premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not strong is either strong or not kind and vice versa.
If someone is both kind and not rich then someone is either happy or patient and vice versa.
Everyone who is quiet is funny.
If someone is either not kind or rich then alice is both funny and not happy.
Everyone who is kind is not brave or brave.
If someone is humble then someone is both strong and not old and vice versa.
Everyone who is curious or kind is not strong.
If susan is either funny or not strong then someone is not generous and vice versa.
Everyone who is both funny and quiet is both not happy and not creative.
If someone is humble or not brave then someone is either wise or not funny.
If someone is both not strong and not funny then lucy is both brave and happy and vice versa.
Everyone who is rich or not wise is happy and vice versa.
If susan is patient or generous then susan is either not quiet or not tall and vice versa.
Everyone who is either happy or not tall is either patient or not kind.
Everyone who is both not tall and rich is either old or not calm and vice versa.
Everyone who is both not humble and tall is not happy and vice versa.
Someone is either not happy or kind.
Mary is both happy and wise.
Mary is both not tall and brave.
Lucy is both old and strong.
Susan is not tall or not rich.
Alice is both not brave and not generous.
John is not calm or kind.
Lucy is either not quiet or rich. | Alice is humble. | contradiction | (![X]:(~strong(X)<=>(strong(X)<~>~kind(X))))&
((?[X]:((kind(X)&~rich(X))))<=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:(quiet(X)=>funny(X)))&
((?[X]:((~kind(X)<~>rich(X))))=>((funny(alice)&~happy(alice))))&
(![X]:(kind(X)=>(~brave(X)|brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((curious(X)|kind(X))=>~strong(X)))&
(((funny(susan)<~>~strong(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((funny(X)&quiet(X))=>(~happy(X)&~creative(X))))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:((wise(X)<~>~funny(X)))))&
((?[X]:((~strong(X)&~funny(X))))<=>((brave(lucy)&happy(lucy))))&
(![X]:((rich(X)|~wise(X))<=>happy(X)))&
(((patient(susan)|generous(susan)))<=>((~quiet(susan)<~>~tall(susan))))&
(![X]:((happy(X)<~>~tall(X))=>(patient(X)<~>~kind(X))))&
(![X]:((~tall(X)&rich(X))<=>(old(X)<~>~calm(X))))&
(![X]:((~humble(X)&tall(X))<=>~happy(X)))&
(?[X]:((~happy(X)<~>kind(X))))&
((happy(mary)&wise(mary)))&
((~tall(mary)&brave(mary)))&
((old(lucy)&strong(lucy)))&
((~tall(susan)|~rich(susan)))&
((~brave(alice)&~generous(alice)))&
((~calm(john)|kind(john)))&
((~quiet(lucy)<~>rich(lucy))) | humble(alice) | [
"p0",
"p3",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2371677153745247316725035
% SZS output start Proof for 2371677153745247316725035
1. ! [X0] : (~strong(X0) <=> (strong(X0) <~> ~kind(X0))) [input p0]
4. ? [X0] : (~kind(X0) <~> rich(X0)) => (~happy(alice) & funny(alice)) [input p3]
12. ! [X0] : ((~wise(X0) | rich(X0)) <=> happy(X0)) [input p11]
16. ! [X0] : ((tall(X0) & ~humble(X0)) <=> ~happy(X0)) [input p15]
17. ? [X0] : (~happy(X0) <~> kind(X0)) [input p16]
25. humble(alice) [input hypothesis]
32. (~happy(alice) & funny(alice)) | ! [X0] : (~kind(X0) <=> rich(X0)) [ennf transformation 4]
40. ! [X0] : ((~strong(X0) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | strong(X0))) [nnf transformation 1]
46. (~happy(alice) & funny(alice)) | ! [X0] : ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))) [nnf transformation 32]
65. ! [X0] : (((~wise(X0) | rich(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) & ~rich(X0)))) [nnf transformation 12]
66. ! [X0] : ((~wise(X0) | rich(X0) | ~happy(X0)) & (happy(X0) | (wise(X0) & ~rich(X0)))) [flattening 65]
72. ! [X0] : (((tall(X0) & ~humble(X0)) | happy(X0)) & (~happy(X0) | (~tall(X0) | humble(X0)))) [nnf transformation 16]
73. ! [X0] : (((tall(X0) & ~humble(X0)) | happy(X0)) & (~happy(X0) | ~tall(X0) | humble(X0))) [flattening 72]
74. ? [X0] : ((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) [nnf transformation 17]
75. ? [X0] : ((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) => ((~kind(sK7) | happy(sK7)) & (kind(sK7) | ~happy(sK7))) [choice axiom]
76. (~kind(sK7) | happy(sK7)) & (kind(sK7) | ~happy(sK7)) [skolemisation 74,75]
78. ~kind(X0) | strong(X0) | strong(X0) [cnf transformation 40]
80. ~strong(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 40]
91. ~happy(alice) | rich(X0) | kind(X0) [cnf transformation 46]
111. ~rich(X0) | happy(X0) [cnf transformation 66]
131. ~humble(X0) | happy(X0) [cnf transformation 73]
133. kind(sK7) | ~happy(sK7) [cnf transformation 76]
147. humble(alice) [cnf transformation 25]
148. ~kind(X0) | strong(X0) [duplicate literal removal 78]
149. ~strong(X0) | ~kind(X0) [duplicate literal removal 80]
150. ~kind(X0) [subsumption resolution 148,149]
167. ~happy(alice) | rich(X0) [subsumption resolution 91,150]
169. 4 <=> ! [X0] : rich(X0) [avatar definition]
170. rich(X0) <- (4) [avatar component clause 169]
172. 5 <=> happy(alice) [avatar definition]
174. ~happy(alice) <- (~5) [avatar component clause 172]
175. 4 | ~5 [avatar split clause 167,172,169]
285. ~happy(sK7) [subsumption resolution 133,150]
307. happy(X0) <- (4) [resolution 111,170]
309. $false <- (4) [resolution 307,285]
310. ~4 [avatar contradiction clause 309]
312. happy(alice) [resolution 131,147]
313. $false <- (~5) [subsumption resolution 312,174]
314. 5 [avatar contradiction clause 313]
315. $false [avatar sat refutation 175,310,314]
% SZS output end Proof for 2371677153745247316725035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not tall or not kind then paul is creative or brave and vice versa.
Everyone who is not curious or funny is both brave and not strong and vice versa.
Everyone who is humble or not strong is funny and vice versa.
Everyone who is generous is not old or quiet and vice versa.
If someone is not humble then john is either not funny or funny.
Everyone who is wise is not happy.
Everyone who is both wise and funny is both patient and not generous and vice versa.
If someone is curious or not calm then mary is strong.
If susan is both not patient and not quiet then mary is either not strong or not curious and vice versa.
Everyone who is both humble and not strong is rich or not funny and vice versa.
Everyone who is either not generous or not happy is curious and vice versa.
Everyone who is not generous or not kind is not creative and vice versa.
If someone is either not quiet or creative then susan is not happy or not creative.
Everyone who is both calm and not tall is not humble and vice versa.
If someone is either not wise or not rich then fred is humble or funny.
If alice is either not wise or not creative then someone is either quiet or brave and vice versa.
Someone is not strong.
Alice is not kind or quiet.
Someone is not humble or patient.
Mary is creative.
Susan is either rich or not funny.
Mary is either strong or generous. | Fred is not curious. | entailment | (((~tall(fred)<~>~kind(fred)))<=>((creative(paul)|brave(paul))))&
(![X]:((~curious(X)|funny(X))<=>(brave(X)&~strong(X))))&
(![X]:((humble(X)|~strong(X))<=>funny(X)))&
(![X]:(generous(X)<=>(~old(X)|quiet(X))))&
((?[X]:(~humble(X)))=>((~funny(john)<~>funny(john))))&
(![X]:(wise(X)=>~happy(X)))&
(![X]:((wise(X)&funny(X))<=>(patient(X)&~generous(X))))&
((?[X]:((curious(X)|~calm(X))))=>(strong(mary)))&
(((~patient(susan)&~quiet(susan)))<=>((~strong(mary)<~>~curious(mary))))&
(![X]:((humble(X)&~strong(X))<=>(rich(X)|~funny(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>curious(X)))&
(![X]:((~generous(X)|~kind(X))<=>~creative(X)))&
((?[X]:((~quiet(X)<~>creative(X))))=>((~happy(susan)|~creative(susan))))&
(![X]:((calm(X)&~tall(X))<=>~humble(X)))&
((?[X]:((~wise(X)<~>~rich(X))))=>((humble(fred)|funny(fred))))&
(((~wise(alice)<~>~creative(alice)))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(?[X]:(~strong(X)))&
((~kind(alice)|quiet(alice)))&
(?[X]:((~humble(X)|patient(X))))&
(creative(mary))&
((rich(susan)<~>~funny(susan)))&
((strong(mary)<~>generous(mary))) | ~curious(fred) | [
"p1",
"p2",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5610330450278748648379852
% SZS output start Proof for 5610330450278748648379852
2. ! [X0] : ((funny(X0) | ~curious(X0)) <=> (~strong(X0) & brave(X0))) [input p1]
3. ! [X0] : ((~strong(X0) | humble(X0)) <=> funny(X0)) [input p2]
8. ? [X0] : (~calm(X0) | curious(X0)) => strong(mary) [input p7]
10. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~funny(X0) | rich(X0))) [input p9]
23. curious(fred) [input hypothesis]
26. strong(mary) | ! [X0] : (calm(X0) & ~curious(X0)) [ennf transformation 8]
33. ! [X0] : (((funny(X0) | ~curious(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (~funny(X0) & curious(X0)))) [nnf transformation 2]
34. ! [X0] : ((funny(X0) | ~curious(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (~funny(X0) & curious(X0)))) [flattening 33]
35. ! [X0] : (((~strong(X0) | humble(X0)) | ~funny(X0)) & (funny(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 3]
36. ! [X0] : ((~strong(X0) | humble(X0) | ~funny(X0)) & (funny(X0) | (strong(X0) & ~humble(X0)))) [flattening 35]
44. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) & ~rich(X0))) & ((~funny(X0) | rich(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 10]
45. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) & ~rich(X0))) & (~funny(X0) | rich(X0) | strong(X0) | ~humble(X0))) [flattening 44]
72. ~strong(X0) | ~funny(X0) [cnf transformation 34]
75. funny(X0) | strong(X0) [cnf transformation 36]
87. strong(mary) | ~curious(X0) [cnf transformation 26]
99. ~strong(X0) | funny(X0) [cnf transformation 45]
130. curious(fred) [cnf transformation 23]
157. 6 <=> strong(mary) [avatar definition]
159. strong(mary) <- (6) [avatar component clause 157]
162. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
163. ~curious(X0) <- (7) [avatar component clause 162]
164. 7 | 6 [avatar split clause 87,157,162]
183. funny(X0) [subsumption resolution 99,75]
259. ~funny(mary) <- (6) [resolution 72,159]
260. $false <- (6) [subsumption resolution 259,183]
261. ~6 [avatar contradiction clause 260]
262. $false <- (7) [resolution 163,130]
264. ~7 [avatar contradiction clause 262]
265. $false [avatar sat refutation 164,261,264]
% SZS output end Proof for 5610330450278748648379852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or generous then someone is funny and vice versa.
Everyone who is not quiet or not generous is calm or not patient and vice versa.
If someone is either not old or old then someone is not calm and vice versa.
Everyone who is not funny or brave is humble or not curious.
If someone is not kind then someone is calm or old and vice versa.
Everyone who is not rich is generous or patient and vice versa.
Everyone who is not patient is not happy.
Everyone who is not generous is both rich and humble.
Everyone who is both not kind and old is rich or brave and vice versa.
Everyone who is not old is wise and vice versa.
If someone is generous or not strong then alice is both humble and not funny and vice versa.
Everyone who is curious is either not happy or happy and vice versa.
If paul is not brave then lucy is both brave and not generous.
Everyone who is both not humble and patient is both funny and brave and vice versa.
Everyone who is both not happy and old is old or not funny and vice versa.
If fred is humble or creative then someone is either not patient or not calm and vice versa.
Someone is not kind.
Lucy is old.
Alice is rich or patient.
Alice is both not funny and generous.
Lucy is either patient or not tall.
Susan is old or not generous.
Someone is not strong or not calm.
Someone is old or not strong. | Alice is curious. | entailment | ((?[X]:((~funny(X)|generous(X))))<=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(calm(X)|~patient(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(humble(X)|~curious(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((calm(X)|old(X)))))&
(![X]:(~rich(X)<=>(generous(X)|patient(X))))&
(![X]:(~patient(X)=>~happy(X)))&
(![X]:(~generous(X)=>(rich(X)&humble(X))))&
(![X]:((~kind(X)&old(X))<=>(rich(X)|brave(X))))&
(![X]:(~old(X)<=>wise(X)))&
((?[X]:((generous(X)|~strong(X))))<=>((humble(alice)&~funny(alice))))&
(![X]:(curious(X)<=>(~happy(X)<~>happy(X))))&
((~brave(paul))=>((brave(lucy)&~generous(lucy))))&
(![X]:((~humble(X)&patient(X))<=>(funny(X)&brave(X))))&
(![X]:((~happy(X)&old(X))<=>(old(X)|~funny(X))))&
(((humble(fred)|creative(fred)))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
(?[X]:(~kind(X)))&
(old(lucy))&
((rich(alice)|patient(alice)))&
((~funny(alice)&generous(alice)))&
((patient(lucy)<~>~tall(lucy)))&
((old(susan)|~generous(susan)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:((old(X)|~strong(X)))) | curious(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5533373333333173046358115
% SZS output start Proof for 5533373333333173046358115
12. ! [X0] : (curious(X0) <=> (~happy(X0) <~> happy(X0))) [input p11]
25. ~curious(alice) [input hypothesis]
29. ! [X0] : ((~happy(X0) <~> happy(X0)) => curious(X0)) [unused predicate definition removal 12]
34. ! [X0] : (curious(X0) | (~happy(X0) <=> happy(X0))) [ennf transformation 29]
63. ! [X0] : (curious(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 34]
114. curious(X0) | happy(X0) | happy(X0) [cnf transformation 63]
115. curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 63]
143. ~curious(alice) [cnf transformation 25]
144. curious(X0) | happy(X0) [duplicate literal removal 114]
145. curious(X0) | ~happy(X0) [duplicate literal removal 115]
229. curious(X0) [subsumption resolution 144,145]
319. $false [subsumption resolution 143,229]
% SZS output end Proof for 5533373333333173046358115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is brave and vice versa.
Everyone who is old is not funny and vice versa.
If fred is either curious or strong then someone is both brave and not kind.
Everyone who is not calm or calm is either not rich or not humble.
If someone is not calm then paul is not funny or quiet.
Everyone who is either tall or not rich is either not wise or not creative.
Everyone who is both curious and calm is either not funny or humble.
If fred is not strong then someone is either not funny or tall.
Everyone who is not strong is strong or quiet and vice versa.
Everyone who is creative is not wise or not old.
Everyone who is creative is both quiet and kind.
Everyone who is either wise or not kind is not funny and vice versa.
If alice is happy then john is quiet and vice versa.
If susan is either funny or curious then someone is either not quiet or not humble and vice versa.
Everyone who is not quiet or not curious is both wise and calm.
If someone is both not wise and rich then someone is both brave and not generous.
Someone is not quiet or patient.
Susan is either kind or not rich.
Someone is not wise.
Someone is not wise or rich.
Paul is creative.
Mary is either not brave or not old.
Mary is not wise.
Fred is not tall or not curious. | John is strong. | contradiction | (![X]:(creative(X)<=>brave(X)))&
(![X]:(old(X)<=>~funny(X)))&
(((curious(fred)<~>strong(fred)))=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~calm(X)|calm(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:(~calm(X)))=>((~funny(paul)|quiet(paul))))&
(![X]:((tall(X)<~>~rich(X))=>(~wise(X)<~>~creative(X))))&
(![X]:((curious(X)&calm(X))=>(~funny(X)<~>humble(X))))&
((~strong(fred))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:(~strong(X)<=>(strong(X)|quiet(X))))&
(![X]:(creative(X)=>(~wise(X)|~old(X))))&
(![X]:(creative(X)=>(quiet(X)&kind(X))))&
(![X]:((wise(X)<~>~kind(X))<=>~funny(X)))&
((happy(alice))<=>(quiet(john)))&
(((funny(susan)<~>curious(susan)))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:((~quiet(X)|~curious(X))=>(wise(X)&calm(X))))&
((?[X]:((~wise(X)&rich(X))))=>(?[X]:((brave(X)&~generous(X)))))&
(?[X]:((~quiet(X)|patient(X))))&
((kind(susan)<~>~rich(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)|rich(X))))&
(creative(paul))&
((~brave(mary)<~>~old(mary)))&
(~wise(mary))&
((~tall(fred)|~curious(fred))) | strong(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6369857777044716249807864
% SZS output start Proof for 6369857777044716249807864
9. ! [X0] : (~strong(X0) <=> (quiet(X0) | strong(X0))) [input p8]
25. strong(john) [input hypothesis]
53. ! [X0] : ((~strong(X0) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | strong(X0))) [nnf transformation 9]
54. ! [X0] : ((~strong(X0) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | strong(X0))) [flattening 53]
92. ~strong(X0) | ~strong(X0) [cnf transformation 54]
125. strong(john) [cnf transformation 25]
127. ~strong(X0) [duplicate literal removal 92]
239. $false [subsumption resolution 125,127]
% SZS output end Proof for 6369857777044716249807864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not curious and not wise.
Everyone who is brave or creative is either not creative or not humble.
If john is both not rich and not happy then someone is either curious or happy.
Everyone who is tall is both not creative and not quiet.
Everyone who is patient is humble or not wise.
Everyone who is not patient is curious or not calm.
If someone is tall then john is either not wise or not kind and vice versa.
If mary is not generous then susan is both rich and not happy and vice versa.
If someone is both not wise and kind then lucy is either curious or not humble.
Everyone who is either curious or old is both patient and not strong.
Everyone who is wise is either not patient or kind and vice versa.
If someone is both not brave and not old then someone is both not strong and not brave.
Everyone who is not rich or creative is either humble or calm and vice versa.
Everyone who is either strong or generous is calm and vice versa.
If someone is both tall and not tall then fred is not brave or generous and vice versa.
Everyone who is either not kind or not patient is not calm or tall and vice versa.
Alice is brave.
Someone is either not brave or generous.
Fred is not rich or not brave.
Paul is not generous.
Someone is both old and happy.
John is not wise. | John is creative. | contradiction | (![X]:(creative(X)=>(~curious(X)&~wise(X))))&
(![X]:((brave(X)|creative(X))=>(~creative(X)<~>~humble(X))))&
(((~rich(john)&~happy(john)))=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:(tall(X)=>(~creative(X)&~quiet(X))))&
(![X]:(patient(X)=>(humble(X)|~wise(X))))&
(![X]:(~patient(X)=>(curious(X)|~calm(X))))&
((?[X]:(tall(X)))<=>((~wise(john)<~>~kind(john))))&
((~generous(mary))<=>((rich(susan)&~happy(susan))))&
((?[X]:((~wise(X)&kind(X))))=>((curious(lucy)<~>~humble(lucy))))&
(![X]:((curious(X)<~>old(X))=>(patient(X)&~strong(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>kind(X))))&
((?[X]:((~brave(X)&~old(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~rich(X)|creative(X))<=>(humble(X)<~>calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>calm(X)))&
((?[X]:((tall(X)&~tall(X))))<=>((~brave(fred)|generous(fred))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~calm(X)|tall(X))))&
(brave(alice))&
(?[X]:((~brave(X)<~>generous(X))))&
((~rich(fred)|~brave(fred)))&
(~generous(paul))&
(?[X]:((old(X)&happy(X))))&
(~wise(john)) | creative(john) | [
"p1",
"p3",
"p6",
"p10",
"p12",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7675432164887606106999419
% SZS output start Proof for 7675432164887606106999419
2. ! [X0] : ((creative(X0) | brave(X0)) => (~creative(X0) <~> ~humble(X0))) [input p1]
4. ! [X0] : (tall(X0) => (~quiet(X0) & ~creative(X0))) [input p3]
7. ? [X0] : tall(X0) <=> (~wise(john) <~> ~kind(john)) [input p6]
11. ! [X0] : (wise(X0) <=> (~patient(X0) <~> kind(X0))) [input p10]
13. ! [X0] : ((creative(X0) | ~rich(X0)) <=> (humble(X0) <~> calm(X0))) [input p12]
16. ! [X0] : ((~kind(X0) <~> ~patient(X0)) <=> (tall(X0) | ~calm(X0))) [input p15]
22. ~wise(john) [input p21]
23. creative(john) [input hypothesis]
25. ! [X0] : (tall(X0) => ~creative(X0)) [pure predicate removal 4]
27. ! [X0] : ((~creative(X0) <~> ~humble(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 2]
30. ! [X0] : (~creative(X0) | ~tall(X0)) [ennf transformation 25]
38. ! [X0] : (((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | (~creative(X0) & ~brave(X0))) [nnf transformation 27]
42. (? [X0] : tall(X0) | ((~wise(john) | kind(john)) & (~kind(john) | wise(john)))) & (((kind(john) | wise(john)) & (~kind(john) | ~wise(john))) | ! [X0] : ~tall(X0)) [nnf transformation 7]
43. (? [X0] : tall(X0) | ((~wise(john) | kind(john)) & (~kind(john) | wise(john)))) & (((kind(john) | wise(john)) & (~kind(john) | ~wise(john))) | ! [X1] : ~tall(X1)) [rectify 42]
44. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
45. (tall(sK1) | ((~wise(john) | kind(john)) & (~kind(john) | wise(john)))) & (((kind(john) | wise(john)) & (~kind(john) | ~wise(john))) | ! [X1] : ~tall(X1)) [skolemisation 43,44]
50. ! [X0] : ((wise(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0)))) & (((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | ~wise(X0))) [nnf transformation 11]
54. ! [X0] : (((creative(X0) | ~rich(X0)) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | (~creative(X0) & rich(X0)))) [nnf transformation 13]
55. ! [X0] : ((creative(X0) | ~rich(X0) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | (~creative(X0) & rich(X0)))) [flattening 54]
62. ! [X0] : ((((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~tall(X0) & calm(X0))) & ((tall(X0) | ~calm(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))))) [nnf transformation 16]
63. ! [X0] : ((((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~tall(X0) & calm(X0))) & (tall(X0) | ~calm(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))))) [flattening 62]
72. ~humble(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 38]
77. ~tall(X0) | ~creative(X0) [cnf transformation 30]
81. kind(john) | wise(john) | ~tall(X1) [cnf transformation 45]
95. kind(X0) | wise(X0) | patient(X0) [cnf transformation 50]
96. ~kind(X0) | ~patient(X0) | wise(X0) [cnf transformation 50]
100. calm(X0) | humble(X0) | ~creative(X0) [cnf transformation 55]
114. ~calm(X0) | tall(X0) | ~patient(X0) | kind(X0) [cnf transformation 63]
115. ~kind(X0) | ~calm(X0) | tall(X0) | patient(X0) [cnf transformation 63]
127. ~wise(john) [cnf transformation 22]
128. creative(john) [cnf transformation 23]
129. ~humble(X0) | ~creative(X0) [duplicate literal removal 72]
149. 5 <=> kind(john) [avatar definition]
150. ~kind(john) <- (~5) [avatar component clause 149]
151. kind(john) <- (5) [avatar component clause 149]
153. 6 <=> wise(john) [avatar definition]
155. ~wise(john) <- (~6) [avatar component clause 153]
163. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
164. ~tall(X1) <- (8) [avatar component clause 163]
165. 8 | 6 | 5 [avatar split clause 81,149,153,163]
209. ~creative(X0) | calm(X0) [subsumption resolution 100,129]
241. ~6 [avatar split clause 127,153]
243. calm(john) [resolution 209,128]
268. 28 <=> patient(john) [avatar definition]
269. ~patient(john) <- (~28) [avatar component clause 268]
270. patient(john) <- (28) [avatar component clause 268]
304. ~patient(john) | wise(john) <- (5) [resolution 96,151]
307. wise(john) <- (5, 28) [subsumption resolution 304,270]
308. $false <- (5, ~6, 28) [subsumption resolution 307,155]
309. ~5 | 6 | ~28 [avatar contradiction clause 308]
310. wise(john) | patient(john) <- (~5) [resolution 150,95]
352. tall(john) | ~patient(john) | kind(john) [resolution 114,243]
354. ~patient(john) | kind(john) <- (8) [subsumption resolution 352,164]
359. ~patient(john) <- (~5, 8) [subsumption resolution 354,150]
360. ~28 | 5 | ~8 [avatar split clause 359,163,149,268]
361. patient(john) <- (~5, ~6) [subsumption resolution 310,155]
362. 28 | 5 | 6 [avatar split clause 361,153,149,268]
380. ~calm(john) | tall(john) | patient(john) <- (5) [resolution 115,151]
383. tall(john) | patient(john) <- (5) [subsumption resolution 380,243]
384. tall(john) <- (5, ~28) [subsumption resolution 383,269]
398. ~creative(john) <- (5, ~28) [resolution 384,77]
399. $false <- (5, ~28) [subsumption resolution 398,128]
400. ~5 | 28 [avatar contradiction clause 399]
401. $false [avatar sat refutation 165,241,309,360,362,400]
% SZS output end Proof for 7675432164887606106999419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both generous and not wise then someone is either creative or patient and vice versa.
If fred is both not generous and creative then lucy is both not calm and old and vice versa.
Everyone who is not curious or not brave is patient.
Everyone who is quiet or happy is not curious.
If lucy is both not brave and calm then mary is either not patient or not quiet.
If someone is either curious or not strong then someone is not funny or not brave and vice versa.
If susan is either not old or not calm then someone is not kind or curious.
Everyone who is both not quiet and not old is both generous and wise and vice versa.
Everyone who is either patient or tall is not rich or not curious and vice versa.
Everyone who is not tall is not quiet.
If fred is either not rich or tall then someone is not funny or generous.
If someone is not generous or not humble then paul is not creative.
Everyone who is either funny or not wise is not rich or not calm.
Everyone who is not quiet is not creative or not generous.
If susan is curious or strong then someone is old or tall and vice versa.
Everyone who is not old is both not calm and not wise.
Lucy is not old or strong.
Mary is not wise or not curious.
Someone is both not curious and funny.
Mary is both not strong and generous.
Someone is not patient or not curious.
Someone is not quiet or not humble.
Someone is either not old or not calm.
Someone is strong or brave. | Lucy is not strong. | contradiction | (((generous(paul)&~wise(paul)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(((~generous(fred)&creative(fred)))<=>((~calm(lucy)&old(lucy))))&
(![X]:((~curious(X)|~brave(X))=>patient(X)))&
(![X]:((quiet(X)|happy(X))=>~curious(X)))&
(((~brave(lucy)&calm(lucy)))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
(((~old(susan)<~>~calm(susan)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&~old(X))<=>(generous(X)&wise(X))))&
(![X]:((patient(X)<~>tall(X))<=>(~rich(X)|~curious(X))))&
(![X]:(~tall(X)=>~quiet(X)))&
(((~rich(fred)<~>tall(fred)))=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~generous(X)|~humble(X))))=>(~creative(paul)))&
(![X]:((funny(X)<~>~wise(X))=>(~rich(X)|~calm(X))))&
(![X]:(~quiet(X)=>(~creative(X)|~generous(X))))&
(((curious(susan)|strong(susan)))<=>(?[X]:((old(X)|tall(X)))))&
(![X]:(~old(X)=>(~calm(X)&~wise(X))))&
((~old(lucy)|strong(lucy)))&
((~wise(mary)|~curious(mary)))&
(?[X]:((~curious(X)&funny(X))))&
((~strong(mary)&generous(mary)))&
(?[X]:((~patient(X)|~curious(X))))&
(?[X]:((~quiet(X)|~humble(X))))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((strong(X)|brave(X)))) | ~strong(lucy) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3275065800482293652888331
% SZS output start Proof for 3275065800482293652888331
3. ! [X0] : ((~brave(X0) | ~curious(X0)) => patient(X0)) [input p2]
4. ! [X0] : ((happy(X0) | quiet(X0)) => ~curious(X0)) [input p3]
8. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (wise(X0) & generous(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~curious(X0) | ~rich(X0))) [input p8]
10. ! [X0] : (~tall(X0) => ~quiet(X0)) [input p9]
16. ! [X0] : (~old(X0) => (~wise(X0) & ~calm(X0))) [input p15]
17. strong(lucy) | ~old(lucy) [input p16]
25. ~strong(lucy) [input hypothesis]
28. ! [X0] : (quiet(X0) => ~curious(X0)) [pure predicate removal 4]
29. ! [X0] : (patient(X0) | (brave(X0) & curious(X0))) [ennf transformation 3]
30. ! [X0] : (~curious(X0) | ~quiet(X0)) [ennf transformation 28]
33. ! [X0] : (~quiet(X0) | tall(X0)) [ennf transformation 10]
40. ! [X0] : ((~wise(X0) & ~calm(X0)) | old(X0)) [ennf transformation 16]
54. ! [X0] : (((~old(X0) & ~quiet(X0)) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | (old(X0) | quiet(X0)))) [nnf transformation 8]
55. ! [X0] : (((~old(X0) & ~quiet(X0)) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | old(X0) | quiet(X0))) [flattening 54]
56. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (curious(X0) & rich(X0))) & ((~curious(X0) | ~rich(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
57. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (curious(X0) & rich(X0))) & (~curious(X0) | ~rich(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 56]
88. curious(X0) | patient(X0) [cnf transformation 29]
90. ~quiet(X0) | ~curious(X0) [cnf transformation 30]
100. quiet(X0) | old(X0) | wise(X0) [cnf transformation 55]
108. ~tall(X0) | ~patient(X0) | curious(X0) [cnf transformation 57]
109. ~quiet(X0) | tall(X0) [cnf transformation 33]
122. ~wise(X0) | old(X0) [cnf transformation 40]
123. strong(lucy) | ~old(lucy) [cnf transformation 17]
134. ~strong(lucy) [cnf transformation 25]
168. 8 <=> old(lucy) [avatar definition]
170. ~old(lucy) <- (~8) [avatar component clause 168]
231. ~tall(X0) | curious(X0) [subsumption resolution 108,88]
290. 35 <=> strong(lucy) [avatar definition]
293. ~8 | 35 [avatar split clause 123,290,168]
332. ~35 [avatar split clause 134,290]
343. old(X0) | wise(X0) | tall(X0) [resolution 100,109]
344. old(X1) | wise(X1) | ~curious(X1) [resolution 100,90]
349. ~curious(X1) | old(X1) [subsumption resolution 344,122]
350. tall(X0) | old(X0) [subsumption resolution 343,122]
375. old(X1) | curious(X1) [resolution 350,231]
377. old(X1) [subsumption resolution 375,349]
390. $false <- (~8) [resolution 377,170]
392. 8 [avatar contradiction clause 390]
393. $false [avatar sat refutation 293,332,392]
% SZS output end Proof for 3275065800482293652888331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or humble is both not happy and wise.
Everyone who is happy or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Everyone who is kind is either kind or not rich.
Everyone who is either brave or not old is both not wise and not calm.
If paul is patient or rich then someone is both not quiet and kind.
Everyone who is either humble or funny is wise and vice versa.
If someone is either not patient or creative then someone is rich or not creative.
John is both not wise and not rich.
Someone is both not brave and not rich.
Paul is not strong or patient.
Someone is creative or patient.
Alice is either not happy or creative.
Lucy is both curious and not funny.
Susan is old.
Alice is not wise. | Fred is funny. | contradiction | (![X]:((rich(X)|humble(X))=>(~happy(X)&wise(X))))&
(![X]:((happy(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
(![X]:(kind(X)=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~old(X))=>(~wise(X)&~calm(X))))&
(((patient(paul)|rich(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((~wise(john)&~rich(john)))&
(?[X]:((~brave(X)&~rich(X))))&
((~strong(paul)|patient(paul)))&
(?[X]:((creative(X)|patient(X))))&
((~happy(alice)<~>creative(alice)))&
((curious(lucy)&~funny(lucy)))&
(old(susan))&
(~wise(alice)) | funny(fred) | [
"p0",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8764384028703999012325261
% SZS output start Proof for 8764384028703999012325261
1. ! [X0] : ((humble(X0) | rich(X0)) => (wise(X0) & ~happy(X0))) [input p0]
5. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~strong(X0) & ~wise(X0))) [input p4]
15. ! [X0] : ((humble(X0) <~> funny(X0)) <=> wise(X0)) [input p14]
25. funny(fred) [input hypothesis]
32. ! [X0] : ((wise(X0) & ~happy(X0)) | (~humble(X0) & ~rich(X0))) [ennf transformation 1]
46. ! [X0] : (((brave(X0) | ~humble(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [flattening 46]
64. ! [X0] : ((((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | ~wise(X0)) & (wise(X0) | ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0))))) [nnf transformation 15]
77. ~humble(X0) | wise(X0) [cnf transformation 32]
88. ~wise(X0) | humble(X0) [cnf transformation 47]
115. wise(X0) | humble(X0) | ~funny(X0) [cnf transformation 64]
117. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 64]
132. funny(fred) [cnf transformation 25]
231. ~funny(X0) | ~wise(X0) [subsumption resolution 117,88]
232. ~funny(X0) | humble(X0) [subsumption resolution 115,231]
291. ~wise(fred) [resolution 231,132]
292. humble(fred) [resolution 232,132]
293. wise(fred) [resolution 292,77]
294. $false [subsumption resolution 293,291]
% SZS output end Proof for 8764384028703999012325261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or wise is both not creative and not quiet.
If someone is both not old and quiet then someone is either funny or not happy and vice versa.
Everyone who is either brave or not funny is either not patient or quiet and vice versa.
Everyone who is both happy and kind is not old or not humble and vice versa.
Everyone who is not kind or not creative is not strong or funny.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is both wise and humble is not strong or wise.
If john is both not creative and not rich then lucy is both not brave and happy.
Someone is either curious or not wise.
Someone is both strong and not generous.
Someone is not kind or not strong.
Someone is both not funny and wise.
Someone is tall or not tall.
Paul is either wise or not old.
Susan is both quiet and not creative. | Paul is not funny. | neutral | (![X]:((~brave(X)<~>wise(X))=>(~creative(X)&~quiet(X))))&
((?[X]:((~old(X)&quiet(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:((happy(X)&kind(X))<=>(~old(X)|~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~strong(X)|funny(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(((~creative(john)&~rich(john)))=>((~brave(lucy)&happy(lucy))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((tall(X)|~tall(X))))&
((wise(paul)<~>~old(paul)))&
((quiet(susan)&~creative(susan))) | ~funny(paul) | [] | null | 0 |
Everyone who is creative or strong is not brave.
If someone is both not quiet and generous then someone is tall or not wise and vice versa.
If someone is either tall or not generous then someone is both calm and not tall and vice versa.
If someone is either not old or creative then someone is either calm or not curious and vice versa.
Everyone who is curious or not curious is not calm or kind.
If mary is not patient or not quiet then john is both humble and brave.
If someone is curious then paul is both not funny and funny.
If susan is not brave then susan is both patient and strong and vice versa.
If someone is curious or kind then someone is either rich or not strong.
Everyone who is creative is not strong and vice versa.
Everyone who is both calm and quiet is both not quiet and strong and vice versa.
Everyone who is both not creative and rich is not calm and vice versa.
Everyone who is either patient or not kind is not tall and vice versa.
Everyone who is both kind and not humble is rich or funny.
If john is either not generous or not tall then fred is either not brave or tall.
Everyone who is both not funny and not generous is both not wise and funny and vice versa.
John is either not patient or not curious.
Someone is either funny or quiet.
Paul is quiet or patient.
Someone is old or not kind.
Someone is both not creative and not patient.
Mary is either happy or wise.
John is quiet. | Susan is not strong. | contradiction | (![X]:((creative(X)|strong(X))=>~brave(X)))&
((?[X]:((~quiet(X)&generous(X))))<=>(?[X]:((tall(X)|~wise(X)))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((calm(X)&~tall(X)))))&
((?[X]:((~old(X)<~>creative(X))))<=>(?[X]:((calm(X)<~>~curious(X)))))&
(![X]:((curious(X)|~curious(X))=>(~calm(X)|kind(X))))&
(((~patient(mary)|~quiet(mary)))=>((humble(john)&brave(john))))&
((?[X]:(curious(X)))=>((~funny(paul)&funny(paul))))&
((~brave(susan))<=>((patient(susan)&strong(susan))))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
(![X]:((calm(X)&quiet(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~creative(X)&rich(X))<=>~calm(X)))&
(![X]:((patient(X)<~>~kind(X))<=>~tall(X)))&
(![X]:((kind(X)&~humble(X))=>(rich(X)|funny(X))))&
(((~generous(john)<~>~tall(john)))=>((~brave(fred)<~>tall(fred))))&
(![X]:((~funny(X)&~generous(X))<=>(~wise(X)&funny(X))))&
((~patient(john)<~>~curious(john)))&
(?[X]:((funny(X)<~>quiet(X))))&
((quiet(paul)|patient(paul)))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:((~creative(X)&~patient(X))))&
((happy(mary)<~>wise(mary)))&
(quiet(john)) | ~strong(susan) | [
"p0",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8344227554329188850934
% SZS output start Proof for 8344227554329188850934
1. ! [X0] : ((strong(X0) | creative(X0)) => ~brave(X0)) [input p0]
8. ~brave(susan) <=> (strong(susan) & patient(susan)) [input p7]
10. ! [X0] : (creative(X0) <=> ~strong(X0)) [input p9]
24. ~strong(susan) [input hypothesis]
31. ! [X0] : (~brave(X0) | (~strong(X0) & ~creative(X0))) [ennf transformation 1]
53. (~brave(susan) | (~strong(susan) | ~patient(susan))) & ((strong(susan) & patient(susan)) | brave(susan)) [nnf transformation 8]
54. (~brave(susan) | ~strong(susan) | ~patient(susan)) & ((strong(susan) & patient(susan)) | brave(susan)) [flattening 53]
59. ! [X0] : ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))) [nnf transformation 10]
77. ~brave(X0) | ~creative(X0) [cnf transformation 31]
105. strong(susan) | brave(susan) [cnf transformation 54]
112. strong(X0) | creative(X0) [cnf transformation 59]
143. ~strong(susan) [cnf transformation 24]
270. 28 <=> brave(susan) [avatar definition]
272. brave(susan) <- (28) [avatar component clause 270]
274. 29 <=> strong(susan) [avatar definition]
275. ~strong(susan) <- (~29) [avatar component clause 274]
277. 28 | 29 [avatar split clause 105,274,270]
366. ~29 [avatar split clause 143,274]
368. ~creative(susan) <- (28) [resolution 77,272]
373. creative(susan) <- (~29) [resolution 112,275]
377. $false <- (28, ~29) [subsumption resolution 373,368]
378. ~28 | 29 [avatar contradiction clause 377]
379. $false [avatar sat refutation 277,366,378]
% SZS output end Proof for 8344227554329188850934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not calm is not old. Everyone who is both old and rich is both not curious and rich and vice versa. If john is both not patient and strong then someone is not tall. If someone is not quiet then someone is not calm or not old and vice versa. Everyone who is not generous or not calm is either not humble or patient. If mary is happy or not calm then lucy is not kind or not happy. Everyone who is wise or not generous is both generous and not tall and vice versa. Everyone who is not patient is curious. Everyone who is not brave is not curious or not old and vice versa. Everyone who is happy or wise is not calm or kind and vice versa. If someone is not calm then someone is either calm or rich. Everyone who is either patient or not creative is not old and vice versa. Everyone who is either creative or happy is either brave or not kind and vice versa. If someone is both brave and creative then someone is both patient and not old and vice versa. Everyone who is both rich and not happy is rich. Everyone who is funny or not generous is kind and vice versa. Someone is humble. Fred is not kind. Someone is generous or curious. Someone is both strong and not creative. Someone is both funny and patient. Someone is quiet. | Lucy is not funny. | neutral | (![X]:((curious(X)&~calm(X))=>~old(X)))&
(![X]:((old(X)&rich(X))<=>(~curious(X)&rich(X))))&
(((~patient(john)&strong(john)))=>(?[X]:(~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|~old(X)))))&
(![X]:((~generous(X)|~calm(X))=>(~humble(X)<~>patient(X))))&
(((happy(mary)|~calm(mary)))=>((~kind(lucy)|~happy(lucy))))&
(![X]:((wise(X)|~generous(X))<=>(generous(X)&~tall(X))))&
(![X]:(~patient(X)=>curious(X)))&
(![X]:(~brave(X)<=>(~curious(X)|~old(X))))&
(![X]:((happy(X)|wise(X))<=>(~calm(X)|kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((patient(X)<~>~creative(X))<=>~old(X)))&
(![X]:((creative(X)<~>happy(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:((brave(X)&creative(X))))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~happy(X))=>rich(X)))&
(![X]:((funny(X)|~generous(X))<=>kind(X)))&
(?[X]:(humble(X)))&
(~kind(fred))&
(?[X]:((generous(X)|curious(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:(quiet(X))) | ~funny(lucy) | [] | null | 0 |
Everyone who is not calm or generous is calm or generous and vice versa.
If someone is not patient or patient then paul is brave or old.
Everyone who is either not strong or not old is not calm and vice versa.
Everyone who is both not calm and not patient is patient.
If someone is both generous and not funny then someone is generous and vice versa.
If mary is either strong or not creative then someone is either not calm or generous.
If alice is not generous or not tall then someone is both not curious and calm and vice versa.
If someone is either patient or not strong then someone is either strong or not creative.
Everyone who is old or not quiet is not old and vice versa.
Everyone who is both not strong and calm is humble or old.
Everyone who is curious or generous is tall or not old and vice versa.
Everyone who is both quiet and not rich is both rich and patient and vice versa.
Everyone who is creative is wise and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is either not generous or calm then susan is both not funny and not old.
If mary is calm then mary is humble and vice versa.
Someone is both not curious and not strong.
Someone is either humble or not rich.
Someone is either not old or curious.
Lucy is strong or not tall.
Susan is either quiet or calm.
Someone is not patient or not brave.
Alice is either not humble or not rich. | Alice is tall. | contradiction | (![X]:((~calm(X)|generous(X))<=>(calm(X)|generous(X))))&
((?[X]:((~patient(X)|patient(X))))=>((brave(paul)|old(paul))))&
(![X]:((~strong(X)<~>~old(X))<=>~calm(X)))&
(![X]:((~calm(X)&~patient(X))=>patient(X)))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(generous(X))))&
(((strong(mary)<~>~creative(mary)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(((~generous(alice)|~tall(alice)))<=>(?[X]:((~curious(X)&calm(X)))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((old(X)|~quiet(X))<=>~old(X)))&
(![X]:((~strong(X)&calm(X))=>(humble(X)|old(X))))&
(![X]:((curious(X)|generous(X))<=>(tall(X)|~old(X))))&
(![X]:((quiet(X)&~rich(X))<=>(rich(X)&patient(X))))&
(![X]:(creative(X)<=>wise(X)))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~generous(X)<~>calm(X))))=>((~funny(susan)&~old(susan))))&
((calm(mary))<=>(humble(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((~old(X)<~>curious(X))))&
((strong(lucy)|~tall(lucy)))&
((quiet(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|~brave(X))))&
((~humble(alice)<~>~rich(alice))) | tall(alice) | [
"p0",
"p6",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8730007807382311935605588
% SZS output start Proof for 8730007807382311935605588
1. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (generous(X0) | calm(X0))) [input p0]
7. (~tall(alice) | ~generous(alice)) <=> ? [X0] : (calm(X0) & ~curious(X0)) [input p6]
13. ! [X0] : (creative(X0) <=> wise(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> ~calm(X0)) [input p13]
17. ? [X0] : (~strong(X0) & ~curious(X0)) [input p16]
24. tall(alice) [input hypothesis]
36. ! [X0] : (((generous(X0) | ~calm(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~generous(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((generous(X0) | ~calm(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | (~generous(X0) & calm(X0)))) [flattening 36]
47. ((~tall(alice) | ~generous(alice)) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X0] : (calm(X0) & ~curious(X0)) | (tall(alice) & generous(alice))) [nnf transformation 7]
48. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X0] : (calm(X0) & ~curious(X0)) | (tall(alice) & generous(alice))) [flattening 47]
49. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X1] : (calm(X1) & ~curious(X1)) | (tall(alice) & generous(alice))) [rectify 48]
50. ? [X1] : (calm(X1) & ~curious(X1)) => (calm(sK3) & ~curious(sK3)) [choice axiom]
51. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & ((calm(sK3) & ~curious(sK3)) | (tall(alice) & generous(alice))) [skolemisation 49,50]
62. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 13]
63. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 14]
66. ? [X0] : (~strong(X0) & ~curious(X0)) => (~strong(sK5) & ~curious(sK5)) [choice axiom]
67. ~strong(sK5) & ~curious(sK5) [skolemisation 17,66]
78. generous(X0) | calm(X0) | calm(X0) [cnf transformation 37]
80. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
100. ~tall(alice) | ~generous(alice) | ~calm(X0) | curious(X0) [cnf transformation 51]
117. wise(X0) | ~creative(X0) [cnf transformation 62]
118. creative(X0) | ~wise(X0) [cnf transformation 62]
121. ~creative(X0) | ~wise(X0) | calm(X0) [cnf transformation 63]
122. creative(X0) | wise(X0) | calm(X0) [cnf transformation 63]
129. ~curious(sK5) [cnf transformation 67]
141. tall(alice) [cnf transformation 24]
147. generous(X0) | calm(X0) [duplicate literal removal 78]
148. generous(X0) | ~calm(X0) [duplicate literal removal 80]
149. generous(X0) [subsumption resolution 147,148]
183. ~tall(alice) | ~calm(X0) | curious(X0) [subsumption resolution 100,149]
185. 8 <=> ! [X0] : (~calm(X0) | curious(X0)) [avatar definition]
186. ~calm(X0) | curious(X0) <- (8) [avatar component clause 185]
188. 9 <=> tall(alice) [avatar definition]
191. 8 | ~9 [avatar split clause 183,188,185]
221. wise(X0) | calm(X0) [subsumption resolution 122,117]
222. ~wise(X0) | calm(X0) [subsumption resolution 121,118]
223. calm(X0) [subsumption resolution 222,221]
267. 9 [avatar split clause 141,188]
268. curious(X0) <- (8) [subsumption resolution 186,223]
269. $false <- (8) [resolution 268,129]
272. ~8 [avatar contradiction clause 269]
273. $false [avatar sat refutation 191,267,272]
% SZS output end Proof for 8730007807382311935605588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either strong or not curious and vice versa. Everyone who is either happy or not generous is both patient and humble and vice versa. Everyone who is quiet is both creative and not funny. If lucy is old or not old then someone is both calm and wise. Everyone who is wise is either not funny or not strong and vice versa. Everyone who is either quiet or not happy is not strong or not curious and vice versa. Everyone who is both generous and quiet is brave or wise and vice versa. Everyone who is both not brave and quiet is patient or not strong and vice versa. Everyone who is both not rich and kind is either not quiet or rich and vice versa. Everyone who is creative or not calm is not old. If mary is tall then someone is either calm or not kind. If someone is either not generous or not humble then john is not rich and vice versa. If lucy is either not curious or not humble then fred is not curious or not happy and vice versa. If someone is rich or strong then alice is both generous and not patient and vice versa. If someone is not patient or generous then someone is not rich or not strong. Someone is either funny or quiet. Fred is either not wise or not strong. Someone is old or not funny. Someone is quiet or tall. Mary is either not generous or not funny. Mary is strong or not kind. Someone is either not kind or wise. Paul is either not quiet or tall. | Alice is strong. | entailment | (![X]:(calm(X)<=>(strong(X)<~>~curious(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(patient(X)&humble(X))))&
(![X]:(quiet(X)=>(creative(X)&~funny(X))))&
(((old(lucy)|~old(lucy)))=>(?[X]:((calm(X)&wise(X)))))&
(![X]:(wise(X)<=>(~funny(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>~happy(X))<=>(~strong(X)|~curious(X))))&
(![X]:((generous(X)&quiet(X))<=>(brave(X)|wise(X))))&
(![X]:((~brave(X)&quiet(X))<=>(patient(X)|~strong(X))))&
(![X]:((~rich(X)&kind(X))<=>(~quiet(X)<~>rich(X))))&
(![X]:((creative(X)|~calm(X))=>~old(X)))&
((tall(mary))=>(?[X]:((calm(X)<~>~kind(X)))))&
((?[X]:((~generous(X)<~>~humble(X))))<=>(~rich(john)))&
(((~curious(lucy)<~>~humble(lucy)))<=>((~curious(fred)|~happy(fred))))&
((?[X]:((rich(X)|strong(X))))<=>((generous(alice)&~patient(alice))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~rich(X)|~strong(X)))))&
(?[X]:((funny(X)<~>quiet(X))))&
((~wise(fred)<~>~strong(fred)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:((quiet(X)|tall(X))))&
((~generous(mary)<~>~funny(mary)))&
((strong(mary)|~kind(mary)))&
(?[X]:((~kind(X)<~>wise(X))))&
((~quiet(paul)<~>tall(paul))) | strong(alice) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3475820565819367738598741
% SZS output start Proof for 3475820565819367738598741
2. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (humble(X0) & patient(X0))) [input p1]
3. ! [X0] : (quiet(X0) => (~funny(X0) & creative(X0))) [input p2]
5. ! [X0] : (wise(X0) <=> (~funny(X0) <~> ~strong(X0))) [input p4]
6. ! [X0] : ((quiet(X0) <~> ~happy(X0)) <=> (~curious(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((quiet(X0) & generous(X0)) <=> (wise(X0) | brave(X0))) [input p6]
8. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> (~strong(X0) | patient(X0))) [input p7]
14. ? [X0] : (strong(X0) | rich(X0)) <=> (~patient(alice) & generous(alice)) [input p13]
17. ~wise(fred) <~> ~strong(fred) [input p16]
24. ~strong(alice) [input hypothesis]
26. ! [X0] : ((~funny(X0) & creative(X0)) | ~quiet(X0)) [ennf transformation 3]
32. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 2]
33. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [flattening 32]
36. ! [X0] : ((wise(X0) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | ~wise(X0))) [nnf transformation 5]
37. ! [X0] : ((((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0))))) [nnf transformation 6]
38. ! [X0] : ((((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0))))) [flattening 37]
39. ! [X0] : (((quiet(X0) & generous(X0)) | (~wise(X0) & ~brave(X0))) & ((wise(X0) | brave(X0)) | (~quiet(X0) | ~generous(X0)))) [nnf transformation 7]
40. ! [X0] : (((quiet(X0) & generous(X0)) | (~wise(X0) & ~brave(X0))) & (wise(X0) | brave(X0) | ~quiet(X0) | ~generous(X0))) [flattening 39]
41. ! [X0] : (((quiet(X0) & ~brave(X0)) | (strong(X0) & ~patient(X0))) & ((~strong(X0) | patient(X0)) | (~quiet(X0) | brave(X0)))) [nnf transformation 8]
42. ! [X0] : (((quiet(X0) & ~brave(X0)) | (strong(X0) & ~patient(X0))) & (~strong(X0) | patient(X0) | ~quiet(X0) | brave(X0))) [flattening 41]
54. (? [X0] : (strong(X0) | rich(X0)) | (patient(alice) | ~generous(alice))) & ((~patient(alice) & generous(alice)) | ! [X0] : (~strong(X0) & ~rich(X0))) [nnf transformation 14]
55. (? [X0] : (strong(X0) | rich(X0)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X0] : (~strong(X0) & ~rich(X0))) [flattening 54]
56. (? [X0] : (strong(X0) | rich(X0)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X1] : (~strong(X1) & ~rich(X1))) [rectify 55]
57. ? [X0] : (strong(X0) | rich(X0)) => (strong(sK3) | rich(sK3)) [choice axiom]
58. ((strong(sK3) | rich(sK3)) | patient(alice) | ~generous(alice)) & ((~patient(alice) & generous(alice)) | ! [X1] : (~strong(X1) & ~rich(X1))) [skolemisation 56,57]
65. (strong(fred) | wise(fred)) & (~strong(fred) | ~wise(fred)) [nnf transformation 17]
79. ~generous(X0) | patient(X0) | ~happy(X0) [cnf transformation 33]
86. ~funny(X0) | ~quiet(X0) [cnf transformation 26]
92. ~wise(X0) | funny(X0) | strong(X0) [cnf transformation 36]
99. ~quiet(X0) | happy(X0) | strong(X0) [cnf transformation 38]
105. ~wise(X0) | quiet(X0) [cnf transformation 40]
110. quiet(X0) | strong(X0) [cnf transformation 42]
132. generous(alice) | ~strong(X1) [cnf transformation 58]
134. ~patient(alice) | ~strong(X1) [cnf transformation 58]
141. strong(fred) | wise(fred) [cnf transformation 65]
151. ~strong(alice) [cnf transformation 24]
230. 16 <=> generous(alice) [avatar definition]
231. generous(alice) <- (16) [avatar component clause 230]
234. 17 <=> patient(alice) [avatar definition]
235. ~patient(alice) <- (~17) [avatar component clause 234]
247. 20 <=> ! [X1] : ~strong(X1) [avatar definition]
248. ~strong(X1) <- (20) [avatar component clause 247]
249. 20 | ~17 [avatar split clause 134,234,247]
254. 20 | 16 [avatar split clause 132,230,247]
282. 28 <=> wise(fred) [avatar definition]
284. wise(fred) <- (28) [avatar component clause 282]
286. 29 <=> strong(fred) [avatar definition]
287. ~strong(fred) <- (~29) [avatar component clause 286]
288. strong(fred) <- (29) [avatar component clause 286]
289. 28 | 29 [avatar split clause 141,286,282]
354. quiet(fred) <- (28) [resolution 105,284]
412. patient(alice) | ~happy(alice) <- (16) [resolution 79,231]
424. ~happy(alice) <- (16, ~17) [subsumption resolution 412,235]
482. funny(fred) | strong(fred) <- (28) [resolution 92,284]
485. funny(fred) <- (28, ~29) [subsumption resolution 482,287]
513. ~quiet(fred) <- (28, ~29) [resolution 485,86]
514. $false <- (28, ~29) [subsumption resolution 513,354]
515. ~28 | 29 [avatar contradiction clause 514]
528. happy(X0) | strong(X0) | strong(X0) [resolution 99,110]
531. happy(X0) | strong(X0) [duplicate literal removal 528]
734. strong(alice) <- (16, ~17) [resolution 531,424]
740. $false <- (16, ~17) [subsumption resolution 734,151]
741. ~16 | 17 [avatar contradiction clause 740]
761. $false <- (20, 29) [resolution 248,288]
768. ~20 | ~29 [avatar contradiction clause 761]
770. $false [avatar sat refutation 249,254,289,515,741,768]
% SZS output end Proof for 3475820565819367738598741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong is either not generous or curious. Everyone who is both rich and quiet is either not calm or tall and vice versa. Everyone who is not generous or not happy is not happy and vice versa. If lucy is both not creative and not funny then someone is strong or rich. If someone is not rich or tall then someone is both brave and tall and vice versa. Everyone who is both not old and not rich is not tall or creative and vice versa. Everyone who is not strong or old is either funny or happy and vice versa. If mary is not brave or quiet then someone is either calm or tall and vice versa. Everyone who is not wise or not generous is both rich and not funny. If paul is both old and not quiet then john is both kind and not old and vice versa. If someone is either not generous or tall then someone is not curious and vice versa. Everyone who is not wise is not happy or not old and vice versa. Everyone who is either not creative or patient is patient or not funny. If mary is curious or not old then someone is rich. If someone is both humble and quiet then someone is both not curious and not humble and vice versa. Everyone who is patient or generous is both rich and funny and vice versa. Someone is both quiet and kind. Alice is not old or not strong. Someone is not kind or tall. Alice is not generous or not humble. | Alice is patient. | contradiction | (![X]:(~strong(X)=>(~generous(X)<~>curious(X))))&
(![X]:((rich(X)&quiet(X))<=>(~calm(X)<~>tall(X))))&
(![X]:((~generous(X)|~happy(X))<=>~happy(X)))&
(((~creative(lucy)&~funny(lucy)))=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~rich(X)|tall(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((~old(X)&~rich(X))<=>(~tall(X)|creative(X))))&
(![X]:((~strong(X)|old(X))<=>(funny(X)<~>happy(X))))&
(((~brave(mary)|quiet(mary)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((~wise(X)|~generous(X))=>(rich(X)&~funny(X))))&
(((old(paul)&~quiet(paul)))<=>((kind(john)&~old(john))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~wise(X)<=>(~happy(X)|~old(X))))&
(![X]:((~creative(X)<~>patient(X))=>(patient(X)|~funny(X))))&
(((curious(mary)|~old(mary)))=>(?[X]:(rich(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:((patient(X)|generous(X))<=>(rich(X)&funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
((~old(alice)|~strong(alice)))&
(?[X]:((~kind(X)|tall(X))))&
((~generous(alice)|~humble(alice))) | patient(alice) | [
"p6",
"p8",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1231716774045199336110853
% SZS output start Proof for 1231716774045199336110853
7. ! [X0] : ((old(X0) | ~strong(X0)) <=> (funny(X0) <~> happy(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | ~wise(X0)) => (~funny(X0) & rich(X0))) [input p8]
12. ! [X0] : (~wise(X0) <=> (~old(X0) | ~happy(X0))) [input p11]
16. ! [X0] : ((generous(X0) | patient(X0)) <=> (funny(X0) & rich(X0))) [input p15]
18. ~strong(alice) | ~old(alice) [input p17]
21. patient(alice) [input hypothesis]
25. ! [X0] : ((~old(X0) | ~happy(X0)) => ~wise(X0)) [unused predicate definition removal 12]
29. ! [X0] : ((~funny(X0) & rich(X0)) | (generous(X0) & wise(X0))) [ennf transformation 9]
30. ! [X0] : (~wise(X0) | (old(X0) & happy(X0))) [ennf transformation 25]
48. ! [X0] : (((old(X0) | ~strong(X0)) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((old(X0) | ~strong(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~old(X0) & strong(X0)))) [flattening 48]
70. ! [X0] : (((generous(X0) | patient(X0)) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 16]
71. ! [X0] : ((generous(X0) | patient(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | (~generous(X0) & ~patient(X0)))) [flattening 70]
100. ~funny(X0) | ~happy(X0) | strong(X0) [cnf transformation 49]
112. ~funny(X0) | wise(X0) [cnf transformation 29]
122. ~wise(X0) | happy(X0) [cnf transformation 30]
123. ~wise(X0) | old(X0) [cnf transformation 30]
134. ~patient(X0) | funny(X0) [cnf transformation 71]
139. ~strong(alice) | ~old(alice) [cnf transformation 18]
142. patient(alice) [cnf transformation 21]
307. 37 <=> old(alice) [avatar definition]
311. 38 <=> strong(alice) [avatar definition]
313. ~strong(alice) <- (~38) [avatar component clause 311]
314. ~37 | ~38 [avatar split clause 139,311,307]
360. funny(alice) [resolution 134,142]
362. wise(alice) [resolution 360,112]
364. old(alice) [resolution 362,123]
365. happy(alice) [resolution 362,122]
368. 37 [avatar split clause 364,307]
491. ~happy(alice) | strong(alice) [resolution 100,360]
495. strong(alice) [subsumption resolution 491,365]
496. $false <- (~38) [subsumption resolution 495,313]
497. 38 [avatar contradiction clause 496]
498. $false [avatar sat refutation 314,368,497]
% SZS output end Proof for 1231716774045199336110853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not calm is not tall or not calm and vice versa. If fred is not humble then alice is either calm or old and vice versa. If susan is either not creative or not humble then john is both strong and old. Everyone who is either rich or kind is humble. Everyone who is old is both happy and patient. Everyone who is both not strong and tall is either brave or creative and vice versa. Everyone who is both not rich and not happy is not curious. Everyone who is strong is either calm or generous and vice versa. Everyone who is either not happy or not funny is both kind and not happy and vice versa. Everyone who is both not strong and not quiet is both not old and not funny. If someone is either tall or not curious then john is generous or brave. Everyone who is either quiet or brave is both brave and happy and vice versa. If someone is either creative or not brave then susan is strong or not patient and vice versa. Everyone who is patient or not generous is both not generous and not calm. If someone is either creative or not calm then john is both strong and not humble. If susan is generous or not old then someone is patient. Someone is not funny. Someone is both kind and not strong. Someone is calm. Someone is not strong. Lucy is both not strong and not rich. Mary is humble or not funny. Susan is not humble. Someone is not happy or not patient. | Susan is creative. | contradiction | (![X]:((~happy(X)|~calm(X))<=>(~tall(X)|~calm(X))))&
((~humble(fred))<=>((calm(alice)<~>old(alice))))&
(((~creative(susan)<~>~humble(susan)))=>((strong(john)&old(john))))&
(![X]:((rich(X)<~>kind(X))=>humble(X)))&
(![X]:(old(X)=>(happy(X)&patient(X))))&
(![X]:((~strong(X)&tall(X))<=>(brave(X)<~>creative(X))))&
(![X]:((~rich(X)&~happy(X))=>~curious(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)&~happy(X))))&
(![X]:((~strong(X)&~quiet(X))=>(~old(X)&~funny(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>((generous(john)|brave(john))))&
(![X]:((quiet(X)<~>brave(X))<=>(brave(X)&happy(X))))&
((?[X]:((creative(X)<~>~brave(X))))<=>((strong(susan)|~patient(susan))))&
(![X]:((patient(X)|~generous(X))=>(~generous(X)&~calm(X))))&
((?[X]:((creative(X)<~>~calm(X))))=>((strong(john)&~humble(john))))&
(((generous(susan)|~old(susan)))=>(?[X]:(patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:(calm(X)))&
(?[X]:(~strong(X)))&
((~strong(lucy)&~rich(lucy)))&
((humble(mary)|~funny(mary)))&
(~humble(susan))&
(?[X]:((~happy(X)|~patient(X)))) | creative(susan) | [
"p2",
"p4",
"p7",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4676431743526400462534260
% SZS output start Proof for 4676431743526400462534260
3. (~creative(susan) <~> ~humble(susan)) => (old(john) & strong(john)) [input p2]
5. ! [X0] : (old(X0) => (patient(X0) & happy(X0))) [input p4]
8. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p7]
14. ! [X0] : ((~generous(X0) | patient(X0)) => (~calm(X0) & ~generous(X0))) [input p13]
23. ~humble(susan) [input p22]
25. creative(susan) [input hypothesis]
26. (old(john) & strong(john)) | (~creative(susan) <=> ~humble(susan)) [ennf transformation 3]
28. ! [X0] : ((patient(X0) & happy(X0)) | ~old(X0)) [ennf transformation 5]
35. ! [X0] : ((~calm(X0) & ~generous(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 14]
41. (old(john) & strong(john)) | ((~creative(susan) | humble(susan)) & (~humble(susan) | creative(susan))) [nnf transformation 26]
45. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 8]
78. strong(john) | ~creative(susan) | humble(susan) [cnf transformation 41]
80. old(john) | ~creative(susan) | humble(susan) [cnf transformation 41]
84. ~old(X0) | patient(X0) [cnf transformation 28]
92. ~strong(X0) | calm(X0) | generous(X0) [cnf transformation 45]
118. ~generous(X0) | ~patient(X0) [cnf transformation 35]
120. ~patient(X0) | ~calm(X0) [cnf transformation 35]
136. ~humble(susan) [cnf transformation 23]
138. creative(susan) [cnf transformation 25]
160. 4 <=> humble(susan) [avatar definition]
164. 5 <=> creative(susan) [avatar definition]
168. 6 <=> old(john) [avatar definition]
170. old(john) <- (6) [avatar component clause 168]
171. 4 | ~5 | 6 [avatar split clause 80,168,164,160]
174. 7 <=> strong(john) [avatar definition]
176. strong(john) <- (7) [avatar component clause 174]
177. 4 | ~5 | 7 [avatar split clause 78,174,164,160]
183. 9 <=> generous(john) [avatar definition]
184. ~generous(john) <- (~9) [avatar component clause 183]
185. generous(john) <- (9) [avatar component clause 183]
260. ~4 [avatar split clause 136,160]
270. 5 [avatar split clause 138,164]
273. patient(john) <- (6) [resolution 84,170]
278. ~patient(john) <- (9) [resolution 118,185]
279. $false <- (6, 9) [subsumption resolution 278,273]
280. ~6 | ~9 [avatar contradiction clause 279]
282. ~calm(john) <- (6) [resolution 273,120]
329. calm(john) | generous(john) <- (7) [resolution 92,176]
331. generous(john) <- (6, 7) [subsumption resolution 329,282]
332. $false <- (6, 7, ~9) [subsumption resolution 331,184]
333. ~6 | ~7 | 9 [avatar contradiction clause 332]
337. $false [avatar sat refutation 171,177,260,270,280,333]
% SZS output end Proof for 4676431743526400462534260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and happy is not tall. If someone is not happy or creative then fred is generous. If someone is either not humble or tall then someone is not strong or strong and vice versa. Everyone who is both generous and not brave is calm. If lucy is both old and rich then someone is curious or generous. Everyone who is rich is humble or wise. Everyone who is not patient is both happy and not old. Everyone who is not rich or patient is either not generous or not kind and vice versa. Everyone who is not wise is rich. Everyone who is either not kind or not humble is kind. If someone is both happy and not brave then paul is brave or quiet and vice versa. Everyone who is either curious or generous is humble and vice versa. Everyone who is either tall or not humble is either creative or strong and vice versa. Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. Someone is old or tall. Someone is either humble or not quiet. Paul is old or curious. Lucy is not generous. Someone is strong. Someone is both not funny and not humble. Someone is either not calm or not tall. Someone is either wise or not patient. | Fred is creative. | contradiction | (![X]:((~creative(X)&happy(X))=>~tall(X)))&
((?[X]:((~happy(X)|creative(X))))=>(generous(fred)))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((generous(X)&~brave(X))=>calm(X)))&
(((old(lucy)&rich(lucy)))=>(?[X]:((curious(X)|generous(X)))))&
(![X]:(rich(X)=>(humble(X)|wise(X))))&
(![X]:(~patient(X)=>(happy(X)&~old(X))))&
(![X]:((~rich(X)|patient(X))<=>(~generous(X)<~>~kind(X))))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:((~kind(X)<~>~humble(X))=>kind(X)))&
((?[X]:((happy(X)&~brave(X))))<=>((brave(paul)|quiet(paul))))&
(![X]:((curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((tall(X)<~>~humble(X))<=>(creative(X)<~>strong(X))))&
(![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
((old(paul)|curious(paul)))&
(~generous(lucy))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((wise(X)<~>~patient(X)))) | creative(fred) | [
"p1",
"p7",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2620212978437413462434179
% SZS output start Proof for 2620212978437413462434179
2. ? [X0] : (creative(X0) | ~happy(X0)) => generous(fred) [input p1]
8. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~generous(X0) <~> ~kind(X0))) [input p7]
10. ! [X0] : ((~kind(X0) <~> ~humble(X0)) => kind(X0)) [input p9]
14. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p13]
15. ! [X0] : (humble(X0) <=> (~patient(X0) | creative(X0))) [input p14]
25. creative(fred) [input hypothesis]
30. generous(fred) | ! [X0] : (~creative(X0) & happy(X0)) [ennf transformation 2]
39. ! [X0] : (kind(X0) | (~kind(X0) <=> ~humble(X0))) [ennf transformation 10]
47. ! [X0] : (((patient(X0) | ~rich(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~patient(X0) & rich(X0)))) [nnf transformation 8]
48. ! [X0] : ((patient(X0) | ~rich(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~patient(X0) & rich(X0)))) [flattening 47]
49. ! [X0] : (kind(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) [nnf transformation 39]
57. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 14]
58. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 57]
59. ! [X0] : ((humble(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | ~humble(X0))) [nnf transformation 15]
60. ! [X0] : ((humble(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ~humble(X0))) [flattening 59]
82. generous(fred) | ~creative(X0) [cnf transformation 30]
95. ~kind(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 48]
101. kind(X0) | ~humble(X0) | kind(X0) [cnf transformation 49]
121. patient(X0) | ~strong(X0) [cnf transformation 58]
122. patient(X0) | strong(X0) [cnf transformation 58]
126. ~creative(X0) | humble(X0) [cnf transformation 60]
147. creative(fred) [cnf transformation 25]
148. ~humble(X0) | kind(X0) [duplicate literal removal 101]
150. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
151. ~creative(X0) <- (1) [avatar component clause 150]
153. 2 <=> generous(fred) [avatar definition]
156. 1 | 2 [avatar split clause 82,153,150]
221. patient(X0) [subsumption resolution 121,122]
296. humble(fred) [resolution 126,147]
298. kind(fred) [resolution 296,148]
317. ~generous(fred) | ~patient(fred) [resolution 95,298]
321. ~generous(fred) [subsumption resolution 317,221]
322. ~2 [avatar split clause 321,153]
323. $false <- (1) [resolution 151,147]
326. ~1 [avatar contradiction clause 323]
327. $false [avatar sat refutation 156,322,326]
% SZS output end Proof for 2620212978437413462434179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not strong.
Everyone who is either brave or not strong is either not funny or not tall and vice versa.
Everyone who is not calm or wise is both happy and not patient and vice versa.
Everyone who is both not brave and not tall is both quiet and strong.
Everyone who is patient is either brave or not wise and vice versa.
If john is happy or calm then someone is either quiet or not tall and vice versa.
If someone is not patient then someone is both not strong and happy and vice versa.
If alice is not calm or wise then mary is both not curious and not generous and vice versa.
Everyone who is quiet or not wise is not kind or kind.
If someone is both old and calm then someone is both not happy and old and vice versa.
If paul is not curious then someone is patient or not brave and vice versa.
If someone is either not brave or funny then someone is calm and vice versa.
Everyone who is either not strong or kind is either not patient or not funny.
Everyone who is both not old and not funny is wise or funny and vice versa.
Everyone who is wise or not strong is tall or not creative and vice versa.
Everyone who is both rich and not kind is tall or not curious and vice versa.
Alice is wise.
Mary is both calm and rich.
Lucy is not happy or not strong.
Someone is both rich and generous.
Someone is not brave or kind. | Paul is rich. | entailment | (![X]:(brave(X)=>~strong(X)))&
(![X]:((brave(X)<~>~strong(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~patient(X))))&
(![X]:((~brave(X)&~tall(X))=>(quiet(X)&strong(X))))&
(![X]:(patient(X)<=>(brave(X)<~>~wise(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((~strong(X)&happy(X)))))&
(((~calm(alice)|wise(alice)))<=>((~curious(mary)&~generous(mary))))&
(![X]:((quiet(X)|~wise(X))=>(~kind(X)|kind(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((~happy(X)&old(X)))))&
((~curious(paul))<=>(?[X]:((patient(X)|~brave(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)|funny(X))))&
(![X]:((wise(X)|~strong(X))<=>(tall(X)|~creative(X))))&
(![X]:((rich(X)&~kind(X))<=>(tall(X)|~curious(X))))&
(wise(alice))&
((calm(mary)&rich(mary)))&
((~happy(lucy)|~strong(lucy)))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((~brave(X)|kind(X)))) | rich(paul) | [
"p10",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3518193770436203642437201
% SZS output start Proof for 3518193770436203642437201
11. ~curious(paul) <=> ? [X0] : (~brave(X0) | patient(X0)) [input p10]
12. ? [X0] : (~brave(X0) <~> funny(X0)) <=> ? [X0] : calm(X0) [input p11]
14. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (funny(X0) | wise(X0))) [input p13]
16. ! [X0] : ((~kind(X0) & rich(X0)) <=> (~curious(X0) | tall(X0))) [input p15]
18. rich(mary) & calm(mary) [input p17]
22. ~rich(paul) [input hypothesis]
25. ? [X0] : (~brave(X0) <~> funny(X0)) <=> ? [X1] : calm(X1) [rectify 12]
53. (~curious(paul) | ! [X0] : (brave(X0) & ~patient(X0))) & (? [X0] : (~brave(X0) | patient(X0)) | curious(paul)) [nnf transformation 11]
54. (~curious(paul) | ! [X0] : (brave(X0) & ~patient(X0))) & (? [X1] : (~brave(X1) | patient(X1)) | curious(paul)) [rectify 53]
55. ? [X1] : (~brave(X1) | patient(X1)) => (~brave(sK5) | patient(sK5)) [choice axiom]
56. (~curious(paul) | ! [X0] : (brave(X0) & ~patient(X0))) & ((~brave(sK5) | patient(sK5)) | curious(paul)) [skolemisation 54,55]
57. (? [X0] : ((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) [nnf transformation 25]
58. (? [X0] : ((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~brave(X3) | ~funny(X3)) & (funny(X3) | brave(X3)))) [rectify 57]
59. ? [X0] : ((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) => ((~funny(sK6) | brave(sK6)) & (funny(sK6) | ~brave(sK6))) [choice axiom]
60. ? [X2] : calm(X2) => calm(sK7) [choice axiom]
61. (((~funny(sK6) | brave(sK6)) & (funny(sK6) | ~brave(sK6))) | ! [X1] : ~calm(X1)) & (calm(sK7) | ! [X3] : ((~brave(X3) | ~funny(X3)) & (funny(X3) | brave(X3)))) [skolemisation 58,60,59]
63. ! [X0] : (((~funny(X0) & ~old(X0)) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | (funny(X0) | old(X0)))) [nnf transformation 14]
64. ! [X0] : (((~funny(X0) & ~old(X0)) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | funny(X0) | old(X0))) [flattening 63]
67. ! [X0] : (((~kind(X0) & rich(X0)) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 16]
68. ! [X0] : (((~kind(X0) & rich(X0)) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | kind(X0) | ~rich(X0))) [flattening 67]
115. ~curious(paul) | brave(X0) [cnf transformation 56]
118. funny(sK6) | ~brave(sK6) | ~calm(X1) [cnf transformation 61]
128. ~funny(X0) | ~funny(X0) [cnf transformation 64]
135. rich(X0) | curious(X0) [cnf transformation 68]
139. calm(mary) [cnf transformation 18]
145. ~rich(paul) [cnf transformation 22]
147. ~funny(X0) [duplicate literal removal 128]
243. 20 <=> ! [X0] : brave(X0) [avatar definition]
244. brave(X0) <- (20) [avatar component clause 243]
246. 21 <=> curious(paul) [avatar definition]
249. 20 | ~21 [avatar split clause 115,246,243]
261. 24 <=> ! [X1] : ~calm(X1) [avatar definition]
262. ~calm(X1) <- (24) [avatar component clause 261]
264. 25 <=> brave(sK6) [avatar definition]
265. ~brave(sK6) <- (~25) [avatar component clause 264]
268. 26 <=> funny(sK6) [avatar definition]
269. funny(sK6) <- (26) [avatar component clause 268]
272. 24 | ~25 | 26 [avatar split clause 118,268,264,261]
316. curious(paul) [resolution 135,145]
319. 21 [avatar split clause 316,246]
321. $false <- (20, ~25) [resolution 244,265]
324. ~20 | 25 [avatar contradiction clause 321]
328. $false <- (24) [resolution 262,139]
331. ~24 [avatar contradiction clause 328]
332. $false <- (26) [subsumption resolution 269,147]
333. ~26 [avatar contradiction clause 332]
334. $false [avatar sat refutation 249,272,319,324,331,333]
% SZS output end Proof for 3518193770436203642437201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either patient or humble then john is either not old or humble. Everyone who is old is not kind and vice versa. If someone is either calm or kind then someone is not strong or wise. Everyone who is patient or generous is curious or not old and vice versa. Everyone who is not humble is kind and vice versa. Everyone who is not calm is not humble and vice versa. Everyone who is either calm or not generous is curious or not creative. If paul is not wise or happy then mary is curious and vice versa. If fred is either not wise or not creative then someone is either curious or strong and vice versa. If someone is not humble or curious then john is not funny or not old and vice versa. If someone is either calm or not brave then susan is not kind and vice versa. Everyone who is not patient or rich is tall or not patient. Everyone who is wise or not rich is either curious or generous. If mary is both not curious and not happy then alice is not happy and vice versa. If someone is not quiet then susan is either not wise or creative. If someone is strong or not creative then someone is either not creative or brave. Lucy is both rich and tall. Someone is happy or not curious. Someone is not curious or not humble. Lucy is generous. Susan is patient or not brave. Someone is not patient or curious. Someone is both not tall and not rich. Someone is not old or funny. | John is not rich. | neutral | ((?[X]:((patient(X)<~>humble(X))))=>((~old(john)<~>humble(john))))&
(![X]:(old(X)<=>~kind(X)))&
((?[X]:((calm(X)<~>kind(X))))=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((patient(X)|generous(X))<=>(curious(X)|~old(X))))&
(![X]:(~humble(X)<=>kind(X)))&
(![X]:(~calm(X)<=>~humble(X)))&
(![X]:((calm(X)<~>~generous(X))=>(curious(X)|~creative(X))))&
(((~wise(paul)|happy(paul)))<=>(curious(mary)))&
(((~wise(fred)<~>~creative(fred)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((?[X]:((~humble(X)|curious(X))))<=>((~funny(john)|~old(john))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(~kind(susan)))&
(![X]:((~patient(X)|rich(X))=>(tall(X)|~patient(X))))&
(![X]:((wise(X)|~rich(X))=>(curious(X)<~>generous(X))))&
(((~curious(mary)&~happy(mary)))<=>(~happy(alice)))&
((?[X]:(~quiet(X)))=>((~wise(susan)<~>creative(susan))))&
((?[X]:((strong(X)|~creative(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
((rich(lucy)&tall(lucy)))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:((~curious(X)|~humble(X))))&
(generous(lucy))&
((patient(susan)|~brave(susan)))&
(?[X]:((~patient(X)|curious(X))))&
(?[X]:((~tall(X)&~rich(X))))&
(?[X]:((~old(X)|funny(X)))) | ~rich(john) | [] | null | 0 |
If paul is either not calm or creative then paul is either quiet or humble and vice versa. If alice is not wise then susan is not old. If someone is either patient or old then someone is brave or not brave and vice versa. Everyone who is old is both not rich and funny. If mary is generous then mary is wise or not generous. Everyone who is both not rich and not happy is humble or not old and vice versa. Everyone who is both wise and not happy is not rich and vice versa. Everyone who is generous or not kind is either not happy or not wise. Everyone who is funny is either generous or not funny. Everyone who is creative or rich is either not wise or not quiet. Everyone who is not funny is either not funny or generous. Everyone who is not old is either brave or not kind and vice versa. If someone is either not tall or brave then paul is not calm or not tall and vice versa. Everyone who is both humble and happy is old and vice versa. If someone is tall then someone is wise or not old and vice versa. If someone is not curious or old then someone is either not wise or not rich and vice versa. Susan is patient. Mary is curious or not humble. Someone is not calm. Fred is either not brave or not tall. Someone is curious. Someone is either patient or happy. Someone is not generous or not old. | Susan is not wise. | contradiction | (((~calm(paul)<~>creative(paul)))<=>((quiet(paul)<~>humble(paul))))&
((~wise(alice))=>(~old(susan)))&
((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:(old(X)=>(~rich(X)&funny(X))))&
((generous(mary))=>((wise(mary)|~generous(mary))))&
(![X]:((~rich(X)&~happy(X))<=>(humble(X)|~old(X))))&
(![X]:((wise(X)&~happy(X))<=>~rich(X)))&
(![X]:((generous(X)|~kind(X))=>(~happy(X)<~>~wise(X))))&
(![X]:(funny(X)=>(generous(X)<~>~funny(X))))&
(![X]:((creative(X)|rich(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~funny(X)<~>generous(X))))&
(![X]:(~old(X)<=>(brave(X)<~>~kind(X))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((~calm(paul)|~tall(paul))))&
(![X]:((humble(X)&happy(X))<=>old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(patient(susan))&
((curious(mary)|~humble(mary)))&
(?[X]:(~calm(X)))&
((~brave(fred)<~>~tall(fred)))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((~generous(X)|~old(X)))) | ~wise(susan) | [
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2664315432935700028336458
% SZS output start Proof for 2664315432935700028336458
4. ! [X0] : (old(X0) => (funny(X0) & ~rich(X0))) [input p3]
6. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (~old(X0) | humble(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & wise(X0)) <=> ~rich(X0)) [input p6]
24. ~wise(susan) [input hypothesis]
29. ! [X0] : ((funny(X0) & ~rich(X0)) | ~old(X0)) [ennf transformation 4]
42. ! [X0] : (((~happy(X0) & ~rich(X0)) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | (happy(X0) | rich(X0)))) [nnf transformation 6]
43. ! [X0] : (((~happy(X0) & ~rich(X0)) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | happy(X0) | rich(X0))) [flattening 42]
44. ! [X0] : (((~happy(X0) & wise(X0)) | rich(X0)) & (~rich(X0) | (happy(X0) | ~wise(X0)))) [nnf transformation 7]
45. ! [X0] : (((~happy(X0) & wise(X0)) | rich(X0)) & (~rich(X0) | happy(X0) | ~wise(X0))) [flattening 44]
93. ~rich(X0) | ~old(X0) [cnf transformation 29]
98. ~rich(X0) | old(X0) [cnf transformation 43]
102. wise(X0) | rich(X0) [cnf transformation 45]
147. ~wise(susan) [cnf transformation 24]
211. ~rich(X0) [subsumption resolution 98,93]
214. wise(X0) [subsumption resolution 102,211]
265. $false [subsumption resolution 147,214]
% SZS output end Proof for 2664315432935700028336458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is humble or not funny then paul is curious or humble. Everyone who is patient is both not tall and funny. Everyone who is both not generous and not creative is both quiet and not funny and vice versa. Everyone who is both not rich and creative is both not brave and brave and vice versa. If someone is kind or happy then someone is calm. If someone is either old or not curious then alice is either old or wise. If someone is either not rich or not happy then someone is either old or not creative. Everyone who is happy is funny and vice versa. If paul is not humble then alice is both not creative and quiet and vice versa. If someone is curious then lucy is strong or kind and vice versa. Everyone who is rich is both curious and not rich and vice versa. Everyone who is humble is both not rich and brave and vice versa. If someone is not wise then susan is generous or not curious and vice versa. If someone is both not generous and calm then paul is not generous and vice versa. If paul is both quiet and not humble then someone is either not creative or not patient. Everyone who is not tall or not happy is either funny or not curious and vice versa. Alice is both not brave and not strong. Susan is quiet. Susan is not old or rich. Someone is funny or not calm. Someone is both not rich and not tall. Fred is both happy and kind. | Alice is wise. | neutral | (((humble(lucy)|~funny(lucy)))=>((curious(paul)|humble(paul))))&
(![X]:(patient(X)=>(~tall(X)&funny(X))))&
(![X]:((~generous(X)&~creative(X))<=>(quiet(X)&~funny(X))))&
(![X]:((~rich(X)&creative(X))<=>(~brave(X)&brave(X))))&
((?[X]:((kind(X)|happy(X))))=>(?[X]:(calm(X))))&
((?[X]:((old(X)<~>~curious(X))))=>((old(alice)<~>wise(alice))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:(happy(X)<=>funny(X)))&
((~humble(paul))<=>((~creative(alice)&quiet(alice))))&
((?[X]:(curious(X)))<=>((strong(lucy)|kind(lucy))))&
(![X]:(rich(X)<=>(curious(X)&~rich(X))))&
(![X]:(humble(X)<=>(~rich(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((generous(susan)|~curious(susan))))&
((?[X]:((~generous(X)&calm(X))))<=>(~generous(paul)))&
(((quiet(paul)&~humble(paul)))=>(?[X]:((~creative(X)<~>~patient(X)))))&
(![X]:((~tall(X)|~happy(X))<=>(funny(X)<~>~curious(X))))&
((~brave(alice)&~strong(alice)))&
(quiet(susan))&
((~old(susan)|rich(susan)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:((~rich(X)&~tall(X))))&
((happy(fred)&kind(fred))) | wise(alice) | [] | null | 0 |
Everyone who is not kind or not patient is both happy and not funny and vice versa. Everyone who is both not curious and not rich is either not patient or quiet and vice versa. If mary is either strong or wise then susan is rich. Everyone who is humble is either not old or not creative. If alice is not tall or generous then someone is not tall or generous and vice versa. If fred is both old and quiet then alice is not kind or not humble and vice versa. If susan is tall then someone is not creative. Everyone who is not happy is both brave and quiet and vice versa. If someone is happy or tall then alice is both not kind and not brave. Everyone who is not wise is both wise and rich. If alice is either not patient or brave then someone is either not creative or brave. Everyone who is not rich is either quiet or not wise and vice versa. Everyone who is not patient is brave or calm and vice versa. If mary is kind or wise then someone is both not humble and not old. If someone is either tall or old then someone is calm. If someone is both tall and kind then someone is humble or generous. Someone is humble or not generous. Susan is either not strong or generous. Paul is both not rich and tall. Mary is both not humble and not brave. Someone is kind. John is both rich and wise. Someone is either calm or not humble. | Susan is happy. | entailment | (![X]:((~kind(X)|~patient(X))<=>(happy(X)&~funny(X))))&
(![X]:((~curious(X)&~rich(X))<=>(~patient(X)<~>quiet(X))))&
(((strong(mary)<~>wise(mary)))=>(rich(susan)))&
(![X]:(humble(X)=>(~old(X)<~>~creative(X))))&
(((~tall(alice)|generous(alice)))<=>(?[X]:((~tall(X)|generous(X)))))&
(((old(fred)&quiet(fred)))<=>((~kind(alice)|~humble(alice))))&
((tall(susan))=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)<=>(brave(X)&quiet(X))))&
((?[X]:((happy(X)|tall(X))))=>((~kind(alice)&~brave(alice))))&
(![X]:(~wise(X)=>(wise(X)&rich(X))))&
(((~patient(alice)<~>brave(alice)))=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:(~rich(X)<=>(quiet(X)<~>~wise(X))))&
(![X]:(~patient(X)<=>(brave(X)|calm(X))))&
(((kind(mary)|wise(mary)))=>(?[X]:((~humble(X)&~old(X)))))&
((?[X]:((tall(X)<~>old(X))))=>(?[X]:(calm(X))))&
((?[X]:((tall(X)&kind(X))))=>(?[X]:((humble(X)|generous(X)))))&
(?[X]:((humble(X)|~generous(X))))&
((~strong(susan)<~>generous(susan)))&
((~rich(paul)&tall(paul)))&
((~humble(mary)&~brave(mary)))&
(?[X]:(kind(X)))&
((rich(john)&wise(john)))&
(?[X]:((calm(X)<~>~humble(X)))) | happy(susan) | [
"p0",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6921457051562831397808604
% SZS output start Proof for 6921457051562831397808604
1. ! [X0] : ((~patient(X0) | ~kind(X0)) <=> (~funny(X0) & happy(X0))) [input p0]
8. ! [X0] : (~happy(X0) <=> (quiet(X0) & brave(X0))) [input p7]
13. ! [X0] : (~patient(X0) <=> (calm(X0) | brave(X0))) [input p12]
24. ~happy(susan) [input hypothesis]
36. ! [X0] : (((~patient(X0) | ~kind(X0)) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | (patient(X0) & kind(X0)))) [nnf transformation 1]
37. ! [X0] : ((~patient(X0) | ~kind(X0) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | (patient(X0) & kind(X0)))) [flattening 36]
51. ! [X0] : ((~happy(X0) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | happy(X0))) [nnf transformation 8]
52. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | happy(X0))) [flattening 51]
57. ! [X0] : ((~patient(X0) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | patient(X0))) [nnf transformation 13]
58. ! [X0] : ((~patient(X0) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | patient(X0))) [flattening 57]
77. happy(X0) | patient(X0) [cnf transformation 37]
101. brave(X0) | happy(X0) [cnf transformation 52]
119. ~brave(X0) | ~patient(X0) [cnf transformation 58]
140. ~happy(susan) [cnf transformation 24]
306. ~patient(X0) | happy(X0) [resolution 119,101]
307. happy(X0) [subsumption resolution 306,77]
308. $false [resolution 307,140]
% SZS output end Proof for 6921457051562831397808604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is both brave and not humble and vice versa.
Everyone who is both not old and not calm is calm or generous and vice versa.
If paul is not wise then paul is old or not wise.
If john is humble then someone is happy.
Everyone who is not generous is both patient and rich.
Everyone who is either creative or strong is happy and vice versa.
If paul is either not brave or not creative then someone is either happy or not brave and vice versa.
If someone is not funny then lucy is old or not calm.
If fred is not patient then susan is either old or humble and vice versa.
If someone is either patient or not strong then susan is not generous or not quiet.
Everyone who is not brave or not rich is not happy.
Everyone who is both brave and not creative is either quiet or not kind.
Everyone who is either calm or not calm is either strong or quiet and vice versa.
If fred is not kind then someone is wise or not creative and vice versa.
If someone is not strong then someone is quiet and vice versa.
Everyone who is generous or not strong is quiet or not curious and vice versa.
Someone is both not generous and curious.
Someone is kind or humble.
Someone is either rich or patient.
Someone is not creative.
Mary is not generous or rich.
Someone is kind.
Someone is not wise.
Someone is not rich or rich. | Fred is calm. | contradiction | (![X]:((~tall(X)<~>~creative(X))<=>(brave(X)&~humble(X))))&
(![X]:((~old(X)&~calm(X))<=>(calm(X)|generous(X))))&
((~wise(paul))=>((old(paul)|~wise(paul))))&
((humble(john))=>(?[X]:(happy(X))))&
(![X]:(~generous(X)=>(patient(X)&rich(X))))&
(![X]:((creative(X)<~>strong(X))<=>happy(X)))&
(((~brave(paul)<~>~creative(paul)))<=>(?[X]:((happy(X)<~>~brave(X)))))&
((?[X]:(~funny(X)))=>((old(lucy)|~calm(lucy))))&
((~patient(fred))<=>((old(susan)<~>humble(susan))))&
((?[X]:((patient(X)<~>~strong(X))))=>((~generous(susan)|~quiet(susan))))&
(![X]:((~brave(X)|~rich(X))=>~happy(X)))&
(![X]:((brave(X)&~creative(X))=>(quiet(X)<~>~kind(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(strong(X)<~>quiet(X))))&
((~kind(fred))<=>(?[X]:((wise(X)|~creative(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|~strong(X))<=>(quiet(X)|~curious(X))))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((kind(X)|humble(X))))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
((~generous(mary)|rich(mary)))&
(?[X]:(kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:((~rich(X)|rich(X)))) | calm(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6391072787506160487370476
% SZS output start Proof for 6391072787506160487370476
2. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (generous(X0) | calm(X0))) [input p1]
25. calm(fred) [input hypothesis]
39. ! [X0] : (((~calm(X0) & ~old(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (calm(X0) | old(X0)))) [nnf transformation 2]
40. ! [X0] : (((~calm(X0) & ~old(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | calm(X0) | old(X0))) [flattening 39]
87. ~calm(X0) | ~calm(X0) [cnf transformation 40]
142. calm(fred) [cnf transformation 25]
148. ~calm(X0) [duplicate literal removal 87]
280. $false [subsumption resolution 142,148]
% SZS output end Proof for 6391072787506160487370476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or wise is both happy and curious.
If susan is both old and quiet then fred is either patient or not strong.
If someone is not curious then someone is old or strong.
If someone is not tall then someone is both calm and not happy and vice versa.
If alice is tall then susan is not happy or creative and vice versa.
Everyone who is both kind and funny is not happy or kind.
If lucy is creative then fred is calm or not curious.
Everyone who is both not generous and not strong is both not patient and creative.
Everyone who is old or curious is calm and vice versa.
If lucy is both not brave and strong then susan is strong.
Everyone who is tall is both curious and not creative and vice versa.
Everyone who is either not rich or rich is both not wise and old and vice versa.
Everyone who is strong or not kind is not generous and vice versa.
Everyone who is not creative is either funny or not wise and vice versa.
Everyone who is not wise is either not kind or not creative and vice versa.
Everyone who is brave is funny or tall and vice versa.
Alice is either not calm or not tall.
John is rich or not kind.
Someone is calm or brave.
Fred is generous or not quiet.
Susan is both curious and not quiet.
John is not strong.
Lucy is both not wise and not patient. | Susan is brave. | entailment | (![X]:((~strong(X)|wise(X))=>(happy(X)&curious(X))))&
(((old(susan)&quiet(susan)))=>((patient(fred)<~>~strong(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((old(X)|strong(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)&~happy(X)))))&
((tall(alice))<=>((~happy(susan)|creative(susan))))&
(![X]:((kind(X)&funny(X))=>(~happy(X)|kind(X))))&
((creative(lucy))=>((calm(fred)|~curious(fred))))&
(![X]:((~generous(X)&~strong(X))=>(~patient(X)&creative(X))))&
(![X]:((old(X)|curious(X))<=>calm(X)))&
(((~brave(lucy)&strong(lucy)))=>(strong(susan)))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~wise(X)&old(X))))&
(![X]:((strong(X)|~kind(X))<=>~generous(X)))&
(![X]:(~creative(X)<=>(funny(X)<~>~wise(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
(![X]:(brave(X)<=>(funny(X)|tall(X))))&
((~calm(alice)<~>~tall(alice)))&
((rich(john)|~kind(john)))&
(?[X]:((calm(X)|brave(X))))&
((generous(fred)|~quiet(fred)))&
((curious(susan)&~quiet(susan)))&
(~strong(john))&
((~wise(lucy)&~patient(lucy))) | brave(susan) | [
"p4",
"p8",
"p10",
"p11",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7592461663699906494936310
% SZS output start Proof for 7592461663699906494936310
5. tall(alice) <=> (creative(susan) | ~happy(susan)) [input p4]
9. ! [X0] : ((curious(X0) | old(X0)) <=> calm(X0)) [input p8]
11. ! [X0] : (tall(X0) <=> (~creative(X0) & curious(X0))) [input p10]
12. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (old(X0) & ~wise(X0))) [input p11]
16. ! [X0] : (brave(X0) <=> (tall(X0) | funny(X0))) [input p15]
17. ~calm(alice) <~> ~tall(alice) [input p16]
21. ~quiet(susan) & curious(susan) [input p20]
24. ~brave(susan) [input hypothesis]
29. curious(susan) [pure predicate removal 21]
52. (tall(alice) | (~creative(susan) & happy(susan))) & ((creative(susan) | ~happy(susan)) | ~tall(alice)) [nnf transformation 5]
53. (tall(alice) | (~creative(susan) & happy(susan))) & (creative(susan) | ~happy(susan) | ~tall(alice)) [flattening 52]
54. ! [X0] : (((curious(X0) | old(X0)) | ~calm(X0)) & (calm(X0) | (~curious(X0) & ~old(X0)))) [nnf transformation 9]
55. ! [X0] : ((curious(X0) | old(X0) | ~calm(X0)) & (calm(X0) | (~curious(X0) & ~old(X0)))) [flattening 54]
56. ! [X0] : ((tall(X0) | (creative(X0) | ~curious(X0))) & ((~creative(X0) & curious(X0)) | ~tall(X0))) [nnf transformation 11]
57. ! [X0] : ((tall(X0) | creative(X0) | ~curious(X0)) & ((~creative(X0) & curious(X0)) | ~tall(X0))) [flattening 56]
58. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 58]
62. ! [X0] : ((brave(X0) | (~tall(X0) & ~funny(X0))) & ((tall(X0) | funny(X0)) | ~brave(X0))) [nnf transformation 16]
63. ! [X0] : ((brave(X0) | (~tall(X0) & ~funny(X0))) & (tall(X0) | funny(X0) | ~brave(X0))) [flattening 62]
64. (tall(alice) | calm(alice)) & (~tall(alice) | ~calm(alice)) [nnf transformation 17]
77. tall(alice) | ~creative(susan) [cnf transformation 53]
81. ~old(X0) | calm(X0) [cnf transformation 55]
87. ~curious(X0) | creative(X0) | tall(X0) [cnf transformation 57]
90. old(X0) | rich(X0) | rich(X0) [cnf transformation 59]
91. old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 59]
106. ~tall(X0) | brave(X0) [cnf transformation 63]
107. ~tall(alice) | ~calm(alice) [cnf transformation 64]
111. curious(susan) [cnf transformation 29]
114. ~brave(susan) [cnf transformation 24]
117. old(X0) | rich(X0) [duplicate literal removal 90]
118. ~rich(X0) | old(X0) [duplicate literal removal 91]
153. 9 <=> creative(susan) [avatar definition]
155. ~creative(susan) <- (~9) [avatar component clause 153]
157. 10 <=> tall(alice) [avatar definition]
160. ~9 | 10 [avatar split clause 77,157,153]
193. old(X0) [subsumption resolution 117,118]
200. 18 <=> calm(alice) [avatar definition]
201. ~calm(alice) <- (~18) [avatar component clause 200]
204. ~18 | ~10 [avatar split clause 107,157,200]
227. calm(X0) [resolution 81,193]
228. $false <- (~18) [resolution 227,201]
229. 18 [avatar contradiction clause 228]
252. creative(susan) | tall(susan) [resolution 87,111]
254. tall(susan) <- (~9) [subsumption resolution 252,155]
255. brave(susan) <- (~9) [resolution 254,106]
257. $false <- (~9) [subsumption resolution 255,114]
258. 9 [avatar contradiction clause 257]
259. $false [avatar sat refutation 160,204,229,258]
% SZS output end Proof for 7592461663699906494936310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or creative then someone is not calm or not kind and vice versa. Everyone who is not happy or strong is either funny or not rich and vice versa. If someone is both wise and brave then fred is both humble and funny. If paul is either not kind or not wise then someone is both brave and humble. Everyone who is either happy or not funny is not quiet or tall and vice versa. If someone is both not brave and not curious then someone is wise and vice versa. Everyone who is either creative or kind is not tall. Everyone who is not curious is not happy. Everyone who is either not old or not humble is happy. If someone is old then someone is either not creative or not tall. If someone is either happy or not strong then someone is quiet. If someone is tall or not curious then paul is either not tall or generous and vice versa. Everyone who is either not kind or not funny is either brave or curious and vice versa. Everyone who is old is both brave and strong and vice versa. Everyone who is either funny or curious is either not creative or not patient. Everyone who is not curious is not humble or patient and vice versa. Someone is either old or patient. Paul is not old or strong. Someone is tall. John is both not rich and kind. Lucy is either old or quiet. Someone is not old. Someone is either humble or not curious. | Paul is not wise. | neutral | ((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((~happy(X)|strong(X))<=>(funny(X)<~>~rich(X))))&
((?[X]:((wise(X)&brave(X))))=>((humble(fred)&funny(fred))))&
(((~kind(paul)<~>~wise(paul)))=>(?[X]:((brave(X)&humble(X)))))&
(![X]:((happy(X)<~>~funny(X))<=>(~quiet(X)|tall(X))))&
((?[X]:((~brave(X)&~curious(X))))<=>(?[X]:(wise(X))))&
(![X]:((creative(X)<~>kind(X))=>~tall(X)))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:((~old(X)<~>~humble(X))=>happy(X)))&
((?[X]:(old(X)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
((?[X]:((happy(X)<~>~strong(X))))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~tall(paul)<~>generous(paul))))&
(![X]:((~kind(X)<~>~funny(X))<=>(brave(X)<~>curious(X))))&
(![X]:(old(X)<=>(brave(X)&strong(X))))&
(![X]:((funny(X)<~>curious(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~curious(X)<=>(~humble(X)|patient(X))))&
(?[X]:((old(X)<~>patient(X))))&
((~old(paul)|strong(paul)))&
(?[X]:(tall(X)))&
((~rich(john)&kind(john)))&
((old(lucy)<~>quiet(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((humble(X)<~>~curious(X)))) | ~wise(paul) | [] | null | 0 |
If alice is not generous or curious 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. If lucy is strong then someone is either not kind or not rich and vice versa. Everyone who is either not curious or rich is not creative or not brave and vice versa. Everyone who is not kind or not patient is both rich and funny. Everyone who is brave or not patient is both not funny and old. If someone is both tall and not kind then alice is not creative and vice versa. Everyone who is either not funny or not happy is either rich or not generous and vice versa. Alice is either not kind or calm. Someone is either not curious or not generous. Paul is not tall. Susan is not old or not wise. Paul is not strong. Fred is happy. Paul is either kind or not rich. Fred is not brave. | Paul is curious. | entailment | (((~generous(alice)|curious(alice)))=>(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))))&
((strong(lucy))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|~patient(X))=>(rich(X)&funny(X))))&
(![X]:((brave(X)|~patient(X))=>(~funny(X)&old(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~creative(alice)))&
(![X]:((~funny(X)<~>~happy(X))<=>(rich(X)<~>~generous(X))))&
((~kind(alice)<~>calm(alice)))&
(?[X]:((~curious(X)<~>~generous(X))))&
(~tall(paul))&
((~old(susan)|~wise(susan)))&
(~strong(paul))&
(happy(fred))&
((kind(paul)<~>~rich(paul)))&
(~brave(fred)) | curious(paul) | [
"p2",
"p3",
"p9",
"p11",
"p12",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 691509885003817290518582
% SZS output start Proof for 691509885003817290518582
3. ! [X0] : ((wise(X0) | ~generous(X0)) => (curious(X0) <~> happy(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | ~rich(X0)) => wise(X0)) [input p3]
10. ! [X0] : (old(X0) <=> (generous(X0) <~> wise(X0))) [input p9]
12. ! [X0] : ((~curious(X0) <~> rich(X0)) <=> (~brave(X0) | ~creative(X0))) [input p11]
13. ! [X0] : ((~patient(X0) | ~kind(X0)) => (funny(X0) & rich(X0))) [input p12]
14. ! [X0] : ((~patient(X0) | brave(X0)) => (old(X0) & ~funny(X0))) [input p13]
16. ! [X0] : ((~funny(X0) <~> ~happy(X0)) <=> (rich(X0) <~> ~generous(X0))) [input p15]
23. kind(paul) <~> ~rich(paul) [input p22]
25. ~curious(paul) [input hypothesis]
28. ! [X0] : ((curious(X0) <~> happy(X0)) | (~wise(X0) & generous(X0))) [ennf transformation 3]
29. ! [X0] : (wise(X0) | (funny(X0) & rich(X0))) [ennf transformation 4]
31. ! [X0] : ((funny(X0) & rich(X0)) | (patient(X0) & kind(X0))) [ennf transformation 13]
32. ! [X0] : ((old(X0) & ~funny(X0)) | (patient(X0) & ~brave(X0))) [ennf transformation 14]
37. ! [X0] : (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (~wise(X0) & generous(X0))) [nnf transformation 28]
54. ! [X0] : ((old(X0) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) & (((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | ~old(X0))) [nnf transformation 10]
59. ! [X0] : ((((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (brave(X0) & creative(X0))) & ((~brave(X0) | ~creative(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))))) [nnf transformation 12]
60. ! [X0] : ((((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (brave(X0) & creative(X0))) & (~brave(X0) | ~creative(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))))) [flattening 59]
65. ! [X0] : ((((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0))))) [nnf transformation 16]
70. (rich(paul) | ~kind(paul)) & (~rich(paul) | kind(paul)) [nnf transformation 23]
76. ~wise(X0) | curious(X0) | happy(X0) [cnf transformation 37]
80. funny(X0) | wise(X0) [cnf transformation 29]
103. ~old(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 54]
115. ~rich(X0) | curious(X0) | brave(X0) [cnf transformation 60]
116. rich(X0) | kind(X0) [cnf transformation 31]
120. ~brave(X0) | ~funny(X0) [cnf transformation 32]
122. ~brave(X0) | old(X0) [cnf transformation 32]
129. ~rich(X0) | generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 65]
144. rich(paul) | ~kind(paul) [cnf transformation 70]
146. ~curious(paul) [cnf transformation 25]
182. 9 <=> old(paul) [avatar definition]
183. old(paul) <- (9) [avatar component clause 182]
317. rich(paul) [subsumption resolution 144,116]
422. curious(paul) | brave(paul) [resolution 115,317]
425. brave(paul) [subsumption resolution 422,146]
445. old(paul) [resolution 425,122]
446. ~funny(paul) [resolution 425,120]
449. 9 [avatar split clause 445,182]
450. ~generous(paul) | ~wise(paul) <- (9) [resolution 183,103]
453. 51 <=> wise(paul) [avatar definition]
454. wise(paul) <- (51) [avatar component clause 453]
457. 52 <=> generous(paul) [avatar definition]
460. ~51 | ~52 | ~9 [avatar split clause 450,182,457,453]
499. generous(paul) | ~happy(paul) | funny(paul) [resolution 129,317]
656. wise(paul) [resolution 446,80]
659. 51 [avatar split clause 656,453]
661. 68 <=> happy(paul) [avatar definition]
662. ~happy(paul) <- (~68) [avatar component clause 661]
665. generous(paul) | ~happy(paul) [subsumption resolution 499,446]
666. ~68 | 52 [avatar split clause 665,457,661]
668. curious(paul) | happy(paul) <- (51) [resolution 454,76]
669. happy(paul) <- (51) [subsumption resolution 668,146]
670. $false <- (51, ~68) [subsumption resolution 669,662]
671. ~51 | 68 [avatar contradiction clause 670]
672. $false [avatar sat refutation 449,460,659,666,671]
% SZS output end Proof for 691509885003817290518582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is rich or patient is both not tall and strong. If fred is not humble then someone is both happy and patient. Everyone who is both not funny and not patient is both not kind and old and vice versa. Everyone who is not humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Alice is either not calm or brave. Someone is wise or not strong. Lucy is not wise or calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. | John is strong. | entailment | (![X]:((rich(X)|patient(X))=>(~tall(X)&strong(X))))&
((~humble(fred))=>(?[X]:((happy(X)&patient(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(~kind(X)&old(X))))&
(![X]:(~humble(X)=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
((~calm(alice)<~>brave(alice)))&
(?[X]:((wise(X)|~strong(X))))&
((~wise(lucy)|calm(lucy)))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X))) | strong(john) | [
"p0",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5912381594140186895391733
% SZS output start Proof for 5912381594140186895391733
1. ! [X0] : ((patient(X0) | rich(X0)) => (strong(X0) & ~tall(X0))) [input p0]
5. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p4]
9. ! [X0] : (~quiet(X0) => patient(X0)) [input p8]
11. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p10]
21. ~strong(john) [input hypothesis]
23. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 5]
24. ! [X0] : ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 1]
27. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 23]
31. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 9]
46. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 11]
47. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 46]
62. ~patient(X0) | strong(X0) [cnf transformation 24]
72. ~quiet(X0) | ~funny(X0) [cnf transformation 27]
82. quiet(X0) | patient(X0) [cnf transformation 31]
85. funny(X0) | patient(X0) [cnf transformation 47]
101. ~strong(john) [cnf transformation 21]
130. 7 <=> strong(john) [avatar definition]
132. ~strong(john) <- (~7) [avatar component clause 130]
212. ~7 [avatar split clause 101,130]
217. patient(X0) | ~funny(X0) [resolution 82,72]
218. patient(X0) [subsumption resolution 217,85]
220. strong(X0) [resolution 218,62]
221. $false <- (~7) [resolution 220,132]
224. 7 [avatar contradiction clause 221]
225. $false [avatar sat refutation 212,224]
% SZS output end Proof for 5912381594140186895391733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then someone is either curious or not curious.
Everyone who is not patient or humble is patient and vice versa.
If susan is both patient and creative then someone is both creative and not wise.
If alice is happy or not quiet then someone is rich.
If someone is happy or not creative then someone is both not wise and not patient and vice versa.
If john is old then alice is not rich.
Everyone who is rich or not calm is brave and vice versa.
Everyone who is not happy is not humble or funny and vice versa.
Everyone who is either not calm or not rich is either not rich or not creative.
If susan is either strong or creative then someone is tall or not kind.
Everyone who is both kind and humble is not funny or patient and vice versa.
If lucy is tall or not generous then someone is either curious or not patient and vice versa.
Everyone who is not humble is both not wise and not patient.
Everyone who is both not wise and not kind is not happy or tall.
Everyone who is both not tall and rich is not wise or brave.
If someone is both strong and brave then someone is both not brave and not patient.
Paul is quiet or not kind.
Someone is not old.
John is not kind or not calm.
Someone is both not quiet and not tall.
Someone is tall.
Someone is either old or rich.
Susan is both humble and kind.
Susan is rich or humble. | Alice is patient. | entailment | ((?[X]:(~wise(X)))=>(?[X]:((curious(X)<~>~curious(X)))))&
(![X]:((~patient(X)|humble(X))<=>patient(X)))&
(((patient(susan)&creative(susan)))=>(?[X]:((creative(X)&~wise(X)))))&
(((happy(alice)|~quiet(alice)))=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|~creative(X))))<=>(?[X]:((~wise(X)&~patient(X)))))&
((old(john))=>(~rich(alice)))&
(![X]:((rich(X)|~calm(X))<=>brave(X)))&
(![X]:(~happy(X)<=>(~humble(X)|funny(X))))&
(![X]:((~calm(X)<~>~rich(X))=>(~rich(X)<~>~creative(X))))&
(((strong(susan)<~>creative(susan)))=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((kind(X)&humble(X))<=>(~funny(X)|patient(X))))&
(((tall(lucy)|~generous(lucy)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:(~humble(X)=>(~wise(X)&~patient(X))))&
(![X]:((~wise(X)&~kind(X))=>(~happy(X)|tall(X))))&
(![X]:((~tall(X)&rich(X))=>(~wise(X)|brave(X))))&
((?[X]:((strong(X)&brave(X))))=>(?[X]:((~brave(X)&~patient(X)))))&
((quiet(paul)|~kind(paul)))&
(?[X]:(~old(X)))&
((~kind(john)|~calm(john)))&
(?[X]:((~quiet(X)&~tall(X))))&
(?[X]:(tall(X)))&
(?[X]:((old(X)<~>rich(X))))&
((humble(susan)&kind(susan)))&
((rich(susan)|humble(susan))) | patient(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 346911119287030083376838
% SZS output start Proof for 346911119287030083376838
2. ! [X0] : ((humble(X0) | ~patient(X0)) <=> patient(X0)) [input p1]
25. ~patient(alice) [input hypothesis]
46. ! [X0] : (((humble(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 2]
47. ! [X0] : ((humble(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & patient(X0)))) [flattening 46]
86. patient(X0) | patient(X0) [cnf transformation 47]
139. ~patient(alice) [cnf transformation 25]
142. patient(X0) [duplicate literal removal 86]
237. $false [subsumption resolution 139,142]
% SZS output end Proof for 346911119287030083376838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not happy then someone is not old.
Everyone who is strong is not rich.
If someone is either not patient or not creative then someone is generous and vice versa.
Everyone who is both not kind and curious is either not quiet or happy and vice versa.
Everyone who is not brave or funny is brave and vice versa.
Everyone who is brave or generous is not happy and vice versa.
If someone is either not patient or creative then someone is happy.
If mary is either not humble or not kind then paul is either tall or kind.
Everyone who is not creative or generous is not tall or rich and vice versa.
If someone is both not wise and not brave then someone is either humble or wise.
If someone is wise or kind then someone is either strong or not generous.
Everyone who is brave or not generous is not wise or creative.
Everyone who is both wise and quiet is wise.
If someone is either wise or not generous then someone is either not happy or rich and vice versa.
Fred is both not curious and not tall.
Someone is patient.
Someone is both strong and not generous.
Mary is either creative or not funny.
Mary is brave or not calm.
Someone is not generous or not rich.
Susan is either tall or not quiet. | Fred is not funny. | contradiction | ((?[X]:((tall(X)&~happy(X))))=>(?[X]:(~old(X))))&
(![X]:(strong(X)=>~rich(X)))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(generous(X))))&
(![X]:((~kind(X)&curious(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((~brave(X)|funny(X))<=>brave(X)))&
(![X]:((brave(X)|generous(X))<=>~happy(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:(happy(X))))&
(((~humble(mary)<~>~kind(mary)))=>((tall(paul)<~>kind(paul))))&
(![X]:((~creative(X)|generous(X))<=>(~tall(X)|rich(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((humble(X)<~>wise(X)))))&
((?[X]:((wise(X)|kind(X))))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((brave(X)|~generous(X))=>(~wise(X)|creative(X))))&
(![X]:((wise(X)&quiet(X))=>wise(X)))&
((?[X]:((wise(X)<~>~generous(X))))<=>(?[X]:((~happy(X)<~>rich(X)))))&
((~curious(fred)&~tall(fred)))&
(?[X]:(patient(X)))&
(?[X]:((strong(X)&~generous(X))))&
((creative(mary)<~>~funny(mary)))&
((brave(mary)|~calm(mary)))&
(?[X]:((~generous(X)|~rich(X))))&
((tall(susan)<~>~quiet(susan))) | ~funny(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5599799188514523792476481
% SZS output start Proof for 5599799188514523792476481
5. ! [X0] : ((funny(X0) | ~brave(X0)) <=> brave(X0)) [input p4]
22. ~funny(fred) [input hypothesis]
47. ! [X0] : (((funny(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 5]
48. ! [X0] : ((funny(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (~funny(X0) & brave(X0)))) [flattening 47]
90. brave(X0) | brave(X0) [cnf transformation 48]
92. funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 48]
133. ~funny(fred) [cnf transformation 22]
134. brave(X0) [duplicate literal removal 90]
135. ~brave(X0) | funny(X0) [duplicate literal removal 92]
262. funny(X0) [resolution 135,134]
263. $false [resolution 262,133]
% SZS output end Proof for 5599799188514523792476481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or quiet is both not happy and calm.
Everyone who is both patient and old is both curious and calm.
Everyone who is not brave or quiet is not strong and vice versa.
If fred is either not quiet or not kind then susan is either kind or not humble and vice versa.
If john is not happy then someone is both not happy and rich.
Everyone who is both not tall and quiet is both rich and not curious.
If paul is either not wise or not kind then someone is both wise and not kind and vice versa.
If someone is creative or not funny then someone is both not patient and strong and vice versa.
If susan is both not tall and not calm then someone is calm and vice versa.
Everyone who is not humble or patient is funny.
Everyone who is not rich or not quiet is not happy or not funny.
Everyone who is both strong and not tall is either kind or generous.
Everyone who is rich is not old or not quiet and vice versa.
Everyone who is either patient or happy is either brave or generous and vice versa.
Everyone who is tall is not rich or not kind.
Everyone who is not old is not curious.
Paul is either kind or happy.
Susan is not rich.
Susan is patient or not strong.
Someone is generous.
Someone is kind or quiet.
Susan is not creative or not funny.
John is not tall.
Alice is tall. | Fred is not calm. | entailment | (![X]:((~calm(X)<~>quiet(X))=>(~happy(X)&calm(X))))&
(![X]:((patient(X)&old(X))=>(curious(X)&calm(X))))&
(![X]:((~brave(X)|quiet(X))<=>~strong(X)))&
(((~quiet(fred)<~>~kind(fred)))<=>((kind(susan)<~>~humble(susan))))&
((~happy(john))=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:((~tall(X)&quiet(X))=>(rich(X)&~curious(X))))&
(((~wise(paul)<~>~kind(paul)))<=>(?[X]:((wise(X)&~kind(X)))))&
((?[X]:((creative(X)|~funny(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
(((~tall(susan)&~calm(susan)))<=>(?[X]:(calm(X))))&
(![X]:((~humble(X)|patient(X))=>funny(X)))&
(![X]:((~rich(X)|~quiet(X))=>(~happy(X)|~funny(X))))&
(![X]:((strong(X)&~tall(X))=>(kind(X)<~>generous(X))))&
(![X]:(rich(X)<=>(~old(X)|~quiet(X))))&
(![X]:((patient(X)<~>happy(X))<=>(brave(X)<~>generous(X))))&
(![X]:(tall(X)=>(~rich(X)|~kind(X))))&
(![X]:(~old(X)=>~curious(X)))&
((kind(paul)<~>happy(paul)))&
(~rich(susan))&
((patient(susan)|~strong(susan)))&
(?[X]:(generous(X)))&
(?[X]:((kind(X)|quiet(X))))&
((~creative(susan)|~funny(susan)))&
(~tall(john))&
(tall(alice)) | ~calm(fred) | [
"p5",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3885956134780482749216864
% SZS output start Proof for 3885956134780482749216864
6. ! [X0] : ((quiet(X0) & ~tall(X0)) => (~curious(X0) & rich(X0))) [input p5]
9. (~calm(susan) & ~tall(susan)) <=> ? [X0] : calm(X0) [input p8]
13. ! [X0] : (rich(X0) <=> (~quiet(X0) | ~old(X0))) [input p12]
18. ~rich(susan) [input p17]
25. calm(fred) [input hypothesis]
31. ! [X0] : ((~curious(X0) & rich(X0)) | (~quiet(X0) | tall(X0))) [ennf transformation 6]
32. ! [X0] : ((~curious(X0) & rich(X0)) | ~quiet(X0) | tall(X0)) [flattening 31]
56. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (calm(susan) | tall(susan))) [nnf transformation 9]
57. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | calm(susan) | tall(susan)) [flattening 56]
58. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | calm(susan) | tall(susan)) [rectify 57]
59. ? [X1] : calm(X1) => calm(sK4) [choice axiom]
60. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (calm(sK4) | calm(susan) | tall(susan)) [skolemisation 58,59]
62. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 13]
63. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ~rich(X0))) [flattening 62]
89. ~quiet(X0) | rich(X0) | tall(X0) [cnf transformation 32]
103. ~tall(susan) | ~calm(X0) [cnf transformation 60]
113. rich(X0) | quiet(X0) [cnf transformation 63]
126. ~rich(susan) [cnf transformation 18]
133. calm(fred) [cnf transformation 25]
229. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
230. ~calm(X0) <- (20) [avatar component clause 229]
237. 22 <=> tall(susan) [avatar definition]
239. ~tall(susan) <- (~22) [avatar component clause 237]
240. 20 | ~22 [avatar split clause 103,237,229]
279. $false <- (20) [resolution 230,133]
280. ~20 [avatar contradiction clause 279]
285. quiet(susan) [resolution 113,126]
309. rich(susan) | tall(susan) [resolution 89,285]
312. tall(susan) [subsumption resolution 309,126]
313. $false <- (~22) [subsumption resolution 312,239]
314. 22 [avatar contradiction clause 313]
316. $false [avatar sat refutation 240,280,314]
% SZS output end Proof for 3885956134780482749216864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is humble and vice versa. If john is either not patient or not kind then someone is not happy and vice versa. Everyone who is either brave or not humble is not creative or not funny. Everyone who is either not tall or not old is not wise and vice versa. If lucy is both not kind and happy then alice is not wise and vice versa. Everyone who is both rich and not tall is both not generous and not rich and vice versa. If john is either creative or not brave then john is either not brave or not patient. Everyone who is not funny or calm is patient and vice versa. If someone is not wise then someone is not funny and vice versa. If someone is both not calm and funny then someone is not humble and vice versa. Everyone who is not old is both not curious and tall. If fred is not quiet or not curious then alice is not happy. Everyone who is not curious or brave is both not creative and patient. Everyone who is not tall or not creative is not creative or calm and vice versa. Everyone who is either not strong or not generous is not happy or curious and vice versa. If someone is curious then someone is either not rich or tall and vice versa. Paul is humble. Paul is both not calm and old. John is either not strong or not calm. Mary is patient. Someone is patient or not humble. John is both funny and not quiet. Someone is humble. Fred is curious or not creative. | Fred is not curious. | neutral | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(((~patient(john)<~>~kind(john)))<=>(?[X]:(~happy(X))))&
(![X]:((brave(X)<~>~humble(X))=>(~creative(X)|~funny(X))))&
(![X]:((~tall(X)<~>~old(X))<=>~wise(X)))&
(((~kind(lucy)&happy(lucy)))<=>(~wise(alice)))&
(![X]:((rich(X)&~tall(X))<=>(~generous(X)&~rich(X))))&
(((creative(john)<~>~brave(john)))=>((~brave(john)<~>~patient(john))))&
(![X]:((~funny(X)|calm(X))<=>patient(X)))&
((?[X]:(~wise(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~old(X)=>(~curious(X)&tall(X))))&
(((~quiet(fred)|~curious(fred)))=>(~happy(alice)))&
(![X]:((~curious(X)|brave(X))=>(~creative(X)&patient(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~creative(X)|calm(X))))&
(![X]:((~strong(X)<~>~generous(X))<=>(~happy(X)|curious(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(humble(paul))&
((~calm(paul)&old(paul)))&
((~strong(john)<~>~calm(john)))&
(patient(mary))&
(?[X]:((patient(X)|~humble(X))))&
((funny(john)&~quiet(john)))&
(?[X]:(humble(X)))&
((curious(fred)|~creative(fred))) | ~curious(fred) | [] | null | 0 |
Everyone who is both not kind and not funny is both not curious and wise.
If someone is tall or kind then susan is either tall or patient and vice versa.
If someone is happy or not funny then lucy is not happy or generous and vice versa.
Everyone who is either not rich or not patient is funny and vice versa.
If john is either not tall or humble then alice is either not happy or quiet and vice versa.
Everyone who is either not kind or not brave is either calm or not funny.
Everyone who is not creative or kind is patient.
Everyone who is both strong and not old is not patient and vice versa.
If someone is not calm or not kind then john is both generous and creative and vice versa.
Everyone who is either wise or creative is both not wise and wise.
Everyone who is both not tall and not rich is both tall and not calm.
Everyone who is not patient is both not kind and kind.
Everyone who is not tall is either generous or humble.
Everyone who is either creative or calm is both not old and not creative and vice versa.
Everyone who is humble is either calm or not humble and vice versa.
If susan is either not rich or not kind then susan is not curious or not brave and vice versa.
Susan is brave or curious.
Lucy is strong.
Someone is not tall or old.
John is funny.
John is brave.
Lucy is not old or generous.
Someone is not brave.
Someone is either not calm or generous. | Lucy is creative. | entailment | (![X]:((~kind(X)&~funny(X))=>(~curious(X)&wise(X))))&
((?[X]:((tall(X)|kind(X))))<=>((tall(susan)<~>patient(susan))))&
((?[X]:((happy(X)|~funny(X))))<=>((~happy(lucy)|generous(lucy))))&
(![X]:((~rich(X)<~>~patient(X))<=>funny(X)))&
(((~tall(john)<~>humble(john)))<=>((~happy(alice)<~>quiet(alice))))&
(![X]:((~kind(X)<~>~brave(X))=>(calm(X)<~>~funny(X))))&
(![X]:((~creative(X)|kind(X))=>patient(X)))&
(![X]:((strong(X)&~old(X))<=>~patient(X)))&
((?[X]:((~calm(X)|~kind(X))))<=>((generous(john)&creative(john))))&
(![X]:((wise(X)<~>creative(X))=>(~wise(X)&wise(X))))&
(![X]:((~tall(X)&~rich(X))=>(tall(X)&~calm(X))))&
(![X]:(~patient(X)=>(~kind(X)&kind(X))))&
(![X]:(~tall(X)=>(generous(X)<~>humble(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~old(X)&~creative(X))))&
(![X]:(humble(X)<=>(calm(X)<~>~humble(X))))&
(((~rich(susan)<~>~kind(susan)))<=>((~curious(susan)|~brave(susan))))&
((brave(susan)|curious(susan)))&
(strong(lucy))&
(?[X]:((~tall(X)|old(X))))&
(funny(john))&
(brave(john))&
((~old(lucy)|generous(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~calm(X)<~>generous(X)))) | creative(lucy) | [
"p6",
"p7",
"p11",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3880185820861999096790524
% SZS output start Proof for 3880185820861999096790524
7. ! [X0] : ((kind(X0) | ~creative(X0)) => patient(X0)) [input p6]
8. ! [X0] : ((~old(X0) & strong(X0)) <=> ~patient(X0)) [input p7]
12. ! [X0] : (~patient(X0) => (kind(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((creative(X0) <~> calm(X0)) <=> (~creative(X0) & ~old(X0))) [input p13]
15. ! [X0] : (humble(X0) <=> (calm(X0) <~> ~humble(X0))) [input p14]
18. strong(lucy) [input p17]
25. ~creative(lucy) [input hypothesis]
29. ! [X0] : (patient(X0) | (~kind(X0) & creative(X0))) [ennf transformation 7]
33. ! [X0] : ((kind(X0) & ~kind(X0)) | patient(X0)) [ennf transformation 12]
47. ! [X0] : (((~old(X0) & strong(X0)) | patient(X0)) & (~patient(X0) | (old(X0) | ~strong(X0)))) [nnf transformation 8]
48. ! [X0] : (((~old(X0) & strong(X0)) | patient(X0)) & (~patient(X0) | old(X0) | ~strong(X0))) [flattening 47]
56. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (creative(X0) | old(X0))) & ((~creative(X0) & ~old(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [nnf transformation 14]
57. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | creative(X0) | old(X0)) & ((~creative(X0) & ~old(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [flattening 56]
58. ! [X0] : ((humble(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0)))) & (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | ~humble(X0))) [nnf transformation 15]
97. ~kind(X0) | patient(X0) [cnf transformation 29]
98. ~strong(X0) | old(X0) | ~patient(X0) [cnf transformation 48]
113. kind(X0) | patient(X0) [cnf transformation 33]
117. ~old(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
122. ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 58]
125. humble(X0) | calm(X0) | humble(X0) [cnf transformation 58]
133. strong(lucy) [cnf transformation 18]
141. ~creative(lucy) [cnf transformation 25]
142. ~humble(X0) | calm(X0) [duplicate literal removal 122]
143. calm(X0) | humble(X0) [duplicate literal removal 125]
249. 22 <=> ! [X1] : calm(X1) [avatar definition]
250. calm(X1) <- (22) [avatar component clause 249]
254. patient(X0) [subsumption resolution 113,97]
255. calm(X0) [subsumption resolution 142,143]
256. 22 [avatar split clause 255,249]
290. 29 <=> old(lucy) [avatar definition]
291. old(lucy) <- (29) [avatar component clause 290]
330. old(lucy) | ~patient(lucy) [resolution 98,133]
335. old(lucy) [subsumption resolution 330,254]
336. 29 [avatar split clause 335,290]
343. creative(lucy) | ~calm(lucy) <- (29) [resolution 117,291]
344. ~calm(lucy) <- (29) [subsumption resolution 343,141]
345. $false <- (22, 29) [subsumption resolution 344,250]
346. ~22 | ~29 [avatar contradiction clause 345]
347. $false [avatar sat refutation 256,336,346]
% SZS output end Proof for 3880185820861999096790524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or generous then paul is not tall or tall. If someone is not calm or calm then lucy is either tall or not curious. Everyone who is both curious and happy is both not kind and not patient and vice versa. Everyone who is either strong or funny is either not creative or not patient. Everyone who is funny or humble is both not quiet and not funny. Everyone who is both quiet and not creative is not wise and vice versa. Everyone who is strong is not calm or not rich and vice versa. If someone is both not funny and humble then someone is not strong or not tall and vice versa. If someone is either not humble or not patient then someone is old. Everyone who is not brave is not calm and vice versa. Everyone who is not wise or curious is either not patient or humble. If someone is curious then someone is either generous or patient and vice versa. If paul is both generous and not kind then lucy is patient or not quiet. Everyone who is both not old and not creative is both not patient and not strong and vice versa. If someone is both wise and humble then alice is strong or not wise. Everyone who is both not humble and old is not curious. Someone is not happy. Fred is not happy or generous. Someone is both rich and not strong. Someone is both not funny and wise. Someone is either funny or not tall. Someone is quiet. Paul is both patient and not quiet. Alice is not humble. | Alice is not kind. | neutral | ((?[X]:((~strong(X)|generous(X))))=>((~tall(paul)|tall(paul))))&
((?[X]:((~calm(X)|calm(X))))=>((tall(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&happy(X))<=>(~kind(X)&~patient(X))))&
(![X]:((strong(X)<~>funny(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((funny(X)|humble(X))=>(~quiet(X)&~funny(X))))&
(![X]:((quiet(X)&~creative(X))<=>~wise(X)))&
(![X]:(strong(X)<=>(~calm(X)|~rich(X))))&
((?[X]:((~funny(X)&humble(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~brave(X)<=>~calm(X)))&
(![X]:((~wise(X)|curious(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(curious(X)))<=>(?[X]:((generous(X)<~>patient(X)))))&
(((generous(paul)&~kind(paul)))=>((patient(lucy)|~quiet(lucy))))&
(![X]:((~old(X)&~creative(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((wise(X)&humble(X))))=>((strong(alice)|~wise(alice))))&
(![X]:((~humble(X)&old(X))=>~curious(X)))&
(?[X]:(~happy(X)))&
((~happy(fred)|generous(fred)))&
(?[X]:((rich(X)&~strong(X))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:(quiet(X)))&
((patient(paul)&~quiet(paul)))&
(~humble(alice)) | ~kind(alice) | [] | null | 0 |
Everyone who is creative is not old or quiet and vice versa.
Everyone who is either wise or not wise is kind or not funny.
If mary is funny or wise then fred is both humble and patient.
If someone is not humble then fred is either wise or patient.
If someone is not generous or old then fred is either brave or not kind and vice versa.
Everyone who is not humble or calm is either not funny or not creative.
If someone is both funny and not strong then susan is either not humble or curious.
Everyone who is funny is not quiet or not tall and vice versa.
Everyone who is both not kind and funny is either not old or quiet.
Everyone who is quiet is either not funny or not rich.
If someone is not strong or not curious then someone is either kind or not quiet and vice versa.
Everyone who is calm or quiet is both not patient and patient and vice versa.
If lucy is either curious or not strong then fred is not creative and vice versa.
Everyone who is calm or tall is old or generous.
If alice is both not patient and not brave then someone is either funny or not strong.
If someone is not patient or patient then someone is either strong or not tall.
Someone is either happy or old.
Mary is patient.
Susan is not happy or not brave.
John is both strong and rich.
Someone is either quiet or not generous.
Susan is both brave and not quiet.
Susan is both not old and rich. | Susan is funny. | entailment | (![X]:(creative(X)<=>(~old(X)|quiet(X))))&
(![X]:((wise(X)<~>~wise(X))=>(kind(X)|~funny(X))))&
(((funny(mary)|wise(mary)))=>((humble(fred)&patient(fred))))&
((?[X]:(~humble(X)))=>((wise(fred)<~>patient(fred))))&
((?[X]:((~generous(X)|old(X))))<=>((brave(fred)<~>~kind(fred))))&
(![X]:((~humble(X)|calm(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~humble(susan)<~>curious(susan))))&
(![X]:(funny(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((~kind(X)&funny(X))=>(~old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&patient(X))))&
(((curious(lucy)<~>~strong(lucy)))<=>(~creative(fred)))&
(![X]:((calm(X)|tall(X))=>(old(X)|generous(X))))&
(((~patient(alice)&~brave(alice)))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|patient(X))))=>(?[X]:((strong(X)<~>~tall(X)))))&
(?[X]:((happy(X)<~>old(X))))&
(patient(mary))&
((~happy(susan)|~brave(susan)))&
((strong(john)&rich(john)))&
(?[X]:((quiet(X)<~>~generous(X))))&
((brave(susan)&~quiet(susan)))&
((~old(susan)&rich(susan))) | funny(susan) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5966092825219194244434592
% SZS output start Proof for 5966092825219194244434592
8. ! [X0] : (funny(X0) <=> (~tall(X0) | ~quiet(X0))) [input p7]
12. ! [X0] : ((quiet(X0) | calm(X0)) <=> (patient(X0) & ~patient(X0))) [input p11]
24. ~funny(susan) [input hypothesis]
51. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ~funny(X0))) [flattening 51]
60. ! [X0] : (((quiet(X0) | calm(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 12]
61. ! [X0] : ((quiet(X0) | calm(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 60]
100. funny(X0) | quiet(X0) [cnf transformation 52]
113. ~patient(X0) | ~quiet(X0) [cnf transformation 61]
115. patient(X0) | ~quiet(X0) [cnf transformation 61]
141. ~funny(susan) [cnf transformation 24]
250. ~quiet(X0) [subsumption resolution 113,115]
327. quiet(susan) [resolution 100,141]
330. $false [subsumption resolution 327,250]
% SZS output end Proof for 5966092825219194244434592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not tall and not generous and vice versa.
If paul is strong or humble then someone is tall or not generous and vice versa.
Everyone who is either not happy or generous is both strong and old.
Everyone who is both strong and tall is both happy and calm and vice versa.
Everyone who is not kind is either strong or not rich and vice versa.
Everyone who is either rich or strong is both patient and not funny and vice versa.
If alice is generous then someone is either generous or not wise.
If mary is calm or not happy then someone is creative or not generous and vice versa.
If lucy is both quiet and kind then john is not old.
Everyone who is generous or not humble is strong or not humble.
Everyone who is either kind or not kind is both generous and not patient.
If someone is both not funny and not brave then someone is either generous or not kind and vice versa.
Everyone who is not kind or kind is both not funny and rich.
If someone is generous or not rich then someone is not calm or not rich.
Everyone who is both calm and brave is not calm or humble.
Alice is either not strong or not kind.
Someone is not creative or funny.
Fred is either curious or old.
Someone is not wise or not humble.
Someone is calm or not patient.
Lucy is creative or not strong. | Alice is not kind. | entailment | (![X]:(~generous(X)<=>(~tall(X)&~generous(X))))&
(((strong(paul)|humble(paul)))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~happy(X)<~>generous(X))=>(strong(X)&old(X))))&
(![X]:((strong(X)&tall(X))<=>(happy(X)&calm(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(![X]:((kind(X)<~>~kind(X))=>(generous(X)&~patient(X))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~kind(X)|kind(X))=>(~funny(X)&rich(X))))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((calm(X)&brave(X))=>(~calm(X)|humble(X))))&
((~strong(alice)<~>~kind(alice)))&
(?[X]:((~creative(X)|funny(X))))&
((curious(fred)<~>old(fred)))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((calm(X)|~patient(X))))&
((creative(lucy)|~strong(lucy))) | ~kind(alice) | [
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4598110128855360509249641
% SZS output start Proof for 4598110128855360509249641
6. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (~funny(X0) & patient(X0))) [input p5]
11. ! [X0] : ((kind(X0) <~> ~kind(X0)) => (~patient(X0) & generous(X0))) [input p10]
13. ! [X0] : ((kind(X0) | ~kind(X0)) => (rich(X0) & ~funny(X0))) [input p12]
16. ~strong(alice) <~> ~kind(alice) [input p15]
22. kind(alice) [input hypothesis]
30. ! [X0] : ((~patient(X0) & generous(X0)) | (kind(X0) <=> ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((rich(X0) & ~funny(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 13]
46. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [flattening 46]
56. ! [X0] : ((~patient(X0) & generous(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
65. (kind(alice) | strong(alice)) & (~kind(alice) | ~strong(alice)) [nnf transformation 16]
92. ~rich(X0) | strong(X0) | patient(X0) [cnf transformation 47]
108. ~patient(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
109. ~patient(X0) | kind(X0) | kind(X0) [cnf transformation 56]
118. rich(X0) | kind(X0) [cnf transformation 31]
119. ~kind(X0) | rich(X0) [cnf transformation 31]
123. ~kind(alice) | ~strong(alice) [cnf transformation 65]
131. kind(alice) [cnf transformation 22]
135. ~patient(X0) | ~kind(X0) [duplicate literal removal 108]
136. ~patient(X0) | kind(X0) [duplicate literal removal 109]
200. ~patient(X0) [subsumption resolution 135,136]
231. rich(X0) [subsumption resolution 118,119]
243. 23 <=> strong(alice) [avatar definition]
244. ~strong(alice) <- (~23) [avatar component clause 243]
247. 24 <=> kind(alice) [avatar definition]
251. ~23 | ~24 [avatar split clause 123,247,243]
281. 24 [avatar split clause 131,247]
322. strong(X0) | patient(X0) [resolution 92,231]
323. strong(X0) [subsumption resolution 322,200]
328. $false <- (~23) [resolution 323,244]
331. 23 [avatar contradiction clause 328]
333. $false [avatar sat refutation 251,281,331]
% SZS output end Proof for 4598110128855360509249641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or old is rich.
Everyone who is either calm or wise is either quiet or not wise.
Everyone who is both not rich and happy is both old and happy.
Everyone who is strong is humble or funny and vice versa.
Everyone who is not brave is old.
If lucy is either kind or not strong then someone is happy or not creative.
Everyone who is both not happy and not tall is both not tall and funny and vice versa.
If alice is either creative or not humble then someone is both not tall and not brave and vice versa.
Everyone who is both not calm and not humble is happy and vice versa.
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.
Paul is both quiet and calm.
Paul is not generous or not wise.
Fred is both brave and generous.
Fred is both patient and funny.
Someone is humble or not funny.
Fred is either creative or not kind.
John is kind. | Alice is patient. | neutral | (![X]:((~rich(X)|old(X))=>rich(X)))&
(![X]:((calm(X)<~>wise(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((~rich(X)&happy(X))=>(old(X)&happy(X))))&
(![X]:(strong(X)<=>(humble(X)|funny(X))))&
(![X]:(~brave(X)=>old(X)))&
(((kind(lucy)<~>~strong(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((~happy(X)&~tall(X))<=>(~tall(X)&funny(X))))&
(((creative(alice)<~>~humble(alice)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~calm(X)&~humble(X))<=>happy(X)))&
((?[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)))&
((brave(fred)&generous(fred)))&
((patient(fred)&funny(fred)))&
(?[X]:((humble(X)|~funny(X))))&
((creative(fred)<~>~kind(fred)))&
(kind(john)) | patient(alice) | [] | null | 0 |
If someone is both rich and not generous then someone is wise and vice versa. If alice is both brave and not creative then john is calm. Everyone who is both not old and old is both humble and tall. If lucy is generous or not calm then someone is both strong and rich. Everyone who is both patient and curious is either not calm or rich. Everyone who is not quiet or not curious is either quiet or tall. Everyone who is both not old and creative is not strong and vice versa. Everyone who is both not wise and generous is patient. If paul is not patient or old then someone is curious. Everyone who is not calm or not tall is kind. If someone is both brave and tall then someone is not brave. Everyone who is generous is both not old and happy. Everyone who is both curious and not old is strong and vice versa. If paul is strong then someone is either not brave or not kind and vice versa. If susan is happy or not kind then someone is either kind or not old and vice versa. If someone is both not curious and not happy then someone is wise. John is patient or funny. Someone is not humble or curious. Lucy is not curious or tall. Someone is both brave and not patient. Someone is both not patient and not kind. Someone is not creative. Paul is either not calm or not curious. Someone is not calm. | Paul is not curious. | neutral | ((?[X]:((rich(X)&~generous(X))))<=>(?[X]:(wise(X))))&
(((brave(alice)&~creative(alice)))=>(calm(john)))&
(![X]:((~old(X)&old(X))=>(humble(X)&tall(X))))&
(((generous(lucy)|~calm(lucy)))=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((patient(X)&curious(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)|~curious(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~old(X)&creative(X))<=>~strong(X)))&
(![X]:((~wise(X)&generous(X))=>patient(X)))&
(((~patient(paul)|old(paul)))=>(?[X]:(curious(X))))&
(![X]:((~calm(X)|~tall(X))=>kind(X)))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:(~brave(X))))&
(![X]:(generous(X)=>(~old(X)&happy(X))))&
(![X]:((curious(X)&~old(X))<=>strong(X)))&
((strong(paul))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((happy(susan)|~kind(susan)))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~curious(X)&~happy(X))))=>(?[X]:(wise(X))))&
((patient(john)|funny(john)))&
(?[X]:((~humble(X)|curious(X))))&
((~curious(lucy)|tall(lucy)))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((~patient(X)&~kind(X))))&
(?[X]:(~creative(X)))&
((~calm(paul)<~>~curious(paul)))&
(?[X]:(~calm(X))) | ~curious(paul) | [] | null | 0 |
If someone is either not kind or generous then paul is not strong. Everyone who is wise is not wise or not rich and vice versa. Everyone who is not curious is both quiet and not tall and vice versa. Everyone who is both not funny and not wise is wise or not curious. If someone is not funny or kind then someone is either not strong or quiet and vice versa. Everyone who is both not generous and not patient is either brave or not humble. Everyone who is both not patient and not calm is wise or not curious and vice versa. If lucy is either not generous or not wise then someone is not generous or funny and vice versa. Everyone who is both not strong and not curious is not creative or not old. If john is both not strong and kind then susan is either not humble or not creative. If someone is calm then someone is not humble or rich and vice versa. If someone is either brave or not rich then fred is either not tall or wise. If someone is not happy then someone is tall or not calm. Everyone who is not happy is either not happy or not calm. If john is brave or funny then someone is either not patient or generous and vice versa. Everyone who is strong is calm or tall and vice versa. Paul is either not rich or not kind. Lucy is kind or calm. John is both not quiet and wise. Susan is wise. Someone is either not old or humble. Someone is not rich or funny. | Lucy is not tall. | neutral | ((?[X]:((~kind(X)<~>generous(X))))=>(~strong(paul)))&
(![X]:(wise(X)<=>(~wise(X)|~rich(X))))&
(![X]:(~curious(X)<=>(quiet(X)&~tall(X))))&
(![X]:((~funny(X)&~wise(X))=>(wise(X)|~curious(X))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:((~generous(X)&~patient(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~patient(X)&~calm(X))<=>(wise(X)|~curious(X))))&
(((~generous(lucy)<~>~wise(lucy)))<=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:((~strong(X)&~curious(X))=>(~creative(X)|~old(X))))&
(((~strong(john)&kind(john)))=>((~humble(susan)<~>~creative(susan))))&
((?[X]:(calm(X)))<=>(?[X]:((~humble(X)|rich(X)))))&
((?[X]:((brave(X)<~>~rich(X))))=>((~tall(fred)<~>wise(fred))))&
((?[X]:(~happy(X)))=>(?[X]:((tall(X)|~calm(X)))))&
(![X]:(~happy(X)=>(~happy(X)<~>~calm(X))))&
(((brave(john)|funny(john)))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:(strong(X)<=>(calm(X)|tall(X))))&
((~rich(paul)<~>~kind(paul)))&
((kind(lucy)|calm(lucy)))&
((~quiet(john)&wise(john)))&
(wise(susan))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((~rich(X)|funny(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is both generous and not curious is rich and vice versa.
If someone is either kind or not strong then fred is either not strong or not generous.
Everyone who is old or patient is calm or not old.
Everyone who is both happy and not calm is both not funny and not patient and vice versa.
If someone is rich or not brave then someone is both calm and strong.
If lucy is either not wise or old then someone is either patient or not strong and vice versa.
If susan is humble then someone is not brave or old and vice versa.
Everyone who is not happy is either not rich or not brave and vice versa.
Everyone who is calm or not creative is both generous and not patient and vice versa.
Everyone who is patient is either not old or brave.
Everyone who is not calm is both generous and rich and vice versa.
Everyone who is strong is not patient and vice versa.
If someone is either quiet or not quiet then fred is not humble and vice versa.
If john is either kind or funny then someone is both not generous and not strong.
Everyone who is not strong is quiet or wise.
Paul is both not strong and quiet.
Someone is not curious or not humble.
Mary is not patient or not quiet.
Someone is quiet.
Someone is not strong.
Someone is strong.
Fred is not strong or not calm. | Fred is not old. | entailment | (![X]:((generous(X)&~curious(X))<=>rich(X)))&
((?[X]:((kind(X)<~>~strong(X))))=>((~strong(fred)<~>~generous(fred))))&
(![X]:((old(X)|patient(X))=>(calm(X)|~old(X))))&
(![X]:((happy(X)&~calm(X))<=>(~funny(X)&~patient(X))))&
((?[X]:((rich(X)|~brave(X))))=>(?[X]:((calm(X)&strong(X)))))&
(((~wise(lucy)<~>old(lucy)))<=>(?[X]:((patient(X)<~>~strong(X)))))&
((humble(susan))<=>(?[X]:((~brave(X)|old(X)))))&
(![X]:(~happy(X)<=>(~rich(X)<~>~brave(X))))&
(![X]:((calm(X)|~creative(X))<=>(generous(X)&~patient(X))))&
(![X]:(patient(X)=>(~old(X)<~>brave(X))))&
(![X]:(~calm(X)<=>(generous(X)&rich(X))))&
(![X]:(strong(X)<=>~patient(X)))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(~humble(fred)))&
(((kind(john)<~>funny(john)))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:(~strong(X)=>(quiet(X)|wise(X))))&
((~strong(paul)&quiet(paul)))&
(?[X]:((~curious(X)|~humble(X))))&
((~patient(mary)|~quiet(mary)))&
(?[X]:(quiet(X)))&
(?[X]:(~strong(X)))&
(?[X]:(strong(X)))&
((~strong(fred)|~calm(fred))) | ~old(fred) | [
"p2",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 444734358029789943536042
% SZS output start Proof for 444734358029789943536042
3. ! [X0] : ((patient(X0) | old(X0)) => (~old(X0) | calm(X0))) [input p2]
9. ! [X0] : ((~creative(X0) | calm(X0)) <=> (~patient(X0) & generous(X0))) [input p8]
12. ! [X0] : (strong(X0) <=> ~patient(X0)) [input p11]
22. ~calm(fred) | ~strong(fred) [input p21]
23. old(fred) [input hypothesis]
26. ! [X0] : ((~old(X0) | calm(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 3]
27. ! [X0] : (~old(X0) | calm(X0) | (~patient(X0) & ~old(X0))) [flattening 26]
50. ! [X0] : (((~creative(X0) | calm(X0)) | (patient(X0) | ~generous(X0))) & ((~patient(X0) & generous(X0)) | (creative(X0) & ~calm(X0)))) [nnf transformation 9]
51. ! [X0] : ((~creative(X0) | calm(X0) | patient(X0) | ~generous(X0)) & ((~patient(X0) & generous(X0)) | (creative(X0) & ~calm(X0)))) [flattening 50]
55. ! [X0] : ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))) [nnf transformation 12]
78. ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 27]
105. ~calm(X0) | ~patient(X0) [cnf transformation 51]
114. strong(X0) | patient(X0) [cnf transformation 55]
131. ~calm(fred) | ~strong(fred) [cnf transformation 22]
132. old(fred) [cnf transformation 23]
135. ~old(X0) | calm(X0) [duplicate literal removal 78]
140. 2 <=> strong(fred) [avatar definition]
141. ~strong(fred) <- (~2) [avatar component clause 140]
173. 9 <=> ! [X0] : (patient(X0) | strong(X0)) [avatar definition]
174. patient(X0) | strong(X0) <- (9) [avatar component clause 173]
222. 9 [avatar split clause 114,173]
273. 29 <=> calm(fred) [avatar definition]
274. calm(fred) <- (29) [avatar component clause 273]
276. ~2 | ~29 [avatar split clause 131,273,140]
293. calm(fred) [resolution 135,132]
296. 29 [avatar split clause 293,273]
297. ~patient(fred) <- (29) [resolution 274,105]
308. strong(fred) <- (9, 29) [resolution 174,297]
311. $false <- (~2, 9, 29) [subsumption resolution 308,141]
312. 2 | ~9 | ~29 [avatar contradiction clause 311]
315. $false [avatar sat refutation 222,276,296,312]
% SZS output end Proof for 444734358029789943536042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and happy is kind and vice versa.
If lucy is quiet or calm then john is creative or not generous.
If alice is both strong and kind then mary is not calm or generous.
If mary is either creative or not patient then someone is either strong or quiet.
Everyone who is strong or wise is either quiet or happy and vice versa.
If someone is not old or not brave then someone is either not kind or not happy.
Everyone who is old or not kind is not generous.
If john is both not old and creative then someone is either kind or generous and vice versa.
Everyone who is not creative or wise is either old or not kind and vice versa.
Everyone who is both not brave and not creative is either quiet or wise.
Everyone who is either not humble or not happy is either not kind or creative and vice versa.
If someone is not generous or humble then someone is not generous and vice versa.
If someone is strong then someone is not wise or humble and vice versa.
If someone is both not calm and not humble then someone is calm or wise and vice versa.
If alice is either patient or funny then susan is patient and vice versa.
Everyone who is both not old and happy is both not wise and quiet.
Someone is calm or brave.
Someone is curious.
Someone is not rich or not brave.
Paul is brave.
Mary is curious.
Someone is both calm and funny. | John is not humble. | entailment | (![X]:((~kind(X)&happy(X))<=>kind(X)))&
(((quiet(lucy)|calm(lucy)))=>((creative(john)|~generous(john))))&
(((strong(alice)&kind(alice)))=>((~calm(mary)|generous(mary))))&
(((creative(mary)<~>~patient(mary)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((strong(X)|wise(X))<=>(quiet(X)<~>happy(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:((old(X)|~kind(X))=>~generous(X)))&
(((~old(john)&creative(john)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((~creative(X)|wise(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~brave(X)&~creative(X))=>(quiet(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~kind(X)<~>creative(X))))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((calm(X)|wise(X)))))&
(((patient(alice)<~>funny(alice)))<=>(patient(susan)))&
(![X]:((~old(X)&happy(X))=>(~wise(X)&quiet(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(brave(paul))&
(curious(mary))&
(?[X]:((calm(X)&funny(X)))) | ~humble(john) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1789191720289450524649555
% SZS output start Proof for 1789191720289450524649555
1. ! [X0] : ((happy(X0) & ~kind(X0)) <=> kind(X0)) [input p0]
6. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X0] : (~kind(X0) <~> ~happy(X0)) [input p5]
9. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (old(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((~humble(X0) <~> ~happy(X0)) <=> (~kind(X0) <~> creative(X0))) [input p10]
23. humble(john) [input hypothesis]
24. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [rectify 6]
31. ? [X0] : ~old(X0) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [pure predicate removal 24]
40. ? [X1] : (~kind(X1) <~> ~happy(X1)) | ! [X0] : old(X0) [ennf transformation 31]
44. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) | kind(X0)))) [nnf transformation 1]
45. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | ~happy(X0) | kind(X0))) [flattening 44]
51. ? [X1] : ((happy(X1) | kind(X1)) & (~happy(X1) | ~kind(X1))) | ! [X0] : old(X0) [nnf transformation 40]
52. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ! [X1] : old(X1) [rectify 51]
53. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) => ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) [choice axiom]
54. ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) | ! [X1] : old(X1) [skolemisation 52,53]
60. ! [X0] : (((wise(X0) | ~creative(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 9]
61. ! [X0] : ((wise(X0) | ~creative(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [flattening 60]
62. ! [X0] : ((((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0))))) [nnf transformation 11]
81. kind(X0) | ~happy(X0) | kind(X0) [cnf transformation 45]
82. ~kind(X0) | ~kind(X0) [cnf transformation 45]
98. happy(sK1) | kind(sK1) | old(X1) [cnf transformation 54]
109. kind(X0) | ~old(X0) | creative(X0) [cnf transformation 61]
116. ~creative(X0) | kind(X0) | ~humble(X0) | happy(X0) [cnf transformation 62]
140. humble(john) [cnf transformation 23]
141. kind(X0) | ~happy(X0) [duplicate literal removal 81]
142. ~kind(X0) [duplicate literal removal 82]
143. ~happy(X0) [subsumption resolution 141,142]
185. kind(sK1) | old(X1) [subsumption resolution 98,143]
186. old(X1) [subsumption resolution 185,142]
190. ~old(X0) | creative(X0) [subsumption resolution 109,142]
191. creative(X0) [subsumption resolution 190,186]
192. kind(X0) | ~humble(X0) | happy(X0) [subsumption resolution 116,191]
193. ~humble(X0) | happy(X0) [subsumption resolution 192,142]
194. ~humble(X0) [subsumption resolution 193,143]
230. $false [subsumption resolution 140,194]
% SZS output end Proof for 1789191720289450524649555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or curious then lucy is not creative or curious. If someone is both not rich and not quiet then john is brave and vice versa. Everyone who is strong or not creative is brave. Everyone who is both not brave and old is either not kind or quiet and vice versa. Everyone who is either not rich or not happy is not brave or tall and vice versa. If someone is not humble or not calm then someone is both brave and strong and vice versa. Everyone who is not quiet or creative is not strong or not patient. Everyone who is both not creative and not curious is either creative or not funny and vice versa. If susan is either not happy or not old then john is either not rich or not old. If alice is both not wise and curious then someone is either creative or wise. If paul is not strong or not calm then someone is kind or old. Everyone who is not rich or kind is either old or wise. If susan is not funny then someone is rich and vice versa. If someone is both not quiet and kind then someone is not brave and vice versa. If susan is wise or quiet then susan is not brave or not wise and vice versa. Everyone who is either wise or rich is creative or not generous. Paul is not calm or not kind. Someone is not brave or not rich. Lucy is not patient or not brave. Susan is calm. Fred is not strong or calm. Paul is not tall. Paul is both not wise and not tall. Someone is patient or not curious. | Paul is not calm. | neutral | ((?[X]:((~old(X)|curious(X))))=>((~creative(lucy)|curious(lucy))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(brave(john)))&
(![X]:((strong(X)|~creative(X))=>brave(X)))&
(![X]:((~brave(X)&old(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(~brave(X)|tall(X))))&
((?[X]:((~humble(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((~quiet(X)|creative(X))=>(~strong(X)|~patient(X))))&
(![X]:((~creative(X)&~curious(X))<=>(creative(X)<~>~funny(X))))&
(((~happy(susan)<~>~old(susan)))=>((~rich(john)<~>~old(john))))&
(((~wise(alice)&curious(alice)))=>(?[X]:((creative(X)<~>wise(X)))))&
(((~strong(paul)|~calm(paul)))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((~rich(X)|kind(X))=>(old(X)<~>wise(X))))&
((~funny(susan))<=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:(~brave(X))))&
(((wise(susan)|quiet(susan)))<=>((~brave(susan)|~wise(susan))))&
(![X]:((wise(X)<~>rich(X))=>(creative(X)|~generous(X))))&
((~calm(paul)|~kind(paul)))&
(?[X]:((~brave(X)|~rich(X))))&
((~patient(lucy)|~brave(lucy)))&
(calm(susan))&
((~strong(fred)|calm(fred)))&
(~tall(paul))&
((~wise(paul)&~tall(paul)))&
(?[X]:((patient(X)|~curious(X)))) | ~calm(paul) | [] | null | 0 |
If susan is old then someone is both happy and patient.
Everyone who is both not funny and not patient is both not kind and old and vice versa.
Everyone who is not humble is both funny and curious.
Everyone who is not generous or funny is both not creative and not quiet.
Everyone who is brave or curious is not humble or not tall and vice versa.
Everyone who is not patient is old or happy.
If john is strong or not brave then someone is either not happy or not strong.
Everyone who is not quiet is patient.
If someone is curious then alice is both creative and generous.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
Paul is either not strong or not calm.
John is either funny or brave.
Mary is both not calm and not rich.
Paul is either not wise or calm. | Alice is strong. | contradiction | ((old(susan))=>(?[X]:((happy(X)&patient(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(~kind(X)&old(X))))&
(![X]:(~humble(X)=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
((~strong(paul)<~>~calm(paul)))&
((funny(john)<~>brave(john)))&
((~calm(mary)&~rich(mary)))&
((~wise(paul)<~>calm(paul))) | strong(alice) | [
"p3",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5968758150982626910740921
% SZS output start Proof for 5968758150982626910740921
4. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p3]
10. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p9]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
20. strong(alice) [input hypothesis]
22. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 4]
25. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 22]
44. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 10]
45. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 44]
51. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
52. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~wise(X0) | ~creative(X0))) [flattening 51]
65. ~creative(X0) | ~funny(X0) [cnf transformation 25]
78. ~wise(X0) | funny(X0) [cnf transformation 45]
89. ~strong(X0) | creative(X0) [cnf transformation 52]
90. wise(X0) | funny(X0) [cnf transformation 52]
108. strong(alice) [cnf transformation 20]
147. 9 <=> creative(alice) [avatar definition]
149. creative(alice) <- (9) [avatar component clause 147]
180. funny(X0) [subsumption resolution 90,78]
208. creative(alice) [resolution 89,108]
211. 9 [avatar split clause 208,147]
212. ~funny(alice) <- (9) [resolution 149,65]
213. $false <- (9) [subsumption resolution 212,180]
214. ~9 [avatar contradiction clause 213]
215. $false [avatar sat refutation 211,214]
% SZS output end Proof for 5968758150982626910740921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is kind or curious. If someone is generous or not rich then someone is both not generous and not humble and vice versa. If someone is either calm or not quiet then someone is not humble. If lucy is both not brave and not curious then someone is not calm or not patient and vice versa. Everyone who is both generous and quiet is not calm and vice versa. If susan is either not tall or not creative then susan is rich and vice versa. If someone is not curious or not strong then susan is either not old or creative. Everyone who is either brave or wise is either not rich or curious. Everyone who is both calm and curious is not curious or happy and vice versa. If paul is calm or not wise then susan is rich and vice versa. Everyone who is brave is wise. If fred is both strong and patient then fred is both old and not happy. If someone is either funny or not happy then someone is both not creative and funny. If fred is either brave or not calm then fred is not generous or happy. Everyone who is happy or not quiet is either not strong or rich. Everyone who is either generous or not curious is not funny and vice versa. Someone is creative. Someone is funny. Alice is wise or not patient. Someone is either not kind or brave. Fred is funny or patient. Someone is both not brave and tall. Alice is both not quiet and kind. Fred is humble or not patient. | Fred is not happy. | contradiction | (![X]:(humble(X)=>(kind(X)|curious(X))))&
((?[X]:((generous(X)|~rich(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
((?[X]:((calm(X)<~>~quiet(X))))=>(?[X]:(~humble(X))))&
(((~brave(lucy)&~curious(lucy)))<=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((generous(X)&quiet(X))<=>~calm(X)))&
(((~tall(susan)<~>~creative(susan)))<=>(rich(susan)))&
((?[X]:((~curious(X)|~strong(X))))=>((~old(susan)<~>creative(susan))))&
(![X]:((brave(X)<~>wise(X))=>(~rich(X)<~>curious(X))))&
(![X]:((calm(X)&curious(X))<=>(~curious(X)|happy(X))))&
(((calm(paul)|~wise(paul)))<=>(rich(susan)))&
(![X]:(brave(X)=>wise(X)))&
(((strong(fred)&patient(fred)))=>((old(fred)&~happy(fred))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(((brave(fred)<~>~calm(fred)))=>((~generous(fred)|happy(fred))))&
(![X]:((happy(X)|~quiet(X))=>(~strong(X)<~>rich(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~funny(X)))&
(?[X]:(creative(X)))&
(?[X]:(funny(X)))&
((wise(alice)|~patient(alice)))&
(?[X]:((~kind(X)<~>brave(X))))&
((funny(fred)|patient(fred)))&
(?[X]:((~brave(X)&tall(X))))&
((~quiet(alice)&kind(alice)))&
((humble(fred)|~patient(fred))) | ~happy(fred) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3866746318755043560843813
% SZS output start Proof for 3866746318755043560843813
4. (~curious(lucy) & ~brave(lucy)) <=> ? [X0] : (~patient(X0) | ~calm(X0)) [input p3]
9. ! [X0] : ((curious(X0) & calm(X0)) <=> (happy(X0) | ~curious(X0))) [input p8]
25. ~happy(fred) [input hypothesis]
50. ((~curious(lucy) & ~brave(lucy)) | ! [X0] : (patient(X0) & calm(X0))) & (? [X0] : (~patient(X0) | ~calm(X0)) | (curious(lucy) | brave(lucy))) [nnf transformation 4]
51. ((~curious(lucy) & ~brave(lucy)) | ! [X0] : (patient(X0) & calm(X0))) & (? [X0] : (~patient(X0) | ~calm(X0)) | curious(lucy) | brave(lucy)) [flattening 50]
52. ((~curious(lucy) & ~brave(lucy)) | ! [X0] : (patient(X0) & calm(X0))) & (? [X1] : (~patient(X1) | ~calm(X1)) | curious(lucy) | brave(lucy)) [rectify 51]
53. ? [X1] : (~patient(X1) | ~calm(X1)) => (~patient(sK3) | ~calm(sK3)) [choice axiom]
54. ((~curious(lucy) & ~brave(lucy)) | ! [X0] : (patient(X0) & calm(X0))) & ((~patient(sK3) | ~calm(sK3)) | curious(lucy) | brave(lucy)) [skolemisation 52,53]
60. ! [X0] : (((curious(X0) & calm(X0)) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 9]
61. ! [X0] : (((curious(X0) & calm(X0)) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | ~curious(X0) | ~calm(X0))) [flattening 60]
91. ~curious(lucy) | calm(X0) [cnf transformation 54]
108. happy(X0) | ~curious(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 61]
111. curious(X0) | curious(X0) [cnf transformation 61]
144. ~happy(fred) [cnf transformation 25]
145. ~calm(X0) | ~curious(X0) | happy(X0) [duplicate literal removal 108]
146. curious(X0) [duplicate literal removal 111]
193. 12 <=> curious(lucy) [avatar definition]
195. ~curious(lucy) <- (~12) [avatar component clause 193]
198. 13 <=> ! [X0] : calm(X0) [avatar definition]
199. calm(X0) <- (13) [avatar component clause 198]
200. 13 | ~12 [avatar split clause 91,193,198]
242. 22 <=> ! [X0] : curious(X0) [avatar definition]
243. curious(X0) <- (22) [avatar component clause 242]
247. 22 [avatar split clause 146,242]
268. 27 <=> happy(fred) [avatar definition]
270. ~happy(fred) <- (~27) [avatar component clause 268]
340. ~27 [avatar split clause 144,268]
341. $false <- (~12, 22) [subsumption resolution 195,243]
342. 12 | ~22 [avatar contradiction clause 341]
380. ~curious(X2) | happy(X2) <- (13) [resolution 145,199]
383. happy(X2) <- (13, 22) [subsumption resolution 380,243]
384. $false <- (13, 22, ~27) [resolution 383,270]
389. ~13 | ~22 | 27 [avatar contradiction clause 384]
390. $false [avatar sat refutation 200,247,340,342,389]
% SZS output end Proof for 3866746318755043560843813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not wise is both not patient and quiet.
If susan is strong then fred is not quiet.
If someone is both not brave and not patient then someone is not generous.
If alice is either not creative or old then susan is humble and vice versa.
Everyone who is not calm is both not funny and brave.
If someone is either not generous or creative then mary is both old and quiet.
Everyone who is both not kind and funny is either not happy or not rich.
Everyone who is both kind and old is not strong.
Everyone who is both not funny and not generous is either happy or not creative and vice versa.
Everyone who is both patient and humble is both not strong and not kind.
If susan is either funny or not humble then someone is wise.
If paul is both not patient and not funny then someone is either not old or humble.
Everyone who is either not funny or not humble is not humble.
Everyone who is not quiet or funny is not patient and vice versa.
Everyone who is tall is either not kind or quiet.
If mary is not old then someone is either not humble or not generous and vice versa.
John is funny.
Someone is both tall and kind.
Someone is generous or wise.
Someone is not curious.
Mary is tall or old.
Alice is not rich or calm.
Mary is either rich or tall.
Someone is not wise. | Alice is calm. | neutral | (![X]:(~wise(X)=>(~patient(X)&quiet(X))))&
((strong(susan))=>(~quiet(fred)))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:(~generous(X))))&
(((~creative(alice)<~>old(alice)))<=>(humble(susan)))&
(![X]:(~calm(X)=>(~funny(X)&brave(X))))&
((?[X]:((~generous(X)<~>creative(X))))=>((old(mary)&quiet(mary))))&
(![X]:((~kind(X)&funny(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((kind(X)&old(X))=>~strong(X)))&
(![X]:((~funny(X)&~generous(X))<=>(happy(X)<~>~creative(X))))&
(![X]:((patient(X)&humble(X))=>(~strong(X)&~kind(X))))&
(((funny(susan)<~>~humble(susan)))=>(?[X]:(wise(X))))&
(((~patient(paul)&~funny(paul)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~funny(X)<~>~humble(X))=>~humble(X)))&
(![X]:((~quiet(X)|funny(X))<=>~patient(X)))&
(![X]:(tall(X)=>(~kind(X)<~>quiet(X))))&
((~old(mary))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
(funny(john))&
(?[X]:((tall(X)&kind(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:(~curious(X)))&
((tall(mary)|old(mary)))&
((~rich(alice)|calm(alice)))&
((rich(mary)<~>tall(mary)))&
(?[X]:(~wise(X))) | calm(alice) | [] | null | 0 |
Everyone who is both happy and old is not humble. If lucy is not brave then someone is either not funny or not curious. If fred is rich then someone is patient or not curious. If alice is both not tall and quiet then lucy is both not calm and not patient and vice versa. Everyone who is not humble is not curious or not happy and vice versa. If lucy is either not brave or not tall then someone is not happy and vice versa. Everyone who is both quiet and not strong is both not wise and curious and vice versa. If someone is either not old or not strong then someone is both not humble and not rich. If someone is both not humble and not strong then mary is patient. Everyone who is not generous is patient or kind and vice versa. If fred is tall or not tall then someone is both strong and kind and vice versa. If paul is both tall and humble then lucy is either not humble or kind. Everyone who is not quiet or humble is both wise and not old and vice versa. Everyone who is not rich is both patient and not kind and vice versa. If susan is both not strong and not kind then someone is both not creative and calm and vice versa. Everyone who is both old and patient is old or not strong. John is both tall and happy. Someone is not brave or not kind. Someone is both not tall and not strong. Fred is both happy and strong. Fred is both creative and not calm. Someone is both not strong and not humble. Someone is both not kind and not brave. Someone is either not curious or not kind. | Mary is creative. | neutral | (![X]:((happy(X)&old(X))=>~humble(X)))&
((~brave(lucy))=>(?[X]:((~funny(X)<~>~curious(X)))))&
((rich(fred))=>(?[X]:((patient(X)|~curious(X)))))&
(((~tall(alice)&quiet(alice)))<=>((~calm(lucy)&~patient(lucy))))&
(![X]:(~humble(X)<=>(~curious(X)|~happy(X))))&
(((~brave(lucy)<~>~tall(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((quiet(X)&~strong(X))<=>(~wise(X)&curious(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>(?[X]:((~humble(X)&~rich(X)))))&
((?[X]:((~humble(X)&~strong(X))))=>(patient(mary)))&
(![X]:(~generous(X)<=>(patient(X)|kind(X))))&
(((tall(fred)|~tall(fred)))<=>(?[X]:((strong(X)&kind(X)))))&
(((tall(paul)&humble(paul)))=>((~humble(lucy)<~>kind(lucy))))&
(![X]:((~quiet(X)|humble(X))<=>(wise(X)&~old(X))))&
(![X]:(~rich(X)<=>(patient(X)&~kind(X))))&
(((~strong(susan)&~kind(susan)))<=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((old(X)&patient(X))=>(old(X)|~strong(X))))&
((tall(john)&happy(john)))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((~tall(X)&~strong(X))))&
((happy(fred)&strong(fred)))&
((creative(fred)&~calm(fred)))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:((~curious(X)<~>~kind(X)))) | creative(mary) | [] | null | 0 |
If fred is not happy or calm then someone is either brave or not strong and vice versa. Everyone who is not kind or humble is either rich or not generous. Everyone who is rich is either generous or not calm. If john is both funny and not kind then someone is not happy or humble. If lucy is not creative or not curious then someone is both wise and happy. If fred is wise then someone is either wise or creative. Everyone who is both not generous and generous is both kind and not old. Everyone who is either kind or tall is patient or tall and vice versa. Everyone who is not patient or not kind is either not curious or not wise and vice versa. If alice is happy then someone is humble or calm and vice versa. If john is both not patient and quiet then someone is brave or rich and vice versa. Everyone who is both tall and wise is patient or not calm and vice versa. Everyone who is both tall and not curious is both tall and wise. Everyone who is both not brave and wise is both strong and wise. Everyone who is not kind is both not calm and quiet and vice versa. Everyone who is either funny or not creative is both creative and not kind and vice versa. John is patient. Someone is either not old or not brave. Alice is not old. Someone is generous or not patient. Mary is not happy. Someone is either not funny or not happy. Someone is both patient and not calm. | Fred is not wise. | contradiction | (((~happy(fred)|calm(fred)))<=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:((~kind(X)|humble(X))=>(rich(X)<~>~generous(X))))&
(![X]:(rich(X)=>(generous(X)<~>~calm(X))))&
(((funny(john)&~kind(john)))=>(?[X]:((~happy(X)|humble(X)))))&
(((~creative(lucy)|~curious(lucy)))=>(?[X]:((wise(X)&happy(X)))))&
((wise(fred))=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:((~generous(X)&generous(X))=>(kind(X)&~old(X))))&
(![X]:((kind(X)<~>tall(X))<=>(patient(X)|tall(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~curious(X)<~>~wise(X))))&
((happy(alice))<=>(?[X]:((humble(X)|calm(X)))))&
(((~patient(john)&quiet(john)))<=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((tall(X)&wise(X))<=>(patient(X)|~calm(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)&wise(X))))&
(![X]:((~brave(X)&wise(X))=>(strong(X)&wise(X))))&
(![X]:(~kind(X)<=>(~calm(X)&quiet(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~kind(X))))&
(patient(john))&
(?[X]:((~old(X)<~>~brave(X))))&
(~old(alice))&
(?[X]:((generous(X)|~patient(X))))&
(~happy(mary))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((patient(X)&~calm(X)))) | ~wise(fred) | [
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2040188449439830688474677
% SZS output start Proof for 2040188449439830688474677
8. ! [X0] : ((kind(X0) <~> tall(X0)) <=> (tall(X0) | patient(X0))) [input p7]
12. ! [X0] : ((wise(X0) & tall(X0)) <=> (~calm(X0) | patient(X0))) [input p11]
15. ! [X0] : (~kind(X0) <=> (quiet(X0) & ~calm(X0))) [input p14]
24. ~wise(fred) [input hypothesis]
51. ! [X0] : ((((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~tall(X0) | ~kind(X0)) & (tall(X0) | kind(X0))) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0))))) [flattening 51]
64. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~wise(X0) | ~tall(X0)))) [nnf transformation 12]
65. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ~wise(X0) | ~tall(X0))) [flattening 64]
66. ! [X0] : ((~kind(X0) | (~quiet(X0) | calm(X0))) & ((quiet(X0) & ~calm(X0)) | kind(X0))) [nnf transformation 15]
67. ! [X0] : ((~kind(X0) | ~quiet(X0) | calm(X0)) & ((quiet(X0) & ~calm(X0)) | kind(X0))) [flattening 66]
101. tall(X0) | patient(X0) | tall(X0) | ~kind(X0) [cnf transformation 52]
106. ~tall(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 52]
124. ~patient(X0) | wise(X0) [cnf transformation 65]
125. wise(X0) | calm(X0) [cnf transformation 65]
130. ~calm(X0) | kind(X0) [cnf transformation 67]
149. ~wise(fred) [cnf transformation 24]
152. tall(X0) | patient(X0) | ~kind(X0) [duplicate literal removal 101]
153. ~tall(X0) | ~kind(X0) [duplicate literal removal 106]
162. 3 <=> calm(fred) [avatar definition]
164. calm(fred) <- (3) [avatar component clause 162]
220. 15 <=> wise(fred) [avatar definition]
222. ~wise(fred) <- (~15) [avatar component clause 220]
233. ~kind(X0) | patient(X0) [subsumption resolution 152,153]
314. ~15 [avatar split clause 149,220]
319. calm(fred) <- (~15) [resolution 125,222]
322. 3 | 15 [avatar split clause 319,220,162]
325. kind(fred) <- (3) [resolution 130,164]
330. patient(fred) <- (3) [resolution 233,325]
331. wise(fred) <- (3) [resolution 330,124]
333. $false <- (3, ~15) [subsumption resolution 331,222]
334. ~3 | 15 [avatar contradiction clause 333]
335. $false [avatar sat refutation 314,322,334]
% SZS output end Proof for 2040188449439830688474677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not happy is both curious and not funny and vice versa. If fred is quiet then someone is not strong or kind. Everyone who is both not curious and not humble is humble and vice versa. Everyone who is wise is not tall. If someone is either quiet or not strong then someone is either tall or quiet. Everyone who is not happy is both creative and not rich. If someone is calm then someone is both strong and funny and vice versa. If john is not rich then paul is either not happy or kind. If alice is not rich then susan is creative or generous. If john is both not happy and generous then someone is either not happy or brave. If lucy is both not calm and strong then someone is either humble or tall. If someone is either not strong or tall then lucy is both not old and not humble and vice versa. If fred is kind then someone is either not creative or not brave. Everyone who is kind or tall is both not curious and funny and vice versa. Everyone who is either humble or quiet is both humble and not kind and vice versa. If susan is both not humble and not generous then alice is either creative or wise and vice versa. Alice is either funny or wise. Someone is both calm and not funny. Paul is curious or not strong. Mary is either brave or wise. Alice is either brave or curious. Paul is both calm and funny. | Mary is generous. | neutral | (![X]:((old(X)<~>~happy(X))<=>(curious(X)&~funny(X))))&
((quiet(fred))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~curious(X)&~humble(X))<=>humble(X)))&
(![X]:(wise(X)=>~tall(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(~happy(X)=>(creative(X)&~rich(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)&funny(X)))))&
((~rich(john))=>((~happy(paul)<~>kind(paul))))&
((~rich(alice))=>((creative(susan)|generous(susan))))&
(((~happy(john)&generous(john)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~calm(lucy)&strong(lucy)))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((~old(lucy)&~humble(lucy))))&
((kind(fred))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((kind(X)|tall(X))<=>(~curious(X)&funny(X))))&
(![X]:((humble(X)<~>quiet(X))<=>(humble(X)&~kind(X))))&
(((~humble(susan)&~generous(susan)))<=>((creative(alice)<~>wise(alice))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((calm(X)&~funny(X))))&
((curious(paul)|~strong(paul)))&
((brave(mary)<~>wise(mary)))&
((brave(alice)<~>curious(alice)))&
((calm(paul)&funny(paul))) | generous(mary) | [] | null | 0 |
Everyone who is not patient is either not patient or funny and vice versa.
Everyone who is not quiet or not calm is both humble and not creative and vice versa.
Everyone who is not brave or not calm is curious and vice versa.
Everyone who is both creative and not brave is either not tall or not humble.
If mary is funny or not kind then someone is funny or not strong and vice versa.
Everyone who is strong is either not old or not tall and vice versa.
Everyone who is kind or humble is not strong and vice versa.
If paul is not patient or not calm then someone is curious and vice versa.
If mary is not calm or rich then alice is creative or tall.
Everyone who is not creative is not patient or happy.
If someone is either calm or strong then john is both not tall and funny.
If paul is both not calm and not brave then someone is either happy or generous and vice versa.
Everyone who is both brave and not funny is both tall and happy.
If susan is either creative or not humble then lucy is either not old or not funny.
Everyone who is either patient or quiet is either brave or tall.
Everyone who is not generous or not humble is either curious or humble and vice versa.
Someone is generous.
Lucy is either not wise or generous.
Lucy is calm.
Someone is either not humble or not calm.
Someone is not funny or not brave.
Someone is both strong and patient.
Lucy is either not happy or generous. | Mary is not humble. | neutral | (![X]:(~patient(X)<=>(~patient(X)<~>funny(X))))&
(![X]:((~quiet(X)|~calm(X))<=>(humble(X)&~creative(X))))&
(![X]:((~brave(X)|~calm(X))<=>curious(X)))&
(![X]:((creative(X)&~brave(X))=>(~tall(X)<~>~humble(X))))&
(((funny(mary)|~kind(mary)))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:(strong(X)<=>(~old(X)<~>~tall(X))))&
(![X]:((kind(X)|humble(X))<=>~strong(X)))&
(((~patient(paul)|~calm(paul)))<=>(?[X]:(curious(X))))&
(((~calm(mary)|rich(mary)))=>((creative(alice)|tall(alice))))&
(![X]:(~creative(X)=>(~patient(X)|happy(X))))&
((?[X]:((calm(X)<~>strong(X))))=>((~tall(john)&funny(john))))&
(((~calm(paul)&~brave(paul)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:((brave(X)&~funny(X))=>(tall(X)&happy(X))))&
(((creative(susan)<~>~humble(susan)))=>((~old(lucy)<~>~funny(lucy))))&
(![X]:((patient(X)<~>quiet(X))=>(brave(X)<~>tall(X))))&
(![X]:((~generous(X)|~humble(X))<=>(curious(X)<~>humble(X))))&
(?[X]:(generous(X)))&
((~wise(lucy)<~>generous(lucy)))&
(calm(lucy))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:((strong(X)&patient(X))))&
((~happy(lucy)<~>generous(lucy))) | ~humble(mary) | [] | null | 0 |
Everyone who is both not creative and wise is patient or not rich and vice versa.
If someone is either not humble or rich then paul is not calm or not brave.
Everyone who is both not old and not patient is not tall.
Everyone who is either patient or generous is not quiet and vice versa.
If someone is both not funny and curious then someone is either generous or not rich.
If someone is either not rich or creative then someone is not rich or not generous.
Everyone who is either happy or tall is rich and vice versa.
If john is both humble and not generous then lucy is kind or not patient and vice versa.
Everyone who is both not brave and not quiet is both wise and generous and vice versa.
If fred is either calm or humble then someone is curious.
Everyone who is funny or brave is both not wise and not curious and vice versa.
If john is humble then someone is not generous.
Everyone who is tall is generous or humble and vice versa.
Everyone who is both not rich and not creative is either funny or brave and vice versa.
Everyone who is both not generous and not kind is quiet or strong.
Everyone who is either humble or not kind is either not happy or brave and vice versa.
Someone is either happy or not kind.
Fred is either not patient or not generous.
Someone is not strong.
Someone is both not curious and rich.
Someone is not curious or patient.
Mary is either patient or curious.
Fred is brave.
Paul is both quiet and old. | John is happy. | contradiction | (![X]:((~creative(X)&wise(X))<=>(patient(X)|~rich(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>((~calm(paul)|~brave(paul))))&
(![X]:((~old(X)&~patient(X))=>~tall(X)))&
(![X]:((patient(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:((~funny(X)&curious(X))))=>(?[X]:((generous(X)<~>~rich(X)))))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((happy(X)<~>tall(X))<=>rich(X)))&
(((humble(john)&~generous(john)))<=>((kind(lucy)|~patient(lucy))))&
(![X]:((~brave(X)&~quiet(X))<=>(wise(X)&generous(X))))&
(((calm(fred)<~>humble(fred)))=>(?[X]:(curious(X))))&
(![X]:((funny(X)|brave(X))<=>(~wise(X)&~curious(X))))&
((humble(john))=>(?[X]:(~generous(X))))&
(![X]:(tall(X)<=>(generous(X)|humble(X))))&
(![X]:((~rich(X)&~creative(X))<=>(funny(X)<~>brave(X))))&
(![X]:((~generous(X)&~kind(X))=>(quiet(X)|strong(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(~happy(X)<~>brave(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
((~patient(fred)<~>~generous(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((~curious(X)&rich(X))))&
(?[X]:((~curious(X)|patient(X))))&
((patient(mary)<~>curious(mary)))&
(brave(fred))&
((quiet(paul)&old(paul))) | happy(john) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 839998479404273391885011
% SZS output start Proof for 839998479404273391885011
1. ! [X0] : ((wise(X0) & ~creative(X0)) <=> (~rich(X0) | patient(X0))) [input p0]
4. ! [X0] : ((patient(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p3]
7. ! [X0] : ((happy(X0) <~> tall(X0)) <=> rich(X0)) [input p6]
8. (~generous(john) & humble(john)) <=> (~patient(lucy) | kind(lucy)) [input p7]
9. ! [X0] : ((~quiet(X0) & ~brave(X0)) <=> (generous(X0) & wise(X0))) [input p8]
11. ! [X0] : ((brave(X0) | funny(X0)) <=> (~curious(X0) & ~wise(X0))) [input p10]
13. ! [X0] : (tall(X0) <=> (humble(X0) | generous(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & ~rich(X0)) <=> (funny(X0) <~> brave(X0))) [input p13]
25. happy(john) [input hypothesis]
38. ! [X0] : (((wise(X0) & ~creative(X0)) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | (~wise(X0) | creative(X0)))) [nnf transformation 1]
39. ! [X0] : (((wise(X0) & ~creative(X0)) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | ~wise(X0) | creative(X0))) [flattening 38]
41. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | quiet(X0)) & (~quiet(X0) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 4]
50. ! [X0] : ((((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ~rich(X0)) & (rich(X0) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0))))) [nnf transformation 7]
51. ((~generous(john) & humble(john)) | (patient(lucy) & ~kind(lucy))) & ((~patient(lucy) | kind(lucy)) | (generous(john) | ~humble(john))) [nnf transformation 8]
52. ((~generous(john) & humble(john)) | (patient(lucy) & ~kind(lucy))) & (~patient(lucy) | kind(lucy) | generous(john) | ~humble(john)) [flattening 51]
53. ! [X0] : (((~quiet(X0) & ~brave(X0)) | (~generous(X0) | ~wise(X0))) & ((generous(X0) & wise(X0)) | (quiet(X0) | brave(X0)))) [nnf transformation 9]
54. ! [X0] : (((~quiet(X0) & ~brave(X0)) | ~generous(X0) | ~wise(X0)) & ((generous(X0) & wise(X0)) | quiet(X0) | brave(X0))) [flattening 53]
58. ! [X0] : (((brave(X0) | funny(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (~brave(X0) & ~funny(X0)))) [nnf transformation 11]
59. ! [X0] : ((brave(X0) | funny(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | (~brave(X0) & ~funny(X0)))) [flattening 58]
62. ! [X0] : ((tall(X0) | (~humble(X0) & ~generous(X0))) & ((humble(X0) | generous(X0)) | ~tall(X0))) [nnf transformation 13]
63. ! [X0] : ((tall(X0) | (~humble(X0) & ~generous(X0))) & (humble(X0) | generous(X0) | ~tall(X0))) [flattening 62]
64. ! [X0] : (((~creative(X0) & ~rich(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (creative(X0) | rich(X0)))) [nnf transformation 14]
65. ! [X0] : (((~creative(X0) & ~rich(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | creative(X0) | rich(X0))) [flattening 64]
80. ~creative(X0) | rich(X0) [cnf transformation 39]
81. ~patient(X0) | wise(X0) [cnf transformation 39]
82. rich(X0) | wise(X0) [cnf transformation 39]
85. ~quiet(X0) | generous(X0) | ~patient(X0) [cnf transformation 41]
88. ~generous(X0) | ~patient(X0) | quiet(X0) [cnf transformation 41]
96. ~happy(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 50]
99. humble(john) | patient(lucy) [cnf transformation 52]
103. quiet(X0) | generous(X0) | brave(X0) [cnf transformation 54]
105. ~quiet(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 54]
108. ~funny(X0) | ~wise(X0) [cnf transformation 59]
109. ~brave(X0) | ~wise(X0) [cnf transformation 59]
116. ~humble(X0) | tall(X0) [cnf transformation 63]
117. brave(X0) | funny(X0) | creative(X0) | rich(X0) [cnf transformation 65]
144. happy(john) [cnf transformation 25]
189. 11 <=> ! [X1] : rich(X1) [avatar definition]
190. rich(X1) <- (11) [avatar component clause 189]
193. 12 <=> patient(lucy) [avatar definition]
195. patient(lucy) <- (12) [avatar component clause 193]
207. 15 <=> humble(john) [avatar definition]
209. humble(john) <- (15) [avatar component clause 207]
210. 12 | 15 [avatar split clause 99,207,193]
233. funny(X0) | brave(X0) | rich(X0) [subsumption resolution 117,80]
309. 31 <=> tall(john) [avatar definition]
337. ~tall(john) | ~rich(john) [resolution 96,144]
344. generous(X1) | brave(X1) | generous(X1) | ~patient(X1) [resolution 103,85]
345. ~patient(X1) | brave(X1) | generous(X1) [duplicate literal removal 344]
374. brave(X3) | rich(X3) | ~wise(X3) [resolution 233,108]
378. rich(X3) | ~wise(X3) [subsumption resolution 374,109]
379. rich(X3) [subsumption resolution 378,82]
380. 11 [avatar split clause 379,189]
472. tall(john) <- (15) [resolution 209,116]
475. ~tall(john) <- (11) [subsumption resolution 337,190]
476. ~31 | ~11 [avatar split clause 475,189,309]
477. 31 | ~15 [avatar split clause 472,207,309]
480. wise(lucy) <- (12) [resolution 195,81]
539. brave(lucy) | generous(lucy) <- (12) [resolution 345,195]
550. 54 <=> generous(lucy) [avatar definition]
552. generous(lucy) <- (54) [avatar component clause 550]
554. 55 <=> brave(lucy) [avatar definition]
556. brave(lucy) <- (55) [avatar component clause 554]
557. 54 | 55 | ~12 [avatar split clause 539,193,554,550]
609. ~patient(lucy) | quiet(lucy) <- (54) [resolution 552,88]
611. quiet(lucy) <- (12, 54) [subsumption resolution 609,195]
792. ~generous(lucy) | ~wise(lucy) <- (12, 54) [resolution 611,105]
795. ~wise(lucy) <- (12, 54) [subsumption resolution 792,552]
796. $false <- (12, 54) [subsumption resolution 795,480]
797. ~12 | ~54 [avatar contradiction clause 796]
806. ~wise(lucy) <- (55) [resolution 556,109]
818. $false <- (12, 55) [subsumption resolution 806,480]
819. ~12 | ~55 [avatar contradiction clause 818]
820. $false [avatar sat refutation 210,380,476,477,557,797,819]
% SZS output end Proof for 839998479404273391885011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both quiet and brave then someone is both not wise and not strong.
Everyone who is not patient or quiet is not old.
Everyone who is either not rich or creative is not humble and vice versa.
If lucy is tall then paul is both not calm and humble.
If lucy is not tall then susan is not kind and vice versa.
Everyone who is wise or not rich is either curious or generous and vice versa.
Everyone who is funny is funny or tall.
If someone is not rich then alice is either brave or not funny.
Everyone who is both not funny and patient is both not funny and not rich and vice versa.
Everyone who is both not tall and curious is not curious or creative and vice versa.
If alice is either not strong or curious then someone is either kind or wise.
Everyone who is patient or old is both quiet and not creative.
If john is both not generous and not tall then susan is both not wise and generous and vice versa.
If john is not happy or creative then someone is either not patient or brave and vice versa.
If john is old or quiet then lucy is both happy and old.
If lucy is either not patient or not generous then alice is both not old and not curious and vice versa.
Susan is creative.
Someone is quiet.
Lucy is humble or not curious.
Mary is either not generous or not happy.
Someone is both rich and tall.
Someone is both not rich and not patient.
Someone is both happy and not wise.
Alice is either not humble or generous. | Paul is calm. | neutral | ((?[X]:((quiet(X)&brave(X))))=>(?[X]:((~wise(X)&~strong(X)))))&
(![X]:((~patient(X)|quiet(X))=>~old(X)))&
(![X]:((~rich(X)<~>creative(X))<=>~humble(X)))&
((tall(lucy))=>((~calm(paul)&humble(paul))))&
((~tall(lucy))<=>(~kind(susan)))&
(![X]:((wise(X)|~rich(X))<=>(curious(X)<~>generous(X))))&
(![X]:(funny(X)=>(funny(X)|tall(X))))&
((?[X]:(~rich(X)))=>((brave(alice)<~>~funny(alice))))&
(![X]:((~funny(X)&patient(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~tall(X)&curious(X))<=>(~curious(X)|creative(X))))&
(((~strong(alice)<~>curious(alice)))=>(?[X]:((kind(X)<~>wise(X)))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~creative(X))))&
(((~generous(john)&~tall(john)))<=>((~wise(susan)&generous(susan))))&
(((~happy(john)|creative(john)))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(((old(john)|quiet(john)))=>((happy(lucy)&old(lucy))))&
(((~patient(lucy)<~>~generous(lucy)))<=>((~old(alice)&~curious(alice))))&
(creative(susan))&
(?[X]:(quiet(X)))&
((humble(lucy)|~curious(lucy)))&
((~generous(mary)<~>~happy(mary)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((happy(X)&~wise(X))))&
((~humble(alice)<~>generous(alice))) | calm(paul) | [] | null | 0 |
Everyone who is both wise and not patient is either happy or not old.
Everyone who is either wise or not calm is either not tall or not strong.
Everyone who is brave or wise is both kind and tall and vice versa.
If alice is not old then someone is both not generous and quiet and vice versa.
Everyone who is not creative is either not old or not rich and vice versa.
Everyone who is not quiet or brave is either happy or generous and vice versa.
Everyone who is either old or calm is either not creative or not patient.
Everyone who is not strong or not quiet is both not patient and not funny and vice versa.
Everyone who is patient is either curious or kind and vice versa.
If someone is not funny then someone is not patient or not funny and vice versa.
Everyone who is not old is patient or not funny.
Everyone who is either not rich or funny is rich or not strong and vice versa.
Everyone who is not humble or not calm is rich and vice versa.
If someone is either strong or humble then fred is not kind or not rich.
Everyone who is either not quiet or rich is either calm or generous and vice versa.
Everyone who is either not wise or not brave is both calm and happy and vice versa.
Mary is brave.
Someone is not wise or not creative.
Lucy is happy.
Someone is either curious or kind.
Lucy is either old or not rich.
Alice is brave or not strong.
Fred is not curious or not rich. | Alice is not brave. | neutral | (![X]:((wise(X)&~patient(X))=>(happy(X)<~>~old(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)<~>~strong(X))))&
(![X]:((brave(X)|wise(X))<=>(kind(X)&tall(X))))&
((~old(alice))<=>(?[X]:((~generous(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(~old(X)<~>~rich(X))))&
(![X]:((~quiet(X)|brave(X))<=>(happy(X)<~>generous(X))))&
(![X]:((old(X)<~>calm(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)<=>(curious(X)<~>kind(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:(~old(X)=>(patient(X)|~funny(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(rich(X)|~strong(X))))&
(![X]:((~humble(X)|~calm(X))<=>rich(X)))&
((?[X]:((strong(X)<~>humble(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~quiet(X)<~>rich(X))<=>(calm(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>(calm(X)&happy(X))))&
(brave(mary))&
(?[X]:((~wise(X)|~creative(X))))&
(happy(lucy))&
(?[X]:((curious(X)<~>kind(X))))&
((old(lucy)<~>~rich(lucy)))&
((brave(alice)|~strong(alice)))&
((~curious(fred)|~rich(fred))) | ~brave(alice) | [] | null | 0 |
Everyone who is both brave and not creative is not generous and vice versa.
If mary is both not generous and not rich then alice is not curious and vice versa.
If mary is not quiet then someone is not humble or funny.
If lucy is either calm or wise then someone is both kind and funny and vice versa.
Everyone who is either humble or wise is both generous and not quiet.
Everyone who is not rich is either strong or curious.
Everyone who is both happy and not brave is either creative or not kind and vice versa.
Everyone who is old or tall is either not creative or generous and vice versa.
If someone is happy or not calm then lucy is quiet or not rich.
Everyone who is either happy or not wise is strong and vice versa.
If mary is happy then lucy is both happy and generous.
Everyone who is both not creative and not tall is creative or curious.
If someone is either not brave or not happy then someone is either not tall or wise and vice versa.
If john is either creative or generous then someone is not tall or old and vice versa.
Everyone who is either not humble or not kind is brave or tall.
Everyone who is not patient or not quiet is both old and creative.
Alice is quiet.
Fred is not generous or not funny.
Someone is not old or wise.
Someone is both not calm and not generous.
Someone is funny.
Alice is both tall and curious. | John is tall. | neutral | (![X]:((brave(X)&~creative(X))<=>~generous(X)))&
(((~generous(mary)&~rich(mary)))<=>(~curious(alice)))&
((~quiet(mary))=>(?[X]:((~humble(X)|funny(X)))))&
(((calm(lucy)<~>wise(lucy)))<=>(?[X]:((kind(X)&funny(X)))))&
(![X]:((humble(X)<~>wise(X))=>(generous(X)&~quiet(X))))&
(![X]:(~rich(X)=>(strong(X)<~>curious(X))))&
(![X]:((happy(X)&~brave(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((old(X)|tall(X))<=>(~creative(X)<~>generous(X))))&
((?[X]:((happy(X)|~calm(X))))=>((quiet(lucy)|~rich(lucy))))&
(![X]:((happy(X)<~>~wise(X))<=>strong(X)))&
((happy(mary))=>((happy(lucy)&generous(lucy))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|curious(X))))&
((?[X]:((~brave(X)<~>~happy(X))))<=>(?[X]:((~tall(X)<~>wise(X)))))&
(((creative(john)<~>generous(john)))<=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((~humble(X)<~>~kind(X))=>(brave(X)|tall(X))))&
(![X]:((~patient(X)|~quiet(X))=>(old(X)&creative(X))))&
(quiet(alice))&
((~generous(fred)|~funny(fred)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((~calm(X)&~generous(X))))&
(?[X]:(funny(X)))&
((tall(alice)&curious(alice))) | tall(john) | [] | null | 0 |
Everyone who is not tall is either creative or not old and vice versa.
Everyone who is not brave is not strong or not rich and vice versa.
If john is either strong or not patient then paul is both happy and not wise.
If john is both not calm and not strong then someone is both not funny and humble and vice versa.
If alice is either not quiet or not old then someone is not strong or brave and vice versa.
If fred is both tall and calm then someone is not creative or wise.
If mary is either not kind or humble then someone is not curious or not brave.
If mary is both not kind and brave then someone is both generous and not patient.
Everyone who is either not happy or tall is wise and vice versa.
If someone is both wise and not wise then alice is both not curious and not humble and vice versa.
Everyone who is not old is either wise or strong.
Everyone who is patient is both not generous and happy.
Everyone who is either wise or not wise is not old.
If someone is either humble or not curious then someone is strong or not tall.
If alice is both not strong and generous then someone is brave and vice versa.
If someone is not rich or not patient then susan is either not patient or not humble.
John is calm.
Someone is either brave or not happy.
Someone is not strong.
Someone is either brave or calm.
Susan is both not happy and wise.
Someone is both not old and kind.
Someone is not old or kind.
Alice is humble. | Alice is not funny. | contradiction | (![X]:(~tall(X)<=>(creative(X)<~>~old(X))))&
(![X]:(~brave(X)<=>(~strong(X)|~rich(X))))&
(((strong(john)<~>~patient(john)))=>((happy(paul)&~wise(paul))))&
(((~calm(john)&~strong(john)))<=>(?[X]:((~funny(X)&humble(X)))))&
(((~quiet(alice)<~>~old(alice)))<=>(?[X]:((~strong(X)|brave(X)))))&
(((tall(fred)&calm(fred)))=>(?[X]:((~creative(X)|wise(X)))))&
(((~kind(mary)<~>humble(mary)))=>(?[X]:((~curious(X)|~brave(X)))))&
(((~kind(mary)&brave(mary)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>wise(X)))&
((?[X]:((wise(X)&~wise(X))))<=>((~curious(alice)&~humble(alice))))&
(![X]:(~old(X)=>(wise(X)<~>strong(X))))&
(![X]:(patient(X)=>(~generous(X)&happy(X))))&
(![X]:((wise(X)<~>~wise(X))=>~old(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(((~strong(alice)&generous(alice)))<=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)|~patient(X))))=>((~patient(susan)<~>~humble(susan))))&
(calm(john))&
(?[X]:((brave(X)<~>~happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)<~>calm(X))))&
((~happy(susan)&wise(susan)))&
(?[X]:((~old(X)&kind(X))))&
(?[X]:((~old(X)|kind(X))))&
(humble(alice)) | ~funny(alice) | [
"p3",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 885711617795460823595586
% SZS output start Proof for 885711617795460823595586
4. (~strong(john) & ~calm(john)) <=> ? [X0] : (humble(X0) & ~funny(X0)) [input p3]
17. calm(john) [input p16]
24. humble(alice) [input p23]
25. ~funny(alice) [input hypothesis]
42. ((~strong(john) & ~calm(john)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X0] : (humble(X0) & ~funny(X0)) | (strong(john) | calm(john))) [nnf transformation 4]
43. ((~strong(john) & ~calm(john)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X0] : (humble(X0) & ~funny(X0)) | strong(john) | calm(john)) [flattening 42]
44. ((~strong(john) & ~calm(john)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X1] : (humble(X1) & ~funny(X1)) | strong(john) | calm(john)) [rectify 43]
45. ? [X1] : (humble(X1) & ~funny(X1)) => (humble(sK0) & ~funny(sK0)) [choice axiom]
46. ((~strong(john) & ~calm(john)) | ! [X0] : (~humble(X0) | funny(X0))) & ((humble(sK0) & ~funny(sK0)) | strong(john) | calm(john)) [skolemisation 44,45]
101. ~calm(john) | ~humble(X0) | funny(X0) [cnf transformation 46]
137. calm(john) [cnf transformation 17]
148. humble(alice) [cnf transformation 24]
149. ~funny(alice) [cnf transformation 25]
173. 5 <=> ! [X0] : (~humble(X0) | funny(X0)) [avatar definition]
174. ~humble(X0) | funny(X0) <- (5) [avatar component clause 173]
177. 6 <=> calm(john) [avatar definition]
180. 5 | ~6 [avatar split clause 101,177,173]
273. 27 <=> humble(alice) [avatar definition]
275. humble(alice) <- (27) [avatar component clause 273]
332. 6 [avatar split clause 137,177]
353. 27 [avatar split clause 148,273]
364. funny(alice) <- (5, 27) [resolution 174,275]
366. $false <- (5, 27) [subsumption resolution 364,149]
367. ~5 | ~27 [avatar contradiction clause 366]
368. $false [avatar sat refutation 180,332,353,367]
% SZS output end Proof for 885711617795460823595586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not generous then fred is both not creative and quiet and vice versa.
If lucy is both old and humble then lucy is quiet or not kind.
Everyone who is both not kind and calm is not old or rich and vice versa.
If someone is both generous and not humble then fred is brave or old.
Everyone who is rich is both happy and not rich and vice versa.
If john is both not humble and tall then mary is humble.
Everyone who is both not quiet and wise is both generous and tall.
Everyone who is curious is both not kind and not calm and vice versa.
Everyone who is either strong or old is not funny.
Everyone who is either not wise or brave is both not brave and funny.
If someone is not wise or not quiet then someone is either not wise or strong.
Everyone who is either not calm or not funny is strong.
If lucy is brave or humble then someone is not generous or humble and vice versa.
Everyone who is patient or not old is both not quiet and tall.
Everyone who is rich is strong or not strong.
If mary is both calm and not creative then susan is both old and not generous.
Someone is not rich or old.
Lucy is either humble or curious.
John is not brave or not rich.
Someone is both humble and not creative.
Alice is not old or not quiet.
Someone is either not curious or not strong.
Someone is not curious or not strong.
Fred is either old or not happy. | Lucy is rich. | contradiction | ((?[X]:((~calm(X)|~generous(X))))<=>((~creative(fred)&quiet(fred))))&
(((old(lucy)&humble(lucy)))=>((quiet(lucy)|~kind(lucy))))&
(![X]:((~kind(X)&calm(X))<=>(~old(X)|rich(X))))&
((?[X]:((generous(X)&~humble(X))))=>((brave(fred)|old(fred))))&
(![X]:(rich(X)<=>(happy(X)&~rich(X))))&
(((~humble(john)&tall(john)))=>(humble(mary)))&
(![X]:((~quiet(X)&wise(X))=>(generous(X)&tall(X))))&
(![X]:(curious(X)<=>(~kind(X)&~calm(X))))&
(![X]:((strong(X)<~>old(X))=>~funny(X)))&
(![X]:((~wise(X)<~>brave(X))=>(~brave(X)&funny(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((~calm(X)<~>~funny(X))=>strong(X)))&
(((brave(lucy)|humble(lucy)))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((patient(X)|~old(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>(strong(X)|~strong(X))))&
(((calm(mary)&~creative(mary)))=>((old(susan)&~generous(susan))))&
(?[X]:((~rich(X)|old(X))))&
((humble(lucy)<~>curious(lucy)))&
((~brave(john)|~rich(john)))&
(?[X]:((humble(X)&~creative(X))))&
((~old(alice)|~quiet(alice)))&
(?[X]:((~curious(X)<~>~strong(X))))&
(?[X]:((~curious(X)|~strong(X))))&
((old(fred)<~>~happy(fred))) | rich(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3992576934071355785147991
% SZS output start Proof for 3992576934071355785147991
5. ! [X0] : (rich(X0) <=> (~rich(X0) & happy(X0))) [input p4]
25. rich(lucy) [input hypothesis]
52. ! [X0] : ((rich(X0) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | ~rich(X0))) [nnf transformation 5]
53. ! [X0] : ((rich(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | ~rich(X0))) [flattening 52]
92. ~rich(X0) | ~rich(X0) [cnf transformation 53]
133. rich(lucy) [cnf transformation 25]
135. ~rich(X0) [duplicate literal removal 92]
293. $false [subsumption resolution 133,135]
% SZS output end Proof for 3992576934071355785147991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either calm or not generous.
Everyone who is either calm or quiet is creative and vice versa.
Everyone who is either rich or not happy is not creative.
If mary is both not happy and not old then someone is humble or tall and vice versa.
Everyone who is either not curious or old is not patient and vice versa.
If john is not brave or not wise then someone is generous and vice versa.
If someone is not wise then john is either not kind or calm.
If someone is strong or tall then someone is either not curious or not quiet and vice versa.
Everyone who is not humble or rich is both funny and not generous.
If someone is either wise or strong then john is funny or not rich.
Everyone who is both not funny and generous is either not quiet or happy and vice versa.
If susan is both creative and not tall then someone is not rich or not kind.
If fred is brave then someone is both not strong and strong.
Everyone who is curious is happy.
If alice is either not rich or creative then fred is brave and vice versa.
If susan is patient or not strong then john is either rich or not funny and vice versa.
Someone is both not strong and not calm.
Someone is either not tall or old.
John is not brave.
Alice is curious or creative.
Someone is kind.
Someone is not happy or strong. | John is happy. | neutral | (![X]:(~rich(X)=>(calm(X)<~>~generous(X))))&
(![X]:((calm(X)<~>quiet(X))<=>creative(X)))&
(![X]:((rich(X)<~>~happy(X))=>~creative(X)))&
(((~happy(mary)&~old(mary)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~curious(X)<~>old(X))<=>~patient(X)))&
(((~brave(john)|~wise(john)))<=>(?[X]:(generous(X))))&
((?[X]:(~wise(X)))=>((~kind(john)<~>calm(john))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((~humble(X)|rich(X))=>(funny(X)&~generous(X))))&
((?[X]:((wise(X)<~>strong(X))))=>((funny(john)|~rich(john))))&
(![X]:((~funny(X)&generous(X))<=>(~quiet(X)<~>happy(X))))&
(((creative(susan)&~tall(susan)))=>(?[X]:((~rich(X)|~kind(X)))))&
((brave(fred))=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:(curious(X)=>happy(X)))&
(((~rich(alice)<~>creative(alice)))<=>(brave(fred)))&
(((patient(susan)|~strong(susan)))<=>((rich(john)<~>~funny(john))))&
(?[X]:((~strong(X)&~calm(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~brave(john))&
((curious(alice)|creative(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|strong(X)))) | happy(john) | [] | null | 0 |
Everyone who is not wise or tall is humble or not curious and vice versa.
If fred is not generous then someone is not calm and vice versa.
If someone is not tall or quiet then someone is either rich or patient.
If someone is rich or not strong then alice is either not strong or not patient.
Everyone who is either not kind or not happy is happy or not generous.
Everyone who is either happy or patient is wise.
Everyone who is both happy and tall is calm or not brave.
Everyone who is both quiet and not humble is quiet.
If someone is both not funny and rich then someone is both not generous and curious and vice versa.
If mary is not happy or not quiet then someone is both not brave and curious.
Everyone who is not brave is humble and vice versa.
Everyone who is either funny or not patient is not tall.
Everyone who is both not strong and quiet is not generous and vice versa.
If paul is both not patient and funny then someone is not quiet or not old.
Everyone who is patient or funny is not strong.
Everyone who is either old or patient is both not rich and not happy.
Someone is both not brave and tall.
Someone is happy or calm.
Alice is either not generous or calm.
Someone is either rich or strong.
Someone is not generous or not wise.
Someone is generous or not wise.
Mary is not patient or not generous.
Fred is not happy. | Mary is tall. | neutral | (![X]:((~wise(X)|tall(X))<=>(humble(X)|~curious(X))))&
((~generous(fred))<=>(?[X]:(~calm(X))))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:((rich(X)<~>patient(X)))))&
((?[X]:((rich(X)|~strong(X))))=>((~strong(alice)<~>~patient(alice))))&
(![X]:((~kind(X)<~>~happy(X))=>(happy(X)|~generous(X))))&
(![X]:((happy(X)<~>patient(X))=>wise(X)))&
(![X]:((happy(X)&tall(X))=>(calm(X)|~brave(X))))&
(![X]:((quiet(X)&~humble(X))=>quiet(X)))&
((?[X]:((~funny(X)&rich(X))))<=>(?[X]:((~generous(X)&curious(X)))))&
(((~happy(mary)|~quiet(mary)))=>(?[X]:((~brave(X)&curious(X)))))&
(![X]:(~brave(X)<=>humble(X)))&
(![X]:((funny(X)<~>~patient(X))=>~tall(X)))&
(![X]:((~strong(X)&quiet(X))<=>~generous(X)))&
(((~patient(paul)&funny(paul)))=>(?[X]:((~quiet(X)|~old(X)))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
(?[X]:((~brave(X)&tall(X))))&
(?[X]:((happy(X)|calm(X))))&
((~generous(alice)<~>calm(alice)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~generous(X)|~wise(X))))&
(?[X]:((generous(X)|~wise(X))))&
((~patient(mary)|~generous(mary)))&
(~happy(fred)) | tall(mary) | [] | null | 0 |
Everyone who is not patient or tall is not calm and vice versa.
If john is old then mary is calm or brave.
If someone is brave or calm then someone is both not calm and not quiet.
Everyone who is generous is either not curious or not calm.
Everyone who is not old is creative.
Everyone who is both not curious and not calm is either not happy or brave and vice versa.
Everyone who is strong or tall is both humble and brave.
If lucy is either generous or not strong then someone is old or not calm and vice versa.
Everyone who is generous is rich or not happy and vice versa.
Everyone who is either not calm or curious is not quiet or humble.
Everyone who is not kind or funny is not brave.
Everyone who is either not creative or tall is either calm or not generous and vice versa.
Everyone who is not wise or not happy is either not generous or not wise and vice versa.
Everyone who is either not wise or quiet is either not generous or wise.
Everyone who is strong is tall or not wise and vice versa.
If paul is not creative or not curious then someone is not wise or not old and vice versa.
Lucy is either humble or old.
Someone is not curious or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous.
Fred is not generous or not patient.
Someone is not wise or not old. | Mary is calm. | entailment | (![X]:((~patient(X)|tall(X))<=>~calm(X)))&
((old(john))=>((calm(mary)|brave(mary))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~calm(X))))&
(![X]:(~old(X)=>creative(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
(![X]:(strong(X)<=>(tall(X)|~wise(X))))&
(((~creative(paul)|~curious(paul)))<=>(?[X]:((~wise(X)|~old(X)))))&
((humble(lucy)<~>old(lucy)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X))))&
((~generous(fred)|~patient(fred)))&
(?[X]:((~wise(X)|~old(X)))) | calm(mary) | [
"p0",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5906952347316359722902527
% SZS output start Proof for 5906952347316359722902527
1. ! [X0] : ((tall(X0) | ~patient(X0)) <=> ~calm(X0)) [input p0]
9. ! [X0] : (generous(X0) <=> (~happy(X0) | rich(X0))) [input p8]
12. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p12]
19. ~creative(mary) <~> tall(mary) [input p18]
24. ~calm(mary) [input hypothesis]
37. ! [X0] : (((tall(X0) | ~patient(X0)) | calm(X0)) & (~calm(X0) | (~tall(X0) & patient(X0)))) [nnf transformation 1]
38. ! [X0] : ((tall(X0) | ~patient(X0) | calm(X0)) & (~calm(X0) | (~tall(X0) & patient(X0)))) [flattening 37]
49. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ~generous(X0))) [nnf transformation 9]
50. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~generous(X0))) [flattening 49]
52. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 12]
53. ! [X0] : (((~happy(X0) | ~wise(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [nnf transformation 13]
54. ! [X0] : ((~happy(X0) | ~wise(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [flattening 53]
66. (~tall(mary) | creative(mary)) & (tall(mary) | ~creative(mary)) [nnf transformation 19]
72. ~calm(X0) | ~tall(X0) [cnf transformation 38]
100. happy(X0) | generous(X0) [cnf transformation 50]
104. ~generous(X0) | calm(X0) | tall(X0) | creative(X0) [cnf transformation 52]
105. ~generous(X0) | calm(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 52]
114. wise(X0) | generous(X0) | wise(X0) [cnf transformation 54]
116. ~happy(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 54]
132. tall(mary) | ~creative(mary) [cnf transformation 66]
133. ~tall(mary) | creative(mary) [cnf transformation 66]
138. ~calm(mary) [cnf transformation 24]
141. wise(X0) | generous(X0) [duplicate literal removal 114]
142. ~happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 116]
148. 2 <=> calm(mary) [avatar definition]
149. ~calm(mary) <- (~2) [avatar component clause 148]
205. ~creative(X0) | ~generous(X0) | ~tall(X0) [subsumption resolution 105,72]
206. ~wise(X0) | generous(X0) [subsumption resolution 142,100]
207. generous(X0) [subsumption resolution 141,206]
256. 24 <=> creative(mary) [avatar definition]
257. ~creative(mary) <- (~24) [avatar component clause 256]
258. creative(mary) <- (24) [avatar component clause 256]
260. 25 <=> tall(mary) [avatar definition]
261. tall(mary) <- (25) [avatar component clause 260]
262. ~tall(mary) <- (~25) [avatar component clause 260]
263. 24 | ~25 [avatar split clause 133,260,256]
264. ~24 | 25 [avatar split clause 132,260,256]
284. ~2 [avatar split clause 138,148]
352. creative(X0) | tall(X0) | calm(X0) [resolution 104,207]
393. tall(mary) | calm(mary) <- (~24) [resolution 352,257]
398. calm(mary) <- (~24, ~25) [subsumption resolution 393,262]
399. $false <- (~2, ~24, ~25) [subsumption resolution 398,149]
400. 2 | 24 | 25 [avatar contradiction clause 399]
402. ~generous(mary) | ~tall(mary) <- (24) [resolution 258,205]
404. ~tall(mary) <- (24) [subsumption resolution 402,207]
405. $false <- (24, 25) [subsumption resolution 404,261]
406. ~24 | ~25 [avatar contradiction clause 405]
407. $false [avatar sat refutation 263,264,284,400,406]
% SZS output end Proof for 5906952347316359722902527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and funny is not generous or generous and vice versa. If someone is both not strong and not old then susan is not wise. Everyone who is creative or old is not creative and vice versa. Everyone who is old is not wise. Everyone who is not generous or creative is rich or creative and vice versa. Everyone who is both not brave and not kind is not curious or not old. Everyone who is either not wise or brave is wise or not quiet. Everyone who is both not curious and strong is both happy and funny and vice versa. Everyone who is not wise or not kind is both humble and calm and vice versa. If someone is old or rich then john is quiet or happy. If mary is either not kind or not rich then someone is either wise or not kind. If fred is rich then someone is strong or not tall and vice versa. Everyone who is either not generous or not patient is not wise. If paul is either curious or tall then someone is both not quiet and strong. Everyone who is both not creative and not happy is not wise. If someone is either humble or patient then paul is strong and vice versa. Mary is either not calm or funny. Someone is not quiet or not tall. Mary is not patient. Someone is either wise or tall. Someone is not curious or strong. Someone is either not rich or rich. Someone is either not patient or not curious. | Fred is generous. | contradiction | (![X]:((~curious(X)&funny(X))<=>(~generous(X)|generous(X))))&
((?[X]:((~strong(X)&~old(X))))=>(~wise(susan)))&
(![X]:((creative(X)|old(X))<=>~creative(X)))&
(![X]:(old(X)=>~wise(X)))&
(![X]:((~generous(X)|creative(X))<=>(rich(X)|creative(X))))&
(![X]:((~brave(X)&~kind(X))=>(~curious(X)|~old(X))))&
(![X]:((~wise(X)<~>brave(X))=>(wise(X)|~quiet(X))))&
(![X]:((~curious(X)&strong(X))<=>(happy(X)&funny(X))))&
(![X]:((~wise(X)|~kind(X))<=>(humble(X)&calm(X))))&
((?[X]:((old(X)|rich(X))))=>((quiet(john)|happy(john))))&
(((~kind(mary)<~>~rich(mary)))=>(?[X]:((wise(X)<~>~kind(X)))))&
((rich(fred))<=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((~generous(X)<~>~patient(X))=>~wise(X)))&
(((curious(paul)<~>tall(paul)))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((~creative(X)&~happy(X))=>~wise(X)))&
((?[X]:((humble(X)<~>patient(X))))<=>(strong(paul)))&
((~calm(mary)<~>funny(mary)))&
(?[X]:((~quiet(X)|~tall(X))))&
(~patient(mary))&
(?[X]:((wise(X)<~>tall(X))))&
(?[X]:((~curious(X)|strong(X))))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((~patient(X)<~>~curious(X)))) | generous(fred) | [
"p0",
"p2",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5256424172625487792481935
% SZS output start Proof for 5256424172625487792481935
1. ! [X0] : ((funny(X0) & ~curious(X0)) <=> (generous(X0) | ~generous(X0))) [input p0]
3. ! [X0] : ((old(X0) | creative(X0)) <=> ~creative(X0)) [input p2]
5. ! [X0] : ((creative(X0) | ~generous(X0)) <=> (creative(X0) | rich(X0))) [input p4]
12. rich(fred) <=> ? [X0] : (~tall(X0) | strong(X0)) [input p11]
14. (curious(paul) <~> tall(paul)) => ? [X0] : (strong(X0) & ~quiet(X0)) [input p13]
24. generous(fred) [input hypothesis]
35. ? [X0] : (strong(X0) & ~quiet(X0)) | (curious(paul) <=> tall(paul)) [ennf transformation 14]
38. ! [X0] : (((funny(X0) & ~curious(X0)) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | (~funny(X0) | curious(X0)))) [nnf transformation 1]
39. ! [X0] : (((funny(X0) & ~curious(X0)) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | ~funny(X0) | curious(X0))) [flattening 38]
40. ! [X0] : (((old(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (~old(X0) & ~creative(X0)))) [nnf transformation 3]
41. ! [X0] : ((old(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (~old(X0) & ~creative(X0)))) [flattening 40]
42. ! [X0] : (((creative(X0) | ~generous(X0)) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | (~creative(X0) & generous(X0)))) [nnf transformation 5]
43. ! [X0] : ((creative(X0) | ~generous(X0) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | (~creative(X0) & generous(X0)))) [flattening 42]
52. (rich(fred) | ! [X0] : (tall(X0) & ~strong(X0))) & (? [X0] : (~tall(X0) | strong(X0)) | ~rich(fred)) [nnf transformation 12]
53. (rich(fred) | ! [X0] : (tall(X0) & ~strong(X0))) & (? [X1] : (~tall(X1) | strong(X1)) | ~rich(fred)) [rectify 52]
54. ? [X1] : (~tall(X1) | strong(X1)) => (~tall(sK1) | strong(sK1)) [choice axiom]
55. (rich(fred) | ! [X0] : (tall(X0) & ~strong(X0))) & ((~tall(sK1) | strong(sK1)) | ~rich(fred)) [skolemisation 53,54]
57. ? [X0] : (strong(X0) & ~quiet(X0)) | ((curious(paul) | ~tall(paul)) & (tall(paul) | ~curious(paul))) [nnf transformation 35]
58. ? [X0] : (strong(X0) & ~quiet(X0)) => (strong(sK2) & ~quiet(sK2)) [choice axiom]
59. (strong(sK2) & ~quiet(sK2)) | ((curious(paul) | ~tall(paul)) & (tall(paul) | ~curious(paul))) [skolemisation 57,58]
79. ~curious(X0) | generous(X0) [cnf transformation 39]
80. ~generous(X0) | ~curious(X0) [cnf transformation 39]
84. ~creative(X0) | ~creative(X0) [cnf transformation 41]
90. creative(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 43]
111. rich(fred) | ~strong(X0) [cnf transformation 55]
112. rich(fred) | tall(X0) [cnf transformation 55]
118. strong(sK2) | curious(paul) | ~tall(paul) [cnf transformation 59]
135. generous(fred) [cnf transformation 24]
137. ~creative(X0) [duplicate literal removal 84]
140. ~curious(X0) [subsumption resolution 79,80]
149. ~rich(X0) | ~generous(X0) [subsumption resolution 90,137]
190. 11 <=> ! [X0] : tall(X0) [avatar definition]
191. tall(X0) <- (11) [avatar component clause 190]
193. 12 <=> rich(fred) [avatar definition]
195. rich(fred) <- (12) [avatar component clause 193]
196. 11 | 12 [avatar split clause 112,193,190]
198. 13 <=> ! [X0] : ~strong(X0) [avatar definition]
199. ~strong(X0) <- (13) [avatar component clause 198]
200. 13 | 12 [avatar split clause 111,193,198]
210. strong(sK2) | ~tall(paul) [subsumption resolution 118,140]
212. 16 <=> tall(paul) [avatar definition]
214. ~tall(paul) <- (~16) [avatar component clause 212]
216. 17 <=> strong(sK2) [avatar definition]
218. strong(sK2) <- (17) [avatar component clause 216]
219. ~16 | 17 [avatar split clause 210,216,212]
277. ~generous(fred) <- (12) [resolution 149,195]
278. $false <- (12) [subsumption resolution 277,135]
279. ~12 [avatar contradiction clause 278]
280. $false <- (11, ~16) [resolution 191,214]
285. ~11 | 16 [avatar contradiction clause 280]
286. $false <- (13, 17) [subsumption resolution 218,199]
287. ~13 | ~17 [avatar contradiction clause 286]
288. $false [avatar sat refutation 196,200,219,279,285,287]
% SZS output end Proof for 5256424172625487792481935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either not wise or wise then someone is kind and vice versa. Everyone who is not humble or strong is both not calm and kind. If someone is both not calm and quiet then john is either not strong or not funny. If paul is rich or not quiet then someone is not humble and vice versa. If someone is both humble and curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Everyone who is humble or not humble is both not rich and brave and vice versa. If someone is either not quiet or not wise then someone is not quiet and vice versa. If mary is not humble then someone is generous and vice versa. If someone is not quiet then paul is not wise. If lucy is not curious or not funny then lucy is either not funny or kind and vice versa. If someone is either strong or curious then someone is not curious or not brave. If fred is not patient then john is not old or wise. If john is funny or brave then mary is not happy or old and vice versa. If someone is both not wise and not calm then alice is both not humble and not old. Someone is kind. Fred is both not funny and calm. Someone is not old. Someone is both tall and creative. Fred is both quiet and generous. Someone is either not curious or brave. Someone is either quiet or not happy. Someone is not curious. | Fred is rich. | contradiction | (((~wise(john)<~>wise(john)))<=>(?[X]:(kind(X))))&
(![X]:((~humble(X)|strong(X))=>(~calm(X)&kind(X))))&
((?[X]:((~calm(X)&quiet(X))))=>((~strong(john)<~>~funny(john))))&
(((rich(paul)|~quiet(paul)))<=>(?[X]:(~humble(X))))&
((?[X]:((humble(X)&curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
(![X]:((humble(X)|~humble(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
((~humble(mary))<=>(?[X]:(generous(X))))&
((?[X]:(~quiet(X)))=>(~wise(paul)))&
(((~curious(lucy)|~funny(lucy)))<=>((~funny(lucy)<~>kind(lucy))))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~curious(X)|~brave(X)))))&
((~patient(fred))=>((~old(john)|wise(john))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
(?[X]:(kind(X)))&
((~funny(fred)&calm(fred)))&
(?[X]:(~old(X)))&
(?[X]:((tall(X)&creative(X))))&
((quiet(fred)&generous(fred)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:(~curious(X))) | rich(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8638384869665299474770906
% SZS output start Proof for 8638384869665299474770906
8. ! [X0] : ((~humble(X0) | humble(X0)) <=> (brave(X0) & ~rich(X0))) [input p7]
25. rich(fred) [input hypothesis]
50. ! [X0] : (((~humble(X0) | humble(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 8]
51. ! [X0] : ((~humble(X0) | humble(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [flattening 50]
108. ~rich(X0) | ~humble(X0) [cnf transformation 51]
109. ~rich(X0) | humble(X0) [cnf transformation 51]
146. rich(fred) [cnf transformation 25]
206. ~rich(X0) [subsumption resolution 108,109]
315. $false [subsumption resolution 146,206]
% SZS output end Proof for 8638384869665299474770906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not brave then susan is both kind and calm. If fred is not rich then someone is either kind or not tall and vice versa. Everyone who is not happy or not kind is both not tall and calm. Everyone who is either not patient or tall is old and vice versa. Everyone who is both happy and not patient is either curious or not old and vice versa. If alice is curious then someone is both not strong and not creative. If mary is either not humble or curious then susan is humble and vice versa. Everyone who is both creative and not tall is both funny and not quiet. Everyone who is happy is strong or not rich. Everyone who is either patient or humble is either strong or not happy and vice versa. Everyone who is kind or wise is not kind and vice versa. If someone is both not rich and old then someone is tall or not kind and vice versa. Everyone who is both old and calm is both brave and not funny. Everyone who is either not brave or not old is not funny or not brave. If paul is curious then mary is both wise and tall. If fred is not rich then someone is both calm and curious and vice versa. Lucy is either happy or not happy. Someone is either not rich or not patient. Someone is brave or not rich. Someone is not happy or not old. Alice is both not patient and not funny. Someone is either not generous or happy. | Paul is funny. | contradiction | ((?[X]:((~generous(X)<~>~brave(X))))=>((kind(susan)&calm(susan))))&
((~rich(fred))<=>(?[X]:((kind(X)<~>~tall(X)))))&
(![X]:((~happy(X)|~kind(X))=>(~tall(X)&calm(X))))&
(![X]:((~patient(X)<~>tall(X))<=>old(X)))&
(![X]:((happy(X)&~patient(X))<=>(curious(X)<~>~old(X))))&
((curious(alice))=>(?[X]:((~strong(X)&~creative(X)))))&
(((~humble(mary)<~>curious(mary)))<=>(humble(susan)))&
(![X]:((creative(X)&~tall(X))=>(funny(X)&~quiet(X))))&
(![X]:(happy(X)=>(strong(X)|~rich(X))))&
(![X]:((patient(X)<~>humble(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((kind(X)|wise(X))<=>~kind(X)))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((old(X)&calm(X))=>(brave(X)&~funny(X))))&
(![X]:((~brave(X)<~>~old(X))=>(~funny(X)|~brave(X))))&
((curious(paul))=>((wise(mary)&tall(mary))))&
((~rich(fred))<=>(?[X]:((calm(X)&curious(X)))))&
((happy(lucy)<~>~happy(lucy)))&
(?[X]:((~rich(X)<~>~patient(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~happy(X)|~old(X))))&
((~patient(alice)&~funny(alice)))&
(?[X]:((~generous(X)<~>happy(X)))) | funny(paul) | [
"p2",
"p3",
"p4",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8389776006329907977145006
% SZS output start Proof for 8389776006329907977145006
3. ! [X0] : ((~kind(X0) | ~happy(X0)) => (calm(X0) & ~tall(X0))) [input p2]
4. ! [X0] : ((~patient(X0) <~> tall(X0)) <=> old(X0)) [input p3]
5. ! [X0] : ((~patient(X0) & happy(X0)) <=> (curious(X0) <~> ~old(X0))) [input p4]
11. ! [X0] : ((wise(X0) | kind(X0)) <=> ~kind(X0)) [input p10]
13. ! [X0] : ((calm(X0) & old(X0)) => (~funny(X0) & brave(X0))) [input p12]
15. curious(paul) => (tall(mary) & wise(mary)) [input p14]
23. funny(paul) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~tall(X0)) | (kind(X0) & happy(X0))) [ennf transformation 3]
33. ! [X0] : ((~funny(X0) & brave(X0)) | (~calm(X0) | ~old(X0))) [ennf transformation 13]
34. ! [X0] : ((~funny(X0) & brave(X0)) | ~calm(X0) | ~old(X0)) [flattening 33]
37. (tall(mary) & wise(mary)) | ~curious(paul) [ennf transformation 15]
43. ! [X0] : ((((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ~old(X0)) & (old(X0) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0))))) [nnf transformation 4]
44. ! [X0] : (((~patient(X0) & happy(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (patient(X0) | ~happy(X0)))) [nnf transformation 5]
45. ! [X0] : (((~patient(X0) & happy(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | patient(X0) | ~happy(X0))) [flattening 44]
50. ! [X0] : (((wise(X0) | kind(X0)) | kind(X0)) & (~kind(X0) | (~wise(X0) & ~kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((wise(X0) | kind(X0) | kind(X0)) & (~kind(X0) | (~wise(X0) & ~kind(X0)))) [flattening 50]
82. ~tall(X0) | kind(X0) [cnf transformation 29]
84. calm(X0) | kind(X0) [cnf transformation 29]
85. old(X0) | tall(X0) | patient(X0) [cnf transformation 43]
94. ~patient(X0) | curious(X0) | old(X0) [cnf transformation 45]
109. ~kind(X0) | ~kind(X0) [cnf transformation 51]
118. ~funny(X0) | ~calm(X0) | ~old(X0) [cnf transformation 34]
122. tall(mary) | ~curious(paul) [cnf transformation 37]
136. funny(paul) [cnf transformation 23]
138. ~kind(X0) [duplicate literal removal 109]
208. 15 <=> curious(paul) [avatar definition]
210. ~curious(paul) <- (~15) [avatar component clause 208]
212. 16 <=> tall(mary) [avatar definition]
214. tall(mary) <- (16) [avatar component clause 212]
215. ~15 | 16 [avatar split clause 122,212,208]
347. 39 <=> old(paul) [avatar definition]
348. ~old(paul) <- (~39) [avatar component clause 347]
349. old(paul) <- (39) [avatar component clause 347]
361. kind(mary) <- (16) [resolution 214,82]
363. $false <- (16) [subsumption resolution 361,138]
364. ~16 [avatar contradiction clause 363]
406. ~calm(paul) | ~old(paul) [resolution 118,136]
407. ~calm(paul) <- (39) [subsumption resolution 406,349]
412. 45 <=> tall(paul) [avatar definition]
413. tall(paul) <- (45) [avatar component clause 412]
414. ~tall(paul) <- (~45) [avatar component clause 412]
416. 46 <=> patient(paul) [avatar definition]
418. patient(paul) <- (46) [avatar component clause 416]
467. kind(paul) <- (39) [resolution 407,84]
468. $false <- (39) [subsumption resolution 467,138]
469. ~39 [avatar contradiction clause 468]
480. tall(paul) | patient(paul) <- (~39) [resolution 348,85]
600. kind(paul) <- (45) [resolution 413,82]
602. $false <- (45) [subsumption resolution 600,138]
603. ~45 [avatar contradiction clause 602]
605. curious(paul) | old(paul) <- (46) [resolution 418,94]
613. old(paul) <- (~15, 46) [subsumption resolution 605,210]
614. $false <- (~15, ~39, 46) [subsumption resolution 613,348]
615. 15 | 39 | ~46 [avatar contradiction clause 614]
616. patient(paul) <- (~39, ~45) [subsumption resolution 480,414]
617. 46 | 39 | 45 [avatar split clause 616,412,347,416]
621. $false [avatar sat refutation 215,364,469,603,615,617]
% SZS output end Proof for 8389776006329907977145006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both tall and quiet and vice versa.
If alice is either not wise or old then someone is either brave or humble.
If lucy is funny or strong then lucy is calm or not creative and vice versa.
Everyone who is either happy or not tall is creative.
Everyone who is both not curious and tall is generous or wise.
Everyone who is either not happy or not creative is kind and vice versa.
If paul is not creative or creative then someone is wise and vice versa.
If paul is either old or not creative then mary is patient.
Everyone who is either not wise or not funny is either not wise or not patient.
If john is either not funny or not kind then someone is both not humble and humble.
If someone is either not humble or not calm then alice is both wise and strong and vice versa.
If someone is either happy or not generous then mary is both not funny and creative.
Everyone who is tall is not generous or not quiet and vice versa.
Everyone who is not funny is wise or not creative and vice versa.
If someone is calm or wise then mary is patient and vice versa.
Everyone who is not quiet or not humble is both not quiet and not calm.
Fred is rich.
Someone is not generous.
Someone is both not curious and not quiet.
Someone is quiet or curious. | Alice is not generous. | neutral | (![X]:(~funny(X)<=>(tall(X)&quiet(X))))&
(((~wise(alice)<~>old(alice)))=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(lucy)|strong(lucy)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((happy(X)<~>~tall(X))=>creative(X)))&
(![X]:((~curious(X)&tall(X))=>(generous(X)|wise(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>kind(X)))&
(((~creative(paul)|creative(paul)))<=>(?[X]:(wise(X))))&
(((old(paul)<~>~creative(paul)))=>(patient(mary)))&
(![X]:((~wise(X)<~>~funny(X))=>(~wise(X)<~>~patient(X))))&
(((~funny(john)<~>~kind(john)))=>(?[X]:((~humble(X)&humble(X)))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>((wise(alice)&strong(alice))))&
((?[X]:((happy(X)<~>~generous(X))))=>((~funny(mary)&creative(mary))))&
(![X]:(tall(X)<=>(~generous(X)|~quiet(X))))&
(![X]:(~funny(X)<=>(wise(X)|~creative(X))))&
((?[X]:((calm(X)|wise(X))))<=>(patient(mary)))&
(![X]:((~quiet(X)|~humble(X))=>(~quiet(X)&~calm(X))))&
(rich(fred))&
(?[X]:(~generous(X)))&
(?[X]:((~curious(X)&~quiet(X))))&
(?[X]:((quiet(X)|curious(X)))) | ~generous(alice) | [] | null | 0 |
If someone is humble then someone is not creative and vice versa. Everyone who is not humble is either not rich or not kind. If someone is either not humble or creative then someone is either calm or humble and vice versa. If lucy is either not creative or curious then john is patient. Everyone who is not brave or not funny is brave and vice versa. Everyone who is curious is not old. If someone is either not happy or brave then alice is funny or tall. Everyone who is not old or calm is both strong and not funny. Everyone who is either happy or not curious is both generous and not old. Everyone who is strong or old is not funny or not brave and vice versa. If mary is not kind or kind then someone is both quiet and not humble and vice versa. If alice is not generous or rich then john is old or creative and vice versa. If someone is strong then lucy is either not rich or humble. Everyone who is both not tall and not rich is patient or wise. Everyone who is either not humble or not tall is both patient and not humble. Everyone who is not brave is either not old or not funny. Someone is both happy and not funny. Someone is strong. Mary is both happy and not wise. Mary is not creative or not happy. Someone is both not curious and strong. Paul is both tall and strong. Susan is either wise or not quiet. Mary is either wise or not generous. | Alice is tall. | entailment | ((?[X]:(humble(X)))<=>(?[X]:(~creative(X))))&
(![X]:(~humble(X)=>(~rich(X)<~>~kind(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>(?[X]:((calm(X)<~>humble(X)))))&
(((~creative(lucy)<~>curious(lucy)))=>(patient(john)))&
(![X]:((~brave(X)|~funny(X))<=>brave(X)))&
(![X]:(curious(X)=>~old(X)))&
((?[X]:((~happy(X)<~>brave(X))))=>((funny(alice)|tall(alice))))&
(![X]:((~old(X)|calm(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)<~>~curious(X))=>(generous(X)&~old(X))))&
(![X]:((strong(X)|old(X))<=>(~funny(X)|~brave(X))))&
(((~kind(mary)|kind(mary)))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((~generous(alice)|rich(alice)))<=>((old(john)|creative(john))))&
((?[X]:(strong(X)))=>((~rich(lucy)<~>humble(lucy))))&
(![X]:((~tall(X)&~rich(X))=>(patient(X)|wise(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(patient(X)&~humble(X))))&
(![X]:(~brave(X)=>(~old(X)<~>~funny(X))))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:(strong(X)))&
((happy(mary)&~wise(mary)))&
((~creative(mary)|~happy(mary)))&
(?[X]:((~curious(X)&strong(X))))&
((tall(paul)&strong(paul)))&
((wise(susan)<~>~quiet(susan)))&
((wise(mary)<~>~generous(mary))) | tall(alice) | [
"p4",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7237323631955675674484063
% SZS output start Proof for 7237323631955675674484063
5. ! [X0] : ((~funny(X0) | ~brave(X0)) <=> brave(X0)) [input p4]
7. ? [X0] : (~happy(X0) <~> brave(X0)) => (tall(alice) | funny(alice)) [input p6]
17. ? [X0] : (~funny(X0) & happy(X0)) [input p16]
25. ~tall(alice) [input hypothesis]
33. (tall(alice) | funny(alice)) | ! [X0] : (~happy(X0) <=> brave(X0)) [ennf transformation 7]
34. tall(alice) | funny(alice) | ! [X0] : (~happy(X0) <=> brave(X0)) [flattening 33]
51. ! [X0] : (((~funny(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & brave(X0)))) [nnf transformation 5]
52. ! [X0] : ((~funny(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & brave(X0)))) [flattening 51]
53. tall(alice) | funny(alice) | ! [X0] : ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))) [nnf transformation 34]
67. ? [X0] : (~funny(X0) & happy(X0)) => (~funny(sK5) & happy(sK5)) [choice axiom]
68. ~funny(sK5) & happy(sK5) [skolemisation 17,67]
87. brave(X0) | brave(X0) [cnf transformation 52]
89. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 52]
92. tall(alice) | funny(alice) | ~happy(X0) | ~brave(X0) [cnf transformation 53]
120. happy(sK5) [cnf transformation 68]
134. ~tall(alice) [cnf transformation 25]
136. brave(X0) [duplicate literal removal 87]
137. ~funny(X0) | ~brave(X0) [duplicate literal removal 89]
190. tall(alice) | funny(alice) | ~happy(X0) [subsumption resolution 92,136]
192. 13 <=> ! [X0] : ~happy(X0) [avatar definition]
193. ~happy(X0) <- (13) [avatar component clause 192]
195. 14 <=> funny(alice) [avatar definition]
197. funny(alice) <- (14) [avatar component clause 195]
199. 15 <=> tall(alice) [avatar definition]
202. 13 | 14 | 15 [avatar split clause 190,199,195,192]
265. ~15 [avatar split clause 134,199]
266. $false <- (13) [resolution 193,120]
269. ~13 [avatar contradiction clause 266]
278. ~brave(alice) <- (14) [resolution 137,197]
280. $false <- (14) [subsumption resolution 278,136]
281. ~14 [avatar contradiction clause 280]
282. $false [avatar sat refutation 202,265,269,281]
% SZS output end Proof for 7237323631955675674484063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or funny then someone is both not happy and not old. Everyone who is not calm is both not curious and curious. Everyone who is not humble is either not kind or not humble. Everyone who is quiet is both curious and tall. If someone is either humble or happy then someone is both kind and not funny and vice versa. Everyone who is either rich or funny is generous or patient. Everyone who is not curious is not strong or not kind. If someone is both creative and not funny then mary is not old and vice versa. Everyone who is not old is kind. Everyone who is not quiet is both wise and not happy and vice versa. Everyone who is not calm or not old is both quiet and not curious and vice versa. If someone is both humble and calm then mary is kind or not patient and vice versa. Everyone who is wise or strong is both not strong and humble. Everyone who is both not humble and not calm is patient or rich and vice versa. If someone is not creative then susan is both not brave and happy and vice versa. John is wise. Someone is both not creative and quiet. Someone is not strong or old. Someone is either not brave or curious. Someone is creative. | John is tall. | entailment | ((?[X]:((kind(X)<~>funny(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:(~calm(X)=>(~curious(X)&curious(X))))&
(![X]:(~humble(X)=>(~kind(X)<~>~humble(X))))&
(![X]:(quiet(X)=>(curious(X)&tall(X))))&
((?[X]:((humble(X)<~>happy(X))))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((rich(X)<~>funny(X))=>(generous(X)|patient(X))))&
(![X]:(~curious(X)=>(~strong(X)|~kind(X))))&
((?[X]:((creative(X)&~funny(X))))<=>(~old(mary)))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~quiet(X)<=>(wise(X)&~happy(X))))&
(![X]:((~calm(X)|~old(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((humble(X)&calm(X))))<=>((kind(mary)|~patient(mary))))&
(![X]:((wise(X)|strong(X))=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)|rich(X))))&
((?[X]:(~creative(X)))<=>((~brave(susan)&happy(susan))))&
(wise(john))&
(?[X]:((~creative(X)&quiet(X))))&
(?[X]:((~strong(X)|old(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:(creative(X))) | tall(john) | [
"p0",
"p3",
"p4",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1634620351068849205303935
% SZS output start Proof for 1634620351068849205303935
1. ? [X0] : (kind(X0) <~> funny(X0)) => ? [X0] : (~old(X0) & ~happy(X0)) [input p0]
4. ! [X0] : (quiet(X0) => (tall(X0) & curious(X0))) [input p3]
5. ? [X0] : (humble(X0) <~> happy(X0)) <=> ? [X0] : (~funny(X0) & kind(X0)) [input p4]
10. ! [X0] : (~quiet(X0) <=> (~happy(X0) & wise(X0))) [input p9]
11. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (~curious(X0) & quiet(X0))) [input p10]
13. ! [X0] : ((strong(X0) | wise(X0)) => (humble(X0) & ~strong(X0))) [input p12]
16. wise(john) [input p15]
21. ~tall(john) [input hypothesis]
22. ? [X0] : (kind(X0) <~> funny(X0)) => ? [X1] : (~old(X1) & ~happy(X1)) [rectify 1]
23. ? [X0] : (humble(X0) <~> happy(X0)) <=> ? [X1] : (~funny(X1) & kind(X1)) [rectify 5]
26. ! [X0] : (wise(X0) => humble(X0)) [pure predicate removal 13]
28. ? [X1] : (~old(X1) & ~happy(X1)) | ! [X0] : (kind(X0) <=> funny(X0)) [ennf transformation 22]
31. ! [X0] : ((tall(X0) & curious(X0)) | ~quiet(X0)) [ennf transformation 4]
33. ! [X0] : (humble(X0) | ~wise(X0)) [ennf transformation 26]
34. ? [X1] : (~old(X1) & ~happy(X1)) | ! [X0] : ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0))) [nnf transformation 28]
35. ? [X0] : (~old(X0) & ~happy(X0)) | ! [X1] : ((kind(X1) | ~funny(X1)) & (funny(X1) | ~kind(X1))) [rectify 34]
36. ? [X0] : (~old(X0) & ~happy(X0)) => (~old(sK0) & ~happy(sK0)) [choice axiom]
37. (~old(sK0) & ~happy(sK0)) | ! [X1] : ((kind(X1) | ~funny(X1)) & (funny(X1) | ~kind(X1))) [skolemisation 35,36]
39. (? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ! [X1] : (funny(X1) | ~kind(X1))) & (? [X1] : (~funny(X1) & kind(X1)) | ! [X0] : ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) [nnf transformation 23]
40. (? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ! [X1] : (funny(X1) | ~kind(X1))) & (? [X2] : (~funny(X2) & kind(X2)) | ! [X3] : ((humble(X3) | ~happy(X3)) & (happy(X3) | ~humble(X3)))) [rectify 39]
41. ? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) => ((~happy(sK1) | ~humble(sK1)) & (happy(sK1) | humble(sK1))) [choice axiom]
42. ? [X2] : (~funny(X2) & kind(X2)) => (~funny(sK2) & kind(sK2)) [choice axiom]
43. (((~happy(sK1) | ~humble(sK1)) & (happy(sK1) | humble(sK1))) | ! [X1] : (funny(X1) | ~kind(X1))) & ((~funny(sK2) & kind(sK2)) | ! [X3] : ((humble(X3) | ~happy(X3)) & (happy(X3) | ~humble(X3)))) [skolemisation 40,42,41]
48. ! [X0] : ((~quiet(X0) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | quiet(X0))) [nnf transformation 10]
49. ! [X0] : ((~quiet(X0) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | quiet(X0))) [flattening 48]
50. ! [X0] : (((~old(X0) | ~calm(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (old(X0) & calm(X0)))) [nnf transformation 11]
51. ! [X0] : ((~old(X0) | ~calm(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | (old(X0) & calm(X0)))) [flattening 50]
73. ~old(sK0) | funny(X1) | ~kind(X1) [cnf transformation 37]
79. ~quiet(X0) | curious(X0) [cnf transformation 31]
80. ~quiet(X0) | tall(X0) [cnf transformation 31]
81. kind(sK2) | happy(X3) | ~humble(X3) [cnf transformation 43]
83. ~funny(sK2) | happy(X3) | ~humble(X3) [cnf transformation 43]
92. ~happy(X0) | quiet(X0) [cnf transformation 49]
95. quiet(X0) | old(X0) [cnf transformation 51]
97. ~curious(X0) | old(X0) [cnf transformation 51]
104. ~wise(X0) | humble(X0) [cnf transformation 33]
113. wise(john) [cnf transformation 16]
119. ~tall(john) [cnf transformation 21]
125. 2 <=> old(sK0) [avatar definition]
127. ~old(sK0) <- (~2) [avatar component clause 125]
130. 3 <=> ! [X1] : (funny(X1) | ~kind(X1)) [avatar definition]
131. ~kind(X1) | funny(X1) <- (3) [avatar component clause 130]
132. 3 | ~2 [avatar split clause 73,125,130]
154. 8 <=> funny(sK2) [avatar definition]
156. ~funny(sK2) <- (~8) [avatar component clause 154]
159. 9 <=> ! [X3] : (happy(X3) | ~humble(X3)) [avatar definition]
160. ~humble(X3) | happy(X3) <- (9) [avatar component clause 159]
161. 9 | ~8 [avatar split clause 83,154,159]
163. 10 <=> kind(sK2) [avatar definition]
165. kind(sK2) <- (10) [avatar component clause 163]
167. 9 | 10 [avatar split clause 81,163,159]
243. old(X1) | curious(X1) [resolution 95,79]
244. old(X1) [subsumption resolution 243,97]
249. $false <- (~2) [resolution 244,127]
250. 2 [avatar contradiction clause 249]
251. humble(john) [resolution 104,113]
256. happy(john) <- (9) [resolution 160,251]
273. quiet(john) <- (9) [resolution 256,92]
283. tall(john) <- (9) [resolution 273,80]
285. $false <- (9) [subsumption resolution 283,119]
286. ~9 [avatar contradiction clause 285]
296. funny(sK2) <- (3, 10) [resolution 165,131]
297. $false <- (3, ~8, 10) [subsumption resolution 296,156]
298. ~3 | 8 | ~10 [avatar contradiction clause 297]
299. $false [avatar sat refutation 132,161,167,250,286,298]
% SZS output end Proof for 1634620351068849205303935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not calm is not quiet or not tall.
Everyone who is not creative or creative is tall or quiet and vice versa.
Everyone who is both not curious and wise is either not humble or not brave.
Everyone who is both funny and not old is both not creative and not quiet and vice versa.
If someone is not rich or not calm then susan is both not old and old and vice versa.
If fred is both not rich and happy then someone is either not strong or not happy and vice versa.
If susan is wise or old then fred is both not funny and wise.
Everyone who is either not happy or not quiet is not tall and vice versa.
If someone is both wise and not curious then someone is both not calm and not kind and vice versa.
If someone is not tall then paul is both generous and old and vice versa.
Everyone who is not humble or not generous is both not curious and not old.
If lucy is not curious or kind then someone is not wise or not calm.
If someone is quiet or funny then someone is both wise and kind.
If susan is either wise or not strong then someone is both not calm and creative.
Everyone who is either humble or rich is wise or not rich.
Someone is either not generous or humble.
Someone is both not kind and not wise.
Someone is either not patient or curious.
John is not quiet.
Someone is strong or not curious.
Mary is either not old or not creative. | Paul is strong. | contradiction | (![X]:((humble(X)|~calm(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~creative(X)|creative(X))<=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((funny(X)&~old(X))<=>(~creative(X)&~quiet(X))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~old(susan)&old(susan))))&
(((~rich(fred)&happy(fred)))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(((wise(susan)|old(susan)))=>((~funny(fred)&wise(fred))))&
(![X]:((~happy(X)<~>~quiet(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~tall(X)))<=>((generous(paul)&old(paul))))&
(![X]:((~humble(X)|~generous(X))=>(~curious(X)&~old(X))))&
(((~curious(lucy)|kind(lucy)))=>(?[X]:((~wise(X)|~calm(X)))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((wise(X)&kind(X)))))&
(((wise(susan)<~>~strong(susan)))=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((humble(X)<~>rich(X))=>(wise(X)|~rich(X))))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(~quiet(john))&
(?[X]:((strong(X)|~curious(X))))&
((~old(mary)<~>~creative(mary))) | strong(paul) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6437108603959837885376372
% SZS output start Proof for 6437108603959837885376372
1. ! [X0] : ((~calm(X0) | humble(X0)) => (~tall(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | tall(X0))) [input p1]
5. ? [X0] : (~calm(X0) | ~rich(X0)) <=> (old(susan) & ~old(susan)) [input p4]
6. (happy(fred) & ~rich(fred)) <=> ? [X0] : (~strong(X0) <~> ~happy(X0)) [input p5]
8. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> ~tall(X0)) [input p7]
9. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X0] : (~kind(X0) & ~calm(X0)) [input p8]
11. ! [X0] : ((~generous(X0) | ~humble(X0)) => (~old(X0) & ~curious(X0))) [input p10]
15. ! [X0] : ((humble(X0) <~> rich(X0)) => (~rich(X0) | wise(X0))) [input p14]
22. strong(paul) [input hypothesis]
23. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X1] : (~kind(X1) & ~calm(X1)) [rectify 9]
25. ! [X0] : ((~tall(X0) | ~quiet(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 1]
26. ! [X0] : (~tall(X0) | ~quiet(X0) | (calm(X0) & ~humble(X0))) [flattening 25]
30. ! [X0] : ((~old(X0) & ~curious(X0)) | (generous(X0) & humble(X0))) [ennf transformation 11]
34. ! [X0] : ((~rich(X0) | wise(X0)) | (humble(X0) <=> rich(X0))) [ennf transformation 15]
35. ! [X0] : (~rich(X0) | wise(X0) | (humble(X0) <=> rich(X0))) [flattening 34]
36. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | (~creative(X0) & creative(X0)))) [flattening 36]
41. (? [X0] : (~calm(X0) | ~rich(X0)) | (~old(susan) | old(susan))) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 5]
42. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [flattening 41]
43. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [rectify 42]
44. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK0) | ~rich(sK0)) [choice axiom]
45. ((~calm(sK0) | ~rich(sK0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [skolemisation 43,44]
46. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X0] : ((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (~happy(fred) | rich(fred))) [nnf transformation 6]
47. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X0] : ((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | ~happy(fred) | rich(fred)) [flattening 46]
48. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (? [X1] : ((happy(X1) | strong(X1)) & (~happy(X1) | ~strong(X1))) | ~happy(fred) | rich(fred)) [rectify 47]
49. ? [X1] : ((happy(X1) | strong(X1)) & (~happy(X1) | ~strong(X1))) => ((happy(sK1) | strong(sK1)) & (~happy(sK1) | ~strong(sK1))) [choice axiom]
50. ((happy(fred) & ~rich(fred)) | ! [X0] : ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(sK1) | strong(sK1)) & (~happy(sK1) | ~strong(sK1))) | ~happy(fred) | rich(fred)) [skolemisation 48,49]
51. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 8]
52. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (kind(X1) | calm(X1))) & (? [X1] : (~kind(X1) & ~calm(X1)) | ! [X0] : (curious(X0) | ~wise(X0))) [nnf transformation 23]
53. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (kind(X1) | calm(X1))) & (? [X2] : (~kind(X2) & ~calm(X2)) | ! [X3] : (curious(X3) | ~wise(X3))) [rectify 52]
54. ? [X0] : (~curious(X0) & wise(X0)) => (~curious(sK2) & wise(sK2)) [choice axiom]
55. ? [X2] : (~kind(X2) & ~calm(X2)) => (~kind(sK3) & ~calm(sK3)) [choice axiom]
56. ((~curious(sK2) & wise(sK2)) | ! [X1] : (kind(X1) | calm(X1))) & ((~kind(sK3) & ~calm(sK3)) | ! [X3] : (curious(X3) | ~wise(X3))) [skolemisation 53,55,54]
70. ! [X0] : (~rich(X0) | wise(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) [nnf transformation 35]
82. ~tall(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 26]
84. quiet(X0) | tall(X0) | creative(X0) [cnf transformation 37]
85. ~creative(X0) | tall(X0) | quiet(X0) [cnf transformation 37]
94. ~old(susan) | rich(X1) [cnf transformation 45]
95. ~old(susan) | calm(X1) [cnf transformation 45]
96. old(susan) | rich(X1) [cnf transformation 45]
97. old(susan) | calm(X1) [cnf transformation 45]
102. ~rich(fred) | ~strong(X0) | happy(X0) [cnf transformation 50]
110. ~tall(X0) | ~happy(X0) | quiet(X0) [cnf transformation 51]
111. ~quiet(X0) | ~happy(X0) | tall(X0) [cnf transformation 51]
113. ~calm(sK3) | curious(X3) | ~wise(X3) [cnf transformation 56]
120. ~curious(X0) | humble(X0) [cnf transformation 30]
135. ~rich(X0) | wise(X0) | humble(X0) | ~rich(X0) [cnf transformation 70]
146. strong(paul) [cnf transformation 22]
147. ~rich(X0) | wise(X0) | humble(X0) [duplicate literal removal 135]
148. tall(X0) | quiet(X0) [subsumption resolution 84,85]
150. 1 <=> ! [X1] : calm(X1) [avatar definition]
151. calm(X1) <- (1) [avatar component clause 150]
153. 2 <=> old(susan) [avatar definition]
156. 1 | 2 [avatar split clause 97,153,150]
158. 3 <=> ! [X1] : rich(X1) [avatar definition]
159. rich(X1) <- (3) [avatar component clause 158]
160. 3 | 2 [avatar split clause 96,153,158]
161. 1 | ~2 [avatar split clause 95,153,150]
162. 3 | ~2 [avatar split clause 94,153,158]
164. 4 <=> ! [X0] : (~strong(X0) | happy(X0)) [avatar definition]
165. ~strong(X0) | happy(X0) <- (4) [avatar component clause 164]
176. 7 <=> rich(fred) [avatar definition]
178. ~rich(fred) <- (~7) [avatar component clause 176]
179. 4 | ~7 [avatar split clause 102,176,164]
207. ~happy(X0) | tall(X0) [subsumption resolution 111,148]
208. ~happy(X0) | quiet(X0) [subsumption resolution 110,207]
223. 16 <=> ! [X3] : (curious(X3) | ~wise(X3)) [avatar definition]
224. ~wise(X3) | curious(X3) <- (16) [avatar component clause 223]
231. 18 <=> calm(sK3) [avatar definition]
233. ~calm(sK3) <- (~18) [avatar component clause 231]
234. 16 | ~18 [avatar split clause 113,231,223]
344. $false <- (1, ~18) [resolution 233,151]
345. ~1 | 18 [avatar contradiction clause 344]
357. $false <- (3, ~7) [subsumption resolution 178,159]
358. ~3 | 7 [avatar contradiction clause 357]
362. happy(paul) <- (4) [resolution 165,146]
378. quiet(paul) <- (4) [resolution 362,208]
379. tall(paul) <- (4) [resolution 362,207]
395. wise(X0) | humble(X0) <- (3) [resolution 147,159]
411. humble(X1) | curious(X1) <- (3, 16) [resolution 395,224]
414. humble(X1) <- (3, 16) [subsumption resolution 411,120]
427. ~quiet(paul) | ~humble(paul) <- (4) [resolution 379,82]
428. ~humble(paul) <- (4) [subsumption resolution 427,378]
429. $false <- (3, 4, 16) [subsumption resolution 428,414]
430. ~3 | ~4 | ~16 [avatar contradiction clause 429]
431. $false [avatar sat refutation 156,160,161,162,179,234,345,358,430]
% SZS output end Proof for 6437108603959837885376372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not rich is either not brave or quiet. Everyone who is funny or not old is both humble and not rich. Everyone who is not wise is creative or generous and vice versa. If someone is brave then lucy is either humble or funny and vice versa. If someone is both patient and tall then john is not tall or not brave and vice versa. Everyone who is not happy is both not tall and not old. If someone is either not tall or not happy then someone is not rich or not patient and vice versa. If lucy is either rich or not generous then mary is not old or not brave and vice versa. If someone is kind then someone is either strong or quiet. Everyone who is either brave or rich is brave and vice versa. If paul is quiet or not brave then alice is humble or kind and vice versa. Everyone who is both calm and not quiet is either not funny or quiet and vice versa. Everyone who is generous or tall is not strong or not wise. Everyone who is both not calm and not kind is both strong and kind. If lucy is either patient or funny then someone is either not brave or rich and vice versa. Everyone who is not creative is not quiet. Susan is both kind and generous. Someone is either wise or humble. Someone is either creative or not patient. Someone is wise or not creative. Someone is both kind and not humble. Fred is both not brave and not curious. Alice is either creative or not curious. John is either generous or not generous. | Fred is brave. | contradiction | (![X]:((wise(X)&~rich(X))=>(~brave(X)<~>quiet(X))))&
(![X]:((funny(X)|~old(X))=>(humble(X)&~rich(X))))&
(![X]:(~wise(X)<=>(creative(X)|generous(X))))&
((?[X]:(brave(X)))<=>((humble(lucy)<~>funny(lucy))))&
((?[X]:((patient(X)&tall(X))))<=>((~tall(john)|~brave(john))))&
(![X]:(~happy(X)=>(~tall(X)&~old(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~rich(X)|~patient(X)))))&
(((rich(lucy)<~>~generous(lucy)))<=>((~old(mary)|~brave(mary))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((brave(X)<~>rich(X))<=>brave(X)))&
(((quiet(paul)|~brave(paul)))<=>((humble(alice)|kind(alice))))&
(![X]:((calm(X)&~quiet(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:((generous(X)|tall(X))=>(~strong(X)|~wise(X))))&
(![X]:((~calm(X)&~kind(X))=>(strong(X)&kind(X))))&
(((patient(lucy)<~>funny(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:(~creative(X)=>~quiet(X)))&
((kind(susan)&generous(susan)))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((kind(X)&~humble(X))))&
((~brave(fred)&~curious(fred)))&
((creative(alice)<~>~curious(alice)))&
((generous(john)<~>~generous(john))) | brave(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5330011125918787802587342
% SZS output start Proof for 5330011125918787802587342
22. ~curious(fred) & ~brave(fred) [input p21]
25. brave(fred) [input hypothesis]
152. ~brave(fred) [cnf transformation 22]
158. brave(fred) [cnf transformation 25]
349. $false [subsumption resolution 158,152]
% SZS output end Proof for 5330011125918787802587342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and not strong then paul is either kind or not generous. Everyone who is both not patient and not strong is patient or not quiet. Everyone who is not generous is either generous or not brave. If paul is curious or not quiet then someone is kind or not generous and vice versa. If fred is quiet or happy then someone is not patient or brave. Everyone who is either quiet or creative is strong and vice versa. Everyone who is both not kind and not creative is not kind or not generous and vice versa. If alice is funny or strong then someone is not tall or quiet. Everyone who is old or curious is calm and vice versa. Everyone who is either not rich or wise is not calm and vice versa. If someone is not patient or generous then paul is both creative and not strong. Everyone who is either not patient or generous is either not curious or not patient. If alice is both rich and not humble then mary is both not calm and not brave. If alice is both not patient and not happy then alice is not happy and vice versa. If fred is both rich and not curious then mary is either not strong or wise. Everyone who is either not kind or not funny is either not kind or curious and vice versa. Fred is rich or not kind. Someone is both curious and happy. Someone is old. Someone is happy or old. Someone is quiet or old. Someone is either strong or not old. | Fred is not generous. | entailment | (((~patient(john)&~strong(john)))=>((kind(paul)<~>~generous(paul))))&
(![X]:((~patient(X)&~strong(X))=>(patient(X)|~quiet(X))))&
(![X]:(~generous(X)=>(generous(X)<~>~brave(X))))&
(((curious(paul)|~quiet(paul)))<=>(?[X]:((kind(X)|~generous(X)))))&
(((quiet(fred)|happy(fred)))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((quiet(X)<~>creative(X))<=>strong(X)))&
(![X]:((~kind(X)&~creative(X))<=>(~kind(X)|~generous(X))))&
(((funny(alice)|strong(alice)))=>(?[X]:((~tall(X)|quiet(X)))))&
(![X]:((old(X)|curious(X))<=>calm(X)))&
(![X]:((~rich(X)<~>wise(X))<=>~calm(X)))&
((?[X]:((~patient(X)|generous(X))))=>((creative(paul)&~strong(paul))))&
(![X]:((~patient(X)<~>generous(X))=>(~curious(X)<~>~patient(X))))&
(((rich(alice)&~humble(alice)))=>((~calm(mary)&~brave(mary))))&
(((~patient(alice)&~happy(alice)))<=>(~happy(alice)))&
(((rich(fred)&~curious(fred)))=>((~strong(mary)<~>wise(mary))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~kind(X)<~>curious(X))))&
((rich(fred)|~kind(fred)))&
(?[X]:((curious(X)&happy(X))))&
(?[X]:(old(X)))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((strong(X)<~>~old(X)))) | ~generous(fred) | [
"p1",
"p3",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 441762346557239572386472
% SZS output start Proof for 441762346557239572386472
2. ! [X0] : ((~strong(X0) & ~patient(X0)) => (~quiet(X0) | patient(X0))) [input p1]
4. (~quiet(paul) | curious(paul)) <=> ? [X0] : (~generous(X0) | kind(X0)) [input p3]
6. ! [X0] : ((quiet(X0) <~> creative(X0)) <=> strong(X0)) [input p5]
7. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (~generous(X0) | ~kind(X0))) [input p6]
11. ? [X0] : (generous(X0) | ~patient(X0)) => (~strong(paul) & creative(paul)) [input p10]
12. ! [X0] : ((~patient(X0) <~> generous(X0)) => (~curious(X0) <~> ~patient(X0))) [input p11]
23. generous(fred) [input hypothesis]
28. ! [X0] : ((~quiet(X0) | patient(X0)) | (strong(X0) | patient(X0))) [ennf transformation 2]
29. ! [X0] : (~quiet(X0) | patient(X0) | strong(X0) | patient(X0)) [flattening 28]
32. (~strong(paul) & creative(paul)) | ! [X0] : (~generous(X0) & patient(X0)) [ennf transformation 11]
33. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | (~patient(X0) <=> generous(X0))) [ennf transformation 12]
38. ((~quiet(paul) | curious(paul)) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | (quiet(paul) & ~curious(paul))) [nnf transformation 4]
39. (~quiet(paul) | curious(paul) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X0] : (~generous(X0) | kind(X0)) | (quiet(paul) & ~curious(paul))) [flattening 38]
40. (~quiet(paul) | curious(paul) | ! [X0] : (generous(X0) & ~kind(X0))) & (? [X1] : (~generous(X1) | kind(X1)) | (quiet(paul) & ~curious(paul))) [rectify 39]
41. ? [X1] : (~generous(X1) | kind(X1)) => (~generous(sK0) | kind(sK0)) [choice axiom]
42. (~quiet(paul) | curious(paul) | ! [X0] : (generous(X0) & ~kind(X0))) & ((~generous(sK0) | kind(sK0)) | (quiet(paul) & ~curious(paul))) [skolemisation 40,41]
45. ! [X0] : ((((~creative(X0) | ~quiet(X0)) & (creative(X0) | quiet(X0))) | ~strong(X0)) & (strong(X0) | ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))))) [nnf transformation 6]
46. ! [X0] : (((~creative(X0) & ~kind(X0)) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 7]
47. ! [X0] : (((~creative(X0) & ~kind(X0)) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | creative(X0) | kind(X0))) [flattening 46]
51. ! [X0] : (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) [nnf transformation 33]
69. ~quiet(X0) | patient(X0) | strong(X0) | patient(X0) [cnf transformation 29]
74. ~quiet(paul) | curious(paul) | ~kind(X0) [cnf transformation 42]
79. ~creative(X0) | quiet(X0) | strong(X0) [cnf transformation 45]
84. ~kind(X0) | generous(X0) [cnf transformation 47]
85. ~creative(X0) | kind(X0) [cnf transformation 47]
95. creative(paul) | ~generous(X0) [cnf transformation 32]
97. ~strong(paul) | ~generous(X0) [cnf transformation 32]
99. ~patient(X0) | ~curious(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 51]
123. generous(fred) [cnf transformation 23]
128. ~curious(X0) | ~patient(X0) | ~generous(X0) [duplicate literal removal 99]
131. ~quiet(X0) | patient(X0) | strong(X0) [duplicate literal removal 69]
141. 3 <=> kind(paul) [avatar definition]
142. kind(paul) <- (3) [avatar component clause 141]
145. 4 <=> generous(paul) [avatar definition]
147. generous(paul) <- (4) [avatar component clause 145]
154. 6 <=> curious(paul) [avatar definition]
156. curious(paul) <- (6) [avatar component clause 154]
158. 7 <=> quiet(paul) [avatar definition]
159. quiet(paul) <- (7) [avatar component clause 158]
163. 8 <=> ! [X0] : ~kind(X0) [avatar definition]
164. ~kind(X0) <- (8) [avatar component clause 163]
165. 8 | 6 | ~7 [avatar split clause 74,158,154,163]
195. 15 <=> ! [X0] : ~generous(X0) [avatar definition]
196. ~generous(X0) <- (15) [avatar component clause 195]
198. 16 <=> strong(paul) [avatar definition]
200. ~strong(paul) <- (~16) [avatar component clause 198]
201. 15 | ~16 [avatar split clause 97,198,195]
207. 18 <=> creative(paul) [avatar definition]
209. creative(paul) <- (18) [avatar component clause 207]
210. 15 | 18 [avatar split clause 95,207,195]
276. $false <- (15) [resolution 196,123]
277. ~15 [avatar contradiction clause 276]
280. kind(paul) <- (18) [resolution 85,209]
283. 3 | ~18 [avatar split clause 280,207,141]
284. generous(paul) <- (3) [resolution 142,84]
287. 4 | ~3 [avatar split clause 284,141,145]
303. quiet(paul) | strong(paul) <- (18) [resolution 79,209]
307. quiet(paul) <- (~16, 18) [subsumption resolution 303,200]
308. 7 | 16 | ~18 [avatar split clause 307,207,198,158]
375. ~patient(paul) | ~generous(paul) <- (6) [resolution 128,156]
385. ~patient(paul) <- (4, 6) [subsumption resolution 375,147]
388. patient(paul) | strong(paul) <- (7) [resolution 131,159]
390. strong(paul) <- (4, 6, 7) [subsumption resolution 388,385]
391. $false <- (4, 6, 7, ~16) [subsumption resolution 390,200]
392. ~4 | ~6 | ~7 | 16 [avatar contradiction clause 391]
404. $false <- (3, 8) [resolution 164,142]
405. ~3 | ~8 [avatar contradiction clause 404]
406. $false [avatar sat refutation 165,201,210,277,283,287,308,392,405]
% SZS output end Proof for 441762346557239572386472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is not happy and vice versa. If john is either calm or humble then fred is not wise or not rich and vice versa. If someone is either not curious or not generous then someone is either creative or not patient. Everyone who is either not quiet or quiet is rich or brave and vice versa. If mary is calm or not rich then mary is not quiet and vice versa. If someone is either not brave or calm then mary is both rich and not humble and vice versa. If someone is either not old or creative then someone is either not old or strong. Everyone who is either not patient or brave is not patient or calm and vice versa. Everyone who is both not generous and patient is both happy and not curious. If mary is not curious then mary is both not kind and kind and vice versa. Everyone who is either kind or not funny is not wise. If someone is either not creative or not happy then someone is funny. Everyone who is both not old and not patient is both not humble and curious and vice versa. If mary is tall then mary is either happy or quiet and vice versa. If someone is both not happy and not tall then someone is both not wise and old and vice versa. If someone is either generous or brave then someone is not rich and vice versa. Someone is quiet. Fred is either curious or not strong. Someone is either not calm or wise. Mary is kind. Alice is either old or not generous. Someone is wise. Someone is brave. Someone is both not rich and happy. | John is humble. | neutral | (![X]:((~rich(X)&~generous(X))<=>~happy(X)))&
(((calm(john)<~>humble(john)))<=>((~wise(fred)|~rich(fred))))&
((?[X]:((~curious(X)<~>~generous(X))))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)|brave(X))))&
(((calm(mary)|~rich(mary)))<=>(~quiet(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((rich(mary)&~humble(mary))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((~old(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>brave(X))<=>(~patient(X)|calm(X))))&
(![X]:((~generous(X)&patient(X))=>(happy(X)&~curious(X))))&
((~curious(mary))<=>((~kind(mary)&kind(mary))))&
(![X]:((kind(X)<~>~funny(X))=>~wise(X)))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:(funny(X))))&
(![X]:((~old(X)&~patient(X))<=>(~humble(X)&curious(X))))&
((tall(mary))<=>((happy(mary)<~>quiet(mary))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~wise(X)&old(X)))))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:(~rich(X))))&
(?[X]:(quiet(X)))&
((curious(fred)<~>~strong(fred)))&
(?[X]:((~calm(X)<~>wise(X))))&
(kind(mary))&
((old(alice)<~>~generous(alice)))&
(?[X]:(wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&happy(X)))) | humble(john) | [] | null | 0 |
Everyone who is brave or quiet is either not brave or not strong and vice versa.
If someone is both not kind and curious then someone is both not happy and quiet and vice versa.
If susan is either old or strong then mary is not happy or quiet.
Everyone who is both not curious and not calm is either not tall or not quiet.
Everyone who is wise is generous and vice versa.
If someone is both humble and not strong then fred is not old and vice versa.
If fred is both not wise and not generous then someone is either old or calm and vice versa.
If someone is curious or not creative then paul is both old and quiet.
Everyone who is both not happy and generous is not calm and vice versa.
Everyone who is not strong is kind or old and vice versa.
Everyone who is kind or old is quiet and vice versa.
Everyone who is both not humble and funny is either not generous or creative and vice versa.
Everyone who is funny or generous is not quiet.
If someone is either tall or kind then fred is calm.
Everyone who is wise or not patient is not generous.
If fred is both quiet and not quiet then mary is happy and vice versa.
Someone is patient or not humble.
Alice is either not calm or not old.
John is not curious or old.
Someone is either not quiet or tall.
Paul is creative or humble.
Alice is both not funny and not strong.
Mary is either humble or wise. | Fred is tall. | neutral | (![X]:((brave(X)|quiet(X))<=>(~brave(X)<~>~strong(X))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((~happy(X)&quiet(X)))))&
(((old(susan)<~>strong(susan)))=>((~happy(mary)|quiet(mary))))&
(![X]:((~curious(X)&~calm(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:(wise(X)<=>generous(X)))&
((?[X]:((humble(X)&~strong(X))))<=>(~old(fred)))&
(((~wise(fred)&~generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((curious(X)|~creative(X))))=>((old(paul)&quiet(paul))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(?[X]:((patient(X)|~humble(X))))&
((~calm(alice)<~>~old(alice)))&
((~curious(john)|old(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((creative(paul)|humble(paul)))&
((~funny(alice)&~strong(alice)))&
((humble(mary)<~>wise(mary))) | tall(fred) | [] | null | 0 |
If someone is both funny and not kind then someone is either old or strong and vice versa. Everyone who is both curious and not wise is not happy or calm and vice versa. If john is either happy or not strong then paul is both not curious and creative. Everyone who is not rich or tall is either tall or not old and vice versa. Everyone who is both not kind and not rich is funny and vice versa. Everyone who is happy is not strong or tall and vice versa. If lucy is not humble then john is either rich or not funny. If paul is both not wise and not rich then someone is not happy or not curious. Everyone who is old is not humble. If mary is quiet then someone is both not creative and not funny and vice versa. Everyone who is not old or brave is both happy and not rich and vice versa. Everyone who is both strong and kind is both not humble and humble. Everyone who is either not rich or not funny is either not tall or not humble. Everyone who is both not patient and rich is brave or not brave. If mary is not calm or happy then someone is either quiet or happy and vice versa. Someone is curious or not funny. Susan is kind or not happy. Someone is not brave or not strong. Someone is not humble or not tall. | John is happy. | entailment | ((?[X]:((funny(X)&~kind(X))))<=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((curious(X)&~wise(X))<=>(~happy(X)|calm(X))))&
(((happy(john)<~>~strong(john)))=>((~curious(paul)&creative(paul))))&
(![X]:((~rich(X)|tall(X))<=>(tall(X)<~>~old(X))))&
(![X]:((~kind(X)&~rich(X))<=>funny(X)))&
(![X]:(happy(X)<=>(~strong(X)|tall(X))))&
((~humble(lucy))=>((rich(john)<~>~funny(john))))&
(((~wise(paul)&~rich(paul)))=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:(old(X)=>~humble(X)))&
((quiet(mary))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:((~old(X)|brave(X))<=>(happy(X)&~rich(X))))&
(![X]:((strong(X)&kind(X))=>(~humble(X)&humble(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(~tall(X)<~>~humble(X))))&
(![X]:((~patient(X)&rich(X))=>(brave(X)|~brave(X))))&
(((~calm(mary)|happy(mary)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
(?[X]:((curious(X)|~funny(X))))&
((kind(susan)|~happy(susan)))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~humble(X)|~tall(X)))) | happy(john) | [
"p3",
"p4",
"p5",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 289740175313813358755421
% SZS output start Proof for 289740175313813358755421
4. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (tall(X0) <~> ~old(X0))) [input p3]
5. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> funny(X0)) [input p4]
6. ! [X0] : (happy(X0) <=> (tall(X0) | ~strong(X0))) [input p5]
9. ! [X0] : (old(X0) => ~humble(X0)) [input p8]
11. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~rich(X0) & happy(X0))) [input p10]
13. ! [X0] : ((~rich(X0) <~> ~funny(X0)) => (~tall(X0) <~> ~humble(X0))) [input p12]
20. ~happy(john) [input hypothesis]
27. ! [X0] : (~humble(X0) | ~old(X0)) [ennf transformation 9]
30. ! [X0] : ((~tall(X0) <~> ~humble(X0)) | (~rich(X0) <=> ~funny(X0))) [ennf transformation 13]
39. ! [X0] : (((tall(X0) | ~rich(X0)) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | (~tall(X0) & rich(X0)))) [nnf transformation 4]
40. ! [X0] : ((tall(X0) | ~rich(X0) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | (~tall(X0) & rich(X0)))) [flattening 39]
41. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) | kind(X0)))) [nnf transformation 5]
42. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | rich(X0) | kind(X0))) [flattening 41]
43. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~happy(X0))) [nnf transformation 6]
44. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~happy(X0))) [flattening 43]
52. ! [X0] : (((brave(X0) | ~old(X0)) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 11]
53. ! [X0] : ((brave(X0) | ~old(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | (~brave(X0) & old(X0)))) [flattening 52]
54. ! [X0] : (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) [nnf transformation 30]
81. ~old(X0) | tall(X0) | rich(X0) [cnf transformation 40]
89. ~rich(X0) | ~funny(X0) [cnf transformation 42]
92. ~tall(X0) | happy(X0) [cnf transformation 44]
96. ~humble(X0) | ~old(X0) [cnf transformation 27]
100. happy(X0) | old(X0) [cnf transformation 53]
110. humble(X0) | tall(X0) | ~rich(X0) | funny(X0) [cnf transformation 54]
121. ~happy(john) [cnf transformation 20]
160. 9 <=> happy(john) [avatar definition]
161. ~happy(john) <- (~9) [avatar component clause 160]
181. 13 <=> rich(john) [avatar definition]
182. rich(john) <- (13) [avatar component clause 181]
227. ~rich(X0) | tall(X0) | humble(X0) [subsumption resolution 110,89]
295. ~9 [avatar split clause 121,160]
309. old(john) <- (~9) [resolution 100,161]
321. tall(john) | rich(john) <- (~9) [resolution 81,309]
378. 43 <=> tall(john) [avatar definition]
380. tall(john) <- (43) [avatar component clause 378]
381. 13 | 43 | 9 [avatar split clause 321,160,378,181]
442. tall(john) | humble(john) <- (13) [resolution 227,182]
445. 51 <=> humble(john) [avatar definition]
447. humble(john) <- (51) [avatar component clause 445]
448. 51 | 43 | ~13 [avatar split clause 442,181,378,445]
543. happy(john) <- (43) [resolution 380,92]
544. $false <- (~9, 43) [subsumption resolution 543,161]
545. 9 | ~43 [avatar contradiction clause 544]
548. ~old(john) <- (51) [resolution 447,96]
549. $false <- (~9, 51) [subsumption resolution 548,309]
550. 9 | ~51 [avatar contradiction clause 549]
551. $false [avatar sat refutation 295,381,448,545,550]
% SZS output end Proof for 289740175313813358755421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or tall is both not humble and not rich and vice versa.
Everyone who is either not quiet or not happy is wise or generous.
Everyone who is curious is calm and vice versa.
Everyone who is not wise or brave is either not funny or not strong.
Everyone who is both kind and quiet is not strong or not kind and vice versa.
If mary is not calm then lucy is both not strong and not rich.
Everyone who is both not quiet and brave is either generous or humble and vice versa.
If someone is patient or brave then fred is either not tall or not funny and vice versa.
If someone is either creative or quiet then lucy is generous or not old and vice versa.
If mary is either not wise or patient then paul is humble.
If someone is either not happy or not old then someone is happy.
Everyone who is brave or not funny is either calm or generous and vice versa.
Everyone who is both not funny and old is both patient and not funny.
If someone is funny then someone is not old or not strong.
Everyone who is wise or not funny is both not rich and not curious.
Everyone who is patient or not patient is both quiet and not generous.
Paul is either old or not quiet.
John is not happy.
Someone is wise. | Lucy is not wise. | neutral | (![X]:((strong(X)|tall(X))<=>(~humble(X)&~rich(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(wise(X)|generous(X))))&
(![X]:(curious(X)<=>calm(X)))&
(![X]:((~wise(X)|brave(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((kind(X)&quiet(X))<=>(~strong(X)|~kind(X))))&
((~calm(mary))=>((~strong(lucy)&~rich(lucy))))&
(![X]:((~quiet(X)&brave(X))<=>(generous(X)<~>humble(X))))&
((?[X]:((patient(X)|brave(X))))<=>((~tall(fred)<~>~funny(fred))))&
((?[X]:((creative(X)<~>quiet(X))))<=>((generous(lucy)|~old(lucy))))&
(((~wise(mary)<~>patient(mary)))=>(humble(paul)))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((brave(X)|~funny(X))<=>(calm(X)<~>generous(X))))&
(![X]:((~funny(X)&old(X))=>(patient(X)&~funny(X))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((wise(X)|~funny(X))=>(~rich(X)&~curious(X))))&
(![X]:((patient(X)|~patient(X))=>(quiet(X)&~generous(X))))&
((old(paul)<~>~quiet(paul)))&
(~happy(john))&
(?[X]:(wise(X))) | ~wise(lucy) | [] | null | 0 |
Everyone who is both not calm and not generous is not creative or not kind. If alice is calm then someone is either wise or patient. If lucy is not funny or kind then someone is either not brave or not patient. If fred is not tall or wise then mary is creative or old and vice versa. If mary is both humble and not patient then susan is not kind and vice versa. If someone is either not funny or strong then mary is either tall or not calm and vice versa. Everyone who is either wise or not calm is not tall or wise. Everyone who is not rich or kind is not calm. If john is happy then someone is wise and vice versa. Everyone who is strong or calm is either wise or not humble and vice versa. If someone is happy or not rich then someone is either not wise or not happy. Everyone who is either creative or not generous is both not funny and generous. Everyone who is not tall or not patient is rich and vice versa. Everyone who is funny or creative is old or not humble. If lucy is rich then fred is curious or tall. If someone is not kind or happy then mary is not rich and vice versa. Fred is not patient. Someone is funny or not creative. Someone is brave or quiet. Paul is both not patient and not wise. Someone is not calm. Susan is tall or old. Someone is not tall or kind. Mary is either kind or not funny. | Lucy is brave. | neutral | (![X]:((~calm(X)&~generous(X))=>(~creative(X)|~kind(X))))&
((calm(alice))=>(?[X]:((wise(X)<~>patient(X)))))&
(((~funny(lucy)|kind(lucy)))=>(?[X]:((~brave(X)<~>~patient(X)))))&
(((~tall(fred)|wise(fred)))<=>((creative(mary)|old(mary))))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
((happy(john))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)|calm(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:((happy(X)|~rich(X))))=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:((creative(X)<~>~generous(X))=>(~funny(X)&generous(X))))&
(![X]:((~tall(X)|~patient(X))<=>rich(X)))&
(![X]:((funny(X)|creative(X))=>(old(X)|~humble(X))))&
((rich(lucy))=>((curious(fred)|tall(fred))))&
((?[X]:((~kind(X)|happy(X))))<=>(~rich(mary)))&
(~patient(fred))&
(?[X]:((funny(X)|~creative(X))))&
(?[X]:((brave(X)|quiet(X))))&
((~patient(paul)&~wise(paul)))&
(?[X]:(~calm(X)))&
((tall(susan)|old(susan)))&
(?[X]:((~tall(X)|kind(X))))&
((kind(mary)<~>~funny(mary))) | brave(lucy) | [] | null | 0 |
Everyone who is both not tall and not quiet is both not wise and not patient.
If someone is either not quiet or not curious then someone is both wise and quiet and vice versa.
Everyone who is both not kind and tall is both not old and brave.
Everyone who is both not patient and curious is kind.
If alice is not calm then mary is not patient or not happy and vice versa.
If mary is generous then lucy is both funny and happy.
Everyone who is either patient or not old is not calm and vice versa.
If someone is either humble or happy then fred is not quiet or not kind.
If someone is either brave or calm then someone is both not humble and not creative and vice versa.
Everyone who is either not kind or curious is quiet and vice versa.
If lucy is either not tall or not generous then john is not humble.
Everyone who is rich or quiet is kind and vice versa.
Everyone who is both tall and calm is either not strong or not tall.
If susan is not curious or patient then mary is wise and vice versa.
Everyone who is not quiet is not old or old and vice versa.
If mary is not tall then someone is both kind and strong and vice versa.
Someone is not creative or not humble.
Someone is both not calm and generous.
Susan is either not brave or quiet.
Fred is patient.
Someone is not rich or old. | Alice is not happy. | neutral | (![X]:((~tall(X)&~quiet(X))=>(~wise(X)&~patient(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((wise(X)&quiet(X)))))&
(![X]:((~kind(X)&tall(X))=>(~old(X)&brave(X))))&
(![X]:((~patient(X)&curious(X))=>kind(X)))&
((~calm(alice))<=>((~patient(mary)|~happy(mary))))&
((generous(mary))=>((funny(lucy)&happy(lucy))))&
(![X]:((patient(X)<~>~old(X))<=>~calm(X)))&
((?[X]:((humble(X)<~>happy(X))))=>((~quiet(fred)|~kind(fred))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:((~kind(X)<~>curious(X))<=>quiet(X)))&
(((~tall(lucy)<~>~generous(lucy)))=>(~humble(john)))&
(![X]:((rich(X)|quiet(X))<=>kind(X)))&
(![X]:((tall(X)&calm(X))=>(~strong(X)<~>~tall(X))))&
(((~curious(susan)|patient(susan)))<=>(wise(mary)))&
(![X]:(~quiet(X)<=>(~old(X)|old(X))))&
((~tall(mary))<=>(?[X]:((kind(X)&strong(X)))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:((~calm(X)&generous(X))))&
((~brave(susan)<~>quiet(susan)))&
(patient(fred))&
(?[X]:((~rich(X)|old(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is either not strong or humble is either tall or kind.
Everyone who is both calm and not happy is not humble.
If someone is both funny and not curious then someone is not old or creative and vice versa.
Everyone who is both not creative and tall is calm and vice versa.
If susan is either wise or not happy then alice is funny or kind and vice versa.
If someone is either not quiet or generous then mary is quiet or strong and vice versa.
Everyone who is both not rich and calm is brave or not strong and vice versa.
Everyone who is humble is calm and vice versa.
If someone is not old or not quiet then someone is both generous and patient.
Everyone who is not happy is both not curious and old and vice versa.
If mary is not calm or not happy then alice is strong or quiet and vice versa.
Everyone who is not calm or not curious is either not patient or quiet.
Everyone who is strong or not curious is not strong.
Everyone who is either creative or not generous is either kind or creative and vice versa.
If someone is both wise and happy then someone is either not patient or funny.
Everyone who is quiet is rich and vice versa.
Someone is either not patient or not curious.
Paul is both not wise and happy.
Fred is both wise and not patient.
Fred is not humble or funny.
Susan is either tall or brave. | Alice is kind. | contradiction | (![X]:((~strong(X)<~>humble(X))=>(tall(X)<~>kind(X))))&
(![X]:((calm(X)&~happy(X))=>~humble(X)))&
((?[X]:((funny(X)&~curious(X))))<=>(?[X]:((~old(X)|creative(X)))))&
(![X]:((~creative(X)&tall(X))<=>calm(X)))&
(((wise(susan)<~>~happy(susan)))<=>((funny(alice)|kind(alice))))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((quiet(mary)|strong(mary))))&
(![X]:((~rich(X)&calm(X))<=>(brave(X)|~strong(X))))&
(![X]:(humble(X)<=>calm(X)))&
((?[X]:((~old(X)|~quiet(X))))=>(?[X]:((generous(X)&patient(X)))))&
(![X]:(~happy(X)<=>(~curious(X)&old(X))))&
(((~calm(mary)|~happy(mary)))<=>((strong(alice)|quiet(alice))))&
(![X]:((~calm(X)|~curious(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((strong(X)|~curious(X))=>~strong(X)))&
(![X]:((creative(X)<~>~generous(X))<=>(kind(X)<~>creative(X))))&
((?[X]:((wise(X)&happy(X))))=>(?[X]:((~patient(X)<~>funny(X)))))&
(![X]:(quiet(X)<=>rich(X)))&
(?[X]:((~patient(X)<~>~curious(X))))&
((~wise(paul)&happy(paul)))&
((wise(fred)&~patient(fred)))&
((~humble(fred)|funny(fred)))&
((tall(susan)<~>brave(susan))) | kind(alice) | [
"p5",
"p6",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2628940415357389016838743
% SZS output start Proof for 2628940415357389016838743
6. ? [X0] : (~quiet(X0) <~> generous(X0)) <=> (strong(mary) | quiet(mary)) [input p5]
7. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~strong(X0) | brave(X0))) [input p6]
13. ! [X0] : ((~curious(X0) | strong(X0)) => ~strong(X0)) [input p12]
14. ! [X0] : ((creative(X0) <~> ~generous(X0)) <=> (kind(X0) <~> creative(X0))) [input p13]
16. ! [X0] : (quiet(X0) <=> rich(X0)) [input p15]
22. kind(alice) [input hypothesis]
31. ! [X0] : (~strong(X0) | (curious(X0) & ~strong(X0))) [ennf transformation 13]
43. (? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~strong(mary) & ~quiet(mary))) & ((strong(mary) | quiet(mary)) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) [nnf transformation 6]
44. (? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~strong(mary) & ~quiet(mary))) & (strong(mary) | quiet(mary) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) [flattening 43]
45. (? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~strong(mary) & ~quiet(mary))) & (strong(mary) | quiet(mary) | ! [X1] : ((~quiet(X1) | ~generous(X1)) & (generous(X1) | quiet(X1)))) [rectify 44]
46. ? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) => ((~generous(sK2) | quiet(sK2)) & (generous(sK2) | ~quiet(sK2))) [choice axiom]
47. (((~generous(sK2) | quiet(sK2)) & (generous(sK2) | ~quiet(sK2))) | (~strong(mary) & ~quiet(mary))) & (strong(mary) | quiet(mary) | ! [X1] : ((~quiet(X1) | ~generous(X1)) & (generous(X1) | quiet(X1)))) [skolemisation 45,46]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (strong(X0) & ~brave(X0))) & ((~strong(X0) | brave(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 7]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (strong(X0) & ~brave(X0))) & (~strong(X0) | brave(X0) | ~calm(X0) | rich(X0))) [flattening 48]
59. ! [X0] : ((((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0))))) [nnf transformation 14]
64. ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))) [nnf transformation 16]
88. strong(mary) | quiet(mary) | generous(X1) | quiet(X1) [cnf transformation 47]
96. ~rich(X0) | strong(X0) [cnf transformation 49]
116. ~strong(X0) | ~strong(X0) [cnf transformation 31]
120. ~creative(X0) | ~kind(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 59]
122. ~generous(X0) | creative(X0) | creative(X0) | ~kind(X0) [cnf transformation 59]
128. ~quiet(X0) | rich(X0) [cnf transformation 64]
139. kind(alice) [cnf transformation 22]
141. ~creative(X0) | ~kind(X0) | ~generous(X0) [duplicate literal removal 120]
142. ~generous(X0) | creative(X0) | ~kind(X0) [duplicate literal removal 122]
144. ~strong(X0) [duplicate literal removal 116]
176. 8 <=> kind(alice) [avatar definition]
177. kind(alice) <- (8) [avatar component clause 176]
198. 12 <=> strong(mary) [avatar definition]
199. strong(mary) <- (12) [avatar component clause 198]
211. 15 <=> quiet(mary) [avatar definition]
212. quiet(mary) <- (15) [avatar component clause 211]
222. 17 <=> ! [X1] : (generous(X1) | quiet(X1)) [avatar definition]
223. generous(X1) | quiet(X1) <- (17) [avatar component clause 222]
224. 17 | 15 | 12 [avatar split clause 88,198,211,222]
241. 21 <=> quiet(alice) [avatar definition]
242. quiet(alice) <- (21) [avatar component clause 241]
243. ~quiet(alice) <- (~21) [avatar component clause 241]
260. ~generous(X0) | ~kind(X0) [subsumption resolution 141,142]
304. 8 [avatar split clause 139,176]
307. $false <- (12) [subsumption resolution 199,144]
308. ~12 [avatar contradiction clause 307]
327. rich(alice) <- (21) [resolution 128,242]
332. rich(mary) <- (15) [resolution 212,128]
334. strong(alice) <- (21) [resolution 327,96]
335. $false <- (21) [subsumption resolution 334,144]
336. ~21 [avatar contradiction clause 335]
346. strong(mary) <- (15) [resolution 332,96]
347. $false <- (15) [subsumption resolution 346,144]
348. ~15 [avatar contradiction clause 347]
352. ~kind(X1) | quiet(X1) <- (17) [resolution 223,260]
369. quiet(alice) <- (8, 17) [resolution 352,177]
370. $false <- (8, 17, ~21) [subsumption resolution 369,243]
371. ~8 | ~17 | 21 [avatar contradiction clause 370]
372. $false [avatar sat refutation 224,304,308,336,348,371]
% SZS output end Proof for 2628940415357389016838743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or strong is not quiet. If someone is not happy then lucy is both not patient and not generous and vice versa. Everyone who is tall is both not happy and rich and vice versa. Everyone who is both strong and happy is not wise or not quiet. If someone is either funny or curious then alice is both not generous and generous. Everyone who is generous is either not creative or not tall and vice versa. Everyone who is not tall or kind is not brave or old. Everyone who is both happy and brave is both patient and not patient and vice versa. Everyone who is not curious is both not kind and funny and vice versa. If paul is not old or not kind then mary is not rich or wise and vice versa. If someone is not curious or strong then john is either quiet or not wise. If lucy is either not tall or not curious then lucy is not kind and vice versa. If someone is both curious and not funny then lucy is both quiet and tall. Everyone who is either happy or patient is both patient and not humble. If paul is either tall or old then someone is patient. Someone is both humble and not quiet. Someone is either not old or wise. Paul is not happy or rich. John is either generous or humble. Mary is calm or generous. | Lucy is generous. | contradiction | (![X]:((wise(X)<~>strong(X))=>~quiet(X)))&
((?[X]:(~happy(X)))<=>((~patient(lucy)&~generous(lucy))))&
(![X]:(tall(X)<=>(~happy(X)&rich(X))))&
(![X]:((strong(X)&happy(X))=>(~wise(X)|~quiet(X))))&
((?[X]:((funny(X)<~>curious(X))))=>((~generous(alice)&generous(alice))))&
(![X]:(generous(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~tall(X)|kind(X))=>(~brave(X)|old(X))))&
(![X]:((happy(X)&brave(X))<=>(patient(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~kind(X)&funny(X))))&
(((~old(paul)|~kind(paul)))<=>((~rich(mary)|wise(mary))))&
((?[X]:((~curious(X)|strong(X))))=>((quiet(john)<~>~wise(john))))&
(((~tall(lucy)<~>~curious(lucy)))<=>(~kind(lucy)))&
((?[X]:((curious(X)&~funny(X))))=>((quiet(lucy)&tall(lucy))))&
(![X]:((happy(X)<~>patient(X))=>(patient(X)&~humble(X))))&
(((tall(paul)<~>old(paul)))=>(?[X]:(patient(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((~old(X)<~>wise(X))))&
((~happy(paul)|rich(paul)))&
((generous(john)<~>humble(john)))&
((calm(mary)|generous(mary))) | generous(lucy) | [
"p1",
"p2",
"p4",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8977883049532779763926018
% SZS output start Proof for 8977883049532779763926018
2. ? [X0] : ~happy(X0) <=> (~generous(lucy) & ~patient(lucy)) [input p1]
3. ! [X0] : (tall(X0) <=> (rich(X0) & ~happy(X0))) [input p2]
5. ? [X0] : (funny(X0) <~> curious(X0)) => (generous(alice) & ~generous(alice)) [input p4]
9. ! [X0] : (~curious(X0) <=> (funny(X0) & ~kind(X0))) [input p8]
12. (~tall(lucy) <~> ~curious(lucy)) <=> ~kind(lucy) [input p11]
13. ? [X0] : (~funny(X0) & curious(X0)) => (tall(lucy) & quiet(lucy)) [input p12]
21. generous(lucy) [input hypothesis]
26. (generous(alice) & ~generous(alice)) | ! [X0] : (funny(X0) <=> curious(X0)) [ennf transformation 5]
30. (tall(lucy) & quiet(lucy)) | ! [X0] : (funny(X0) | ~curious(X0)) [ennf transformation 13]
34. (? [X0] : ~happy(X0) | (generous(lucy) | patient(lucy))) & ((~generous(lucy) & ~patient(lucy)) | ! [X0] : happy(X0)) [nnf transformation 2]
35. (? [X0] : ~happy(X0) | generous(lucy) | patient(lucy)) & ((~generous(lucy) & ~patient(lucy)) | ! [X0] : happy(X0)) [flattening 34]
36. (? [X0] : ~happy(X0) | generous(lucy) | patient(lucy)) & ((~generous(lucy) & ~patient(lucy)) | ! [X1] : happy(X1)) [rectify 35]
37. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
38. (~happy(sK0) | generous(lucy) | patient(lucy)) & ((~generous(lucy) & ~patient(lucy)) | ! [X1] : happy(X1)) [skolemisation 36,37]
39. ! [X0] : ((tall(X0) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | ~tall(X0))) [nnf transformation 3]
40. ! [X0] : ((tall(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | ~tall(X0))) [flattening 39]
41. (generous(alice) & ~generous(alice)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))) [nnf transformation 26]
45. ! [X0] : ((~curious(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | curious(X0))) [nnf transformation 9]
46. ! [X0] : ((~curious(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | curious(X0))) [flattening 45]
50. (((curious(lucy) | tall(lucy)) & (~curious(lucy) | ~tall(lucy))) | kind(lucy)) & (~kind(lucy) | ((~tall(lucy) | curious(lucy)) & (~curious(lucy) | tall(lucy)))) [nnf transformation 12]
64. ~generous(lucy) | happy(X1) [cnf transformation 38]
66. ~tall(X0) | ~happy(X0) [cnf transformation 40]
70. ~generous(alice) | curious(X0) | ~funny(X0) [cnf transformation 41]
72. generous(alice) | curious(X0) | ~funny(X0) [cnf transformation 41]
84. ~kind(X0) | curious(X0) [cnf transformation 46]
85. curious(X0) | funny(X0) [cnf transformation 46]
86. ~curious(X0) | ~funny(X0) | kind(X0) [cnf transformation 46]
95. ~kind(lucy) | ~curious(lucy) | tall(lucy) [cnf transformation 50]
100. tall(lucy) | funny(X0) | ~curious(X0) [cnf transformation 30]
114. generous(lucy) [cnf transformation 21]
121. 2 <=> generous(lucy) [avatar definition]
130. 4 <=> ! [X1] : happy(X1) [avatar definition]
131. happy(X1) <- (4) [avatar component clause 130]
132. 4 | ~2 [avatar split clause 64,121,130]
139. 6 <=> generous(alice) [avatar definition]
144. 7 <=> ! [X0] : (curious(X0) | ~funny(X0)) [avatar definition]
145. curious(X0) | ~funny(X0) <- (7) [avatar component clause 144]
146. 7 | 6 [avatar split clause 72,139,144]
148. 7 | ~6 [avatar split clause 70,139,144]
183. 15 <=> ! [X0] : curious(X0) [avatar definition]
184. curious(X0) <- (15) [avatar component clause 183]
190. 16 <=> tall(lucy) [avatar definition]
192. tall(lucy) <- (16) [avatar component clause 190]
199. 18 <=> kind(lucy) [avatar definition]
200. ~kind(lucy) <- (~18) [avatar component clause 199]
203. ~kind(lucy) | tall(lucy) [subsumption resolution 95,84]
204. 16 | ~18 [avatar split clause 203,199,190]
205. tall(lucy) | funny(X0) [subsumption resolution 100,85]
207. 19 <=> ! [X0] : funny(X0) [avatar definition]
208. funny(X0) <- (19) [avatar component clause 207]
209. 19 | 16 [avatar split clause 205,190,207]
255. 2 [avatar split clause 114,121]
256. curious(X0) <- (7, 19) [subsumption resolution 145,208]
257. 15 | ~7 | ~19 [avatar split clause 256,207,144,183]
279. ~funny(X1) | kind(X1) <- (15) [resolution 86,184]
280. kind(X1) <- (15, 19) [subsumption resolution 279,208]
281. $false <- (15, ~18, 19) [resolution 280,200]
283. ~15 | 18 | ~19 [avatar contradiction clause 281]
291. ~happy(lucy) <- (16) [resolution 192,66]
292. $false <- (4, 16) [subsumption resolution 291,131]
293. ~4 | ~16 [avatar contradiction clause 292]
294. $false [avatar sat refutation 132,146,148,204,209,255,257,283,293]
% SZS output end Proof for 8977883049532779763926018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or humble is tall and vice versa.
If someone is either tall or old then someone is both not creative and not kind.
If someone is not quiet then mary is not generous or not tall.
Everyone who is either generous or happy is both old and not creative.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
Someone is not patient.
Susan is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble. | Alice is kind. | entailment | (![X]:((creative(X)<~>humble(X))<=>tall(X)))&
((?[X]:((tall(X)<~>old(X))))=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:(~quiet(X)))=>((~generous(mary)|~tall(mary))))&
(![X]:((generous(X)<~>happy(X))=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
(?[X]:(~patient(X)))&
((curious(susan)|~old(susan)))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john))) | kind(alice) | [
"p0",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p13",
"p14",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4080377229159599236115633
% SZS output start Proof for 4080377229159599236115633
1. ! [X0] : ((creative(X0) <~> humble(X0)) <=> tall(X0)) [input p0]
5. ? [X0] : ~kind(X0) => (quiet(paul) <~> curious(paul)) [input p4]
6. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~wise(X0) & humble(X0))) [input p5]
9. ! [X0] : (~wise(X0) => (~kind(X0) & kind(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | happy(X0)) => humble(X0)) [input p9]
11. ! [X0] : ((~happy(X0) <~> brave(X0)) => (~rich(X0) & ~strong(X0))) [input p10]
13. ! [X0] : (~strong(X0) <=> (rich(X0) <~> strong(X0))) [input p12]
14. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (creative(X0) <~> ~brave(X0))) [input p13]
15. (wise(alice) <~> tall(alice)) => ~curious(paul) [input p14]
21. ~quiet(paul) & tall(paul) [input p20]
22. ~kind(alice) <~> humble(alice) [input p21]
24. ~kind(alice) [input hypothesis]
30. (quiet(paul) <~> curious(paul)) | ! [X0] : kind(X0) [ennf transformation 5]
31. ! [X0] : ((~kind(X0) & kind(X0)) | wise(X0)) [ennf transformation 9]
32. ! [X0] : (humble(X0) | (curious(X0) & ~happy(X0))) [ennf transformation 10]
33. ! [X0] : ((~rich(X0) & ~strong(X0)) | (~happy(X0) <=> brave(X0))) [ennf transformation 11]
35. ~curious(paul) | (wise(alice) <=> tall(alice)) [ennf transformation 15]
37. ! [X0] : ((((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | ~tall(X0)) & (tall(X0) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))))) [nnf transformation 1]
43. ((~curious(paul) | ~quiet(paul)) & (curious(paul) | quiet(paul))) | ! [X0] : kind(X0) [nnf transformation 30]
44. ! [X0] : (((calm(X0) | ~strong(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 6]
45. ! [X0] : ((calm(X0) | ~strong(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [flattening 44]
53. ! [X0] : ((~rich(X0) & ~strong(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) [nnf transformation 33]
55. ! [X0] : ((~strong(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | strong(X0))) [nnf transformation 13]
56. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 14]
57. ~curious(paul) | ((wise(alice) | ~tall(alice)) & (tall(alice) | ~wise(alice))) [nnf transformation 35]
61. (~humble(alice) | kind(alice)) & (humble(alice) | ~kind(alice)) [nnf transformation 22]
64. ~tall(X0) | creative(X0) | humble(X0) [cnf transformation 37]
75. curious(paul) | quiet(paul) | kind(X0) [cnf transformation 43]
79. ~wise(X0) | strong(X0) [cnf transformation 45]
92. kind(X0) | wise(X0) [cnf transformation 31]
93. ~kind(X0) | wise(X0) [cnf transformation 31]
94. ~happy(X0) | humble(X0) [cnf transformation 32]
96. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 53]
104. strong(X0) | rich(X0) | strong(X0) [cnf transformation 55]
107. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 55]
114. ~strong(X0) | ~rich(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 56]
116. ~curious(paul) | tall(alice) | ~wise(alice) [cnf transformation 57]
125. ~quiet(paul) [cnf transformation 21]
127. ~humble(alice) | kind(alice) [cnf transformation 61]
129. ~kind(alice) [cnf transformation 24]
130. strong(X0) | rich(X0) [duplicate literal removal 104]
131. ~strong(X0) | rich(X0) [duplicate literal removal 107]
165. 8 <=> ! [X0] : kind(X0) [avatar definition]
166. kind(X0) <- (8) [avatar component clause 165]
168. 9 <=> quiet(paul) [avatar definition]
172. 10 <=> curious(paul) [avatar definition]
176. 8 | 9 | 10 [avatar split clause 75,172,168,165]
204. wise(X0) [subsumption resolution 92,93]
207. rich(X0) [subsumption resolution 130,131]
209. ~brave(X0) | ~strong(X0) | ~creative(X0) [subsumption resolution 114,207]
212. ~curious(paul) | tall(alice) [subsumption resolution 116,204]
214. 17 <=> tall(alice) [avatar definition]
216. tall(alice) <- (17) [avatar component clause 214]
217. 17 | ~10 [avatar split clause 212,172,214]
237. ~9 [avatar split clause 125,168]
239. 22 <=> kind(alice) [avatar definition]
240. ~kind(alice) <- (~22) [avatar component clause 239]
243. 23 <=> humble(alice) [avatar definition]
245. ~humble(alice) <- (~23) [avatar component clause 243]
246. 22 | ~23 [avatar split clause 127,243,239]
249. ~22 [avatar split clause 129,239]
254. strong(X0) [resolution 79,204]
270. creative(alice) | humble(alice) <- (17) [resolution 64,216]
280. creative(alice) <- (17, ~23) [subsumption resolution 270,245]
315. brave(X0) | happy(X0) [resolution 96,254]
338. ~strong(X1) | ~creative(X1) | happy(X1) [resolution 209,315]
339. ~creative(X1) | happy(X1) [subsumption resolution 338,254]
342. happy(alice) <- (17, ~23) [resolution 339,280]
349. humble(alice) <- (17, ~23) [resolution 342,94]
352. $false <- (17, ~23) [subsumption resolution 349,245]
353. ~17 | 23 [avatar contradiction clause 352]
355. $false <- (8, ~22) [resolution 166,240]
358. ~8 | 22 [avatar contradiction clause 355]
359. $false [avatar sat refutation 176,217,237,246,249,353,358]
% SZS output end Proof for 4080377229159599236115633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not wise is both not generous and not quiet and vice versa.
If someone is either old or rich then paul is not old or strong and vice versa.
Everyone who is old is patient and vice versa.
If someone is not strong or strong then someone is creative or happy.
Everyone who is not rich is either not quiet or creative.
If someone is not tall then someone is either humble or strong and vice versa.
If someone is generous or not curious then someone is either not old or wise and vice versa.
Everyone who is not curious is happy or strong.
If fred is not quiet then lucy is either not generous or funny.
Everyone who is both not brave and curious is either strong or not generous and vice versa.
If mary is not old then someone is both generous and brave.
If someone is rich then alice is both not tall and curious.
Everyone who is both tall and not rich is not wise or not rich and vice versa.
If paul is either wise or creative then someone is quiet and vice versa.
Everyone who is not brave or not humble is strong or not wise and vice versa.
If alice is either not curious or not kind then mary is happy or funny and vice versa.
Someone is not brave.
John is not brave or not creative.
Someone is either not creative or not quiet.
Paul is not quiet.
Susan is not generous.
Fred is either funny or curious.
Susan is rich. | Fred is not rich. | neutral | (![X]:((patient(X)&~wise(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((old(X)<~>rich(X))))<=>((~old(paul)|strong(paul))))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:(~rich(X)=>(~quiet(X)<~>creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((humble(X)<~>strong(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~old(X)<~>wise(X)))))&
(![X]:(~curious(X)=>(happy(X)|strong(X))))&
((~quiet(fred))=>((~generous(lucy)<~>funny(lucy))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)<~>~generous(X))))&
((~old(mary))=>(?[X]:((generous(X)&brave(X)))))&
((?[X]:(rich(X)))=>((~tall(alice)&curious(alice))))&
(![X]:((tall(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(((wise(paul)<~>creative(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~humble(X))<=>(strong(X)|~wise(X))))&
(((~curious(alice)<~>~kind(alice)))<=>((happy(mary)|funny(mary))))&
(?[X]:(~brave(X)))&
((~brave(john)|~creative(john)))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~quiet(paul))&
(~generous(susan))&
((funny(fred)<~>curious(fred)))&
(rich(susan)) | ~rich(fred) | [] | null | 0 |
Everyone who is not humble or not generous is both not funny and not curious and vice versa. Everyone who is either not tall or strong is either not quiet or strong. If alice is both not strong and not curious then fred is either wise or not quiet and vice versa. Everyone who is either tall or old is both not curious and not kind. Everyone who is either old or not brave is curious or generous and vice versa. Everyone who is tall is not humble or brave. Everyone who is both rich and not generous is both rich and funny and vice versa. If paul is not rich or not creative then someone is strong or not tall. Everyone who is not humble or not old is quiet and vice versa. If mary is not curious or curious then susan is not creative or not calm. Everyone who is kind is both quiet and patient and vice versa. If john is either not happy or not old then alice is both kind and humble and vice versa. If someone is kind then someone is not quiet and vice versa. Everyone who is tall is both tall and not patient. If paul is calm then someone is not tall and vice versa. If alice is not strong or quiet then fred is rich or wise and vice versa. Mary is both not rich and generous. John is not calm. Someone is both not creative and not tall. Someone is either not old or patient. Someone is either brave or calm. Someone is creative. Someone is both not calm and not patient. John is either not curious or not strong. | John is not old. | neutral | (![X]:((~humble(X)|~generous(X))<=>(~funny(X)&~curious(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~quiet(X)<~>strong(X))))&
(((~strong(alice)&~curious(alice)))<=>((wise(fred)<~>~quiet(fred))))&
(![X]:((tall(X)<~>old(X))=>(~curious(X)&~kind(X))))&
(![X]:((old(X)<~>~brave(X))<=>(curious(X)|generous(X))))&
(![X]:(tall(X)=>(~humble(X)|brave(X))))&
(![X]:((rich(X)&~generous(X))<=>(rich(X)&funny(X))))&
(((~rich(paul)|~creative(paul)))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((~humble(X)|~old(X))<=>quiet(X)))&
(((~curious(mary)|curious(mary)))=>((~creative(susan)|~calm(susan))))&
(![X]:(kind(X)<=>(quiet(X)&patient(X))))&
(((~happy(john)<~>~old(john)))<=>((kind(alice)&humble(alice))))&
((?[X]:(kind(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(tall(X)=>(tall(X)&~patient(X))))&
((calm(paul))<=>(?[X]:(~tall(X))))&
(((~strong(alice)|quiet(alice)))<=>((rich(fred)|wise(fred))))&
((~rich(mary)&generous(mary)))&
(~calm(john))&
(?[X]:((~creative(X)&~tall(X))))&
(?[X]:((~old(X)<~>patient(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)&~patient(X))))&
((~curious(john)<~>~strong(john))) | ~old(john) | [] | null | 0 |
Everyone who is both not kind and old is not kind.
Everyone who is either funny or old is not wise or not calm.
If susan is both not wise and quiet then someone is humble or quiet.
Everyone who is either curious or not kind is both not calm and old and vice versa.
If john is not creative then susan is both not brave and not curious and vice versa.
If susan is quiet or creative then someone is strong.
Everyone who is not strong or wise is not calm or funny.
If alice is either happy or old then someone is wise and vice versa.
Everyone who is strong is humble.
If lucy is not curious then john is kind or wise and vice versa.
Everyone who is both kind and not quiet is not strong and vice versa.
Everyone who is either kind or generous is not old or not funny and vice versa.
Everyone who is both not strong and not wise is happy.
If someone is either not old or happy then susan is kind or happy and vice versa.
If john is not patient or not old then fred is generous or happy.
Everyone who is not creative or wise is either creative or not patient.
Susan is not strong or not brave.
Someone is not strong or not tall.
Alice is creative.
Someone is both not tall and patient.
Lucy is not tall or not happy.
John is either not tall or generous.
Someone is not quiet or not curious.
Susan is old or not brave. | Fred is not quiet. | neutral | (![X]:((~kind(X)&old(X))=>~kind(X)))&
(![X]:((funny(X)<~>old(X))=>(~wise(X)|~calm(X))))&
(((~wise(susan)&quiet(susan)))=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:((curious(X)<~>~kind(X))<=>(~calm(X)&old(X))))&
((~creative(john))<=>((~brave(susan)&~curious(susan))))&
(((quiet(susan)|creative(susan)))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|wise(X))=>(~calm(X)|funny(X))))&
(((happy(alice)<~>old(alice)))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)=>humble(X)))&
((~curious(lucy))<=>((kind(john)|wise(john))))&
(![X]:((kind(X)&~quiet(X))<=>~strong(X)))&
(![X]:((kind(X)<~>generous(X))<=>(~old(X)|~funny(X))))&
(![X]:((~strong(X)&~wise(X))=>happy(X)))&
((?[X]:((~old(X)<~>happy(X))))<=>((kind(susan)|happy(susan))))&
(((~patient(john)|~old(john)))=>((generous(fred)|happy(fred))))&
(![X]:((~creative(X)|wise(X))=>(creative(X)<~>~patient(X))))&
((~strong(susan)|~brave(susan)))&
(?[X]:((~strong(X)|~tall(X))))&
(creative(alice))&
(?[X]:((~tall(X)&patient(X))))&
((~tall(lucy)|~happy(lucy)))&
((~tall(john)<~>generous(john)))&
(?[X]:((~quiet(X)|~curious(X))))&
((old(susan)|~brave(susan))) | ~quiet(fred) | [] | null | 0 |
If someone is brave or not generous then fred is strong or not old. Everyone who is strong is both not creative and quiet and vice versa. Everyone who is either generous or rich is both quiet and not creative and vice versa. Everyone who is generous or not happy is not generous and vice versa. Everyone who is generous or strong is both not patient and quiet. Everyone who is both calm and not generous is funny or not curious and vice versa. Everyone who is not wise is either old or not creative. If someone is either not generous or strong then someone is both not creative and brave. If someone is not old or generous then someone is not brave or wise and vice versa. If someone is either rich or kind then paul is not calm or funny and vice versa. Everyone who is curious or strong is happy or quiet and vice versa. Everyone who is kind or not kind is not tall or not happy. Everyone who is both rich and not wise is both quiet and not strong and vice versa. Everyone who is both patient and funny is not creative or not strong and vice versa. Everyone who is not patient is not brave. Paul is either rich or not tall. Mary is calm. Someone is not creative. John is not creative or not kind. Someone is both kind and not tall. Susan is not tall or not calm. | Fred is not creative. | neutral | ((?[X]:((brave(X)|~generous(X))))=>((strong(fred)|~old(fred))))&
(![X]:(strong(X)<=>(~creative(X)&quiet(X))))&
(![X]:((generous(X)<~>rich(X))<=>(quiet(X)&~creative(X))))&
(![X]:((generous(X)|~happy(X))<=>~generous(X)))&
(![X]:((generous(X)|strong(X))=>(~patient(X)&quiet(X))))&
(![X]:((calm(X)&~generous(X))<=>(funny(X)|~curious(X))))&
(![X]:(~wise(X)=>(old(X)<~>~creative(X))))&
((?[X]:((~generous(X)<~>strong(X))))=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((rich(X)<~>kind(X))))<=>((~calm(paul)|funny(paul))))&
(![X]:((curious(X)|strong(X))<=>(happy(X)|quiet(X))))&
(![X]:((kind(X)|~kind(X))=>(~tall(X)|~happy(X))))&
(![X]:((rich(X)&~wise(X))<=>(quiet(X)&~strong(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~strong(X))))&
(![X]:(~patient(X)=>~brave(X)))&
((rich(paul)<~>~tall(paul)))&
(calm(mary))&
(?[X]:(~creative(X)))&
((~creative(john)|~kind(john)))&
(?[X]:((kind(X)&~tall(X))))&
((~tall(susan)|~calm(susan))) | ~creative(fred) | [] | null | 0 |
Everyone who is not strong or not funny is either not patient or not curious and vice versa.
If someone is either not patient or not old then someone is either quiet or rich and vice versa.
Everyone who is strong or curious is both not wise and not brave.
Everyone who is not funny is both not generous and quiet and vice versa.
If someone is happy or not curious then susan is either calm or rich and vice versa.
If someone is either not calm or calm then someone is both rich and old.
If someone is either funny or old then alice is not old.
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.
Alice is both not generous and not creative.
Fred is not patient or not curious.
Someone is either brave or kind.
Susan is creative.
Alice is not happy or not generous.
Someone is tall or not kind.
Someone is both not rich and not kind.
Susan is humble. | Fred is curious. | neutral | (![X]:((~strong(X)|~funny(X))<=>(~patient(X)<~>~curious(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((strong(X)|curious(X))=>(~wise(X)&~brave(X))))&
(![X]:(~funny(X)<=>(~generous(X)&quiet(X))))&
((?[X]:((happy(X)|~curious(X))))<=>((calm(susan)<~>rich(susan))))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((funny(X)<~>old(X))))=>(~old(alice)))&
(![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))))&
((~generous(alice)&~creative(alice)))&
((~patient(fred)|~curious(fred)))&
(?[X]:((brave(X)<~>kind(X))))&
(creative(susan))&
((~happy(alice)|~generous(alice)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(humble(susan)) | curious(fred) | [] | null | 0 |
If someone is both not kind and wise then john is old.
If fred is wise or not strong then someone is both not creative and wise and vice versa.
Everyone who is either rich or creative is both not calm and tall and vice versa.
Everyone who is both curious and quiet is not brave and vice versa.
If someone is happy or not kind then john is not old.
Everyone who is wise is both not happy and not wise.
If someone is not curious then someone is both not quiet and rich and vice versa.
Everyone who is either not curious or funny is funny or not rich.
Everyone who is not curious or not strong is not quiet or not happy.
Everyone who is generous or not quiet is both creative and tall.
If fred is not calm or kind then someone is both wise and not tall.
Everyone who is not generous or wise is tall or generous and vice versa.
If paul is either not brave or not funny then mary is either tall or not curious and vice versa.
Everyone who is either not creative or not calm is not quiet and vice versa.
Everyone who is both curious and not creative is both humble and strong and vice versa.
Everyone who is patient is either not calm or generous and vice versa.
Lucy is both patient and not kind.
Someone is both not quiet and brave.
Someone is either quiet or old.
Someone is funny or happy.
Paul is not wise.
Someone is either curious or quiet. | John is not happy. | neutral | ((?[X]:((~kind(X)&wise(X))))=>(old(john)))&
(((wise(fred)|~strong(fred)))<=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(~calm(X)&tall(X))))&
(![X]:((curious(X)&quiet(X))<=>~brave(X)))&
((?[X]:((happy(X)|~kind(X))))=>(~old(john)))&
(![X]:(wise(X)=>(~happy(X)&~wise(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((~curious(X)<~>funny(X))=>(funny(X)|~rich(X))))&
(![X]:((~curious(X)|~strong(X))=>(~quiet(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(creative(X)&tall(X))))&
(((~calm(fred)|kind(fred)))=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~generous(X)|wise(X))<=>(tall(X)|generous(X))))&
(((~brave(paul)<~>~funny(paul)))<=>((tall(mary)<~>~curious(mary))))&
(![X]:((~creative(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((curious(X)&~creative(X))<=>(humble(X)&strong(X))))&
(![X]:(patient(X)<=>(~calm(X)<~>generous(X))))&
((patient(lucy)&~kind(lucy)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((quiet(X)<~>old(X))))&
(?[X]:((funny(X)|happy(X))))&
(~wise(paul))&
(?[X]:((curious(X)<~>quiet(X)))) | ~happy(john) | [] | null | 0 |
If someone is not quiet then susan is both old and brave.
Everyone who is humble or rich is not old.
Everyone who is funny is either not humble or curious and vice versa.
If john is not happy then someone is not humble.
Everyone who is both calm and not wise is not quiet and vice versa.
Everyone who is both curious and not wise is either not kind or not rich and vice versa.
If susan is not rich or generous then john is not calm or creative and vice versa.
Everyone who is either not wise or wise is not quiet or not generous and vice versa.
If someone is either not quiet or strong then someone is both patient and humble.
If john is both not happy and old then fred is not creative and vice versa.
If someone is not curious or rich then someone is either not generous or not kind and vice versa.
Everyone who is either brave or not strong is both tall and creative and vice versa.
Everyone who is tall or kind is curious or happy and vice versa.
If someone is not patient or wise then someone is not creative and vice versa.
If susan is both strong and not funny then someone is patient or humble.
Everyone who is either brave or calm is both not humble and patient.
Someone is not rich.
Mary is not calm or not patient.
Mary is both wise and funny.
Paul is generous or not patient.
Someone is curious.
Someone is both rich and happy.
Paul is humble.
John is humble. | Mary is not patient. | neutral | ((?[X]:(~quiet(X)))=>((old(susan)&brave(susan))))&
(![X]:((humble(X)|rich(X))=>~old(X)))&
(![X]:(funny(X)<=>(~humble(X)<~>curious(X))))&
((~happy(john))=>(?[X]:(~humble(X))))&
(![X]:((calm(X)&~wise(X))<=>~quiet(X)))&
(![X]:((curious(X)&~wise(X))<=>(~kind(X)<~>~rich(X))))&
(((~rich(susan)|generous(susan)))<=>((~calm(john)|creative(john))))&
(![X]:((~wise(X)<~>wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~quiet(X)<~>strong(X))))=>(?[X]:((patient(X)&humble(X)))))&
(((~happy(john)&old(john)))<=>(~creative(fred)))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(tall(X)&creative(X))))&
(![X]:((tall(X)|kind(X))<=>(curious(X)|happy(X))))&
((?[X]:((~patient(X)|wise(X))))<=>(?[X]:(~creative(X))))&
(((strong(susan)&~funny(susan)))=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((brave(X)<~>calm(X))=>(~humble(X)&patient(X))))&
(?[X]:(~rich(X)))&
((~calm(mary)|~patient(mary)))&
((wise(mary)&funny(mary)))&
((generous(paul)|~patient(paul)))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)&happy(X))))&
(humble(paul))&
(humble(john)) | ~patient(mary) | [] | null | 0 |
If someone is calm or not happy then alice is strong and vice versa.
If someone is both not generous and patient then someone is either funny or generous and vice versa.
Everyone who is both generous and not rich is not happy or not brave and vice versa.
If mary is both humble and not strong then paul is either not generous or rich and vice versa.
Everyone who is patient or curious is either calm or not funny.
If someone is rich or curious then alice is both old and not rich.
If someone is not quiet then someone is wise.
If john is not wise then someone is tall or old.
Everyone who is both not curious and creative is not strong and vice versa.
Everyone who is either not rich or quiet is either strong or not creative and vice versa.
If lucy is humble then fred is not quiet.
Everyone who is generous or funny is not patient and vice versa.
Everyone who is both curious and not strong is rich or old and vice versa.
If someone is both not happy and strong then fred is either strong or not happy.
If someone is old or not wise then john is either not strong or funny and vice versa.
If alice is either not rich or not generous then someone is patient or happy.
Paul is not happy or creative.
Someone is either not curious or brave.
Someone is either not wise or wise.
Lucy is strong.
Fred is not wise. | Alice is not strong. | neutral | ((?[X]:((calm(X)|~happy(X))))<=>(strong(alice)))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~happy(X)|~brave(X))))&
(((humble(mary)&~strong(mary)))<=>((~generous(paul)<~>rich(paul))))&
(![X]:((patient(X)|curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((rich(X)|curious(X))))=>((old(alice)&~rich(alice))))&
((?[X]:(~quiet(X)))=>(?[X]:(wise(X))))&
((~wise(john))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~curious(X)&creative(X))<=>~strong(X)))&
(![X]:((~rich(X)<~>quiet(X))<=>(strong(X)<~>~creative(X))))&
((humble(lucy))=>(~quiet(fred)))&
(![X]:((generous(X)|funny(X))<=>~patient(X)))&
(![X]:((curious(X)&~strong(X))<=>(rich(X)|old(X))))&
((?[X]:((~happy(X)&strong(X))))=>((strong(fred)<~>~happy(fred))))&
((?[X]:((old(X)|~wise(X))))<=>((~strong(john)<~>funny(john))))&
(((~rich(alice)<~>~generous(alice)))=>(?[X]:((patient(X)|happy(X)))))&
((~happy(paul)|creative(paul)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~wise(X)<~>wise(X))))&
(strong(lucy))&
(~wise(fred)) | ~strong(alice) | [] | null | 0 |
Everyone who is not strong or not curious is wise.
If lucy is both not patient and happy then susan is tall.
Everyone who is either calm or quiet is not old or not humble.
Everyone who is not humble is both not rich and calm and vice versa.
Everyone who is not kind is not rich and vice versa.
If paul is strong or quiet then someone is both not strong and not humble and vice versa.
If fred is not creative or not brave then fred is either strong or not old and vice versa.
If fred is not creative or wise then someone is not humble or not wise and vice versa.
Everyone who is either not strong or strong is happy and vice versa.
If fred is quiet then someone is both not quiet and not generous.
Everyone who is both not strong and rich is either not old or not patient.
Everyone who is not curious is quiet.
Everyone who is not curious is quiet or kind and vice versa.
If lucy is funny or not rich then someone is not funny or tall and vice versa.
If lucy is old then someone is wise or not brave and vice versa.
Everyone who is quiet is both humble and not patient and vice versa.
Someone is either not old or humble.
Someone is not old or not tall.
Someone is both not patient and kind.
Someone is not patient.
Someone is not quiet or rich.
Someone is either quiet or creative. | Lucy is quiet. | neutral | (![X]:((~strong(X)|~curious(X))=>wise(X)))&
(((~patient(lucy)&happy(lucy)))=>(tall(susan)))&
(![X]:((calm(X)<~>quiet(X))=>(~old(X)|~humble(X))))&
(![X]:(~humble(X)<=>(~rich(X)&calm(X))))&
(![X]:(~kind(X)<=>~rich(X)))&
(((strong(paul)|quiet(paul)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(((~creative(fred)|~brave(fred)))<=>((strong(fred)<~>~old(fred))))&
(((~creative(fred)|wise(fred)))<=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~strong(X)<~>strong(X))<=>happy(X)))&
((quiet(fred))=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:((~strong(X)&rich(X))=>(~old(X)<~>~patient(X))))&
(![X]:(~curious(X)=>quiet(X)))&
(![X]:(~curious(X)<=>(quiet(X)|kind(X))))&
(((funny(lucy)|~rich(lucy)))<=>(?[X]:((~funny(X)|tall(X)))))&
((old(lucy))<=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~patient(X))))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~patient(X)&kind(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((quiet(X)<~>creative(X)))) | quiet(lucy) | [] | null | 0 |
If someone is patient then lucy is either happy or tall and vice versa.
Everyone who is not kind is rich or wise.
Everyone who is funny is not old or not happy and vice versa.
Everyone who is both calm and not strong is creative or not humble.
Everyone who is curious or not happy is strong or not brave and vice versa.
Everyone who is both not wise and not old is either old or patient and vice versa.
Everyone who is not calm or old is not strong or quiet and vice versa.
If paul is either rich or not generous then someone is patient or tall and vice versa.
Everyone who is not quiet is either not happy or quiet and vice versa.
If susan is happy or rich then paul is tall and vice versa.
If someone is not brave or not creative then paul is humble and vice versa.
If someone is not quiet or creative then paul is both kind and not curious and vice versa.
Everyone who is both kind and patient is either not happy or not rich.
Everyone who is either curious or old is both not brave and happy.
Everyone who is both not happy and not curious is both not kind and humble and vice versa.
If someone is patient or calm then mary is either not calm or not funny.
Someone is not wise.
Someone is both rich and not kind.
Lucy is generous.
Someone is either not tall or not rich.
Lucy is quiet.
Lucy is not wise or not patient.
Someone is patient.
John is either funny or not calm. | Paul is not funny. | contradiction | ((?[X]:(patient(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:(~kind(X)=>(rich(X)|wise(X))))&
(![X]:(funny(X)<=>(~old(X)|~happy(X))))&
(![X]:((calm(X)&~strong(X))=>(creative(X)|~humble(X))))&
(![X]:((curious(X)|~happy(X))<=>(strong(X)|~brave(X))))&
(![X]:((~wise(X)&~old(X))<=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)|old(X))<=>(~strong(X)|quiet(X))))&
(((rich(paul)<~>~generous(paul)))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>quiet(X))))&
(((happy(susan)|rich(susan)))<=>(tall(paul)))&
((?[X]:((~brave(X)|~creative(X))))<=>(humble(paul)))&
((?[X]:((~quiet(X)|creative(X))))<=>((kind(paul)&~curious(paul))))&
(![X]:((kind(X)&patient(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((curious(X)<~>old(X))=>(~brave(X)&happy(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)&humble(X))))&
((?[X]:((patient(X)|calm(X))))=>((~calm(mary)<~>~funny(mary))))&
(?[X]:(~wise(X)))&
(?[X]:((rich(X)&~kind(X))))&
(generous(lucy))&
(?[X]:((~tall(X)<~>~rich(X))))&
(quiet(lucy))&
((~wise(lucy)|~patient(lucy)))&
(?[X]:(patient(X)))&
((funny(john)<~>~calm(john))) | ~funny(paul) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7409569001480911221411232
% SZS output start Proof for 7409569001480911221411232
3. ! [X0] : (funny(X0) <=> (~happy(X0) | ~old(X0))) [input p2]
9. ! [X0] : (~quiet(X0) <=> (~happy(X0) <~> quiet(X0))) [input p8]
25. ~funny(paul) [input hypothesis]
38. ! [X0] : ((funny(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | ~funny(X0))) [nnf transformation 3]
39. ! [X0] : ((funny(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | ~funny(X0))) [flattening 38]
50. ! [X0] : ((~quiet(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | quiet(X0))) [nnf transformation 9]
84. funny(X0) | happy(X0) [cnf transformation 39]
106. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 50]
109. ~quiet(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 50]
146. ~funny(paul) [cnf transformation 25]
147. quiet(X0) | ~happy(X0) [duplicate literal removal 106]
148. ~quiet(X0) | ~happy(X0) [duplicate literal removal 109]
196. ~happy(X0) [subsumption resolution 147,148]
311. happy(paul) [resolution 84,146]
314. $false [subsumption resolution 311,196]
% SZS output end Proof for 7409569001480911221411232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is old or not generous then paul is either funny or not quiet.
Everyone who is not funny is patient or tall.
Everyone who is either not creative or not quiet is either rich or not brave and vice versa.
If someone is generous then someone is both not creative and old.
Everyone who is generous or not funny is either not calm or not humble and vice versa.
Everyone who is happy or brave is both not creative and not rich and vice versa.
Everyone who is happy is not funny or kind.
Everyone who is both not brave and generous is strong or not rich.
If alice is both brave and quiet then someone is not humble or not happy and vice versa.
Everyone who is both not rich and not kind is both not happy and calm.
Everyone who is not patient is both quiet and not creative and vice versa.
Everyone who is both not wise and not curious is not happy or not rich.
If someone is happy then someone is either not curious or not generous and vice versa.
If someone is both not curious and humble then someone is both not kind and wise.
If someone is quiet or rich then someone is either happy or kind.
If fred is both not patient and not happy then someone is either not strong or tall.
John is wise.
Someone is either not quiet or quiet.
Someone is either not rich or not calm.
Someone is either generous or wise. | Paul is calm. | neutral | (((old(lucy)|~generous(lucy)))=>((funny(paul)<~>~quiet(paul))))&
(![X]:(~funny(X)=>(patient(X)|tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(rich(X)<~>~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((generous(X)|~funny(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((happy(X)|brave(X))<=>(~creative(X)&~rich(X))))&
(![X]:(happy(X)=>(~funny(X)|kind(X))))&
(![X]:((~brave(X)&generous(X))=>(strong(X)|~rich(X))))&
(((brave(alice)&quiet(alice)))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~rich(X)&~kind(X))=>(~happy(X)&calm(X))))&
(![X]:(~patient(X)<=>(quiet(X)&~creative(X))))&
(![X]:((~wise(X)&~curious(X))=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:((happy(X)<~>kind(X)))))&
(((~patient(fred)&~happy(fred)))=>(?[X]:((~strong(X)<~>tall(X)))))&
(wise(john))&
(?[X]:((~quiet(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>wise(X)))) | calm(paul) | [] | null | 0 |
If someone is either not kind or not rich then mary is both not brave and not humble.
Everyone who is both humble and not curious is not generous or not calm and vice versa.
Everyone who is not curious is old or not kind and vice versa.
Everyone who is not humble is strong.
If john is either not creative or not kind then fred is both not quiet and old.
Everyone who is not happy or patient is generous.
Everyone who is both rich and patient is not kind or not wise and vice versa.
Everyone who is not strong or not brave is both funny and wise.
If someone is brave then susan is not wise and vice versa.
Everyone who is not curious is both not brave and not funny and vice versa.
Everyone who is quiet or funny is both not creative and happy and vice versa.
Everyone who is creative or not humble is either not patient or rich and vice versa.
Everyone who is not wise is brave and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
Someone is both patient and happy.
Fred is old or curious.
Mary is old or not creative.
Someone is either not old or humble. | John is brave. | entailment | ((?[X]:((~kind(X)<~>~rich(X))))=>((~brave(mary)&~humble(mary))))&
(![X]:((humble(X)&~curious(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~curious(X)<=>(old(X)|~kind(X))))&
(![X]:(~humble(X)=>strong(X)))&
(((~creative(john)<~>~kind(john)))=>((~quiet(fred)&old(fred))))&
(![X]:((~happy(X)|patient(X))=>generous(X)))&
(![X]:((rich(X)&patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)&wise(X))))&
((?[X]:(brave(X)))<=>(~wise(susan)))&
(![X]:(~curious(X)<=>(~brave(X)&~funny(X))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)&happy(X))))&
(![X]:((creative(X)|~humble(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~wise(X)<=>brave(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
(?[X]:((patient(X)&happy(X))))&
((old(fred)|curious(fred)))&
((old(mary)|~creative(mary)))&
(?[X]:((~old(X)<~>humble(X)))) | brave(john) | [
"p2",
"p4",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1305849668333006661350580
% SZS output start Proof for 1305849668333006661350580
3. ! [X0] : (~curious(X0) <=> (~kind(X0) | old(X0))) [input p2]
5. (~creative(john) <~> ~kind(john)) => (old(fred) & ~quiet(fred)) [input p4]
8. ! [X0] : ((~brave(X0) | ~strong(X0)) => (wise(X0) & funny(X0))) [input p7]
10. ! [X0] : (~curious(X0) <=> (~funny(X0) & ~brave(X0))) [input p9]
11. ! [X0] : ((funny(X0) | quiet(X0)) <=> (happy(X0) & ~creative(X0))) [input p10]
19. ~brave(john) [input hypothesis]
20. ! [X0] : (~brave(X0) => (wise(X0) & funny(X0))) [pure predicate removal 8]
23. (old(fred) & ~quiet(fred)) | (~creative(john) <=> ~kind(john)) [ennf transformation 5]
25. ! [X0] : ((wise(X0) & funny(X0)) | brave(X0)) [ennf transformation 20]
31. ! [X0] : ((~curious(X0) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | curious(X0))) [nnf transformation 3]
32. ! [X0] : ((~curious(X0) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | curious(X0))) [flattening 31]
33. (old(fred) & ~quiet(fred)) | ((~creative(john) | kind(john)) & (~kind(john) | creative(john))) [nnf transformation 23]
40. ! [X0] : ((~curious(X0) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [nnf transformation 10]
41. ! [X0] : ((~curious(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [flattening 40]
42. ! [X0] : (((funny(X0) | quiet(X0)) | (~happy(X0) | creative(X0))) & ((happy(X0) & ~creative(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 11]
43. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0) | creative(X0)) & ((happy(X0) & ~creative(X0)) | (~funny(X0) & ~quiet(X0)))) [flattening 42]
62. ~old(X0) | ~curious(X0) [cnf transformation 32]
63. ~curious(X0) | kind(X0) [cnf transformation 32]
66. old(fred) | ~kind(john) | creative(john) [cnf transformation 33]
75. funny(X0) | brave(X0) [cnf transformation 25]
79. ~brave(X0) | curious(X0) [cnf transformation 41]
80. ~funny(X0) | curious(X0) [cnf transformation 41]
83. ~funny(X0) | ~creative(X0) [cnf transformation 43]
102. ~brave(john) [cnf transformation 19]
122. 5 <=> kind(john) [avatar definition]
123. ~kind(john) <- (~5) [avatar component clause 122]
126. 6 <=> creative(john) [avatar definition]
127. creative(john) <- (6) [avatar component clause 126]
130. 7 <=> old(fred) [avatar definition]
132. old(fred) <- (7) [avatar component clause 130]
134. 6 | ~5 | 7 [avatar split clause 66,130,122,126]
155. 12 <=> curious(fred) [avatar definition]
156. ~curious(fred) <- (~12) [avatar component clause 155]
178. ~curious(fred) <- (7) [resolution 62,132]
179. ~12 | ~7 [avatar split clause 178,130,155]
191. curious(X0) | brave(X0) [resolution 80,75]
192. curious(X0) [subsumption resolution 191,79]
193. kind(X0) [resolution 192,63]
196. $false <- (~12) [resolution 192,156]
197. 12 [avatar contradiction clause 196]
198. $false <- (~5) [subsumption resolution 123,193]
199. 5 [avatar contradiction clause 198]
200. ~creative(X0) | brave(X0) [resolution 83,75]
265. brave(john) <- (6) [resolution 200,127]
267. $false <- (6) [subsumption resolution 265,102]
268. ~6 [avatar contradiction clause 267]
269. $false [avatar sat refutation 134,179,197,199,268]
% SZS output end Proof for 1305849668333006661350580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not funny or tall and vice versa.
If someone is either curious or funny then alice is both not strong and quiet.
If someone is both tall and not old then someone is patient.
If someone is either calm or funny then paul is tall or not happy and vice versa.
Everyone who is either not patient or not quiet is both not generous and humble and vice versa.
If fred is either not calm or not happy then fred is creative and vice versa.
Everyone who is either not tall or not happy is both not funny and kind.
Everyone who is both not calm and happy is both not wise and not quiet.
If alice is happy or not creative then someone is both creative and not kind.
Everyone who is either not happy or rich is not funny and vice versa.
Everyone who is either calm or not strong is either not wise or not old and vice versa.
If someone is not calm then john is not tall or not kind.
Everyone who is funny is rich or creative and vice versa.
Everyone who is not curious or not humble is kind and vice versa.
If fred is both humble and not brave then lucy is both happy and not generous.
If fred is both not wise and not old then someone is humble and vice versa.
Someone is either not quiet or old.
Someone is both patient and not generous.
Someone is both patient and not quiet.
Someone is both old and creative.
Mary is humble.
Lucy is not wise.
Someone is both not wise and not humble.
Paul is both not patient and wise. | Lucy is rich. | contradiction | (![X]:(~wise(X)<=>(~funny(X)|tall(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~strong(alice)&quiet(alice))))&
((?[X]:((tall(X)&~old(X))))=>(?[X]:(patient(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>((tall(paul)|~happy(paul))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~generous(X)&humble(X))))&
(((~calm(fred)<~>~happy(fred)))<=>(creative(fred)))&
(![X]:((~tall(X)<~>~happy(X))=>(~funny(X)&kind(X))))&
(![X]:((~calm(X)&happy(X))=>(~wise(X)&~quiet(X))))&
(((happy(alice)|~creative(alice)))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>~funny(X)))&
(![X]:((calm(X)<~>~strong(X))<=>(~wise(X)<~>~old(X))))&
((?[X]:(~calm(X)))=>((~tall(john)|~kind(john))))&
(![X]:(funny(X)<=>(rich(X)|creative(X))))&
(![X]:((~curious(X)|~humble(X))<=>kind(X)))&
(((humble(fred)&~brave(fred)))=>((happy(lucy)&~generous(lucy))))&
(((~wise(fred)&~old(fred)))<=>(?[X]:(humble(X))))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((patient(X)&~quiet(X))))&
(?[X]:((old(X)&creative(X))))&
(humble(mary))&
(~wise(lucy))&
(?[X]:((~wise(X)&~humble(X))))&
((~patient(paul)&wise(paul))) | rich(lucy) | [
"p0",
"p6",
"p9",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6453244105407436414337623
% SZS output start Proof for 6453244105407436414337623
1. ! [X0] : (~wise(X0) <=> (tall(X0) | ~funny(X0))) [input p0]
7. ! [X0] : ((~tall(X0) <~> ~happy(X0)) => (kind(X0) & ~funny(X0))) [input p6]
10. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> ~funny(X0)) [input p9]
13. ! [X0] : (funny(X0) <=> (creative(X0) | rich(X0))) [input p12]
22. ~wise(lucy) [input p21]
25. rich(lucy) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~funny(X0)) | (~tall(X0) <=> ~happy(X0))) [ennf transformation 7]
36. ! [X0] : ((~wise(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | wise(X0))) [nnf transformation 1]
37. ! [X0] : ((~wise(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | wise(X0))) [flattening 36]
50. ! [X0] : ((kind(X0) & ~funny(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) [nnf transformation 30]
53. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | funny(X0)) & (~funny(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 10]
55. ! [X0] : ((funny(X0) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 13]
56. ! [X0] : ((funny(X0) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | ~funny(X0))) [flattening 55]
75. ~funny(X0) | tall(X0) | wise(X0) [cnf transformation 37]
100. ~tall(X0) | ~funny(X0) | happy(X0) [cnf transformation 50]
110. ~rich(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 53]
123. ~rich(X0) | funny(X0) [cnf transformation 56]
140. ~wise(lucy) [cnf transformation 22]
145. rich(lucy) [cnf transformation 25]
279. funny(lucy) [resolution 123,145]
286. tall(lucy) | wise(lucy) [resolution 75,279]
297. tall(lucy) [subsumption resolution 286,140]
348. ~funny(lucy) | happy(lucy) [resolution 297,100]
352. 39 <=> happy(lucy) [avatar definition]
354. happy(lucy) <- (39) [avatar component clause 352]
360. happy(lucy) [subsumption resolution 348,279]
361. 39 [avatar split clause 360,352]
379. ~happy(lucy) | ~funny(lucy) [resolution 110,145]
381. ~funny(lucy) <- (39) [subsumption resolution 379,354]
382. $false <- (39) [subsumption resolution 381,279]
383. ~39 [avatar contradiction clause 382]
384. $false [avatar sat refutation 361,383]
% SZS output end Proof for 6453244105407436414337623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not rich is not creative or not tall and vice versa.
Everyone who is patient or not quiet is both not kind and not rich and vice versa.
Everyone who is both humble and not strong is either creative or curious and vice versa.
Everyone who is both not creative and not tall is quiet or happy and vice versa.
If fred is not generous or old then someone is happy.
Everyone who is both calm and not generous is calm or old and vice versa.
Everyone who is both funny and curious is not curious or curious.
If susan is both not old and not wise then alice is both not patient and not quiet and vice versa.
If fred is not generous then mary is quiet and vice versa.
Everyone who is either not kind or patient is both not generous and not tall.
If someone is both generous and not humble then someone is not old or not wise.
Everyone who is either tall or not old is not wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
John is both not brave and not curious.
Someone is happy or calm.
Lucy is not wise or happy.
Someone is brave.
Mary is curious or rich.
Someone is both not quiet and not happy.
Susan is not creative. | John is calm. | neutral | (![X]:((humble(X)<~>~rich(X))<=>(~creative(X)|~tall(X))))&
(![X]:((patient(X)|~quiet(X))<=>(~kind(X)&~rich(X))))&
(![X]:((humble(X)&~strong(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~creative(X)&~tall(X))<=>(quiet(X)|happy(X))))&
(((~generous(fred)|old(fred)))=>(?[X]:(happy(X))))&
(![X]:((calm(X)&~generous(X))<=>(calm(X)|old(X))))&
(![X]:((funny(X)&curious(X))=>(~curious(X)|curious(X))))&
(((~old(susan)&~wise(susan)))<=>((~patient(alice)&~quiet(alice))))&
((~generous(fred))<=>(quiet(mary)))&
(![X]:((~kind(X)<~>patient(X))=>(~generous(X)&~tall(X))))&
((?[X]:((generous(X)&~humble(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((tall(X)<~>~old(X))<=>~wise(X)))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
((~brave(john)&~curious(john)))&
(?[X]:((happy(X)|calm(X))))&
((~wise(lucy)|happy(lucy)))&
(?[X]:(brave(X)))&
((curious(mary)|rich(mary)))&
(?[X]:((~quiet(X)&~happy(X))))&
(~creative(susan)) | calm(john) | [] | null | 0 |
If someone is either not creative or wise then someone is curious and vice versa.
Everyone who is both kind and not kind is rich and vice versa.
If fred is both not quiet and not creative then someone is both not kind and not brave and vice versa.
Everyone who is not creative or strong is not quiet.
If alice is not quiet or not tall then lucy is humble and vice versa.
Everyone who is either not wise or patient is both not rich and kind.
Everyone who is not patient is both funny and brave and vice versa.
If susan is either old or not strong then someone is old.
If someone is not kind or calm then someone is both not rich and funny and vice versa.
If someone is not calm then someone is either not strong or not kind.
If someone is not kind or not curious then someone is kind or not old.
Everyone who is humble is not quiet or not funny and vice versa.
If alice is both not generous and generous then susan is either not patient or kind and vice versa.
Everyone who is patient is both not creative and curious.
If someone is both quiet and creative then susan is both patient and not kind.
If lucy is both not old and not patient then someone is either creative or not wise and vice versa.
Someone is not funny or not old.
John is both not happy and patient.
Lucy is both not kind and not curious.
Susan is both not strong and not happy.
Someone is not strong.
Alice is either brave or not funny.
Someone is tall or not tall. | Susan is tall. | neutral | ((?[X]:((~creative(X)<~>wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))<=>rich(X)))&
(((~quiet(fred)&~creative(fred)))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~creative(X)|strong(X))=>~quiet(X)))&
(((~quiet(alice)|~tall(alice)))<=>(humble(lucy)))&
(![X]:((~wise(X)<~>patient(X))=>(~rich(X)&kind(X))))&
(![X]:(~patient(X)<=>(funny(X)&brave(X))))&
(((old(susan)<~>~strong(susan)))=>(?[X]:(old(X))))&
((?[X]:((~kind(X)|calm(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
((?[X]:((~kind(X)|~curious(X))))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(((~generous(alice)&generous(alice)))<=>((~patient(susan)<~>kind(susan))))&
(![X]:(patient(X)=>(~creative(X)&curious(X))))&
((?[X]:((quiet(X)&creative(X))))=>((patient(susan)&~kind(susan))))&
(((~old(lucy)&~patient(lucy)))<=>(?[X]:((creative(X)<~>~wise(X)))))&
(?[X]:((~funny(X)|~old(X))))&
((~happy(john)&patient(john)))&
((~kind(lucy)&~curious(lucy)))&
((~strong(susan)&~happy(susan)))&
(?[X]:(~strong(X)))&
((brave(alice)<~>~funny(alice)))&
(?[X]:((tall(X)|~tall(X)))) | tall(susan) | [] | null | 0 |
Everyone who is either not calm or not quiet is both not happy and not calm and vice versa. If someone is both strong and humble then someone is both funny and tall and vice versa. Everyone who is old is not calm. If john is both not creative and quiet then someone is not wise or rich and vice versa. If lucy is either not creative or curious then lucy is happy or tall. If paul is both not curious and not wise then susan is not kind or not creative and vice versa. If someone is both calm and humble then fred is both not old and quiet. Everyone who is not curious or not rich is both humble and brave. Everyone who is either not funny or not wise is either rich or not funny. Everyone who is not humble is either not calm or happy and vice versa. If john is both strong and brave then paul is both not humble and not strong and vice versa. If someone is either calm or not wise then alice is not curious or funny. Everyone who is not kind is wise or generous and vice versa. If fred is either not curious or not rich then someone is generous or not wise. Everyone who is either calm or quiet is both not funny and happy and vice versa. Everyone who is either not humble or humble is not humble. Someone is not strong or happy. Someone is either not old or brave. Susan is not tall. Someone is not kind. Susan is both not humble and not wise. Paul is either curious or not wise. | Fred is not old. | entailment | (![X]:((~calm(X)<~>~quiet(X))<=>(~happy(X)&~calm(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((funny(X)&tall(X)))))&
(![X]:(old(X)=>~calm(X)))&
(((~creative(john)&quiet(john)))<=>(?[X]:((~wise(X)|rich(X)))))&
(((~creative(lucy)<~>curious(lucy)))=>((happy(lucy)|tall(lucy))))&
(((~curious(paul)&~wise(paul)))<=>((~kind(susan)|~creative(susan))))&
((?[X]:((calm(X)&humble(X))))=>((~old(fred)&quiet(fred))))&
(![X]:((~curious(X)|~rich(X))=>(humble(X)&brave(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(rich(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(((strong(john)&brave(john)))<=>((~humble(paul)&~strong(paul))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~curious(alice)|funny(alice))))&
(![X]:(~kind(X)<=>(wise(X)|generous(X))))&
(((~curious(fred)<~>~rich(fred)))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~funny(X)&happy(X))))&
(![X]:((~humble(X)<~>humble(X))=>~humble(X)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(~tall(susan))&
(?[X]:(~kind(X)))&
((~humble(susan)&~wise(susan)))&
((curious(paul)<~>~wise(paul))) | ~old(fred) | [
"p0",
"p2",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4733000472894288667789831
% SZS output start Proof for 4733000472894288667789831
1. ! [X0] : ((~calm(X0) <~> ~quiet(X0)) <=> (~calm(X0) & ~happy(X0))) [input p0]
3. ! [X0] : (old(X0) => ~calm(X0)) [input p2]
10. ! [X0] : (~humble(X0) <=> (~calm(X0) <~> happy(X0))) [input p9]
15. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> (happy(X0) & ~funny(X0))) [input p14]
16. ! [X0] : ((~humble(X0) <~> humble(X0)) => ~humble(X0)) [input p15]
23. old(fred) [input hypothesis]
25. ! [X0] : (~calm(X0) | ~old(X0)) [ennf transformation 3]
34. ! [X0] : (~humble(X0) | (~humble(X0) <=> humble(X0))) [ennf transformation 16]
35. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (calm(X0) | happy(X0))) & ((~calm(X0) & ~happy(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [nnf transformation 1]
36. ! [X0] : ((((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | calm(X0) | happy(X0)) & ((~calm(X0) & ~happy(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))))) [flattening 35]
51. ! [X0] : ((~humble(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | humble(X0))) [nnf transformation 10]
60. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [flattening 60]
62. ! [X0] : (~humble(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 34]
76. quiet(X0) | calm(X0) | calm(X0) | happy(X0) [cnf transformation 36]
81. ~old(X0) | ~calm(X0) [cnf transformation 25]
105. ~happy(X0) | calm(X0) | humble(X0) [cnf transformation 51]
122. happy(X0) | calm(X0) | ~quiet(X0) [cnf transformation 61]
126. ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 62]
136. old(fred) [cnf transformation 23]
138. ~humble(X0) [duplicate literal removal 126]
142. quiet(X0) | calm(X0) | happy(X0) [duplicate literal removal 76]
244. 23 <=> old(fred) [avatar definition]
245. old(fred) <- (23) [avatar component clause 244]
304. happy(X0) | calm(X0) [subsumption resolution 122,142]
326. 23 [avatar split clause 136,244]
331. ~calm(fred) <- (23) [resolution 81,245]
344. calm(X0) | humble(X0) | calm(X0) [resolution 105,304]
345. calm(X0) | humble(X0) [duplicate literal removal 344]
346. calm(X0) [subsumption resolution 345,138]
347. $false <- (23) [resolution 346,331]
350. ~23 [avatar contradiction clause 347]
352. $false [avatar sat refutation 326,350]
% SZS output end Proof for 4733000472894288667789831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not creative then paul is not kind.
Everyone who is patient is not generous or generous.
If mary is either not tall or tall then someone is either patient or humble and vice versa.
If someone is either not curious or generous then lucy is not kind or not happy and vice versa.
If someone is both not kind and not patient then someone is both curious and quiet.
If someone is not humble then john is either brave or rich and vice versa.
If paul is not humble or old then someone is either not creative or not strong.
If alice is both creative and tall then someone is funny and vice versa.
If someone is both not curious and not tall then someone is either curious or not old and vice versa.
Everyone who is not tall or not brave is both kind and curious.
Everyone who is tall or happy is not brave or humble.
If alice is not patient then mary is either not creative or brave and vice versa.
Everyone who is not strong or not wise is both calm and not humble and vice versa.
Everyone who is both not funny and patient is either wise or not wise and vice versa.
Everyone who is both generous and brave is either wise or not calm.
Everyone who is rich or not patient is old.
Lucy is funny or generous.
Mary is both not funny and brave.
Someone is both not funny and humble.
Someone is creative.
Someone is both happy and wise.
Lucy is wise or happy.
Lucy is not tall or not quiet.
Paul is wise or tall. | Lucy is not wise. | contradiction | ((~creative(fred))=>(~kind(paul)))&
(![X]:(patient(X)=>(~generous(X)|generous(X))))&
(((~tall(mary)<~>tall(mary)))<=>(?[X]:((patient(X)<~>humble(X)))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~kind(lucy)|~happy(lucy))))&
((?[X]:((~kind(X)&~patient(X))))=>(?[X]:((curious(X)&quiet(X)))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(![X]:((~funny(X)&patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((generous(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:((rich(X)|~patient(X))=>old(X)))&
((funny(lucy)|generous(lucy)))&
((~funny(mary)&brave(mary)))&
(?[X]:((~funny(X)&humble(X))))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)&wise(X))))&
((wise(lucy)|happy(lucy)))&
((~tall(lucy)|~quiet(lucy)))&
((wise(paul)|tall(paul))) | ~wise(lucy) | [
"p3",
"p9",
"p10",
"p12",
"p13",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2421636273760399353823365
% SZS output start Proof for 2421636273760399353823365
4. ? [X0] : (~curious(X0) <~> generous(X0)) <=> (~happy(lucy) | ~kind(lucy)) [input p3]
10. ! [X0] : ((~brave(X0) | ~tall(X0)) => (curious(X0) & kind(X0))) [input p9]
11. ! [X0] : ((happy(X0) | tall(X0)) => (humble(X0) | ~brave(X0))) [input p10]
13. ! [X0] : ((~wise(X0) | ~strong(X0)) <=> (~humble(X0) & calm(X0))) [input p12]
14. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p13]
15. ! [X0] : ((brave(X0) & generous(X0)) => (wise(X0) <~> ~calm(X0))) [input p14]
17. generous(lucy) | funny(lucy) [input p16]
22. happy(lucy) | wise(lucy) [input p21]
25. ~wise(lucy) [input hypothesis]
33. ! [X0] : ((curious(X0) & kind(X0)) | (brave(X0) & tall(X0))) [ennf transformation 10]
34. ! [X0] : ((humble(X0) | ~brave(X0)) | (~happy(X0) & ~tall(X0))) [ennf transformation 11]
35. ! [X0] : (humble(X0) | ~brave(X0) | (~happy(X0) & ~tall(X0))) [flattening 34]
36. ! [X0] : ((wise(X0) <~> ~calm(X0)) | (~brave(X0) | ~generous(X0))) [ennf transformation 15]
37. ! [X0] : ((wise(X0) <~> ~calm(X0)) | ~brave(X0) | ~generous(X0)) [flattening 36]
43. (? [X0] : ((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (happy(lucy) & kind(lucy))) & ((~happy(lucy) | ~kind(lucy)) | ! [X0] : ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 4]
44. (? [X0] : ((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X0] : ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [flattening 43]
45. (? [X0] : ((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : ((~curious(X1) | ~generous(X1)) & (generous(X1) | curious(X1)))) [rectify 44]
46. ? [X0] : ((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) => ((~generous(sK1) | curious(sK1)) & (generous(sK1) | ~curious(sK1))) [choice axiom]
47. (((~generous(sK1) | curious(sK1)) & (generous(sK1) | ~curious(sK1))) | (happy(lucy) & kind(lucy))) & (~happy(lucy) | ~kind(lucy) | ! [X1] : ((~curious(X1) | ~generous(X1)) & (generous(X1) | curious(X1)))) [skolemisation 45,46]
69. ! [X0] : (((~wise(X0) | ~strong(X0)) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | (wise(X0) & strong(X0)))) [nnf transformation 13]
70. ! [X0] : ((~wise(X0) | ~strong(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | (wise(X0) & strong(X0)))) [flattening 69]
71. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~patient(X0) | funny(X0)))) [nnf transformation 14]
72. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~patient(X0) | funny(X0))) [flattening 71]
73. ! [X0] : (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ~brave(X0) | ~generous(X0)) [nnf transformation 37]
91. ~happy(lucy) | ~kind(lucy) | ~curious(X1) | ~generous(X1) [cnf transformation 47]
115. tall(X0) | kind(X0) [cnf transformation 33]
116. brave(X0) | kind(X0) [cnf transformation 33]
118. brave(X0) | curious(X0) [cnf transformation 33]
119. ~brave(X0) | humble(X0) | ~tall(X0) [cnf transformation 35]
126. calm(X0) | wise(X0) [cnf transformation 70]
128. ~humble(X0) | wise(X0) [cnf transformation 70]
132. ~funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 72]
133. ~funny(X0) | wise(X0) | wise(X0) [cnf transformation 72]
136. ~calm(X0) | wise(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 73]
137. calm(X0) | ~wise(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 73]
140. generous(lucy) | funny(lucy) [cnf transformation 17]
148. happy(lucy) | wise(lucy) [cnf transformation 22]
151. ~wise(lucy) [cnf transformation 25]
152. ~funny(X0) | ~wise(X0) [duplicate literal removal 132]
153. ~funny(X0) | wise(X0) [duplicate literal removal 133]
186. 6 <=> happy(lucy) [avatar definition]
199. 9 <=> kind(lucy) [avatar definition]
200. ~kind(lucy) <- (~9) [avatar component clause 199]
206. 10 <=> ! [X1] : (~curious(X1) | ~generous(X1)) [avatar definition]
207. ~curious(X1) | ~generous(X1) <- (10) [avatar component clause 206]
208. 10 | ~9 | ~6 [avatar split clause 91,186,199,206]
266. 23 <=> ! [X0] : ~funny(X0) [avatar definition]
267. ~funny(X0) <- (23) [avatar component clause 266]
332. ~funny(X0) [subsumption resolution 152,153]
333. 23 [avatar split clause 332,266]
334. ~brave(X0) | calm(X0) | ~generous(X0) [subsumption resolution 137,126]
335. ~brave(X0) | wise(X0) | ~generous(X0) [subsumption resolution 136,334]
337. 37 <=> funny(lucy) [avatar definition]
339. funny(lucy) <- (37) [avatar component clause 337]
341. 38 <=> generous(lucy) [avatar definition]
343. generous(lucy) <- (38) [avatar component clause 341]
344. 37 | 38 [avatar split clause 140,341,337]
347. 39 <=> wise(lucy) [avatar definition]
348. ~wise(lucy) <- (~39) [avatar component clause 347]
350. 39 | 6 [avatar split clause 148,186,347]
369. ~39 [avatar split clause 151,347]
372. $false <- (23, 37) [resolution 339,267]
373. ~23 | ~37 [avatar contradiction clause 372]
394. humble(X1) | ~tall(X1) | kind(X1) [resolution 119,116]
397. humble(X1) | kind(X1) [subsumption resolution 394,115]
449. ~generous(X0) | wise(X0) | curious(X0) [resolution 335,118]
460. wise(X0) | kind(X0) [resolution 397,128]
466. 53 <=> curious(lucy) [avatar definition]
468. curious(lucy) <- (53) [avatar component clause 466]
501. ~generous(lucy) <- (10, 53) [resolution 468,207]
502. $false <- (10, 38, 53) [subsumption resolution 501,343]
503. ~10 | ~38 | ~53 [avatar contradiction clause 502]
506. wise(lucy) | curious(lucy) <- (38) [resolution 449,343]
507. curious(lucy) <- (38, ~39) [subsumption resolution 506,348]
510. 53 | ~38 | 39 [avatar split clause 507,347,341,466]
517. kind(lucy) <- (~39) [resolution 460,348]
518. $false <- (~9, ~39) [subsumption resolution 517,200]
519. 9 | 39 [avatar contradiction clause 518]
520. $false [avatar sat refutation 208,333,344,350,369,373,503,510,519]
% SZS output end Proof for 2421636273760399353823365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either curious or not strong then susan is either not generous or not rich and vice versa.
If someone is quiet then someone is both not tall and not curious and vice versa.
If alice is not rich then fred is both not generous and generous.
If john is not quiet or humble then someone is both generous and brave and vice versa.
Everyone who is either not old or strong is old and vice versa.
Everyone who is both strong and not funny is generous and vice versa.
If someone is either kind or happy then mary is quiet and vice versa.
Everyone who is not happy or humble is not patient.
If paul is old or kind then someone is not curious.
If john is wise then someone is old or funny and vice versa.
If someone is both old and not happy then someone is either not funny or not curious.
If lucy is not rich or wise then someone is not funny or not calm.
Everyone who is both not funny and not kind is both curious and not curious and vice versa.
If someone is both not rich and old then someone is both not kind and not brave and vice versa.
Everyone who is either not strong or wise is not happy and vice versa.
If someone is not quiet or not curious then paul is not patient or not kind.
Fred is either not calm or rich.
Someone is happy.
Someone is either not humble or kind.
Someone is either not rich or strong.
Someone is tall.
Fred is either not old or kind.
Someone is not wise or quiet.
Someone is both kind and brave. | John is patient. | contradiction | (((curious(fred)<~>~strong(fred)))<=>((~generous(susan)<~>~rich(susan))))&
((?[X]:(quiet(X)))<=>(?[X]:((~tall(X)&~curious(X)))))&
((~rich(alice))=>((~generous(fred)&generous(fred))))&
(((~quiet(john)|humble(john)))<=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((~old(X)<~>strong(X))<=>old(X)))&
(![X]:((strong(X)&~funny(X))<=>generous(X)))&
((?[X]:((kind(X)<~>happy(X))))<=>(quiet(mary)))&
(![X]:((~happy(X)|humble(X))=>~patient(X)))&
(((old(paul)|kind(paul)))=>(?[X]:(~curious(X))))&
((wise(john))<=>(?[X]:((old(X)|funny(X)))))&
((?[X]:((old(X)&~happy(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~rich(lucy)|wise(lucy)))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)&~curious(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>~happy(X)))&
((?[X]:((~quiet(X)|~curious(X))))=>((~patient(paul)|~kind(paul))))&
((~calm(fred)<~>rich(fred)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:(tall(X)))&
((~old(fred)<~>kind(fred)))&
(?[X]:((~wise(X)|quiet(X))))&
(?[X]:((kind(X)&brave(X)))) | patient(john) | [
"p4",
"p7",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7790235215330893455189495
% SZS output start Proof for 7790235215330893455189495
5. ! [X0] : ((~old(X0) <~> strong(X0)) <=> old(X0)) [input p4]
8. ! [X0] : ((humble(X0) | ~happy(X0)) => ~patient(X0)) [input p7]
10. wise(john) <=> ? [X0] : (funny(X0) | old(X0)) [input p9]
13. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (~curious(X0) & curious(X0))) [input p12]
15. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> ~happy(X0)) [input p14]
22. ~old(fred) <~> kind(fred) [input p21]
25. patient(john) [input hypothesis]
30. ! [X0] : (~patient(X0) | (~humble(X0) & happy(X0))) [ennf transformation 8]
47. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 5]
56. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & (? [X0] : (funny(X0) | old(X0)) | ~wise(john)) [nnf transformation 10]
57. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & (? [X1] : (funny(X1) | old(X1)) | ~wise(john)) [rectify 56]
58. ? [X1] : (funny(X1) | old(X1)) => (funny(sK5) | old(sK5)) [choice axiom]
59. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & ((funny(sK5) | old(sK5)) | ~wise(john)) [skolemisation 57,58]
66. ! [X0] : (((~kind(X0) & ~funny(X0)) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 13]
67. ! [X0] : (((~kind(X0) & ~funny(X0)) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | kind(X0) | funny(X0))) [flattening 66]
73. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | happy(X0)) & (~happy(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 15]
85. (~kind(fred) | old(fred)) & (kind(fred) | ~old(fred)) [nnf transformation 22]
108. old(X0) | strong(X0) | old(X0) [cnf transformation 47]
110. strong(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
119. ~patient(X0) | happy(X0) [cnf transformation 30]
124. wise(john) | ~old(X0) [cnf transformation 59]
125. wise(john) | ~funny(X0) [cnf transformation 59]
130. curious(X0) | kind(X0) | funny(X0) [cnf transformation 67]
131. ~curious(X0) | kind(X0) | funny(X0) [cnf transformation 67]
139. ~happy(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 73]
153. ~kind(fred) | old(fred) [cnf transformation 85]
157. patient(john) [cnf transformation 25]
158. old(X0) | strong(X0) [duplicate literal removal 108]
159. ~old(X0) | strong(X0) [duplicate literal removal 110]
239. strong(X0) [subsumption resolution 158,159]
278. 25 <=> ! [X0] : ~funny(X0) [avatar definition]
279. ~funny(X0) <- (25) [avatar component clause 278]
281. 26 <=> wise(john) [avatar definition]
283. wise(john) <- (26) [avatar component clause 281]
284. 25 | 26 [avatar split clause 125,281,278]
286. 27 <=> ! [X0] : ~old(X0) [avatar definition]
287. ~old(X0) <- (27) [avatar component clause 286]
288. 27 | 26 [avatar split clause 124,281,286]
329. kind(X0) | funny(X0) [subsumption resolution 130,131]
357. ~wise(X0) | ~happy(X0) [subsumption resolution 139,239]
392. 50 <=> old(fred) [avatar definition]
394. old(fred) <- (50) [avatar component clause 392]
396. 51 <=> kind(fred) [avatar definition]
398. ~kind(fred) <- (~51) [avatar component clause 396]
399. 50 | ~51 [avatar split clause 153,396,392]
412. happy(john) [resolution 119,157]
429. funny(fred) <- (~51) [resolution 329,398]
433. $false <- (25, ~51) [subsumption resolution 429,279]
434. ~25 | 51 [avatar contradiction clause 433]
457. ~happy(john) <- (26) [resolution 357,283]
459. $false <- (26) [subsumption resolution 457,412]
460. ~26 [avatar contradiction clause 459]
465. $false <- (27, 50) [resolution 394,287]
468. ~27 | ~50 [avatar contradiction clause 465]
469. $false [avatar sat refutation 284,288,399,434,460,468]
% SZS output end Proof for 7790235215330893455189495
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or creative then someone is kind or not strong and vice versa. Everyone who is kind or creative is not strong. Everyone who is either not brave or kind is either brave or not kind and vice versa. Everyone who is tall or old is happy or strong and vice versa. Everyone who is both not rich and not generous is not funny or tall and vice versa. If susan is quiet then someone is both not generous and humble and vice versa. Everyone who is either brave or not humble is humble or not curious and vice versa. If someone is either not funny or calm then fred is both not kind and not brave. Everyone who is brave is not humble. If lucy is either not happy or not wise then fred is either not patient or patient. If someone is both not wise and not strong then john is both tall and patient. Everyone who is both kind and curious is not old. Everyone who is either not patient or wise is humble or not rich. Everyone who is not humble or old is both not calm and strong. If someone is happy then someone is both not rich and creative. Everyone who is humble is either kind or not old. Someone is both not kind and not humble. John is either calm or not wise. Someone is wise or not tall. Someone is both not kind and not calm. Fred is both old and not calm. Someone is either not funny or not curious. Someone is either not quiet or quiet. Fred is rich. | Susan is not strong. | contradiction | ((?[X]:((~generous(X)<~>creative(X))))<=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((kind(X)|creative(X))=>~strong(X)))&
(![X]:((~brave(X)<~>kind(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((tall(X)|old(X))<=>(happy(X)|strong(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~funny(X)|tall(X))))&
((quiet(susan))<=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((brave(X)<~>~humble(X))<=>(humble(X)|~curious(X))))&
((?[X]:((~funny(X)<~>calm(X))))=>((~kind(fred)&~brave(fred))))&
(![X]:(brave(X)=>~humble(X)))&
(((~happy(lucy)<~>~wise(lucy)))=>((~patient(fred)<~>patient(fred))))&
((?[X]:((~wise(X)&~strong(X))))=>((tall(john)&patient(john))))&
(![X]:((kind(X)&curious(X))=>~old(X)))&
(![X]:((~patient(X)<~>wise(X))=>(humble(X)|~rich(X))))&
(![X]:((~humble(X)|old(X))=>(~calm(X)&strong(X))))&
((?[X]:(happy(X)))=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:(humble(X)=>(kind(X)<~>~old(X))))&
(?[X]:((~kind(X)&~humble(X))))&
((calm(john)<~>~wise(john)))&
(?[X]:((wise(X)|~tall(X))))&
(?[X]:((~kind(X)&~calm(X))))&
((old(fred)&~calm(fred)))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>quiet(X))))&
(rich(fred)) | ~strong(susan) | [
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4626005246456740194747436
% SZS output start Proof for 4626005246456740194747436
7. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (~curious(X0) | humble(X0))) [input p6]
9. ! [X0] : (brave(X0) => ~humble(X0)) [input p8]
14. ! [X0] : ((old(X0) | ~humble(X0)) => (strong(X0) & ~calm(X0))) [input p13]
25. ~strong(susan) [input hypothesis]
30. ! [X0] : (~humble(X0) | ~brave(X0)) [ennf transformation 9]
37. ! [X0] : ((strong(X0) & ~calm(X0)) | (~old(X0) & humble(X0))) [ennf transformation 14]
54. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 7]
55. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 54]
106. ~humble(X0) | brave(X0) | ~humble(X0) [cnf transformation 55]
114. ~humble(X0) | ~brave(X0) [cnf transformation 30]
126. strong(X0) | humble(X0) [cnf transformation 37]
146. ~strong(susan) [cnf transformation 25]
148. ~humble(X0) | brave(X0) [duplicate literal removal 106]
158. 1 <=> ! [X1] : strong(X1) [avatar definition]
159. strong(X1) <- (1) [avatar component clause 158]
228. ~humble(X0) [subsumption resolution 114,148]
244. strong(X0) [subsumption resolution 126,228]
245. 1 [avatar split clause 244,158]
280. $false <- (1) [resolution 159,146]
281. ~1 [avatar contradiction clause 280]
282. $false [avatar sat refutation 245,281]
% SZS output end Proof for 4626005246456740194747436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not creative or not calm.
If someone is both rich and not rich then someone is wise or not old.
Everyone who is not generous or not creative is both creative and patient.
Everyone who is not kind is both not wise and not happy and vice versa.
Everyone who is both wise and not happy is patient or not brave and vice versa.
If alice is brave then lucy is not humble or not patient.
If susan is both not rich and strong then someone is both not brave and not funny.
If someone is not old then john is either brave or happy.
Everyone who is wise is either curious or old.
Everyone who is not patient or wise is both humble and strong and vice versa.
Everyone who is not calm is either not brave or not creative and vice versa.
If someone is happy then john is either not rich or strong and vice versa.
Everyone who is curious or not quiet is not kind and vice versa.
If john is both not patient and not calm then someone is both wise and not creative and vice versa.
If susan is both humble and not kind then alice is old.
If mary is not curious then alice is both tall and not humble.
Lucy is both not brave and not happy.
Mary is either not calm or not wise.
Paul is both quiet and wise.
Lucy is not rich or quiet.
Alice is either not curious or brave.
Someone is quiet or generous.
Someone is not curious.
Paul is not kind or not funny. | Mary is calm. | entailment | (![X]:(~curious(X)=>(~creative(X)|~calm(X))))&
((?[X]:((rich(X)&~rich(X))))=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~generous(X)|~creative(X))=>(creative(X)&patient(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~happy(X))))&
(![X]:((wise(X)&~happy(X))<=>(patient(X)|~brave(X))))&
((brave(alice))=>((~humble(lucy)|~patient(lucy))))&
(((~rich(susan)&strong(susan)))=>(?[X]:((~brave(X)&~funny(X)))))&
((?[X]:(~old(X)))=>((brave(john)<~>happy(john))))&
(![X]:(wise(X)=>(curious(X)<~>old(X))))&
(![X]:((~patient(X)|wise(X))<=>(humble(X)&strong(X))))&
(![X]:(~calm(X)<=>(~brave(X)<~>~creative(X))))&
((?[X]:(happy(X)))<=>((~rich(john)<~>strong(john))))&
(![X]:((curious(X)|~quiet(X))<=>~kind(X)))&
(((~patient(john)&~calm(john)))<=>(?[X]:((wise(X)&~creative(X)))))&
(((humble(susan)&~kind(susan)))=>(old(alice)))&
((~curious(mary))=>((tall(alice)&~humble(alice))))&
((~brave(lucy)&~happy(lucy)))&
((~calm(mary)<~>~wise(mary)))&
((quiet(paul)&wise(paul)))&
((~rich(lucy)|quiet(lucy)))&
((~curious(alice)<~>brave(alice)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:(~curious(X)))&
((~kind(paul)|~funny(paul))) | calm(mary) | [
"p3",
"p4",
"p9",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9125188467100829597310469
% SZS output start Proof for 9125188467100829597310469
4. ! [X0] : (~kind(X0) <=> (~happy(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((~happy(X0) & wise(X0)) <=> (~brave(X0) | patient(X0))) [input p4]
10. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (strong(X0) & humble(X0))) [input p9]
13. ! [X0] : ((~quiet(X0) | curious(X0)) <=> ~kind(X0)) [input p12]
16. ~curious(mary) => (~humble(alice) & tall(alice)) [input p15]
18. ~calm(mary) <~> ~wise(mary) [input p17]
25. ~calm(mary) [input hypothesis]
27. ~curious(mary) => ~humble(alice) [pure predicate removal 16]
44. ~humble(alice) | curious(mary) [ennf transformation 27]
48. ! [X0] : ((~kind(X0) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | kind(X0))) [nnf transformation 4]
49. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | kind(X0))) [flattening 48]
50. ! [X0] : (((~happy(X0) & wise(X0)) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | (happy(X0) | ~wise(X0)))) [nnf transformation 5]
51. ! [X0] : (((~happy(X0) & wise(X0)) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | happy(X0) | ~wise(X0))) [flattening 50]
56. ! [X0] : (((wise(X0) | ~patient(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~wise(X0) & patient(X0)))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | ~patient(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~wise(X0) & patient(X0)))) [flattening 56]
63. ! [X0] : (((~quiet(X0) | curious(X0)) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~curious(X0)))) [nnf transformation 13]
64. ! [X0] : ((~quiet(X0) | curious(X0) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~curious(X0)))) [flattening 63]
70. (wise(mary) | calm(mary)) & (~wise(mary) | ~calm(mary)) [nnf transformation 18]
78. ~wise(X0) | kind(X0) [cnf transformation 49]
82. ~patient(X0) | wise(X0) [cnf transformation 51]
92. humble(X0) | patient(X0) [cnf transformation 57]
93. ~wise(X0) | humble(X0) [cnf transformation 57]
105. ~kind(X0) | ~curious(X0) [cnf transformation 64]
113. ~humble(alice) | curious(mary) [cnf transformation 44]
117. wise(mary) | calm(mary) [cnf transformation 70]
124. ~calm(mary) [cnf transformation 25]
217. 20 <=> curious(mary) [avatar definition]
221. 21 <=> humble(alice) [avatar definition]
223. ~humble(alice) <- (~21) [avatar component clause 221]
224. 20 | ~21 [avatar split clause 113,221,217]
226. 22 <=> calm(mary) [avatar definition]
230. 23 <=> wise(mary) [avatar definition]
232. wise(mary) <- (23) [avatar component clause 230]
233. 22 | 23 [avatar split clause 117,230,226]
250. ~22 [avatar split clause 124,226]
252. kind(mary) <- (23) [resolution 78,232]
264. patient(alice) <- (~21) [resolution 92,223]
292. ~curious(mary) <- (23) [resolution 105,252]
293. ~20 | ~23 [avatar split clause 292,230,217]
296. wise(alice) <- (~21) [resolution 264,82]
361. humble(alice) <- (~21) [resolution 296,93]
365. $false <- (~21) [subsumption resolution 361,223]
366. 21 [avatar contradiction clause 365]
367. $false [avatar sat refutation 224,233,250,293,366]
% SZS output end Proof for 9125188467100829597310469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is generous and vice versa.
Everyone who is both not curious and happy is either not old or humble and vice versa.
Everyone who is both curious and happy is both patient and generous.
If someone is not rich then someone is either calm or happy.
Everyone who is quiet or strong is both kind and curious and vice versa.
Everyone who is patient or not brave is not creative or old.
If fred is either not humble or rich then fred is wise and vice versa.
Everyone who is either funny or kind is both not tall and not rich and vice versa.
If mary is not patient or humble then paul is either not rich or brave and vice versa.
If someone is either creative or not strong then someone is generous and vice versa.
Everyone who is either creative or not humble is either not tall or brave and vice versa.
Everyone who is not old is not creative or generous and vice versa.
Everyone who is either creative or not creative is both curious and humble.
Everyone who is patient or not quiet is not funny or not wise.
Everyone who is both not quiet and not strong is both patient and kind and vice versa.
If someone is not quiet then lucy is both not generous and curious.
Fred is quiet.
Someone is either not old or not calm.
Someone is strong or rich.
Someone is not humble or curious.
Someone is kind.
Susan is not happy or not brave. | Paul is generous. | neutral | (![X]:(~tall(X)<=>generous(X)))&
(![X]:((~curious(X)&happy(X))<=>(~old(X)<~>humble(X))))&
(![X]:((curious(X)&happy(X))=>(patient(X)&generous(X))))&
((?[X]:(~rich(X)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((quiet(X)|strong(X))<=>(kind(X)&curious(X))))&
(![X]:((patient(X)|~brave(X))=>(~creative(X)|old(X))))&
(((~humble(fred)<~>rich(fred)))<=>(wise(fred)))&
(![X]:((funny(X)<~>kind(X))<=>(~tall(X)&~rich(X))))&
(((~patient(mary)|humble(mary)))<=>((~rich(paul)<~>brave(paul))))&
((?[X]:((creative(X)<~>~strong(X))))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(~tall(X)<~>brave(X))))&
(![X]:(~old(X)<=>(~creative(X)|generous(X))))&
(![X]:((creative(X)<~>~creative(X))=>(curious(X)&humble(X))))&
(![X]:((patient(X)|~quiet(X))=>(~funny(X)|~wise(X))))&
(![X]:((~quiet(X)&~strong(X))<=>(patient(X)&kind(X))))&
((?[X]:(~quiet(X)))=>((~generous(lucy)&curious(lucy))))&
(quiet(fred))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:(kind(X)))&
((~happy(susan)|~brave(susan))) | generous(paul) | [] | null | 0 |
Everyone who is curious 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.
If john is not curious or not funny then someone is generous and vice versa.
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.
If someone is both rich and happy then someone is not funny or not brave.
John is not rich or old.
Someone is not wise.
Someone is both curious and not rich.
Alice is not happy or tall.
Someone is either wise or happy.
Someone is quiet.
Someone is both patient and humble.
Someone is either creative or wise. | Alice is not creative. | neutral | (![X]:(curious(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)))&
(((~curious(john)|~funny(john)))<=>(?[X]:(generous(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))))&
((?[X]:((rich(X)&happy(X))))=>(?[X]:((~funny(X)|~brave(X)))))&
((~rich(john)|old(john)))&
(?[X]:(~wise(X)))&
(?[X]:((curious(X)&~rich(X))))&
((~happy(alice)|tall(alice)))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:((creative(X)<~>wise(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is both generous and not funny is not tall or not calm and vice versa. If someone is either brave or not creative then paul is wise and vice versa. If someone is curious then alice is both brave and not happy. If someone is not generous or not old then alice is calm or not calm. Everyone who is both not rich and rich is old and vice versa. Everyone who is both old and kind is either tall or not wise and vice versa. If john is either not wise or not curious then fred is either not happy or not old. Everyone who is funny or not wise is not tall. Everyone who is either not wise or not rich is both not kind and patient. If someone is tall or strong then mary is either not generous or calm and vice versa. If alice is not strong then someone is both not creative and not quiet and vice versa. If john is either not rich or not patient then someone is either not creative or not wise and vice versa. Everyone who is either not happy or curious is not creative or kind. If someone is old or generous then fred is either not rich or not happy and vice versa. Everyone who is either not generous or old is both not brave and not strong. Someone is either not old or not brave. Susan is either old or not old. Someone is tall or brave. Someone is both not old and happy. Susan is either happy or not quiet. Someone is not wise or not quiet. Someone is not strong. Paul is patient or creative. | Paul is not brave. | neutral | (![X]:((generous(X)&~funny(X))<=>(~tall(X)|~calm(X))))&
((?[X]:((brave(X)<~>~creative(X))))<=>(wise(paul)))&
((?[X]:(curious(X)))=>((brave(alice)&~happy(alice))))&
((?[X]:((~generous(X)|~old(X))))=>((calm(alice)|~calm(alice))))&
(![X]:((~rich(X)&rich(X))<=>old(X)))&
(![X]:((old(X)&kind(X))<=>(tall(X)<~>~wise(X))))&
(((~wise(john)<~>~curious(john)))=>((~happy(fred)<~>~old(fred))))&
(![X]:((funny(X)|~wise(X))=>~tall(X)))&
(![X]:((~wise(X)<~>~rich(X))=>(~kind(X)&patient(X))))&
((?[X]:((tall(X)|strong(X))))<=>((~generous(mary)<~>calm(mary))))&
((~strong(alice))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(((~rich(john)<~>~patient(john)))<=>(?[X]:((~creative(X)<~>~wise(X)))))&
(![X]:((~happy(X)<~>curious(X))=>(~creative(X)|kind(X))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
((old(susan)<~>~old(susan)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~old(X)&happy(X))))&
((happy(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:(~strong(X)))&
((patient(paul)|creative(paul))) | ~brave(paul) | [] | null | 0 |
Everyone who is generous or kind is not old.
Everyone who is patient or not brave is humble.
Everyone who is humble or not funny is either wise or not kind.
If paul is either old or wise then someone is both wise and not strong.
If susan is both funny and brave then paul is not happy or calm and vice versa.
Everyone who is kind or brave is either not brave or not quiet.
If paul is both not old and calm then someone is both not brave and not calm and vice versa.
Everyone who is both not quiet and not kind is happy.
Everyone who is patient or humble is funny.
Everyone who is patient is not old and vice versa.
Everyone who is creative or not old is generous or not curious and vice versa.
If fred is either brave or curious then fred is patient and vice versa.
If someone is either not tall or happy then someone is both not wise and not kind.
If someone is either not kind or strong then lucy is tall.
Everyone who is either not curious or calm is quiet.
Everyone who is not wise or not humble is either generous or not kind and vice versa.
Someone is both calm and brave.
Someone is not tall or not happy.
Lucy is both not calm and creative.
Fred is either not old or curious.
Someone is strong.
Someone is not strong.
Someone is both not old and humble. | Paul is funny. | entailment | (![X]:((generous(X)|kind(X))=>~old(X)))&
(![X]:((patient(X)|~brave(X))=>humble(X)))&
(![X]:((humble(X)|~funny(X))=>(wise(X)<~>~kind(X))))&
(((old(paul)<~>wise(paul)))=>(?[X]:((wise(X)&~strong(X)))))&
(((funny(susan)&brave(susan)))<=>((~happy(paul)|calm(paul))))&
(![X]:((kind(X)|brave(X))=>(~brave(X)<~>~quiet(X))))&
(((~old(paul)&calm(paul)))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(![X]:((patient(X)|humble(X))=>funny(X)))&
(![X]:(patient(X)<=>~old(X)))&
(![X]:((creative(X)|~old(X))<=>(generous(X)|~curious(X))))&
(((brave(fred)<~>curious(fred)))<=>(patient(fred)))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:((~wise(X)&~kind(X)))))&
((?[X]:((~kind(X)<~>strong(X))))=>(tall(lucy)))&
(![X]:((~curious(X)<~>calm(X))=>quiet(X)))&
(![X]:((~wise(X)|~humble(X))<=>(generous(X)<~>~kind(X))))&
(?[X]:((calm(X)&brave(X))))&
(?[X]:((~tall(X)|~happy(X))))&
((~calm(lucy)&creative(lucy)))&
((~old(fred)<~>curious(fred)))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&humble(X)))) | funny(paul) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p8",
"p9",
"p10",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1245696773327648692755308
% SZS output start Proof for 1245696773327648692755308
1. ! [X0] : ((kind(X0) | generous(X0)) => ~old(X0)) [input p0]
2. ! [X0] : ((~brave(X0) | patient(X0)) => humble(X0)) [input p1]
3. ! [X0] : ((~funny(X0) | humble(X0)) => (wise(X0) <~> ~kind(X0))) [input p2]
6. ! [X0] : ((brave(X0) | kind(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p5]
7. (calm(paul) & ~old(paul)) <=> ? [X0] : (~calm(X0) & ~brave(X0)) [input p6]
9. ! [X0] : ((humble(X0) | patient(X0)) => funny(X0)) [input p8]
10. ! [X0] : (patient(X0) <=> ~old(X0)) [input p9]
11. ! [X0] : ((~old(X0) | creative(X0)) <=> (~curious(X0) | generous(X0))) [input p10]
15. ! [X0] : ((~curious(X0) <~> calm(X0)) => quiet(X0)) [input p14]
16. ! [X0] : ((~humble(X0) | ~wise(X0)) <=> (generous(X0) <~> ~kind(X0))) [input p15]
19. creative(lucy) & ~calm(lucy) [input p18]
24. ~funny(paul) [input hypothesis]
26. ! [X0] : (~old(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 1]
27. ! [X0] : (humble(X0) | (brave(X0) & ~patient(X0))) [ennf transformation 2]
28. ! [X0] : ((wise(X0) <~> ~kind(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 3]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 6]
33. ! [X0] : (funny(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 9]
36. ! [X0] : (quiet(X0) | (~curious(X0) <=> calm(X0))) [ennf transformation 15]
37. ! [X0] : (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | (funny(X0) & ~humble(X0))) [nnf transformation 28]
43. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~brave(X0) & ~kind(X0))) [nnf transformation 30]
44. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X0] : (~calm(X0) & ~brave(X0)) | (~calm(paul) | old(paul))) [nnf transformation 7]
45. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X0] : (~calm(X0) & ~brave(X0)) | ~calm(paul) | old(paul)) [flattening 44]
46. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & (? [X1] : (~calm(X1) & ~brave(X1)) | ~calm(paul) | old(paul)) [rectify 45]
47. ? [X1] : (~calm(X1) & ~brave(X1)) => (~calm(sK1) & ~brave(sK1)) [choice axiom]
48. ((calm(paul) & ~old(paul)) | ! [X0] : (calm(X0) | brave(X0))) & ((~calm(sK1) & ~brave(sK1)) | ~calm(paul) | old(paul)) [skolemisation 46,47]
49. ! [X0] : ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))) [nnf transformation 10]
50. ! [X0] : (((~old(X0) | creative(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (old(X0) & ~creative(X0)))) [nnf transformation 11]
51. ! [X0] : ((~old(X0) | creative(X0) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | (old(X0) & ~creative(X0)))) [flattening 50]
58. ! [X0] : (quiet(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 36]
59. ! [X0] : (((~humble(X0) | ~wise(X0)) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0)))) & (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (humble(X0) & wise(X0)))) [nnf transformation 16]
60. ! [X0] : ((~humble(X0) | ~wise(X0) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0)))) & (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (humble(X0) & wise(X0)))) [flattening 59]
72. ~old(X0) | ~generous(X0) [cnf transformation 26]
73. ~old(X0) | ~kind(X0) [cnf transformation 26]
74. ~patient(X0) | humble(X0) [cnf transformation 27]
76. ~humble(X0) | wise(X0) | ~kind(X0) [cnf transformation 37]
78. ~wise(X0) | kind(X0) | ~humble(X0) [cnf transformation 37]
90. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 43]
95. ~old(paul) | calm(X0) | brave(X0) [cnf transformation 48]
98. ~patient(X0) | funny(X0) [cnf transformation 33]
101. patient(X0) | old(X0) [cnf transformation 49]
102. ~curious(X0) | generous(X0) | ~creative(X0) [cnf transformation 51]
116. curious(X0) | calm(X0) | quiet(X0) [cnf transformation 58]
120. ~generous(X0) | kind(X0) | wise(X0) [cnf transformation 60]
122. ~humble(X0) | ~wise(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 60]
127. ~calm(lucy) [cnf transformation 19]
128. creative(lucy) [cnf transformation 19]
135. ~funny(paul) [cnf transformation 24]
136. ~quiet(X0) | ~brave(X0) [duplicate literal removal 90]
142. 2 <=> old(paul) [avatar definition]
179. 9 <=> ! [X0] : (calm(X0) | brave(X0)) [avatar definition]
180. calm(X0) | brave(X0) <- (9) [avatar component clause 179]
182. 9 | ~2 [avatar split clause 95,142,179]
239. ~wise(X0) | ~humble(X0) | ~generous(X0) [subsumption resolution 122,78]
259. funny(X1) | old(X1) [resolution 101,98]
260. humble(X2) | old(X2) [resolution 101,74]
290. old(paul) [resolution 259,135]
293. 2 [avatar split clause 290,142]
320. brave(lucy) <- (9) [resolution 180,127]
336. ~creative(X1) | quiet(X1) | generous(X1) | calm(X1) [resolution 116,102]
376. old(X0) | wise(X0) | ~kind(X0) [resolution 260,76]
379. ~kind(X0) | wise(X0) [subsumption resolution 376,73]
409. 41 <=> kind(lucy) [avatar definition]
410. ~kind(lucy) <- (~41) [avatar component clause 409]
411. kind(lucy) <- (41) [avatar component clause 409]
483. quiet(lucy) | generous(lucy) | calm(lucy) [resolution 336,128]
484. quiet(lucy) | generous(lucy) [subsumption resolution 483,127]
486. 51 <=> generous(lucy) [avatar definition]
488. generous(lucy) <- (51) [avatar component clause 486]
490. 52 <=> quiet(lucy) [avatar definition]
492. quiet(lucy) <- (52) [avatar component clause 490]
493. 51 | 52 [avatar split clause 484,490,486]
504. 54 <=> wise(lucy) [avatar definition]
506. wise(lucy) <- (54) [avatar component clause 504]
535. kind(lucy) | wise(lucy) <- (51) [resolution 488,120]
537. wise(lucy) <- (~41, 51) [subsumption resolution 535,410]
538. 54 | 41 | ~51 [avatar split clause 537,486,409,504]
539. ~brave(lucy) <- (52) [resolution 492,136]
540. $false <- (9, 52) [subsumption resolution 539,320]
541. ~9 | ~52 [avatar contradiction clause 540]
552. wise(lucy) <- (41) [resolution 379,411]
553. 54 | ~41 [avatar split clause 552,409,504]
563. ~humble(lucy) | ~generous(lucy) <- (54) [resolution 506,239]
566. ~humble(lucy) <- (51, 54) [subsumption resolution 563,488]
573. old(lucy) <- (51, 54) [resolution 566,260]
577. ~generous(lucy) <- (51, 54) [resolution 573,72]
580. $false <- (51, 54) [subsumption resolution 577,488]
581. ~51 | ~54 [avatar contradiction clause 580]
582. $false [avatar sat refutation 182,293,493,538,541,553,581]
% SZS output end Proof for 1245696773327648692755308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not tall is not tall or funny and vice versa.
Everyone who is both not generous and wise is both old and not tall.
Everyone who is either quiet or old is generous.
Everyone who is humble is not kind.
Everyone who is either kind or not wise is either humble or not patient.
Everyone who is either not strong or funny is rich.
If someone is either funny or not brave then someone is not tall or kind.
If someone is not creative or not tall then someone is both happy and not tall and vice versa.
Everyone who is either tall or not creative is not humble or not generous and vice versa.
If someone is quiet then someone is both strong and old and vice versa.
If lucy is not tall or not curious then someone is both creative and not old and vice versa.
If lucy is either not quiet or generous then someone is not funny or not humble and vice versa.
Everyone who is both not creative and happy is not generous.
If someone is not rich then someone is not happy or not brave and vice versa.
If lucy is not brave or not tall then someone is either not rich or curious and vice versa.
Everyone who is both not wise and not tall is both not curious and kind and vice versa.
Someone is happy.
Mary is not funny or strong.
Mary is both generous and kind.
Alice is both humble and not wise.
John is both humble and not generous.
Paul is either kind or brave.
Alice is not happy or not funny.
Alice is either not wise or happy. | Lucy is not curious. | neutral | (![X]:((~strong(X)&~tall(X))<=>(~tall(X)|funny(X))))&
(![X]:((~generous(X)&wise(X))=>(old(X)&~tall(X))))&
(![X]:((quiet(X)<~>old(X))=>generous(X)))&
(![X]:(humble(X)=>~kind(X)))&
(![X]:((kind(X)<~>~wise(X))=>(humble(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>funny(X))=>rich(X)))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((~tall(X)|kind(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(~humble(X)|~generous(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((strong(X)&old(X)))))&
(((~tall(lucy)|~curious(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(((~quiet(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|~humble(X)))))&
(![X]:((~creative(X)&happy(X))=>~generous(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~happy(X)|~brave(X)))))&
(((~brave(lucy)|~tall(lucy)))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~wise(X)&~tall(X))<=>(~curious(X)&kind(X))))&
(?[X]:(happy(X)))&
((~funny(mary)|strong(mary)))&
((generous(mary)&kind(mary)))&
((humble(alice)&~wise(alice)))&
((humble(john)&~generous(john)))&
((kind(paul)<~>brave(paul)))&
((~happy(alice)|~funny(alice)))&
((~wise(alice)<~>happy(alice))) | ~curious(lucy) | [] | null | 0 |
If someone is either not calm or wise then lucy is quiet. Everyone who is both not calm and not brave is not quiet or quiet. If someone is rich then someone is either quiet or not wise and vice versa. Everyone who is rich or not quiet is both quiet and strong. If alice is not kind or rich then someone is either not quiet or not kind. Everyone who is old is both not humble and not brave. Everyone who is not generous or kind is brave or not tall and vice versa. Everyone who is either not rich or not curious is both tall and brave. Everyone who is both not calm and not humble is creative or not old. Everyone who is both calm and not kind is both not rich and not patient and vice versa. Everyone who is both strong and not rich is either wise or old and vice versa. If someone is kind then someone is both not patient and rich. Everyone who is curious or not wise is both not tall and not strong. Everyone who is both not calm and old is either not curious or not rich. Everyone who is either brave or not strong is either not patient or strong and vice versa. Someone is strong or not rich. Someone is not curious. Susan is funny. Mary is either not curious or not humble. Someone is not generous or brave. Fred is not brave or brave. Alice is both creative and quiet. | Lucy is tall. | contradiction | ((?[X]:((~calm(X)<~>wise(X))))=>(quiet(lucy)))&
(![X]:((~calm(X)&~brave(X))=>(~quiet(X)|quiet(X))))&
((?[X]:(rich(X)))<=>(?[X]:((quiet(X)<~>~wise(X)))))&
(![X]:((rich(X)|~quiet(X))=>(quiet(X)&strong(X))))&
(((~kind(alice)|rich(alice)))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:(old(X)=>(~humble(X)&~brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(brave(X)|~tall(X))))&
(![X]:((~rich(X)<~>~curious(X))=>(tall(X)&brave(X))))&
(![X]:((~calm(X)&~humble(X))=>(creative(X)|~old(X))))&
(![X]:((calm(X)&~kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((strong(X)&~rich(X))<=>(wise(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((curious(X)|~wise(X))=>(~tall(X)&~strong(X))))&
(![X]:((~calm(X)&old(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)<~>strong(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(~curious(X)))&
(funny(susan))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((~brave(fred)|brave(fred)))&
((creative(alice)&quiet(alice))) | tall(lucy) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5159394911564551904377940
% SZS output start Proof for 5159394911564551904377940
3. ? [X0] : rich(X0) <=> ? [X0] : (quiet(X0) <~> ~wise(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) | rich(X0)) => (strong(X0) & quiet(X0))) [input p3]
6. ! [X0] : (old(X0) => (~brave(X0) & ~humble(X0))) [input p5]
8. ! [X0] : ((~rich(X0) <~> ~curious(X0)) => (brave(X0) & tall(X0))) [input p7]
11. ! [X0] : ((~rich(X0) & strong(X0)) <=> (wise(X0) <~> old(X0))) [input p10]
13. ! [X0] : ((~wise(X0) | curious(X0)) => (~strong(X0) & ~tall(X0))) [input p12]
23. tall(lucy) [input hypothesis]
24. ? [X0] : rich(X0) <=> ? [X1] : (quiet(X1) <~> ~wise(X1)) [rectify 3]
32. ! [X0] : ((strong(X0) & quiet(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 4]
34. ! [X0] : ((~brave(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 6]
35. ! [X0] : ((brave(X0) & tall(X0)) | (~rich(X0) <=> ~curious(X0))) [ennf transformation 8]
37. ! [X0] : ((~strong(X0) & ~tall(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 13]
41. (? [X0] : rich(X0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (? [X1] : ((wise(X1) | ~quiet(X1)) & (~wise(X1) | quiet(X1))) | ! [X0] : ~rich(X0)) [nnf transformation 24]
42. (? [X0] : rich(X0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (? [X2] : ((wise(X2) | ~quiet(X2)) & (~wise(X2) | quiet(X2))) | ! [X3] : ~rich(X3)) [rectify 41]
43. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
44. ? [X2] : ((wise(X2) | ~quiet(X2)) & (~wise(X2) | quiet(X2))) => ((wise(sK1) | ~quiet(sK1)) & (~wise(sK1) | quiet(sK1))) [choice axiom]
45. (rich(sK0) | ! [X1] : ((quiet(X1) | wise(X1)) & (~wise(X1) | ~quiet(X1)))) & (((wise(sK1) | ~quiet(sK1)) & (~wise(sK1) | quiet(sK1))) | ! [X3] : ~rich(X3)) [skolemisation 42,44,43]
51. ! [X0] : ((brave(X0) & tall(X0)) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) [nnf transformation 35]
54. ! [X0] : (((~rich(X0) & strong(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((~rich(X0) & strong(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | rich(X0) | ~strong(X0))) [flattening 54]
73. rich(sK0) | ~wise(X1) | ~quiet(X1) [cnf transformation 45]
76. quiet(X0) | quiet(X0) [cnf transformation 32]
77. ~rich(X0) | strong(X0) [cnf transformation 32]
84. ~old(X0) | ~brave(X0) [cnf transformation 34]
92. ~rich(X0) | brave(X0) | curious(X0) [cnf transformation 51]
101. ~rich(X0) | old(X0) | ~wise(X0) [cnf transformation 55]
106. ~tall(X0) | wise(X0) [cnf transformation 37]
107. ~curious(X0) | ~strong(X0) [cnf transformation 37]
108. ~strong(X0) | wise(X0) [cnf transformation 37]
126. tall(lucy) [cnf transformation 23]
131. quiet(X0) [duplicate literal removal 76]
148. 5 <=> rich(sK0) [avatar definition]
150. rich(sK0) <- (5) [avatar component clause 148]
153. 6 <=> ! [X1] : (~wise(X1) | ~quiet(X1)) [avatar definition]
154. ~wise(X1) | ~quiet(X1) <- (6) [avatar component clause 153]
155. 6 | 5 [avatar split clause 73,148,153]
223. ~wise(X1) <- (6) [subsumption resolution 154,131]
225. wise(lucy) [resolution 106,126]
226. $false <- (6) [subsumption resolution 225,223]
227. ~6 [avatar contradiction clause 226]
228. strong(sK0) <- (5) [resolution 150,77]
231. wise(sK0) <- (5) [resolution 108,228]
252. 22 <=> curious(sK0) [avatar definition]
253. ~curious(sK0) <- (~22) [avatar component clause 252]
254. curious(sK0) <- (22) [avatar component clause 252]
267. ~strong(sK0) <- (22) [resolution 254,107]
269. $false <- (5, 22) [subsumption resolution 267,228]
270. ~5 | ~22 [avatar contradiction clause 269]
272. brave(sK0) | curious(sK0) <- (5) [resolution 92,150]
273. brave(sK0) <- (5, ~22) [subsumption resolution 272,253]
306. old(sK0) | ~wise(sK0) <- (5) [resolution 101,150]
307. old(sK0) <- (5) [subsumption resolution 306,231]
309. ~brave(sK0) <- (5) [resolution 307,84]
310. $false <- (5, ~22) [subsumption resolution 309,273]
311. ~5 | 22 [avatar contradiction clause 310]
312. $false [avatar sat refutation 155,227,270,311]
% SZS output end Proof for 5159394911564551904377940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Paul is curious. | contradiction | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | curious(paul) | [
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2385088893808430234579339
% SZS output start Proof for 2385088893808430234579339
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p13]
22. curious(paul) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 9]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
49. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | brave(X0)) & (~brave(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 8]
56. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 14]
57. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 56]
99. ~rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 48]
105. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 49]
108. ~quiet(X0) | ~brave(X0) [cnf transformation 32]
110. ~brave(X0) | patient(X0) [cnf transformation 32]
127. ~patient(X0) | quiet(X0) [cnf transformation 57]
139. curious(paul) [cnf transformation 22]
140. ~rich(X0) | ~creative(X0) [duplicate literal removal 99]
141. ~rich(X0) | creative(X0) [duplicate literal removal 100]
243. ~rich(X0) [subsumption resolution 140,141]
244. ~curious(X0) | brave(X0) [subsumption resolution 105,243]
272. brave(paul) [resolution 244,139]
274. patient(paul) [resolution 272,110]
320. quiet(paul) [resolution 274,127]
366. ~brave(paul) [resolution 320,108]
368. $false [subsumption resolution 366,272]
% SZS output end Proof for 2385088893808430234579339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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