=> curious(john) [avatar definition]
254. curious(john) <- (23) [avatar component clause 253]
266. 26 <=> ! [X1] : generous(X1) [avatar definition]
267. generous(X1) <- (26) [avatar component clause 266]
269. 26 | 23 [avatar split clause 136,253,266]
348. patient(X0) | ~generous(X0) [resolution 140,133]
388. ~funny(john) | generous(john) <- (23) [resolution 121,254]
391. generous(john) <- (23) [subsumption resolution 388,154]
431. ~generous(X0) [subsumption resolution 348,112]
432. $false <- (23) [subsumption resolution 391,431]
433. ~23 [avatar contradiction clause 432]
434. $false <- (26) [subsumption resolution 267,431]
435. ~26 [avatar contradiction clause 434]
436. $false [avatar sat refutation 269,433,435]
% SZS output end Proof for 7321095769235260340513521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is not generous and vice versa. Everyone who is not generous or not funny is funny. Everyone who is old is not creative and vice versa. If someone is either not creative or creative then alice is either rich or kind and vice versa. Everyone who is both not rich and not happy is strong. If fred is kind or patient then susan is both wise and not generous. Everyone who is tall is both not rich and not humble. Everyone who is both not humble and strong is not wise or creative. If lucy is both kind and not tall then john is curious and vice versa. If fred is quiet then someone is either curious or wise. Everyone who is both not brave and not happy is creative or quiet. If someone is both not tall and not wise then someone is not humble or creative and vice versa. Everyone who is both kind and not curious is not old or rich and vice versa. Everyone who is both strong and not tall is not calm. Everyone who is both not humble and not quiet is not kind. If mary is either happy or not calm then someone is either brave or not rich. Paul is either not strong or not funny. Paul is either not strong or rich. Lucy is either not brave or quiet. Someone is either old or rich. Mary is either creative or not calm. Someone is either not funny or not happy. Mary is not wise. Someone is rich or kind. | Paul is not happy. | contradiction | (![X]:((quiet(X)&~funny(X))<=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:(old(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
(![X]:((~humble(X)&~quiet(X))=>~kind(X)))&
(((happy(mary)<~>~calm(mary)))=>(?[X]:((brave(X)<~>~rich(X)))))&
((~strong(paul)<~>~funny(paul)))&
((~strong(paul)<~>rich(paul)))&
((~brave(lucy)<~>quiet(lucy)))&
(?[X]:((old(X)<~>rich(X))))&
((creative(mary)<~>~calm(mary)))&
(?[X]:((~funny(X)<~>~happy(X))))&
(~wise(mary))&
(?[X]:((rich(X)|kind(X)))) | ~happy(paul) | [
"p1",
"p4",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5763408787691280293943082
% SZS output start Proof for 5763408787691280293943082
2. ! [X0] : ((~funny(X0) | ~generous(X0)) => funny(X0)) [input p1]
5. ! [X0] : ((~happy(X0) & ~rich(X0)) => strong(X0)) [input p4]
17. ~strong(paul) <~> ~funny(paul) [input p16]
18. ~strong(paul) <~> rich(paul) [input p17]
25. ~happy(paul) [input hypothesis]
28. ! [X0] : (funny(X0) | (funny(X0) & generous(X0))) [ennf transformation 2]
29. ! [X0] : (strong(X0) | (happy(X0) | rich(X0))) [ennf transformation 5]
30. ! [X0] : (strong(X0) | happy(X0) | rich(X0)) [flattening 29]
65. (funny(paul) | strong(paul)) & (~funny(paul) | ~strong(paul)) [nnf transformation 17]
66. (~rich(paul) | strong(paul)) & (rich(paul) | ~strong(paul)) [nnf transformation 18]
81. funny(X0) | funny(X0) [cnf transformation 28]
92. strong(X0) | happy(X0) | rich(X0) [cnf transformation 30]
120. ~funny(paul) | ~strong(paul) [cnf transformation 65]
123. ~rich(paul) | strong(paul) [cnf transformation 66]
134. ~happy(paul) [cnf transformation 25]
139. funny(X0) [duplicate literal removal 81]
248. ~strong(paul) [subsumption resolution 120,139]
249. ~rich(paul) [subsumption resolution 123,248]
293. happy(paul) | rich(paul) [resolution 92,248]
294. rich(paul) [subsumption resolution 293,134]
295. $false [subsumption resolution 294,249]
% SZS output end Proof for 5763408787691280293943082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not humble then someone is both not quiet and calm and vice versa. If someone is both brave and calm then mary is patient or not generous and vice versa. Everyone who is not old or not humble is not tall or happy and vice versa. Everyone who is both curious and quiet is not brave. Everyone who is not old is both not tall and not happy. If someone is brave or not creative then susan is both brave and not kind and vice versa. Everyone who is not calm or not humble is not tall and vice versa. Everyone who is not funny or kind is either not patient or humble and vice versa. If someone is either not patient or not creative then someone is humble and vice versa. Everyone who is either not curious or curious is rich and vice versa. Everyone who is either happy or not creative is both not brave and funny and vice versa. If alice is not wise or calm then john is both not kind and old. Everyone who is not patient is both not creative and not old. Everyone who is both brave and not humble is not tall. Everyone who is happy or curious is either not calm or old. If fred is calm or not calm then alice is not tall. Mary is either tall or generous. Someone is either not rich or creative. Someone is either tall or funny. Someone is both not strong and not patient. Mary is both brave and not calm. Someone is either not generous or humble. Fred is either creative or old. Someone is not tall. | John is not rich. | contradiction | ((?[X]:((wise(X)|~humble(X))))<=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
(((calm(fred)|~calm(fred)))=>(~tall(alice)))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
((creative(fred)<~>old(fred)))&
(?[X]:(~tall(X))) | ~rich(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2245113396491309843274465
% SZS output start Proof for 2245113396491309843274465
10. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> rich(X0)) [input p9]
25. ~rich(john) [input hypothesis]
64. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~rich(X0)) & (rich(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 10]
118. rich(X0) | curious(X0) | curious(X0) [cnf transformation 64]
119. rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 64]
155. ~rich(john) [cnf transformation 25]
156. rich(X0) | curious(X0) [duplicate literal removal 118]
157. rich(X0) | ~curious(X0) [duplicate literal removal 119]
264. rich(X0) [subsumption resolution 156,157]
334. $false [subsumption resolution 155,264]
% SZS output end Proof for 2245113396491309843274465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not funny then john is both not rich and not kind and vice versa.
Everyone who is not brave is not generous or generous and vice versa.
Everyone who is both not brave and funny is patient.
If someone is both generous and happy then someone is old or humble and vice versa.
Everyone who is both not wise and tall is both humble and calm.
If someone is creative then someone is both patient and not rich.
Everyone who is not brave or not generous is funny and vice versa.
If someone is old or not generous then someone is not patient and vice versa.
If someone is both not strong and not old then someone is both not wise and not patient.
If susan is either funny or not rich then someone is either not tall or tall.
Everyone who is both not strong and not rich is either brave or not wise.
If john is both humble and not curious then lucy is either not calm or not strong and vice versa.
If fred is either not generous or funny then alice is calm or patient.
If susan is not calm or quiet then someone is not funny or curious and vice versa.
Everyone who is both not funny and not humble is both not old and strong.
If fred is either not tall or kind then someone is not patient.
Alice is old or funny.
Someone is happy.
Fred is either creative or happy.
Someone is calm or funny.
Susan is either not curious or tall.
Susan is either not generous or wise.
Someone is humble or strong. | Susan is not wise. | contradiction | ((?[X]:((~quiet(X)&~funny(X))))<=>((~rich(john)&~kind(john))))&
(![X]:(~brave(X)<=>(~generous(X)|generous(X))))&
(![X]:((~brave(X)&funny(X))=>patient(X)))&
((?[X]:((generous(X)&happy(X))))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~wise(X)&tall(X))=>(humble(X)&calm(X))))&
((?[X]:(creative(X)))=>(?[X]:((patient(X)&~rich(X)))))&
(![X]:((~brave(X)|~generous(X))<=>funny(X)))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(((funny(susan)<~>~rich(susan)))=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((~strong(X)&~rich(X))=>(brave(X)<~>~wise(X))))&
(((humble(john)&~curious(john)))<=>((~calm(lucy)<~>~strong(lucy))))&
(((~generous(fred)<~>funny(fred)))=>((calm(alice)|patient(alice))))&
(((~calm(susan)|quiet(susan)))<=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((~funny(X)&~humble(X))=>(~old(X)&strong(X))))&
(((~tall(fred)<~>kind(fred)))=>(?[X]:(~patient(X))))&
((old(alice)|funny(alice)))&
(?[X]:(happy(X)))&
((creative(fred)<~>happy(fred)))&
(?[X]:((calm(X)|funny(X))))&
((~curious(susan)<~>tall(susan)))&
((~generous(susan)<~>wise(susan)))&
(?[X]:((humble(X)|strong(X)))) | ~wise(susan) | [
"p1",
"p2",
"p6",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3698896941586724407476878
% SZS output start Proof for 3698896941586724407476878
2. ! [X0] : (~brave(X0) <=> (generous(X0) | ~generous(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~brave(X0)) => patient(X0)) [input p2]
7. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> funny(X0)) [input p6]
8. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X0] : ~patient(X0) [input p7]
22. ~generous(susan) <~> wise(susan) [input p21]
24. ~wise(susan) [input hypothesis]
27. ? [X0] : (~generous(X0) | old(X0)) <=> ? [X1] : ~patient(X1) [rectify 8]
29. ! [X0] : (patient(X0) | (~funny(X0) | brave(X0))) [ennf transformation 3]
30. ! [X0] : (patient(X0) | ~funny(X0) | brave(X0)) [flattening 29]
48. ! [X0] : ((~brave(X0) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | brave(X0))) [nnf transformation 2]
49. ! [X0] : ((~brave(X0) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | brave(X0))) [flattening 48]
58. ! [X0] : (((~generous(X0) | ~brave(X0)) | ~funny(X0)) & (funny(X0) | (generous(X0) & brave(X0)))) [nnf transformation 7]
59. ! [X0] : ((~generous(X0) | ~brave(X0) | ~funny(X0)) & (funny(X0) | (generous(X0) & brave(X0)))) [flattening 58]
60. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (generous(X0) & ~old(X0))) [nnf transformation 27]
61. (? [X0] : (~generous(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (generous(X3) & ~old(X3))) [rectify 60]
62. ? [X0] : (~generous(X0) | old(X0)) => (~generous(sK4) | old(sK4)) [choice axiom]
63. ? [X2] : ~patient(X2) => ~patient(sK5) [choice axiom]
64. ((~generous(sK4) | old(sK4)) | ! [X1] : patient(X1)) & (~patient(sK5) | ! [X3] : (generous(X3) & ~old(X3))) [skolemisation 61,63,62]
89. (~wise(susan) | generous(susan)) & (wise(susan) | ~generous(susan)) [nnf transformation 22]
97. ~brave(X0) | generous(X0) [cnf transformation 49]
98. ~generous(X0) | ~brave(X0) [cnf transformation 49]
99. patient(X0) | ~funny(X0) | brave(X0) [cnf transformation 30]
109. funny(X0) | brave(X0) [cnf transformation 59]
113. ~patient(sK5) | generous(X3) [cnf transformation 64]
146. wise(susan) | ~generous(susan) [cnf transformation 89]
149. ~wise(susan) [cnf transformation 24]
173. ~brave(X0) [subsumption resolution 97,98]
174. ~funny(X0) | patient(X0) [subsumption resolution 99,173]
218. funny(X0) [subsumption resolution 109,173]
220. 16 <=> ! [X1] : patient(X1) [avatar definition]
221. patient(X1) <- (16) [avatar component clause 220]
232. 19 <=> ! [X3] : generous(X3) [avatar definition]
233. generous(X3) <- (19) [avatar component clause 232]
235. 20 <=> patient(sK5) [avatar definition]
237. ~patient(sK5) <- (~20) [avatar component clause 235]
238. 19 | ~20 [avatar split clause 113,235,232]
345. 42 <=> generous(susan) [avatar definition]
346. ~generous(susan) <- (~42) [avatar component clause 345]
349. 43 <=> wise(susan) [avatar definition]
353. ~42 | 43 [avatar split clause 146,349,345]
363. ~43 [avatar split clause 149,349]
375. patient(X0) [resolution 174,218]
376. 16 [avatar split clause 375,220]
377. $false <- (16, ~20) [resolution 221,237]
382. ~16 | 20 [avatar contradiction clause 377]
385. $false <- (19, ~42) [resolution 233,346]
390. ~19 | 42 [avatar contradiction clause 385]
391. $false [avatar sat refutation 238,353,363,376,382,390]
% SZS output end Proof for 3698896941586724407476878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not patient is either not funny or not happy.
Everyone who is either generous or creative is creative or not creative.
If someone is not creative or tall then susan is either generous or not patient and vice versa.
Everyone who is not wise or not funny is not generous or not rich and vice versa.
If alice is not kind then someone is either rich or not curious.
Everyone who is either calm or not calm is old or funny.
Everyone who is patient or brave is kind.
Everyone who is not rich is brave or not happy and vice versa.
If someone is both not brave and not generous then mary is not old or patient and vice versa.
Everyone who is both not rich and not humble is either brave or not creative and vice versa.
If someone is not creative then alice is patient or kind.
Everyone who is either brave or tall is both not brave and not patient.
Everyone who is not humble is either creative or not kind.
Everyone who is not wise or not patient is both wise and not patient and vice versa.
Everyone who is not brave is both kind and old and vice versa.
If fred is not generous then someone is both not creative and funny.
John is either kind or not wise.
Someone is humble.
Someone is either quiet or tall.
Fred is happy or not quiet.
Alice is funny or not kind.
Someone is both calm and tall.
Susan is either not strong or patient.
Fred is either old or not rich. | Susan is old. | entailment | (![X]:((brave(X)<~>~patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((generous(X)<~>creative(X))=>(creative(X)|~creative(X))))&
((?[X]:((~creative(X)|tall(X))))<=>((generous(susan)<~>~patient(susan))))&
(![X]:((~wise(X)|~funny(X))<=>(~generous(X)|~rich(X))))&
((~kind(alice))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((calm(X)<~>~calm(X))=>(old(X)|funny(X))))&
(![X]:((patient(X)|brave(X))=>kind(X)))&
(![X]:(~rich(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~brave(X)&~generous(X))))<=>((~old(mary)|patient(mary))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)<~>~creative(X))))&
((?[X]:(~creative(X)))=>((patient(alice)|kind(alice))))&
(![X]:((brave(X)<~>tall(X))=>(~brave(X)&~patient(X))))&
(![X]:(~humble(X)=>(creative(X)<~>~kind(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&~patient(X))))&
(![X]:(~brave(X)<=>(kind(X)&old(X))))&
((~generous(fred))=>(?[X]:((~creative(X)&funny(X)))))&
((kind(john)<~>~wise(john)))&
(?[X]:(humble(X)))&
(?[X]:((quiet(X)<~>tall(X))))&
((happy(fred)|~quiet(fred)))&
((funny(alice)|~kind(alice)))&
(?[X]:((calm(X)&tall(X))))&
((~strong(susan)<~>patient(susan)))&
((old(fred)<~>~rich(fred))) | old(susan) | [
"p3",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2408664697668625845169559
% SZS output start Proof for 2408664697668625845169559
4. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> (~rich(X0) | ~generous(X0))) [input p3]
6. ! [X0] : ((calm(X0) <~> ~calm(X0)) => (funny(X0) | old(X0))) [input p5]
8. ! [X0] : (~rich(X0) <=> (~happy(X0) | brave(X0))) [input p7]
14. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (~patient(X0) & wise(X0))) [input p13]
15. ! [X0] : (~brave(X0) <=> (old(X0) & kind(X0))) [input p14]
25. ~old(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) | old(X0)) | (calm(X0) <=> ~calm(X0))) [ennf transformation 6]
31. ! [X0] : (funny(X0) | old(X0) | (calm(X0) <=> ~calm(X0))) [flattening 30]
44. ! [X0] : (((~funny(X0) | ~wise(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (funny(X0) & wise(X0)))) [nnf transformation 4]
45. ! [X0] : ((~funny(X0) | ~wise(X0) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | (funny(X0) & wise(X0)))) [flattening 44]
49. ! [X0] : (funny(X0) | old(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) [nnf transformation 31]
50. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | rich(X0))) [nnf transformation 8]
51. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | rich(X0))) [flattening 50]
61. ! [X0] : (((~patient(X0) | ~wise(X0)) | (patient(X0) | ~wise(X0))) & ((~patient(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 14]
62. ! [X0] : ((~patient(X0) | ~wise(X0) | patient(X0) | ~wise(X0)) & ((~patient(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [flattening 61]
63. ! [X0] : ((~brave(X0) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | brave(X0))) [nnf transformation 15]
64. ! [X0] : ((~brave(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | brave(X0))) [flattening 63]
92. ~wise(X0) | ~funny(X0) | rich(X0) [cnf transformation 45]
95. funny(X0) | old(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 49]
96. funny(X0) | old(X0) | calm(X0) | calm(X0) [cnf transformation 49]
100. ~rich(X0) | ~brave(X0) [cnf transformation 51]
121. wise(X0) | patient(X0) [cnf transformation 62]
122. ~patient(X0) | wise(X0) [cnf transformation 62]
126. old(X0) | brave(X0) [cnf transformation 64]
143. ~old(susan) [cnf transformation 25]
147. funny(X0) | old(X0) | ~calm(X0) [duplicate literal removal 95]
148. old(X0) | funny(X0) | calm(X0) [duplicate literal removal 96]
193. old(X0) | funny(X0) [subsumption resolution 147,148]
222. wise(X0) [subsumption resolution 121,122]
277. brave(susan) [resolution 126,143]
284. funny(susan) [resolution 193,143]
292. ~funny(X0) | rich(X0) [resolution 92,222]
376. rich(susan) [resolution 292,284]
406. ~brave(susan) [resolution 376,100]
407. $false [subsumption resolution 406,277]
% SZS output end Proof for 2408664697668625845169559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and tall is either not kind or not curious and vice versa.
Everyone who is both not calm and calm is either patient or strong.
If mary is tall or rich then someone is not old or old.
Everyone who is patient is not humble or tall and vice versa.
If someone is calm or quiet then someone is either not generous or not kind.
Everyone who is not humble is not brave or not kind and vice versa.
If someone is not quiet or not strong then susan is both happy and patient and vice versa.
If someone is either not calm or generous then susan is both not funny and not tall and vice versa.
If someone is not tall or generous then alice is not patient or quiet.
Everyone who is both wise and kind is either not humble or not old.
Everyone who is tall or kind is both not calm and not patient.
Everyone who is humble is funny and vice versa.
If paul is either happy or not rich then someone is old and vice versa.
If someone is not happy or not rich then susan is both strong and happy.
Everyone who is both calm and not calm is kind and vice versa.
If mary is either patient or not creative then someone is either funny or calm and vice versa.
Someone is happy.
Paul is strong.
John is calm.
Lucy is not quiet.
Someone is not happy or not quiet.
Someone is either not patient or creative.
Alice is either strong or happy. | Alice is kind. | contradiction | (![X]:((~curious(X)&tall(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&calm(X))=>(patient(X)<~>strong(X))))&
(((tall(mary)|rich(mary)))=>(?[X]:((~old(X)|old(X)))))&
(![X]:(patient(X)<=>(~humble(X)|tall(X))))&
((?[X]:((calm(X)|quiet(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:(~humble(X)<=>(~brave(X)|~kind(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((happy(susan)&patient(susan))))&
((?[X]:((~calm(X)<~>generous(X))))<=>((~funny(susan)&~tall(susan))))&
((?[X]:((~tall(X)|generous(X))))=>((~patient(alice)|quiet(alice))))&
(![X]:((wise(X)&kind(X))=>(~humble(X)<~>~old(X))))&
(![X]:((tall(X)|kind(X))=>(~calm(X)&~patient(X))))&
(![X]:(humble(X)<=>funny(X)))&
(((happy(paul)<~>~rich(paul)))<=>(?[X]:(old(X))))&
((?[X]:((~happy(X)|~rich(X))))=>((strong(susan)&happy(susan))))&
(![X]:((calm(X)&~calm(X))<=>kind(X)))&
(((patient(mary)<~>~creative(mary)))<=>(?[X]:((funny(X)<~>calm(X)))))&
(?[X]:(happy(X)))&
(strong(paul))&
(calm(john))&
(~quiet(lucy))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
((strong(alice)<~>happy(alice))) | kind(alice) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3330061109634255886921398
% SZS output start Proof for 3330061109634255886921398
11. ! [X0] : ((kind(X0) | tall(X0)) => (~patient(X0) & ~calm(X0))) [input p10]
15. ! [X0] : ((~calm(X0) & calm(X0)) <=> kind(X0)) [input p14]
24. kind(alice) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~calm(X0)) | (~kind(X0) & ~tall(X0))) [ennf transformation 11]
63. ! [X0] : (((~calm(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~calm(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | calm(X0) | ~calm(X0))) [flattening 63]
111. ~calm(X0) | ~kind(X0) [cnf transformation 33]
125. calm(X0) | ~kind(X0) [cnf transformation 64]
144. kind(alice) [cnf transformation 24]
271. ~kind(X0) [subsumption resolution 125,111]
331. $false [subsumption resolution 144,271]
% SZS output end Proof for 3330061109634255886921398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not happy then mary is rich or old and vice versa.
Everyone who is both not happy and curious is humble and vice versa.
Everyone who is either curious or tall is brave or strong.
Everyone who is rich is not creative.
If someone is either wise or calm then lucy is either not calm or generous.
If someone is old or not patient then someone is not creative.
If someone is not happy or not kind then susan is tall or creative.
Everyone who is both funny and curious is either not rich or not kind.
If someone is funny or curious then someone is either happy or not brave and vice versa.
Everyone who is not happy or quiet is both old and not brave and vice versa.
Everyone who is both curious and not strong is not kind or not happy and vice versa.
Everyone who is patient is not generous and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not quiet or creative is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
Susan is not brave.
Alice is calm.
Someone is rich or kind.
Mary is not creative or not humble.
Someone is not humble or wise.
Someone is both brave and curious.
Someone is either humble or not patient. | Susan is not curious. | neutral | ((?[X]:((rich(X)|~happy(X))))<=>((rich(mary)|old(mary))))&
(![X]:((~happy(X)&curious(X))<=>humble(X)))&
(![X]:((curious(X)<~>tall(X))=>(brave(X)|strong(X))))&
(![X]:(rich(X)=>~creative(X)))&
((?[X]:((wise(X)<~>calm(X))))=>((~calm(lucy)<~>generous(lucy))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((tall(susan)|creative(susan))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
(~brave(susan))&
(calm(alice))&
(?[X]:((rich(X)|kind(X))))&
((~creative(mary)|~humble(mary)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is not old or old is both not brave and not strong and vice versa.
Everyone who is kind or rich is either not tall or wise and vice versa.
Everyone who is funny or wise is either kind or happy and vice versa.
If someone is brave then someone is curious or calm and vice versa.
Everyone who is both humble and happy is not brave and vice versa.
Everyone who is not rich or happy is both not calm and not old.
Everyone who is both not wise and not old is old and vice versa.
Everyone who is old or not rich is both funny and not wise.
Everyone who is creative or not happy is not kind or quiet and vice versa.
If someone is both not kind and not generous then someone is both tall and not rich and vice versa.
Everyone who is not rich is both patient and not wise.
Everyone who is generous or not funny is not funny or not kind and vice versa.
Everyone who is both not kind and not tall is not happy or calm.
If lucy is rich or humble then lucy is not rich or not patient.
Everyone who is not wise or not happy is not curious or rich.
Paul is creative or not funny.
Someone is not quiet or funny.
Paul is either tall or not humble.
Fred is both not brave and creative.
Lucy is not funny or wise. | Lucy is rich. | entailment | (![X]:((~old(X)|old(X))<=>(~brave(X)&~strong(X))))&
(![X]:((kind(X)|rich(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((funny(X)|wise(X))<=>(kind(X)<~>happy(X))))&
((?[X]:(brave(X)))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((humble(X)&happy(X))<=>~brave(X)))&
(![X]:((~rich(X)|happy(X))=>(~calm(X)&~old(X))))&
(![X]:((~wise(X)&~old(X))<=>old(X)))&
(![X]:((old(X)|~rich(X))=>(funny(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(~kind(X)|quiet(X))))&
((?[X]:((~kind(X)&~generous(X))))<=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:(~rich(X)=>(patient(X)&~wise(X))))&
(![X]:((generous(X)|~funny(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~kind(X)&~tall(X))=>(~happy(X)|calm(X))))&
(((rich(lucy)|humble(lucy)))=>((~rich(lucy)|~patient(lucy))))&
(![X]:((~wise(X)|~happy(X))=>(~curious(X)|rich(X))))&
((creative(paul)|~funny(paul)))&
(?[X]:((~quiet(X)|funny(X))))&
((tall(paul)<~>~humble(paul)))&
((~brave(fred)&creative(fred)))&
((~funny(lucy)|wise(lucy))) | rich(lucy) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8190014915260632693631362
% SZS output start Proof for 8190014915260632693631362
1. ! [X0] : ((old(X0) | ~old(X0)) <=> (~strong(X0) & ~brave(X0))) [input p0]
5. ! [X0] : ((happy(X0) & humble(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : ((happy(X0) | ~rich(X0)) => (~old(X0) & ~calm(X0))) [input p5]
7. ! [X0] : ((~old(X0) & ~wise(X0)) <=> old(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | old(X0)) => (~wise(X0) & funny(X0))) [input p7]
21. ~rich(lucy) [input hypothesis]
24. ! [X0] : ((~old(X0) & ~calm(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 6]
25. ! [X0] : ((~wise(X0) & funny(X0)) | (rich(X0) & ~old(X0))) [ennf transformation 8]
33. ! [X0] : (((old(X0) | ~old(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (~old(X0) & old(X0)))) [nnf transformation 1]
34. ! [X0] : ((old(X0) | ~old(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (~old(X0) & old(X0)))) [flattening 33]
44. ! [X0] : (((happy(X0) & humble(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) | ~humble(X0)))) [nnf transformation 5]
45. ! [X0] : (((happy(X0) & humble(X0)) | brave(X0)) & (~brave(X0) | ~happy(X0) | ~humble(X0))) [flattening 44]
46. ! [X0] : (((~old(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | (old(X0) | wise(X0)))) [nnf transformation 7]
47. ! [X0] : (((~old(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | old(X0) | wise(X0))) [flattening 46]
60. ~brave(X0) | old(X0) [cnf transformation 34]
61. ~brave(X0) | ~old(X0) [cnf transformation 34]
82. happy(X0) | brave(X0) [cnf transformation 45]
86. ~old(X0) | ~happy(X0) [cnf transformation 24]
87. old(X0) | old(X0) | wise(X0) [cnf transformation 47]
93. ~wise(X0) | rich(X0) [cnf transformation 25]
120. ~rich(lucy) [cnf transformation 21]
122. old(X0) | wise(X0) [duplicate literal removal 87]
125. ~brave(X0) [subsumption resolution 60,61]
128. happy(X0) [subsumption resolution 82,125]
130. ~old(X0) [subsumption resolution 86,128]
131. wise(X0) [subsumption resolution 122,130]
132. rich(X0) [subsumption resolution 93,131]
159. $false [subsumption resolution 120,132]
% SZS output end Proof for 8190014915260632693631362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both wise and funny and vice versa.
If paul is not tall then someone is not quiet.
Everyone who is happy or not wise is not happy or not generous and vice versa.
If someone is not wise then mary is either not rich or not happy and vice versa.
Everyone who is both funny and not wise is either strong or brave and vice versa.
If mary is both not brave and not wise then susan is funny or not happy and vice versa.
If fred is not patient then someone is calm or not quiet.
If someone is funny or not funny then alice is not brave and vice versa.
Everyone who is not brave or funny is either not wise or rich and vice versa.
Everyone who is not creative or quiet is either not happy or not brave.
Everyone who is either not tall or not humble is creative or not humble and vice versa.
If someone is creative or not creative then alice is both not creative and not wise and vice versa.
If susan is curious then paul is strong or not creative and vice versa.
Everyone who is strong or not quiet is funny or wise.
Everyone who is both curious and not kind is patient and vice versa.
Everyone who is both not generous and not brave is not kind.
Lucy is either kind or happy.
John is either not patient or not calm.
Someone is both not tall and calm.
Mary is either rich or not humble.
Someone is both not tall and happy.
Someone is either not old or humble. | Mary is not tall. | contradiction | (![X]:(~funny(X)<=>(wise(X)&funny(X))))&
((~tall(paul))=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)|~wise(X))<=>(~happy(X)|~generous(X))))&
((?[X]:(~wise(X)))<=>((~rich(mary)<~>~happy(mary))))&
(![X]:((funny(X)&~wise(X))<=>(strong(X)<~>brave(X))))&
(((~brave(mary)&~wise(mary)))<=>((funny(susan)|~happy(susan))))&
((~patient(fred))=>(?[X]:((calm(X)|~quiet(X)))))&
((?[X]:((funny(X)|~funny(X))))<=>(~brave(alice)))&
(![X]:((~brave(X)|funny(X))<=>(~wise(X)<~>rich(X))))&
(![X]:((~creative(X)|quiet(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(alice)&~wise(alice))))&
((curious(susan))<=>((strong(paul)|~creative(paul))))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)|wise(X))))&
(![X]:((curious(X)&~kind(X))<=>patient(X)))&
(![X]:((~generous(X)&~brave(X))=>~kind(X)))&
((kind(lucy)<~>happy(lucy)))&
((~patient(john)<~>~calm(john)))&
(?[X]:((~tall(X)&calm(X))))&
((rich(mary)<~>~humble(mary)))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~old(X)<~>humble(X)))) | ~tall(mary) | [
"p0",
"p5",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1911108816290120255716406
% SZS output start Proof for 1911108816290120255716406
1. ! [X0] : (~funny(X0) <=> (funny(X0) & wise(X0))) [input p0]
6. (~wise(mary) & ~brave(mary)) <=> (~happy(susan) | funny(susan)) [input p5]
9. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (~wise(X0) <~> rich(X0))) [input p8]
11. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~humble(X0) | creative(X0))) [input p10]
20. rich(mary) <~> ~humble(mary) [input p19]
23. ~tall(mary) [input hypothesis]
31. ! [X0] : ((~funny(X0) | (~funny(X0) | ~wise(X0))) & ((funny(X0) & wise(X0)) | funny(X0))) [nnf transformation 1]
32. ! [X0] : ((~funny(X0) | ~funny(X0) | ~wise(X0)) & ((funny(X0) & wise(X0)) | funny(X0))) [flattening 31]
43. ((~wise(mary) & ~brave(mary)) | (happy(susan) & ~funny(susan))) & ((~happy(susan) | funny(susan)) | (wise(mary) | brave(mary))) [nnf transformation 6]
44. ((~wise(mary) & ~brave(mary)) | (happy(susan) & ~funny(susan))) & (~happy(susan) | funny(susan) | wise(mary) | brave(mary)) [flattening 43]
51. ! [X0] : (((funny(X0) | ~brave(X0)) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 9]
52. ! [X0] : ((funny(X0) | ~brave(X0) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (~funny(X0) & brave(X0)))) [flattening 51]
54. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 11]
55. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [flattening 54]
69. (humble(mary) | ~rich(mary)) & (~humble(mary) | rich(mary)) [nnf transformation 20]
76. funny(X0) | funny(X0) [cnf transformation 32]
96. ~wise(mary) | ~funny(susan) [cnf transformation 44]
105. ~rich(X0) | wise(X0) | ~funny(X0) [cnf transformation 52]
117. humble(X0) | tall(X0) | humble(X0) [cnf transformation 55]
138. ~humble(mary) | rich(mary) [cnf transformation 69]
144. ~tall(mary) [cnf transformation 23]
146. humble(X0) | tall(X0) [duplicate literal removal 117]
149. funny(X0) [duplicate literal removal 76]
165. 4 <=> rich(mary) [avatar definition]
166. rich(mary) <- (4) [avatar component clause 165]
186. 8 <=> wise(mary) [avatar definition]
188. ~wise(mary) <- (~8) [avatar component clause 186]
190. ~wise(mary) [subsumption resolution 96,149]
191. ~8 [avatar split clause 190,186]
213. ~rich(X0) | wise(X0) [subsumption resolution 105,149]
269. 24 <=> humble(mary) [avatar definition]
270. ~humble(mary) <- (~24) [avatar component clause 269]
273. 4 | ~24 [avatar split clause 138,269,165]
286. tall(mary) <- (~24) [resolution 146,270]
288. $false <- (~24) [subsumption resolution 286,144]
289. 24 [avatar contradiction clause 288]
290. wise(mary) <- (4) [resolution 213,166]
291. $false <- (4, ~8) [subsumption resolution 290,188]
292. ~4 | 8 [avatar contradiction clause 291]
293. $false [avatar sat refutation 191,273,289,292]
% SZS output end Proof for 1911108816290120255716406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not humble is both calm and creative and vice versa. Everyone who is both not brave and strong is not quiet or not old. If someone is quiet or brave then someone is both not kind and tall. Everyone who is not funny or not kind is both strong and not tall. If someone is either strong or humble then alice is not curious or not rich. If lucy is either not rich or not humble then someone is both not calm and tall and vice versa. If john is both calm and not rich then lucy is either not generous or not quiet and vice versa. If someone is either not funny or calm then someone is both not quiet and not strong. Everyone who is both not funny and patient is not creative and vice versa. If someone is not old then john is either not creative or humble and vice versa. Everyone who is either not tall or not creative is both curious and old and vice versa. Everyone who is both not tall and not calm is either happy or not old. Everyone who is rich or not humble is both not humble and strong and vice versa. If someone is either not brave or not rich then mary is both humble and not wise. Everyone who is either not humble or curious is calm or not tall and vice versa. Fred is not kind. Mary is both humble and patient. Paul is both patient and not calm. Alice is either kind or brave. Someone is either not wise or not strong. Susan is both not creative and not old. Fred is not wise. | Susan is brave. | contradiction | (![X]:((~calm(X)&~humble(X))<=>(calm(X)&creative(X))))&
(![X]:((~brave(X)&strong(X))=>(~quiet(X)|~old(X))))&
((?[X]:((quiet(X)|brave(X))))=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((~funny(X)|~kind(X))=>(strong(X)&~tall(X))))&
((?[X]:((strong(X)<~>humble(X))))=>((~curious(alice)|~rich(alice))))&
(((~rich(lucy)<~>~humble(lucy)))<=>(?[X]:((~calm(X)&tall(X)))))&
(((calm(john)&~rich(john)))<=>((~generous(lucy)<~>~quiet(lucy))))&
((?[X]:((~funny(X)<~>calm(X))))=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((~funny(X)&patient(X))<=>~creative(X)))&
((?[X]:(~old(X)))<=>((~creative(john)<~>humble(john))))&
(![X]:((~tall(X)<~>~creative(X))<=>(curious(X)&old(X))))&
(![X]:((~tall(X)&~calm(X))=>(happy(X)<~>~old(X))))&
(![X]:((rich(X)|~humble(X))<=>(~humble(X)&strong(X))))&
((?[X]:((~brave(X)<~>~rich(X))))=>((humble(mary)&~wise(mary))))&
(![X]:((~humble(X)<~>curious(X))<=>(calm(X)|~tall(X))))&
(~kind(fred))&
((humble(mary)&patient(mary)))&
((patient(paul)&~calm(paul)))&
((kind(alice)<~>brave(alice)))&
(?[X]:((~wise(X)<~>~strong(X))))&
((~creative(susan)&~old(susan)))&
(~wise(fred)) | brave(susan) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5629146634607204663181481
% SZS output start Proof for 5629146634607204663181481
3. ? [X0] : (brave(X0) | quiet(X0)) => ? [X0] : (tall(X0) & ~kind(X0)) [input p2]
4. ! [X0] : ((~kind(X0) | ~funny(X0)) => (~tall(X0) & strong(X0))) [input p3]
23. brave(susan) [input hypothesis]
24. ? [X0] : (brave(X0) | quiet(X0)) => ? [X1] : (tall(X1) & ~kind(X1)) [rectify 3]
28. ? [X1] : (tall(X1) & ~kind(X1)) | ! [X0] : (~brave(X0) & ~quiet(X0)) [ennf transformation 24]
29. ! [X0] : ((~tall(X0) & strong(X0)) | (kind(X0) & funny(X0))) [ennf transformation 4]
38. ? [X0] : (tall(X0) & ~kind(X0)) | ! [X1] : (~brave(X1) & ~quiet(X1)) [rectify 28]
39. ? [X0] : (tall(X0) & ~kind(X0)) => (tall(sK0) & ~kind(sK0)) [choice axiom]
40. (tall(sK0) & ~kind(sK0)) | ! [X1] : (~brave(X1) & ~quiet(X1)) [skolemisation 38,39]
76. ~kind(sK0) | ~brave(X1) [cnf transformation 40]
78. tall(sK0) | ~brave(X1) [cnf transformation 40]
82. ~tall(X0) | kind(X0) [cnf transformation 29]
143. brave(susan) [cnf transformation 23]
147. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
148. ~brave(X1) <- (1) [avatar component clause 147]
150. 2 <=> tall(sK0) [avatar definition]
152. tall(sK0) <- (2) [avatar component clause 150]
153. 1 | 2 [avatar split clause 78,150,147]
159. 4 <=> kind(sK0) [avatar definition]
161. ~kind(sK0) <- (~4) [avatar component clause 159]
162. 1 | ~4 [avatar split clause 76,159,147]
308. kind(sK0) <- (2) [resolution 82,152]
309. $false <- (2, ~4) [subsumption resolution 308,161]
310. ~2 | 4 [avatar contradiction clause 309]
311. $false <- (1) [resolution 148,143]
312. ~1 [avatar contradiction clause 311]
313. $false [avatar sat refutation 153,162,310,312]
% SZS output end Proof for 5629146634607204663181481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or humble is not curious or humble and vice versa.
Everyone who is not happy or not humble is either not rich or brave and vice versa.
Everyone who is not strong or not brave is not old and vice versa.
If someone is either old or not generous then lucy is patient or calm.
Everyone who is not funny or quiet is either patient or generous.
Everyone who is brave is curious or not generous.
If mary is not funny or not tall then someone is both not generous and not humble.
Everyone who is happy is not rich or kind and vice versa.
Everyone who is old is humble.
Everyone who is quiet or not patient is strong and vice versa.
If someone is both not generous and funny then someone is not generous or not rich and vice versa.
Everyone who is not quiet is either not tall or rich and vice versa.
Everyone who is quiet is both not curious and not old.
If someone is not kind or not strong then alice is both kind and rich.
Everyone who is calm is both kind and funny and vice versa.
Everyone who is not generous or calm is tall or not brave and vice versa.
Someone is not funny or creative.
John is both creative and not tall.
Alice is either not brave or not funny.
Someone is both not kind and not generous.
Someone is both not calm and curious.
John is kind or not strong.
Susan is both funny and not curious.
Susan is either happy or curious. | Lucy is creative. | neutral | (![X]:((tall(X)|humble(X))<=>(~curious(X)|humble(X))))&
(![X]:((~happy(X)|~humble(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~strong(X)|~brave(X))<=>~old(X)))&
((?[X]:((old(X)<~>~generous(X))))=>((patient(lucy)|calm(lucy))))&
(![X]:((~funny(X)|quiet(X))=>(patient(X)<~>generous(X))))&
(![X]:(brave(X)=>(curious(X)|~generous(X))))&
(((~funny(mary)|~tall(mary)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(happy(X)<=>(~rich(X)|kind(X))))&
(![X]:(old(X)=>humble(X)))&
(![X]:((quiet(X)|~patient(X))<=>strong(X)))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>rich(X))))&
(![X]:(quiet(X)=>(~curious(X)&~old(X))))&
((?[X]:((~kind(X)|~strong(X))))=>((kind(alice)&rich(alice))))&
(![X]:(calm(X)<=>(kind(X)&funny(X))))&
(![X]:((~generous(X)|calm(X))<=>(tall(X)|~brave(X))))&
(?[X]:((~funny(X)|creative(X))))&
((creative(john)&~tall(john)))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~calm(X)&curious(X))))&
((kind(john)|~strong(john)))&
((funny(susan)&~curious(susan)))&
((happy(susan)<~>curious(susan))) | creative(lucy) | [] | null | 0 |
Everyone who is both happy and not patient is either not curious or generous.
Everyone who is either not creative or patient is calm or not rich.
Everyone who is both generous and not creative is either not tall or brave.
If someone is both happy and patient then someone is not humble and vice versa.
If someone is not patient then someone is not creative or not old and vice versa.
If paul is either not tall or tall then fred is both strong and calm and vice versa.
If someone is either curious or brave then someone is either funny or not funny.
Everyone who is not curious is quiet and vice versa.
Everyone who is not quiet is not curious or happy and vice versa.
If john is not funny or quiet then someone is either not kind or curious.
Everyone who is either not patient or happy is either brave or not brave and vice versa.
Everyone who is both not happy and rich is both not quiet and brave and vice versa.
Everyone who is not strong or not brave is strong or not generous.
Everyone who is not funny is both not brave and not tall and vice versa.
If susan is not wise then paul is either humble or not curious and vice versa.
Everyone who is both not creative and patient is either tall or not kind and vice versa.
Susan is generous or strong.
Fred is both not rich and patient.
John is either patient or rich.
Someone is either not funny or tall. | John is not funny. | neutral | (![X]:((happy(X)&~patient(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~creative(X)<~>patient(X))=>(calm(X)|~rich(X))))&
(![X]:((generous(X)&~creative(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~creative(X)|~old(X)))))&
(((~tall(paul)<~>tall(paul)))<=>((strong(fred)&calm(fred))))&
((?[X]:((curious(X)<~>brave(X))))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:(~quiet(X)<=>(~curious(X)|happy(X))))&
(((~funny(john)|quiet(john)))=>(?[X]:((~kind(X)<~>curious(X)))))&
(![X]:((~patient(X)<~>happy(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((~happy(X)&rich(X))<=>(~quiet(X)&brave(X))))&
(![X]:((~strong(X)|~brave(X))=>(strong(X)|~generous(X))))&
(![X]:(~funny(X)<=>(~brave(X)&~tall(X))))&
((~wise(susan))<=>((humble(paul)<~>~curious(paul))))&
(![X]:((~creative(X)&patient(X))<=>(tall(X)<~>~kind(X))))&
((generous(susan)|strong(susan)))&
((~rich(fred)&patient(fred)))&
((patient(john)<~>rich(john)))&
(?[X]:((~funny(X)<~>tall(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is both not creative and curious is either strong or wise and vice versa.
Everyone who is not curious or funny is either not strong or not generous and vice versa.
If someone is not wise or calm then mary is either old or not kind and vice versa.
If alice is not funny or not old then someone is both curious and not patient.
Everyone who is not old or not strong is both not generous and tall and vice versa.
Everyone who is either humble or happy is not quiet.
If alice is not quiet or happy then alice is both not brave and not calm and vice versa.
If someone is brave or not funny then lucy is either funny or calm.
If someone is not funny then someone is kind and vice versa.
Everyone who is not funny or tall is both generous and funny and vice versa.
Everyone who is either not curious or happy is both brave and calm.
If mary is not wise or not patient then alice is quiet or kind and vice versa.
Everyone who is either not creative or old is not happy or generous and vice versa.
Everyone who is happy or not humble is not strong.
Everyone who is both not strong and not generous is tall or not creative.
Everyone who is creative is funny or creative and vice versa.
Mary is humble or not patient.
Lucy is patient.
Someone is both brave and not kind.
Paul is not quiet.
Someone is either not kind or patient.
Someone is curious. | Lucy is humble. | entailment | (![X]:((~creative(X)&curious(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~curious(X)|funny(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:((~wise(X)|calm(X))))<=>((old(mary)<~>~kind(mary))))&
(((~funny(alice)|~old(alice)))=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~generous(X)&tall(X))))&
(![X]:((humble(X)<~>happy(X))=>~quiet(X)))&
(((~quiet(alice)|happy(alice)))<=>((~brave(alice)&~calm(alice))))&
((?[X]:((brave(X)|~funny(X))))=>((funny(lucy)<~>calm(lucy))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((~funny(X)|tall(X))<=>(generous(X)&funny(X))))&
(![X]:((~curious(X)<~>happy(X))=>(brave(X)&calm(X))))&
(((~wise(mary)|~patient(mary)))<=>((quiet(alice)|kind(alice))))&
(![X]:((~creative(X)<~>old(X))<=>(~happy(X)|generous(X))))&
(![X]:((happy(X)|~humble(X))=>~strong(X)))&
(![X]:((~strong(X)&~generous(X))=>(tall(X)|~creative(X))))&
(![X]:(creative(X)<=>(funny(X)|creative(X))))&
((humble(mary)|~patient(mary)))&
(patient(lucy))&
(?[X]:((brave(X)&~kind(X))))&
(~quiet(paul))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:(curious(X))) | humble(lucy) | [
"p4",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7298334059556054932670311
% SZS output start Proof for 7298334059556054932670311
5. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (funny(X0) & generous(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | happy(X0)) => ~strong(X0)) [input p13]
23. ~humble(lucy) [input hypothesis]
29. ! [X0] : (~strong(X0) | (humble(X0) & ~happy(X0))) [ennf transformation 14]
42. ! [X0] : (((~strong(X0) | ~old(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [nnf transformation 5]
43. ! [X0] : ((~strong(X0) | ~old(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [flattening 42]
53. ! [X0] : (((tall(X0) | ~funny(X0)) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((tall(X0) | ~funny(X0) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [flattening 53]
92. ~generous(X0) | strong(X0) [cnf transformation 43]
94. tall(X0) | strong(X0) [cnf transformation 43]
110. ~tall(X0) | generous(X0) [cnf transformation 54]
129. ~strong(X0) | humble(X0) [cnf transformation 29]
142. ~humble(lucy) [cnf transformation 23]
283. generous(X0) | strong(X0) [resolution 110,94]
285. strong(X0) [subsumption resolution 283,92]
293. humble(X0) [resolution 129,285]
294. $false [resolution 293,142]
% SZS output end Proof for 7298334059556054932670311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and creative then someone is both not curious and rich.
Everyone who is both not old and not kind is either not happy or not kind and vice versa.
Everyone who is both creative and not calm is either not strong or quiet and vice versa.
Everyone who is both generous and kind is not curious and vice versa.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not generous is both calm and not humble.
If someone is both curious and not old then alice is both funny and calm and vice versa.
Everyone who is both patient and not creative is not patient or rich and vice versa.
Everyone who is happy is not humble or patient.
Everyone who is curious or not happy is not funny and vice versa.
If someone is either quiet or brave then paul is both humble and tall.
Everyone who is either creative or not brave is both strong and curious and vice versa.
If someone is either tall or quiet then paul is kind or humble and vice versa.
If someone is not curious or not patient then someone is both patient and not strong and vice versa.
If alice is both tall and not wise then someone is both funny and not quiet and vice versa.
Lucy is brave or kind.
Someone is humble or brave.
Lucy is curious.
Fred is not wise or not brave. | Alice is wise. | neutral | (((~curious(alice)&creative(alice)))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&kind(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~humble(X))))&
((?[X]:((curious(X)&~old(X))))<=>((funny(alice)&calm(alice))))&
(![X]:((patient(X)&~creative(X))<=>(~patient(X)|rich(X))))&
(![X]:(happy(X)=>(~humble(X)|patient(X))))&
(![X]:((curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>((humble(paul)&tall(paul))))&
(![X]:((creative(X)<~>~brave(X))<=>(strong(X)&curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((kind(paul)|humble(paul))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(((tall(alice)&~wise(alice)))<=>(?[X]:((funny(X)&~quiet(X)))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((humble(X)|brave(X))))&
(curious(lucy))&
((~wise(fred)|~brave(fred))) | wise(alice) | [] | null | 0 |
If mary is both not generous and not rich then someone is either not patient or rich and vice versa.
Everyone who is either not wise or not quiet is not wise.
Everyone who is both brave and not humble is either creative or old and vice versa.
If mary is both not strong and rich then someone is not calm and vice versa.
Everyone who is not rich is either kind or not kind.
If susan is either not rich or curious then someone is either rich or not tall and vice versa.
Everyone who is either not happy or not kind is not quiet.
If someone is not creative or not wise then fred is both wise and not rich and vice versa.
If someone is not generous then someone is funny and vice versa.
Everyone who is funny is either quiet or funny.
If john is not humble then john is curious or not curious and vice versa.
Everyone who is either old or strong is both not curious and not patient and vice versa.
Everyone who is either quiet or not wise is not rich and vice versa.
Everyone who is not calm is both generous and funny.
If mary is not tall or not funny then someone is quiet or tall and vice versa.
If someone is not funny or not rich then fred is both not happy and not creative and vice versa.
Lucy is either not old or wise.
Someone is either not wise or tall.
Alice is both happy and not tall.
Paul is both tall and not calm.
Someone is not humble or not patient.
Mary is not quiet or happy.
John is either brave or not rich. | Fred is not humble. | neutral | (((~generous(mary)&~rich(mary)))<=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>~quiet(X))=>~wise(X)))&
(![X]:((brave(X)&~humble(X))<=>(creative(X)<~>old(X))))&
(((~strong(mary)&rich(mary)))<=>(?[X]:(~calm(X))))&
(![X]:(~rich(X)=>(kind(X)<~>~kind(X))))&
(((~rich(susan)<~>curious(susan)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>~quiet(X)))&
((?[X]:((~creative(X)|~wise(X))))<=>((wise(fred)&~rich(fred))))&
((?[X]:(~generous(X)))<=>(?[X]:(funny(X))))&
(![X]:(funny(X)=>(quiet(X)<~>funny(X))))&
((~humble(john))<=>((curious(john)|~curious(john))))&
(![X]:((old(X)<~>strong(X))<=>(~curious(X)&~patient(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>~rich(X)))&
(![X]:(~calm(X)=>(generous(X)&funny(X))))&
(((~tall(mary)|~funny(mary)))<=>(?[X]:((quiet(X)|tall(X)))))&
((?[X]:((~funny(X)|~rich(X))))<=>((~happy(fred)&~creative(fred))))&
((~old(lucy)<~>wise(lucy)))&
(?[X]:((~wise(X)<~>tall(X))))&
((happy(alice)&~tall(alice)))&
((tall(paul)&~calm(paul)))&
(?[X]:((~humble(X)|~patient(X))))&
((~quiet(mary)|happy(mary)))&
((brave(john)<~>~rich(john))) | ~humble(fred) | [] | null | 0 |
Everyone who is generous is not creative or tall and vice versa.
Everyone who is both kind and funny is wise or generous.
If alice is either not generous or tall then paul is both funny and wise.
If someone is either generous or not kind then someone is either not happy or generous and vice versa.
Everyone who is not rich or wise is either patient or not creative.
If someone is both not curious and not strong then someone is not generous.
Everyone who is either not calm or not humble is not brave or brave and vice versa.
Everyone who is either not old or creative is not old.
If susan is old or rich then susan is both humble and not humble and vice versa.
If paul is both not patient and calm then someone is not wise.
Everyone who is not brave is both not humble and not tall.
Everyone who is not wise is funny.
If someone is either not quiet or not tall then someone is both not funny and not quiet and vice versa.
Everyone who is creative is both funny and not patient.
If mary is either kind or not old then lucy is happy or tall.
Everyone who is generous is not curious or patient and vice versa.
Mary is not brave.
Paul is not creative.
Someone is strong.
Someone is generous.
Someone is either not calm or not strong.
Someone is either calm or not patient.
Someone is funny.
Someone is either not patient or patient. | Susan is curious. | contradiction | (![X]:(generous(X)<=>(~creative(X)|tall(X))))&
(![X]:((kind(X)&funny(X))=>(wise(X)|generous(X))))&
(((~generous(alice)<~>tall(alice)))=>((funny(paul)&wise(paul))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~rich(X)|wise(X))=>(patient(X)<~>~creative(X))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~brave(X)|brave(X))))&
(![X]:((~old(X)<~>creative(X))=>~old(X)))&
(((old(susan)|rich(susan)))<=>((humble(susan)&~humble(susan))))&
(((~patient(paul)&calm(paul)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)=>(~humble(X)&~tall(X))))&
(![X]:(~wise(X)=>funny(X)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(creative(X)=>(funny(X)&~patient(X))))&
(((kind(mary)<~>~old(mary)))=>((happy(lucy)|tall(lucy))))&
(![X]:(generous(X)<=>(~curious(X)|patient(X))))&
(~brave(mary))&
(~creative(paul))&
(?[X]:(strong(X)))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>patient(X)))) | curious(susan) | [
"p0",
"p4",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 271149696091664923777101
% SZS output start Proof for 271149696091664923777101
1. ! [X0] : (generous(X0) <=> (tall(X0) | ~creative(X0))) [input p0]
5. ! [X0] : ((wise(X0) | ~rich(X0)) => (patient(X0) <~> ~creative(X0))) [input p4]
9. (rich(susan) | old(susan)) <=> (~humble(susan) & humble(susan)) [input p8]
14. ! [X0] : (creative(X0) => (~patient(X0) & funny(X0))) [input p13]
16. ! [X0] : (generous(X0) <=> (patient(X0) | ~curious(X0))) [input p15]
25. curious(susan) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (~wise(X0) & rich(X0))) [ennf transformation 5]
39. ! [X0] : ((~patient(X0) & funny(X0)) | ~creative(X0)) [ennf transformation 14]
42. ! [X0] : ((generous(X0) | (~tall(X0) & creative(X0))) & ((tall(X0) | ~creative(X0)) | ~generous(X0))) [nnf transformation 1]
43. ! [X0] : ((generous(X0) | (~tall(X0) & creative(X0))) & (tall(X0) | ~creative(X0) | ~generous(X0))) [flattening 42]
50. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~wise(X0) & rich(X0))) [nnf transformation 32]
57. ((rich(susan) | old(susan)) | (humble(susan) | ~humble(susan))) & ((~humble(susan) & humble(susan)) | (~rich(susan) & ~old(susan))) [nnf transformation 9]
58. (rich(susan) | old(susan) | humble(susan) | ~humble(susan)) & ((~humble(susan) & humble(susan)) | (~rich(susan) & ~old(susan))) [flattening 57]
67. ! [X0] : ((generous(X0) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | ~generous(X0))) [nnf transformation 16]
68. ! [X0] : ((generous(X0) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | ~generous(X0))) [flattening 67]
85. creative(X0) | generous(X0) [cnf transformation 43]
100. ~creative(X0) | patient(X0) | rich(X0) [cnf transformation 50]
102. ~patient(X0) | creative(X0) | rich(X0) [cnf transformation 50]
114. humble(susan) | ~rich(susan) [cnf transformation 58]
116. ~humble(susan) | ~rich(susan) [cnf transformation 58]
129. ~patient(X0) | ~creative(X0) [cnf transformation 39]
132. ~curious(X0) | patient(X0) | ~generous(X0) [cnf transformation 68]
134. ~patient(X0) | generous(X0) [cnf transformation 68]
146. curious(susan) [cnf transformation 25]
219. 15 <=> rich(susan) [avatar definition]
221. ~rich(susan) <- (~15) [avatar component clause 219]
223. 16 <=> humble(susan) [avatar definition]
226. ~15 | ~16 [avatar split clause 116,223,219]
232. ~15 | 16 [avatar split clause 114,223,219]
327. patient(X0) | rich(X0) | generous(X0) [resolution 100,85]
328. rich(X0) | generous(X0) [subsumption resolution 327,134]
331. generous(susan) <- (~15) [resolution 328,221]
335. patient(susan) | ~generous(susan) [resolution 132,146]
337. patient(susan) <- (~15) [subsumption resolution 335,331]
339. creative(susan) | rich(susan) <- (~15) [resolution 337,102]
341. ~creative(susan) <- (~15) [resolution 337,129]
347. 37 <=> creative(susan) [avatar definition]
351. creative(susan) <- (~15) [subsumption resolution 339,221]
352. 37 | 15 [avatar split clause 351,219,347]
353. ~37 | 15 [avatar split clause 341,219,347]
354. $false [avatar sat refutation 226,232,352,353]
% SZS output end Proof for 271149696091664923777101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not tall is both brave and not generous. Everyone who is happy is not old and vice versa. Everyone who is not happy is both generous and calm. Everyone who is old or rich is kind. Everyone who is funny is not creative or not kind. Everyone who is not humble or old is rich or not curious. If lucy is curious then fred is either strong or creative. Everyone who is both humble and generous is both kind and happy. Everyone who is either not generous or not curious is either not brave or not tall and vice versa. Everyone who is not creative is tall or not old and vice versa. Everyone who is humble or generous is humble. Everyone who is both happy and not rich is funny. Everyone who is not wise is quiet or not kind and vice versa. If lucy is either patient or not funny then someone is both not patient and not tall and vice versa. If susan is both quiet and not creative then lucy is both curious and not calm. If someone is not generous then john is either not tall or not patient and vice versa. Someone is not happy or not quiet. John is both not brave and not humble. John is either tall or not generous. Someone is not wise. Lucy is both patient and not funny. Susan is either not happy or not humble. Someone is not calm. Mary is not wise. | Lucy is rich. | entailment | (![X]:((funny(X)&~tall(X))=>(brave(X)&~generous(X))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(tall(X)|~old(X))))&
(![X]:((humble(X)|generous(X))=>humble(X)))&
(![X]:((happy(X)&~rich(X))=>funny(X)))&
(![X]:(~wise(X)<=>(quiet(X)|~kind(X))))&
(((patient(lucy)<~>~funny(lucy)))<=>(?[X]:((~patient(X)&~tall(X)))))&
(((quiet(susan)&~creative(susan)))=>((curious(lucy)&~calm(lucy))))&
((?[X]:(~generous(X)))<=>((~tall(john)<~>~patient(john))))&
(?[X]:((~happy(X)|~quiet(X))))&
((~brave(john)&~humble(john)))&
((tall(john)<~>~generous(john)))&
(?[X]:(~wise(X)))&
((patient(lucy)&~funny(lucy)))&
((~happy(susan)<~>~humble(susan)))&
(?[X]:(~calm(X)))&
(~wise(mary)) | rich(lucy) | [
"p2",
"p7",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6593608566451401538431935
% SZS output start Proof for 6593608566451401538431935
3. ! [X0] : (~happy(X0) => (calm(X0) & generous(X0))) [input p2]
8. ! [X0] : ((generous(X0) & humble(X0)) => (happy(X0) & kind(X0))) [input p7]
11. ! [X0] : ((generous(X0) | humble(X0)) => humble(X0)) [input p10]
12. ! [X0] : ((~rich(X0) & happy(X0)) => funny(X0)) [input p11]
21. ~funny(lucy) & patient(lucy) [input p20]
25. ~rich(lucy) [input hypothesis]
29. ! [X0] : ((calm(X0) & generous(X0)) | happy(X0)) [ennf transformation 3]
36. ! [X0] : ((happy(X0) & kind(X0)) | (~generous(X0) | ~humble(X0))) [ennf transformation 8]
37. ! [X0] : ((happy(X0) & kind(X0)) | ~generous(X0) | ~humble(X0)) [flattening 36]
38. ! [X0] : (humble(X0) | (~generous(X0) & ~humble(X0))) [ennf transformation 11]
39. ! [X0] : (funny(X0) | (rich(X0) | ~happy(X0))) [ennf transformation 12]
40. ! [X0] : (funny(X0) | rich(X0) | ~happy(X0)) [flattening 39]
70. happy(X0) | generous(X0) [cnf transformation 29]
80. happy(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 37]
93. ~generous(X0) | humble(X0) [cnf transformation 38]
94. ~happy(X0) | rich(X0) | funny(X0) [cnf transformation 40]
115. ~funny(lucy) [cnf transformation 21]
120. ~rich(lucy) [cnf transformation 25]
135. ~humble(X0) | happy(X0) [subsumption resolution 80,70]
144. 6 <=> funny(lucy) [avatar definition]
145. ~funny(lucy) <- (~6) [avatar component clause 144]
209. ~6 [avatar split clause 115,144]
222. rich(X0) | funny(X0) | generous(X0) [resolution 94,70]
295. funny(lucy) | generous(lucy) [resolution 222,120]
297. generous(lucy) <- (~6) [subsumption resolution 295,145]
301. humble(lucy) <- (~6) [resolution 297,93]
438. happy(lucy) <- (~6) [resolution 301,135]
460. rich(lucy) | funny(lucy) <- (~6) [resolution 438,94]
461. funny(lucy) <- (~6) [subsumption resolution 460,120]
462. $false <- (~6) [subsumption resolution 461,145]
463. 6 [avatar contradiction clause 462]
464. $false [avatar sat refutation 209,463]
% SZS output end Proof for 6593608566451401538431935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or creative is curious or not humble. Everyone who is both calm and brave is curious or not happy. Everyone who is not funny or wise is curious or not kind and vice versa. Everyone who is strong is both patient and not rich. If someone is both tall and patient then someone is not strong. Everyone who is patient or not humble is both not patient and tall. Everyone who is not quiet or happy is not wise or not curious. Everyone who is either happy or strong is either not happy or patient. If someone is patient or not creative then someone is generous or tall and vice versa. If someone is humble or not wise then someone is either not creative or quiet. If lucy is either not humble or not strong then mary is both not rich and calm and vice versa. Everyone who is both old and not creative is not happy and vice versa. If susan is not creative or not tall then paul is kind. Everyone who is either funny or creative is wise or rich and vice versa. If mary is not brave then paul is both strong and not tall. Everyone who is not creative is both kind and wise. Mary is either not humble or not tall. Paul is calm or funny. Mary is not wise or not creative. Someone is kind. | Susan is quiet. | entailment | (![X]:((kind(X)<~>creative(X))=>(curious(X)|~humble(X))))&
(![X]:((calm(X)&brave(X))=>(curious(X)|~happy(X))))&
(![X]:((~funny(X)|wise(X))<=>(curious(X)|~kind(X))))&
(![X]:(strong(X)=>(patient(X)&~rich(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~strong(X))))&
(![X]:((patient(X)|~humble(X))=>(~patient(X)&tall(X))))&
(![X]:((~quiet(X)|happy(X))=>(~wise(X)|~curious(X))))&
(![X]:((happy(X)<~>strong(X))=>(~happy(X)<~>patient(X))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((humble(X)|~wise(X))))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((~humble(lucy)<~>~strong(lucy)))<=>((~rich(mary)&calm(mary))))&
(![X]:((old(X)&~creative(X))<=>~happy(X)))&
(((~creative(susan)|~tall(susan)))=>(kind(paul)))&
(![X]:((funny(X)<~>creative(X))<=>(wise(X)|rich(X))))&
((~brave(mary))=>((strong(paul)&~tall(paul))))&
(![X]:(~creative(X)=>(kind(X)&wise(X))))&
((~humble(mary)<~>~tall(mary)))&
((calm(paul)|funny(paul)))&
((~wise(mary)|~creative(mary)))&
(?[X]:(kind(X))) | quiet(susan) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4251984479642754963421798
% SZS output start Proof for 4251984479642754963421798
3. ! [X0] : ((wise(X0) | ~funny(X0)) <=> (~kind(X0) | curious(X0))) [input p2]
4. ! [X0] : (strong(X0) => (~rich(X0) & patient(X0))) [input p3]
6. ! [X0] : ((~humble(X0) | patient(X0)) => (tall(X0) & ~patient(X0))) [input p5]
7. ! [X0] : ((happy(X0) | ~quiet(X0)) => (~curious(X0) | ~wise(X0))) [input p6]
8. ! [X0] : ((happy(X0) <~> strong(X0)) => (~happy(X0) <~> patient(X0))) [input p7]
12. ! [X0] : ((~creative(X0) & old(X0)) <=> ~happy(X0)) [input p11]
16. ! [X0] : (~creative(X0) => (wise(X0) & kind(X0))) [input p15]
21. ~quiet(susan) [input hypothesis]
29. ! [X0] : ((~rich(X0) & patient(X0)) | ~strong(X0)) [ennf transformation 4]
31. ! [X0] : ((tall(X0) & ~patient(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 6]
32. ! [X0] : ((~curious(X0) | ~wise(X0)) | (~happy(X0) & quiet(X0))) [ennf transformation 7]
33. ! [X0] : (~curious(X0) | ~wise(X0) | (~happy(X0) & quiet(X0))) [flattening 32]
34. ! [X0] : ((~happy(X0) <~> patient(X0)) | (happy(X0) <=> strong(X0))) [ennf transformation 8]
38. ! [X0] : ((wise(X0) & kind(X0)) | creative(X0)) [ennf transformation 16]
40. ! [X0] : (((wise(X0) | ~funny(X0)) | (kind(X0) & ~curious(X0))) & ((~kind(X0) | curious(X0)) | (~wise(X0) & funny(X0)))) [nnf transformation 3]
41. ! [X0] : ((wise(X0) | ~funny(X0) | (kind(X0) & ~curious(X0))) & (~kind(X0) | curious(X0) | (~wise(X0) & funny(X0)))) [flattening 40]
45. ! [X0] : (((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 34]
57. ! [X0] : (((~creative(X0) & old(X0)) | happy(X0)) & (~happy(X0) | (creative(X0) | ~old(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & old(X0)) | happy(X0)) & (~happy(X0) | creative(X0) | ~old(X0))) [flattening 57]
68. ~wise(X0) | curious(X0) | ~kind(X0) [cnf transformation 41]
71. ~strong(X0) | patient(X0) [cnf transformation 29]
74. ~patient(X0) | ~patient(X0) [cnf transformation 31]
78. ~wise(X0) | ~curious(X0) | quiet(X0) [cnf transformation 33]
80. patient(X0) | ~happy(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
100. ~creative(X0) | happy(X0) [cnf transformation 58]
111. creative(X0) | kind(X0) [cnf transformation 38]
112. wise(X0) | creative(X0) [cnf transformation 38]
118. ~quiet(susan) [cnf transformation 21]
119. patient(X0) | ~happy(X0) | strong(X0) [duplicate literal removal 80]
121. ~patient(X0) [duplicate literal removal 74]
130. ~happy(X0) | strong(X0) [subsumption resolution 119,121]
207. 19 <=> creative(susan) [avatar definition]
209. creative(susan) <- (19) [avatar component clause 207]
304. happy(susan) <- (19) [resolution 209,100]
317. curious(X0) | ~kind(X0) | creative(X0) [resolution 68,112]
318. curious(X0) | creative(X0) [subsumption resolution 317,111]
333. ~curious(X0) | quiet(X0) | creative(X0) [resolution 78,112]
334. quiet(X0) | creative(X0) [subsumption resolution 333,318]
341. strong(susan) <- (19) [resolution 304,130]
519. creative(susan) [resolution 334,118]
538. patient(susan) <- (19) [resolution 341,71]
539. $false <- (19) [subsumption resolution 538,121]
540. ~19 [avatar contradiction clause 539]
542. 19 [avatar split clause 519,207]
543. $false [avatar sat refutation 540,542]
% SZS output end Proof for 4251984479642754963421798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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