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 either rich or patient is generous. Everyone who is patient is both brave and funny and vice versa. Everyone who is wise is both creative and not strong and vice versa. Everyone who is either calm or not quiet is quiet and vice versa. Everyone who is either not kind or old is either not funny or happy and vice versa. If susan is both not funny and not happy then susan is not rich or not quiet and vice versa. Everyone who is creative is tall. Everyone who is either not humble or patient is both brave and not old and vice versa. If someone is curious then john is either not creative or not wise and vice versa. If someone is not kind then susan is old and vice versa. Everyone who is not happy or not brave is not kind or not calm and vice versa. Everyone who is not creative or not old is either calm or not calm and vice versa. Everyone who is either not wise or not kind is not funny or kind and vice versa. Everyone who is happy is not rich and vice versa. If lucy is rich then fred is rich and vice versa. Everyone who is either generous or curious is either quiet or strong and vice versa. Someone is either patient or not happy. Lucy is both calm and not tall. Someone is not strong or rich. Alice is not funny. John is funny. Paul is funny or not patient. Someone is both not wise and kind. Someone is either not calm or funny. | Susan is old. | entailment | (![X]:((rich(X)<~>patient(X))=>generous(X)))&
(![X]:(patient(X)<=>(brave(X)&funny(X))))&
(![X]:(wise(X)<=>(creative(X)&~strong(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>quiet(X)))&
(![X]:((~kind(X)<~>old(X))<=>(~funny(X)<~>happy(X))))&
(((~funny(susan)&~happy(susan)))<=>((~rich(susan)|~quiet(susan))))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((~humble(X)<~>patient(X))<=>(brave(X)&~old(X))))&
((?[X]:(curious(X)))<=>((~creative(john)<~>~wise(john))))&
((?[X]:(~kind(X)))<=>(old(susan)))&
(![X]:((~happy(X)|~brave(X))<=>(~kind(X)|~calm(X))))&
(![X]:((~creative(X)|~old(X))<=>(calm(X)<~>~calm(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(~funny(X)|kind(X))))&
(![X]:(happy(X)<=>~rich(X)))&
((rich(lucy))<=>(rich(fred)))&
(![X]:((generous(X)<~>curious(X))<=>(quiet(X)<~>strong(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
((calm(lucy)&~tall(lucy)))&
(?[X]:((~strong(X)|rich(X))))&
(~funny(alice))&
(funny(john))&
((funny(paul)|~patient(paul)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~calm(X)<~>funny(X)))) | old(susan) | [
"p3",
"p5",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 651248055170971140961162
% SZS output start Proof for 651248055170971140961162
4. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> quiet(X0)) [input p3]
6. (~happy(susan) & ~funny(susan)) <=> (~quiet(susan) | ~rich(susan)) [input p5]
10. ? [X0] : ~kind(X0) <=> old(susan) [input p9]
11. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> (~calm(X0) | ~kind(X0))) [input p10]
14. ! [X0] : (happy(X0) <=> ~rich(X0)) [input p13]
25. ~old(susan) [input hypothesis]
33. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | ~quiet(X0)) & (quiet(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 4]
35. ((~happy(susan) & ~funny(susan)) | (quiet(susan) & rich(susan))) & ((~quiet(susan) | ~rich(susan)) | (happy(susan) | funny(susan))) [nnf transformation 6]
36. ((~happy(susan) & ~funny(susan)) | (quiet(susan) & rich(susan))) & (~quiet(susan) | ~rich(susan) | happy(susan) | funny(susan)) [flattening 35]
43. (? [X0] : ~kind(X0) | ~old(susan)) & (old(susan) | ! [X0] : kind(X0)) [nnf transformation 10]
44. (? [X0] : ~kind(X0) | ~old(susan)) & (old(susan) | ! [X1] : kind(X1)) [rectify 43]
45. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
46. (~kind(sK1) | ~old(susan)) & (old(susan) | ! [X1] : kind(X1)) [skolemisation 44,45]
47. ! [X0] : (((~brave(X0) | ~happy(X0)) | (calm(X0) & kind(X0))) & ((~calm(X0) | ~kind(X0)) | (brave(X0) & happy(X0)))) [nnf transformation 11]
48. ! [X0] : ((~brave(X0) | ~happy(X0) | (calm(X0) & kind(X0))) & (~calm(X0) | ~kind(X0) | (brave(X0) & happy(X0)))) [flattening 47]
53. ! [X0] : ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))) [nnf transformation 14]
75. quiet(X0) | calm(X0) | quiet(X0) [cnf transformation 33]
76. ~quiet(X0) | calm(X0) | ~quiet(X0) [cnf transformation 33]
89. ~happy(susan) | rich(susan) [cnf transformation 36]
102. old(susan) | kind(X1) [cnf transformation 46]
104. ~calm(X0) | ~kind(X0) | happy(X0) [cnf transformation 48]
120. ~happy(X0) | ~rich(X0) [cnf transformation 53]
144. ~old(susan) [cnf transformation 25]
149. quiet(X0) | calm(X0) [duplicate literal removal 75]
150. ~quiet(X0) | calm(X0) [duplicate literal removal 76]
151. calm(X0) [subsumption resolution 149,150]
157. 2 <=> happy(susan) [avatar definition]
159. ~happy(susan) <- (~2) [avatar component clause 157]
162. 3 <=> rich(susan) [avatar definition]
164. rich(susan) <- (3) [avatar component clause 162]
165. 3 | ~2 [avatar split clause 89,157,162]
196. 9 <=> old(susan) [avatar definition]
205. 11 <=> ! [X1] : kind(X1) [avatar definition]
206. kind(X1) <- (11) [avatar component clause 205]
207. 11 | 9 [avatar split clause 102,196,205]
209. ~kind(X0) | happy(X0) [subsumption resolution 104,151]
242. ~9 [avatar split clause 144,196]
253. happy(X0) <- (11) [resolution 209,206]
267. $false <- (~2, 11) [resolution 253,159]
269. ~rich(X0) <- (11) [resolution 253,120]
271. 2 | ~11 [avatar contradiction clause 267]
335. $false <- (3, 11) [resolution 269,164]
336. ~3 | ~11 [avatar contradiction clause 335]
337. $false [avatar sat refutation 165,207,242,271,336]
% SZS output end Proof for 651248055170971140961162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not tall then susan is not quiet.
If someone is not strong then someone is either happy or calm.
Everyone who is humble or not humble is both not creative and curious.
Everyone who is patient is either not old or not creative and vice versa.
Everyone who is strong or happy is strong or not happy and vice versa.
If someone is generous then someone is both not rich and calm.
Everyone who is not strong is either funny or not creative and vice versa.
Everyone who is not quiet is both curious and not strong.
Everyone who is both not curious and not old is both rich and patient.
If fred is not wise then mary is wise or not tall and vice versa.
Everyone who is either not tall or not quiet is either generous or not humble.
Everyone who is not strong is humble.
If someone is not humble or curious then paul is either tall or patient.
If paul is happy or not tall then someone is quiet.
If john is both rich and not rich then paul is either not creative or not wise and vice versa.
If paul is both not rich and happy then someone is either calm or humble.
Paul is not funny or quiet.
Someone is funny.
Someone is not old or not patient.
Alice is either not generous or not kind.
Lucy is either not kind or not creative.
Alice is curious. | Alice is kind. | entailment | ((?[X]:((~rich(X)|~tall(X))))=>(~quiet(susan)))&
((?[X]:(~strong(X)))=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((humble(X)|~humble(X))=>(~creative(X)&curious(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~creative(X))))&
(![X]:((strong(X)|happy(X))<=>(strong(X)|~happy(X))))&
((?[X]:(generous(X)))=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:(~strong(X)<=>(funny(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>(curious(X)&~strong(X))))&
(![X]:((~curious(X)&~old(X))=>(rich(X)&patient(X))))&
((~wise(fred))<=>((wise(mary)|~tall(mary))))&
(![X]:((~tall(X)<~>~quiet(X))=>(generous(X)<~>~humble(X))))&
(![X]:(~strong(X)=>humble(X)))&
((?[X]:((~humble(X)|curious(X))))=>((tall(paul)<~>patient(paul))))&
(((happy(paul)|~tall(paul)))=>(?[X]:(quiet(X))))&
(((rich(john)&~rich(john)))<=>((~creative(paul)<~>~wise(paul))))&
(((~rich(paul)&happy(paul)))=>(?[X]:((calm(X)<~>humble(X)))))&
((~funny(paul)|quiet(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|~patient(X))))&
((~generous(alice)<~>~kind(alice)))&
((~kind(lucy)<~>~creative(lucy)))&
(curious(alice)) | kind(alice) | [
"p0",
"p4",
"p5",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5984935376361422752533454
% SZS output start Proof for 5984935376361422752533454
1. ? [X0] : (~tall(X0) | ~rich(X0)) => ~quiet(susan) [input p0]
5. ! [X0] : ((happy(X0) | strong(X0)) <=> (~happy(X0) | strong(X0))) [input p4]
6. ? [X0] : generous(X0) => ? [X0] : (calm(X0) & ~rich(X0)) [input p5]
8. ! [X0] : (~quiet(X0) => (~strong(X0) & curious(X0))) [input p7]
20. ~generous(alice) <~> ~kind(alice) [input p19]
23. ~kind(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : (calm(X1) & ~rich(X1)) [rectify 6]
26. ~quiet(susan) | ! [X0] : (tall(X0) & rich(X0)) [ennf transformation 1]
29. ? [X1] : (calm(X1) & ~rich(X1)) | ! [X0] : ~generous(X0) [ennf transformation 25]
30. ! [X0] : ((~strong(X0) & curious(X0)) | quiet(X0)) [ennf transformation 8]
44. ! [X0] : (((happy(X0) | strong(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (~happy(X0) & ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : ((happy(X0) | strong(X0) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | (~happy(X0) & ~strong(X0)))) [flattening 44]
46. ? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : ~generous(X1) [rectify 29]
47. ? [X0] : (calm(X0) & ~rich(X0)) => (calm(sK1) & ~rich(sK1)) [choice axiom]
48. (calm(sK1) & ~rich(sK1)) | ! [X1] : ~generous(X1) [skolemisation 46,47]
65. (kind(alice) | generous(alice)) & (~kind(alice) | ~generous(alice)) [nnf transformation 20]
67. ~quiet(susan) | rich(X0) [cnf transformation 26]
80. ~happy(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
82. happy(X0) | strong(X0) | happy(X0) [cnf transformation 45]
83. ~rich(sK1) | ~generous(X1) [cnf transformation 48]
90. ~strong(X0) | quiet(X0) [cnf transformation 30]
119. kind(alice) | generous(alice) [cnf transformation 65]
123. ~kind(alice) [cnf transformation 23]
124. ~happy(X0) | strong(X0) [duplicate literal removal 80]
125. happy(X0) | strong(X0) [duplicate literal removal 82]
130. 2 <=> quiet(susan) [avatar definition]
132. ~quiet(susan) <- (~2) [avatar component clause 130]
135. 3 <=> ! [X0] : rich(X0) [avatar definition]
136. rich(X0) <- (3) [avatar component clause 135]
137. 3 | ~2 [avatar split clause 67,130,135]
139. 4 <=> ! [X1] : strong(X1) [avatar definition]
140. strong(X1) <- (4) [avatar component clause 139]
155. strong(X0) [subsumption resolution 124,125]
156. 4 [avatar split clause 155,139]
158. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
159. ~generous(X1) <- (7) [avatar component clause 158]
166. 9 <=> rich(sK1) [avatar definition]
168. ~rich(sK1) <- (~9) [avatar component clause 166]
169. 7 | ~9 [avatar split clause 83,166,158]
251. 25 <=> generous(alice) [avatar definition]
253. generous(alice) <- (25) [avatar component clause 251]
255. 26 <=> kind(alice) [avatar definition]
258. 25 | 26 [avatar split clause 119,255,251]
261. ~26 [avatar split clause 123,255]
262. $false <- (7, 25) [resolution 253,159]
263. ~7 | ~25 [avatar contradiction clause 262]
264. quiet(X0) <- (4) [resolution 90,140]
265. $false <- (~2, 4) [resolution 264,132]
266. 2 | ~4 [avatar contradiction clause 265]
269. $false <- (3, ~9) [resolution 136,168]
270. ~3 | 9 [avatar contradiction clause 269]
271. $false [avatar sat refutation 137,156,169,258,261,263,266,270]
% SZS output end Proof for 5984935376361422752533454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not tall is both not funny and not rich.
Everyone who is old or creative is both calm and not strong and vice versa.
If someone is tall or calm then someone is not rich or not old.
If someone is not funny or generous then someone is both wise and old and vice versa.
Everyone who is quiet or not tall is both humble and not brave.
If someone is not strong then alice is generous and vice versa.
Everyone who is either not generous or not old is either not brave or patient and vice versa.
If someone is either not tall or not calm then john is both humble and curious and vice versa.
Everyone who is both kind and not old is both not brave and kind and vice versa.
Everyone who is not quiet is either not curious or strong and vice versa.
Everyone who is either not kind or generous is both tall and quiet.
If mary is both curious and strong then fred is either funny or rich.
If mary is kind or not kind then someone is generous or not patient and vice versa.
Everyone who is not brave is not kind or strong.
Everyone who is both not wise and generous is either not kind or old.
Everyone who is both not happy and kind is not calm or not creative.
Susan is either not happy or kind.
Mary is either tall or generous.
John is not brave.
Someone is both rich and not kind.
Susan is both not old and not quiet.
Someone is both generous and not curious.
Lucy is happy.
Someone is not brave or funny. | Fred is not funny. | neutral | (![X]:((calm(X)<~>~tall(X))=>(~funny(X)&~rich(X))))&
(![X]:((old(X)|creative(X))<=>(calm(X)&~strong(X))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:((~rich(X)|~old(X)))))&
((?[X]:((~funny(X)|generous(X))))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:((quiet(X)|~tall(X))=>(humble(X)&~brave(X))))&
((?[X]:(~strong(X)))<=>(generous(alice)))&
(![X]:((~generous(X)<~>~old(X))<=>(~brave(X)<~>patient(X))))&
((?[X]:((~tall(X)<~>~calm(X))))<=>((humble(john)&curious(john))))&
(![X]:((kind(X)&~old(X))<=>(~brave(X)&kind(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>strong(X))))&
(![X]:((~kind(X)<~>generous(X))=>(tall(X)&quiet(X))))&
(((curious(mary)&strong(mary)))=>((funny(fred)<~>rich(fred))))&
(((kind(mary)|~kind(mary)))<=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:(~brave(X)=>(~kind(X)|strong(X))))&
(![X]:((~wise(X)&generous(X))=>(~kind(X)<~>old(X))))&
(![X]:((~happy(X)&kind(X))=>(~calm(X)|~creative(X))))&
((~happy(susan)<~>kind(susan)))&
((tall(mary)<~>generous(mary)))&
(~brave(john))&
(?[X]:((rich(X)&~kind(X))))&
((~old(susan)&~quiet(susan)))&
(?[X]:((generous(X)&~curious(X))))&
(happy(lucy))&
(?[X]:((~brave(X)|funny(X)))) | ~funny(fred) | [] | null | 0 |
If susan is not calm or happy then susan is either curious or not humble and vice versa. If lucy is both not funny and not calm then someone is either strong or funny and vice versa. If fred is either not old or strong then susan is creative and vice versa. Everyone who is not kind or not funny is not quiet or not funny and vice versa. If paul is not calm or not brave then someone is not rich and vice versa. If someone is curious or not generous then alice is both curious and brave. If lucy is both funny and not wise then lucy is curious and vice versa. If paul is patient or not kind then paul is old and vice versa. If someone is not tall then susan is not calm or not rich and vice versa. Everyone who is generous is brave or tall. Everyone who is either generous or wise is brave and vice versa. Everyone who is old is either patient or funny and vice versa. If paul is either strong or not quiet then someone is both calm and not calm. If someone is happy then someone is either not kind or old and vice versa. If someone is both kind and not humble then someone is not tall or happy and vice versa. If someone is not brave or not happy then susan is either quiet or curious and vice versa. Someone is either rich or not quiet. Paul is not quiet or not generous. Paul is funny or not tall. Paul is both not rich and funny. Paul is either not creative or brave. Someone is both quiet and curious. Someone is either not strong or brave. John is both not old and brave. | Paul is not patient. | entailment | (((~calm(susan)|happy(susan)))<=>((curious(susan)<~>~humble(susan))))&
(((~funny(lucy)&~calm(lucy)))<=>(?[X]:((strong(X)<~>funny(X)))))&
(((~old(fred)<~>strong(fred)))<=>(creative(susan)))&
(![X]:((~kind(X)|~funny(X))<=>(~quiet(X)|~funny(X))))&
(((~calm(paul)|~brave(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((curious(X)|~generous(X))))=>((curious(alice)&brave(alice))))&
(((funny(lucy)&~wise(lucy)))<=>(curious(lucy)))&
(((patient(paul)|~kind(paul)))<=>(old(paul)))&
((?[X]:(~tall(X)))<=>((~calm(susan)|~rich(susan))))&
(![X]:(generous(X)=>(brave(X)|tall(X))))&
(![X]:((generous(X)<~>wise(X))<=>brave(X)))&
(![X]:(old(X)<=>(patient(X)<~>funny(X))))&
(((strong(paul)<~>~quiet(paul)))=>(?[X]:((calm(X)&~calm(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((kind(X)&~humble(X))))<=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((~brave(X)|~happy(X))))<=>((quiet(susan)<~>curious(susan))))&
(?[X]:((rich(X)<~>~quiet(X))))&
((~quiet(paul)|~generous(paul)))&
((funny(paul)|~tall(paul)))&
((~rich(paul)&funny(paul)))&
((~creative(paul)<~>brave(paul)))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((~strong(X)<~>brave(X))))&
((~old(john)&brave(john))) | ~patient(paul) | [
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 749118114017836410155922
% SZS output start Proof for 749118114017836410155922
8. (~kind(paul) | patient(paul)) <=> old(paul) [input p7]
12. ! [X0] : (old(X0) <=> (patient(X0) <~> funny(X0))) [input p11]
20. funny(paul) & ~rich(paul) [input p19]
25. patient(paul) [input hypothesis]
49. ((~kind(paul) | patient(paul)) | ~old(paul)) & (old(paul) | (kind(paul) & ~patient(paul))) [nnf transformation 8]
50. (~kind(paul) | patient(paul) | ~old(paul)) & (old(paul) | (kind(paul) & ~patient(paul))) [flattening 49]
57. ! [X0] : ((old(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ~old(X0))) [nnf transformation 12]
114. old(paul) | ~patient(paul) [cnf transformation 50]
126. ~patient(X0) | ~funny(X0) | ~old(X0) [cnf transformation 57]
153. funny(paul) [cnf transformation 20]
162. patient(paul) [cnf transformation 25]
277. 24 <=> old(paul) [avatar definition]
278. old(paul) <- (24) [avatar component clause 277]
281. 25 <=> patient(paul) [avatar definition]
283. patient(paul) <- (25) [avatar component clause 281]
290. ~25 | 24 [avatar split clause 114,277,281]
410. 52 <=> funny(paul) [avatar definition]
412. funny(paul) <- (52) [avatar component clause 410]
418. 52 [avatar split clause 153,410]
435. 25 [avatar split clause 162,281]
528. ~funny(paul) | ~old(paul) <- (25) [resolution 126,283]
529. ~old(paul) <- (25, 52) [subsumption resolution 528,412]
530. $false <- (24, 25, 52) [subsumption resolution 529,278]
531. ~24 | ~25 | ~52 [avatar contradiction clause 530]
532. $false [avatar sat refutation 290,418,435,531]
% SZS output end Proof for 749118114017836410155922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or brave is either happy or not old and vice versa.
If someone is calm or old then someone is either curious or not brave and vice versa.
Everyone who is not old is not happy or happy and vice versa.
If susan is tall or not strong then alice is both not tall and wise.
If someone is either not humble or quiet then john is wise or patient and vice versa.
If fred is not wise or brave then someone is not brave and vice versa.
If susan is calm or not calm then john is not wise or old.
Everyone who is both not patient and rich is not happy or not rich.
If someone is happy then lucy is both not strong and rich and vice versa.
If someone is not happy or calm then someone is not tall or not curious and vice versa.
If mary is not creative then someone is not strong and vice versa.
If fred is both old and not humble then alice is generous.
If lucy is both rich and not patient then someone is happy or kind and vice versa.
If someone is not humble or patient then lucy is not kind or humble and vice versa.
If susan is both not kind and wise then someone is both quiet and kind.
Everyone who is happy or not curious is strong or not curious.
Lucy is not rich.
Someone is curious.
Someone is generous.
Someone is either not rich or patient.
Someone is not calm or not old.
Someone is both strong and not rich. | Susan is creative. | neutral | (![X]:((humble(X)<~>brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>(~happy(X)|happy(X))))&
(((tall(susan)|~strong(susan)))=>((~tall(alice)&wise(alice))))&
((?[X]:((~humble(X)<~>quiet(X))))<=>((wise(john)|patient(john))))&
(((~wise(fred)|brave(fred)))<=>(?[X]:(~brave(X))))&
(((calm(susan)|~calm(susan)))=>((~wise(john)|old(john))))&
(![X]:((~patient(X)&rich(X))=>(~happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>((~strong(lucy)&rich(lucy))))&
((?[X]:((~happy(X)|calm(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
((~creative(mary))<=>(?[X]:(~strong(X))))&
(((old(fred)&~humble(fred)))=>(generous(alice)))&
(((rich(lucy)&~patient(lucy)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~kind(lucy)|humble(lucy))))&
(((~kind(susan)&wise(susan)))=>(?[X]:((quiet(X)&kind(X)))))&
(![X]:((happy(X)|~curious(X))=>(strong(X)|~curious(X))))&
(~rich(lucy))&
(?[X]:(curious(X)))&
(?[X]:(generous(X)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((strong(X)&~rich(X)))) | creative(susan) | [] | null | 0 |
If someone is not strong or not quiet then someone is not funny or not brave. If alice is not wise or calm then someone is not quiet or old. Everyone who is both happy and curious is either not tall or not curious and vice versa. If mary is both wise and humble then someone is either old or generous. If someone is either humble or patient then someone is either not kind or not tall. If someone is both patient and not patient then lucy is not old or creative and vice versa. Everyone who is not curious or not kind is both not kind and not patient. If lucy is both creative and not calm then someone is wise and vice versa. If someone is both not old and not humble then fred is not patient or humble and vice versa. Everyone who is both not calm and funny is either kind or not tall. If alice is not calm then someone is either happy or funny and vice versa. If fred is old or quiet then someone is not brave and vice versa. If susan is generous or not funny then fred is tall. Everyone who is either not calm or calm is both not curious and happy and vice versa. If john is both calm and not humble then someone is both not happy and humble. If someone is not old then mary is not calm or not creative and vice versa. Someone is not brave. Someone is both strong and quiet. Paul is both creative and not strong. Someone is not wise. Alice is either not strong or not rich. Paul is curious or old. | Fred is curious. | contradiction | ((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)|~brave(X)))))&
(((~wise(alice)|calm(alice)))=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((happy(X)&curious(X))<=>(~tall(X)<~>~curious(X))))&
(((wise(mary)&humble(mary)))=>(?[X]:((old(X)<~>generous(X)))))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((patient(X)&~patient(X))))<=>((~old(lucy)|creative(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&~calm(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)&~humble(X))))<=>((~patient(fred)|humble(fred))))&
(![X]:((~calm(X)&funny(X))=>(kind(X)<~>~tall(X))))&
((~calm(alice))<=>(?[X]:((happy(X)<~>funny(X)))))&
(((old(fred)|quiet(fred)))<=>(?[X]:(~brave(X))))&
(((generous(susan)|~funny(susan)))=>(tall(fred)))&
(![X]:((~calm(X)<~>calm(X))<=>(~curious(X)&happy(X))))&
(((calm(john)&~humble(john)))=>(?[X]:((~happy(X)&humble(X)))))&
((?[X]:(~old(X)))<=>((~calm(mary)|~creative(mary))))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)&quiet(X))))&
((creative(paul)&~strong(paul)))&
(?[X]:(~wise(X)))&
((~strong(alice)<~>~rich(alice)))&
((curious(paul)|old(paul))) | curious(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1861732168636252749696571
% SZS output start Proof for 1861732168636252749696571
14. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (happy(X0) & ~curious(X0))) [input p13]
23. curious(fred) [input hypothesis]
76. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 14]
77. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 76]
136. ~curious(X0) | calm(X0) | calm(X0) [cnf transformation 77]
137. ~curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 77]
156. curious(fred) [cnf transformation 23]
157. ~curious(X0) | calm(X0) [duplicate literal removal 136]
158. ~curious(X0) | ~calm(X0) [duplicate literal removal 137]
339. ~curious(X0) [subsumption resolution 157,158]
384. $false [subsumption resolution 156,339]
% SZS output end Proof for 1861732168636252749696571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both kind and not rich then someone is not wise or quiet.
Everyone who is either funny or not kind is not rich or not old and vice versa.
Everyone who is not calm or calm is not rich or not quiet.
If someone is generous then someone is not kind and vice versa.
If alice is both curious and calm then someone is not tall and vice versa.
Everyone who is not curious is either strong or creative.
If paul is both not happy and not kind then mary is not happy.
If someone is both not curious and generous then mary is not patient and vice versa.
If someone is calm then someone is both not tall and not humble and vice versa.
If paul is both quiet and not rich then mary is kind or generous and vice versa.
Everyone who is calm or happy is not funny.
Everyone who is old is both wise and generous.
Everyone who is both creative and not creative is happy or not happy.
If someone is either not old or not quiet then someone is quiet or rich and vice versa.
Everyone who is happy or not kind is not wise and vice versa.
Everyone who is either curious or tall is not kind and vice versa.
Someone is either happy or tall.
Alice is wise.
Someone is both not funny and patient.
Paul is both not curious and not generous.
Someone is both generous and wise.
Alice is both not rich and generous.
Someone is wise or kind.
Someone is not tall or funny. | Paul is tall. | entailment | (((kind(alice)&~rich(alice)))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:((funny(X)<~>~kind(X))<=>(~rich(X)|~old(X))))&
(![X]:((~calm(X)|calm(X))=>(~rich(X)|~quiet(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~kind(X))))&
(((curious(alice)&calm(alice)))<=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)=>(strong(X)<~>creative(X))))&
(((~happy(paul)&~kind(paul)))=>(~happy(mary)))&
((?[X]:((~curious(X)&generous(X))))<=>(~patient(mary)))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(((quiet(paul)&~rich(paul)))<=>((kind(mary)|generous(mary))))&
(![X]:((calm(X)|happy(X))=>~funny(X)))&
(![X]:(old(X)=>(wise(X)&generous(X))))&
(![X]:((creative(X)&~creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((happy(X)|~kind(X))<=>~wise(X)))&
(![X]:((curious(X)<~>tall(X))<=>~kind(X)))&
(?[X]:((happy(X)<~>tall(X))))&
(wise(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~curious(paul)&~generous(paul)))&
(?[X]:((generous(X)&wise(X))))&
((~rich(alice)&generous(alice)))&
(?[X]:((wise(X)|kind(X))))&
(?[X]:((~tall(X)|funny(X)))) | tall(paul) | [
"p1",
"p4",
"p10",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7138470840383496607626177
% SZS output start Proof for 7138470840383496607626177
2. ! [X0] : ((funny(X0) <~> ~kind(X0)) <=> (~old(X0) | ~rich(X0))) [input p1]
5. (calm(alice) & curious(alice)) <=> ? [X0] : ~tall(X0) [input p4]
11. ! [X0] : ((happy(X0) | calm(X0)) => ~funny(X0)) [input p10]
15. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~wise(X0)) [input p14]
18. wise(alice) [input p17]
22. generous(alice) & ~rich(alice) [input p21]
25. ~tall(paul) [input hypothesis]
36. ! [X0] : (~funny(X0) | (~happy(X0) & ~calm(X0))) [ennf transformation 11]
42. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [nnf transformation 2]
43. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [flattening 42]
49. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (~calm(alice) | ~curious(alice))) [nnf transformation 5]
50. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~calm(alice) | ~curious(alice)) [flattening 49]
51. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~calm(alice) | ~curious(alice)) [rectify 50]
52. ? [X1] : ~tall(X1) => ~tall(sK3) [choice axiom]
53. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (~tall(sK3) | ~calm(alice) | ~curious(alice)) [skolemisation 51,52]
71. ! [X0] : (((~kind(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 15]
72. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [flattening 71]
88. ~kind(X0) | funny(X0) | rich(X0) [cnf transformation 43]
98. calm(alice) | tall(X0) [cnf transformation 53]
113. ~calm(X0) | ~funny(X0) [cnf transformation 36]
125. ~wise(X0) | kind(X0) [cnf transformation 72]
133. wise(alice) [cnf transformation 18]
140. ~rich(alice) [cnf transformation 22]
144. ~tall(paul) [cnf transformation 25]
146. 1 <=> kind(alice) [avatar definition]
147. kind(alice) <- (1) [avatar component clause 146]
150. 2 <=> rich(alice) [avatar definition]
151. ~rich(alice) <- (~2) [avatar component clause 150]
180. 9 <=> ! [X0] : tall(X0) [avatar definition]
181. tall(X0) <- (9) [avatar component clause 180]
183. 10 <=> calm(alice) [avatar definition]
185. calm(alice) <- (10) [avatar component clause 183]
186. 9 | 10 [avatar split clause 98,183,180]
315. ~2 [avatar split clause 140,150]
328. $false <- (9) [resolution 181,144]
329. ~9 [avatar contradiction clause 328]
330. ~funny(alice) <- (10) [resolution 113,185]
335. kind(alice) [resolution 125,133]
340. 1 [avatar split clause 335,146]
348. funny(alice) | rich(alice) <- (1) [resolution 88,147]
359. rich(alice) <- (1, 10) [subsumption resolution 348,330]
360. $false <- (1, ~2, 10) [subsumption resolution 359,151]
361. ~1 | 2 | ~10 [avatar contradiction clause 360]
371. $false [avatar sat refutation 186,315,329,340,361]
% SZS output end Proof for 7138470840383496607626177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and not calm then someone is both tall and not tall. If someone is funny then alice is strong or not generous. Everyone who is not strong or kind is both calm and not old. Everyone who is not brave or not strong is old or wise. If someone is not curious or old then someone is not quiet. If someone is wise then paul is not patient or curious. Everyone who is strong or not tall is either rich or old. Everyone who is both generous and strong is both not rich and not brave. If alice is both happy and generous then alice is not quiet or not humble and vice versa. If someone is both generous and not rich then someone is curious and vice versa. If someone is both happy and wise then fred is both not funny and quiet and vice versa. Everyone who is curious is not calm. If someone is not quiet then susan is both not curious and not strong. Everyone who is both not kind and quiet is both creative and not rich. If lucy is not wise or wise then lucy is both patient and not rich and vice versa. If someone is both not brave and humble then susan is not curious or calm and vice versa. Alice is either humble or wise. Someone is not strong. Lucy is both not strong and not kind. Susan is both not humble and wise. Someone is quiet or not brave. Susan is patient or tall. Someone is humble or not strong. Someone is wise. | Alice is curious. | neutral | ((?[X]:((patient(X)&~calm(X))))=>(?[X]:((tall(X)&~tall(X)))))&
((?[X]:(funny(X)))=>((strong(alice)|~generous(alice))))&
(![X]:((~strong(X)|kind(X))=>(calm(X)&~old(X))))&
(![X]:((~brave(X)|~strong(X))=>(old(X)|wise(X))))&
((?[X]:((~curious(X)|old(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(wise(X)))=>((~patient(paul)|curious(paul))))&
(![X]:((strong(X)|~tall(X))=>(rich(X)<~>old(X))))&
(![X]:((generous(X)&strong(X))=>(~rich(X)&~brave(X))))&
(((happy(alice)&generous(alice)))<=>((~quiet(alice)|~humble(alice))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:(curious(X))))&
((?[X]:((happy(X)&wise(X))))<=>((~funny(fred)&quiet(fred))))&
(![X]:(curious(X)=>~calm(X)))&
((?[X]:(~quiet(X)))=>((~curious(susan)&~strong(susan))))&
(![X]:((~kind(X)&quiet(X))=>(creative(X)&~rich(X))))&
(((~wise(lucy)|wise(lucy)))<=>((patient(lucy)&~rich(lucy))))&
((?[X]:((~brave(X)&humble(X))))<=>((~curious(susan)|calm(susan))))&
((humble(alice)<~>wise(alice)))&
(?[X]:(~strong(X)))&
((~strong(lucy)&~kind(lucy)))&
((~humble(susan)&wise(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
((patient(susan)|tall(susan)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(wise(X))) | curious(alice) | [] | null | 0 |
If paul is both patient and not calm then someone is tall or generous and vice versa. Everyone who is either wise or not funny is both not happy and funny and vice versa. If someone is both not funny and brave then someone is both not patient and happy. Everyone who is not strong is funny or tall and vice versa. If paul is happy or not brave then lucy is tall and vice versa. Everyone who is both curious and humble is either curious or not generous and vice versa. Everyone who is quiet or rich is not wise or patient and vice versa. If paul is strong or not old then someone is either not creative or not brave. Everyone who is both old and happy is both not wise and curious and vice versa. Everyone who is both not curious and humble is either tall or humble. Everyone who is humble or not brave is both patient and quiet. If fred is both not funny and kind then mary is not creative and vice versa. Everyone who is either curious or tall is not patient. Everyone who is either not old or not generous is either not old or not humble. If someone is both not funny and not old then paul is either brave or patient. If someone is both old and not creative then someone is not old and vice versa. Susan is both not quiet and not strong. Mary is both quiet and wise. Alice is both not tall and not curious. Someone is both happy and funny. John is either not creative or quiet. Paul is creative. Someone is both not curious and happy. Lucy is kind. | Alice is not humble. | neutral | (((patient(paul)&~calm(paul)))<=>(?[X]:((tall(X)|generous(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>(~happy(X)&funny(X))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:(~strong(X)<=>(funny(X)|tall(X))))&
(((happy(paul)|~brave(paul)))<=>(tall(lucy)))&
(![X]:((curious(X)&humble(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((quiet(X)|rich(X))<=>(~wise(X)|patient(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(((~funny(fred)&kind(fred)))<=>(~creative(mary)))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((~funny(X)&~old(X))))=>((brave(paul)<~>patient(paul))))&
((?[X]:((old(X)&~creative(X))))<=>(?[X]:(~old(X))))&
((~quiet(susan)&~strong(susan)))&
((quiet(mary)&wise(mary)))&
((~tall(alice)&~curious(alice)))&
(?[X]:((happy(X)&funny(X))))&
((~creative(john)<~>quiet(john)))&
(creative(paul))&
(?[X]:((~curious(X)&happy(X))))&
(kind(lucy)) | ~humble(alice) | [] | null | 0 |
Everyone who is either kind or creative is both not rich and not wise and vice versa.
Everyone who is rich or humble is funny and vice versa.
Everyone who is quiet or not tall is funny or not quiet and vice versa.
If someone is either curious or not creative then someone is both calm and not brave and vice versa.
If someone is kind or generous then someone is both quiet and not funny and vice versa.
If someone is either old or quiet then susan is either kind or strong.
Everyone who is either kind or not calm is either not tall or calm and vice versa.
If john is either patient or creative then mary is wise or funny.
Everyone who is both not strong and wise is not curious and vice versa.
Everyone who is not kind or kind is either kind or calm.
Everyone who is both humble and tall is either old or not rich.
If someone is both old and not rich then someone is patient or curious and vice versa.
Everyone who is patient is not patient or not humble and vice versa.
If someone is not quiet or rich then someone is both calm and creative and vice versa.
If someone is patient then someone is not quiet or not happy.
John is not rich.
Someone is either patient or humble.
Someone is both not old and creative.
Mary is not humble or generous.
John is calm or funny. | Susan is not curious. | contradiction | (![X]:((kind(X)<~>creative(X))<=>(~rich(X)&~wise(X))))&
(![X]:((rich(X)|humble(X))<=>funny(X)))&
(![X]:((quiet(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
((?[X]:((curious(X)<~>~creative(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((quiet(X)&~funny(X)))))&
((?[X]:((old(X)<~>quiet(X))))=>((kind(susan)<~>strong(susan))))&
(![X]:((kind(X)<~>~calm(X))<=>(~tall(X)<~>calm(X))))&
(((patient(john)<~>creative(john)))=>((wise(mary)|funny(mary))))&
(![X]:((~strong(X)&wise(X))<=>~curious(X)))&
(![X]:((~kind(X)|kind(X))=>(kind(X)<~>calm(X))))&
(![X]:((humble(X)&tall(X))=>(old(X)<~>~rich(X))))&
((?[X]:((old(X)&~rich(X))))<=>(?[X]:((patient(X)|curious(X)))))&
(![X]:(patient(X)<=>(~patient(X)|~humble(X))))&
((?[X]:((~quiet(X)|rich(X))))<=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)|~happy(X)))))&
(~rich(john))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~old(X)&creative(X))))&
((~humble(mary)|generous(mary)))&
((calm(john)|funny(john))) | ~curious(susan) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8577592173632942993147566
% SZS output start Proof for 8577592173632942993147566
2. ! [X0] : ((humble(X0) | rich(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (~quiet(X0) | funny(X0))) [input p2]
5. ? [X0] : (generous(X0) | kind(X0)) <=> ? [X0] : (~funny(X0) & quiet(X0)) [input p4]
6. ? [X0] : (old(X0) <~> quiet(X0)) => (kind(susan) <~> strong(susan)) [input p5]
9. ! [X0] : ((wise(X0) & ~strong(X0)) <=> ~curious(X0)) [input p8]
12. ? [X0] : (~rich(X0) & old(X0)) <=> ? [X0] : (curious(X0) | patient(X0)) [input p11]
13. ! [X0] : (patient(X0) <=> (~humble(X0) | ~patient(X0))) [input p12]
21. ~curious(susan) [input hypothesis]
23. ? [X0] : (generous(X0) | kind(X0)) <=> ? [X1] : (~funny(X1) & quiet(X1)) [rectify 5]
24. ? [X0] : (~rich(X0) & old(X0)) <=> ? [X1] : (curious(X1) | patient(X1)) [rectify 12]
28. (kind(susan) <~> strong(susan)) | ! [X0] : (old(X0) <=> quiet(X0)) [ennf transformation 6]
36. ! [X0] : (((humble(X0) | rich(X0)) | ~funny(X0)) & (funny(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 2]
37. ! [X0] : ((humble(X0) | rich(X0) | ~funny(X0)) & (funny(X0) | (~humble(X0) & ~rich(X0)))) [flattening 36]
38. ! [X0] : (((~tall(X0) | quiet(X0)) | (quiet(X0) & ~funny(X0))) & ((~quiet(X0) | funny(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 3]
39. ! [X0] : ((~tall(X0) | quiet(X0) | (quiet(X0) & ~funny(X0))) & (~quiet(X0) | funny(X0) | (tall(X0) & ~quiet(X0)))) [flattening 38]
45. (? [X0] : (generous(X0) | kind(X0)) | ! [X1] : (funny(X1) | ~quiet(X1))) & (? [X1] : (~funny(X1) & quiet(X1)) | ! [X0] : (~generous(X0) & ~kind(X0))) [nnf transformation 23]
46. (? [X0] : (generous(X0) | kind(X0)) | ! [X1] : (funny(X1) | ~quiet(X1))) & (? [X2] : (~funny(X2) & quiet(X2)) | ! [X3] : (~generous(X3) & ~kind(X3))) [rectify 45]
47. ? [X0] : (generous(X0) | kind(X0)) => (generous(sK2) | kind(sK2)) [choice axiom]
48. ? [X2] : (~funny(X2) & quiet(X2)) => (~funny(sK3) & quiet(sK3)) [choice axiom]
49. ((generous(sK2) | kind(sK2)) | ! [X1] : (funny(X1) | ~quiet(X1))) & ((~funny(sK3) & quiet(sK3)) | ! [X3] : (~generous(X3) & ~kind(X3))) [skolemisation 46,48,47]
50. ((~strong(susan) | ~kind(susan)) & (strong(susan) | kind(susan))) | ! [X0] : ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0))) [nnf transformation 28]
53. ! [X0] : (((wise(X0) & ~strong(X0)) | curious(X0)) & (~curious(X0) | (~wise(X0) | strong(X0)))) [nnf transformation 9]
54. ! [X0] : (((wise(X0) & ~strong(X0)) | curious(X0)) & (~curious(X0) | ~wise(X0) | strong(X0))) [flattening 53]
57. (? [X0] : (~rich(X0) & old(X0)) | ! [X1] : (~curious(X1) & ~patient(X1))) & (? [X1] : (curious(X1) | patient(X1)) | ! [X0] : (rich(X0) | ~old(X0))) [nnf transformation 24]
58. (? [X0] : (~rich(X0) & old(X0)) | ! [X1] : (~curious(X1) & ~patient(X1))) & (? [X2] : (curious(X2) | patient(X2)) | ! [X3] : (rich(X3) | ~old(X3))) [rectify 57]
59. ? [X0] : (~rich(X0) & old(X0)) => (~rich(sK4) & old(sK4)) [choice axiom]
60. ? [X2] : (curious(X2) | patient(X2)) => (curious(sK5) | patient(sK5)) [choice axiom]
61. ((~rich(sK4) & old(sK4)) | ! [X1] : (~curious(X1) & ~patient(X1))) & ((curious(sK5) | patient(sK5)) | ! [X3] : (rich(X3) | ~old(X3))) [skolemisation 58,60,59]
62. ! [X0] : ((patient(X0) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 13]
63. ! [X0] : ((patient(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | ~patient(X0))) [flattening 62]
82. ~funny(X0) | rich(X0) | humble(X0) [cnf transformation 37]
83. ~quiet(X0) | funny(X0) | ~quiet(X0) [cnf transformation 39]
93. quiet(sK3) | ~kind(X3) [cnf transformation 49]
95. ~funny(sK3) | ~kind(X3) [cnf transformation 49]
98. strong(susan) | kind(susan) | quiet(X0) | ~old(X0) [cnf transformation 50]
113. ~strong(X0) | curious(X0) [cnf transformation 54]
122. old(sK4) | ~patient(X1) [cnf transformation 61]
124. ~rich(sK4) | ~patient(X1) [cnf transformation 61]
126. ~humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 63]
127. patient(X0) | patient(X0) [cnf transformation 63]
141. ~curious(susan) [cnf transformation 21]
142. ~humble(X0) | ~patient(X0) [duplicate literal removal 126]
143. patient(X0) [duplicate literal removal 127]
150. ~quiet(X0) | funny(X0) [duplicate literal removal 83]
187. 9 <=> funny(sK3) [avatar definition]
189. ~funny(sK3) <- (~9) [avatar component clause 187]
192. 10 <=> ! [X3] : ~kind(X3) [avatar definition]
193. ~kind(X3) <- (10) [avatar component clause 192]
194. 10 | ~9 [avatar split clause 95,187,192]
196. 11 <=> quiet(sK3) [avatar definition]
198. quiet(sK3) <- (11) [avatar component clause 196]
200. 10 | 11 [avatar split clause 93,196,192]
205. 13 <=> kind(susan) [avatar definition]
206. kind(susan) <- (13) [avatar component clause 205]
209. 14 <=> strong(susan) [avatar definition]
210. strong(susan) <- (14) [avatar component clause 209]
214. 15 <=> ! [X0] : (quiet(X0) | ~old(X0)) [avatar definition]
215. ~old(X0) | quiet(X0) <- (15) [avatar component clause 214]
218. 15 | 13 | 14 [avatar split clause 98,209,205,214]
243. 21 <=> rich(sK4) [avatar definition]
248. 22 <=> ! [X1] : ~patient(X1) [avatar definition]
249. ~patient(X1) <- (22) [avatar component clause 248]
250. 22 | ~21 [avatar split clause 124,243,248]
252. 23 <=> old(sK4) [avatar definition]
254. old(sK4) <- (23) [avatar component clause 252]
256. 22 | 23 [avatar split clause 122,252,248]
269. ~humble(X0) [subsumption resolution 142,143]
312. $false <- (22) [subsumption resolution 249,143]
313. ~22 [avatar contradiction clause 312]
321. $false <- (10, 13) [resolution 206,193]
322. ~10 | ~13 [avatar contradiction clause 321]
332. curious(susan) <- (14) [resolution 210,113]
333. $false <- (14) [subsumption resolution 332,141]
334. ~14 [avatar contradiction clause 333]
338. funny(sK3) <- (11) [resolution 198,150]
339. $false <- (~9, 11) [subsumption resolution 338,189]
340. 9 | ~11 [avatar contradiction clause 339]
344. quiet(sK4) <- (15, 23) [resolution 215,254]
347. funny(sK4) <- (15, 23) [resolution 344,150]
365. rich(sK4) | humble(sK4) <- (15, 23) [resolution 82,347]
369. rich(sK4) <- (15, 23) [subsumption resolution 365,269]
370. 21 | ~15 | ~23 [avatar split clause 369,252,214,243]
371. $false [avatar sat refutation 194,200,218,250,256,313,322,334,340,370]
% SZS output end Proof for 8577592173632942993147566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not calm is both not quiet and humble. If someone is either not strong or not creative then fred is either creative or not old. Everyone who is both not curious and old is kind and vice versa. Everyone who is quiet or calm is not curious and vice versa. Everyone who is not humble is calm. Everyone who is both patient and funny is curious or rich. Everyone who is not rich or patient is both happy and not quiet and vice versa. If lucy is either not tall or patient then susan is brave and vice versa. Everyone who is patient is old or calm and vice versa. If someone is either quiet or brave then john is either tall or quiet. If someone is not wise then john is not funny or not wise and vice versa. If mary is not humble then someone is not creative or quiet and vice versa. If fred is either not creative or not brave then someone is curious or rich and vice versa. Everyone who is either happy or brave is not rich. Everyone who is generous or patient is either not quiet or kind. If someone is calm or happy then lucy is either quiet or not quiet. Someone is not old or not brave. Someone is patient or old. Someone is not kind or not happy. Paul is generous or not creative. Lucy is not strong or strong. Someone is either funny or not brave. Someone is both not rich and calm. | Mary is not happy. | neutral | (![X]:((funny(X)|~calm(X))=>(~quiet(X)&humble(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>((creative(fred)<~>~old(fred))))&
(![X]:((~curious(X)&old(X))<=>kind(X)))&
(![X]:((quiet(X)|calm(X))<=>~curious(X)))&
(![X]:(~humble(X)=>calm(X)))&
(![X]:((patient(X)&funny(X))=>(curious(X)|rich(X))))&
(![X]:((~rich(X)|patient(X))<=>(happy(X)&~quiet(X))))&
(((~tall(lucy)<~>patient(lucy)))<=>(brave(susan)))&
(![X]:(patient(X)<=>(old(X)|calm(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((tall(john)<~>quiet(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)|~wise(john))))&
((~humble(mary))<=>(?[X]:((~creative(X)|quiet(X)))))&
(((~creative(fred)<~>~brave(fred)))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((happy(X)<~>brave(X))=>~rich(X)))&
(![X]:((generous(X)|patient(X))=>(~quiet(X)<~>kind(X))))&
((?[X]:((calm(X)|happy(X))))=>((quiet(lucy)<~>~quiet(lucy))))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~kind(X)|~happy(X))))&
((generous(paul)|~creative(paul)))&
((~strong(lucy)|strong(lucy)))&
(?[X]:((funny(X)<~>~brave(X))))&
(?[X]:((~rich(X)&calm(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is not patient is both not funny and not brave.
Everyone who is both not creative and not generous is not quiet.
If alice is not generous or strong then mary is calm and vice versa.
If someone is not creative then lucy is both not calm and not kind and vice versa.
Everyone who is both calm and creative is either tall or creative.
If someone is funny then mary is either not kind or old and vice versa.
Everyone who is both old and rich is either wise or not rich and vice versa.
Everyone who is either not curious or not calm is both not quiet and strong.
Everyone who is humble or not tall is either happy or strong and vice versa.
If susan is rich or not strong then someone is patient or not creative.
If fred is either not generous or not tall then someone is either happy or not kind and vice versa.
Everyone who is wise is happy and vice versa.
Everyone who is both not creative and not generous is either not generous or not strong.
If someone is either quiet or not patient then susan is brave and vice versa.
Everyone who is brave is both generous and not strong.
If someone is both happy and creative then someone is either not kind or not calm.
Someone is either not humble or happy.
Mary is creative.
John is either not generous or funny.
Paul is old or not humble.
Alice is patient or curious.
Lucy is both kind and brave.
Someone is not happy or happy. | Lucy is not patient. | contradiction | (![X]:(~patient(X)=>(~funny(X)&~brave(X))))&
(![X]:((~creative(X)&~generous(X))=>~quiet(X)))&
(((~generous(alice)|strong(alice)))<=>(calm(mary)))&
((?[X]:(~creative(X)))<=>((~calm(lucy)&~kind(lucy))))&
(![X]:((calm(X)&creative(X))=>(tall(X)<~>creative(X))))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>old(mary))))&
(![X]:((old(X)&rich(X))<=>(wise(X)<~>~rich(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((humble(X)|~tall(X))<=>(happy(X)<~>strong(X))))&
(((rich(susan)|~strong(susan)))=>(?[X]:((patient(X)|~creative(X)))))&
(((~generous(fred)<~>~tall(fred)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((~creative(X)&~generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(brave(susan)))&
(![X]:(brave(X)=>(generous(X)&~strong(X))))&
((?[X]:((happy(X)&creative(X))))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(?[X]:((~humble(X)<~>happy(X))))&
(creative(mary))&
((~generous(john)<~>funny(john)))&
((old(paul)|~humble(paul)))&
((patient(alice)|curious(alice)))&
((kind(lucy)&brave(lucy)))&
(?[X]:((~happy(X)|happy(X)))) | ~patient(lucy) | [
"p0",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6100128215155951779278438
% SZS output start Proof for 6100128215155951779278438
1. ! [X0] : (~patient(X0) => (~brave(X0) & ~funny(X0))) [input p0]
22. brave(lucy) & kind(lucy) [input p21]
24. ~patient(lucy) [input hypothesis]
26. ! [X0] : ((~brave(X0) & ~funny(X0)) | patient(X0)) [ennf transformation 1]
77. ~brave(X0) | patient(X0) [cnf transformation 26]
137. brave(lucy) [cnf transformation 22]
139. ~patient(lucy) [cnf transformation 24]
322. patient(lucy) [resolution 77,137]
324. $false [subsumption resolution 322,139]
% SZS output end Proof for 6100128215155951779278438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is either not quiet or generous and vice versa.
Everyone who is either old or not brave is not humble or patient.
Everyone who is either not strong or not humble is either wise or not happy.
Everyone who is both kind and patient is quiet and vice versa.
Everyone who is either not funny or not rich is not wise or not creative.
Everyone who is curious or brave is both generous and not happy and vice versa.
Everyone who is either not brave or generous is rich or calm.
Everyone who is wise is not creative or not rich and vice versa.
If alice is not quiet or not wise then fred is either not tall or not humble.
Everyone who is brave is not wise.
Everyone who is both not creative and not rich is either happy or not old.
Everyone who is either not humble or brave is creative.
If lucy is either happy or curious then someone is not funny or funny.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Someone is patient or creative.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient.
Someone is happy.
Someone is either not humble or not curious. | Lucy is not happy. | neutral | (![X]:(happy(X)<=>(~quiet(X)<~>generous(X))))&
(![X]:((old(X)<~>~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)&patient(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~rich(X))=>(~wise(X)|~creative(X))))&
(![X]:((curious(X)|brave(X))<=>(generous(X)&~happy(X))))&
(![X]:((~brave(X)<~>generous(X))=>(rich(X)|calm(X))))&
(![X]:(wise(X)<=>(~creative(X)|~rich(X))))&
(((~quiet(alice)|~wise(alice)))=>((~tall(fred)<~>~humble(fred))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:((~creative(X)&~rich(X))=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>brave(X))=>creative(X)))&
(((happy(lucy)<~>curious(lucy)))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(?[X]:((patient(X)|creative(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~happy(lucy) | [] | null | 0 |
If someone is calm or not calm then paul is not patient or not calm and vice versa. Everyone who is not creative or not quiet is either not tall or brave. Everyone who is not patient is creative and vice versa. Everyone who is creative is either funny or not generous and vice versa. If someone is both patient and not curious then someone is happy and vice versa. Everyone who is both generous and not patient is not strong or not patient and vice versa. Everyone who is both wise and not rich is either not patient or not old. Everyone who is either not old or not calm is either not brave or not generous. Everyone who is either kind or not humble is both happy and not wise. If someone is either generous or kind then alice is not rich. Everyone who is tall or happy is both calm and not tall. If paul is humble or not humble then someone is not tall and vice versa. If someone is old then someone is not funny and vice versa. If someone is not wise or not patient then mary is both not patient and humble. If someone is both calm and patient then someone is both creative and rich and vice versa. Everyone who is both not strong and calm is both not strong and not tall and vice versa. Someone is patient. Someone is wise or humble. Lucy is not patient. Someone is not quiet or not curious. Someone is not humble. Someone is not old. Paul is not humble. | Paul is not calm. | neutral | ((?[X]:((calm(X)|~calm(X))))<=>((~patient(paul)|~calm(paul))))&
(![X]:((~creative(X)|~quiet(X))=>(~tall(X)<~>brave(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:(creative(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:(happy(X))))&
(![X]:((generous(X)&~patient(X))<=>(~strong(X)|~patient(X))))&
(![X]:((wise(X)&~rich(X))=>(~patient(X)<~>~old(X))))&
(![X]:((~old(X)<~>~calm(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~humble(X))=>(happy(X)&~wise(X))))&
((?[X]:((generous(X)<~>kind(X))))=>(~rich(alice)))&
(![X]:((tall(X)|happy(X))=>(calm(X)&~tall(X))))&
(((humble(paul)|~humble(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:(old(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~wise(X)|~patient(X))))=>((~patient(mary)&humble(mary))))&
((?[X]:((calm(X)&patient(X))))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~strong(X)&calm(X))<=>(~strong(X)&~tall(X))))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)|humble(X))))&
(~patient(lucy))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
(~humble(paul)) | ~calm(paul) | [] | null | 0 |
Everyone who is either quiet or brave is both not wise and brave.
If fred is tall then paul is not brave or not tall.
Everyone who is not quiet or not wise is funny.
If alice is quiet or not humble then someone is happy and vice versa.
Everyone who is not calm or strong is both not creative and not happy and vice versa.
If someone is humble or not calm then someone is both generous and not humble.
Everyone who is either not strong or not curious is tall and vice versa.
If someone is not calm or old then john is both brave and not wise and vice versa.
Everyone who is not funny or brave is not creative.
If john is both not generous and not rich then lucy is rich.
If someone is both not calm and old then someone is both not patient and not curious and vice versa.
If paul is either not kind or wise then john is both not kind and funny.
Everyone who is tall is not strong and vice versa.
If john is both not kind and not wise then fred is not curious or quiet.
Everyone who is humble is either not rich or not calm and vice versa.
Everyone who is strong or kind is either not generous or strong.
Mary is not brave or not creative.
Fred is both not kind and not calm.
Someone is not strong.
Someone is both not old and funny.
Someone is either creative or kind.
Someone is not tall. | Paul is not tall. | neutral | (![X]:((quiet(X)<~>brave(X))=>(~wise(X)&brave(X))))&
((tall(fred))=>((~brave(paul)|~tall(paul))))&
(![X]:((~quiet(X)|~wise(X))=>funny(X)))&
(((quiet(alice)|~humble(alice)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|strong(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((~calm(X)|old(X))))<=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|brave(X))=>~creative(X)))&
(((~generous(john)&~rich(john)))=>(rich(lucy)))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((~kind(paul)<~>wise(paul)))=>((~kind(john)&funny(john))))&
(![X]:(tall(X)<=>~strong(X)))&
(((~kind(john)&~wise(john)))=>((~curious(fred)|quiet(fred))))&
(![X]:(humble(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((strong(X)|kind(X))=>(~generous(X)<~>strong(X))))&
((~brave(mary)|~creative(mary)))&
((~kind(fred)&~calm(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&funny(X))))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:(~tall(X))) | ~tall(paul) | [] | null | 0 |
If mary is both not happy and rich then someone is either not quiet or kind and vice versa.
Everyone who is calm or humble is not strong or patient.
Everyone who is either patient or not humble is not patient or not quiet.
Everyone who is either not curious or not brave is rich or not tall and vice versa.
If mary is both not creative and not humble then someone is rich.
Everyone who is both kind and quiet is tall or rich and vice versa.
If someone is both rich and calm then someone is either humble or brave and vice versa.
Everyone who is either not tall or not quiet is either not generous or not humble and vice versa.
Everyone who is both old and not strong is both not happy and not wise and vice versa.
If someone is either not brave or creative then lucy is not strong or not tall.
Everyone who is humble is patient.
Everyone who is both not wise and generous is both not generous and quiet and vice versa.
If paul is generous then someone is not strong.
If alice is not happy or not humble then someone is not happy or funny and vice versa.
If mary is strong then susan is both calm and not generous and vice versa.
Everyone who is both funny and not wise is not creative or generous and vice versa.
Someone is not brave or happy.
Alice is funny.
Someone is both not funny and patient.
Paul is both not generous and funny.
Someone is either not patient or not old. | Mary is not humble. | entailment | (((~happy(mary)&rich(mary)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)|patient(X))))&
(![X]:((patient(X)<~>~humble(X))=>(~patient(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(rich(X)|~tall(X))))&
(((~creative(mary)&~humble(mary)))=>(?[X]:(rich(X))))&
(![X]:((kind(X)&quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((old(X)&~strong(X))<=>(~happy(X)&~wise(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>((~strong(lucy)|~tall(lucy))))&
(![X]:(humble(X)=>patient(X)))&
(![X]:((~wise(X)&generous(X))<=>(~generous(X)&quiet(X))))&
((generous(paul))=>(?[X]:(~strong(X))))&
(((~happy(alice)|~humble(alice)))<=>(?[X]:((~happy(X)|funny(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(?[X]:((~brave(X)|happy(X))))&
(funny(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~generous(paul)&funny(paul)))&
(?[X]:((~patient(X)<~>~old(X)))) | ~humble(mary) | [
"p2",
"p5",
"p7",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4998770283085119814552572
% SZS output start Proof for 4998770283085119814552572
3. ! [X0] : ((patient(X0) <~> ~humble(X0)) => (~quiet(X0) | ~patient(X0))) [input p2]
6. ! [X0] : ((quiet(X0) & kind(X0)) <=> (rich(X0) | tall(X0))) [input p5]
8. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> (~generous(X0) <~> ~humble(X0))) [input p7]
11. ! [X0] : (humble(X0) => patient(X0)) [input p10]
12. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (quiet(X0) & ~generous(X0))) [input p11]
16. ! [X0] : ((~wise(X0) & funny(X0)) <=> (generous(X0) | ~creative(X0))) [input p15]
22. humble(mary) [input hypothesis]
26. ! [X0] : ((~quiet(X0) | ~patient(X0)) | (patient(X0) <=> ~humble(X0))) [ennf transformation 3]
27. ! [X0] : (~quiet(X0) | ~patient(X0) | (patient(X0) <=> ~humble(X0))) [flattening 26]
32. ! [X0] : (patient(X0) | ~humble(X0)) [ennf transformation 11]
39. ! [X0] : (~quiet(X0) | ~patient(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) [nnf transformation 27]
44. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ~quiet(X0) | ~kind(X0))) [flattening 44]
51. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 8]
55. ! [X0] : (((generous(X0) & ~wise(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 12]
56. ! [X0] : (((generous(X0) & ~wise(X0)) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | ~generous(X0) | wise(X0))) [flattening 55]
66. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 16]
67. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | wise(X0) | ~funny(X0))) [flattening 66]
83. ~quiet(X0) | ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 39]
95. ~tall(X0) | quiet(X0) [cnf transformation 45]
109. quiet(X0) | tall(X0) | ~humble(X0) | generous(X0) [cnf transformation 51]
117. ~humble(X0) | patient(X0) [cnf transformation 32]
118. ~generous(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
134. ~wise(X0) | ~generous(X0) [cnf transformation 67]
143. humble(mary) [cnf transformation 22]
144. ~generous(X0) | wise(X0) [duplicate literal removal 118]
146. ~patient(X0) | ~quiet(X0) | ~humble(X0) [duplicate literal removal 83]
180. 8 <=> humble(mary) [avatar definition]
182. humble(mary) <- (8) [avatar component clause 180]
220. ~humble(X0) | quiet(X0) | generous(X0) [subsumption resolution 109,95]
289. ~generous(X0) [subsumption resolution 134,144]
310. 8 [avatar split clause 143,180]
313. patient(mary) <- (8) [resolution 117,182]
346. ~quiet(mary) | ~humble(mary) <- (8) [resolution 146,313]
365. ~quiet(mary) <- (8) [subsumption resolution 346,182]
366. quiet(mary) | generous(mary) <- (8) [resolution 220,182]
367. generous(mary) <- (8) [subsumption resolution 366,365]
368. $false <- (8) [subsumption resolution 367,289]
369. ~8 [avatar contradiction clause 368]
370. $false [avatar sat refutation 310,369]
% SZS output end Proof for 4998770283085119814552572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not strong is either not wise or creative.
If someone is both not generous and patient then someone is both kind and not kind.
If fred is both wise and generous then paul is either funny or creative and vice versa.
If someone is both happy and patient then mary is wise or generous and vice versa.
Everyone who is both generous and not quiet is not old and vice versa.
Everyone who is not curious is not happy or not generous.
Everyone who is generous or patient is not quiet or not tall and vice versa.
If fred is either not brave or patient then someone is either brave or not rich.
Everyone who is creative or old is not quiet.
If someone is not strong then someone is not funny or not strong.
If someone is strong or not humble then alice is either not creative or not calm.
If john is curious or happy then lucy is tall or not creative.
If someone is either rich or strong then mary is either not curious or patient and vice versa.
If paul is not funny then mary is either quiet or not funny and vice versa.
Everyone who is not quiet or not rich is either quiet or not rich and vice versa.
Fred is not patient or brave.
Someone is both creative and generous.
Someone is wise or funny.
Paul is generous or not rich.
John is funny.
Someone is not patient or not generous.
Someone is humble or generous.
Someone is not rich or humble. | John is rich. | contradiction | (![X]:((old(X)&~strong(X))=>(~wise(X)<~>creative(X))))&
((?[X]:((~generous(X)&patient(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(((wise(fred)&generous(fred)))<=>((funny(paul)<~>creative(paul))))&
((?[X]:((happy(X)&patient(X))))<=>((wise(mary)|generous(mary))))&
(![X]:((generous(X)&~quiet(X))<=>~old(X)))&
(![X]:(~curious(X)=>(~happy(X)|~generous(X))))&
(![X]:((generous(X)|patient(X))<=>(~quiet(X)|~tall(X))))&
(((~brave(fred)<~>patient(fred)))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:((creative(X)|old(X))=>~quiet(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~funny(X)|~strong(X)))))&
((?[X]:((strong(X)|~humble(X))))=>((~creative(alice)<~>~calm(alice))))&
(((curious(john)|happy(john)))=>((tall(lucy)|~creative(lucy))))&
((?[X]:((rich(X)<~>strong(X))))<=>((~curious(mary)<~>patient(mary))))&
((~funny(paul))<=>((quiet(mary)<~>~funny(mary))))&
(![X]:((~quiet(X)|~rich(X))<=>(quiet(X)<~>~rich(X))))&
((~patient(fred)|brave(fred)))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((wise(X)|funny(X))))&
((generous(paul)|~rich(paul)))&
(funny(john))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~rich(X)|humble(X)))) | rich(john) | [
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3975667261792526298638744
% SZS output start Proof for 3975667261792526298638744
5. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~old(X0)) [input p4]
9. ! [X0] : ((old(X0) | creative(X0)) => ~quiet(X0)) [input p8]
15. ! [X0] : ((~rich(X0) | ~quiet(X0)) <=> (quiet(X0) <~> ~rich(X0))) [input p14]
24. rich(john) [input hypothesis]
27. ! [X0] : (~old(X0) => (~quiet(X0) & generous(X0))) [unused predicate definition removal 5]
34. ! [X0] : ((~quiet(X0) & generous(X0)) | old(X0)) [ennf transformation 27]
38. ! [X0] : (~quiet(X0) | (~old(X0) & ~creative(X0))) [ennf transformation 9]
68. ! [X0] : (((~rich(X0) | ~quiet(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (rich(X0) & quiet(X0)))) [nnf transformation 15]
69. ! [X0] : ((~rich(X0) | ~quiet(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (rich(X0) & quiet(X0)))) [flattening 68]
92. ~quiet(X0) | old(X0) [cnf transformation 34]
103. ~quiet(X0) | ~old(X0) [cnf transformation 38]
121. ~rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
134. rich(john) [cnf transformation 24]
135. ~rich(X0) | quiet(X0) [duplicate literal removal 121]
213. ~quiet(X0) [subsumption resolution 103,92]
295. ~rich(X0) [subsumption resolution 135,213]
315. $false [subsumption resolution 134,295]
% SZS output end Proof for 3975667261792526298638744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is either not brave or not tall and vice versa.
Everyone who is both not quiet and patient is not patient or old and vice versa.
If mary is either humble or not rich then susan is both calm and happy and vice versa.
Everyone who is tall is either not old or generous and vice versa.
Everyone who is patient or calm is either not rich or not strong and vice versa.
If lucy is either not funny or not generous then someone is either not patient or generous.
If fred is rich then lucy is patient or rich and vice versa.
Everyone who is both patient and generous is not calm or not creative and vice versa.
If someone is not quiet then fred is not humble.
If someone is not brave then someone is tall and vice versa.
Everyone who is not calm or humble is either humble or kind.
Everyone who is old or funny is both not brave and quiet.
Everyone who is either strong or not humble is happy or old and vice versa.
Everyone who is both not generous and not kind is tall.
Someone is wise.
Alice is strong.
Lucy is wise or curious.
Someone is generous.
Someone is both humble and not calm.
Someone is not happy.
Paul is funny or strong.
Fred is not funny. | Alice is old. | contradiction | ((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(![X]:((~quiet(X)&patient(X))<=>(~patient(X)|old(X))))&
(((humble(mary)<~>~rich(mary)))<=>((calm(susan)&happy(susan))))&
(![X]:(tall(X)<=>(~old(X)<~>generous(X))))&
(![X]:((patient(X)|calm(X))<=>(~rich(X)<~>~strong(X))))&
(((~funny(lucy)<~>~generous(lucy)))=>(?[X]:((~patient(X)<~>generous(X)))))&
((rich(fred))<=>((patient(lucy)|rich(lucy))))&
(![X]:((patient(X)&generous(X))<=>(~calm(X)|~creative(X))))&
((?[X]:(~quiet(X)))=>(~humble(fred)))&
((?[X]:(~brave(X)))<=>(?[X]:(tall(X))))&
(![X]:((~calm(X)|humble(X))=>(humble(X)<~>kind(X))))&
(![X]:((old(X)|funny(X))=>(~brave(X)&quiet(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)|old(X))))&
(![X]:((~generous(X)&~kind(X))=>tall(X)))&
(?[X]:(wise(X)))&
(strong(alice))&
((wise(lucy)|curious(lucy)))&
(?[X]:(generous(X)))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:(~happy(X)))&
((funny(paul)|strong(paul)))&
(~funny(fred)) | old(alice) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7738009672470165970988064
% SZS output start Proof for 7738009672470165970988064
2. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (old(X0) | ~patient(X0))) [input p1]
12. ! [X0] : ((funny(X0) | old(X0)) => (quiet(X0) & ~brave(X0))) [input p11]
23. old(alice) [input hypothesis]
31. ! [X0] : ((quiet(X0) & ~brave(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 12]
39. ! [X0] : (((patient(X0) & ~quiet(X0)) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | (~patient(X0) | quiet(X0)))) [nnf transformation 2]
40. ! [X0] : (((patient(X0) & ~quiet(X0)) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~patient(X0) | quiet(X0))) [flattening 39]
73. ~quiet(X0) | ~old(X0) [cnf transformation 40]
113. quiet(X0) | ~old(X0) [cnf transformation 31]
129. old(alice) [cnf transformation 23]
235. ~old(X0) [subsumption resolution 113,73]
247. $false [subsumption resolution 129,235]
% SZS output end Proof for 7738009672470165970988064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble or curious then someone is either creative or strong.
Everyone who is funny is not old or calm and vice versa.
If lucy is creative then someone is either happy or rich.
If paul is not tall then paul is either kind or not generous and vice versa.
If someone is generous then someone is both not old and tall.
Everyone who is both not creative and calm is either not humble or not generous and vice versa.
If someone is both not strong and not kind then someone is rich and vice versa.
If someone is either curious or not patient then susan is both not curious and rich and vice versa.
Everyone who is either not patient or not wise is not funny and vice versa.
Everyone who is not rich or patient is both tall and not kind and vice versa.
If john is strong or generous then someone is rich or calm.
If someone is not curious or not humble then someone is both not old and not happy.
Everyone who is either curious or not happy is both not kind and creative and vice versa.
If john is not tall or not quiet then someone is curious and vice versa.
Everyone who is not quiet or tall is both happy and not rich and vice versa.
Everyone who is happy or patient is not generous.
Someone is wise.
Someone is both not brave and creative.
Someone is generous.
Fred is both not calm and funny.
Fred is either not rich or not generous.
Alice is either kind or not tall.
Susan is both not old and funny. | Paul is tall. | contradiction | (((~humble(alice)|curious(alice)))=>(?[X]:((creative(X)<~>strong(X)))))&
(![X]:(funny(X)<=>(~old(X)|calm(X))))&
((creative(lucy))=>(?[X]:((happy(X)<~>rich(X)))))&
((~tall(paul))<=>((kind(paul)<~>~generous(paul))))&
((?[X]:(generous(X)))=>(?[X]:((~old(X)&tall(X)))))&
(![X]:((~creative(X)&calm(X))<=>(~humble(X)<~>~generous(X))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:((curious(X)<~>~patient(X))))<=>((~curious(susan)&rich(susan))))&
(![X]:((~patient(X)<~>~wise(X))<=>~funny(X)))&
(![X]:((~rich(X)|patient(X))<=>(tall(X)&~kind(X))))&
(((strong(john)|generous(john)))=>(?[X]:((rich(X)|calm(X)))))&
((?[X]:((~curious(X)|~humble(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(~kind(X)&creative(X))))&
(((~tall(john)|~quiet(john)))<=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|tall(X))<=>(happy(X)&~rich(X))))&
(![X]:((happy(X)|patient(X))=>~generous(X)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:(generous(X)))&
((~calm(fred)&funny(fred)))&
((~rich(fred)<~>~generous(fred)))&
((kind(alice)<~>~tall(alice)))&
((~old(susan)&funny(susan))) | tall(paul) | [
"p3",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8795825133317011668753621
% SZS output start Proof for 8795825133317011668753621
4. ~tall(paul) <=> (kind(paul) <~> ~generous(paul)) [input p3]
10. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~kind(X0) & tall(X0))) [input p9]
15. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> (~rich(X0) & happy(X0))) [input p14]
16. ! [X0] : ((patient(X0) | happy(X0)) => ~generous(X0)) [input p15]
24. tall(paul) [input hypothesis]
34. ! [X0] : (~generous(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 16]
43. (~tall(paul) | ((kind(paul) | generous(paul)) & (~generous(paul) | ~kind(paul)))) & (((generous(paul) | ~kind(paul)) & (~generous(paul) | kind(paul))) | tall(paul)) [nnf transformation 4]
60. ! [X0] : (((patient(X0) | ~rich(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 10]
61. ! [X0] : ((patient(X0) | ~rich(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | (~patient(X0) & rich(X0)))) [flattening 60]
74. ! [X0] : (((tall(X0) | ~quiet(X0)) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | (~tall(X0) & quiet(X0)))) [nnf transformation 15]
75. ! [X0] : ((tall(X0) | ~quiet(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | (~tall(X0) & quiet(X0)))) [flattening 74]
96. ~tall(paul) | kind(paul) | generous(paul) [cnf transformation 43]
120. ~kind(X0) | rich(X0) [cnf transformation 61]
139. ~tall(X0) | happy(X0) [cnf transformation 75]
141. ~tall(X0) | ~rich(X0) [cnf transformation 75]
143. ~generous(X0) | ~happy(X0) [cnf transformation 34]
156. tall(paul) [cnf transformation 24]
192. 8 <=> generous(paul) [avatar definition]
194. generous(paul) <- (8) [avatar component clause 192]
196. 9 <=> kind(paul) [avatar definition]
198. kind(paul) <- (9) [avatar component clause 196]
200. 10 <=> tall(paul) [avatar definition]
201. tall(paul) <- (10) [avatar component clause 200]
203. 8 | 9 | ~10 [avatar split clause 96,200,196,192]
343. 10 [avatar split clause 156,200]
352. rich(paul) <- (9) [resolution 120,198]
354. happy(paul) <- (10) [resolution 139,201]
362. ~rich(paul) <- (10) [resolution 141,201]
365. $false <- (9, 10) [subsumption resolution 362,352]
366. ~9 | ~10 [avatar contradiction clause 365]
368. ~happy(paul) <- (8) [resolution 143,194]
369. $false <- (8, 10) [subsumption resolution 368,354]
370. ~8 | ~10 [avatar contradiction clause 369]
371. $false [avatar sat refutation 203,343,366,370]
% SZS output end Proof for 8795825133317011668753621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or calm is calm or not curious. If someone is not rich or creative then mary is not rich or creative and vice versa. Everyone who is not creative or not funny is either not happy or not creative and vice versa. If lucy is quiet or rich then alice is rich or quiet. Everyone who is either not funny or not patient is calm and vice versa. Everyone who is not patient or not funny is either curious or happy and vice versa. If someone is both happy and not wise then someone is wise. If someone is either not humble or humble then someone is not funny or not calm and vice versa. If someone is both not wise and creative then someone is either brave or kind and vice versa. If someone is either not humble or not brave then fred is both not generous and not tall. If fred is either old or wise then someone is kind and vice versa. If john is either tall or rich then lucy is old or generous and vice versa. If someone is not kind then someone is both not quiet and not creative and vice versa. If mary is either not strong or wise then paul is both funny and not old. If someone is not humble then someone is generous or funny. If someone is either not funny or brave then alice is both not curious and humble. Someone is either not kind or not humble. Someone is either not generous or not rich. Someone is both not tall and kind. Someone is either not old or funny. Lucy is either tall or quiet. Alice is either not funny or not kind. Someone is funny or curious. Alice is both rich and not humble. | Lucy is old. | neutral | (![X]:((~strong(X)|calm(X))=>(calm(X)|~curious(X))))&
((?[X]:((~rich(X)|creative(X))))<=>((~rich(mary)|creative(mary))))&
(![X]:((~creative(X)|~funny(X))<=>(~happy(X)<~>~creative(X))))&
(((quiet(lucy)|rich(lucy)))=>((rich(alice)|quiet(alice))))&
(![X]:((~funny(X)<~>~patient(X))<=>calm(X)))&
(![X]:((~patient(X)|~funny(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((happy(X)&~wise(X))))=>(?[X]:(wise(X))))&
((?[X]:((~humble(X)<~>humble(X))))<=>(?[X]:((~funny(X)|~calm(X)))))&
((?[X]:((~wise(X)&creative(X))))<=>(?[X]:((brave(X)<~>kind(X)))))&
((?[X]:((~humble(X)<~>~brave(X))))=>((~generous(fred)&~tall(fred))))&
(((old(fred)<~>wise(fred)))<=>(?[X]:(kind(X))))&
(((tall(john)<~>rich(john)))<=>((old(lucy)|generous(lucy))))&
((?[X]:(~kind(X)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
(((~strong(mary)<~>wise(mary)))=>((funny(paul)&~old(paul))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)|funny(X)))))&
((?[X]:((~funny(X)<~>brave(X))))=>((~curious(alice)&humble(alice))))&
(?[X]:((~kind(X)<~>~humble(X))))&
(?[X]:((~generous(X)<~>~rich(X))))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((~old(X)<~>funny(X))))&
((tall(lucy)<~>quiet(lucy)))&
((~funny(alice)<~>~kind(alice)))&
(?[X]:((funny(X)|curious(X))))&
((rich(alice)&~humble(alice))) | old(lucy) | [] | null | 0 |
Everyone who is either creative or kind is both curious and not generous and vice versa.
Everyone who is either tall or not humble is either brave or not calm and vice versa.
Everyone who is either creative or not funny is humble.
Everyone who is happy or wise is both not calm and not patient.
If alice is happy then fred is not patient or not creative.
If someone is either not funny or curious then someone is either rich or not generous.
If john is either not old or not generous then alice is both strong and not happy and vice versa.
Everyone who is both strong and not calm is humble and vice versa.
Everyone who is either funny or not happy is either not curious or not creative and vice versa.
Everyone who is both not happy and not generous is curious and vice versa.
Everyone who is not quiet or not creative is not tall and vice versa.
If susan is either old or not calm then fred is either not strong or not tall.
If mary is either not happy or not strong then someone is not humble and vice versa.
If someone is funny or not happy then someone is either kind or brave and vice versa.
Everyone who is funny or brave is either not old or not creative and vice versa.
Everyone who is either not brave or strong is quiet and vice versa.
Someone is calm or old.
Someone is both not generous and brave.
Alice is either old or not rich.
Fred is both not tall and kind.
Someone is curious or not strong.
Someone is old or calm.
Someone is generous. | Mary is strong. | entailment | (![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~funny(X))=>humble(X)))&
(![X]:((happy(X)|wise(X))=>(~calm(X)&~patient(X))))&
((happy(alice))=>((~patient(fred)|~creative(fred))))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((rich(X)<~>~generous(X)))))&
(((~old(john)<~>~generous(john)))<=>((strong(alice)&~happy(alice))))&
(![X]:((strong(X)&~calm(X))<=>humble(X)))&
(![X]:((funny(X)<~>~happy(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~happy(X)&~generous(X))<=>curious(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(((old(susan)<~>~calm(susan)))=>((~strong(fred)<~>~tall(fred))))&
(((~happy(mary)<~>~strong(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((funny(X)|brave(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>strong(X))<=>quiet(X)))&
(?[X]:((calm(X)|old(X))))&
(?[X]:((~generous(X)&brave(X))))&
((old(alice)<~>~rich(alice)))&
((~tall(fred)&kind(fred)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((old(X)|calm(X))))&
(?[X]:(generous(X))) | strong(mary) | [
"p2",
"p7",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 642346500126072865683677
% SZS output start Proof for 642346500126072865683677
3. ! [X0] : ((creative(X0) <~> ~funny(X0)) => humble(X0)) [input p2]
8. ! [X0] : ((~calm(X0) & strong(X0)) <=> humble(X0)) [input p7]
9. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p8]
10. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> curious(X0)) [input p9]
13. (~happy(mary) <~> ~strong(mary)) <=> ? [X0] : ~humble(X0) [input p12]
24. ~strong(mary) [input hypothesis]
30. ! [X0] : (humble(X0) | (creative(X0) <=> ~funny(X0))) [ennf transformation 3]
37. ! [X0] : (humble(X0) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) [nnf transformation 30]
44. ! [X0] : (((~calm(X0) & strong(X0)) | ~humble(X0)) & (humble(X0) | (calm(X0) | ~strong(X0)))) [nnf transformation 8]
45. ! [X0] : (((~calm(X0) & strong(X0)) | ~humble(X0)) & (humble(X0) | calm(X0) | ~strong(X0))) [flattening 44]
46. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 9]
47. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (generous(X0) | happy(X0)))) [nnf transformation 10]
48. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | generous(X0) | happy(X0))) [flattening 47]
52. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [nnf transformation 13]
53. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [rectify 52]
54. ? [X1] : ~humble(X1) => ~humble(sK1) [choice axiom]
55. (((strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary))) | ! [X0] : humble(X0)) & (~humble(sK1) | ((~happy(mary) | strong(mary)) & (~strong(mary) | happy(mary)))) [skolemisation 53,54]
89. ~funny(X0) | humble(X0) | ~creative(X0) [cnf transformation 37]
90. funny(X0) | creative(X0) | humble(X0) [cnf transformation 37]
103. ~humble(X0) | strong(X0) [cnf transformation 45]
107. ~happy(X0) | curious(X0) | creative(X0) | ~funny(X0) [cnf transformation 46]
109. ~happy(X0) | funny(X0) | ~creative(X0) | curious(X0) [cnf transformation 46]
114. ~happy(X0) | ~curious(X0) [cnf transformation 48]
126. strong(mary) | happy(mary) | humble(X0) [cnf transformation 55]
153. ~strong(mary) [cnf transformation 24]
215. 13 <=> ! [X0] : humble(X0) [avatar definition]
216. humble(X0) <- (13) [avatar component clause 215]
218. 14 <=> happy(mary) [avatar definition]
220. happy(mary) <- (14) [avatar component clause 218]
222. 15 <=> strong(mary) [avatar definition]
223. ~strong(mary) <- (~15) [avatar component clause 222]
225. 13 | 14 | 15 [avatar split clause 126,222,218,215]
305. ~15 [avatar split clause 153,222]
311. ~curious(mary) <- (14) [resolution 114,220]
562. curious(mary) | creative(mary) | ~funny(mary) <- (14) [resolution 107,220]
566. creative(mary) | ~funny(mary) <- (14) [subsumption resolution 562,311]
568. 67 <=> funny(mary) [avatar definition]
569. funny(mary) <- (67) [avatar component clause 568]
570. ~funny(mary) <- (~67) [avatar component clause 568]
572. 68 <=> creative(mary) [avatar definition]
573. ~creative(mary) <- (~68) [avatar component clause 572]
574. creative(mary) <- (68) [avatar component clause 572]
575. ~67 | 68 | ~14 [avatar split clause 566,218,572,568]
596. funny(mary) | ~creative(mary) | curious(mary) <- (14) [resolution 109,220]
604. creative(mary) | humble(mary) <- (~67) [resolution 570,90]
605. humble(mary) <- (~67, ~68) [subsumption resolution 604,573]
769. strong(mary) <- (~67, ~68) [resolution 605,103]
780. $false <- (~15, ~67, ~68) [subsumption resolution 769,223]
781. 15 | 67 | 68 [avatar contradiction clause 780]
782. funny(mary) | ~creative(mary) <- (14) [subsumption resolution 596,311]
783. ~68 | 67 | ~14 [avatar split clause 782,218,568,572]
787. humble(mary) | ~creative(mary) <- (67) [resolution 569,89]
788. humble(mary) <- (67, 68) [subsumption resolution 787,574]
964. strong(mary) <- (67, 68) [resolution 788,103]
965. $false <- (~15, 67, 68) [subsumption resolution 964,223]
966. 15 | ~67 | ~68 [avatar contradiction clause 965]
990. strong(X1) <- (13) [resolution 216,103]
1003. $false <- (13, ~15) [resolution 990,223]
1006. ~13 | 15 [avatar contradiction clause 1003]
1008. $false [avatar sat refutation 225,305,575,781,783,966,1006]
% SZS output end Proof for 642346500126072865683677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not curious is kind and vice versa.
If someone is not brave or calm then someone is not brave or kind and vice versa.
Everyone who is either not calm or not kind is calm and vice versa.
If someone is happy or not calm then john is either not generous or old and vice versa.
Everyone who is not funny is not tall.
If someone is both kind and not tall then someone is not curious or generous and vice versa.
Everyone who is not strong is happy and vice versa.
If someone is either not patient or not strong then lucy is either not rich or not wise and vice versa.
Everyone who is happy is quiet or happy and vice versa.
Everyone who is either not creative or rich is both not strong and quiet.
If lucy is either not curious or happy then susan is not patient or not brave.
If someone is not quiet or not happy then susan is humble or rich and vice versa.
Everyone who is either not strong or happy is brave.
Everyone who is either not wise or generous is either not curious or not old and vice versa.
If susan is either wise or quiet then lucy is not quiet and vice versa.
If someone is both happy and not patient then someone is either not happy or not quiet.
Someone is both not quiet and rich.
Someone is either patient or old.
Lucy is both not wise and quiet.
Someone is happy or strong.
Susan is patient or not happy.
Someone is either wise or not curious.
Mary is either not quiet or not kind.
Someone is both not calm and not quiet. | Mary is happy. | entailment | (![X]:((brave(X)&~curious(X))<=>kind(X)))&
((?[X]:((~brave(X)|calm(X))))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~calm(X)<~>~kind(X))<=>calm(X)))&
((?[X]:((happy(X)|~calm(X))))<=>((~generous(john)<~>old(john))))&
(![X]:(~funny(X)=>~tall(X)))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
((?[X]:((~patient(X)<~>~strong(X))))<=>((~rich(lucy)<~>~wise(lucy))))&
(![X]:(happy(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>rich(X))=>(~strong(X)&quiet(X))))&
(((~curious(lucy)<~>happy(lucy)))=>((~patient(susan)|~brave(susan))))&
((?[X]:((~quiet(X)|~happy(X))))<=>((humble(susan)|rich(susan))))&
(![X]:((~strong(X)<~>happy(X))=>brave(X)))&
(![X]:((~wise(X)<~>generous(X))<=>(~curious(X)<~>~old(X))))&
(((wise(susan)<~>quiet(susan)))<=>(~quiet(lucy)))&
((?[X]:((happy(X)&~patient(X))))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(?[X]:((~quiet(X)&rich(X))))&
(?[X]:((patient(X)<~>old(X))))&
((~wise(lucy)&quiet(lucy)))&
(?[X]:((happy(X)|strong(X))))&
((patient(susan)|~happy(susan)))&
(?[X]:((wise(X)<~>~curious(X))))&
((~quiet(mary)<~>~kind(mary)))&
(?[X]:((~calm(X)&~quiet(X)))) | happy(mary) | [
"p2",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8897414903405673370891663
% SZS output start Proof for 8897414903405673370891663
3. ! [X0] : ((~calm(X0) <~> ~kind(X0)) <=> calm(X0)) [input p2]
9. ! [X0] : (happy(X0) <=> (happy(X0) | quiet(X0))) [input p8]
23. ~quiet(mary) <~> ~kind(mary) [input p22]
25. ~happy(mary) [input hypothesis]
42. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~calm(X0)) & (calm(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [nnf transformation 3]
57. ! [X0] : ((happy(X0) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | ~happy(X0))) [nnf transformation 9]
58. ! [X0] : ((happy(X0) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~happy(X0))) [flattening 57]
83. (kind(mary) | quiet(mary)) & (~kind(mary) | ~quiet(mary)) [nnf transformation 23]
93. calm(X0) | ~kind(X0) | calm(X0) [cnf transformation 42]
95. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 42]
119. ~quiet(X0) | happy(X0) [cnf transformation 58]
158. kind(mary) | quiet(mary) [cnf transformation 83]
161. ~happy(mary) [cnf transformation 25]
162. calm(X0) | ~kind(X0) [duplicate literal removal 93]
163. ~kind(X0) | ~calm(X0) [duplicate literal removal 95]
165. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
166. ~kind(X1) <- (1) [avatar component clause 165]
193. ~kind(X0) [subsumption resolution 162,163]
194. 1 [avatar split clause 193,165]
384. 47 <=> quiet(mary) [avatar definition]
386. quiet(mary) <- (47) [avatar component clause 384]
388. 48 <=> kind(mary) [avatar definition]
390. kind(mary) <- (48) [avatar component clause 388]
391. 47 | 48 [avatar split clause 158,388,384]
402. happy(mary) <- (47) [resolution 119,386]
404. $false <- (47) [subsumption resolution 402,161]
405. ~47 [avatar contradiction clause 404]
406. $false <- (1, 48) [subsumption resolution 390,166]
407. ~1 | ~48 [avatar contradiction clause 406]
408. $false [avatar sat refutation 194,391,405,407]
% SZS output end Proof for 8897414903405673370891663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not humble and not brave then fred is both not humble and wise and vice versa. If mary is both creative and not happy then mary is either brave or curious. If someone is humble then paul is either calm or kind and vice versa. Everyone who is not humble is patient. Everyone who is both not patient and not humble is either generous or not generous. If someone is both not patient and old then someone is either not kind or not calm. Everyone who is not wise is tall and vice versa. Everyone who is not brave or not humble is either curious or tall. Everyone who is either rich or creative is both not rich and wise. Everyone who is funny or tall is tall and vice versa. Everyone who is not old or not funny is both not humble and not quiet. If lucy is humble then alice is either not generous or tall and vice versa. If someone is both not calm and funny then someone is not funny or brave and vice versa. If mary is tall or not humble then someone is either wise or funny. If someone is both wise and funny then alice is old and vice versa. If fred is either not curious or brave then someone is both patient and not old. Alice is either not strong or strong. Lucy is either generous or rich. Mary is not curious. Mary is not old. Fred is both not kind and rich. Paul is not old. Paul is not rich or not tall. Someone is either not wise or humble. | Alice is humble. | contradiction | (((~humble(john)&~brave(john)))<=>((~humble(fred)&wise(fred))))&
(((creative(mary)&~happy(mary)))=>((brave(mary)<~>curious(mary))))&
((?[X]:(humble(X)))<=>((calm(paul)<~>kind(paul))))&
(![X]:(~humble(X)=>patient(X)))&
(![X]:((~patient(X)&~humble(X))=>(generous(X)<~>~generous(X))))&
((?[X]:((~patient(X)&old(X))))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~wise(X)<=>tall(X)))&
(![X]:((~brave(X)|~humble(X))=>(curious(X)<~>tall(X))))&
(![X]:((rich(X)<~>creative(X))=>(~rich(X)&wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(mary)|~humble(mary)))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((wise(X)&funny(X))))<=>(old(alice)))&
(((~curious(fred)<~>brave(fred)))=>(?[X]:((patient(X)&~old(X)))))&
((~strong(alice)<~>strong(alice)))&
((generous(lucy)<~>rich(lucy)))&
(~curious(mary))&
(~old(mary))&
((~kind(fred)&rich(fred)))&
(~old(paul))&
((~rich(paul)|~tall(paul)))&
(?[X]:((~wise(X)<~>humble(X)))) | humble(alice) | [
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6884390573736849475505721
% SZS output start Proof for 6884390573736849475505721
7. ! [X0] : (~wise(X0) <=> tall(X0)) [input p6]
10. ! [X0] : ((tall(X0) | funny(X0)) <=> tall(X0)) [input p9]
11. ! [X0] : ((~funny(X0) | ~old(X0)) => (~quiet(X0) & ~humble(X0))) [input p10]
15. ? [X0] : (funny(X0) & wise(X0)) <=> old(alice) [input p14]
25. humble(alice) [input hypothesis]
28. ! [X0] : ((~funny(X0) | ~old(X0)) => ~humble(X0)) [pure predicate removal 11]
36. ! [X0] : (~humble(X0) | (funny(X0) & old(X0))) [ennf transformation 28]
45. ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))) [nnf transformation 7]
48. ! [X0] : (((tall(X0) | funny(X0)) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~funny(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | funny(X0) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~funny(X0)))) [flattening 48]
59. (? [X0] : (funny(X0) & wise(X0)) | ~old(alice)) & (old(alice) | ! [X0] : (~funny(X0) | ~wise(X0))) [nnf transformation 15]
60. (? [X0] : (funny(X0) & wise(X0)) | ~old(alice)) & (old(alice) | ! [X1] : (~funny(X1) | ~wise(X1))) [rectify 59]
61. ? [X0] : (funny(X0) & wise(X0)) => (funny(sK4) & wise(sK4)) [choice axiom]
62. ((funny(sK4) & wise(sK4)) | ~old(alice)) & (old(alice) | ! [X1] : (~funny(X1) | ~wise(X1))) [skolemisation 60,61]
80. ~tall(X0) | ~wise(X0) [cnf transformation 45]
89. ~funny(X0) | tall(X0) [cnf transformation 49]
92. ~humble(X0) | old(X0) [cnf transformation 36]
108. wise(sK4) | ~old(alice) [cnf transformation 62]
109. funny(sK4) | ~old(alice) [cnf transformation 62]
124. humble(alice) [cnf transformation 25]
232. 23 <=> old(alice) [avatar definition]
236. 24 <=> funny(sK4) [avatar definition]
238. funny(sK4) <- (24) [avatar component clause 236]
239. ~23 | 24 [avatar split clause 109,236,232]
241. 25 <=> wise(sK4) [avatar definition]
244. ~23 | 25 [avatar split clause 108,241,232]
296. tall(sK4) <- (24) [resolution 89,238]
298. old(alice) [resolution 92,124]
303. ~wise(sK4) <- (24) [resolution 296,80]
306. 23 [avatar split clause 298,232]
307. ~25 | ~24 [avatar split clause 303,236,241]
308. $false [avatar sat refutation 239,244,306,307]
% SZS output end Proof for 6884390573736849475505721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or brave then someone is not tall or patient and vice versa. If someone is both not quiet and happy then alice is both not strong and not calm. If someone is both not calm and not humble then someone is not calm. Everyone who is either not creative or not rich is both quiet and not old and vice versa. If someone is generous then mary is happy or quiet and vice versa. If someone is either not curious or not patient then someone is kind. If lucy is happy or old then someone is happy or quiet and vice versa. If someone is both kind and not quiet then someone is either old or happy and vice versa. If john is wise then someone is not strong or creative and vice versa. If john is strong or not strong then alice is not tall and vice versa. If someone is either not brave or old then someone is not funny. If someone is brave or rich then paul is humble and vice versa. If paul is both not calm and not strong then someone is either not patient or old and vice versa. Everyone who is not calm is not old and vice versa. Everyone who is not humble is either calm or old. John is humble or not generous. Someone is either not generous or strong. John is either not calm or not funny. Lucy is strong or not wise. | Alice is strong. | neutral | ((?[X]:((old(X)|brave(X))))<=>(?[X]:((~tall(X)|patient(X)))))&
((?[X]:((~quiet(X)&happy(X))))=>((~strong(alice)&~calm(alice))))&
((?[X]:((~calm(X)&~humble(X))))=>(?[X]:(~calm(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(quiet(X)&~old(X))))&
((?[X]:(generous(X)))<=>((happy(mary)|quiet(mary))))&
((?[X]:((~curious(X)<~>~patient(X))))=>(?[X]:(kind(X))))&
(((happy(lucy)|old(lucy)))<=>(?[X]:((happy(X)|quiet(X)))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((old(X)<~>happy(X)))))&
((wise(john))<=>(?[X]:((~strong(X)|creative(X)))))&
(((strong(john)|~strong(john)))<=>(~tall(alice)))&
((?[X]:((~brave(X)<~>old(X))))=>(?[X]:(~funny(X))))&
((?[X]:((brave(X)|rich(X))))<=>(humble(paul)))&
(((~calm(paul)&~strong(paul)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:(~humble(X)=>(calm(X)<~>old(X))))&
((humble(john)|~generous(john)))&
(?[X]:((~generous(X)<~>strong(X))))&
((~calm(john)<~>~funny(john)))&
((strong(lucy)|~wise(lucy))) | strong(alice) | [] | null | 0 |
Everyone who is curious or not kind is not calm.
Everyone who is not kind or funny is either not rich or quiet.
Everyone who is not creative or not happy is either not kind or tall and vice versa.
Everyone who is either not humble or brave is not tall or not wise.
Everyone who is both calm and tall is not wise and vice versa.
Everyone who is either not humble or not creative is not generous.
Everyone who is both not strong and not calm is tall or kind and vice versa.
Everyone who is both not patient and generous is either generous or not funny.
If someone is either brave or not generous then someone is both not happy and funny and vice versa.
If someone is not strong then susan is strong and vice versa.
Everyone who is both not wise and not funny is generous or not tall.
Everyone who is either quiet or generous is either patient or strong and vice versa.
Everyone who is not happy or not patient is either curious or not rich and vice versa.
Everyone who is rich or happy is either creative or not happy.
Everyone who is both funny and calm is either not generous or not quiet and vice versa.
If alice is not generous then alice is either not patient or kind.
Someone is creative or not tall.
Mary is either humble or not creative.
Someone is not happy.
Someone is either not tall or not calm.
Someone is both not strong and not kind.
Mary is not patient.
Someone is not kind or not strong. | Susan is not brave. | neutral | (![X]:((curious(X)|~kind(X))=>~calm(X)))&
(![X]:((~kind(X)|funny(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((~creative(X)|~happy(X))<=>(~kind(X)<~>tall(X))))&
(![X]:((~humble(X)<~>brave(X))=>(~tall(X)|~wise(X))))&
(![X]:((calm(X)&tall(X))<=>~wise(X)))&
(![X]:((~humble(X)<~>~creative(X))=>~generous(X)))&
(![X]:((~strong(X)&~calm(X))<=>(tall(X)|kind(X))))&
(![X]:((~patient(X)&generous(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((brave(X)<~>~generous(X))))<=>(?[X]:((~happy(X)&funny(X)))))&
((?[X]:(~strong(X)))<=>(strong(susan)))&
(![X]:((~wise(X)&~funny(X))=>(generous(X)|~tall(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(patient(X)<~>strong(X))))&
(![X]:((~happy(X)|~patient(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((rich(X)|happy(X))=>(creative(X)<~>~happy(X))))&
(![X]:((funny(X)&calm(X))<=>(~generous(X)<~>~quiet(X))))&
((~generous(alice))=>((~patient(alice)<~>kind(alice))))&
(?[X]:((creative(X)|~tall(X))))&
((humble(mary)<~>~creative(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>~calm(X))))&
(?[X]:((~strong(X)&~kind(X))))&
(~patient(mary))&
(?[X]:((~kind(X)|~strong(X)))) | ~brave(susan) | [] | null | 0 |
Everyone who is both not rich and not generous is not rich or wise. Everyone who is either not humble or kind is both wise and humble and vice versa. If susan is not brave or strong then someone is both wise and not strong and vice versa. Everyone who is not calm is not old and vice versa. Everyone who is both not quiet and creative is tall or strong. If mary is curious or tall then lucy is not old. If paul is calm or not funny then paul is wise or kind. Everyone who is either rich or creative is both generous and wise and vice versa. If alice is curious then john is both creative and calm and vice versa. If alice is both brave and humble then paul is not happy or happy and vice versa. If someone is both not strong and funny then someone is either not creative or brave. Everyone who is either not humble or wise is either not generous or wise. If someone is strong or not kind then someone is both strong and wise. Everyone who is both funny and kind is either creative or tall. Everyone who is either not quiet or not happy is happy. Susan is both generous and tall. Mary is either not old or rich. John is not patient or strong. Paul is either tall or not curious. Paul is not humble or creative. | Susan is not wise. | neutral | (![X]:((~rich(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(wise(X)&humble(X))))&
(((~brave(susan)|strong(susan)))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~quiet(X)&creative(X))=>(tall(X)|strong(X))))&
(((curious(mary)|tall(mary)))=>(~old(lucy)))&
(((calm(paul)|~funny(paul)))=>((wise(paul)|kind(paul))))&
(![X]:((rich(X)<~>creative(X))<=>(generous(X)&wise(X))))&
((curious(alice))<=>((creative(john)&calm(john))))&
(((brave(alice)&humble(alice)))<=>((~happy(paul)|happy(paul))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:((~humble(X)<~>wise(X))=>(~generous(X)<~>wise(X))))&
((?[X]:((strong(X)|~kind(X))))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)&kind(X))=>(creative(X)<~>tall(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>happy(X)))&
((generous(susan)&tall(susan)))&
((~old(mary)<~>rich(mary)))&
((~patient(john)|strong(john)))&
((tall(paul)<~>~curious(paul)))&
((~humble(paul)|creative(paul))) | ~wise(susan) | [] | null | 0 |
If paul is rich or not curious then paul is not old or calm.
If john is not wise then fred is both creative and calm and vice versa.
Everyone who is both not curious and not quiet is either not tall or not rich.
If mary is either generous or not creative then susan is either brave or not strong and vice versa.
Everyone who is both not funny and patient is both rich and tall.
Everyone who is brave is not creative or strong.
Everyone who is patient is either not happy or creative.
If someone is both not old and funny then alice is both not creative and not curious.
Everyone who is both generous and not generous is not curious or not generous and vice versa.
If fred is brave then someone is not generous and vice versa.
Everyone who is not quiet or not patient is not curious.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
If someone is both not kind and not patient then john is not strong or not brave and vice versa.
Everyone who is rich is not quiet or old and vice versa.
Someone is either curious or funny.
Lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet.
Susan is both brave and strong. | Paul is not creative. | neutral | (((rich(paul)|~curious(paul)))=>((~old(paul)|calm(paul))))&
((~wise(john))<=>((creative(fred)&calm(fred))))&
(![X]:((~curious(X)&~quiet(X))=>(~tall(X)<~>~rich(X))))&
(((generous(mary)<~>~creative(mary)))<=>((brave(susan)<~>~strong(susan))))&
(![X]:((~funny(X)&patient(X))=>(rich(X)&tall(X))))&
(![X]:(brave(X)=>(~creative(X)|strong(X))))&
(![X]:(patient(X)=>(~happy(X)<~>creative(X))))&
((?[X]:((~old(X)&funny(X))))=>((~creative(alice)&~curious(alice))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)|~generous(X))))&
((brave(fred))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~patient(X))=>~curious(X)))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(![X]:(rich(X)<=>(~quiet(X)|old(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((~rich(lucy)|~brave(lucy)))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred)))&
((brave(susan)&strong(susan))) | ~creative(paul) | [] | null | 0 |
Everyone who is not happy or brave is both kind and quiet.
If mary is either not old or kind then fred is rich.
Everyone who is either calm or not curious is happy.
If someone is both not humble and not kind then paul is not creative or not old.
If someone is strong or not rich then someone is either not rich or not kind and vice versa.
Everyone who is both quiet and not creative is tall or strong and vice versa.
Everyone who is both old and not funny is not generous or not funny and vice versa.
Everyone who is both not strong and not humble is either wise or not tall and vice versa.
Everyone who is not old is both not tall and strong and vice versa.
If lucy is strong or not old then someone is patient or humble and vice versa.
Everyone who is both not happy and wise is not generous or creative and vice versa.
If mary is not rich then john is patient or not funny.
Everyone who is wise is both not funny and not old.
If mary is wise or strong then lucy is both curious and not rich and vice versa.
If someone is both not tall and not wise then someone is not funny and vice versa.
John is either generous or humble.
Paul is both not wise and humble.
Someone is generous.
Susan is generous.
John is not old or not kind.
Someone is not tall or tall. | John is humble. | contradiction | (![X]:((~happy(X)|brave(X))=>(kind(X)&quiet(X))))&
(((~old(mary)<~>kind(mary)))=>(rich(fred)))&
(![X]:((calm(X)<~>~curious(X))=>happy(X)))&
((?[X]:((~humble(X)&~kind(X))))=>((~creative(paul)|~old(paul))))&
((?[X]:((strong(X)|~rich(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((quiet(X)&~creative(X))<=>(tall(X)|strong(X))))&
(![X]:((old(X)&~funny(X))<=>(~generous(X)|~funny(X))))&
(![X]:((~strong(X)&~humble(X))<=>(wise(X)<~>~tall(X))))&
(![X]:(~old(X)<=>(~tall(X)&strong(X))))&
(((strong(lucy)|~old(lucy)))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~happy(X)&wise(X))<=>(~generous(X)|creative(X))))&
((~rich(mary))=>((patient(john)|~funny(john))))&
(![X]:(wise(X)=>(~funny(X)&~old(X))))&
(((wise(mary)|strong(mary)))<=>((curious(lucy)&~rich(lucy))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:(~funny(X))))&
((generous(john)<~>humble(john)))&
((~wise(paul)&humble(paul)))&
(?[X]:(generous(X)))&
(generous(susan))&
((~old(john)|~kind(john)))&
(?[X]:((~tall(X)|tall(X)))) | humble(john) | [
"p0",
"p6",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3612261255648892517131128
% SZS output start Proof for 3612261255648892517131128
1. ! [X0] : ((brave(X0) | ~happy(X0)) => (quiet(X0) & kind(X0))) [input p0]
7. ! [X0] : ((~funny(X0) & old(X0)) <=> (~funny(X0) | ~generous(X0))) [input p6]
11. ! [X0] : ((wise(X0) & ~happy(X0)) <=> (creative(X0) | ~generous(X0))) [input p10]
16. generous(john) <~> humble(john) [input p15]
20. ~kind(john) | ~old(john) [input p19]
22. humble(john) [input hypothesis]
25. ! [X0] : (~happy(X0) => (quiet(X0) & kind(X0))) [pure predicate removal 1]
26. ! [X0] : ((quiet(X0) & kind(X0)) | happy(X0)) [ennf transformation 25]
43. ! [X0] : (((~funny(X0) & old(X0)) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | (funny(X0) | ~old(X0)))) [nnf transformation 7]
44. ! [X0] : (((~funny(X0) & old(X0)) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | funny(X0) | ~old(X0))) [flattening 43]
54. ! [X0] : (((wise(X0) & ~happy(X0)) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | (~wise(X0) | happy(X0)))) [nnf transformation 11]
55. ! [X0] : (((wise(X0) & ~happy(X0)) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ~wise(X0) | happy(X0))) [flattening 54]
63. (~humble(john) | ~generous(john)) & (humble(john) | generous(john)) [nnf transformation 16]
68. kind(X0) | happy(X0) [cnf transformation 26]
87. generous(X0) | old(X0) [cnf transformation 44]
105. ~happy(X0) | generous(X0) [cnf transformation 55]
121. ~humble(john) | ~generous(john) [cnf transformation 63]
126. ~kind(john) | ~old(john) [cnf transformation 20]
128. humble(john) [cnf transformation 22]
273. 33 <=> generous(john) [avatar definition]
275. ~generous(john) <- (~33) [avatar component clause 273]
277. 34 <=> humble(john) [avatar definition]
280. ~33 | ~34 [avatar split clause 121,277,273]
283. 35 <=> old(john) [avatar definition]
287. 36 <=> kind(john) [avatar definition]
289. ~kind(john) <- (~36) [avatar component clause 287]
290. ~35 | ~36 [avatar split clause 126,287,283]
291. 34 [avatar split clause 128,277]
300. old(john) <- (~33) [resolution 87,275]
303. 35 | 33 [avatar split clause 300,273,283]
304. happy(john) <- (~36) [resolution 289,68]
313. generous(john) <- (~36) [resolution 105,304]
314. $false <- (~33, ~36) [subsumption resolution 313,275]
315. 33 | 36 [avatar contradiction clause 314]
316. $false [avatar sat refutation 280,290,291,303,315]
% SZS output end Proof for 3612261255648892517131128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or generous is not kind or not quiet.
Everyone who is funny or not generous is brave or curious and vice versa.
If alice is both not curious and not brave then someone is either calm or not strong and vice versa.
If someone is both funny and wise then someone is either patient or not old.
Everyone who is either old or not strong is kind and vice versa.
Everyone who is not old is both kind and not creative and vice versa.
If someone is both old and patient then mary is either kind or rich and vice versa.
Everyone who is either strong or quiet is not generous and vice versa.
Everyone who is brave is quiet or not happy.
Everyone who is both not kind and not funny is not creative or not humble and vice versa.
Everyone who is not creative or not brave is strong and vice versa.
Everyone who is either rich or creative is either not curious or not tall and vice versa.
If someone is old or quiet then someone is either not calm or not kind and vice versa.
If mary is both not wise and not generous then someone is both brave and humble.
If paul is either brave or not wise then paul is not funny or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Mary is either not happy or funny.
Fred is either kind or not quiet.
Fred is not kind.
Alice is either not patient or not rich.
Someone is creative or not strong.
Someone is not funny.
Someone is both tall and happy.
Someone is either not brave or patient. | Mary is kind. | neutral | (![X]:((~rich(X)<~>generous(X))=>(~kind(X)|~quiet(X))))&
(![X]:((funny(X)|~generous(X))<=>(brave(X)|curious(X))))&
(((~curious(alice)&~brave(alice)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((old(X)<~>~strong(X))<=>kind(X)))&
(![X]:(~old(X)<=>(kind(X)&~creative(X))))&
((?[X]:((old(X)&patient(X))))<=>((kind(mary)<~>rich(mary))))&
(![X]:((strong(X)<~>quiet(X))<=>~generous(X)))&
(![X]:(brave(X)=>(quiet(X)|~happy(X))))&
(![X]:((~kind(X)&~funny(X))<=>(~creative(X)|~humble(X))))&
(![X]:((~creative(X)|~brave(X))<=>strong(X)))&
(![X]:((rich(X)<~>creative(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(((~wise(mary)&~generous(mary)))=>(?[X]:((brave(X)&humble(X)))))&
(((brave(paul)<~>~wise(paul)))<=>((~funny(paul)|curious(paul))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
((~happy(mary)<~>funny(mary)))&
((kind(fred)<~>~quiet(fred)))&
(~kind(fred))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~brave(X)<~>patient(X)))) | kind(mary) | [] | null | 0 |
Everyone who is either old or tall is both not funny and quiet. Everyone who is strong or not calm is either strong or not old and vice versa. Everyone who is both calm and brave is wise or generous and vice versa. If fred is both tall and not calm then someone is both wise and kind. Everyone who is both creative and not kind is both wise and brave and vice versa. Everyone who is either not tall or funny is rich. If susan is both generous and not tall then someone is either funny or not rich and vice versa. Everyone who is quiet or generous is not funny or not brave and vice versa. Everyone who is both old and creative is not patient. If fred is both not curious and not patient then someone is either patient or not strong. Everyone who is kind is both not calm and not old. Everyone who is either not old or old is creative. Everyone who is both creative and not calm is kind or not funny and vice versa. If alice is creative or not brave then someone is tall. If someone is not humble or not funny then john is not generous or not quiet and vice versa. Everyone who is old or humble is both tall and generous and vice versa. Someone is patient. Paul is either not quiet or old. Susan is patient or not quiet. Someone is either old or not humble. Mary is kind. | Susan is wise. | contradiction | (![X]:((old(X)<~>tall(X))=>(~funny(X)&quiet(X))))&
(![X]:((strong(X)|~calm(X))<=>(strong(X)<~>~old(X))))&
(![X]:((calm(X)&brave(X))<=>(wise(X)|generous(X))))&
(((tall(fred)&~calm(fred)))=>(?[X]:((wise(X)&kind(X)))))&
(![X]:((creative(X)&~kind(X))<=>(wise(X)&brave(X))))&
(![X]:((~tall(X)<~>funny(X))=>rich(X)))&
(((generous(susan)&~tall(susan)))<=>(?[X]:((funny(X)<~>~rich(X)))))&
(![X]:((quiet(X)|generous(X))<=>(~funny(X)|~brave(X))))&
(![X]:((old(X)&creative(X))=>~patient(X)))&
(((~curious(fred)&~patient(fred)))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:(kind(X)=>(~calm(X)&~old(X))))&
(![X]:((~old(X)<~>old(X))=>creative(X)))&
(![X]:((creative(X)&~calm(X))<=>(kind(X)|~funny(X))))&
(((creative(alice)|~brave(alice)))=>(?[X]:(tall(X))))&
((?[X]:((~humble(X)|~funny(X))))<=>((~generous(john)|~quiet(john))))&
(![X]:((old(X)|humble(X))<=>(tall(X)&generous(X))))&
(?[X]:(patient(X)))&
((~quiet(paul)<~>old(paul)))&
((patient(susan)|~quiet(susan)))&
(?[X]:((old(X)<~>~humble(X))))&
(kind(mary)) | wise(susan) | [
"p1",
"p2",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 539067158042222978111591
% SZS output start Proof for 539067158042222978111591
2. ! [X0] : ((~calm(X0) | strong(X0)) <=> (strong(X0) <~> ~old(X0))) [input p1]
3. ! [X0] : ((brave(X0) & calm(X0)) <=> (generous(X0) | wise(X0))) [input p2]
8. ! [X0] : ((generous(X0) | quiet(X0)) <=> (~brave(X0) | ~funny(X0))) [input p7]
13. ! [X0] : ((~calm(X0) & creative(X0)) <=> (~funny(X0) | kind(X0))) [input p12]
16. ! [X0] : ((humble(X0) | old(X0)) <=> (generous(X0) & tall(X0))) [input p15]
22. wise(susan) [input hypothesis]
34. ! [X0] : (((~calm(X0) | strong(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | (calm(X0) & ~strong(X0)))) [nnf transformation 2]
35. ! [X0] : ((~calm(X0) | strong(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | (calm(X0) & ~strong(X0)))) [flattening 34]
36. ! [X0] : (((brave(X0) & calm(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (~brave(X0) | ~calm(X0)))) [nnf transformation 3]
37. ! [X0] : (((brave(X0) & calm(X0)) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | ~brave(X0) | ~calm(X0))) [flattening 36]
48. ! [X0] : (((generous(X0) | quiet(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (~generous(X0) & ~quiet(X0)))) [nnf transformation 8]
49. ! [X0] : ((generous(X0) | quiet(X0) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | (~generous(X0) & ~quiet(X0)))) [flattening 48]
51. ! [X0] : (((~calm(X0) & creative(X0)) | (funny(X0) & ~kind(X0))) & ((~funny(X0) | kind(X0)) | (calm(X0) | ~creative(X0)))) [nnf transformation 13]
52. ! [X0] : (((~calm(X0) & creative(X0)) | (funny(X0) & ~kind(X0))) & (~funny(X0) | kind(X0) | calm(X0) | ~creative(X0))) [flattening 51]
60. ! [X0] : (((humble(X0) | old(X0)) | (~generous(X0) | ~tall(X0))) & ((generous(X0) & tall(X0)) | (~humble(X0) & ~old(X0)))) [nnf transformation 16]
61. ! [X0] : ((humble(X0) | old(X0) | ~generous(X0) | ~tall(X0)) & ((generous(X0) & tall(X0)) | (~humble(X0) & ~old(X0)))) [flattening 60]
74. old(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 35]
77. ~calm(X0) | strong(X0) | strong(X0) | old(X0) [cnf transformation 35]
79. ~wise(X0) | calm(X0) [cnf transformation 37]
82. ~generous(X0) | brave(X0) [cnf transformation 37]
98. ~brave(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 49]
110. ~calm(X0) | funny(X0) [cnf transformation 52]
119. ~old(X0) | generous(X0) [cnf transformation 61]
129. wise(susan) [cnf transformation 22]
132. ~strong(X0) | old(X0) [duplicate literal removal 74]
133. ~calm(X0) | strong(X0) | old(X0) [duplicate literal removal 77]
167. 8 <=> generous(susan) [avatar definition]
169. generous(susan) <- (8) [avatar component clause 167]
183. ~generous(X0) | ~funny(X0) [subsumption resolution 98,82]
252. calm(susan) [resolution 79,129]
256. funny(susan) [resolution 110,252]
263. 25 <=> old(susan) [avatar definition]
265. old(susan) <- (25) [avatar component clause 263]
300. strong(susan) | old(susan) [resolution 133,252]
301. old(susan) [subsumption resolution 300,132]
302. 25 [avatar split clause 301,263]
380. generous(susan) <- (25) [resolution 265,119]
399. 8 | ~25 [avatar split clause 380,263,167]
402. ~funny(susan) <- (8) [resolution 169,183]
405. $false <- (8) [subsumption resolution 402,256]
406. ~8 [avatar contradiction clause 405]
407. $false [avatar sat refutation 302,399,406]
% SZS output end Proof for 539067158042222978111591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not strong is either not generous or kind.
Everyone who is both not humble and quiet is calm or not rich.
If mary is either quiet or not happy then mary is both rich and creative and vice versa.
If someone is either brave or not funny then someone is both strong and not tall and vice versa.
Everyone who is both funny and happy is tall or not kind.
If someone is curious then alice is either rich or not creative.
Everyone who is strong or not quiet is not quiet or creative and vice versa.
If susan is not tall or brave then fred is brave or not creative.
If lucy is both not brave and creative then someone is either not brave or calm and vice versa.
If someone is rich then lucy is either not brave or not kind and vice versa.
If someone is generous or not strong then someone is rich or strong.
Everyone who is not wise is quiet or not calm.
Everyone who is quiet or not old is either not creative or not old and vice versa.
If fred is curious or not patient then someone is either rich or not quiet.
Everyone who is both quiet and not kind is both not kind and funny and vice versa.
Everyone who is not brave or strong is both brave and not quiet and vice versa.
Mary is not happy or generous.
Paul is either strong or wise.
Alice is not rich or not brave.
Someone is quiet.
Someone is not kind.
Paul is rich.
Mary is strong.
Mary is wise or not kind. | Mary is creative. | entailment | (![X]:((kind(X)<~>~strong(X))=>(~generous(X)<~>kind(X))))&
(![X]:((~humble(X)&quiet(X))=>(calm(X)|~rich(X))))&
(((quiet(mary)<~>~happy(mary)))<=>((rich(mary)&creative(mary))))&
((?[X]:((brave(X)<~>~funny(X))))<=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((funny(X)&happy(X))=>(tall(X)|~kind(X))))&
((?[X]:(curious(X)))=>((rich(alice)<~>~creative(alice))))&
(![X]:((strong(X)|~quiet(X))<=>(~quiet(X)|creative(X))))&
(((~tall(susan)|brave(susan)))=>((brave(fred)|~creative(fred))))&
(((~brave(lucy)&creative(lucy)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
((?[X]:(rich(X)))<=>((~brave(lucy)<~>~kind(lucy))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:(~wise(X)=>(quiet(X)|~calm(X))))&
(![X]:((quiet(X)|~old(X))<=>(~creative(X)<~>~old(X))))&
(((curious(fred)|~patient(fred)))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~kind(X)&funny(X))))&
(![X]:((~brave(X)|strong(X))<=>(brave(X)&~quiet(X))))&
((~happy(mary)|generous(mary)))&
((strong(paul)<~>wise(paul)))&
((~rich(alice)|~brave(alice)))&
(?[X]:(quiet(X)))&
(?[X]:(~kind(X)))&
(rich(paul))&
(strong(mary))&
((wise(mary)|~kind(mary))) | creative(mary) | [
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1952208179988469515210103
% SZS output start Proof for 1952208179988469515210103
13. ! [X0] : ((~old(X0) | quiet(X0)) <=> (~creative(X0) <~> ~old(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (~quiet(X0) & brave(X0))) [input p15]
23. strong(mary) [input p22]
25. ~creative(mary) [input hypothesis]
62. ! [X0] : (((~old(X0) | quiet(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (old(X0) & ~quiet(X0)))) [nnf transformation 13]
63. ! [X0] : ((~old(X0) | quiet(X0) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (old(X0) & ~quiet(X0)))) [flattening 62]
66. ! [X0] : (((strong(X0) | ~brave(X0)) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 16]
67. ! [X0] : ((strong(X0) | ~brave(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | (~strong(X0) & brave(X0)))) [flattening 66]
112. old(X0) | creative(X0) | old(X0) [cnf transformation 63]
113. ~old(X0) | quiet(X0) | ~old(X0) | creative(X0) [cnf transformation 63]
122. ~quiet(X0) | ~strong(X0) [cnf transformation 67]
131. strong(mary) [cnf transformation 23]
133. ~creative(mary) [cnf transformation 25]
136. old(X0) | creative(X0) [duplicate literal removal 112]
137. ~old(X0) | quiet(X0) | creative(X0) [duplicate literal removal 113]
145. 2 <=> creative(mary) [avatar definition]
147. ~creative(mary) <- (~2) [avatar component clause 145]
149. 3 <=> quiet(mary) [avatar definition]
150. quiet(mary) <- (3) [avatar component clause 149]
151. ~quiet(mary) <- (~3) [avatar component clause 149]
295. ~2 [avatar split clause 133,145]
305. ~strong(mary) <- (3) [resolution 122,150]
306. $false <- (3) [subsumption resolution 305,131]
307. ~3 [avatar contradiction clause 306]
332. quiet(X0) | creative(X0) | creative(X0) [resolution 137,136]
333. creative(X0) | quiet(X0) [duplicate literal removal 332]
340. quiet(mary) <- (~2) [resolution 333,147]
343. $false <- (~2, ~3) [subsumption resolution 340,151]
344. 2 | 3 [avatar contradiction clause 343]
345. $false [avatar sat refutation 295,307,344]
% SZS output end Proof for 1952208179988469515210103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or not strong then someone is not old and vice versa.
Everyone who is both not tall and rich is both strong and not curious and vice versa.
Everyone who is both patient and not wise is kind.
Everyone who is either not strong or generous is either not creative or not happy and vice versa.
If someone is strong or not tall then fred is not quiet or tall and vice versa.
If someone is both not funny and generous then fred is both funny and humble and vice versa.
If someone is both tall and not strong then susan is either not wise or not curious.
If someone is either not calm or not curious then susan is both not calm and not old and vice versa.
Everyone who is old or tall is not humble.
Everyone who is both kind and not patient is not humble and vice versa.
If susan is not calm then paul is strong or calm.
Everyone who is strong or quiet is not humble or old.
If mary is both not strong and generous then someone is either not calm or not generous.
If alice is both not happy and not tall then someone is not strong and vice versa.
Everyone who is creative or not tall is not creative or creative and vice versa.
Everyone who is either not curious or not patient is not patient or curious and vice versa.
Someone is either patient or old.
Someone is not generous or curious.
Someone is either not strong or not creative.
Fred is not humble.
Alice is both not quiet and not humble.
Someone is either humble or not happy.
Someone is happy or curious. | Paul is not wise. | neutral | (((~tall(alice)<~>~strong(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~tall(X)&rich(X))<=>(strong(X)&~curious(X))))&
(![X]:((patient(X)&~wise(X))=>kind(X)))&
(![X]:((~strong(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~quiet(fred)|tall(fred))))&
((?[X]:((~funny(X)&generous(X))))<=>((funny(fred)&humble(fred))))&
((?[X]:((tall(X)&~strong(X))))=>((~wise(susan)<~>~curious(susan))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~calm(susan)&~old(susan))))&
(![X]:((old(X)|tall(X))=>~humble(X)))&
(![X]:((kind(X)&~patient(X))<=>~humble(X)))&
((~calm(susan))=>((strong(paul)|calm(paul))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)|old(X))))&
(((~strong(mary)&generous(mary)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(((~happy(alice)&~tall(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((creative(X)|~tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~patient(X)|curious(X))))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(~humble(fred))&
((~quiet(alice)&~humble(alice)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:((happy(X)|curious(X)))) | ~wise(paul) | [] | null | 0 |
Everyone who is both not kind and not tall is not happy or calm.
If lucy is rich or humble then lucy is not rich or not patient.
Everyone who is not wise or not happy is not curious or rich.
Everyone who is not strong is funny or brave and vice versa.
Everyone who is not tall or old is not wise and vice versa.
If alice is both creative and tall then someone is funny or not generous and vice versa.
Everyone who is either not strong or happy is not happy and vice versa.
Everyone who is both curious and tall is rich and vice versa.
If someone is not funny or funny then alice is either not wise or not humble and vice versa.
If alice is both tall and not patient then someone is happy and vice versa.
Everyone who is either kind or patient is humble and vice versa.
Everyone who is not patient or not wise is both not kind and brave.
If someone is generous or wise then someone is not tall or generous.
Everyone who is either curious or wise is not rich and vice versa.
If someone is both patient and tall then susan is funny.
Everyone who is creative or kind is both strong and not generous.
Someone is either not generous or not calm.
Someone is not rich.
Fred is either not tall or not curious.
John is old or not patient.
Someone is happy or calm.
Alice is not patient.
Someone is not creative. | Fred is wise. | entailment | (![X]:((~kind(X)&~tall(X))=>(~happy(X)|calm(X))))&
(((rich(lucy)|humble(lucy)))=>((~rich(lucy)|~patient(lucy))))&
(![X]:((~wise(X)|~happy(X))=>(~curious(X)|rich(X))))&
(![X]:(~strong(X)<=>(funny(X)|brave(X))))&
(![X]:((~tall(X)|old(X))<=>~wise(X)))&
(((creative(alice)&tall(alice)))<=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((~strong(X)<~>happy(X))<=>~happy(X)))&
(![X]:((curious(X)&tall(X))<=>rich(X)))&
((?[X]:((~funny(X)|funny(X))))<=>((~wise(alice)<~>~humble(alice))))&
(((tall(alice)&~patient(alice)))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>humble(X)))&
(![X]:((~patient(X)|~wise(X))=>(~kind(X)&brave(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((curious(X)<~>wise(X))<=>~rich(X)))&
((?[X]:((patient(X)&tall(X))))=>(funny(susan)))&
(![X]:((creative(X)|kind(X))=>(strong(X)&~generous(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:(~rich(X)))&
((~tall(fred)<~>~curious(fred)))&
((old(john)|~patient(john)))&
(?[X]:((happy(X)|calm(X))))&
(~patient(alice))&
(?[X]:(~creative(X))) | wise(fred) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6602176723458026260162156
% SZS output start Proof for 6602176723458026260162156
3. ! [X0] : ((~happy(X0) | ~wise(X0)) => (rich(X0) | ~curious(X0))) [input p2]
8. ! [X0] : ((tall(X0) & curious(X0)) <=> rich(X0)) [input p7]
14. ! [X0] : ((curious(X0) <~> wise(X0)) <=> ~rich(X0)) [input p13]
24. ~wise(fred) [input hypothesis]
30. ! [X0] : ((rich(X0) | ~curious(X0)) | (happy(X0) & wise(X0))) [ennf transformation 3]
31. ! [X0] : (rich(X0) | ~curious(X0) | (happy(X0) & wise(X0))) [flattening 30]
46. ! [X0] : (((tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (~tall(X0) | ~curious(X0)))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | ~tall(X0) | ~curious(X0))) [flattening 46]
61. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | rich(X0)) & (~rich(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 14]
75. rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
93. curious(X0) | ~rich(X0) [cnf transformation 47]
114. ~rich(X0) | wise(X0) | ~curious(X0) [cnf transformation 61]
116. wise(X0) | curious(X0) | rich(X0) [cnf transformation 61]
132. ~wise(fred) [cnf transformation 24]
224. wise(X0) | rich(X0) [subsumption resolution 116,75]
225. ~rich(X0) | wise(X0) [subsumption resolution 114,93]
226. wise(X0) [subsumption resolution 225,224]
276. $false [subsumption resolution 132,226]
% SZS output end Proof for 6602176723458026260162156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or not creative is not calm or not patient. If someone is both calm and not creative then someone is not kind and vice versa. Everyone who is kind is both kind and not old. If someone is both not old and tall then someone is either brave or humble and vice versa. If alice is both funny and not brave then fred is not strong or not rich. Everyone who is either calm or quiet is not generous or quiet and vice versa. Everyone who is not wise or not quiet is both not brave and wise and vice versa. Everyone who is kind or quiet is not quiet or tall. Everyone who is quiet is both not creative and not calm and vice versa. If alice is not kind then alice is both not kind and calm and vice versa. Everyone who is both not happy and not patient is either not kind or not humble and vice versa. Everyone who is generous or kind is creative and vice versa. Everyone who is either not funny or not generous is not wise or funny. If paul is either strong or brave then someone is both brave and quiet and vice versa. If someone is both rich and not calm then someone is either curious or funny and vice versa. Everyone who is either humble or patient is either not funny or curious. Lucy is both brave and not happy. Susan is both humble and curious. Someone is not generous. Fred is calm or not humble. Someone is calm or not generous. Fred is both not generous and not funny. Someone is both quiet and rich. | Lucy is kind. | contradiction | (![X]:((rich(X)<~>~creative(X))=>(~calm(X)|~patient(X))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:(~kind(X))))&
(![X]:(kind(X)=>(kind(X)&~old(X))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(alice)&~brave(alice)))=>((~strong(fred)|~rich(fred))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((brave(lucy)&~happy(lucy)))&
((humble(susan)&curious(susan)))&
(?[X]:(~generous(X)))&
((calm(fred)|~humble(fred)))&
(?[X]:((calm(X)|~generous(X))))&
((~generous(fred)&~funny(fred)))&
(?[X]:((quiet(X)&rich(X)))) | kind(lucy) | [
"p6",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2985717808316089908164737
% SZS output start Proof for 2985717808316089908164737
7. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (wise(X0) & ~brave(X0))) [input p6]
9. ! [X0] : (quiet(X0) <=> (~calm(X0) & ~creative(X0))) [input p8]
12. ! [X0] : ((kind(X0) | generous(X0)) <=> creative(X0)) [input p11]
17. ~happy(lucy) & brave(lucy) [input p16]
24. kind(lucy) [input hypothesis]
51. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 7]
52. ! [X0] : ((~quiet(X0) | ~wise(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | (quiet(X0) & wise(X0)))) [flattening 51]
53. ! [X0] : ((quiet(X0) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | ~quiet(X0))) [nnf transformation 9]
54. ! [X0] : ((quiet(X0) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | ~quiet(X0))) [flattening 53]
59. ! [X0] : (((kind(X0) | generous(X0)) | ~creative(X0)) & (creative(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 12]
60. ! [X0] : ((kind(X0) | generous(X0) | ~creative(X0)) & (creative(X0) | (~kind(X0) & ~generous(X0)))) [flattening 59]
99. ~brave(X0) | quiet(X0) [cnf transformation 52]
105. ~quiet(X0) | ~creative(X0) [cnf transformation 54]
118. ~kind(X0) | creative(X0) [cnf transformation 60]
138. brave(lucy) [cnf transformation 17]
149. kind(lucy) [cnf transformation 24]
306. quiet(lucy) [resolution 99,138]
310. ~creative(lucy) [resolution 105,306]
311. creative(lucy) [resolution 118,149]
313. $false [subsumption resolution 311,310]
% SZS output end Proof for 2985717808316089908164737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not kind is not rich.
Everyone who is humble is curious.
If someone is not strong or not funny then someone is not happy or not generous and vice versa.
If someone is either old or calm then paul is not wise or creative.
If alice is both not old and old then someone is brave or not tall and vice versa.
If someone is either kind or not humble then someone is both not calm and not tall.
Everyone who is either curious or not old is not old or not patient and vice versa.
Everyone who is not strong is calm or funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
Mary is not generous or strong.
Someone is funny.
Paul is not patient.
Alice is both not happy and not calm.
Alice is not creative or not generous.
Paul is quiet. | Mary is curious. | neutral | (![X]:((~strong(X)<~>~kind(X))=>~rich(X)))&
(![X]:(humble(X)=>curious(X)))&
((?[X]:((~strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~generous(X)))))&
((?[X]:((old(X)<~>calm(X))))=>((~wise(paul)|creative(paul))))&
(((~old(alice)&old(alice)))<=>(?[X]:((brave(X)|~tall(X)))))&
((?[X]:((kind(X)<~>~humble(X))))=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((curious(X)<~>~old(X))<=>(~old(X)|~patient(X))))&
(![X]:(~strong(X)=>(calm(X)|funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
((~generous(mary)|strong(mary)))&
(?[X]:(funny(X)))&
(~patient(paul))&
((~happy(alice)&~calm(alice)))&
((~creative(alice)|~generous(alice)))&
(quiet(paul)) | curious(mary) | [] | null | 0 |
Everyone who is tall or curious is patient.
Everyone who is both not kind and happy is generous or happy and vice versa.
If someone is calm or curious then fred is both creative and funny.
Everyone who is not happy is patient or not happy.
If fred is both tall and not happy then fred is not strong and vice versa.
If lucy is both not brave and not wise then someone is not rich or curious and vice versa.
Everyone who is either tall or calm is both not quiet and not calm.
If lucy is both not strong and curious then someone is not kind or brave and vice versa.
Everyone who is both brave and not humble is not patient.
Everyone who is calm is not kind or old.
Everyone who is funny is either not old or not patient and vice versa.
Everyone who is not generous is both old and creative.
Everyone who is both patient and not patient is either wise or not rich.
Everyone who is both not tall and not patient is either strong or not tall.
Everyone who is both not generous and kind is quiet or rich and vice versa.
If lucy is creative then someone is both not generous and brave and vice versa.
Someone is brave.
Paul is either not quiet or humble.
Someone is either not calm or patient.
Someone is either generous or not funny.
Alice is either calm or not humble.
Someone is both tall and patient.
Someone is not strong.
Paul is old or not patient. | Fred is not strong. | contradiction | (![X]:((tall(X)|curious(X))=>patient(X)))&
(![X]:((~kind(X)&happy(X))<=>(generous(X)|happy(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(fred)&funny(fred))))&
(![X]:(~happy(X)=>(patient(X)|~happy(X))))&
(((tall(fred)&~happy(fred)))<=>(~strong(fred)))&
(((~brave(lucy)&~wise(lucy)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((tall(X)<~>calm(X))=>(~quiet(X)&~calm(X))))&
(((~strong(lucy)&curious(lucy)))<=>(?[X]:((~kind(X)|brave(X)))))&
(![X]:((brave(X)&~humble(X))=>~patient(X)))&
(![X]:(calm(X)=>(~kind(X)|old(X))))&
(![X]:(funny(X)<=>(~old(X)<~>~patient(X))))&
(![X]:(~generous(X)=>(old(X)&creative(X))))&
(![X]:((patient(X)&~patient(X))=>(wise(X)<~>~rich(X))))&
(![X]:((~tall(X)&~patient(X))=>(strong(X)<~>~tall(X))))&
(![X]:((~generous(X)&kind(X))<=>(quiet(X)|rich(X))))&
((creative(lucy))<=>(?[X]:((~generous(X)&brave(X)))))&
(?[X]:(brave(X)))&
((~quiet(paul)<~>humble(paul)))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
((calm(alice)<~>~humble(alice)))&
(?[X]:((tall(X)&patient(X))))&
(?[X]:(~strong(X)))&
((old(paul)|~patient(paul))) | ~strong(fred) | [
"p0",
"p1",
"p2",
"p4",
"p7",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1513732524498844611805636
% SZS output start Proof for 1513732524498844611805636
1. ! [X0] : ((curious(X0) | tall(X0)) => patient(X0)) [input p0]
2. ! [X0] : ((happy(X0) & ~kind(X0)) <=> (happy(X0) | generous(X0))) [input p1]
3. ? [X0] : (curious(X0) | calm(X0)) => (funny(fred) & creative(fred)) [input p2]
5. (~happy(fred) & tall(fred)) <=> ~strong(fred) [input p4]
8. (curious(lucy) & ~strong(lucy)) <=> ? [X0] : (brave(X0) | ~kind(X0)) [input p7]
11. ! [X0] : (funny(X0) <=> (~old(X0) <~> ~patient(X0))) [input p10]
12. ! [X0] : (~generous(X0) => (creative(X0) & old(X0))) [input p11]
17. ? [X0] : brave(X0) [input p16]
25. ~strong(fred) [input hypothesis]
26. ! [X0] : (patient(X0) | (~curious(X0) & ~tall(X0))) [ennf transformation 1]
27. (funny(fred) & creative(fred)) | ! [X0] : (~curious(X0) & ~calm(X0)) [ennf transformation 3]
35. ! [X0] : ((creative(X0) & old(X0)) | generous(X0)) [ennf transformation 12]
40. ! [X0] : (((happy(X0) & ~kind(X0)) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | (~happy(X0) | kind(X0)))) [nnf transformation 2]
41. ! [X0] : (((happy(X0) & ~kind(X0)) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | ~happy(X0) | kind(X0))) [flattening 40]
42. ((~happy(fred) & tall(fred)) | strong(fred)) & (~strong(fred) | (happy(fred) | ~tall(fred))) [nnf transformation 5]
43. ((~happy(fred) & tall(fred)) | strong(fred)) & (~strong(fred) | happy(fred) | ~tall(fred)) [flattening 42]
50. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X0] : (brave(X0) | ~kind(X0)) | (~curious(lucy) | strong(lucy))) [nnf transformation 8]
51. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X0] : (brave(X0) | ~kind(X0)) | ~curious(lucy) | strong(lucy)) [flattening 50]
52. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & (? [X1] : (brave(X1) | ~kind(X1)) | ~curious(lucy) | strong(lucy)) [rectify 51]
53. ? [X1] : (brave(X1) | ~kind(X1)) => (brave(sK1) | ~kind(sK1)) [choice axiom]
54. ((curious(lucy) & ~strong(lucy)) | ! [X0] : (~brave(X0) & kind(X0))) & ((brave(sK1) | ~kind(sK1)) | ~curious(lucy) | strong(lucy)) [skolemisation 52,53]
55. ! [X0] : ((funny(X0) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~funny(X0))) [nnf transformation 11]
64. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
65. brave(sK3) [skolemisation 17,64]
78. ~tall(X0) | patient(X0) [cnf transformation 26]
83. ~generous(X0) | happy(X0) [cnf transformation 41]
88. funny(fred) | ~curious(X0) [cnf transformation 27]
91. tall(fred) | strong(fred) [cnf transformation 43]
92. ~happy(fred) | strong(fred) [cnf transformation 43]
106. curious(lucy) | ~brave(X0) [cnf transformation 54]
109. ~old(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 55]
113. old(X0) | generous(X0) [cnf transformation 35]
127. brave(sK3) [cnf transformation 65]
140. ~strong(fred) [cnf transformation 25]
144. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
145. ~curious(X0) <- (1) [avatar component clause 144]
147. 2 <=> funny(fred) [avatar definition]
149. funny(fred) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 88,147,144]
162. 5 <=> strong(fred) [avatar definition]
166. 6 <=> happy(fred) [avatar definition]
168. ~happy(fred) <- (~6) [avatar component clause 166]
169. 5 | ~6 [avatar split clause 92,166,162]
171. 7 <=> tall(fred) [avatar definition]
173. tall(fred) <- (7) [avatar component clause 171]
174. 5 | 7 [avatar split clause 91,171,162]
201. 13 <=> ! [X0] : ~brave(X0) [avatar definition]
202. ~brave(X0) <- (13) [avatar component clause 201]
204. 14 <=> curious(lucy) [avatar definition]
206. curious(lucy) <- (14) [avatar component clause 204]
207. 13 | 14 [avatar split clause 106,204,201]
296. ~5 [avatar split clause 140,162]
298. patient(fred) <- (7) [resolution 78,173]
318. ~funny(X0) | ~patient(X0) | generous(X0) [resolution 109,113]
341. $false <- (13) [resolution 202,127]
342. ~13 [avatar contradiction clause 341]
360. ~patient(fred) | generous(fred) <- (2) [resolution 318,149]
361. generous(fred) <- (2, 7) [subsumption resolution 360,298]
370. happy(fred) <- (2, 7) [resolution 361,83]
372. $false <- (2, ~6, 7) [subsumption resolution 370,168]
373. ~2 | 6 | ~7 [avatar contradiction clause 372]
379. $false <- (1, 14) [resolution 145,206]
380. ~1 | ~14 [avatar contradiction clause 379]
381. $false [avatar sat refutation 150,169,174,207,296,342,373,380]
% SZS output end Proof for 1513732524498844611805636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is both creative and generous and vice versa.
Everyone who is either funny or tall is both creative and not brave and vice versa.
If someone is not kind then someone is both not wise and not tall.
Everyone who is either generous or rich is either not tall or tall and vice versa.
If lucy is both not curious and strong then fred is quiet and vice versa.
Everyone who is tall is both not patient and not humble.
If someone is not calm then someone is not old or not brave and vice versa.
If lucy is not quiet or calm then someone is not rich or not funny.
If susan is both happy and not kind then someone is not funny and vice versa.
Everyone who is not strong or brave is not kind.
If someone is either not humble or tall then someone is both not rich and wise and vice versa.
If someone is not humble or tall then susan is funny or generous.
Everyone who is both not rich and tall is quiet and vice versa.
If fred is both brave and not brave then someone is both not quiet and generous and vice versa.
Everyone who is both happy and patient is either funny or generous and vice versa.
Everyone who is both quiet and not funny is both tall and quiet and vice versa.
Fred is both wise and not tall.
Someone is wise or not humble.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative. | Susan is rich. | entailment | (![X]:((~patient(X)<~>~calm(X))<=>(creative(X)&generous(X))))&
(![X]:((funny(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>tall(X))))&
(((~curious(lucy)&strong(lucy)))<=>(quiet(fred)))&
(![X]:(tall(X)=>(~patient(X)&~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~quiet(lucy)|calm(lucy)))=>(?[X]:((~rich(X)|~funny(X)))))&
(((happy(susan)&~kind(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)|brave(X))=>~kind(X)))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((~humble(X)|tall(X))))=>((funny(susan)|generous(susan))))&
(![X]:((~rich(X)&tall(X))<=>quiet(X)))&
(((brave(fred)&~brave(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((happy(X)&patient(X))<=>(funny(X)<~>generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(tall(X)&quiet(X))))&
((wise(fred)&~tall(fred)))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john))) | rich(susan) | [
"p3",
"p5",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7346644534287886324734982
% SZS output start Proof for 7346644534287886324734982
4. ! [X0] : ((generous(X0) <~> rich(X0)) <=> (~tall(X0) <~> tall(X0))) [input p3]
6. ! [X0] : (tall(X0) => (~humble(X0) & ~patient(X0))) [input p5]
13. ! [X0] : ((tall(X0) & ~rich(X0)) <=> quiet(X0)) [input p12]
14. (~brave(fred) & brave(fred)) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p13]
15. ! [X0] : ((patient(X0) & happy(X0)) <=> (funny(X0) <~> generous(X0))) [input p14]
16. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (quiet(X0) & tall(X0))) [input p15]
22. ~rich(susan) [input hypothesis]
27. ! [X0] : ((~humble(X0) & ~patient(X0)) | ~tall(X0)) [ennf transformation 6]
39. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [nnf transformation 4]
59. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~tall(X0) | rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | ~tall(X0) | rich(X0))) [flattening 59]
61. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | (brave(fred) | ~brave(fred))) [nnf transformation 14]
62. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | brave(fred) | ~brave(fred)) [flattening 61]
63. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X1] : (generous(X1) & ~quiet(X1)) | brave(fred) | ~brave(fred)) [rectify 62]
64. ? [X1] : (generous(X1) & ~quiet(X1)) => (generous(sK7) & ~quiet(sK7)) [choice axiom]
65. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & ((generous(sK7) & ~quiet(sK7)) | brave(fred) | ~brave(fred)) [skolemisation 63,64]
66. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 15]
67. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ~patient(X0) | ~happy(X0))) [flattening 66]
68. ! [X0] : (((~funny(X0) & quiet(X0)) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 16]
69. ! [X0] : (((~funny(X0) & quiet(X0)) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | funny(X0) | ~quiet(X0))) [flattening 68]
94. rich(X0) | generous(X0) | tall(X0) | tall(X0) [cnf transformation 39]
95. rich(X0) | generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 39]
101. ~tall(X0) | ~patient(X0) [cnf transformation 27]
123. ~quiet(X0) | tall(X0) [cnf transformation 60]
126. brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
127. ~brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
133. ~generous(X0) | funny(X0) | patient(X0) [cnf transformation 67]
137. ~funny(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 69]
145. ~rich(susan) [cnf transformation 22]
146. rich(X0) | generous(X0) | tall(X0) [duplicate literal removal 94]
147. rich(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 95]
164. rich(X0) | generous(X0) [subsumption resolution 146,147]
272. 28 <=> funny(susan) [avatar definition]
273. ~funny(susan) <- (~28) [avatar component clause 272]
276. 29 <=> generous(susan) [avatar definition]
278. generous(susan) <- (29) [avatar component clause 276]
285. 31 <=> ! [X0] : (~generous(X0) | quiet(X0)) [avatar definition]
286. ~generous(X0) | quiet(X0) <- (31) [avatar component clause 285]
288. 32 <=> brave(fred) [avatar definition]
291. 31 | ~32 [avatar split clause 127,288,285]
292. 31 | 32 [avatar split clause 126,288,285]
293. ~quiet(X0) | ~funny(X0) [subsumption resolution 137,123]
315. generous(susan) [resolution 164,145]
318. 29 [avatar split clause 315,276]
328. quiet(susan) <- (29, 31) [resolution 286,278]
331. ~funny(susan) <- (29, 31) [resolution 328,293]
332. tall(susan) <- (29, 31) [resolution 328,123]
336. ~28 | ~29 | ~31 [avatar split clause 331,285,276,272]
341. ~patient(susan) <- (29, 31) [resolution 332,101]
382. funny(susan) | patient(susan) <- (29) [resolution 133,278]
385. patient(susan) <- (~28, 29) [subsumption resolution 382,273]
386. $false <- (~28, 29, 31) [subsumption resolution 385,341]
387. 28 | ~29 | ~31 [avatar contradiction clause 386]
392. $false [avatar sat refutation 291,292,318,336,387]
% SZS output end Proof for 7346644534287886324734982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not happy and not kind then someone is either not happy or brave and vice versa. If alice is either not rich or strong then alice is happy. If paul is both not funny and not kind then susan is not old and vice versa. Everyone who is kind or not funny is both not rich and humble and vice versa. Everyone who is not calm or not creative is either not calm or wise. Everyone who is tall or calm is either not tall or not creative. If john is wise then someone is both not strong and wise. Everyone who is both creative and wise is strong or not wise. Everyone who is both not rich and not old is not strong or strong and vice versa. If someone is not old then alice is calm or not brave and vice versa. Everyone who is not creative or not rich is either happy or not calm and vice versa. If someone is both happy and tall then someone is either not humble or patient. Everyone who is happy is not funny or not old. If john is both funny and strong then someone is not strong and vice versa. Everyone who is brave is both not quiet and not strong and vice versa. Everyone who is not patient is both wise and tall and vice versa. Someone is not funny. Susan is either tall or old. Someone is not generous. Someone is not generous or not brave. Someone is not calm or wise. Paul is rich or calm. Someone is not kind. Paul is either not wise or generous. | Alice is not old. | entailment | ((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~rich(alice)<~>strong(alice)))=>(happy(alice)))&
(((~funny(paul)&~kind(paul)))<=>(~old(susan)))&
(![X]:((kind(X)|~funny(X))<=>(~rich(X)&humble(X))))&
(![X]:((~calm(X)|~creative(X))=>(~calm(X)<~>wise(X))))&
(![X]:((tall(X)|calm(X))=>(~tall(X)<~>~creative(X))))&
((wise(john))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((creative(X)&wise(X))=>(strong(X)|~wise(X))))&
(![X]:((~rich(X)&~old(X))<=>(~strong(X)|strong(X))))&
((?[X]:(~old(X)))<=>((calm(alice)|~brave(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(happy(X)<~>~calm(X))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:(happy(X)=>(~funny(X)|~old(X))))&
(((funny(john)&strong(john)))<=>(?[X]:(~strong(X))))&
(![X]:(brave(X)<=>(~quiet(X)&~strong(X))))&
(![X]:(~patient(X)<=>(wise(X)&tall(X))))&
(?[X]:(~funny(X)))&
((tall(susan)<~>old(susan)))&
(?[X]:(~generous(X)))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~calm(X)|wise(X))))&
((rich(paul)|calm(paul)))&
(?[X]:(~kind(X)))&
((~wise(paul)<~>generous(paul))) | ~old(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2165802297883524985862382
% SZS output start Proof for 2165802297883524985862382
9. ! [X0] : ((~old(X0) & ~rich(X0)) <=> (strong(X0) | ~strong(X0))) [input p8]
25. old(alice) [input hypothesis]
51. ! [X0] : (((~old(X0) & ~rich(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (old(X0) | rich(X0)))) [nnf transformation 9]
52. ! [X0] : (((~old(X0) & ~rich(X0)) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | old(X0) | rich(X0))) [flattening 51]
115. ~old(X0) | strong(X0) [cnf transformation 52]
116. ~old(X0) | ~strong(X0) [cnf transformation 52]
148. old(alice) [cnf transformation 25]
226. ~old(X0) [subsumption resolution 115,116]
301. $false [subsumption resolution 148,226]
% SZS output end Proof for 2165802297883524985862382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then susan is both happy and not creative and vice versa.
If susan is both generous and not brave then someone is both happy and not creative.
Everyone who is not brave or not funny is not curious or not patient.
Everyone who is not brave or kind is not brave or brave and vice versa.
Everyone who is funny or not kind is either not strong or curious.
If someone is not rich then lucy is quiet and vice versa.
Everyone who is not happy is both strong and tall.
If mary is both not happy and not kind then fred is both not brave and calm.
Everyone who is both not curious and not tall is tall and vice versa.
Everyone who is not strong is happy.
Everyone who is both not kind and not happy is both not tall and not old and vice versa.
If someone is not kind then lucy is both old and not rich and vice versa.
If someone is not wise or rich then fred is not humble and vice versa.
If someone is either not brave or not funny then fred is both happy and not humble and vice versa.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is both old and not happy is brave.
Someone is funny or not humble.
Alice is both not humble and generous.
Someone is not patient.
Someone is not humble.
Someone is happy.
Lucy is not strong or funny.
Someone is generous. | Mary is happy. | entailment | ((?[X]:(creative(X)))<=>((happy(susan)&~creative(susan))))&
(((generous(susan)&~brave(susan)))=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~brave(X)|~funny(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)|kind(X))<=>(~brave(X)|brave(X))))&
(![X]:((funny(X)|~kind(X))=>(~strong(X)<~>curious(X))))&
((?[X]:(~rich(X)))<=>(quiet(lucy)))&
(![X]:(~happy(X)=>(strong(X)&tall(X))))&
(((~happy(mary)&~kind(mary)))=>((~brave(fred)&calm(fred))))&
(![X]:((~curious(X)&~tall(X))<=>tall(X)))&
(![X]:(~strong(X)=>happy(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)&~old(X))))&
((?[X]:(~kind(X)))<=>((old(lucy)&~rich(lucy))))&
((?[X]:((~wise(X)|rich(X))))<=>(~humble(fred)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((old(X)&~happy(X))=>brave(X)))&
(?[X]:((funny(X)|~humble(X))))&
((~humble(alice)&generous(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(~humble(X)))&
(?[X]:(happy(X)))&
((~strong(lucy)|funny(lucy)))&
(?[X]:(generous(X))) | happy(mary) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4952821451459824750365772
% SZS output start Proof for 4952821451459824750365772
7. ! [X0] : (~happy(X0) => (tall(X0) & strong(X0))) [input p6]
9. ! [X0] : ((~tall(X0) & ~curious(X0)) <=> tall(X0)) [input p8]
24. ~happy(mary) [input hypothesis]
31. ! [X0] : ((tall(X0) & strong(X0)) | happy(X0)) [ennf transformation 7]
51. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) | curious(X0)))) [nnf transformation 9]
52. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | tall(X0) | curious(X0))) [flattening 51]
95. tall(X0) | happy(X0) [cnf transformation 31]
99. ~tall(X0) | ~tall(X0) [cnf transformation 52]
128. ~happy(mary) [cnf transformation 24]
132. ~tall(X0) [duplicate literal removal 99]
185. 12 <=> happy(mary) [avatar definition]
186. ~happy(mary) <- (~12) [avatar component clause 185]
282. ~12 [avatar split clause 128,185]
284. happy(X0) [resolution 95,132]
286. $false <- (~12) [resolution 284,186]
287. 12 [avatar contradiction clause 286]
289. $false [avatar sat refutation 282,287]
% SZS output end Proof for 4952821451459824750365772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or funny then someone is not strong. Everyone who is both not creative and not wise is curious or brave. If someone is both not wise and not kind then someone is humble or old. If someone is not tall then someone is both not creative and not brave. If someone is not funny then fred is either wise or patient and vice versa. Everyone who is brave is not calm or strong and vice versa. Everyone who is either happy or humble is creative and vice versa. If someone is both quiet and not patient then someone is both not wise and not funny and vice versa. Everyone who is both not humble and happy is both not strong and old. If someone is not happy or not curious then someone is both tall and humble and vice versa. If someone is both not curious and not wise then someone is tall or humble. Everyone who is both not brave and funny is brave and vice versa. Everyone who is either old or not wise is both not strong and curious. Everyone who is both not kind and not strong is not tall or humble and vice versa. Everyone who is quiet or creative is both patient and wise and vice versa. If john is either quiet or not calm then susan is not tall or patient and vice versa. Someone is both not kind and not quiet. Alice is either not happy or calm. Susan is either not tall or tall. Someone is both rich and not humble. Someone is rich or humble. Lucy is funny or not patient. Fred is not tall or not rich. | Lucy is patient. | contradiction | ((?[X]:((creative(X)|funny(X))))=>(?[X]:(~strong(X))))&
(![X]:((~creative(X)&~wise(X))=>(curious(X)|brave(X))))&
((?[X]:((~wise(X)&~kind(X))))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
((?[X]:(~funny(X)))<=>((wise(fred)<~>patient(fred))))&
(![X]:(brave(X)<=>(~calm(X)|strong(X))))&
(![X]:((happy(X)<~>humble(X))<=>creative(X)))&
((?[X]:((quiet(X)&~patient(X))))<=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((~humble(X)&happy(X))=>(~strong(X)&old(X))))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((tall(X)&humble(X)))))&
((?[X]:((~curious(X)&~wise(X))))=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((~brave(X)&funny(X))<=>brave(X)))&
(![X]:((old(X)<~>~wise(X))=>(~strong(X)&curious(X))))&
(![X]:((~kind(X)&~strong(X))<=>(~tall(X)|humble(X))))&
(![X]:((quiet(X)|creative(X))<=>(patient(X)&wise(X))))&
(((quiet(john)<~>~calm(john)))<=>((~tall(susan)|patient(susan))))&
(?[X]:((~kind(X)&~quiet(X))))&
((~happy(alice)<~>calm(alice)))&
((~tall(susan)<~>tall(susan)))&
(?[X]:((rich(X)&~humble(X))))&
(?[X]:((rich(X)|humble(X))))&
((funny(lucy)|~patient(lucy)))&
((~tall(fred)|~rich(fred))) | patient(lucy) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5755614823867682798616193
% SZS output start Proof for 5755614823867682798616193
12. ! [X0] : ((funny(X0) & ~brave(X0)) <=> brave(X0)) [input p11]
22. ~patient(lucy) | funny(lucy) [input p21]
24. patient(lucy) [input hypothesis]
69. ! [X0] : (((funny(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~funny(X0) | brave(X0)))) [nnf transformation 12]
70. ! [X0] : (((funny(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~funny(X0) | brave(X0))) [flattening 69]
115. brave(X0) | ~funny(X0) | brave(X0) [cnf transformation 70]
116. ~brave(X0) | ~brave(X0) [cnf transformation 70]
147. ~patient(lucy) | funny(lucy) [cnf transformation 22]
149. patient(lucy) [cnf transformation 24]
150. brave(X0) | ~funny(X0) [duplicate literal removal 115]
151. ~brave(X0) [duplicate literal removal 116]
153. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
154. ~funny(X1) <- (1) [avatar component clause 153]
276. ~funny(X0) [subsumption resolution 150,151]
277. 1 [avatar split clause 276,153]
321. 38 <=> funny(lucy) [avatar definition]
323. funny(lucy) <- (38) [avatar component clause 321]
325. 39 <=> patient(lucy) [avatar definition]
328. 38 | ~39 [avatar split clause 147,325,321]
338. 39 [avatar split clause 149,325]
345. $false <- (1, 38) [resolution 323,154]
346. ~1 | ~38 [avatar contradiction clause 345]
347. $false [avatar sat refutation 277,328,338,346]
% SZS output end Proof for 5755614823867682798616193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not old or quiet then someone is quiet or not funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If fred is either kind or not generous then mary is patient.
Everyone who is not calm is both tall and wise.
Everyone who is old is both creative and funny.
Everyone who is both patient and tall is not happy and vice versa.
Everyone who is either not quiet or not wise is both creative and not calm and vice versa.
Everyone who is not kind or creative is not rich or not happy.
If lucy is both not creative and not wise then someone is both rich and not calm.
If someone is not curious or curious then someone is not tall or not happy.
If alice is wise then someone is not tall or funny and vice versa.
If someone is either not rich or kind then someone is old.
Everyone who is both tall and not patient is either rich or kind.
If fred is both creative and not humble then fred is not patient and vice versa.
Everyone who is both kind and not old is both not creative and curious.
Everyone who is patient or brave is both not wise and not kind and vice versa.
Someone is both generous and kind.
Someone is not kind.
Someone is not humble.
Someone is happy or funny.
Someone is happy or not rich.
Mary is calm.
Someone is not generous.
John is curious. | Susan is not old. | entailment | (((~old(susan)<~>quiet(susan)))<=>(?[X]:((quiet(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((kind(fred)<~>~generous(fred)))=>(patient(mary)))&
(![X]:(~calm(X)=>(tall(X)&wise(X))))&
(![X]:(old(X)=>(creative(X)&funny(X))))&
(![X]:((patient(X)&tall(X))<=>~happy(X)))&
(![X]:((~quiet(X)<~>~wise(X))<=>(creative(X)&~calm(X))))&
(![X]:((~kind(X)|creative(X))=>(~rich(X)|~happy(X))))&
(((~creative(lucy)&~wise(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~tall(X)|~happy(X)))))&
((wise(alice))<=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:((~rich(X)<~>kind(X))))=>(?[X]:(old(X))))&
(![X]:((tall(X)&~patient(X))=>(rich(X)<~>kind(X))))&
(((creative(fred)&~humble(fred)))<=>(~patient(fred)))&
(![X]:((kind(X)&~old(X))=>(~creative(X)&curious(X))))&
(![X]:((patient(X)|brave(X))<=>(~wise(X)&~kind(X))))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((happy(X)|~rich(X))))&
(calm(mary))&
(?[X]:(~generous(X)))&
(curious(john)) | ~old(susan) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7716614321307774253912267
% SZS output start Proof for 7716614321307774253912267
1. (~old(susan) <~> quiet(susan)) <=> ? [X0] : (~funny(X0) | quiet(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> calm(X0)) [input p1]
4. ! [X0] : (~calm(X0) => (wise(X0) & tall(X0))) [input p3]
5. ! [X0] : (old(X0) => (funny(X0) & creative(X0))) [input p4]
7. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (~calm(X0) & creative(X0))) [input p6]
11. wise(alice) <=> ? [X0] : (funny(X0) | ~tall(X0)) [input p10]
25. old(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & tall(X0)) | calm(X0)) [ennf transformation 4]
30. ! [X0] : ((funny(X0) & creative(X0)) | ~old(X0)) [ennf transformation 5]
41. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X0] : (~funny(X0) | quiet(X0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [nnf transformation 1]
42. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & (? [X1] : (~funny(X1) | quiet(X1)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [rectify 41]
43. ? [X1] : (~funny(X1) | quiet(X1)) => (~funny(sK0) | quiet(sK0)) [choice axiom]
44. (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (funny(X0) & ~quiet(X0))) & ((~funny(sK0) | quiet(sK0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) [skolemisation 42,43]
45. ! [X0] : ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))) [nnf transformation 2]
49. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 7]
50. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [flattening 49]
56. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & (? [X0] : (funny(X0) | ~tall(X0)) | ~wise(alice)) [nnf transformation 11]
57. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & (? [X1] : (funny(X1) | ~tall(X1)) | ~wise(alice)) [rectify 56]
58. ? [X1] : (funny(X1) | ~tall(X1)) => (funny(sK3) | ~tall(sK3)) [choice axiom]
59. (wise(alice) | ! [X0] : (~funny(X0) & tall(X0))) & ((funny(sK3) | ~tall(sK3)) | ~wise(alice)) [skolemisation 57,58]
83. quiet(susan) | ~old(susan) | ~quiet(X0) [cnf transformation 44]
84. quiet(susan) | ~old(susan) | funny(X0) [cnf transformation 44]
87. calm(X0) | quiet(X0) [cnf transformation 45]
88. ~calm(X0) | ~quiet(X0) [cnf transformation 45]
92. wise(X0) | calm(X0) [cnf transformation 29]
93. ~old(X0) | creative(X0) [cnf transformation 30]
100. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 50]
102. ~wise(X0) | ~quiet(X0) | calm(X0) | ~creative(X0) [cnf transformation 50]
112. wise(alice) | ~funny(X0) [cnf transformation 59]
136. old(susan) [cnf transformation 25]
138. 1 <=> ! [X0] : funny(X0) [avatar definition]
139. funny(X0) <- (1) [avatar component clause 138]
141. 2 <=> old(susan) [avatar definition]
143. old(susan) <- (2) [avatar component clause 141]
145. 3 <=> quiet(susan) [avatar definition]
150. 4 <=> ! [X0] : ~quiet(X0) [avatar definition]
151. ~quiet(X0) <- (4) [avatar component clause 150]
153. 1 | ~2 | 3 [avatar split clause 84,145,141,138]
154. 4 | ~2 | 3 [avatar split clause 83,145,141,150]
179. ~wise(X0) | calm(X0) | ~creative(X0) [subsumption resolution 102,87]
180. ~creative(X0) | calm(X0) [subsumption resolution 179,92]
181. ~wise(X0) | ~calm(X0) [subsumption resolution 100,88]
217. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
218. ~funny(X0) <- (18) [avatar component clause 217]
220. 19 <=> wise(alice) [avatar definition]
222. wise(alice) <- (19) [avatar component clause 220]
223. 18 | 19 [avatar split clause 112,220,217]
282. 2 [avatar split clause 136,141]
287. creative(susan) <- (2) [resolution 93,143]
299. calm(susan) <- (2) [resolution 180,287]
302. ~calm(alice) <- (19) [resolution 181,222]
304. quiet(alice) <- (19) [resolution 302,87]
320. ~quiet(susan) <- (2) [resolution 299,88]
323. ~3 | ~2 [avatar split clause 320,141,145]
352. $false <- (4, 19) [resolution 304,151]
354. ~4 | ~19 [avatar contradiction clause 352]
355. $false <- (1, 18) [subsumption resolution 218,139]
356. ~1 | ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 153,154,223,282,323,354,356]
% SZS output end Proof for 7716614321307774253912267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is either not funny or happy and vice versa.
Everyone who is not tall or not quiet is generous and vice versa.
Everyone who is not funny or not strong is wise and vice versa.
Everyone who is either not humble or happy is not generous.
Everyone who is both not curious and not kind is both not humble and not happy and vice versa.
Everyone who is not humble is kind.
If mary is not humble or calm then john is curious.
Everyone who is both patient and wise is both kind and calm.
If someone is both brave and not patient then susan is generous or not generous and vice versa.
If john is not rich then someone is creative and vice versa.
If john is not wise or generous then paul is either generous or not generous and vice versa.
Everyone who is strong is both tall and not generous and vice versa.
Everyone who is either not creative or old is both not tall and patient and vice versa.
Everyone who is quiet or not quiet is either not rich or old and vice versa.
If lucy is not creative then alice is curious or generous.
Everyone who is quiet or not old is not patient or not strong.
Fred is funny.
Someone is both generous and not quiet.
Someone is either quiet or not strong.
Lucy is not strong or calm.
Someone is either calm or curious.
Lucy is strong or not generous.
Susan is generous. | Mary is not wise. | neutral | (![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~funny(X)|~strong(X))<=>wise(X)))&
(![X]:((~humble(X)<~>happy(X))=>~generous(X)))&
(![X]:((~curious(X)&~kind(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~humble(mary)|calm(mary)))=>(curious(john)))&
(![X]:((patient(X)&wise(X))=>(kind(X)&calm(X))))&
((?[X]:((brave(X)&~patient(X))))<=>((generous(susan)|~generous(susan))))&
((~rich(john))<=>(?[X]:(creative(X))))&
(((~wise(john)|generous(john)))<=>((generous(paul)<~>~generous(paul))))&
(![X]:(strong(X)<=>(tall(X)&~generous(X))))&
(![X]:((~creative(X)<~>old(X))<=>(~tall(X)&patient(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)<~>old(X))))&
((~creative(lucy))=>((curious(alice)|generous(alice))))&
(![X]:((quiet(X)|~old(X))=>(~patient(X)|~strong(X))))&
(funny(fred))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
((~strong(lucy)|calm(lucy)))&
(?[X]:((calm(X)<~>curious(X))))&
((strong(lucy)|~generous(lucy)))&
(generous(susan)) | ~wise(mary) | [] | null | 0 |
If someone is both not humble and humble then alice is either not generous or not happy. Everyone who is funny or not brave is either not brave or not funny and vice versa. If someone is calm or brave then fred is either happy or not quiet and vice versa. If someone is both not funny and creative then someone is either not happy or old. If someone is wise then paul is either generous or not calm. Everyone who is both not kind and not brave is rich. If susan is patient then someone is both not happy and funny. If someone is both not strong and patient then someone is both generous and not tall and vice versa. Everyone who is calm or tall is not creative and vice versa. Everyone who is not patient or not generous is both not brave and not humble and vice versa. Everyone who is either creative or not wise is either not patient or strong. Everyone who is calm or not creative is either not creative or wise and vice versa. Everyone who is both not humble and quiet is not funny or curious. If susan is not rich or old then someone is not generous and vice versa. Everyone who is both humble and rich is not patient or not funny and vice versa. If alice is not creative then someone is not generous or generous. Someone is brave or tall. Someone is not generous. Someone is either calm or funny. Someone is not happy. Fred is not tall. Someone is either not happy or not kind. Someone is either happy or funny. | Alice is not patient. | contradiction | ((?[X]:((~humble(X)&humble(X))))=>((~generous(alice)<~>~happy(alice))))&
(![X]:((funny(X)|~brave(X))<=>(~brave(X)<~>~funny(X))))&
((?[X]:((calm(X)|brave(X))))<=>((happy(fred)<~>~quiet(fred))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
((?[X]:(wise(X)))=>((generous(paul)<~>~calm(paul))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((patient(susan))=>(?[X]:((~happy(X)&funny(X)))))&
((?[X]:((~strong(X)&patient(X))))<=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((calm(X)|tall(X))<=>~creative(X)))&
(![X]:((~patient(X)|~generous(X))<=>(~brave(X)&~humble(X))))&
(![X]:((creative(X)<~>~wise(X))=>(~patient(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~humble(X)&quiet(X))=>(~funny(X)|curious(X))))&
(((~rich(susan)|old(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)&rich(X))<=>(~patient(X)|~funny(X))))&
((~creative(alice))=>(?[X]:((~generous(X)|generous(X)))))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(~tall(fred))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((happy(X)<~>funny(X)))) | ~patient(alice) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1704308048005067999572501
% SZS output start Proof for 1704308048005067999572501
10. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~humble(X0) & ~brave(X0))) [input p9]
15. ! [X0] : ((rich(X0) & humble(X0)) <=> (~funny(X0) | ~patient(X0))) [input p14]
24. ~patient(alice) [input hypothesis]
57. ! [X0] : (((~generous(X0) | ~patient(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 10]
58. ! [X0] : ((~generous(X0) | ~patient(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | (generous(X0) & patient(X0)))) [flattening 57]
67. ! [X0] : (((rich(X0) & humble(X0)) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 15]
68. ! [X0] : (((rich(X0) & humble(X0)) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~rich(X0) | ~humble(X0))) [flattening 67]
116. ~humble(X0) | patient(X0) [cnf transformation 58]
133. humble(X0) | patient(X0) [cnf transformation 68]
148. ~patient(alice) [cnf transformation 24]
249. patient(X0) [subsumption resolution 133,116]
265. $false [subsumption resolution 148,249]
% SZS output end Proof for 1704308048005067999572501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not curious then someone is either not brave or not wise and vice versa.
Everyone who is both calm and brave is strong.
Everyone who is not rich is both not brave and not humble.
If susan is either quiet or not wise then alice is not rich or strong and vice versa.
If someone is either patient or kind then someone is both not happy and happy.
Everyone who is not calm is either humble or patient and vice versa.
If someone is either humble or patient then paul is not quiet or not wise and vice versa.
Everyone who is both patient and not creative is not brave and vice versa.
If paul is either not calm or not generous then susan is funny and vice versa.
Everyone who is old is not strong.
If lucy is both strong and not curious then someone is calm or not funny.
If someone is either old or strong then lucy is both patient and not patient and vice versa.
Everyone who is not brave or humble is not brave and vice versa.
Everyone who is strong or not humble is curious or not calm and vice versa.
Everyone who is both not tall and not humble is either not curious or happy and vice versa.
Alice is not creative.
Lucy is either tall or old.
Alice is happy or rich.
Someone is not creative or not rich. | Susan is kind. | entailment | ((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((calm(X)&brave(X))=>strong(X)))&
(![X]:(~rich(X)=>(~brave(X)&~humble(X))))&
(((quiet(susan)<~>~wise(susan)))<=>((~rich(alice)|strong(alice))))&
((?[X]:((patient(X)<~>kind(X))))=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:(~calm(X)<=>(humble(X)<~>patient(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>((~quiet(paul)|~wise(paul))))&
(![X]:((patient(X)&~creative(X))<=>~brave(X)))&
(((~calm(paul)<~>~generous(paul)))<=>(funny(susan)))&
(![X]:(old(X)=>~strong(X)))&
(((strong(lucy)&~curious(lucy)))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((old(X)<~>strong(X))))<=>((patient(lucy)&~patient(lucy))))&
(![X]:((~brave(X)|humble(X))<=>~brave(X)))&
(![X]:((strong(X)|~humble(X))<=>(curious(X)|~calm(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~curious(X)<~>happy(X))))&
(~creative(alice))&
((tall(lucy)<~>old(lucy)))&
((happy(alice)|rich(alice)))&
(?[X]:((~creative(X)|~rich(X)))) | kind(susan) | [
"p1",
"p4",
"p5",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7949325296976585997949042
% SZS output start Proof for 7949325296976585997949042
2. ! [X0] : ((brave(X0) & calm(X0)) => strong(X0)) [input p1]
5. ? [X0] : (patient(X0) <~> kind(X0)) => ? [X0] : (happy(X0) & ~happy(X0)) [input p4]
6. ! [X0] : (~calm(X0) <=> (humble(X0) <~> patient(X0))) [input p5]
8. ! [X0] : ((~creative(X0) & patient(X0)) <=> ~brave(X0)) [input p7]
10. ! [X0] : (old(X0) => ~strong(X0)) [input p9]
12. ? [X0] : (old(X0) <~> strong(X0)) <=> (~patient(lucy) & patient(lucy)) [input p11]
13. ! [X0] : ((humble(X0) | ~brave(X0)) <=> ~brave(X0)) [input p12]
20. ~kind(susan) [input hypothesis]
22. ? [X0] : (patient(X0) <~> kind(X0)) => ? [X1] : (happy(X1) & ~happy(X1)) [rectify 5]
23. ! [X0] : (strong(X0) | (~brave(X0) | ~calm(X0))) [ennf transformation 2]
24. ! [X0] : (strong(X0) | ~brave(X0) | ~calm(X0)) [flattening 23]
26. ? [X1] : (happy(X1) & ~happy(X1)) | ! [X0] : (patient(X0) <=> kind(X0)) [ennf transformation 22]
27. ! [X0] : (~strong(X0) | ~old(X0)) [ennf transformation 10]
37. ? [X1] : (happy(X1) & ~happy(X1)) | ! [X0] : ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))) [nnf transformation 26]
38. ? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1))) [rectify 37]
39. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK2) & ~happy(sK2)) [choice axiom]
40. (happy(sK2) & ~happy(sK2)) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1))) [skolemisation 38,39]
41. ! [X0] : ((~calm(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | calm(X0))) [nnf transformation 6]
47. ! [X0] : (((~creative(X0) & patient(X0)) | brave(X0)) & (~brave(X0) | (creative(X0) | ~patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((~creative(X0) & patient(X0)) | brave(X0)) & (~brave(X0) | creative(X0) | ~patient(X0))) [flattening 47]
52. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (patient(lucy) | ~patient(lucy))) & ((~patient(lucy) & patient(lucy)) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [nnf transformation 12]
53. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [flattening 52]
54. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : ((old(X1) | ~strong(X1)) & (strong(X1) | ~old(X1)))) [rectify 53]
55. ? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) => ((~strong(sK5) | ~old(sK5)) & (strong(sK5) | old(sK5))) [choice axiom]
56. (((~strong(sK5) | ~old(sK5)) & (strong(sK5) | old(sK5))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : ((old(X1) | ~strong(X1)) & (strong(X1) | ~old(X1)))) [skolemisation 54,55]
57. ! [X0] : (((humble(X0) | ~brave(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) & brave(X0)))) [nnf transformation 13]
58. ! [X0] : ((humble(X0) | ~brave(X0) | brave(X0)) & (~brave(X0) | (~humble(X0) & brave(X0)))) [flattening 57]
74. ~brave(X0) | strong(X0) | ~calm(X0) [cnf transformation 24]
83. ~happy(sK2) | kind(X1) | ~patient(X1) [cnf transformation 40]
85. happy(sK2) | kind(X1) | ~patient(X1) [cnf transformation 40]
87. patient(X0) | humble(X0) | calm(X0) [cnf transformation 41]
88. ~patient(X0) | ~humble(X0) | calm(X0) [cnf transformation 41]
98. patient(X0) | brave(X0) [cnf transformation 48]
104. ~old(X0) | ~strong(X0) [cnf transformation 27]
107. patient(lucy) | old(X1) | ~strong(X1) [cnf transformation 56]
109. ~patient(lucy) | old(X1) | ~strong(X1) [cnf transformation 56]
113. ~humble(X0) | ~brave(X0) [cnf transformation 58]
130. ~kind(susan) [cnf transformation 20]
193. 14 <=> happy(sK2) [avatar definition]
198. 15 <=> ! [X1] : (kind(X1) | ~patient(X1)) [avatar definition]
199. ~patient(X1) | kind(X1) <- (15) [avatar component clause 198]
200. 15 | 14 [avatar split clause 85,193,198]
202. 15 | ~14 [avatar split clause 83,193,198]
264. ~patient(lucy) | ~strong(X1) [subsumption resolution 109,104]
266. 29 <=> ! [X1] : ~strong(X1) [avatar definition]
267. ~strong(X1) <- (29) [avatar component clause 266]
269. 30 <=> patient(lucy) [avatar definition]
272. 29 | ~30 [avatar split clause 264,269,266]
278. patient(lucy) | ~strong(X1) [subsumption resolution 107,104]
279. 29 | 30 [avatar split clause 278,269,266]
315. kind(X0) | brave(X0) <- (15) [resolution 199,98]
320. kind(X0) | calm(X0) | humble(X0) <- (15) [resolution 87,199]
322. ~humble(X1) | calm(X1) | brave(X1) [resolution 88,98]
325. ~humble(X1) | calm(X1) [subsumption resolution 322,113]
326. brave(susan) <- (15) [resolution 315,130]
328. strong(susan) | ~calm(susan) <- (15) [resolution 326,74]
330. ~calm(susan) <- (15, 29) [subsumption resolution 328,267]
359. calm(susan) | humble(susan) <- (15) [resolution 320,130]
361. humble(susan) <- (15, 29) [subsumption resolution 359,330]
368. calm(susan) <- (15, 29) [resolution 361,325]
376. $false <- (15, 29) [subsumption resolution 368,330]
377. ~15 | ~29 [avatar contradiction clause 376]
378. $false [avatar sat refutation 200,202,272,279,377]
% SZS output end Proof for 7949325296976585997949042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not creative is both not quiet and not funny and vice versa. Everyone who is not kind is either not old or not brave and vice versa. Everyone who is happy or not patient is either not kind or not quiet. Everyone who is quiet or not funny is not creative. Everyone who is happy is kind and vice versa. Everyone who is not happy is not rich and vice versa. If someone is not rich or not old then someone is creative or not happy. If someone is not old or not patient then paul is wise. Everyone who is not creative is either not kind or quiet and vice versa. If someone is funny or not old then someone is either tall or happy. If someone is either not rich or wise then someone is not patient. Everyone who is calm is curious or generous. Everyone who is quiet or rich is either not wise or happy. Everyone who is calm is either funny or not curious and vice versa. Someone is not curious. Someone is brave or strong. Lucy is curious. Fred is calm. Susan is curious or not strong. John is not humble. | Paul is funny. | entailment | (![X]:((funny(X)&~creative(X))<=>(~quiet(X)&~funny(X))))&
(![X]:(~kind(X)<=>(~old(X)<~>~brave(X))))&
(![X]:((happy(X)|~patient(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:((quiet(X)|~funny(X))=>~creative(X)))&
(![X]:(happy(X)<=>kind(X)))&
(![X]:(~happy(X)<=>~rich(X)))&
((?[X]:((~rich(X)|~old(X))))=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~old(X)|~patient(X))))=>(wise(paul)))&
(![X]:(~creative(X)<=>(~kind(X)<~>quiet(X))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~patient(X))))&
(![X]:(calm(X)=>(curious(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)|strong(X))))&
(curious(lucy))&
(calm(fred))&
((curious(susan)|~strong(susan)))&
(~humble(john)) | funny(paul) | [
"p0",
"p2",
"p3",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 288172913076864374658118
% SZS output start Proof for 288172913076864374658118
1. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p0]
3. ! [X0] : ((~patient(X0) | happy(X0)) => (~kind(X0) <~> ~quiet(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | quiet(X0)) => ~creative(X0)) [input p3]
5. ! [X0] : (happy(X0) <=> kind(X0)) [input p4]
9. ! [X0] : (~creative(X0) <=> (~kind(X0) <~> quiet(X0))) [input p8]
21. ~funny(paul) [input hypothesis]
28. ! [X0] : ((~kind(X0) <~> ~quiet(X0)) | (patient(X0) & ~happy(X0))) [ennf transformation 3]
29. ! [X0] : (~creative(X0) | (funny(X0) & ~quiet(X0))) [ennf transformation 4]
36. ! [X0] : (((~creative(X0) & funny(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : (((~creative(X0) & funny(X0)) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | creative(X0) | ~funny(X0))) [flattening 36]
39. ! [X0] : (((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | (patient(X0) & ~happy(X0))) [nnf transformation 28]
40. ! [X0] : ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))) [nnf transformation 5]
45. ! [X0] : ((~creative(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | creative(X0))) [nnf transformation 9]
62. funny(X0) | funny(X0) | quiet(X0) [cnf transformation 37]
68. ~happy(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 39]
72. ~quiet(X0) | ~creative(X0) [cnf transformation 29]
75. ~kind(X0) | happy(X0) [cnf transformation 40]
83. ~quiet(X0) | kind(X0) | creative(X0) [cnf transformation 45]
84. ~creative(X0) | quiet(X0) | kind(X0) [cnf transformation 45]
103. ~funny(paul) [cnf transformation 21]
105. quiet(X0) | funny(X0) [duplicate literal removal 62]
131. ~creative(X0) | kind(X0) [subsumption resolution 84,72]
132. ~quiet(X0) | kind(X0) [subsumption resolution 83,131]
180. kind(X0) | funny(X0) [resolution 132,105]
181. happy(X0) | funny(X0) [resolution 180,75]
216. ~kind(X0) | ~quiet(X0) | funny(X0) [resolution 68,181]
218. ~quiet(X0) | funny(X0) [subsumption resolution 216,180]
219. funny(X0) [subsumption resolution 218,105]
264. $false [resolution 219,103]
% SZS output end Proof for 288172913076864374658118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or wise then someone is generous and vice versa.
Everyone who is both kind and funny is both funny and not happy.
Everyone who is either not quiet or strong is either creative or curious.
If paul is either not funny or old then john is both happy and funny and vice versa.
Everyone who is not rich or not funny is both kind and wise and vice versa.
If lucy is both not funny and not strong then someone is rich and vice versa.
Everyone who is patient or not strong is either not quiet or not rich.
Everyone who is creative is either tall or not generous and vice versa.
Everyone who is not calm is tall or not calm.
Everyone who is not quiet is not brave.
Everyone who is quiet is both not calm and not curious and vice versa.
Everyone who is curious is either not kind or not generous.
Everyone who is not funny or tall is either not calm or quiet.
Everyone who is not calm is not wise or brave.
If alice is either not wise or happy then mary is calm.
Everyone who is either curious or calm is not kind.
Someone is either generous or not old.
Someone is not creative or not funny.
Alice is either not patient or old.
Fred is either not funny or not creative.
Someone is either not calm or not rich.
Susan is not happy or not old.
Someone is both not generous and kind.
Someone is either happy or generous. | Fred is curious. | contradiction | (((~generous(susan)|wise(susan)))<=>(?[X]:(generous(X))))&
(![X]:((kind(X)&funny(X))=>(funny(X)&~happy(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>curious(X))))&
(((~funny(paul)<~>old(paul)))<=>((happy(john)&funny(john))))&
(![X]:((~rich(X)|~funny(X))<=>(kind(X)&wise(X))))&
(((~funny(lucy)&~strong(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((patient(X)|~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(creative(X)<=>(tall(X)<~>~generous(X))))&
(![X]:(~calm(X)=>(tall(X)|~calm(X))))&
(![X]:(~quiet(X)=>~brave(X)))&
(![X]:(quiet(X)<=>(~calm(X)&~curious(X))))&
(![X]:(curious(X)=>(~kind(X)<~>~generous(X))))&
(![X]:((~funny(X)|tall(X))=>(~calm(X)<~>quiet(X))))&
(![X]:(~calm(X)=>(~wise(X)|brave(X))))&
(((~wise(alice)<~>happy(alice)))=>(calm(mary)))&
(![X]:((curious(X)<~>calm(X))=>~kind(X)))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((~creative(X)|~funny(X))))&
((~patient(alice)<~>old(alice)))&
((~funny(fred)<~>~creative(fred)))&
(?[X]:((~calm(X)<~>~rich(X))))&
((~happy(susan)|~old(susan)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((happy(X)<~>generous(X)))) | curious(fred) | [
"p4",
"p5",
"p7",
"p10",
"p11",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7086884018212258370745275
% SZS output start Proof for 7086884018212258370745275
5. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (wise(X0) & kind(X0))) [input p4]
6. (~strong(lucy) & ~funny(lucy)) <=> ? [X0] : rich(X0) [input p5]
8. ! [X0] : (creative(X0) <=> (tall(X0) <~> ~generous(X0))) [input p7]
11. ! [X0] : (quiet(X0) <=> (~curious(X0) & ~calm(X0))) [input p10]
12. ! [X0] : (curious(X0) => (~kind(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((tall(X0) | ~funny(X0)) => (~calm(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((curious(X0) <~> calm(X0)) => ~kind(X0)) [input p15]
20. ~funny(fred) <~> ~creative(fred) [input p19]
25. curious(fred) [input hypothesis]
33. ! [X0] : ((~kind(X0) <~> ~generous(X0)) | ~curious(X0)) [ennf transformation 12]
34. ! [X0] : ((~calm(X0) <~> quiet(X0)) | (~tall(X0) & funny(X0))) [ennf transformation 13]
38. ! [X0] : (~kind(X0) | (curious(X0) <=> calm(X0))) [ennf transformation 16]
47. ! [X0] : (((~funny(X0) | ~rich(X0)) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | (funny(X0) & rich(X0)))) [nnf transformation 5]
48. ! [X0] : ((~funny(X0) | ~rich(X0) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | (funny(X0) & rich(X0)))) [flattening 47]
49. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | (strong(lucy) | funny(lucy))) [nnf transformation 6]
50. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | strong(lucy) | funny(lucy)) [flattening 49]
51. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | strong(lucy) | funny(lucy)) [rectify 50]
52. ? [X1] : rich(X1) => rich(sK1) [choice axiom]
53. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (rich(sK1) | strong(lucy) | funny(lucy)) [skolemisation 51,52]
55. ! [X0] : ((creative(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | ~creative(X0))) [nnf transformation 8]
56. ! [X0] : ((quiet(X0) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ~quiet(X0))) [nnf transformation 11]
57. ! [X0] : ((quiet(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ~quiet(X0))) [flattening 56]
58. ! [X0] : (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ~curious(X0)) [nnf transformation 33]
59. ! [X0] : (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~tall(X0) & funny(X0))) [nnf transformation 34]
61. ! [X0] : (~kind(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) [nnf transformation 38]
68. (creative(fred) | funny(fred)) & (~creative(fred) | ~funny(fred)) [nnf transformation 20]
92. rich(X0) | kind(X0) [cnf transformation 48]
93. funny(X0) | kind(X0) [cnf transformation 48]
98. ~funny(lucy) | ~rich(X0) [cnf transformation 53]
107. tall(X0) | creative(X0) | generous(X0) [cnf transformation 55]
110. ~calm(X0) | ~quiet(X0) [cnf transformation 57]
112. calm(X0) | curious(X0) | quiet(X0) [cnf transformation 57]
113. ~curious(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 58]
115. quiet(X0) | ~calm(X0) | funny(X0) [cnf transformation 59]
116. quiet(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 59]
117. ~quiet(X0) | calm(X0) | funny(X0) [cnf transformation 59]
118. ~quiet(X0) | calm(X0) | ~tall(X0) [cnf transformation 59]
122. ~curious(X0) | calm(X0) | ~kind(X0) [cnf transformation 61]
129. ~creative(fred) | ~funny(fred) [cnf transformation 68]
138. curious(fred) [cnf transformation 25]
180. 9 <=> ! [X0] : ~rich(X0) [avatar definition]
181. ~rich(X0) <- (9) [avatar component clause 180]
188. 11 <=> funny(lucy) [avatar definition]
190. ~funny(lucy) <- (~11) [avatar component clause 188]
191. 9 | ~11 [avatar split clause 98,188,180]
197. ~tall(X0) | ~quiet(X0) [subsumption resolution 118,110]
198. ~quiet(X0) | funny(X0) [subsumption resolution 117,110]
199. ~calm(X0) | ~tall(X0) [subsumption resolution 116,197]
200. ~calm(X0) | funny(X0) [subsumption resolution 115,110]
245. 22 <=> funny(fred) [avatar definition]
246. ~funny(fred) <- (~22) [avatar component clause 245]
249. 23 <=> creative(fred) [avatar definition]
253. ~22 | ~23 [avatar split clause 129,249,245]
283. kind(X0) <- (9) [resolution 92,181]
330. curious(X0) | quiet(X0) | funny(X0) [resolution 112,200]
333. curious(X0) | funny(X0) [subsumption resolution 330,198]
336. ~kind(fred) | ~generous(fred) [resolution 113,138]
338. ~generous(fred) <- (9) [subsumption resolution 336,283]
357. calm(fred) | ~kind(fred) [resolution 122,138]
358. calm(X0) | ~kind(X0) | funny(X0) [resolution 122,333]
359. calm(fred) <- (9) [subsumption resolution 357,283]
360. calm(X0) | funny(X0) <- (9) [subsumption resolution 358,283]
361. funny(X0) <- (9) [subsumption resolution 360,200]
363. ~tall(fred) <- (9) [resolution 359,199]
441. creative(fred) | generous(fred) <- (9) [resolution 363,107]
445. creative(fred) <- (9) [subsumption resolution 441,338]
446. 23 | ~9 [avatar split clause 445,180,249]
447. $false <- (9, ~22) [subsumption resolution 246,361]
448. ~9 | 22 [avatar contradiction clause 447]
490. calm(X0) | funny(X0) [subsumption resolution 358,93]
491. funny(X0) [subsumption resolution 490,200]
511. $false <- (~11) [subsumption resolution 190,491]
512. 11 [avatar contradiction clause 511]
513. $false [avatar sat refutation 191,253,446,448,512]
% SZS output end Proof for 7086884018212258370745275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is either not creative or creative.
Everyone who is either generous or not strong is either creative or not old and vice versa.
If someone is both generous and not generous then mary is calm.
Everyone who is both funny and not strong is both not quiet and not funny and vice versa.
Everyone who is not strong is both not brave and brave.
If john is not old or not calm then someone is creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
Alice is either quiet or curious.
Someone is not old or not quiet.
Someone is not rich or wise.
Lucy is either happy or not strong.
Someone is either not patient or old.
Someone is not happy or not tall. | Alice is not happy. | contradiction | (![X]:((humble(X)|~creative(X))=>(~creative(X)<~>creative(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(creative(X)<~>~old(X))))&
((?[X]:((generous(X)&~generous(X))))=>(calm(mary)))&
(![X]:((funny(X)&~strong(X))<=>(~quiet(X)&~funny(X))))&
(![X]:(~strong(X)=>(~brave(X)&brave(X))))&
(((~old(john)|~calm(john)))=>(?[X]:(creative(X))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
((quiet(alice)<~>curious(alice)))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~rich(X)|wise(X))))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((~happy(X)|~tall(X)))) | ~happy(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1140660677204599131554765
% SZS output start Proof for 1140660677204599131554765
13. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p12]
23. ~happy(alice) [input hypothesis]
54. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 13]
55. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 54]
113. happy(X0) | ~old(X0) [cnf transformation 55]
114. happy(X0) | old(X0) [cnf transformation 55]
131. ~happy(alice) [cnf transformation 23]
185. happy(X0) [subsumption resolution 113,114]
212. $false [subsumption resolution 131,185]
% SZS output end Proof for 1140660677204599131554765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or rich is both creative and generous and vice versa.
If someone is both not generous and humble then someone is either not curious or tall.
If someone is either funny or not calm then mary is curious and vice versa.
Everyone who is either tall or not quiet is both funny and happy.
If someone is not quiet or kind then someone is both quiet and tall.
Everyone who is both tall and not generous is creative.
If someone is not creative or rich then someone is both generous and tall.
If someone is either not generous or not humble then someone is wise.
If someone is either patient or creative then someone is old or calm.
Everyone who is either wise or not funny is happy and vice versa.
If someone is either not funny or not brave then someone is both happy and quiet.
Everyone who is either not tall or not generous is not curious or creative and vice versa.
If someone is either wise or not calm then lucy is not humble and vice versa.
If someone is either creative or strong then someone is both not wise and wise.
Everyone who is both not generous and not strong is not creative.
If mary is either creative or not patient then someone is both not rich and rich.
Someone is both wise and not kind.
Fred is wise.
Someone is both generous and strong.
Someone is generous or not rich.
Lucy is both not old and brave.
Someone is either humble or brave.
Someone is either not rich or wise. | Mary is not generous. | contradiction | (![X]:((quiet(X)|rich(X))<=>(creative(X)&generous(X))))&
((?[X]:((~generous(X)&humble(X))))=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:((funny(X)<~>~calm(X))))<=>(curious(mary)))&
(![X]:((tall(X)<~>~quiet(X))=>(funny(X)&happy(X))))&
((?[X]:((~quiet(X)|kind(X))))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((tall(X)&~generous(X))=>creative(X)))&
((?[X]:((~creative(X)|rich(X))))=>(?[X]:((generous(X)&tall(X)))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((old(X)|calm(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>happy(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~curious(X)|creative(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(~humble(lucy)))&
((?[X]:((creative(X)<~>strong(X))))=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((~generous(X)&~strong(X))=>~creative(X)))&
(((creative(mary)<~>~patient(mary)))=>(?[X]:((~rich(X)&rich(X)))))&
(?[X]:((wise(X)&~kind(X))))&
(wise(fred))&
(?[X]:((generous(X)&strong(X))))&
(?[X]:((generous(X)|~rich(X))))&
((~old(lucy)&brave(lucy)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((~rich(X)<~>wise(X)))) | ~generous(mary) | [
"p0",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7144573482013516653505233
% SZS output start Proof for 7144573482013516653505233
1. ! [X0] : ((rich(X0) | quiet(X0)) <=> (generous(X0) & creative(X0))) [input p0]
5. ? [X0] : (kind(X0) | ~quiet(X0)) => ? [X0] : (tall(X0) & quiet(X0)) [input p4]
12. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (creative(X0) | ~curious(X0))) [input p11]
24. ~generous(mary) [input hypothesis]
26. ? [X0] : (kind(X0) | ~quiet(X0)) => ? [X1] : (tall(X1) & quiet(X1)) [rectify 5]
33. ? [X0] : ~quiet(X0) => ? [X1] : (tall(X1) & quiet(X1)) [pure predicate removal 26]
37. ? [X1] : (tall(X1) & quiet(X1)) | ! [X0] : quiet(X0) [ennf transformation 33]
49. ! [X0] : (((rich(X0) | quiet(X0)) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | (~rich(X0) & ~quiet(X0)))) [nnf transformation 1]
50. ! [X0] : ((rich(X0) | quiet(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | (~rich(X0) & ~quiet(X0)))) [flattening 49]
60. ? [X0] : (tall(X0) & quiet(X0)) | ! [X1] : quiet(X1) [rectify 37]
61. ? [X0] : (tall(X0) & quiet(X0)) => (tall(sK2) & quiet(sK2)) [choice axiom]
62. (tall(sK2) & quiet(sK2)) | ! [X1] : quiet(X1) [skolemisation 60,61]
79. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 12]
80. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 79]
104. ~quiet(X0) | creative(X0) [cnf transformation 50]
106. ~quiet(X0) | generous(X0) [cnf transformation 50]
119. quiet(sK2) | quiet(X1) [cnf transformation 62]
120. tall(sK2) | quiet(X1) [cnf transformation 62]
139. ~tall(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 80]
166. ~generous(mary) [cnf transformation 24]
203. 9 <=> ! [X1] : quiet(X1) [avatar definition]
204. quiet(X1) <- (9) [avatar component clause 203]
206. 10 <=> tall(sK2) [avatar definition]
208. tall(sK2) <- (10) [avatar component clause 206]
209. 9 | 10 [avatar split clause 120,206,203]
211. 11 <=> quiet(sK2) [avatar definition]
213. quiet(sK2) <- (11) [avatar component clause 211]
214. 9 | 11 [avatar split clause 119,211,203]
352. creative(sK2) <- (11) [resolution 213,104]
353. generous(sK2) <- (11) [resolution 106,213]
443. ~generous(sK2) | ~creative(sK2) <- (10) [resolution 139,208]
445. ~creative(sK2) <- (10, 11) [subsumption resolution 443,353]
446. $false <- (10, 11) [subsumption resolution 445,352]
447. ~10 | ~11 [avatar contradiction clause 446]
473. generous(X0) <- (9) [resolution 204,106]
503. $false <- (9) [resolution 473,166]
507. ~9 [avatar contradiction clause 503]
508. $false [avatar sat refutation 209,214,447,507]
% SZS output end Proof for 7144573482013516653505233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both patient and not funny and vice versa. Everyone who is not patient is not humble or not rich and vice versa. Everyone who is not funny or creative is either not happy or not calm. If susan is not wise then someone is old and vice versa. If mary is both old and not patient then someone is either not funny or humble and vice versa. If mary is not old then mary is either not funny or not brave and vice versa. If someone is either not strong or kind then someone is patient. Everyone who is curious is either not calm or funny. If mary is calm or not kind then someone is not calm or strong and vice versa. If lucy is both not quiet and not calm then alice is not curious. Everyone who is generous or not calm is humble or old and vice versa. If someone is not calm then someone is not humble and vice versa. Everyone who is either curious or happy is quiet or not funny and vice versa. Everyone who is not happy or brave is either not curious or calm. Everyone who is either patient or not old is not funny. If someone is either not quiet or creative then alice is both not kind and not generous and vice versa. Someone is kind. Mary is both not happy and brave. Someone is not old or funny. Someone is not kind. Someone is either tall or not strong. Fred is strong. Mary is tall. Mary is not generous. | Susan is not curious. | entailment | (![X]:(calm(X)<=>(patient(X)&~funny(X))))&
(![X]:(~patient(X)<=>(~humble(X)|~rich(X))))&
(![X]:((~funny(X)|creative(X))=>(~happy(X)<~>~calm(X))))&
((~wise(susan))<=>(?[X]:(old(X))))&
(((old(mary)&~patient(mary)))<=>(?[X]:((~funny(X)<~>humble(X)))))&
((~old(mary))<=>((~funny(mary)<~>~brave(mary))))&
((?[X]:((~strong(X)<~>kind(X))))=>(?[X]:(patient(X))))&
(![X]:(curious(X)=>(~calm(X)<~>funny(X))))&
(((calm(mary)|~kind(mary)))<=>(?[X]:((~calm(X)|strong(X)))))&
(((~quiet(lucy)&~calm(lucy)))=>(~curious(alice)))&
(![X]:((generous(X)|~calm(X))<=>(humble(X)|old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~humble(X))))&
(![X]:((curious(X)<~>happy(X))<=>(quiet(X)|~funny(X))))&
(![X]:((~happy(X)|brave(X))=>(~curious(X)<~>calm(X))))&
(![X]:((patient(X)<~>~old(X))=>~funny(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>((~kind(alice)&~generous(alice))))&
(?[X]:(kind(X)))&
((~happy(mary)&brave(mary)))&
(?[X]:((~old(X)|funny(X))))&
(?[X]:(~kind(X)))&
(?[X]:((tall(X)<~>~strong(X))))&
(strong(fred))&
(tall(mary))&
(~generous(mary)) | ~curious(susan) | [
"p0",
"p2",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9015074158602885284947847
% SZS output start Proof for 9015074158602885284947847
1. ! [X0] : (calm(X0) <=> (~funny(X0) & patient(X0))) [input p0]
3. ! [X0] : ((creative(X0) | ~funny(X0)) => (~happy(X0) <~> ~calm(X0))) [input p2]
8. ! [X0] : (curious(X0) => (~calm(X0) <~> funny(X0))) [input p7]
13. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~funny(X0) | quiet(X0))) [input p12]
14. ! [X0] : ((brave(X0) | ~happy(X0)) => (~curious(X0) <~> calm(X0))) [input p13]
25. curious(susan) [input hypothesis]
28. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 3]
30. ! [X0] : ((~calm(X0) <~> funny(X0)) | ~curious(X0)) [ennf transformation 8]
33. ! [X0] : ((~curious(X0) <~> calm(X0)) | (~brave(X0) & happy(X0))) [ennf transformation 14]
35. ! [X0] : ((calm(X0) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 1]
36. ! [X0] : ((calm(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [flattening 35]
39. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | (~creative(X0) & funny(X0))) [nnf transformation 28]
54. ! [X0] : (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~curious(X0)) [nnf transformation 30]
67. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (funny(X0) & ~quiet(X0))) & ((~funny(X0) | quiet(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 13]
68. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (funny(X0) & ~quiet(X0))) & (~funny(X0) | quiet(X0) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [flattening 67]
69. ! [X0] : (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | (~brave(X0) & happy(X0))) [nnf transformation 33]
86. ~funny(X0) | ~calm(X0) [cnf transformation 36]
91. ~calm(X0) | ~happy(X0) | funny(X0) [cnf transformation 39]
109. funny(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 54]
110. ~funny(X0) | calm(X0) | ~curious(X0) [cnf transformation 54]
127. ~happy(X0) | ~curious(X0) | funny(X0) [cnf transformation 68]
128. calm(X0) | ~curious(X0) | happy(X0) [cnf transformation 69]
130. ~calm(X0) | curious(X0) | happy(X0) [cnf transformation 69]
150. curious(susan) [cnf transformation 25]
151. ~calm(X0) | ~happy(X0) [subsumption resolution 91,86]
217. ~funny(X0) | ~curious(X0) [subsumption resolution 110,86]
218. ~calm(X0) | ~curious(X0) [subsumption resolution 109,217]
271. ~happy(X0) | ~curious(X0) [subsumption resolution 127,217]
274. ~calm(X0) | curious(X0) [subsumption resolution 130,151]
275. ~calm(X0) [subsumption resolution 274,218]
277. ~curious(X0) | happy(X0) [subsumption resolution 128,275]
278. ~curious(X0) [subsumption resolution 277,271]
327. $false [subsumption resolution 150,278]
% SZS output end Proof for 9015074158602885284947847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and calm then someone is either not humble or not quiet and vice versa.
Everyone who is not creative is not tall and vice versa.
Everyone who is either strong or not brave is not happy and vice versa.
Everyone who is either not calm or wise is not calm.
Everyone who is rich is both not strong and happy and vice versa.
Everyone who is either not old or generous is wise and vice versa.
If mary is both strong and kind then someone is either happy or humble.
If lucy is both brave and curious then mary is not curious or not calm and vice versa.
If lucy is brave then someone is either happy or not kind and vice versa.
If alice is both kind and funny then someone is either old or patient and vice versa.
If someone is either kind or humble then susan is not kind or happy.
If john is not happy then someone is either not humble or not kind.
Everyone who is brave is not generous and vice versa.
Everyone who is both not rich and not tall is wise.
If fred is either not quiet or brave then alice is not creative or calm.
If paul is old or not happy then someone is not wise and vice versa.
Mary is either rich or brave.
Someone is either curious or humble.
John is patient.
John is both not happy and funny.
John is not strong.
Someone is both not tall and not creative.
Paul is either happy or creative.
Mary is either strong or not tall. | Susan is happy. | neutral | ((?[X]:((patient(X)&calm(X))))<=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((strong(X)<~>~brave(X))<=>~happy(X)))&
(![X]:((~calm(X)<~>wise(X))=>~calm(X)))&
(![X]:(rich(X)<=>(~strong(X)&happy(X))))&
(![X]:((~old(X)<~>generous(X))<=>wise(X)))&
(((strong(mary)&kind(mary)))=>(?[X]:((happy(X)<~>humble(X)))))&
(((brave(lucy)&curious(lucy)))<=>((~curious(mary)|~calm(mary))))&
((brave(lucy))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(((kind(alice)&funny(alice)))<=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((kind(X)<~>humble(X))))=>((~kind(susan)|happy(susan))))&
((~happy(john))=>(?[X]:((~humble(X)<~>~kind(X)))))&
(![X]:(brave(X)<=>~generous(X)))&
(![X]:((~rich(X)&~tall(X))=>wise(X)))&
(((~quiet(fred)<~>brave(fred)))=>((~creative(alice)|calm(alice))))&
(((old(paul)|~happy(paul)))<=>(?[X]:(~wise(X))))&
((rich(mary)<~>brave(mary)))&
(?[X]:((curious(X)<~>humble(X))))&
(patient(john))&
((~happy(john)&funny(john)))&
(~strong(john))&
(?[X]:((~tall(X)&~creative(X))))&
((happy(paul)<~>creative(paul)))&
((strong(mary)<~>~tall(mary))) | happy(susan) | [] | null | 0 |
Everyone who is both not funny and not curious is both not funny and happy and vice versa.
Everyone who is both not curious and not creative is brave.
Everyone who is happy or not funny is humble or brave and vice versa.
If susan is both not old and not quiet then someone is not brave or not humble and vice versa.
Everyone who is kind or not strong is either old or not wise and vice versa.
Everyone who is kind or not quiet is both not curious and not brave.
Everyone who is not quiet is both strong and not tall.
Everyone who is generous or strong is wise and vice versa.
If someone is not calm or happy then susan is not old or not quiet and vice versa.
Everyone who is either not funny or strong is not calm or not curious and vice versa.
Everyone who is humble is not curious and vice versa.
If someone is wise or not rich then someone is generous or not curious.
If mary is calm then someone is happy and vice versa.
Everyone who is either not curious or strong is either not happy or happy.
If someone is old or quiet then someone is calm or creative and vice versa.
Everyone who is not brave is either rich or not brave.
Someone is not tall.
Fred is not brave or quiet.
Susan is not rich or not funny.
Lucy is either calm or not wise.
Someone is brave or curious.
John is either not quiet or not generous.
Someone is both not rich and not creative.
Someone is not funny or strong. | Mary is not funny. | neutral | (![X]:((~funny(X)&~curious(X))<=>(~funny(X)&happy(X))))&
(![X]:((~curious(X)&~creative(X))=>brave(X)))&
(![X]:((happy(X)|~funny(X))<=>(humble(X)|brave(X))))&
(((~old(susan)&~quiet(susan)))<=>(?[X]:((~brave(X)|~humble(X)))))&
(![X]:((kind(X)|~strong(X))<=>(old(X)<~>~wise(X))))&
(![X]:((kind(X)|~quiet(X))=>(~curious(X)&~brave(X))))&
(![X]:(~quiet(X)=>(strong(X)&~tall(X))))&
(![X]:((generous(X)|strong(X))<=>wise(X)))&
((?[X]:((~calm(X)|happy(X))))<=>((~old(susan)|~quiet(susan))))&
(![X]:((~funny(X)<~>strong(X))<=>(~calm(X)|~curious(X))))&
(![X]:(humble(X)<=>~curious(X)))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((generous(X)|~curious(X)))))&
((calm(mary))<=>(?[X]:(happy(X))))&
(![X]:((~curious(X)<~>strong(X))=>(~happy(X)<~>happy(X))))&
((?[X]:((old(X)|quiet(X))))<=>(?[X]:((calm(X)|creative(X)))))&
(![X]:(~brave(X)=>(rich(X)<~>~brave(X))))&
(?[X]:(~tall(X)))&
((~brave(fred)|quiet(fred)))&
((~rich(susan)|~funny(susan)))&
((calm(lucy)<~>~wise(lucy)))&
(?[X]:((brave(X)|curious(X))))&
((~quiet(john)<~>~generous(john)))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:((~funny(X)|strong(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is not tall or not creative is generous or not generous.
Everyone who is old or quiet is both not rich and not happy and vice versa.
Everyone who is not strong is both strong and kind and vice versa.
Everyone who is not rich is both brave and not creative.
If mary is either creative or calm then alice is either not old or not tall.
Everyone who is not strong or not creative is both not quiet and not curious.
Everyone who is both kind and generous is wise or patient.
Everyone who is not humble or happy is either curious or funny.
Everyone who is both humble and calm is both happy and kind.
If someone is not calm or old then alice is either not wise or generous.
Everyone who is not funny is either rich or not calm.
Everyone who is both not calm and happy is strong and vice versa.
If someone is either kind or not wise then fred is both not rich and not patient and vice versa.
If someone is either not funny or kind then someone is both generous and not kind and vice versa.
Everyone who is either not kind or not calm is both rich and old.
Everyone who is not old or kind is humble and vice versa.
Someone is not creative.
Alice is both strong and creative.
Susan is either wise or quiet.
Mary is both patient and funny.
Someone is either brave or not old. | Susan is curious. | contradiction | (![X]:((~tall(X)|~creative(X))=>(generous(X)|~generous(X))))&
(![X]:((old(X)|quiet(X))<=>(~rich(X)&~happy(X))))&
(![X]:(~strong(X)<=>(strong(X)&kind(X))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(((creative(mary)<~>calm(mary)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~strong(X)|~creative(X))=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)&generous(X))=>(wise(X)|patient(X))))&
(![X]:((~humble(X)|happy(X))=>(curious(X)<~>funny(X))))&
(![X]:((humble(X)&calm(X))=>(happy(X)&kind(X))))&
((?[X]:((~calm(X)|old(X))))=>((~wise(alice)<~>generous(alice))))&
(![X]:(~funny(X)=>(rich(X)<~>~calm(X))))&
(![X]:((~calm(X)&happy(X))<=>strong(X)))&
((?[X]:((kind(X)<~>~wise(X))))<=>((~rich(fred)&~patient(fred))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~calm(X))=>(rich(X)&old(X))))&
(![X]:((~old(X)|kind(X))<=>humble(X)))&
(?[X]:(~creative(X)))&
((strong(alice)&creative(alice)))&
((wise(susan)<~>quiet(susan)))&
((patient(mary)&funny(mary)))&
(?[X]:((brave(X)<~>~old(X)))) | curious(susan) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7052620350678992369981630
% SZS output start Proof for 7052620350678992369981630
3. ! [X0] : (~strong(X0) <=> (kind(X0) & strong(X0))) [input p2]
4. ! [X0] : (~rich(X0) => (~creative(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) => (~curious(X0) & ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~humble(X0)) => (curious(X0) <~> funny(X0))) [input p7]
11. ! [X0] : (~funny(X0) => (rich(X0) <~> ~calm(X0))) [input p10]
12. ! [X0] : ((happy(X0) & ~calm(X0)) <=> strong(X0)) [input p11]
22. curious(susan) [input hypothesis]
26. ! [X0] : ((~creative(X0) & brave(X0)) | rich(X0)) [ennf transformation 4]
28. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (creative(X0) & strong(X0))) [ennf transformation 6]
31. ! [X0] : ((curious(X0) <~> funny(X0)) | (~happy(X0) & humble(X0))) [ennf transformation 8]
35. ! [X0] : ((rich(X0) <~> ~calm(X0)) | funny(X0)) [ennf transformation 11]
39. ! [X0] : ((~strong(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | strong(X0))) [nnf transformation 3]
40. ! [X0] : ((~strong(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | strong(X0))) [flattening 39]
42. ! [X0] : (((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | (~happy(X0) & humble(X0))) [nnf transformation 31]
44. ! [X0] : (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | funny(X0)) [nnf transformation 35]
45. ! [X0] : (((happy(X0) & ~calm(X0)) | ~strong(X0)) & (strong(X0) | (~happy(X0) | calm(X0)))) [nnf transformation 12]
46. ! [X0] : (((happy(X0) & ~calm(X0)) | ~strong(X0)) & (strong(X0) | ~happy(X0) | calm(X0))) [flattening 45]
73. strong(X0) | strong(X0) [cnf transformation 40]
77. ~creative(X0) | rich(X0) [cnf transformation 26]
85. ~curious(X0) | creative(X0) [cnf transformation 28]
90. ~funny(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 42]
98. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 44]
100. ~calm(X0) | ~strong(X0) [cnf transformation 46]
101. happy(X0) | ~strong(X0) [cnf transformation 46]
130. curious(susan) [cnf transformation 22]
131. strong(X0) [duplicate literal removal 73]
171. happy(X0) [subsumption resolution 101,131]
172. ~calm(X0) [subsumption resolution 100,131]
265. creative(susan) [resolution 85,130]
266. rich(susan) [resolution 265,77]
314. calm(susan) | funny(susan) [resolution 98,266]
317. funny(susan) [subsumption resolution 314,172]
346. ~curious(susan) | ~happy(susan) [resolution 317,90]
349. ~happy(susan) [subsumption resolution 346,130]
350. $false [subsumption resolution 349,171]
% SZS output end Proof for 7052620350678992369981630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and happy is not strong. If lucy is not calm then someone is not calm. If susan is either not quiet or patient then paul is both not quiet and strong and vice versa. Everyone who is either curious or not rich is both not old and not rich and vice versa. If someone is either not rich or not humble then fred is either humble or kind and vice versa. If mary is not generous or not brave then someone is either not wise or not old and vice versa. If fred is humble then someone is either not humble or not tall. If someone is both not quiet and tall then someone is quiet and vice versa. Everyone who is not creative is not tall or creative and vice versa. Everyone who is not quiet or not old is both not quiet and calm. Everyone who is both calm and not generous is both kind and not rich and vice versa. Everyone who is either generous or patient is both old and not old. Everyone who is curious or not funny is not brave or strong. If lucy is rich or generous then someone is either not old or not humble and vice versa. Everyone who is not humble or kind is either not curious or brave and vice versa. Someone is not curious or humble. Someone is either not curious or kind. Mary is both not tall and not quiet. Someone is both humble and rich. Mary is either kind or not tall. Mary is both not tall and not wise. Someone is curious or kind. Alice is both not happy and not old. | Alice is curious. | contradiction | (![X]:((~calm(X)&happy(X))=>~strong(X)))&
((~calm(lucy))=>(?[X]:(~calm(X))))&
(((~quiet(susan)<~>patient(susan)))<=>((~quiet(paul)&strong(paul))))&
(![X]:((curious(X)<~>~rich(X))<=>(~old(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((humble(fred)<~>kind(fred))))&
(((~generous(mary)|~brave(mary)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
((~tall(mary)&~quiet(mary)))&
(?[X]:((humble(X)&rich(X))))&
((kind(mary)<~>~tall(mary)))&
((~tall(mary)&~wise(mary)))&
(?[X]:((curious(X)|kind(X))))&
((~happy(alice)&~old(alice))) | curious(alice) | [
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7527545488095200800329114
% SZS output start Proof for 7527545488095200800329114
4. ! [X0] : ((curious(X0) <~> ~rich(X0)) <=> (~rich(X0) & ~old(X0))) [input p3]
23. ~old(alice) & ~happy(alice) [input p22]
24. curious(alice) [input hypothesis]
28. ~old(alice) [pure predicate removal 23]
39. ! [X0] : ((((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0))))) [nnf transformation 4]
40. ! [X0] : ((((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0))))) [flattening 39]
89. ~rich(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 40]
92. rich(X0) | ~curious(X0) | rich(X0) | old(X0) [cnf transformation 40]
152. ~old(alice) [cnf transformation 28]
153. curious(alice) [cnf transformation 24]
156. ~rich(X0) | ~curious(X0) [duplicate literal removal 89]
157. ~curious(X0) | rich(X0) | old(X0) [duplicate literal removal 92]
469. rich(alice) | old(alice) [resolution 157,153]
470. rich(alice) [subsumption resolution 469,152]
486. ~curious(alice) [resolution 470,156]
488. $false [subsumption resolution 486,153]
% SZS output end Proof for 7527545488095200800329114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and curious is either not funny or old and vice versa.
Everyone who is both happy and not generous is either strong or tall.
Everyone who is either kind or not humble is both not creative and creative and vice versa.
Everyone who is both humble and creative is both tall and kind and vice versa.
If john is either not brave or not kind then alice is quiet.
Everyone who is either kind or patient is creative or kind.
If someone is generous or not generous then lucy is not strong.
If paul is both curious and not brave then someone is either not humble or not strong and vice versa.
Everyone who is humble is not generous or not strong.
Everyone who is either not humble or not generous is not tall or not happy and vice versa.
If someone is either not old or not tall then lucy is either not calm or creative and vice versa.
Everyone who is not creative is not old or generous.
Everyone who is happy or rich is patient.
If someone is both brave and creative then lucy is either not tall or creative and vice versa.
Everyone who is brave or not quiet is both strong and tall.
If someone is either tall or brave then someone is tall and vice versa.
Someone is old.
Paul is either not quiet or old.
John is both not generous and not curious.
Someone is tall or brave.
Someone is not humble or quiet.
Someone is either not kind or strong.
Fred is not generous.
Someone is generous or not curious. | John is patient. | contradiction | (![X]:((brave(X)&curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((happy(X)&~generous(X))=>(strong(X)<~>tall(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~creative(X)&creative(X))))&
(![X]:((humble(X)&creative(X))<=>(tall(X)&kind(X))))&
(((~brave(john)<~>~kind(john)))=>(quiet(alice)))&
(![X]:((kind(X)<~>patient(X))=>(creative(X)|kind(X))))&
((?[X]:((generous(X)|~generous(X))))=>(~strong(lucy)))&
(((curious(paul)&~brave(paul)))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~generous(X)|~strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((~old(X)<~>~tall(X))))<=>((~calm(lucy)<~>creative(lucy))))&
(![X]:(~creative(X)=>(~old(X)|generous(X))))&
(![X]:((happy(X)|rich(X))=>patient(X)))&
((?[X]:((brave(X)&creative(X))))<=>((~tall(lucy)<~>creative(lucy))))&
(![X]:((brave(X)|~quiet(X))=>(strong(X)&tall(X))))&
((?[X]:((tall(X)<~>brave(X))))<=>(?[X]:(tall(X))))&
(?[X]:(old(X)))&
((~quiet(paul)<~>old(paul)))&
((~generous(john)&~curious(john)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
(~generous(fred))&
(?[X]:((generous(X)|~curious(X)))) | patient(john) | [
"p2",
"p3",
"p5",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7775056539703381634764213
% SZS output start Proof for 7775056539703381634764213
3. ! [X0] : ((kind(X0) <~> ~humble(X0)) <=> (creative(X0) & ~creative(X0))) [input p2]
4. ! [X0] : ((creative(X0) & humble(X0)) <=> (kind(X0) & tall(X0))) [input p3]
6. ! [X0] : ((kind(X0) <~> patient(X0)) => (kind(X0) | creative(X0))) [input p5]
10. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (~happy(X0) | ~tall(X0))) [input p9]
19. ~curious(john) & ~generous(john) [input p18]
25. patient(john) [input hypothesis]
31. ! [X0] : ((kind(X0) | creative(X0)) | (kind(X0) <=> patient(X0))) [ennf transformation 6]
32. ! [X0] : (kind(X0) | creative(X0) | (kind(X0) <=> patient(X0))) [flattening 31]
43. ! [X0] : ((((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) | creative(X0))) & ((creative(X0) & ~creative(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))))) [nnf transformation 3]
44. ! [X0] : ((((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | ~creative(X0) | creative(X0)) & ((creative(X0) & ~creative(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))))) [flattening 43]
45. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 4]
46. ! [X0] : (((creative(X0) & humble(X0)) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | ~creative(X0) | ~humble(X0))) [flattening 45]
48. ! [X0] : (kind(X0) | creative(X0) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0)))) [nnf transformation 32]
54. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 10]
55. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [flattening 54]
89. ~creative(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 44]
90. ~creative(X0) | kind(X0) | humble(X0) [cnf transformation 44]
91. ~humble(X0) | creative(X0) | ~kind(X0) [cnf transformation 44]
92. creative(X0) | kind(X0) | humble(X0) [cnf transformation 44]
96. kind(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 46]
97. humble(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 46]
102. kind(X0) | creative(X0) | kind(X0) | ~patient(X0) [cnf transformation 48]
116. humble(X0) | generous(X0) | tall(X0) [cnf transformation 55]
145. ~generous(john) [cnf transformation 19]
153. patient(john) [cnf transformation 25]
154. ~patient(X0) | creative(X0) | kind(X0) [duplicate literal removal 102]
155. humble(X0) | kind(X0) [subsumption resolution 90,92]
156. ~humble(X0) | ~kind(X0) [subsumption resolution 89,91]
157. ~kind(X0) | ~tall(X0) [subsumption resolution 97,156]
158. ~creative(X0) | ~humble(X0) [subsumption resolution 96,156]
160. 1 <=> kind(john) [avatar definition]
161. ~kind(john) <- (~1) [avatar component clause 160]
162. kind(john) <- (1) [avatar component clause 160]
408. generous(X4) | tall(X4) | ~kind(X4) [resolution 116,156]
413. ~kind(X4) | generous(X4) [subsumption resolution 408,157]
448. creative(john) | kind(john) [resolution 154,153]
449. creative(john) <- (~1) [subsumption resolution 448,161]
461. ~humble(john) <- (~1) [resolution 449,158]
590. kind(john) <- (~1) [resolution 461,155]
593. $false <- (~1) [subsumption resolution 590,161]
594. 1 [avatar contradiction clause 593]
600. generous(john) <- (1) [resolution 162,413]
603. $false <- (1) [subsumption resolution 600,145]
604. ~1 [avatar contradiction clause 603]
611. $false [avatar sat refutation 594,604]
% SZS output end Proof for 7775056539703381634764213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then susan is both generous and not rich.
Everyone who is rich or not tall is either funny or not creative.
If someone is happy or patient then someone is curious or not calm and vice versa.
Everyone who is both not brave and curious is either not curious or not quiet.
If someone is both brave and tall then paul is either creative or not tall.
Everyone who is wise is not strong and vice versa.
Everyone who is either strong or rich is both not rich and not curious and vice versa.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
Everyone who is not wise is either wise or generous and vice versa.
Everyone who is both curious and happy is strong or not brave and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Fred is happy.
Someone is rich or not old.
Someone is either calm or rich.
Someone is not patient or happy.
Someone is not calm.
Someone is not strong or not funny.
Someone is both kind and not old. | Lucy is not brave. | contradiction | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((rich(X)|~tall(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((happy(X)|patient(X))))<=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((~brave(X)&curious(X))=>(~curious(X)<~>~quiet(X))))&
((?[X]:((brave(X)&tall(X))))=>((creative(paul)<~>~tall(paul))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:(~wise(X)<=>(wise(X)<~>generous(X))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((kind(X)&~old(X)))) | ~brave(lucy) | [
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5227828417609255592787107
% SZS output start Proof for 5227828417609255592787107
11. ! [X0] : ((brave(X0) <~> generous(X0)) => (quiet(X0) & brave(X0))) [input p10]
14. ! [X0] : (~wise(X0) <=> (wise(X0) <~> generous(X0))) [input p13]
24. ~brave(lucy) [input hypothesis]
36. ! [X0] : ((quiet(X0) & brave(X0)) | (brave(X0) <=> generous(X0))) [ennf transformation 11]
54. ! [X0] : ((quiet(X0) & brave(X0)) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0)))) [nnf transformation 36]
58. ! [X0] : ((~wise(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | wise(X0))) [nnf transformation 14]
111. brave(X0) | brave(X0) | ~generous(X0) [cnf transformation 54]
122. generous(X0) | wise(X0) | wise(X0) [cnf transformation 58]
124. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 58]
142. ~brave(lucy) [cnf transformation 24]
143. generous(X0) | wise(X0) [duplicate literal removal 122]
144. ~wise(X0) | generous(X0) [duplicate literal removal 124]
145. ~generous(X0) | brave(X0) [duplicate literal removal 111]
252. generous(X0) [subsumption resolution 143,144]
317. brave(X0) [resolution 145,252]
318. $false [resolution 317,142]
% SZS output end Proof for 5227828417609255592787107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or calm is patient and vice versa.
If lucy is kind then susan is not kind.
Everyone who is calm or not curious is either not patient or tall.
If someone is either not happy or not strong then susan is both funny and kind and vice versa.
If susan is either not funny or happy then someone is either not generous or generous.
If fred is wise then john is either happy or not happy and vice versa.
Everyone who is either wise or not brave is humble or generous.
Everyone who is strong is happy.
Everyone who is either not calm or not old is not humble and vice versa.
If john is either old or not brave then lucy is both wise and kind and vice versa.
If fred is wise or not strong then paul is strong.
If someone is creative or rich then someone is either calm or not happy and vice versa.
Everyone who is either not tall or not patient is both creative and brave.
Everyone who is not wise or kind is both funny and not strong and vice versa.
If fred is funny or curious then alice is not strong or kind and vice versa.
Paul is either calm or not generous.
Someone is not wise.
Susan is either not old or old.
Lucy is not quiet.
John is not wise.
Lucy is calm.
Someone is not strong. | Fred is creative. | neutral | (![X]:((~curious(X)|calm(X))<=>patient(X)))&
((kind(lucy))=>(~kind(susan)))&
(![X]:((calm(X)|~curious(X))=>(~patient(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>~strong(X))))<=>((funny(susan)&kind(susan))))&
(((~funny(susan)<~>happy(susan)))=>(?[X]:((~generous(X)<~>generous(X)))))&
((wise(fred))<=>((happy(john)<~>~happy(john))))&
(![X]:((wise(X)<~>~brave(X))=>(humble(X)|generous(X))))&
(![X]:(strong(X)=>happy(X)))&
(![X]:((~calm(X)<~>~old(X))<=>~humble(X)))&
(((old(john)<~>~brave(john)))<=>((wise(lucy)&kind(lucy))))&
(((wise(fred)|~strong(fred)))=>(strong(paul)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>(creative(X)&brave(X))))&
(![X]:((~wise(X)|kind(X))<=>(funny(X)&~strong(X))))&
(((funny(fred)|curious(fred)))<=>((~strong(alice)|kind(alice))))&
((calm(paul)<~>~generous(paul)))&
(?[X]:(~wise(X)))&
((~old(susan)<~>old(susan)))&
(~quiet(lucy))&
(~wise(john))&
(calm(lucy))&
(?[X]:(~strong(X))) | creative(fred) | [] | null | 0 |
Everyone who is either tall or not old is humble or wise.
Everyone who is either curious or generous is both not wise and humble.
Everyone who is both funny and not old is both not creative and generous.
Everyone who is either not tall or not patient is both patient and not creative.
Everyone who is both not strong and quiet is wise and vice versa.
Everyone who is not creative or not brave is either creative or not brave and vice versa.
If fred is either not kind or patient then someone is either not curious or not kind.
If lucy is not tall then someone is curious.
If susan is both not tall and not old then fred is strong or curious and vice versa.
Everyone who is not creative or brave is either creative or not happy and vice versa.
Everyone who is old is both not wise and not curious.
If someone is both not quiet and not brave then mary is both not tall and not quiet and vice versa.
Everyone who is either not old or curious is either wise or not quiet and vice versa.
Everyone who is both not funny and old is both patient and funny.
Everyone who is both brave and funny is both not humble and curious.
If someone is not calm or not generous then mary is not rich or not creative and vice versa.
Fred is not rich.
John is not calm.
Someone is both kind and generous.
Someone is both old and kind.
Someone is either not curious or calm.
Alice is either creative or funny. | John is generous. | neutral | (![X]:((tall(X)<~>~old(X))=>(humble(X)|wise(X))))&
(![X]:((curious(X)<~>generous(X))=>(~wise(X)&humble(X))))&
(![X]:((funny(X)&~old(X))=>(~creative(X)&generous(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(patient(X)&~creative(X))))&
(![X]:((~strong(X)&quiet(X))<=>wise(X)))&
(![X]:((~creative(X)|~brave(X))<=>(creative(X)<~>~brave(X))))&
(((~kind(fred)<~>patient(fred)))=>(?[X]:((~curious(X)<~>~kind(X)))))&
((~tall(lucy))=>(?[X]:(curious(X))))&
(((~tall(susan)&~old(susan)))<=>((strong(fred)|curious(fred))))&
(![X]:((~creative(X)|brave(X))<=>(creative(X)<~>~happy(X))))&
(![X]:(old(X)=>(~wise(X)&~curious(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>((~tall(mary)&~quiet(mary))))&
(![X]:((~old(X)<~>curious(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~funny(X)&old(X))=>(patient(X)&funny(X))))&
(![X]:((brave(X)&funny(X))=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~rich(mary)|~creative(mary))))&
(~rich(fred))&
(~calm(john))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((old(X)&kind(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
((creative(alice)<~>funny(alice))) | generous(john) | [] | null | 0 |
If alice is rich then lucy is either strong or not kind.
If paul is rich then someone is either strong or not happy and vice versa.
Everyone who is not curious or not generous is generous and vice versa.
Everyone who is both not kind and not strong is not creative or wise.
Everyone who is humble is quiet.
If lucy is calm or strong then someone is either curious or not wise.
Everyone who is not happy or not tall is both happy and rich.
Everyone who is not brave or generous is both patient and calm.
If paul is old or not rich then alice is both not patient and not quiet.
Everyone who is old is either not curious or rich.
Everyone who is not humble or creative is both not brave and not kind and vice versa.
If mary is both wise and not creative then mary is patient or not calm and vice versa.
If someone is both creative and not wise then fred is patient.
If someone is both quiet and not happy then alice is not old.
If mary is humble then mary is both generous and strong and vice versa.
Someone is not brave.
Someone is not kind or not wise.
John is not calm or calm.
Alice is not generous or creative.
Susan is creative or brave.
Someone is patient.
Someone is both patient and not old.
Paul is both patient and strong. | Susan is not calm. | contradiction | ((rich(alice))=>((strong(lucy)<~>~kind(lucy))))&
((rich(paul))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((~curious(X)|~generous(X))<=>generous(X)))&
(![X]:((~kind(X)&~strong(X))=>(~creative(X)|wise(X))))&
(![X]:(humble(X)=>quiet(X)))&
(((calm(lucy)|strong(lucy)))=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((~happy(X)|~tall(X))=>(happy(X)&rich(X))))&
(![X]:((~brave(X)|generous(X))=>(patient(X)&calm(X))))&
(((old(paul)|~rich(paul)))=>((~patient(alice)&~quiet(alice))))&
(![X]:(old(X)=>(~curious(X)<~>rich(X))))&
(![X]:((~humble(X)|creative(X))<=>(~brave(X)&~kind(X))))&
(((wise(mary)&~creative(mary)))<=>((patient(mary)|~calm(mary))))&
((?[X]:((creative(X)&~wise(X))))=>(patient(fred)))&
((?[X]:((quiet(X)&~happy(X))))=>(~old(alice)))&
((humble(mary))<=>((generous(mary)&strong(mary))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~wise(X))))&
((~calm(john)|calm(john)))&
((~generous(alice)|creative(alice)))&
((creative(susan)|brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)&~old(X))))&
((patient(paul)&strong(paul))) | ~calm(susan) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 35044833690684853663275
% SZS output start Proof for 35044833690684853663275
3. ! [X0] : ((~generous(X0) | ~curious(X0)) <=> generous(X0)) [input p2]
8. ! [X0] : ((generous(X0) | ~brave(X0)) => (calm(X0) & patient(X0))) [input p7]
24. ~calm(susan) [input hypothesis]
36. ! [X0] : ((calm(X0) & patient(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 8]
44. ! [X0] : (((~generous(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & curious(X0)))) [nnf transformation 3]
45. ! [X0] : ((~generous(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & curious(X0)))) [flattening 44]
70. generous(X0) | generous(X0) [cnf transformation 45]
83. calm(X0) | ~generous(X0) [cnf transformation 36]
109. ~calm(susan) [cnf transformation 24]
111. generous(X0) [duplicate literal removal 70]
165. calm(X0) [subsumption resolution 83,111]
206. $false [subsumption resolution 109,165]
% SZS output end Proof for 35044833690684853663275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or rich is either not generous or wise and vice versa. Everyone who is either not kind or old is humble or not humble. Everyone who is both not creative and not generous is not funny and vice versa. Everyone who is either not rich or patient is both funny and not quiet. Everyone who is either not tall or not wise is both wise and not tall and vice versa. Everyone who is either kind or not happy is either curious or not patient and vice versa. Everyone who is old or not funny is not brave. Everyone who is either not kind or quiet is not calm or tall. If mary is not humble or happy then someone is tall or wise and vice versa. Everyone who is brave is curious. Everyone who is either curious or not old is both not strong and not humble and vice versa. Everyone who is both wise and not funny is either strong or wise and vice versa. Everyone who is both old and brave is rich or not strong. Everyone who is not humble is either not rich or not kind. Everyone who is rich is either not brave or not curious. Everyone who is not strong is not old and vice versa. Someone is not humble or rich. Mary is not curious. Fred is either not creative or not funny. Someone is both not old and tall. Mary is both not calm and not generous. Someone is either not happy or humble. Susan is not old. | Fred is not patient. | neutral | (![X]:((brave(X)|rich(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~kind(X)<~>old(X))=>(humble(X)|~humble(X))))&
(![X]:((~creative(X)&~generous(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)&~quiet(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(wise(X)&~tall(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((old(X)|~funny(X))=>~brave(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~calm(X)|tall(X))))&
(((~humble(mary)|happy(mary)))<=>(?[X]:((tall(X)|wise(X)))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((curious(X)<~>~old(X))<=>(~strong(X)&~humble(X))))&
(![X]:((wise(X)&~funny(X))<=>(strong(X)<~>wise(X))))&
(![X]:((old(X)&brave(X))=>(rich(X)|~strong(X))))&
(![X]:(~humble(X)=>(~rich(X)<~>~kind(X))))&
(![X]:(rich(X)=>(~brave(X)<~>~curious(X))))&
(![X]:(~strong(X)<=>~old(X)))&
(?[X]:((~humble(X)|rich(X))))&
(~curious(mary))&
((~creative(fred)<~>~funny(fred)))&
(?[X]:((~old(X)&tall(X))))&
((~calm(mary)&~generous(mary)))&
(?[X]:((~happy(X)<~>humble(X))))&
(~old(susan)) | ~patient(fred) | [] | null | 0 |
Everyone who is both patient and not funny is not rich or rich and vice versa.
Everyone who is not creative or not quiet is either not calm or funny and vice versa.
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
Mary is generous.
Someone is kind or strong.
Lucy is not tall or not rich.
Mary is tall.
Fred is generous.
Alice is calm or strong. | Fred is quiet. | entailment | (![X]:((patient(X)&~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(~calm(X)<~>funny(X))))&
(![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
(generous(mary))&
(?[X]:((kind(X)|strong(X))))&
((~tall(lucy)|~rich(lucy)))&
(tall(mary))&
(generous(fred))&
((calm(alice)|strong(alice))) | quiet(fred) | [
"p0",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6215241071136391122123623
% SZS output start Proof for 6215241071136391122123623
1. ! [X0] : ((~funny(X0) & patient(X0)) <=> (rich(X0) | ~rich(X0))) [input p0]
4. ! [X0] : ((curious(X0) | ~curious(X0)) <=> generous(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p6]
21. ~quiet(fred) [input hypothesis]
24. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 6]
29. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 1]
30. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | funny(X0) | ~patient(X0))) [flattening 29]
33. ! [X0] : (((curious(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 4]
34. ! [X0] : ((curious(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [flattening 33]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 7]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | funny(X0) | patient(X0))) [flattening 36]
59. patient(X0) | rich(X0) [cnf transformation 30]
60. ~rich(X0) | patient(X0) [cnf transformation 30]
71. generous(X0) | curious(X0) [cnf transformation 34]
72. ~curious(X0) | generous(X0) [cnf transformation 34]
79. ~curious(X0) | quiet(X0) [cnf transformation 24]
82. ~patient(X0) | ~generous(X0) | curious(X0) [cnf transformation 37]
113. ~quiet(fred) [cnf transformation 21]
115. patient(X0) [subsumption resolution 59,60]
119. generous(X0) [subsumption resolution 71,72]
120. ~generous(X0) | curious(X0) [subsumption resolution 82,115]
121. curious(X0) [subsumption resolution 120,119]
197. quiet(X0) [resolution 79,121]
199. $false [resolution 197,113]
% SZS output end Proof for 6215241071136391122123623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or calm then susan is generous or happy. Everyone who is both not humble and patient is both not happy and strong and vice versa. Everyone who is not patient is both not funny and strong. If someone is either patient or not curious then someone is kind and vice versa. If someone is either not old or not funny then fred is either not creative or not rich. Everyone who is either rich or not rich is not creative and vice versa. If susan is patient then someone is funny or not creative. If someone is either curious or funny then someone is both not kind and happy. Everyone who is both curious and rich is not funny or not creative and vice versa. If john is brave or old then john is both not strong and kind and vice versa. If mary is either creative or not quiet then lucy is both generous and not calm and vice versa. Everyone who is either creative or not quiet is both brave and not funny and vice versa. If someone is both tall and not patient then someone is both not rich and not quiet and vice versa. Everyone who is funny is not brave and vice versa. Everyone who is not wise or curious is kind. Everyone who is not humble or curious is generous. Someone is not humble or calm. Alice is not tall. Someone is not brave. Someone is both humble and calm. Alice is either not humble or not calm. Fred is both curious and generous. Someone is not old. Someone is both not brave and not old. | Susan is not generous. | contradiction | ((?[X]:((rich(X)|calm(X))))=>((generous(susan)|happy(susan))))&
(![X]:((~humble(X)&patient(X))<=>(~happy(X)&strong(X))))&
(![X]:(~patient(X)=>(~funny(X)&strong(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~creative(fred)<~>~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>~creative(X)))&
((patient(susan))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:((curious(X)<~>funny(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((curious(X)&rich(X))<=>(~funny(X)|~creative(X))))&
(((brave(john)|old(john)))<=>((~strong(john)&kind(john))))&
(((creative(mary)<~>~quiet(mary)))<=>((generous(lucy)&~calm(lucy))))&
(![X]:((creative(X)<~>~quiet(X))<=>(brave(X)&~funny(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:(funny(X)<=>~brave(X)))&
(![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(?[X]:((~humble(X)|calm(X))))&
(~tall(alice))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)&calm(X))))&
((~humble(alice)<~>~calm(alice)))&
((curious(fred)&generous(fred)))&
(?[X]:(~old(X)))&
(?[X]:((~brave(X)&~old(X)))) | ~generous(susan) | [
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 21704427698333922589136
% SZS output start Proof for 21704427698333922589136
6. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> ~creative(X0)) [input p5]
9. ! [X0] : ((rich(X0) & curious(X0)) <=> (~creative(X0) | ~funny(X0))) [input p8]
16. ! [X0] : ((curious(X0) | ~humble(X0)) => generous(X0)) [input p15]
25. ~generous(susan) [input hypothesis]
37. ! [X0] : (generous(X0) | (~curious(X0) & humble(X0))) [ennf transformation 16]
46. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | creative(X0)) & (~creative(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 6]
53. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~rich(X0) | ~curious(X0)))) [nnf transformation 9]
54. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~rich(X0) | ~curious(X0))) [flattening 53]
94. ~creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
95. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 46]
105. curious(X0) | creative(X0) [cnf transformation 54]
133. generous(X0) | ~curious(X0) [cnf transformation 37]
146. ~generous(susan) [cnf transformation 25]
147. ~creative(X0) | ~rich(X0) [duplicate literal removal 94]
148. ~creative(X0) | rich(X0) [duplicate literal removal 95]
208. ~creative(X0) [subsumption resolution 147,148]
228. curious(X0) [subsumption resolution 105,208]
282. generous(X0) [subsumption resolution 133,228]
302. $false [subsumption resolution 146,282]
% SZS output end Proof for 21704427698333922589136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not calm or old and vice versa. If someone is not creative then paul is either generous or not strong and vice versa. Everyone who is both not wise and creative is either not strong or not brave and vice versa. Everyone who is old is either generous or calm. Everyone who is patient is happy and vice versa. Everyone who is creative is not old. If john is both patient and not tall then someone is both humble and kind and vice versa. Everyone who is not funny is creative. Everyone who is either humble or calm is either kind or not kind. If someone is either not creative or humble then paul is not kind and vice versa. Everyone who is either not curious or not creative is curious or not wise. Everyone who is not curious or strong is either funny or quiet. Everyone who is kind is either tall or not creative and vice versa. Everyone who is tall is happy. If john is either not calm or creative then mary is kind. If lucy is funny or curious then someone is not curious and vice versa. Mary is both not curious and generous. Someone is generous. Someone is either not tall or calm. Lucy is not strong. Someone is either not generous or wise. Someone is either calm or not generous. Someone is old or not tall. Paul is brave. | John is not tall. | neutral | (![X]:(~creative(X)<=>(~calm(X)|old(X))))&
((?[X]:(~creative(X)))<=>((generous(paul)<~>~strong(paul))))&
(![X]:((~wise(X)&creative(X))<=>(~strong(X)<~>~brave(X))))&
(![X]:(old(X)=>(generous(X)<~>calm(X))))&
(![X]:(patient(X)<=>happy(X)))&
(![X]:(creative(X)=>~old(X)))&
(((patient(john)&~tall(john)))<=>(?[X]:((humble(X)&kind(X)))))&
(![X]:(~funny(X)=>creative(X)))&
(![X]:((humble(X)<~>calm(X))=>(kind(X)<~>~kind(X))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(~kind(paul)))&
(![X]:((~curious(X)<~>~creative(X))=>(curious(X)|~wise(X))))&
(![X]:((~curious(X)|strong(X))=>(funny(X)<~>quiet(X))))&
(![X]:(kind(X)<=>(tall(X)<~>~creative(X))))&
(![X]:(tall(X)=>happy(X)))&
(((~calm(john)<~>creative(john)))=>(kind(mary)))&
(((funny(lucy)|curious(lucy)))<=>(?[X]:(~curious(X))))&
((~curious(mary)&generous(mary)))&
(?[X]:(generous(X)))&
(?[X]:((~tall(X)<~>calm(X))))&
(~strong(lucy))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
(?[X]:((old(X)|~tall(X))))&
(brave(paul)) | ~tall(john) | [] | null | 0 |
If paul is not patient then someone is both wise and not calm and vice versa.
Everyone who is not brave is either brave or happy and vice versa.
Everyone who is not creative or not quiet is both not humble and not funny.
Everyone who is either creative or kind is both not calm and old and vice versa.
Everyone who is calm is not funny.
Everyone who is either old or not calm is both rich and old and vice versa.
Everyone who is not curious is either happy or calm.
Everyone who is both old and patient is either tall or not patient and vice versa.
If paul is generous then fred is not happy or kind and vice versa.
If fred is humble then alice is not funny.
If someone is strong or not wise then susan is not wise or tall and vice versa.
Everyone who is both quiet and happy is either not humble or patient.
If lucy is rich then someone is both old and not humble.
Everyone who is both not creative and happy is brave.
Everyone who is creative is either patient or humble and vice versa.
Everyone who is either rich or not calm is wise.
Mary is either not curious or curious.
Fred is patient.
Someone is both creative and not generous.
John is either kind or not tall.
Someone is not kind.
Paul is either patient or not happy.
Alice is curious or happy. | Alice is not curious. | contradiction | ((~patient(paul))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:(~brave(X)<=>(brave(X)<~>happy(X))))&
(![X]:((~creative(X)|~quiet(X))=>(~humble(X)&~funny(X))))&
(![X]:((creative(X)<~>kind(X))<=>(~calm(X)&old(X))))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:((old(X)<~>~calm(X))<=>(rich(X)&old(X))))&
(![X]:(~curious(X)=>(happy(X)<~>calm(X))))&
(![X]:((old(X)&patient(X))<=>(tall(X)<~>~patient(X))))&
((generous(paul))<=>((~happy(fred)|kind(fred))))&
((humble(fred))=>(~funny(alice)))&
((?[X]:((strong(X)|~wise(X))))<=>((~wise(susan)|tall(susan))))&
(![X]:((quiet(X)&happy(X))=>(~humble(X)<~>patient(X))))&
((rich(lucy))=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((~creative(X)&happy(X))=>brave(X)))&
(![X]:(creative(X)<=>(patient(X)<~>humble(X))))&
(![X]:((rich(X)<~>~calm(X))=>wise(X)))&
((~curious(mary)<~>curious(mary)))&
(patient(fred))&
(?[X]:((creative(X)&~generous(X))))&
((kind(john)<~>~tall(john)))&
(?[X]:(~kind(X)))&
((patient(paul)<~>~happy(paul)))&
((curious(alice)|happy(alice))) | ~curious(alice) | [
"p0",
"p1",
"p5",
"p6",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4842710900016462341333473
% SZS output start Proof for 4842710900016462341333473
1. ~patient(paul) <=> ? [X0] : (~calm(X0) & wise(X0)) [input p0]
2. ! [X0] : (~brave(X0) <=> (brave(X0) <~> happy(X0))) [input p1]
6. ! [X0] : ((old(X0) <~> ~calm(X0)) <=> (old(X0) & rich(X0))) [input p5]
7. ! [X0] : (~curious(X0) => (happy(X0) <~> calm(X0))) [input p6]
16. ! [X0] : ((rich(X0) <~> ~calm(X0)) => wise(X0)) [input p15]
22. patient(paul) <~> ~happy(paul) [input p21]
24. ~curious(alice) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> calm(X0)) | curious(X0)) [ennf transformation 7]
35. ! [X0] : (wise(X0) | (rich(X0) <=> ~calm(X0))) [ennf transformation 16]
36. (~patient(paul) | ! [X0] : (calm(X0) | ~wise(X0))) & (? [X0] : (~calm(X0) & wise(X0)) | patient(paul)) [nnf transformation 1]
37. (~patient(paul) | ! [X0] : (calm(X0) | ~wise(X0))) & (? [X1] : (~calm(X1) & wise(X1)) | patient(paul)) [rectify 36]
38. ? [X1] : (~calm(X1) & wise(X1)) => (~calm(sK0) & wise(sK0)) [choice axiom]
39. (~patient(paul) | ! [X0] : (calm(X0) | ~wise(X0))) & ((~calm(sK0) & wise(sK0)) | patient(paul)) [skolemisation 37,38]
40. ! [X0] : ((~brave(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0)))) & (((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | brave(X0))) [nnf transformation 2]
43. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [nnf transformation 6]
44. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [flattening 43]
45. ! [X0] : (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | curious(X0)) [nnf transformation 29]
59. ! [X0] : (wise(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) [nnf transformation 35]
66. (happy(paul) | ~patient(paul)) & (~happy(paul) | patient(paul)) [nnf transformation 22]
69. ~patient(paul) | calm(X0) | ~wise(X0) [cnf transformation 39]
70. happy(X0) | brave(X0) | brave(X0) [cnf transformation 40]
72. ~brave(X0) | happy(X0) | ~brave(X0) [cnf transformation 40]
85. old(X0) | old(X0) | calm(X0) [cnf transformation 44]
87. calm(X0) | ~old(X0) | ~old(X0) | ~rich(X0) [cnf transformation 44]
89. ~calm(X0) | ~happy(X0) | curious(X0) [cnf transformation 45]
113. rich(X0) | wise(X0) | calm(X0) [cnf transformation 59]
122. ~happy(paul) | patient(paul) [cnf transformation 66]
125. ~curious(alice) [cnf transformation 24]
128. old(X0) | calm(X0) [duplicate literal removal 85]
129. ~rich(X0) | ~old(X0) | calm(X0) [duplicate literal removal 87]
130. happy(X0) | brave(X0) [duplicate literal removal 70]
131. ~brave(X0) | happy(X0) [duplicate literal removal 72]
133. 1 <=> ! [X0] : (calm(X0) | ~wise(X0)) [avatar definition]
134. ~wise(X0) | calm(X0) <- (1) [avatar component clause 133]
136. 2 <=> patient(paul) [avatar definition]
139. 1 | ~2 [avatar split clause 69,136,133]
150. happy(X0) [subsumption resolution 130,131]
151. ~calm(X0) | curious(X0) [subsumption resolution 89,150]
222. patient(paul) [subsumption resolution 122,150]
223. 2 [avatar split clause 222,136]
286. ~old(X0) | calm(X0) | wise(X0) | calm(X0) [resolution 129,113]
287. ~old(X0) | calm(X0) | wise(X0) [duplicate literal removal 286]
288. calm(X0) | wise(X0) [subsumption resolution 287,128]
289. calm(X0) <- (1) [subsumption resolution 288,134]
290. curious(X0) <- (1) [resolution 289,151]
312. $false <- (1) [resolution 290,125]
313. ~1 [avatar contradiction clause 312]
314. $false [avatar sat refutation 139,223,313]
% SZS output end Proof for 4842710900016462341333473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not old then paul is either calm or not tall. Everyone who is not creative or not old is either funny or not old and vice versa. Everyone who is both not curious and not funny is both creative and not quiet. If john is either not tall or rich then alice is not rich and vice versa. Everyone who is old is not tall. Everyone who is wise or quiet is not rich. Everyone who is either kind or generous is both tall and curious. If someone is either creative or quiet then someone is both old and tall and vice versa. If someone is not humble or wise then someone is both calm and quiet and vice versa. If susan is funny then alice is humble. If someone is both not quiet and not patient then someone is not wise. If someone is kind or not old then susan is both patient and not quiet. Everyone who is kind or not funny is both funny and tall. Everyone who is not strong or happy is both not calm and not rich and vice versa. Everyone who is either not wise or not brave is not curious. Someone is either not humble or strong. Someone is not wise. Someone is brave or not brave. Mary is not curious or tall. Someone is not quiet or not curious. Someone is not happy. Someone is not strong or brave. | Susan is not wise. | entailment | ((~old(fred))=>((calm(paul)<~>~tall(paul))))&
(![X]:((~creative(X)|~old(X))<=>(funny(X)<~>~old(X))))&
(![X]:((~curious(X)&~funny(X))=>(creative(X)&~quiet(X))))&
(((~tall(john)<~>rich(john)))<=>(~rich(alice)))&
(![X]:(old(X)=>~tall(X)))&
(![X]:((wise(X)|quiet(X))=>~rich(X)))&
(![X]:((kind(X)<~>generous(X))=>(tall(X)&curious(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((calm(X)&quiet(X)))))&
((funny(susan))=>(humble(alice)))&
((?[X]:((~quiet(X)&~patient(X))))=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|~old(X))))=>((patient(susan)&~quiet(susan))))&
(![X]:((kind(X)|~funny(X))=>(funny(X)&tall(X))))&
(![X]:((~strong(X)|happy(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~wise(X)<~>~brave(X))=>~curious(X)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~brave(X))))&
((~curious(mary)|tall(mary)))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~strong(X)|brave(X)))) | ~wise(susan) | [
"p1",
"p4",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4260632992985836434190558
% SZS output start Proof for 4260632992985836434190558
2. ! [X0] : ((~old(X0) | ~creative(X0)) <=> (funny(X0) <~> ~old(X0))) [input p1]
5. ! [X0] : (old(X0) => ~tall(X0)) [input p4]
8. ? [X0] : (creative(X0) <~> quiet(X0)) <=> ? [X0] : (tall(X0) & old(X0)) [input p7]
9. ? [X0] : (wise(X0) | ~humble(X0)) <=> ? [X0] : (quiet(X0) & calm(X0)) [input p8]
13. ! [X0] : ((~funny(X0) | kind(X0)) => (tall(X0) & funny(X0))) [input p12]
23. wise(susan) [input hypothesis]
24. ? [X0] : (creative(X0) <~> quiet(X0)) <=> ? [X1] : (tall(X1) & old(X1)) [rectify 8]
25. ? [X0] : (wise(X0) | ~humble(X0)) <=> ? [X1] : (quiet(X1) & calm(X1)) [rectify 9]
32. ! [X0] : (~tall(X0) | ~old(X0)) [ennf transformation 5]
37. ! [X0] : ((tall(X0) & funny(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 13]
40. ! [X0] : (((~old(X0) | ~creative(X0)) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) & (((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (old(X0) & creative(X0)))) [nnf transformation 2]
41. ! [X0] : ((~old(X0) | ~creative(X0) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) & (((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (old(X0) & creative(X0)))) [flattening 40]
44. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ! [X1] : (~tall(X1) | ~old(X1))) & (? [X1] : (tall(X1) & old(X1)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 24]
45. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ! [X1] : (~tall(X1) | ~old(X1))) & (? [X2] : (tall(X2) & old(X2)) | ! [X3] : ((creative(X3) | ~quiet(X3)) & (quiet(X3) | ~creative(X3)))) [rectify 44]
46. ? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) => ((~quiet(sK0) | ~creative(sK0)) & (quiet(sK0) | creative(sK0))) [choice axiom]
47. ? [X2] : (tall(X2) & old(X2)) => (tall(sK1) & old(sK1)) [choice axiom]
48. (((~quiet(sK0) | ~creative(sK0)) & (quiet(sK0) | creative(sK0))) | ! [X1] : (~tall(X1) | ~old(X1))) & ((tall(sK1) & old(sK1)) | ! [X3] : ((creative(X3) | ~quiet(X3)) & (quiet(X3) | ~creative(X3)))) [skolemisation 45,47,46]
49. (? [X0] : (wise(X0) | ~humble(X0)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & (? [X1] : (quiet(X1) & calm(X1)) | ! [X0] : (~wise(X0) & humble(X0))) [nnf transformation 25]
50. (? [X0] : (wise(X0) | ~humble(X0)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & (? [X2] : (quiet(X2) & calm(X2)) | ! [X3] : (~wise(X3) & humble(X3))) [rectify 49]
51. ? [X0] : (wise(X0) | ~humble(X0)) => (wise(sK2) | ~humble(sK2)) [choice axiom]
52. ? [X2] : (quiet(X2) & calm(X2)) => (quiet(sK3) & calm(sK3)) [choice axiom]
53. ((wise(sK2) | ~humble(sK2)) | ! [X1] : (~quiet(X1) | ~calm(X1))) & ((quiet(sK3) & calm(sK3)) | ! [X3] : (~wise(X3) & humble(X3))) [skolemisation 50,52,51]
75. old(X0) | ~funny(X0) | old(X0) [cnf transformation 41]
76. ~old(X0) | ~creative(X0) | ~old(X0) | ~funny(X0) [cnf transformation 41]
84. ~tall(X0) | ~old(X0) [cnf transformation 32]
94. tall(sK1) | creative(X3) | ~quiet(X3) [cnf transformation 48]
100. quiet(sK3) | ~wise(X3) [cnf transformation 53]
106. funny(X0) | funny(X0) [cnf transformation 37]
124. wise(susan) [cnf transformation 23]
125. funny(X0) [duplicate literal removal 106]
126. ~funny(X0) | old(X0) [duplicate literal removal 75]
127. ~funny(X0) | ~creative(X0) | ~old(X0) [duplicate literal removal 76]
159. 7 <=> ! [X3] : (creative(X3) | ~quiet(X3)) [avatar definition]
160. ~quiet(X3) | creative(X3) <- (7) [avatar component clause 159]
162. 8 <=> tall(sK1) [avatar definition]
164. tall(sK1) <- (8) [avatar component clause 162]
165. 7 | 8 [avatar split clause 94,162,159]
189. 14 <=> ! [X3] : ~wise(X3) [avatar definition]
190. ~wise(X3) <- (14) [avatar component clause 189]
192. 15 <=> quiet(sK3) [avatar definition]
194. quiet(sK3) <- (15) [avatar component clause 192]
195. 14 | 15 [avatar split clause 100,192,189]
216. 20 <=> ! [X0] : old(X0) [avatar definition]
217. old(X0) <- (20) [avatar component clause 216]
268. $false <- (14) [resolution 190,124]
269. ~14 [avatar contradiction clause 268]
275. old(X1) [resolution 126,125]
276. 20 [avatar split clause 275,216]
277. creative(sK3) <- (7, 15) [resolution 160,194]
299. ~creative(X1) | ~old(X1) [resolution 127,125]
301. ~creative(X1) <- (20) [subsumption resolution 299,217]
304. $false <- (7, 15, 20) [resolution 301,277]
305. ~7 | ~15 | ~20 [avatar contradiction clause 304]
306. ~old(sK1) <- (8) [resolution 164,84]
307. $false <- (8, 20) [subsumption resolution 306,217]
308. ~8 | ~20 [avatar contradiction clause 307]
309. $false [avatar sat refutation 165,195,269,276,305,308]
% SZS output end Proof for 4260632992985836434190558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or happy is both not creative and quiet and vice versa. If someone is not calm then someone is not wise or brave. Everyone who is kind is either not patient or tall and vice versa. Everyone who is both patient and not creative is not creative or brave. Everyone who is not quiet or rich is both happy and kind. If fred is both not tall and tall then someone is both not happy and generous. Everyone who is not brave is both not patient and not happy. Everyone who is both not strong and quiet is not calm and vice versa. If someone is brave then someone is both not tall and tall. If john is not patient or humble then someone is not humble. If alice is both generous and not wise then lucy is not quiet and vice versa. Everyone who is not tall is not calm and vice versa. If paul is both not humble and not patient then someone is strong or not quiet and vice versa. Everyone who is either rich or not funny is both not calm and calm and vice versa. If someone is both not strong and tall then someone is old. Everyone who is quiet or wise is patient or not curious. Someone is both not curious and not generous. Someone is generous or creative. John is not generous. Paul is curious or not tall. Fred is kind. Paul is calm or not tall. Fred is not curious. | Alice is happy. | contradiction | (![X]:((patient(X)|happy(X))<=>(~creative(X)&quiet(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(kind(X)<=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)&~creative(X))=>(~creative(X)|brave(X))))&
(![X]:((~quiet(X)|rich(X))=>(happy(X)&kind(X))))&
(((~tall(fred)&tall(fred)))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(~brave(X)=>(~patient(X)&~happy(X))))&
(![X]:((~strong(X)&quiet(X))<=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:((~tall(X)&tall(X)))))&
(((~patient(john)|humble(john)))=>(?[X]:(~humble(X))))&
(((generous(alice)&~wise(alice)))<=>(~quiet(lucy)))&
(![X]:(~tall(X)<=>~calm(X)))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:(old(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~curious(X))))&
(?[X]:((~curious(X)&~generous(X))))&
(?[X]:((generous(X)|creative(X))))&
(~generous(john))&
((curious(paul)|~tall(paul)))&
(kind(fred))&
((calm(paul)|~tall(paul)))&
(~curious(fred)) | happy(alice) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7034891000160274326875485
% SZS output start Proof for 7034891000160274326875485
7. ! [X0] : (~brave(X0) => (~happy(X0) & ~patient(X0))) [input p6]
9. ? [X0] : brave(X0) => ? [X0] : (tall(X0) & ~tall(X0)) [input p8]
24. happy(alice) [input hypothesis]
26. ? [X0] : brave(X0) => ? [X1] : (tall(X1) & ~tall(X1)) [rectify 9]
37. ! [X0] : ((~happy(X0) & ~patient(X0)) | brave(X0)) [ennf transformation 7]
38. ? [X1] : (tall(X1) & ~tall(X1)) | ! [X0] : ~brave(X0) [ennf transformation 26]
52. ? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : ~brave(X1) [rectify 38]
53. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK2) & ~tall(sK2)) [choice axiom]
54. (tall(sK2) & ~tall(sK2)) | ! [X1] : ~brave(X1) [skolemisation 52,53]
87. ~happy(X0) | brave(X0) [cnf transformation 37]
91. ~tall(sK2) | ~brave(X1) [cnf transformation 54]
92. tall(sK2) | ~brave(X1) [cnf transformation 54]
121. happy(alice) [cnf transformation 24]
137. 4 <=> ! [X1] : ~brave(X1) [avatar definition]
138. ~brave(X1) <- (4) [avatar component clause 137]
140. 5 <=> tall(sK2) [avatar definition]
143. 4 | 5 [avatar split clause 92,140,137]
144. 4 | ~5 [avatar split clause 91,140,137]
214. brave(alice) [resolution 87,121]
215. $false <- (4) [subsumption resolution 214,138]
216. ~4 [avatar contradiction clause 215]
217. $false [avatar sat refutation 143,144,216]
% SZS output end Proof for 7034891000160274326875485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not rich and not humble then lucy is either wise or patient and vice versa.
Everyone who is tall or not humble is not generous.
Everyone who is either not generous or old is both not kind and patient.
Everyone who is both not patient and not quiet is funny or not strong and vice versa.
Everyone who is both patient and not quiet is tall or kind.
Everyone who is either not happy or wise is both wise and brave.
If lucy is either not strong or not curious then someone is not humble or not kind and vice versa.
If someone is generous then someone is either not kind or wise.
If someone is either not funny or funny then paul is not funny or curious and vice versa.
Everyone who is either quiet or not kind is old or not kind and vice versa.
Everyone who is either quiet or not wise is both humble and not curious and vice versa.
Everyone who is not humble or not creative is either not strong or creative and vice versa.
Everyone who is either not quiet or calm is not curious or quiet.
Everyone who is both tall and happy is both creative and tall and vice versa.
Everyone who is not humble or patient is both tall and not quiet.
Everyone who is humble is happy or quiet.
Someone is either brave or not funny.
Someone is both not calm and strong.
Fred is not wise.
Someone is not generous or not rich.
Alice is either kind or not kind.
John is generous.
Someone is either not calm or strong.
Someone is not creative or not kind. | John is happy. | entailment | (((~rich(mary)&~humble(mary)))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((tall(X)|~humble(X))=>~generous(X)))&
(![X]:((~generous(X)<~>old(X))=>(~kind(X)&patient(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&~quiet(X))=>(tall(X)|kind(X))))&
(![X]:((~happy(X)<~>wise(X))=>(wise(X)&brave(X))))&
(((~strong(lucy)<~>~curious(lucy)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((~kind(X)<~>wise(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~funny(paul)|curious(paul))))&
(![X]:((quiet(X)<~>~kind(X))<=>(old(X)|~kind(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>(humble(X)&~curious(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~curious(X)|quiet(X))))&
(![X]:((tall(X)&happy(X))<=>(creative(X)&tall(X))))&
(![X]:((~humble(X)|patient(X))=>(tall(X)&~quiet(X))))&
(![X]:(humble(X)=>(happy(X)|quiet(X))))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((~calm(X)&strong(X))))&
(~wise(fred))&
(?[X]:((~generous(X)|~rich(X))))&
((kind(alice)<~>~kind(alice)))&
(generous(john))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((~creative(X)|~kind(X)))) | happy(john) | [
"p1",
"p2",
"p9",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5176068227888911086469137
% SZS output start Proof for 5176068227888911086469137
2. ! [X0] : ((~humble(X0) | tall(X0)) => ~generous(X0)) [input p1]
3. ! [X0] : ((~generous(X0) <~> old(X0)) => (patient(X0) & ~kind(X0))) [input p2]
10. ! [X0] : ((quiet(X0) <~> ~kind(X0)) <=> (~kind(X0) | old(X0))) [input p9]
16. ! [X0] : (humble(X0) => (quiet(X0) | happy(X0))) [input p15]
22. generous(john) [input p21]
25. ~happy(john) [input hypothesis]
27. ! [X0] : (~generous(X0) | (humble(X0) & ~tall(X0))) [ennf transformation 2]
28. ! [X0] : ((patient(X0) & ~kind(X0)) | (~generous(X0) <=> old(X0))) [ennf transformation 3]
36. ! [X0] : ((quiet(X0) | happy(X0)) | ~humble(X0)) [ennf transformation 16]
37. ! [X0] : (quiet(X0) | happy(X0) | ~humble(X0)) [flattening 36]
40. ! [X0] : ((patient(X0) & ~kind(X0)) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 28]
57. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (kind(X0) & ~old(X0))) & ((~kind(X0) | old(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [nnf transformation 10]
58. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (kind(X0) & ~old(X0))) & (~kind(X0) | old(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [flattening 57]
86. ~generous(X0) | humble(X0) [cnf transformation 27]
88. ~kind(X0) | ~generous(X0) | ~old(X0) [cnf transformation 40]
115. ~kind(X0) | old(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 58]
120. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 58]
143. ~humble(X0) | happy(X0) | quiet(X0) [cnf transformation 37]
152. generous(john) [cnf transformation 22]
156. ~happy(john) [cnf transformation 25]
160. ~kind(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 115]
161. ~quiet(X0) | kind(X0) [duplicate literal removal 120]
244. ~quiet(X0) | old(X0) [subsumption resolution 160,161]
284. humble(john) [resolution 86,152]
326. happy(john) | quiet(john) [resolution 143,284]
329. quiet(john) [subsumption resolution 326,156]
471. kind(john) [resolution 329,161]
472. old(john) [resolution 329,244]
519. ~generous(john) | ~old(john) [resolution 471,88]
521. ~old(john) [subsumption resolution 519,152]
522. $false [subsumption resolution 521,472]
% SZS output end Proof for 5176068227888911086469137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or brave is wise or not old and vice versa. Everyone who is either not curious or curious is not strong and vice versa. If mary is not tall or not creative then paul is wise or not funny and vice versa. Everyone who is either curious or humble is both rich and not rich. Everyone who is both wise and not calm is either not patient or not old and vice versa. If someone is not curious then someone is kind. If someone is either not calm or not tall then mary is quiet. Everyone who is creative is both patient and not strong and vice versa. Everyone who is either not quiet or not humble is both not curious and creative and vice versa. Everyone who is not humble is both happy and not quiet. Everyone who is either not kind or strong is either calm or not creative and vice versa. Everyone who is wise is both not creative and generous. Everyone who is not quiet or not wise is either not curious or curious and vice versa. If someone is both generous and not strong then fred is quiet. Everyone who is not old or not patient is both not old and not calm and vice versa. Everyone who is humble or not brave is both not patient and not generous. Paul is not strong. Paul is both rich and not tall. Someone is not old or quiet. Mary is either funny or creative. Someone is both not happy and not wise. | Fred is not humble. | contradiction | (![X]:((~old(X)|brave(X))<=>(wise(X)|~old(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~strong(X)))&
(((~tall(mary)|~creative(mary)))<=>((wise(paul)|~funny(paul))))&
(![X]:((curious(X)<~>humble(X))=>(rich(X)&~rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>~old(X))))&
((?[X]:(~curious(X)))=>(?[X]:(kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(quiet(mary)))&
(![X]:(creative(X)<=>(patient(X)&~strong(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~quiet(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(calm(X)<~>~creative(X))))&
(![X]:(wise(X)=>(~creative(X)&generous(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((generous(X)&~strong(X))))=>(quiet(fred)))&
(![X]:((~old(X)|~patient(X))<=>(~old(X)&~calm(X))))&
(![X]:((humble(X)|~brave(X))=>(~patient(X)&~generous(X))))&
(~strong(paul))&
((rich(paul)&~tall(paul)))&
(?[X]:((~old(X)|quiet(X))))&
((funny(mary)<~>creative(mary)))&
(?[X]:((~happy(X)&~wise(X)))) | ~humble(fred) | [
"p1",
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 34723742841921284688988
% SZS output start Proof for 34723742841921284688988
2. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> ~strong(X0)) [input p1]
4. ! [X0] : ((curious(X0) <~> humble(X0)) => (~rich(X0) & rich(X0))) [input p3]
6. ? [X0] : ~curious(X0) => ? [X0] : kind(X0) [input p5]
8. ! [X0] : (creative(X0) <=> (~strong(X0) & patient(X0))) [input p7]
9. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) <=> (creative(X0) & ~curious(X0))) [input p8]
10. ! [X0] : (~humble(X0) => (~quiet(X0) & happy(X0))) [input p9]
11. ! [X0] : ((~kind(X0) <~> strong(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p10]
15. ! [X0] : ((~patient(X0) | ~old(X0)) <=> (~calm(X0) & ~old(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | humble(X0)) => (~generous(X0) & ~patient(X0))) [input p15]
22. ~humble(fred) [input hypothesis]
23. ? [X0] : ~curious(X0) => ? [X1] : kind(X1) [rectify 6]
24. ! [X0] : ((~rich(X0) & rich(X0)) | (curious(X0) <=> humble(X0))) [ennf transformation 4]
25. ? [X1] : kind(X1) | ! [X0] : curious(X0) [ennf transformation 23]
27. ! [X0] : ((~quiet(X0) & happy(X0)) | humble(X0)) [ennf transformation 10]
30. ! [X0] : ((~generous(X0) & ~patient(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 16]
33. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | strong(X0)) & (~strong(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 2]
36. ! [X0] : ((~rich(X0) & rich(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 24]
39. ? [X0] : kind(X0) | ! [X1] : curious(X1) [rectify 25]
40. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
41. kind(sK0) | ! [X1] : curious(X1) [skolemisation 39,40]
43. ! [X0] : ((creative(X0) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [nnf transformation 8]
44. ! [X0] : ((creative(X0) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [flattening 43]
45. ! [X0] : ((((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | (~creative(X0) | curious(X0))) & ((creative(X0) & ~curious(X0)) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))))) [nnf transformation 9]
46. ! [X0] : ((((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | ~creative(X0) | curious(X0)) & ((creative(X0) & ~curious(X0)) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))))) [flattening 45]
47. ! [X0] : ((((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0))))) [nnf transformation 11]
50. ! [X0] : (((~patient(X0) | ~old(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (patient(X0) & old(X0)))) [nnf transformation 15]
51. ! [X0] : ((~patient(X0) | ~old(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (patient(X0) & old(X0)))) [flattening 50]
61. ~strong(X0) | curious(X0) | curious(X0) [cnf transformation 33]
62. ~strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 33]
69. rich(X0) | humble(X0) | ~curious(X0) [cnf transformation 36]
71. ~rich(X0) | humble(X0) | ~curious(X0) [cnf transformation 36]
79. kind(sK0) | curious(X1) [cnf transformation 41]
82. ~creative(X0) | patient(X0) [cnf transformation 44]
84. creative(X0) | strong(X0) | ~patient(X0) [cnf transformation 44]
90. humble(X0) | quiet(X0) | ~creative(X0) | curious(X0) [cnf transformation 46]
92. ~quiet(X0) | humble(X0) [cnf transformation 27]
98. strong(X0) | ~kind(X0) | calm(X0) | creative(X0) [cnf transformation 47]
113. ~calm(X0) | patient(X0) [cnf transformation 51]
115. ~patient(X0) | ~humble(X0) [cnf transformation 30]
127. ~humble(fred) [cnf transformation 22]
130. ~strong(X0) | curious(X0) [duplicate literal removal 61]
131. ~strong(X0) | ~curious(X0) [duplicate literal removal 62]
132. ~strong(X0) [subsumption resolution 130,131]
154. ~curious(X0) | humble(X0) [subsumption resolution 69,71]
156. 5 <=> ! [X1] : curious(X1) [avatar definition]
157. curious(X1) <- (5) [avatar component clause 156]
159. 6 <=> kind(sK0) [avatar definition]
161. kind(sK0) <- (6) [avatar component clause 159]
162. 5 | 6 [avatar split clause 79,159,156]
175. ~patient(X0) | creative(X0) [subsumption resolution 84,132]
176. ~creative(X0) | quiet(X0) | humble(X0) [subsumption resolution 90,154]
178. ~kind(X0) | calm(X0) | creative(X0) [subsumption resolution 98,132]
216. humble(X0) <- (5) [resolution 154,157]
217. $false <- (5) [resolution 216,127]
221. ~5 [avatar contradiction clause 217]
238. calm(sK0) | creative(sK0) <- (6) [resolution 178,161]
240. 15 <=> creative(sK0) [avatar definition]
241. ~creative(sK0) <- (~15) [avatar component clause 240]
242. creative(sK0) <- (15) [avatar component clause 240]
244. 16 <=> calm(sK0) [avatar definition]
246. calm(sK0) <- (16) [avatar component clause 244]
247. 15 | 16 | ~6 [avatar split clause 238,159,244,240]
251. quiet(sK0) | humble(sK0) <- (15) [resolution 242,176]
253. patient(sK0) <- (15) [resolution 242,82]
254. humble(sK0) <- (15) [subsumption resolution 251,92]
261. ~humble(sK0) <- (15) [resolution 253,115]
263. $false <- (15) [subsumption resolution 261,254]
264. ~15 [avatar contradiction clause 263]
269. patient(sK0) <- (16) [resolution 246,113]
275. creative(sK0) <- (16) [resolution 269,175]
278. $false <- (~15, 16) [subsumption resolution 275,241]
279. 15 | ~16 [avatar contradiction clause 278]
280. $false [avatar sat refutation 162,221,247,264,279]
% SZS output end Proof for 34723742841921284688988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is generous or not happy and vice versa.
Everyone who is not quiet is not brave and vice versa.
If john is both not curious and not tall then someone is not quiet or creative and vice versa.
Everyone who is rich or not curious is either not kind or happy and vice versa.
Everyone who is rich or not rich is either not old or not generous and vice versa.
If john is not quiet or strong then mary is both not curious and tall and vice versa.
Everyone who is generous or not brave is either wise or humble and vice versa.
If susan is both not curious and not happy then someone is both humble and not humble and vice versa.
If someone is both not patient and not happy then someone is not funny or not tall.
Everyone who is either brave or calm is not tall.
If someone is not humble then mary is both brave and patient.
If someone is old then paul is not happy or brave and vice versa.
Everyone who is either creative or not humble is both old and not humble and vice versa.
Everyone who is not humble is generous or wise and vice versa.
Someone is tall.
Someone is either curious or not rich.
Someone is funny or rich.
Mary is either generous or old.
Someone is either old or not patient.
Someone is not funny.
Paul is rich or tall.
Someone is not curious or funny. | Mary is not curious. | entailment | (![X]:(~patient(X)<=>(generous(X)|~happy(X))))&
(![X]:(~quiet(X)<=>~brave(X)))&
(((~curious(john)&~tall(john)))<=>(?[X]:((~quiet(X)|creative(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~kind(X)<~>happy(X))))&
(![X]:((rich(X)|~rich(X))<=>(~old(X)<~>~generous(X))))&
(((~quiet(john)|strong(john)))<=>((~curious(mary)&tall(mary))))&
(![X]:((generous(X)|~brave(X))<=>(wise(X)<~>humble(X))))&
(((~curious(susan)&~happy(susan)))<=>(?[X]:((humble(X)&~humble(X)))))&
((?[X]:((~patient(X)&~happy(X))))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((brave(X)<~>calm(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>((brave(mary)&patient(mary))))&
((?[X]:(old(X)))<=>((~happy(paul)|brave(paul))))&
(![X]:((creative(X)<~>~humble(X))<=>(old(X)&~humble(X))))&
(![X]:(~humble(X)<=>(generous(X)|wise(X))))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((funny(X)|rich(X))))&
((generous(mary)<~>old(mary)))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
((rich(paul)|tall(paul)))&
(?[X]:((~curious(X)|funny(X)))) | ~curious(mary) | [
"p0",
"p1",
"p5",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5468726228005551611490395
% SZS output start Proof for 5468726228005551611490395
1. ! [X0] : (~patient(X0) <=> (~happy(X0) | generous(X0))) [input p0]
2. ! [X0] : (~quiet(X0) <=> ~brave(X0)) [input p1]
6. (strong(john) | ~quiet(john)) <=> (tall(mary) & ~curious(mary)) [input p5]
7. ! [X0] : ((~brave(X0) | generous(X0)) <=> (wise(X0) <~> humble(X0))) [input p6]
11. ? [X0] : ~humble(X0) => (patient(mary) & brave(mary)) [input p10]
14. ! [X0] : (~humble(X0) <=> (wise(X0) | generous(X0))) [input p13]
23. curious(mary) [input hypothesis]
27. (patient(mary) & brave(mary)) | ! [X0] : humble(X0) [ennf transformation 11]
28. ! [X0] : ((~patient(X0) | (happy(X0) & ~generous(X0))) & ((~happy(X0) | generous(X0)) | patient(X0))) [nnf transformation 1]
29. ! [X0] : ((~patient(X0) | (happy(X0) & ~generous(X0))) & (~happy(X0) | generous(X0) | patient(X0))) [flattening 28]
30. ! [X0] : ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0))) [nnf transformation 2]
40. ((strong(john) | ~quiet(john)) | (~tall(mary) | curious(mary))) & ((tall(mary) & ~curious(mary)) | (~strong(john) & quiet(john))) [nnf transformation 6]
41. (strong(john) | ~quiet(john) | ~tall(mary) | curious(mary)) & ((tall(mary) & ~curious(mary)) | (~strong(john) & quiet(john))) [flattening 40]
42. ! [X0] : (((~brave(X0) | generous(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (brave(X0) & ~generous(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | generous(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (brave(X0) & ~generous(X0)))) [flattening 42]
60. ! [X0] : ((~humble(X0) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | humble(X0))) [nnf transformation 14]
61. ! [X0] : ((~humble(X0) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | humble(X0))) [flattening 60]
78. ~generous(X0) | ~patient(X0) [cnf transformation 29]
81. ~quiet(X0) | brave(X0) [cnf transformation 30]
99. ~curious(mary) | quiet(john) [cnf transformation 41]
104. ~generous(X0) | wise(X0) | humble(X0) [cnf transformation 43]
108. ~wise(X0) | generous(X0) | humble(X0) | ~brave(X0) [cnf transformation 43]
109. ~humble(X0) | generous(X0) | wise(X0) | ~brave(X0) [cnf transformation 43]
117. brave(mary) | humble(X0) [cnf transformation 27]
118. patient(mary) | humble(X0) [cnf transformation 27]
128. wise(X0) | generous(X0) | humble(X0) [cnf transformation 61]
129. ~humble(X0) | ~generous(X0) [cnf transformation 61]
130. ~humble(X0) | ~wise(X0) [cnf transformation 61]
142. curious(mary) [cnf transformation 23]
175. 7 <=> curious(mary) [avatar definition]
183. 9 <=> quiet(john) [avatar definition]
184. quiet(john) <- (9) [avatar component clause 183]
194. 9 | ~7 [avatar split clause 99,175,183]
223. 17 <=> ! [X0] : humble(X0) [avatar definition]
224. humble(X0) <- (17) [avatar component clause 223]
226. 18 <=> patient(mary) [avatar definition]
228. patient(mary) <- (18) [avatar component clause 226]
229. 17 | 18 [avatar split clause 118,226,223]
231. 19 <=> brave(mary) [avatar definition]
233. brave(mary) <- (19) [avatar component clause 231]
234. 17 | 19 [avatar split clause 117,231,223]
253. humble(X0) | wise(X0) [subsumption resolution 128,104]
301. 7 [avatar split clause 142,175]
302. brave(john) <- (9) [resolution 81,184]
317. ~generous(X2) | wise(X2) [resolution 253,129]
387. generous(X2) | wise(X2) | ~brave(X2) | wise(X2) [resolution 109,253]
388. generous(X2) | wise(X2) | ~brave(X2) [duplicate literal removal 387]
390. ~brave(X2) | wise(X2) [subsumption resolution 388,317]
393. wise(john) <- (9) [resolution 390,302]
394. wise(mary) <- (19) [resolution 390,233]
419. generous(mary) | humble(mary) | ~brave(mary) <- (19) [resolution 394,108]
429. generous(mary) | humble(mary) <- (19) [subsumption resolution 419,233]
431. 46 <=> humble(mary) [avatar definition]
433. humble(mary) <- (46) [avatar component clause 431]
435. 47 <=> generous(mary) [avatar definition]
437. generous(mary) <- (47) [avatar component clause 435]
438. 46 | 47 | ~19 [avatar split clause 429,231,435,431]
467. ~wise(mary) <- (46) [resolution 433,130]
469. $false <- (19, 46) [subsumption resolution 467,394]
470. ~19 | ~46 [avatar contradiction clause 469]
482. ~patient(mary) <- (47) [resolution 437,78]
483. $false <- (18, 47) [subsumption resolution 482,228]
484. ~18 | ~47 [avatar contradiction clause 483]
501. ~wise(X4) <- (17) [resolution 224,130]
510. $false <- (9, 17) [resolution 501,393]
511. ~9 | ~17 [avatar contradiction clause 510]
512. $false [avatar sat refutation 194,229,234,301,438,470,484,511]
% SZS output end Proof for 5468726228005551611490395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not creative is wise or generous.
Everyone who is both rich and happy is either happy or not happy.
Everyone who is not old is both not curious and old and vice versa.
Everyone who is patient is either kind or curious.
If someone is both strong and not kind then lucy is either not creative or quiet and vice versa.
Everyone who is both generous and strong is creative or wise and vice versa.
If fred is both not kind and curious then john is brave or not old.
If someone is both not quiet and not happy then john is wise or not brave.
If someone is not patient then someone is patient and vice versa.
If alice is either not calm or creative then someone is both happy and wise.
If lucy is not calm then john is both not quiet and not creative.
If paul is curious or calm then someone is not kind and vice versa.
Everyone who is both happy and brave is either brave or not strong and vice versa.
Everyone who is kind is both old and not old.
If fred is not generous then someone is both generous and not kind.
Everyone who is quiet is not creative and vice versa.
Someone is both not strong and humble.
Someone is either tall or not rich.
Lucy is tall or wise.
Someone is rich or strong.
Someone is patient or not strong.
Alice is either strong or old. | Fred is not strong. | entailment | (![X]:((~quiet(X)<~>~creative(X))=>(wise(X)|generous(X))))&
(![X]:((rich(X)&happy(X))=>(happy(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(~curious(X)&old(X))))&
(![X]:(patient(X)=>(kind(X)<~>curious(X))))&
((?[X]:((strong(X)&~kind(X))))<=>((~creative(lucy)<~>quiet(lucy))))&
(![X]:((generous(X)&strong(X))<=>(creative(X)|wise(X))))&
(((~kind(fred)&curious(fred)))=>((brave(john)|~old(john))))&
((?[X]:((~quiet(X)&~happy(X))))=>((wise(john)|~brave(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(patient(X))))&
(((~calm(alice)<~>creative(alice)))=>(?[X]:((happy(X)&wise(X)))))&
((~calm(lucy))=>((~quiet(john)&~creative(john))))&
(((curious(paul)|calm(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)&brave(X))<=>(brave(X)<~>~strong(X))))&
(![X]:(kind(X)=>(old(X)&~old(X))))&
((~generous(fred))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
((tall(lucy)|wise(lucy)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((patient(X)|~strong(X))))&
((strong(alice)<~>old(alice))) | ~strong(fred) | [
"p2",
"p4",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7154634328137525832304243
% SZS output start Proof for 7154634328137525832304243
3. ! [X0] : (~old(X0) <=> (old(X0) & ~curious(X0))) [input p2]
5. ? [X0] : (~kind(X0) & strong(X0)) <=> (~creative(lucy) <~> quiet(lucy)) [input p4]
14. ! [X0] : (kind(X0) => (~old(X0) & old(X0))) [input p13]
16. ! [X0] : (quiet(X0) <=> ~creative(X0)) [input p15]
23. strong(fred) [input hypothesis]
37. ! [X0] : ((~old(X0) & old(X0)) | ~kind(X0)) [ennf transformation 14]
41. ! [X0] : ((~old(X0) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | old(X0))) [flattening 41]
44. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X0] : (kind(X0) | ~strong(X0))) [nnf transformation 5]
45. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [rectify 44]
46. ? [X0] : (~kind(X0) & strong(X0)) => (~kind(sK0) & strong(sK0)) [choice axiom]
47. ((~kind(sK0) & strong(sK0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [skolemisation 45,46]
67. ! [X0] : ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))) [nnf transformation 16]
83. old(X0) | old(X0) [cnf transformation 42]
87. quiet(lucy) | ~creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
88. ~quiet(lucy) | creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
118. ~old(X0) | ~kind(X0) [cnf transformation 37]
121. ~creative(X0) | ~quiet(X0) [cnf transformation 67]
122. creative(X0) | quiet(X0) [cnf transformation 67]
131. strong(fred) [cnf transformation 23]
134. old(X0) [duplicate literal removal 83]
139. 1 <=> quiet(lucy) [avatar definition]
140. quiet(lucy) <- (1) [avatar component clause 139]
141. ~quiet(lucy) <- (~1) [avatar component clause 139]
143. 2 <=> creative(lucy) [avatar definition]
144. creative(lucy) <- (2) [avatar component clause 143]
145. ~creative(lucy) <- (~2) [avatar component clause 143]
159. 5 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
160. kind(X1) | ~strong(X1) <- (5) [avatar component clause 159]
161. 5 | 2 | ~1 [avatar split clause 88,139,143,159]
162. 5 | ~2 | 1 [avatar split clause 87,139,143,159]
254. ~kind(X0) [subsumption resolution 118,134]
315. quiet(lucy) <- (~2) [resolution 122,145]
318. $false <- (~1, ~2) [subsumption resolution 315,141]
319. 1 | 2 [avatar contradiction clause 318]
322. ~quiet(lucy) <- (2) [resolution 144,121]
325. $false <- (1, 2) [subsumption resolution 322,140]
326. ~1 | ~2 [avatar contradiction clause 325]
327. ~strong(X1) <- (5) [subsumption resolution 160,254]
335. $false <- (5) [resolution 327,131]
338. ~5 [avatar contradiction clause 335]
339. $false [avatar sat refutation 161,162,319,326,338]
% SZS output end Proof for 7154634328137525832304243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not tall or not generous then someone is creative.
If someone is both not old and rich then alice is not old or humble and vice versa.
Everyone who is both brave and not creative is not brave or not rich and vice versa.
If someone is both kind and happy then john is both curious and generous and vice versa.
Everyone who is not calm or curious is not humble or not curious.
If someone is either old or brave then someone is not rich or wise and vice versa.
If someone is both old and not calm then someone is funny or kind and vice versa.
Everyone who is both not patient and not brave is not humble or not rich and vice versa.
If mary is funny then someone is both not curious and not creative.
If fred is not calm then susan is quiet or curious and vice versa.
Everyone who is either quiet or creative is both generous and not funny and vice versa.
If someone is both not rich and not strong then someone is either not calm or tall and vice versa.
If susan is both not patient and not humble then fred is either not tall or calm and vice versa.
Everyone who is both brave and not quiet is either happy or not rich and vice versa.
If lucy is not happy then john is not rich and vice versa.
Everyone who is both kind and not calm is either quiet or generous.
Someone is old or patient.
Someone is either not happy or wise.
John is either not patient or old.
Paul is either strong or old.
Someone is not old. | Alice is curious. | contradiction | (((~tall(john)|~generous(john)))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)&rich(X))))<=>((~old(alice)|humble(alice))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((kind(X)&happy(X))))<=>((curious(john)&generous(john))))&
(![X]:((~calm(X)|curious(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)<~>brave(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~patient(X)&~brave(X))<=>(~humble(X)|~rich(X))))&
((funny(mary))=>(?[X]:((~curious(X)&~creative(X)))))&
((~calm(fred))<=>((quiet(susan)|curious(susan))))&
(![X]:((quiet(X)<~>creative(X))<=>(generous(X)&~funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((~calm(X)<~>tall(X)))))&
(((~patient(susan)&~humble(susan)))<=>((~tall(fred)<~>calm(fred))))&
(![X]:((brave(X)&~quiet(X))<=>(happy(X)<~>~rich(X))))&
((~happy(lucy))<=>(~rich(john)))&
(![X]:((kind(X)&~calm(X))=>(quiet(X)<~>generous(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
((~patient(john)<~>old(john)))&
((strong(paul)<~>old(paul)))&
(?[X]:(~old(X))) | curious(alice) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6654939519918102550975517
% SZS output start Proof for 6654939519918102550975517
3. ! [X0] : ((~creative(X0) & brave(X0)) <=> (~rich(X0) | ~brave(X0))) [input p2]
5. ! [X0] : ((curious(X0) | ~calm(X0)) => (~curious(X0) | ~humble(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~rich(X0) | ~humble(X0))) [input p7]
22. curious(alice) [input hypothesis]
27. ! [X0] : ((~curious(X0) | ~humble(X0)) | (~curious(X0) & calm(X0))) [ennf transformation 5]
28. ! [X0] : (~curious(X0) | ~humble(X0) | (~curious(X0) & calm(X0))) [flattening 27]
39. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | (creative(X0) | ~brave(X0)))) [nnf transformation 3]
40. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | creative(X0) | ~brave(X0))) [flattening 39]
56. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 8]
57. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | brave(X0) | patient(X0))) [flattening 56]
92. brave(X0) | brave(X0) [cnf transformation 40]
101. ~curious(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 28]
116. ~brave(X0) | humble(X0) [cnf transformation 57]
159. curious(alice) [cnf transformation 22]
160. ~curious(X0) | ~humble(X0) [duplicate literal removal 101]
162. brave(X0) [duplicate literal removal 92]
280. humble(X0) [subsumption resolution 116,162]
422. ~humble(alice) [resolution 160,159]
423. $false [subsumption resolution 422,280]
% SZS output end Proof for 6654939519918102550975517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not brave then someone is tall or not humble.
Everyone who is both quiet and not funny is not kind.
Everyone who is either creative or not quiet is curious.
If mary is both not strong and not rich then someone is generous.
Everyone who is not curious or happy is not curious.
Everyone who is patient is creative.
Everyone who is both happy and not creative is not quiet or patient and vice versa.
If mary is either wise or generous then susan is not patient and vice versa.
Everyone who is either not brave or not curious is not brave and vice versa.
If someone is either funny or not curious then susan is not patient or humble and vice versa.
Everyone who is old or wise is old or not kind and vice versa.
Everyone who is both not patient and creative is either patient or not humble.
Everyone who is brave or patient is kind or rich and vice versa.
Everyone who is not curious is tall and vice versa.
Everyone who is both happy and kind is creative or not curious and vice versa.
If someone is both not old and not strong then paul is either not generous or calm and vice versa.
Someone is either not funny or calm.
Lucy is brave.
Someone is either curious or generous.
Someone is either patient or not happy.
Someone is either not wise or brave.
Lucy is humble or not rich. | Paul is brave. | neutral | ((?[X]:((~curious(X)&~brave(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((quiet(X)&~funny(X))=>~kind(X)))&
(![X]:((creative(X)<~>~quiet(X))=>curious(X)))&
(((~strong(mary)&~rich(mary)))=>(?[X]:(generous(X))))&
(![X]:((~curious(X)|happy(X))=>~curious(X)))&
(![X]:(patient(X)=>creative(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|patient(X))))&
(((wise(mary)<~>generous(mary)))<=>(~patient(susan)))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>((~patient(susan)|humble(susan))))&
(![X]:((old(X)|wise(X))<=>(old(X)|~kind(X))))&
(![X]:((~patient(X)&creative(X))=>(patient(X)<~>~humble(X))))&
(![X]:((brave(X)|patient(X))<=>(kind(X)|rich(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((happy(X)&kind(X))<=>(creative(X)|~curious(X))))&
((?[X]:((~old(X)&~strong(X))))<=>((~generous(paul)<~>calm(paul))))&
(?[X]:((~funny(X)<~>calm(X))))&
(brave(lucy))&
(?[X]:((curious(X)<~>generous(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~wise(X)<~>brave(X))))&
((humble(lucy)|~rich(lucy))) | brave(paul) | [] | null | 0 |
If someone is both strong and not old then someone is wise.
If lucy is either quiet or wise then mary is either creative or curious and vice versa.
Everyone who is wise is not strong or not brave.
Everyone who is either humble or brave is not brave and vice versa.
Everyone who is either not patient or not quiet is either not humble or curious and vice versa.
Everyone who is both humble and happy is either not tall or funny and vice versa.
If someone is not funny then fred is either not tall or not old.
If john is curious then john is not curious or calm.
If someone is either quiet or kind then lucy is both not generous and not wise.
Everyone who is humble is not happy or old.
Everyone who is tall or old is not tall or strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Someone is both creative and not calm.
Someone is not generous.
Alice is happy or funny.
Mary is not creative.
Someone is not calm or strong.
Alice is not old or funny.
Alice is both not quiet and creative. | Fred is old. | entailment | ((?[X]:((strong(X)&~old(X))))=>(?[X]:(wise(X))))&
(((quiet(lucy)<~>wise(lucy)))<=>((creative(mary)<~>curious(mary))))&
(![X]:(wise(X)=>(~strong(X)|~brave(X))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~generous(X)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice))) | old(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8104167009151842145681192
% SZS output start Proof for 8104167009151842145681192
12. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p11]
24. ~old(fred) [input hypothesis]
26. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 12]
37. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 26]
52. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 37]
53. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
54. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 52,53]
109. ~wise(sK1) | old(X1) [cnf transformation 54]
111. wise(sK1) | old(X1) [cnf transformation 54]
135. ~old(fred) [cnf transformation 24]
188. 9 <=> old(fred) [avatar definition]
189. ~old(fred) <- (~9) [avatar component clause 188]
218. 15 <=> ! [X1] : old(X1) [avatar definition]
219. old(X1) <- (15) [avatar component clause 218]
221. 16 <=> wise(sK1) [avatar definition]
224. 15 | 16 [avatar split clause 111,221,218]
229. 15 | ~16 [avatar split clause 109,221,218]
293. ~9 [avatar split clause 135,188]
296. $false <- (~9, 15) [subsumption resolution 189,219]
297. 9 | ~15 [avatar contradiction clause 296]
300. $false [avatar sat refutation 224,229,293,297]
% SZS output end Proof for 8104167009151842145681192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative then mary is happy.
If mary is either not strong or kind then someone is both calm and not generous.
Everyone who is either not brave or creative is strong or patient.
Everyone who is not strong is not funny and vice versa.
If someone is wise then fred is either not calm or creative and vice versa.
If paul is not wise then lucy is both rich and not happy.
If paul is both generous and calm then fred is brave or quiet and vice versa.
If someone is both quiet and not happy then john is both not creative and curious and vice versa.
Everyone who is either not curious or tall is both strong and not rich.
If someone is not calm or not kind then fred is humble.
Everyone who is both not rich and not kind is both humble and not happy.
If someone is not creative or not humble then susan is either not funny or not strong.
Everyone who is either curious or not calm is both not brave and not creative.
Everyone who is not calm is not brave and vice versa.
If someone is strong then john is both strong and old.
Everyone who is both not funny and not kind is both humble and creative and vice versa.
Lucy is both calm and not curious.
Alice is tall or old.
Fred is not humble or humble.
Someone is not creative or not funny.
Paul is old.
Someone is not curious or not patient.
Someone is not curious.
Someone is either happy or not patient. | Fred is funny. | contradiction | (((~patient(fred)<~>~creative(fred)))=>(happy(mary)))&
(((~strong(mary)<~>kind(mary)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((~brave(X)<~>creative(X))=>(strong(X)|patient(X))))&
(![X]:(~strong(X)<=>~funny(X)))&
((?[X]:(wise(X)))<=>((~calm(fred)<~>creative(fred))))&
((~wise(paul))=>((rich(lucy)&~happy(lucy))))&
(((generous(paul)&calm(paul)))<=>((brave(fred)|quiet(fred))))&
((?[X]:((quiet(X)&~happy(X))))<=>((~creative(john)&curious(john))))&
(![X]:((~curious(X)<~>tall(X))=>(strong(X)&~rich(X))))&
((?[X]:((~calm(X)|~kind(X))))=>(humble(fred)))&
(![X]:((~rich(X)&~kind(X))=>(humble(X)&~happy(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((~funny(susan)<~>~strong(susan))))&
(![X]:((curious(X)<~>~calm(X))=>(~brave(X)&~creative(X))))&
(![X]:(~calm(X)<=>~brave(X)))&
((?[X]:(strong(X)))=>((strong(john)&old(john))))&
(![X]:((~funny(X)&~kind(X))<=>(humble(X)&creative(X))))&
((calm(lucy)&~curious(lucy)))&
((tall(alice)|old(alice)))&
((~humble(fred)|humble(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(old(paul))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~patient(X)))) | funny(fred) | [
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2018834079090150703456210
% SZS output start Proof for 2018834079090150703456210
4. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p3]
12. ? [X0] : (~humble(X0) | ~creative(X0)) => (~funny(susan) <~> ~strong(susan)) [input p11]
16. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (creative(X0) & humble(X0))) [input p15]
25. funny(fred) [input hypothesis]
38. (~funny(susan) <~> ~strong(susan)) | ! [X0] : (humble(X0) & creative(X0)) [ennf transformation 12]
46. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 4]
59. ((strong(susan) | funny(susan)) & (~strong(susan) | ~funny(susan))) | ! [X0] : (humble(X0) & creative(X0)) [nnf transformation 38]
62. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 16]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | kind(X0) | funny(X0))) [flattening 62]
81. ~funny(X0) | strong(X0) [cnf transformation 46]
82. ~strong(X0) | funny(X0) [cnf transformation 46]
106. ~strong(susan) | ~funny(susan) | creative(X0) [cnf transformation 59]
107. ~strong(susan) | ~funny(susan) | humble(X0) [cnf transformation 59]
108. strong(susan) | funny(susan) | creative(X0) [cnf transformation 59]
109. strong(susan) | funny(susan) | humble(X0) [cnf transformation 59]
119. ~humble(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 63]
129. funny(fred) [cnf transformation 25]
249. funny(susan) | humble(X0) [subsumption resolution 109,82]
251. 26 <=> ! [X0] : humble(X0) [avatar definition]
252. humble(X0) <- (26) [avatar component clause 251]
254. 27 <=> funny(susan) [avatar definition]
257. 26 | 27 [avatar split clause 249,254,251]
258. funny(susan) | creative(X0) [subsumption resolution 108,82]
260. 28 <=> ! [X0] : creative(X0) [avatar definition]
261. creative(X0) <- (28) [avatar component clause 260]
262. 28 | 27 [avatar split clause 258,254,260]
263. ~funny(susan) | humble(X0) [subsumption resolution 107,81]
264. 26 | ~27 [avatar split clause 263,254,251]
265. ~funny(susan) | creative(X0) [subsumption resolution 106,81]
266. 28 | ~27 [avatar split clause 265,254,260]
350. ~creative(X2) | ~funny(X2) <- (26) [resolution 119,252]
352. ~funny(X2) <- (26, 28) [subsumption resolution 350,261]
353. $false <- (26, 28) [resolution 352,129]
357. ~26 | ~28 [avatar contradiction clause 353]
358. $false [avatar sat refutation 257,262,264,266,357]
% SZS output end Proof for 2018834079090150703456210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not generous then someone is not strong or not patient and vice versa.
If someone is not calm then mary is either curious or not humble and vice versa.
If paul is calm or generous then john is not happy.
Everyone who is both not rich and happy is either not strong or kind and vice versa.
Everyone who is both happy and not brave is either old or not patient.
Everyone who is not creative or generous is calm and vice versa.
If fred is either patient or not humble then someone is not brave and vice versa.
If paul is patient or not rich then someone is either not quiet or curious and vice versa.
Everyone who is not rich is patient or curious.
If john is not patient or humble then fred is either not funny or old and vice versa.
If someone is either not generous or not kind then alice is not tall and vice versa.
If someone is both not generous and not kind then someone is either strong or not tall and vice versa.
Everyone who is brave or not kind is not patient and vice versa.
Everyone who is either strong or humble is either not rich or kind and vice versa.
Everyone who is both humble and not humble is either not wise or curious.
Everyone who is not strong or wise is both calm and not kind and vice versa.
Someone is either not curious or kind.
Someone is either not rich or not kind.
Someone is either not strong or not quiet.
Alice is calm or not funny.
Someone is not calm or not rich.
Someone is both not wise and quiet.
Someone is old or rich.
Someone is both not calm and patient. | Fred is not rich. | entailment | ((?[X]:((humble(X)&~generous(X))))<=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:(~calm(X)))<=>((curious(mary)<~>~humble(mary))))&
(((calm(paul)|generous(paul)))=>(~happy(john)))&
(![X]:((~rich(X)&happy(X))<=>(~strong(X)<~>kind(X))))&
(![X]:((happy(X)&~brave(X))=>(old(X)<~>~patient(X))))&
(![X]:((~creative(X)|generous(X))<=>calm(X)))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:(~brave(X))))&
(((patient(paul)|~rich(paul)))<=>(?[X]:((~quiet(X)<~>curious(X)))))&
(![X]:(~rich(X)=>(patient(X)|curious(X))))&
(((~patient(john)|humble(john)))<=>((~funny(fred)<~>old(fred))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>(~tall(alice)))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((brave(X)|~kind(X))<=>~patient(X)))&
(![X]:((strong(X)<~>humble(X))<=>(~rich(X)<~>kind(X))))&
(![X]:((humble(X)&~humble(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~strong(X)|wise(X))<=>(calm(X)&~kind(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((calm(alice)|~funny(alice)))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:((~wise(X)&quiet(X))))&
(?[X]:((old(X)|rich(X))))&
(?[X]:((~calm(X)&patient(X)))) | ~rich(fred) | [
"p3",
"p6",
"p12",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1881652951406564545279988
% SZS output start Proof for 1881652951406564545279988
4. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (~strong(X0) <~> kind(X0))) [input p3]
7. (patient(fred) <~> ~humble(fred)) <=> ? [X0] : ~brave(X0) [input p6]
13. ! [X0] : ((~kind(X0) | brave(X0)) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((strong(X0) <~> humble(X0)) <=> (~rich(X0) <~> kind(X0))) [input p13]
16. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (~kind(X0) & calm(X0))) [input p15]
24. ? [X0] : (patient(X0) & ~calm(X0)) [input p23]
25. rich(fred) [input hypothesis]
44. ! [X0] : (((happy(X0) & ~rich(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0)))) & (((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~happy(X0) | rich(X0)))) [nnf transformation 4]
45. ! [X0] : (((happy(X0) & ~rich(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0)))) & (((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ~happy(X0) | rich(X0))) [flattening 44]
49. (((humble(fred) | ~patient(fred)) & (~humble(fred) | patient(fred))) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ((patient(fred) | humble(fred)) & (~humble(fred) | ~patient(fred)))) [nnf transformation 7]
50. (((humble(fred) | ~patient(fred)) & (~humble(fred) | patient(fred))) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ((patient(fred) | humble(fred)) & (~humble(fred) | ~patient(fred)))) [rectify 49]
51. ? [X1] : ~brave(X1) => ~brave(sK3) [choice axiom]
52. (((humble(fred) | ~patient(fred)) & (~humble(fred) | patient(fred))) | ! [X0] : brave(X0)) & (~brave(sK3) | ((patient(fred) | humble(fred)) & (~humble(fred) | ~patient(fred)))) [skolemisation 50,51]
69. ! [X0] : (((~kind(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [nnf transformation 13]
70. ! [X0] : ((~kind(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [flattening 69]
71. ! [X0] : ((((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0)))) & (((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))))) [nnf transformation 14]
73. ! [X0] : (((wise(X0) | ~strong(X0)) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | (~wise(X0) & strong(X0)))) [nnf transformation 16]
74. ! [X0] : ((wise(X0) | ~strong(X0) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | (~wise(X0) & strong(X0)))) [flattening 73]
90. ? [X0] : (patient(X0) & ~calm(X0)) => (patient(sK14) & ~calm(sK14)) [choice axiom]
91. patient(sK14) & ~calm(sK14) [skolemisation 24,90]
105. ~rich(X0) | kind(X0) | strong(X0) [cnf transformation 45]
106. ~kind(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 45]
116. ~humble(fred) | patient(fred) | brave(X0) [cnf transformation 52]
141. ~brave(X0) | ~patient(X0) [cnf transformation 70]
142. ~patient(X0) | kind(X0) [cnf transformation 70]
144. kind(X0) | ~rich(X0) | humble(X0) | ~strong(X0) [cnf transformation 71]
149. humble(X0) | strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 71]
156. ~kind(X0) | strong(X0) [cnf transformation 74]
171. patient(sK14) [cnf transformation 91]
172. rich(fred) [cnf transformation 25]
237. 15 <=> ! [X0] : brave(X0) [avatar definition]
238. brave(X0) <- (15) [avatar component clause 237]
240. 16 <=> patient(fred) [avatar definition]
241. patient(fred) <- (16) [avatar component clause 240]
244. 17 <=> humble(fred) [avatar definition]
248. 15 | 16 | ~17 [avatar split clause 116,244,240,237]
358. humble(X0) | ~rich(X0) | ~kind(X0) [subsumption resolution 149,106]
361. kind(X0) | ~rich(X0) | humble(X0) [subsumption resolution 144,105]
362. ~rich(X0) | humble(X0) [subsumption resolution 361,358]
425. humble(fred) [resolution 362,172]
429. 17 [avatar split clause 425,244]
433. kind(fred) <- (16) [resolution 241,142]
439. ~strong(fred) | ~rich(fred) <- (16) [resolution 433,106]
440. strong(fred) <- (16) [resolution 433,156]
441. ~strong(fred) <- (16) [subsumption resolution 439,172]
442. $false <- (16) [subsumption resolution 440,441]
443. ~16 [avatar contradiction clause 442]
445. ~patient(X0) <- (15) [resolution 238,141]
458. $false <- (15) [resolution 445,171]
459. ~15 [avatar contradiction clause 458]
460. $false [avatar sat refutation 248,429,443,459]
% SZS output end Proof for 1881652951406564545279988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not old is humble or not old.
Everyone who is calm or generous is both not tall and not patient.
Everyone who is both not funny and funny is strong or tall.
If someone is not curious or curious then someone is either rich or brave.
If someone is either not quiet or not strong then mary is not old or quiet and vice versa.
Everyone who is either not patient or strong is both not tall and not creative and vice versa.
Everyone who is both not rich and not wise is quiet or not kind and vice versa.
Everyone who is both funny and not creative is either not calm or kind and vice versa.
If fred is both not funny and not creative then someone is both not old and humble and vice versa.
Everyone who is happy or not kind is both not tall and not quiet.
Everyone who is either not old or curious is either wise or not quiet and vice versa.
Everyone who is both not funny and old is both patient and funny.
Everyone who is both brave and funny is both not humble and curious.
If someone is not calm or not generous then mary is not rich or not creative and vice versa.
Everyone who is both rich and not calm is either generous or happy.
Everyone who is both not patient and funny is either rich or kind and vice versa.
Someone is both not funny and not curious.
Someone is either old or not calm.
Paul is wise or creative.
Fred is not funny or calm.
Fred is both not humble and not quiet.
Someone is not old.
Lucy is quiet.
Someone is not rich or not strong. | Mary is not creative. | neutral | (![X]:((tall(X)<~>~old(X))=>(humble(X)|~old(X))))&
(![X]:((calm(X)|generous(X))=>(~tall(X)&~patient(X))))&
(![X]:((~funny(X)&funny(X))=>(strong(X)|tall(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((rich(X)<~>brave(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>((~old(mary)|quiet(mary))))&
(![X]:((~patient(X)<~>strong(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~rich(X)&~wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:((funny(X)&~creative(X))<=>(~calm(X)<~>kind(X))))&
(((~funny(fred)&~creative(fred)))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((happy(X)|~kind(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~old(X)<~>curious(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~funny(X)&old(X))=>(patient(X)&funny(X))))&
(![X]:((brave(X)&funny(X))=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>((~rich(mary)|~creative(mary))))&
(![X]:((rich(X)&~calm(X))=>(generous(X)<~>happy(X))))&
(![X]:((~patient(X)&funny(X))<=>(rich(X)<~>kind(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((old(X)<~>~calm(X))))&
((wise(paul)|creative(paul)))&
((~funny(fred)|calm(fred)))&
((~humble(fred)&~quiet(fred)))&
(?[X]:(~old(X)))&
(quiet(lucy))&
(?[X]:((~rich(X)|~strong(X)))) | ~creative(mary) | [] | null | 0 |
Everyone who is either not brave or creative is not humble. If someone is both not patient and patient then lucy is not patient and vice versa. Everyone who is old is both calm and not kind. Everyone who is not strong or wise is both happy and quiet. If someone is both not brave and not happy then someone is patient and vice versa. Everyone who is not funny or strong is generous. Everyone who is patient is not old. Everyone who is not wise is either not quiet or not curious. Everyone who is creative is not patient. If john is either not rich or rich then lucy is rich. Everyone who is tall is either not happy or not quiet and vice versa. If alice is creative or not creative then mary is wise or generous. Everyone who is either tall or not generous is not strong or wise. Everyone who is either not patient or happy is both not generous and strong and vice versa. If someone is either not generous or funny then someone is either brave or not quiet and vice versa. If lucy is calm then someone is not patient or not old. Lucy is either not humble or not funny. Fred is happy or brave. Someone is humble or kind. Someone is either not quiet or curious. Someone is not tall. | John is kind. | neutral | (![X]:((~brave(X)<~>creative(X))=>~humble(X)))&
((?[X]:((~patient(X)&patient(X))))<=>(~patient(lucy)))&
(![X]:(old(X)=>(calm(X)&~kind(X))))&
(![X]:((~strong(X)|wise(X))=>(happy(X)&quiet(X))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))=>generous(X)))&
(![X]:(patient(X)=>~old(X)))&
(![X]:(~wise(X)=>(~quiet(X)<~>~curious(X))))&
(![X]:(creative(X)=>~patient(X)))&
(((~rich(john)<~>rich(john)))=>(rich(lucy)))&
(![X]:(tall(X)<=>(~happy(X)<~>~quiet(X))))&
(((creative(alice)|~creative(alice)))=>((wise(mary)|generous(mary))))&
(![X]:((tall(X)<~>~generous(X))=>(~strong(X)|wise(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~generous(X)&strong(X))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((calm(lucy))=>(?[X]:((~patient(X)|~old(X)))))&
((~humble(lucy)<~>~funny(lucy)))&
((happy(fred)|brave(fred)))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:((~quiet(X)<~>curious(X))))&
(?[X]:(~tall(X))) | kind(john) | [] | null | 0 |
Everyone who is quiet or not funny is either not funny or not happy and vice versa. Everyone who is either curious or creative is both not wise and not quiet and vice versa. Everyone who is both not rich and humble is humble. Everyone who is humble is both tall and not brave and vice versa. Everyone who is curious is tall. If fred is brave then someone is either not kind or humble. If john is either quiet or not rich then someone is not curious. Everyone who is humble is both not kind and not humble and vice versa. If someone is both curious and not kind then susan is either not patient or happy and vice versa. Everyone who is calm or not generous is both patient and curious and vice versa. Everyone who is either not curious or not strong is not happy or humble and vice versa. Everyone who is either quiet or strong is both not quiet and kind. Everyone who is creative or not funny is not curious or not kind. If someone is not old or not humble then lucy is either not humble or not calm and vice versa. If mary is not calm or not brave then susan is both patient and funny. Someone is generous or brave. Alice is creative. Lucy is not calm or funny. Someone is not calm or not old. Lucy is both brave and kind. Someone is both patient and not calm. Someone is either curious or not brave. | Fred is strong. | neutral | (![X]:((quiet(X)|~funny(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:((curious(X)<~>creative(X))<=>(~wise(X)&~quiet(X))))&
(![X]:((~rich(X)&humble(X))=>humble(X)))&
(![X]:(humble(X)<=>(tall(X)&~brave(X))))&
(![X]:(curious(X)=>tall(X)))&
((brave(fred))=>(?[X]:((~kind(X)<~>humble(X)))))&
(((quiet(john)<~>~rich(john)))=>(?[X]:(~curious(X))))&
(![X]:(humble(X)<=>(~kind(X)&~humble(X))))&
((?[X]:((curious(X)&~kind(X))))<=>((~patient(susan)<~>happy(susan))))&
(![X]:((calm(X)|~generous(X))<=>(patient(X)&curious(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(~happy(X)|humble(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~quiet(X)&kind(X))))&
(![X]:((creative(X)|~funny(X))=>(~curious(X)|~kind(X))))&
((?[X]:((~old(X)|~humble(X))))<=>((~humble(lucy)<~>~calm(lucy))))&
(((~calm(mary)|~brave(mary)))=>((patient(susan)&funny(susan))))&
(?[X]:((generous(X)|brave(X))))&
(creative(alice))&
((~calm(lucy)|funny(lucy)))&
(?[X]:((~calm(X)|~old(X))))&
((brave(lucy)&kind(lucy)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:((curious(X)<~>~brave(X)))) | strong(fred) | [] | null | 0 |
Everyone who is not calm is not kind or not funny and vice versa. If someone is either not funny or strong then someone is either rich or quiet and vice versa. If alice is both quiet and not funny then someone is either not tall or brave. Everyone who is either not generous or strong is both patient and generous and vice versa. Everyone who is both wise and happy is not calm and vice versa. If someone is either not generous or creative then someone is either not generous or tall. If someone is quiet then mary is both strong and not patient and vice versa. If someone is both strong and rich then john is both not creative and not calm and vice versa. Everyone who is both quiet and tall is happy or patient and vice versa. Everyone who is patient or not tall is quiet. If someone is kind or not rich then someone is not patient and vice versa. Everyone who is wise or not happy is not kind or not calm and vice versa. If john is both brave and not patient then alice is both funny and curious and vice versa. Everyone who is not brave or old is kind or funny. Everyone who is both not kind and not happy is both curious and not curious and vice versa. If john is not strong then someone is both old and tall. Someone is not generous. Paul is not creative. Someone is either brave or calm. Mary is either funny or not strong. Fred is calm. Susan is rich or not generous. Someone is both not patient and kind. | Alice is not curious. | neutral | (![X]:(~calm(X)<=>(~kind(X)|~funny(X))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(((quiet(alice)&~funny(alice)))=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:((~generous(X)<~>strong(X))<=>(patient(X)&generous(X))))&
(![X]:((wise(X)&happy(X))<=>~calm(X)))&
((?[X]:((~generous(X)<~>creative(X))))=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:(quiet(X)))<=>((strong(mary)&~patient(mary))))&
((?[X]:((strong(X)&rich(X))))<=>((~creative(john)&~calm(john))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)|patient(X))))&
(![X]:((patient(X)|~tall(X))=>quiet(X)))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((wise(X)|~happy(X))<=>(~kind(X)|~calm(X))))&
(((brave(john)&~patient(john)))<=>((funny(alice)&curious(alice))))&
(![X]:((~brave(X)|old(X))=>(kind(X)|funny(X))))&
(![X]:((~kind(X)&~happy(X))<=>(curious(X)&~curious(X))))&
((~strong(john))=>(?[X]:((old(X)&tall(X)))))&
(?[X]:(~generous(X)))&
(~creative(paul))&
(?[X]:((brave(X)<~>calm(X))))&
((funny(mary)<~>~strong(mary)))&
(calm(fred))&
((rich(susan)|~generous(susan)))&
(?[X]:((~patient(X)&kind(X)))) | ~curious(alice) | [] | null | 0 |
If mary is both not generous and tall then paul is both happy and not generous.
Everyone who is either not quiet or quiet is generous.
If someone is either tall or rich then someone is both rich and funny and vice versa.
If someone is not funny or humble then john is both not brave and not old.
If mary is either not funny or not wise then mary is not humble and vice versa.
Everyone who is tall or humble is not brave or not patient and vice versa.
If mary is either not kind or quiet then lucy is generous or not patient and vice versa.
If someone is not generous then someone is either humble or not old and vice versa.
Everyone who is happy is both not tall and not calm.
Everyone who is both not tall and calm is rich.
Everyone who is either creative or not tall is not humble.
Everyone who is tall is kind.
Everyone who is brave or not quiet is either generous or not tall.
If mary is patient then mary is both not patient and rich and vice versa.
Everyone who is either calm or curious is not kind or not patient.
If john is both kind and creative then someone is either brave or patient and vice versa.
Someone is both patient and not quiet.
John is not humble.
Someone is rich.
Someone is not wise or not patient.
Fred is tall.
Lucy is not calm. | John is kind. | entailment | (((~generous(mary)&tall(mary)))=>((happy(paul)&~generous(paul))))&
(![X]:((~quiet(X)<~>quiet(X))=>generous(X)))&
((?[X]:((tall(X)<~>rich(X))))<=>(?[X]:((rich(X)&funny(X)))))&
((?[X]:((~funny(X)|humble(X))))=>((~brave(john)&~old(john))))&
(((~funny(mary)<~>~wise(mary)))<=>(~humble(mary)))&
(![X]:((tall(X)|humble(X))<=>(~brave(X)|~patient(X))))&
(((~kind(mary)<~>quiet(mary)))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((humble(X)<~>~old(X)))))&
(![X]:(happy(X)=>(~tall(X)&~calm(X))))&
(![X]:((~tall(X)&calm(X))=>rich(X)))&
(![X]:((creative(X)<~>~tall(X))=>~humble(X)))&
(![X]:(tall(X)=>kind(X)))&
(![X]:((brave(X)|~quiet(X))=>(generous(X)<~>~tall(X))))&
((patient(mary))<=>((~patient(mary)&rich(mary))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)|~patient(X))))&
(((kind(john)&creative(john)))<=>(?[X]:((brave(X)<~>patient(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
(~humble(john))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)|~patient(X))))&
(tall(fred))&
(~calm(lucy)) | kind(john) | [
"p1",
"p5",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5092449473372617209940282
% SZS output start Proof for 5092449473372617209940282
2. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => generous(X0)) [input p1]
6. ! [X0] : ((humble(X0) | tall(X0)) <=> (~patient(X0) | ~brave(X0))) [input p5]
13. ! [X0] : ((~quiet(X0) | brave(X0)) => (generous(X0) <~> ~tall(X0))) [input p12]
16. (creative(john) & kind(john)) <=> ? [X0] : (brave(X0) <~> patient(X0)) [input p15]
17. ? [X0] : (~quiet(X0) & patient(X0)) [input p16]
23. ~kind(john) [input hypothesis]
28. ! [X0] : (generous(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 2]
35. ! [X0] : ((generous(X0) <~> ~tall(X0)) | (quiet(X0) & ~brave(X0))) [ennf transformation 13]
38. ! [X0] : (generous(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 28]
45. ! [X0] : (((humble(X0) | tall(X0)) | (patient(X0) & brave(X0))) & ((~patient(X0) | ~brave(X0)) | (~humble(X0) & ~tall(X0)))) [nnf transformation 6]
46. ! [X0] : ((humble(X0) | tall(X0) | (patient(X0) & brave(X0))) & (~patient(X0) | ~brave(X0) | (~humble(X0) & ~tall(X0)))) [flattening 45]
55. ! [X0] : (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (quiet(X0) & ~brave(X0))) [nnf transformation 35]
59. ((creative(john) & kind(john)) | ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (? [X0] : ((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (~creative(john) | ~kind(john))) [nnf transformation 16]
60. ((creative(john) & kind(john)) | ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (? [X0] : ((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~creative(john) | ~kind(john)) [flattening 59]
61. ((creative(john) & kind(john)) | ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (? [X1] : ((~patient(X1) | ~brave(X1)) & (patient(X1) | brave(X1))) | ~creative(john) | ~kind(john)) [rectify 60]
62. ? [X1] : ((~patient(X1) | ~brave(X1)) & (patient(X1) | brave(X1))) => ((~patient(sK4) | ~brave(sK4)) & (patient(sK4) | brave(sK4))) [choice axiom]
63. ((creative(john) & kind(john)) | ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(sK4) | ~brave(sK4)) & (patient(sK4) | brave(sK4))) | ~creative(john) | ~kind(john)) [skolemisation 61,62]
64. ? [X0] : (~quiet(X0) & patient(X0)) => (~quiet(sK5) & patient(sK5)) [choice axiom]
65. ~quiet(sK5) & patient(sK5) [skolemisation 17,64]
72. generous(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
73. generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
88. ~patient(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 46]
111. tall(X0) | ~generous(X0) | quiet(X0) [cnf transformation 55]
120. kind(john) | brave(X0) | ~patient(X0) [cnf transformation 63]
123. patient(sK5) [cnf transformation 65]
124. ~quiet(sK5) [cnf transformation 65]
130. ~kind(john) [cnf transformation 23]
133. generous(X0) | quiet(X0) [duplicate literal removal 72]
134. ~quiet(X0) | generous(X0) [duplicate literal removal 73]
153. generous(X0) [subsumption resolution 133,134]
239. quiet(X0) | tall(X0) [subsumption resolution 111,153]
253. 24 <=> ! [X0] : (brave(X0) | ~patient(X0)) [avatar definition]
254. ~patient(X0) | brave(X0) <- (24) [avatar component clause 253]
265. 27 <=> kind(john) [avatar definition]
268. 24 | 27 [avatar split clause 120,265,253]
289. ~27 [avatar split clause 130,265]
315. tall(sK5) [resolution 239,124]
330. brave(sK5) <- (24) [resolution 254,123]
333. ~brave(sK5) | ~tall(sK5) [resolution 88,123]
334. ~tall(sK5) <- (24) [subsumption resolution 333,330]
335. $false <- (24) [subsumption resolution 334,315]
336. ~24 [avatar contradiction clause 335]
337. $false [avatar sat refutation 268,289,336]
% SZS output end Proof for 5092449473372617209940282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and funny then someone is quiet or not tall and vice versa. Everyone who is not strong or not calm is not happy and vice versa. Everyone who is both strong and not kind is both not quiet and strong and vice versa. Everyone who is either patient or not creative is both not curious and not generous and vice versa. If fred is funny or not humble then john is either not generous or not calm and vice versa. Everyone who is both strong and curious is either not kind or not rich. Everyone who is both not calm and not patient is both not calm and tall. Everyone who is both not calm and wise is not old. Everyone who is not strong is either old or not curious and vice versa. Everyone who is both not brave and not kind is kind and vice versa. If someone is both old and not curious then someone is kind or not creative and vice versa. If someone is generous or wise then alice is not tall or wise and vice versa. If someone is either not humble or not brave then someone is strong or funny and vice versa. Everyone who is either quiet or not rich is not quiet or not humble. Everyone who is both not calm and old is either not rich or funny. Everyone who is both not tall and patient is quiet or funny and vice versa. Mary is not funny or brave. Paul is either quiet or curious. Someone is funny. Someone is not generous or not calm. Alice is both not patient and rich. Someone is both not funny and not strong. Someone is not funny. | John is kind. | contradiction | ((?[X]:((generous(X)&funny(X))))<=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~strong(X)|~calm(X))<=>~happy(X)))&
(![X]:((strong(X)&~kind(X))<=>(~quiet(X)&strong(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~curious(X)&~generous(X))))&
(((funny(fred)|~humble(fred)))<=>((~generous(john)<~>~calm(john))))&
(![X]:((strong(X)&curious(X))=>(~kind(X)<~>~rich(X))))&
(![X]:((~calm(X)&~patient(X))=>(~calm(X)&tall(X))))&
(![X]:((~calm(X)&wise(X))=>~old(X)))&
(![X]:(~strong(X)<=>(old(X)<~>~curious(X))))&
(![X]:((~brave(X)&~kind(X))<=>kind(X)))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((generous(X)|wise(X))))<=>((~tall(alice)|wise(alice))))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(?[X]:((strong(X)|funny(X)))))&
(![X]:((quiet(X)<~>~rich(X))=>(~quiet(X)|~humble(X))))&
(![X]:((~calm(X)&old(X))=>(~rich(X)<~>funny(X))))&
(![X]:((~tall(X)&patient(X))<=>(quiet(X)|funny(X))))&
((~funny(mary)|brave(mary)))&
((quiet(paul)<~>curious(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|~calm(X))))&
((~patient(alice)&rich(alice)))&
(?[X]:((~funny(X)&~strong(X))))&
(?[X]:(~funny(X))) | kind(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7406094104993347992504783
% SZS output start Proof for 7406094104993347992504783
10. ! [X0] : ((~kind(X0) & ~brave(X0)) <=> kind(X0)) [input p9]
24. kind(john) [input hypothesis]
51. ! [X0] : (((~kind(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | brave(X0)))) [nnf transformation 10]
52. ! [X0] : (((~kind(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | brave(X0))) [flattening 51]
113. ~kind(X0) | ~kind(X0) [cnf transformation 52]
148. kind(john) [cnf transformation 24]
151. ~kind(X0) [duplicate literal removal 113]
299. $false [subsumption resolution 148,151]
% SZS output end Proof for 7406094104993347992504783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not curious and not brave.
Everyone who is both not patient and curious is happy or not tall and vice versa.
If alice is not funny or patient then lucy is not brave or not humble.
Everyone who is both not generous and kind is both not creative and funny.
Everyone who is not calm is both not wise and not kind and vice versa.
If someone is brave or not creative then paul is both kind and not strong.
Everyone who is either happy or not calm is both funny and not curious and vice versa.
Everyone who is not quiet or not patient is not calm.
If someone is either old or brave then john is not old or not creative.
If someone is kind then paul is not patient or kind and vice versa.
Everyone who is funny is creative or not brave and vice versa.
If someone is humble then lucy is not old or not quiet and vice versa.
Everyone who is both patient and old is either not tall or not strong and vice versa.
Everyone who is brave is both not strong and happy.
If lucy is not kind then someone is both not old and creative and vice versa.
If someone is happy or strong then lucy is either strong or rich and vice versa.
Someone is both not tall and rich.
Alice is either not calm or strong.
John is both not wise and old.
Lucy is not generous or not happy.
Fred is both strong and creative.
Alice is both tall and calm.
Paul is patient or not curious.
Someone is both strong and tall. | Lucy is not humble. | neutral | (![X]:(~curious(X)=>(~curious(X)&~brave(X))))&
(![X]:((~patient(X)&curious(X))<=>(happy(X)|~tall(X))))&
(((~funny(alice)|patient(alice)))=>((~brave(lucy)|~humble(lucy))))&
(![X]:((~generous(X)&kind(X))=>(~creative(X)&funny(X))))&
(![X]:(~calm(X)<=>(~wise(X)&~kind(X))))&
((?[X]:((brave(X)|~creative(X))))=>((kind(paul)&~strong(paul))))&
(![X]:((happy(X)<~>~calm(X))<=>(funny(X)&~curious(X))))&
(![X]:((~quiet(X)|~patient(X))=>~calm(X)))&
((?[X]:((old(X)<~>brave(X))))=>((~old(john)|~creative(john))))&
((?[X]:(kind(X)))<=>((~patient(paul)|kind(paul))))&
(![X]:(funny(X)<=>(creative(X)|~brave(X))))&
((?[X]:(humble(X)))<=>((~old(lucy)|~quiet(lucy))))&
(![X]:((patient(X)&old(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:(brave(X)=>(~strong(X)&happy(X))))&
((~kind(lucy))<=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:((happy(X)|strong(X))))<=>((strong(lucy)<~>rich(lucy))))&
(?[X]:((~tall(X)&rich(X))))&
((~calm(alice)<~>strong(alice)))&
((~wise(john)&old(john)))&
((~generous(lucy)|~happy(lucy)))&
((strong(fred)&creative(fred)))&
((tall(alice)&calm(alice)))&
((patient(paul)|~curious(paul)))&
(?[X]:((strong(X)&tall(X)))) | ~humble(lucy) | [] | null | 0 |
If someone is not strong or curious then alice is both old and not patient and vice versa.
Everyone who is both quiet and calm is both not brave and not happy.
Everyone who is either creative or old is not old.
Everyone who is both not creative and curious is either humble or not curious and vice versa.
If lucy is not humble then paul is not kind or not creative.
If someone is either humble or not calm then someone is not curious and vice versa.
Everyone who is generous is both not generous and funny.
If fred is creative or not happy then lucy is not curious or not humble and vice versa.
If someone is humble then mary is both not calm and curious and vice versa.
Everyone who is not funny is brave.
Everyone who is either not brave or not rich is both not patient and not generous.
Everyone who is both tall and not brave is not tall and vice versa.
Everyone who is not creative or wise is calm or rich and vice versa.
Everyone who is brave or strong is both happy and kind.
If someone is both generous and creative then someone is quiet and vice versa.
If susan is wise then susan is not happy and vice versa.
Someone is either not old or wise.
John is not kind or not funny.
Paul is not generous.
Mary is either not happy or rich.
Paul is not calm.
Susan is creative or not curious. | John is brave. | entailment | ((?[X]:((~strong(X)|curious(X))))<=>((old(alice)&~patient(alice))))&
(![X]:((quiet(X)&calm(X))=>(~brave(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))=>~old(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)<~>~curious(X))))&
((~humble(lucy))=>((~kind(paul)|~creative(paul))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)=>(~generous(X)&funny(X))))&
(((creative(fred)|~happy(fred)))<=>((~curious(lucy)|~humble(lucy))))&
((?[X]:(humble(X)))<=>((~calm(mary)&curious(mary))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~brave(X)<~>~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
(![X]:((~creative(X)|wise(X))<=>(calm(X)|rich(X))))&
(![X]:((brave(X)|strong(X))=>(happy(X)&kind(X))))&
((?[X]:((generous(X)&creative(X))))<=>(?[X]:(quiet(X))))&
((wise(susan))<=>(~happy(susan)))&
(?[X]:((~old(X)<~>wise(X))))&
((~kind(john)|~funny(john)))&
(~generous(paul))&
((~happy(mary)<~>rich(mary)))&
(~calm(paul))&
((creative(susan)|~curious(susan))) | brave(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 29325741050185909706771
% SZS output start Proof for 29325741050185909706771
12. ! [X0] : ((~brave(X0) & tall(X0)) <=> ~tall(X0)) [input p11]
23. ~brave(john) [input hypothesis]
56. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 12]
57. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | ~tall(X0))) [flattening 56]
104. ~tall(X0) | brave(X0) | ~tall(X0) [cnf transformation 57]
105. tall(X0) | tall(X0) [cnf transformation 57]
128. ~brave(john) [cnf transformation 23]
129. ~tall(X0) | brave(X0) [duplicate literal removal 104]
130. tall(X0) [duplicate literal removal 105]
235. brave(X0) [subsumption resolution 129,130]
270. $false [subsumption resolution 128,235]
% SZS output end Proof for 29325741050185909706771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not brave is either happy or tall.
If someone is not creative then fred is not wise.
If someone is happy or not wise then someone is both old and kind and vice versa.
Everyone who is both not happy and not quiet is old or tall and vice versa.
Everyone who is not humble or not brave is funny.
If john is not wise then someone is either rich or patient.
Everyone who is calm or not rich is not patient.
Everyone who is both not strong and not old is not quiet or not kind and vice versa.
Everyone who is not patient is creative and vice versa.
Everyone who is humble or quiet is not generous or quiet.
If someone is old or not patient then susan is either funny or not curious and vice versa.
If someone is not brave then someone is not humble and vice versa.
Everyone who is not humble or calm is either humble or not wise.
Lucy is both not quiet and rich.
Paul is happy or not happy.
Mary is both not kind and tall.
John is calm.
John is not patient or humble.
Fred is not old. | Lucy is not tall. | contradiction | (![X]:((brave(X)|~brave(X))=>(happy(X)<~>tall(X))))&
((?[X]:(~creative(X)))=>(~wise(fred)))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:((old(X)&kind(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(old(X)|tall(X))))&
(![X]:((~humble(X)|~brave(X))=>funny(X)))&
((~wise(john))=>(?[X]:((rich(X)<~>patient(X)))))&
(![X]:((calm(X)|~rich(X))=>~patient(X)))&
(![X]:((~strong(X)&~old(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:((humble(X)|quiet(X))=>(~generous(X)|quiet(X))))&
((?[X]:((old(X)|~patient(X))))<=>((funny(susan)<~>~curious(susan))))&
((?[X]:(~brave(X)))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|calm(X))=>(humble(X)<~>~wise(X))))&
((~quiet(lucy)&rich(lucy)))&
((happy(paul)|~happy(paul)))&
((~kind(mary)&tall(mary)))&
(calm(john))&
((~patient(john)|humble(john)))&
(~old(fred)) | ~tall(lucy) | [
"p0",
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7543483443437012854915493
% SZS output start Proof for 7543483443437012854915493
1. ! [X0] : ((~brave(X0) | brave(X0)) => (happy(X0) <~> tall(X0))) [input p0]
3. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X0] : (kind(X0) & old(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (tall(X0) | old(X0))) [input p3]
8. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p7]
20. ~tall(lucy) [input hypothesis]
21. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X1] : (kind(X1) & old(X1)) [rectify 3]
24. ! [X0] : ((happy(X0) <~> tall(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 1]
30. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (brave(X0) & ~brave(X0))) [nnf transformation 24]
31. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X1] : (kind(X1) & old(X1)) | ! [X0] : (wise(X0) & ~happy(X0))) [nnf transformation 21]
32. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X2] : (kind(X2) & old(X2)) | ! [X3] : (wise(X3) & ~happy(X3))) [rectify 31]
33. ? [X0] : (~wise(X0) | happy(X0)) => (~wise(sK0) | happy(sK0)) [choice axiom]
34. ? [X2] : (kind(X2) & old(X2)) => (kind(sK1) & old(sK1)) [choice axiom]
35. ((~wise(sK0) | happy(sK0)) | ! [X1] : (~kind(X1) | ~old(X1))) & ((kind(sK1) & old(sK1)) | ! [X3] : (wise(X3) & ~happy(X3))) [skolemisation 32,34,33]
36. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 4]
37. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | quiet(X0) | happy(X0))) [flattening 36]
41. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (old(X0) | strong(X0)))) [nnf transformation 8]
42. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | old(X0) | strong(X0))) [flattening 41]
54. tall(X0) | happy(X0) | ~brave(X0) [cnf transformation 30]
55. tall(X0) | happy(X0) | brave(X0) [cnf transformation 30]
59. old(sK1) | ~happy(X3) [cnf transformation 35]
67. ~quiet(X0) | ~old(X0) [cnf transformation 37]
78. ~old(X0) | quiet(X0) [cnf transformation 42]
102. ~tall(lucy) [cnf transformation 20]
105. tall(X0) | happy(X0) [subsumption resolution 54,55]
135. 8 <=> ! [X3] : ~happy(X3) [avatar definition]
136. ~happy(X3) <- (8) [avatar component clause 135]
139. 9 <=> old(sK1) [avatar definition]
141. old(sK1) <- (9) [avatar component clause 139]
143. 8 | 9 [avatar split clause 59,139,135]
158. ~old(X0) [subsumption resolution 78,67]
210. $false <- (9) [subsumption resolution 141,158]
211. ~9 [avatar contradiction clause 210]
233. happy(lucy) [resolution 105,102]
235. $false <- (8) [subsumption resolution 233,136]
236. ~8 [avatar contradiction clause 235]
237. $false [avatar sat refutation 143,211,236]
% SZS output end Proof for 7543483443437012854915493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is strong and vice versa. Everyone who is either happy or not funny is tall or not quiet. If john is either kind or rich then someone is either not rich or kind. Everyone who is either not old or not strong is not happy or not brave and vice versa. Everyone who is either not creative or not kind is generous or calm and vice versa. If alice is either rich or happy then mary is both happy and not wise and vice versa. Everyone who is either calm or strong is humble or not old and vice versa. Everyone who is either brave or calm is either not humble or not strong and vice versa. Everyone who is not funny is both not calm and curious. If someone is quiet then someone is either humble or not strong and vice versa. If someone is brave or happy then someone is both funny and not curious and vice versa. If someone is either not patient or quiet then someone is not brave or not wise. If someone is both not creative and not tall then paul is tall or not patient and vice versa. Everyone who is not brave is both not patient and not rich. If susan is not kind or not calm then someone is both not patient and not happy and vice versa. If susan is either kind or strong then fred is either not calm or not humble and vice versa. Someone is quiet. Someone is either rich or creative. Lucy is either tall or generous. Alice is either not tall or quiet. John is brave. Someone is not creative or humble. Susan is either not old or rich. Lucy is either not rich or funny. | Alice is calm. | entailment | (![X]:(old(X)<=>strong(X)))&
(![X]:((happy(X)<~>~funny(X))=>(tall(X)|~quiet(X))))&
(((kind(john)<~>rich(john)))=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~strong(X))<=>(~happy(X)|~brave(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(generous(X)|calm(X))))&
(((rich(alice)<~>happy(alice)))<=>((happy(mary)&~wise(mary))))&
(![X]:((calm(X)<~>strong(X))<=>(humble(X)|~old(X))))&
(![X]:((brave(X)<~>calm(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:(~funny(X)=>(~calm(X)&curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((brave(X)|happy(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>((tall(paul)|~patient(paul))))&
(![X]:(~brave(X)=>(~patient(X)&~rich(X))))&
(((~kind(susan)|~calm(susan)))<=>(?[X]:((~patient(X)&~happy(X)))))&
(((kind(susan)<~>strong(susan)))<=>((~calm(fred)<~>~humble(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((rich(X)<~>creative(X))))&
((tall(lucy)<~>generous(lucy)))&
((~tall(alice)<~>quiet(alice)))&
(brave(john))&
(?[X]:((~creative(X)|humble(X))))&
((~old(susan)<~>rich(susan)))&
((~rich(lucy)<~>funny(lucy))) | calm(alice) | [
"p0",
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8848809593155640071378383
% SZS output start Proof for 8848809593155640071378383
1. ! [X0] : (old(X0) <=> strong(X0)) [input p0]
4. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~brave(X0) | ~happy(X0))) [input p3]
7. ! [X0] : ((calm(X0) <~> strong(X0)) <=> (~old(X0) | humble(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p7]
25. ~calm(alice) [input hypothesis]
35. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 1]
40. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & ((~brave(X0) | ~happy(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 4]
41. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (brave(X0) & happy(X0))) & (~brave(X0) | ~happy(X0) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 40]
46. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [flattening 46]
48. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 8]
85. ~old(X0) | strong(X0) [cnf transformation 35]
86. ~strong(X0) | old(X0) [cnf transformation 35]
96. ~strong(X0) | ~old(X0) | brave(X0) [cnf transformation 41]
98. strong(X0) | old(X0) | brave(X0) [cnf transformation 41]
112. ~old(X0) | humble(X0) | calm(X0) | ~strong(X0) [cnf transformation 47]
113. ~humble(X0) | calm(X0) | strong(X0) [cnf transformation 47]
114. strong(X0) | calm(X0) | old(X0) [cnf transformation 47]
117. ~strong(X0) | ~humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 48]
119. strong(X0) | humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 48]
171. ~calm(alice) [cnf transformation 25]
192. brave(X0) | old(X0) [subsumption resolution 98,86]
194. ~strong(X0) | brave(X0) [subsumption resolution 96,192]
218. calm(X0) | old(X0) [subsumption resolution 114,86]
219. ~strong(X0) | calm(X0) | humble(X0) [subsumption resolution 112,86]
224. ~brave(X0) | calm(X0) | humble(X0) [subsumption resolution 119,219]
225. ~humble(X0) | calm(X0) | ~brave(X0) [subsumption resolution 117,113]
226. ~brave(X0) | calm(X0) [subsumption resolution 225,224]
442. old(alice) [resolution 218,171]
503. strong(alice) [resolution 442,85]
730. brave(alice) [resolution 503,194]
857. calm(alice) [resolution 730,226]
858. $false [subsumption resolution 857,171]
% SZS output end Proof for 8848809593155640071378383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not calm is funny.
If someone is either strong or quiet then someone is both not happy and not curious.
If someone is not wise then someone is not happy or not brave.
Everyone who is not tall is either generous or funny.
Everyone who is patient is either generous or not generous and vice versa.
Everyone who is generous is creative or not brave and vice versa.
If susan is not humble or not creative then fred is tall and vice versa.
Everyone who is either brave or calm is both kind and not funny.
Everyone who is tall is calm or brave and vice versa.
If lucy is both calm and not old then john is not rich or patient and vice versa.
Everyone who is both not funny and old is not funny.
Everyone who is not funny or not wise is either not rich or not generous.
Everyone who is both not rich and not happy is either not old or not creative.
If paul is both generous and happy then alice is happy or tall.
Everyone who is both patient and kind is not kind or calm and vice versa.
Everyone who is both not wise and old is wise and vice versa.
Fred is humble or wise.
Susan is either not kind or patient.
Alice is either not funny or tall.
Lucy is not patient or funny.
Someone is not brave or quiet.
Someone is either creative or not old. | Fred is not generous. | neutral | (![X]:((rich(X)<~>~calm(X))=>funny(X)))&
((?[X]:((strong(X)<~>quiet(X))))=>(?[X]:((~happy(X)&~curious(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:(~tall(X)=>(generous(X)<~>funny(X))))&
(![X]:(patient(X)<=>(generous(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(creative(X)|~brave(X))))&
(((~humble(susan)|~creative(susan)))<=>(tall(fred)))&
(![X]:((brave(X)<~>calm(X))=>(kind(X)&~funny(X))))&
(![X]:(tall(X)<=>(calm(X)|brave(X))))&
(((calm(lucy)&~old(lucy)))<=>((~rich(john)|patient(john))))&
(![X]:((~funny(X)&old(X))=>~funny(X)))&
(![X]:((~funny(X)|~wise(X))=>(~rich(X)<~>~generous(X))))&
(![X]:((~rich(X)&~happy(X))=>(~old(X)<~>~creative(X))))&
(((generous(paul)&happy(paul)))=>((happy(alice)|tall(alice))))&
(![X]:((patient(X)&kind(X))<=>(~kind(X)|calm(X))))&
(![X]:((~wise(X)&old(X))<=>wise(X)))&
((humble(fred)|wise(fred)))&
((~kind(susan)<~>patient(susan)))&
((~funny(alice)<~>tall(alice)))&
((~patient(lucy)|funny(lucy)))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:((creative(X)<~>~old(X)))) | ~generous(fred) | [] | null | 0 |
If susan is either patient or curious then someone is not wise or old and vice versa.
Everyone who is both funny and not quiet is not generous.
If someone is not humble or patient then someone is not brave.
Everyone who is either not old or rich is not rich and vice versa.
If fred is patient then someone is funny or happy.
Everyone who is both not wise and quiet is patient or not brave.
Everyone who is either not curious or tall is creative and vice versa.
If lucy is both not old and strong then john is either rich or not curious.
If alice is either not funny or not strong then someone is either calm or old and vice versa.
If alice is not wise or not calm then paul is either not creative or wise.
Everyone who is not creative or not rich is both funny and not curious and vice versa.
If john is both rich and creative then paul is old or strong and vice versa.
If someone is not patient then susan is calm and vice versa.
Everyone who is not curious or tall is tall or calm and vice versa.
Everyone who is both not humble and patient is both calm and patient.
If someone is not kind then someone is both not creative and not brave.
Mary is not creative or not tall.
Someone is quiet or tall.
Someone is both not creative and not kind.
Someone is rich.
Mary is wise.
Someone is not old. | Mary is not curious. | entailment | (((patient(susan)<~>curious(susan)))<=>(?[X]:((~wise(X)|old(X)))))&
(![X]:((funny(X)&~quiet(X))=>~generous(X)))&
((?[X]:((~humble(X)|patient(X))))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)<~>rich(X))<=>~rich(X)))&
((patient(fred))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~wise(X)&quiet(X))=>(patient(X)|~brave(X))))&
(![X]:((~curious(X)<~>tall(X))<=>creative(X)))&
(((~old(lucy)&strong(lucy)))=>((rich(john)<~>~curious(john))))&
(((~funny(alice)<~>~strong(alice)))<=>(?[X]:((calm(X)<~>old(X)))))&
(((~wise(alice)|~calm(alice)))=>((~creative(paul)<~>wise(paul))))&
(![X]:((~creative(X)|~rich(X))<=>(funny(X)&~curious(X))))&
(((rich(john)&creative(john)))<=>((old(paul)|strong(paul))))&
((?[X]:(~patient(X)))<=>(calm(susan)))&
(![X]:((~curious(X)|tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&patient(X))=>(calm(X)&patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
((~creative(mary)|~tall(mary)))&
(?[X]:((quiet(X)|tall(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:(rich(X)))&
(wise(mary))&
(?[X]:(~old(X))) | ~curious(mary) | [
"p6",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5468032162781081264195330
% SZS output start Proof for 5468032162781081264195330
7. ! [X0] : ((~curious(X0) <~> tall(X0)) <=> creative(X0)) [input p6]
11. ! [X0] : ((~rich(X0) | ~creative(X0)) <=> (~curious(X0) & funny(X0))) [input p10]
17. ~tall(mary) | ~creative(mary) [input p16]
23. curious(mary) [input hypothesis]
42. ! [X0] : ((((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~creative(X0)) & (creative(X0) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0))))) [nnf transformation 7]
49. ! [X0] : (((~rich(X0) | ~creative(X0)) | (curious(X0) | ~funny(X0))) & ((~curious(X0) & funny(X0)) | (rich(X0) & creative(X0)))) [nnf transformation 11]
50. ! [X0] : ((~rich(X0) | ~creative(X0) | curious(X0) | ~funny(X0)) & ((~curious(X0) & funny(X0)) | (rich(X0) & creative(X0)))) [flattening 49]
80. ~creative(X0) | ~curious(X0) | tall(X0) [cnf transformation 42]
98. ~curious(X0) | creative(X0) [cnf transformation 50]
113. ~tall(mary) | ~creative(mary) [cnf transformation 17]
119. curious(mary) [cnf transformation 23]
259. 29 <=> creative(mary) [avatar definition]
260. creative(mary) <- (29) [avatar component clause 259]
263. 30 <=> tall(mary) [avatar definition]
265. ~tall(mary) <- (~30) [avatar component clause 263]
266. ~29 | ~30 [avatar split clause 113,263,259]
272. creative(mary) [resolution 98,119]
276. 29 [avatar split clause 272,259]
327. ~curious(mary) | tall(mary) <- (29) [resolution 80,260]
330. tall(mary) <- (29) [subsumption resolution 327,119]
331. $false <- (29, ~30) [subsumption resolution 330,265]
332. ~29 | 30 [avatar contradiction clause 331]
334. $false [avatar sat refutation 266,276,332]
% SZS output end Proof for 5468032162781081264195330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or happy then paul is both patient and humble.
Everyone who is both not creative and brave is quiet or wise.
Everyone who is either old or not kind is both patient and humble and vice versa.
Everyone who is not calm or strong is not quiet and vice versa.
If someone is old then alice is either wise or not calm and vice versa.
Everyone who is patient is both brave and not generous and vice versa.
Everyone who is either old or funny is funny or not wise.
If paul is either brave or not funny then john is both strong and not strong.
If lucy is both patient and not strong then someone is either not rich or not humble and vice versa.
Everyone who is not patient or patient is both humble and patient.
Everyone who is both not curious and not strong is kind or not funny.
Everyone who is both not curious and not wise is brave or not happy and vice versa.
Everyone who is not quiet is either curious or generous.
If someone is not creative then paul is either not quiet or not tall and vice versa.
Everyone who is funny or not strong is both patient and brave.
If mary is not old then someone is kind or quiet and vice versa.
Someone is either not tall or not quiet.
Someone is either not generous or not rich.
Mary is old or happy.
Someone is quiet.
Someone is not quiet or not rich. | Mary is kind. | contradiction | (((wise(lucy)|happy(lucy)))=>((patient(paul)&humble(paul))))&
(![X]:((~creative(X)&brave(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)|strong(X))<=>~quiet(X)))&
((?[X]:(old(X)))<=>((wise(alice)<~>~calm(alice))))&
(![X]:(patient(X)<=>(brave(X)&~generous(X))))&
(![X]:((old(X)<~>funny(X))=>(funny(X)|~wise(X))))&
(((brave(paul)<~>~funny(paul)))=>((strong(john)&~strong(john))))&
(((patient(lucy)&~strong(lucy)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~patient(X)|patient(X))=>(humble(X)&patient(X))))&
(![X]:((~curious(X)&~strong(X))=>(kind(X)|~funny(X))))&
(![X]:((~curious(X)&~wise(X))<=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~generous(X)<~>~rich(X))))&
((old(mary)|happy(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)|~rich(X)))) | kind(mary) | [
"p2",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1792968219610802294128309
% SZS output start Proof for 1792968219610802294128309
3. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (humble(X0) & patient(X0))) [input p2]
10. ! [X0] : ((patient(X0) | ~patient(X0)) => (patient(X0) & humble(X0))) [input p9]
16. ~old(mary) <=> ? [X0] : (quiet(X0) | kind(X0)) [input p15]
20. ? [X0] : quiet(X0) [input p19]
22. kind(mary) [input hypothesis]
29. ! [X0] : ((patient(X0) & humble(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 10]
34. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 3]
35. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [flattening 34]
58. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & (? [X0] : (quiet(X0) | kind(X0)) | old(mary)) [nnf transformation 16]
59. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & (? [X1] : (quiet(X1) | kind(X1)) | old(mary)) [rectify 58]
60. ? [X1] : (quiet(X1) | kind(X1)) => (quiet(sK3) | kind(sK3)) [choice axiom]
61. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & ((quiet(sK3) | kind(sK3)) | old(mary)) [skolemisation 59,60]
68. ? [X0] : quiet(X0) => quiet(sK6) [choice axiom]
69. quiet(sK6) [skolemisation 20,68]
81. ~kind(X0) | old(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 35]
106. humble(X0) | ~patient(X0) [cnf transformation 29]
107. patient(X0) | patient(X0) [cnf transformation 29]
127. ~old(mary) | ~quiet(X0) [cnf transformation 61]
133. quiet(sK6) [cnf transformation 69]
135. kind(mary) [cnf transformation 22]
136. patient(X0) [duplicate literal removal 107]
221. humble(X0) [subsumption resolution 106,136]
242. 22 <=> ! [X0] : ~quiet(X0) [avatar definition]
243. ~quiet(X0) <- (22) [avatar component clause 242]
245. 23 <=> old(mary) [avatar definition]
247. ~old(mary) <- (~23) [avatar component clause 245]
248. 22 | ~23 [avatar split clause 127,245,242]
299. $false <- (22) [resolution 243,133]
300. ~22 [avatar contradiction clause 299]
354. old(mary) | ~humble(mary) | ~patient(mary) [resolution 81,135]
360. ~humble(mary) | ~patient(mary) <- (~23) [subsumption resolution 354,247]
361. ~patient(mary) <- (~23) [subsumption resolution 360,221]
362. $false <- (~23) [subsumption resolution 361,136]
363. 23 [avatar contradiction clause 362]
368. $false [avatar sat refutation 248,300,363]
% SZS output end Proof for 1792968219610802294128309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is wise or kind is not kind or wise and vice versa. Everyone who is both not patient and humble is generous or rich and vice versa. Everyone who is either happy or not funny is either funny or not calm. If alice is funny then someone is either not quiet or rich. If someone is brave or generous then someone is both not funny and not wise and vice versa. Everyone who is either generous or not wise is both creative and not brave and vice versa. Everyone who is both rich and old is either not wise or tall. If someone is not tall then someone is either not funny or not tall and vice versa. If someone is either not patient or not creative then paul is funny or not strong. If someone is both happy and not funny then someone is either not humble or calm and vice versa. Everyone who is either not old or patient is both not humble and strong and vice versa. If alice is quiet then someone is either brave or quiet and vice versa. Everyone who is not old or not wise is not kind. Everyone who is not patient or not tall is not brave and vice versa. Everyone who is not rich is both not creative and not humble and vice versa. If john is brave then someone is either kind or not humble and vice versa. Mary is either curious or humble. Someone is not brave. John is not happy or generous. Mary is calm or not wise. | Paul is brave. | contradiction | (![X]:((wise(X)|kind(X))<=>(~kind(X)|wise(X))))&
(![X]:((~patient(X)&humble(X))<=>(generous(X)|rich(X))))&
(![X]:((happy(X)<~>~funny(X))=>(funny(X)<~>~calm(X))))&
((funny(alice))=>(?[X]:((~quiet(X)<~>rich(X)))))&
((?[X]:((brave(X)|generous(X))))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((generous(X)<~>~wise(X))<=>(creative(X)&~brave(X))))&
(![X]:((rich(X)&old(X))=>(~wise(X)<~>tall(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~funny(X)<~>~tall(X)))))&
((?[X]:((~patient(X)<~>~creative(X))))=>((funny(paul)|~strong(paul))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:((~humble(X)<~>calm(X)))))&
(![X]:((~old(X)<~>patient(X))<=>(~humble(X)&strong(X))))&
((quiet(alice))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((~old(X)|~wise(X))=>~kind(X)))&
(![X]:((~patient(X)|~tall(X))<=>~brave(X)))&
(![X]:(~rich(X)<=>(~creative(X)&~humble(X))))&
((brave(john))<=>(?[X]:((kind(X)<~>~humble(X)))))&
((curious(mary)<~>humble(mary)))&
(?[X]:(~brave(X)))&
((~happy(john)|generous(john)))&
((calm(mary)|~wise(mary))) | brave(paul) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 863488448163028119127808
% SZS output start Proof for 863488448163028119127808
1. ! [X0] : ((kind(X0) | wise(X0)) <=> (wise(X0) | ~kind(X0))) [input p0]
5. ? [X0] : (generous(X0) | brave(X0)) <=> ? [X0] : (~wise(X0) & ~funny(X0)) [input p4]
21. brave(paul) [input hypothesis]
22. ? [X0] : (generous(X0) | brave(X0)) <=> ? [X1] : (~wise(X1) & ~funny(X1)) [rectify 5]
32. ! [X0] : (((kind(X0) | wise(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (~kind(X0) & ~wise(X0)))) [nnf transformation 1]
33. ! [X0] : ((kind(X0) | wise(X0) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | (~kind(X0) & ~wise(X0)))) [flattening 32]
40. (? [X0] : (generous(X0) | brave(X0)) | ! [X1] : (wise(X1) | funny(X1))) & (? [X1] : (~wise(X1) & ~funny(X1)) | ! [X0] : (~generous(X0) & ~brave(X0))) [nnf transformation 22]
41. (? [X0] : (generous(X0) | brave(X0)) | ! [X1] : (wise(X1) | funny(X1))) & (? [X2] : (~wise(X2) & ~funny(X2)) | ! [X3] : (~generous(X3) & ~brave(X3))) [rectify 40]
42. ? [X0] : (generous(X0) | brave(X0)) => (generous(sK1) | brave(sK1)) [choice axiom]
43. ? [X2] : (~wise(X2) & ~funny(X2)) => (~wise(sK2) & ~funny(sK2)) [choice axiom]
44. ((generous(sK1) | brave(sK1)) | ! [X1] : (wise(X1) | funny(X1))) & ((~wise(sK2) & ~funny(sK2)) | ! [X3] : (~generous(X3) & ~brave(X3))) [skolemisation 41,43,42]
77. wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 33]
78. kind(X0) | wise(X0) | kind(X0) [cnf transformation 33]
93. ~wise(sK2) | ~brave(X3) [cnf transformation 44]
143. brave(paul) [cnf transformation 21]
146. wise(X0) | ~kind(X0) [duplicate literal removal 77]
147. kind(X0) | wise(X0) [duplicate literal removal 78]
148. wise(X0) [subsumption resolution 146,147]
164. ~brave(X3) [subsumption resolution 93,148]
268. $false [subsumption resolution 143,164]
% SZS output end Proof for 863488448163028119127808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm then someone is either calm or not funny and vice versa.
If susan is not old or not brave then fred is either not generous or kind.
If someone is either humble or tall then someone is either not patient or not funny.
If someone is either kind or rich then someone is tall or strong.
If fred is not happy then john is either not kind or not brave.
Everyone who is both not creative and not old is either not strong or calm and vice versa.
Everyone who is both creative and not kind is creative and vice versa.
Everyone who is both funny and calm is curious or not creative and vice versa.
If john is not humble or not brave then someone is either not curious or wise and vice versa.
If alice is either tall or humble then lucy is both not brave and not funny and vice versa.
If someone is rich or strong then john is not happy.
Everyone who is not quiet or patient is both happy and rich and vice versa.
Everyone who is funny or not curious is both humble and not kind.
Everyone who is not calm is either not generous or not creative.
Everyone who is not patient or rich is either generous or old.
Everyone who is happy is not funny or creative and vice versa.
Someone is generous or brave.
John is not creative or not strong.
Someone is either calm or not wise.
Lucy is either creative or patient. | Alice is generous. | neutral | ((~calm(john))<=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~old(susan)|~brave(susan)))=>((~generous(fred)<~>kind(fred))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)<~>rich(X))))=>(?[X]:((tall(X)|strong(X)))))&
((~happy(fred))=>((~kind(john)<~>~brave(john))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((creative(X)&~kind(X))<=>creative(X)))&
(![X]:((funny(X)&calm(X))<=>(curious(X)|~creative(X))))&
(((~humble(john)|~brave(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((tall(alice)<~>humble(alice)))<=>((~brave(lucy)&~funny(lucy))))&
((?[X]:((rich(X)|strong(X))))=>(~happy(john)))&
(![X]:((~quiet(X)|patient(X))<=>(happy(X)&rich(X))))&
(![X]:((funny(X)|~curious(X))=>(humble(X)&~kind(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~creative(X))))&
(![X]:((~patient(X)|rich(X))=>(generous(X)<~>old(X))))&
(![X]:(happy(X)<=>(~funny(X)|creative(X))))&
(?[X]:((generous(X)|brave(X))))&
((~creative(john)|~strong(john)))&
(?[X]:((calm(X)<~>~wise(X))))&
((creative(lucy)<~>patient(lucy))) | generous(alice) | [] | null | 0 |
If fred is either not generous or not humble then alice is both not quiet and generous.
If john is either not wise or creative then paul is not rich.
If someone is not funny then mary is either not old or curious.
If john is not funny then paul is rich and vice versa.
If alice is both happy and rich then someone is creative or wise and vice versa.
Everyone who is either quiet or kind is rich.
Everyone who is either not creative or generous is both not happy and not humble.
Everyone who is generous or not tall is not calm or wise.
If someone is strong or not funny then someone is happy and vice versa.
Everyone who is either calm or kind is either not humble or not curious and vice versa.
Everyone who is both not strong and not humble is not quiet and vice versa.
Everyone who is generous or not generous is tall and vice versa.
Everyone who is either not creative or calm is not kind.
Everyone who is both not curious and funny is either happy or curious.
Everyone who is creative or generous is both not curious and funny.
If someone is brave or calm then lucy is either strong or not strong and vice versa.
Fred is both not brave and kind.
Someone is either not quiet or not brave.
John is not brave or quiet.
Susan is quiet or wise.
Someone is not brave or happy.
Someone is either curious or not creative.
Someone is either not funny or generous. | Mary is curious. | neutral | (((~generous(fred)<~>~humble(fred)))=>((~quiet(alice)&generous(alice))))&
(((~wise(john)<~>creative(john)))=>(~rich(paul)))&
((?[X]:(~funny(X)))=>((~old(mary)<~>curious(mary))))&
((~funny(john))<=>(rich(paul)))&
(((happy(alice)&rich(alice)))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((quiet(X)<~>kind(X))=>rich(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~happy(X)&~humble(X))))&
(![X]:((generous(X)|~tall(X))=>(~calm(X)|wise(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((calm(X)<~>kind(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~strong(X)&~humble(X))<=>~quiet(X)))&
(![X]:((generous(X)|~generous(X))<=>tall(X)))&
(![X]:((~creative(X)<~>calm(X))=>~kind(X)))&
(![X]:((~curious(X)&funny(X))=>(happy(X)<~>curious(X))))&
(![X]:((creative(X)|generous(X))=>(~curious(X)&funny(X))))&
((?[X]:((brave(X)|calm(X))))<=>((strong(lucy)<~>~strong(lucy))))&
((~brave(fred)&kind(fred)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
((~brave(john)|quiet(john)))&
((quiet(susan)|wise(susan)))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:((~funny(X)<~>generous(X)))) | curious(mary) | [] | null | 0 |
If someone is either not humble or happy then fred is not wise or not tall and vice versa.
If fred is not brave or generous then fred is both not creative and not patient.
Everyone who is not funny or not humble is not calm.
If paul is creative or not funny then fred is creative and vice versa.
Everyone who is either not wise or rich is humble or tall.
Everyone who is either not brave or not wise is either kind or old and vice versa.
If someone is not creative then someone is either not calm or not rich.
If someone is not tall then someone is wise and vice versa.
Everyone who is either not quiet or strong is curious and vice versa.
Everyone who is either kind or not kind is both generous and curious and vice versa.
Everyone who is not strong is not creative and vice versa.
If someone is curious or calm then john is not rich.
Everyone who is either not generous or rich is not happy or brave.
Everyone who is either not curious or not kind is quiet and vice versa.
Someone is either rich or kind.
Lucy is either not wise or curious.
Susan is happy or not generous.
Mary is both not wise and not patient.
Lucy is humble or not brave.
Someone is both humble and not brave.
Someone is quiet or not calm.
Someone is both not happy and old. | Susan is not humble. | neutral | ((?[X]:((~humble(X)<~>happy(X))))<=>((~wise(fred)|~tall(fred))))&
(((~brave(fred)|generous(fred)))=>((~creative(fred)&~patient(fred))))&
(![X]:((~funny(X)|~humble(X))=>~calm(X)))&
(((creative(paul)|~funny(paul)))<=>(creative(fred)))&
(![X]:((~wise(X)<~>rich(X))=>(humble(X)|tall(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>old(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>curious(X)))&
(![X]:((kind(X)<~>~kind(X))<=>(generous(X)&curious(X))))&
(![X]:(~strong(X)<=>~creative(X)))&
((?[X]:((curious(X)|calm(X))))=>(~rich(john)))&
(![X]:((~generous(X)<~>rich(X))=>(~happy(X)|brave(X))))&
(![X]:((~curious(X)<~>~kind(X))<=>quiet(X)))&
(?[X]:((rich(X)<~>kind(X))))&
((~wise(lucy)<~>curious(lucy)))&
((happy(susan)|~generous(susan)))&
((~wise(mary)&~patient(mary)))&
((humble(lucy)|~brave(lucy)))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((~happy(X)&old(X)))) | ~humble(susan) | [] | null | 0 |
If susan is either happy or funny then someone is either kind or not patient. If someone is wise or generous then someone is both patient and not generous and vice versa. Everyone who is either strong or not strong is kind and vice versa. Everyone who is both not brave and old is not generous or not brave and vice versa. If john is rich then someone is either not creative or not happy. Everyone who is tall or funny is either not old or kind. Everyone who is quiet or patient is funny. If paul is happy or not calm then susan is calm and vice versa. Everyone who is creative is not curious or curious and vice versa. Everyone who is not strong is generous or curious. Everyone who is either not humble or funny is both old and not quiet and vice versa. Everyone who is both wise and not kind is curious and vice versa. Everyone who is either not rich or not curious is both patient and humble and vice versa. Everyone who is not patient or not humble is both not strong and tall. Everyone who is either generous or not patient is not patient. If someone is either patient or not old then someone is not generous or calm. Alice is not curious. Alice is either not curious or not quiet. Paul is both rich and funny. Paul is old. Someone is either not creative or wise. Someone is not calm or not humble. | Susan is not wise. | neutral | (((happy(susan)<~>funny(susan)))=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((strong(X)<~>~strong(X))<=>kind(X)))&
(![X]:((~brave(X)&old(X))<=>(~generous(X)|~brave(X))))&
((rich(john))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:((tall(X)|funny(X))=>(~old(X)<~>kind(X))))&
(![X]:((quiet(X)|patient(X))=>funny(X)))&
(((happy(paul)|~calm(paul)))<=>(calm(susan)))&
(![X]:(creative(X)<=>(~curious(X)|curious(X))))&
(![X]:(~strong(X)=>(generous(X)|curious(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(old(X)&~quiet(X))))&
(![X]:((wise(X)&~kind(X))<=>curious(X)))&
(![X]:((~rich(X)<~>~curious(X))<=>(patient(X)&humble(X))))&
(![X]:((~patient(X)|~humble(X))=>(~strong(X)&tall(X))))&
(![X]:((generous(X)<~>~patient(X))=>~patient(X)))&
((?[X]:((patient(X)<~>~old(X))))=>(?[X]:((~generous(X)|calm(X)))))&
(~curious(alice))&
((~curious(alice)<~>~quiet(alice)))&
((rich(paul)&funny(paul)))&
(old(paul))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((~calm(X)|~humble(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is not strong or strong is both wise and rich and vice versa. Everyone who is either not brave or kind is either patient or generous and vice versa. If someone is either brave or not brave then fred is either not patient or rich and vice versa. If susan is either not brave or not wise then john is both not humble and humble. Everyone who is both old and calm is either not rich or strong. If someone is not tall or not creative then someone is both not patient and not old and vice versa. If john is both strong and patient then someone is not calm or not wise. Everyone who is both quiet and curious is not creative and vice versa. If lucy is either not old or not generous then mary is both wise and calm and vice versa. If fred is brave then someone is either tall or quiet and vice versa. If someone is not calm then susan is both not brave and not patient and vice versa. Everyone who is either humble or not happy is rich or not funny. Everyone who is not tall or not quiet is not old or generous. If alice is both not happy and not funny then someone is generous. If lucy is not old then someone is patient and vice versa. Everyone who is funny or not wise is either not funny or not humble. Fred is happy. Someone is funny. Susan is not tall. John is not wise or not humble. Someone is kind. Someone is either not calm or calm. Fred is not tall or creative. | Mary is calm. | entailment | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~patient(fred)<~>rich(fred))))&
(((~brave(susan)<~>~wise(susan)))=>((~humble(john)&humble(john))))&
(![X]:((old(X)&calm(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(((~happy(alice)&~funny(alice)))=>(?[X]:(generous(X))))&
((~old(lucy))<=>(?[X]:(patient(X))))&
(![X]:((funny(X)|~wise(X))=>(~funny(X)<~>~humble(X))))&
(happy(fred))&
(?[X]:(funny(X)))&
(~tall(susan))&
((~wise(john)|~humble(john)))&
(?[X]:(kind(X)))&
(?[X]:((~calm(X)<~>calm(X))))&
((~tall(fred)|creative(fred))) | calm(mary) | [
"p0",
"p3",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6315196251227958041961119
% SZS output start Proof for 6315196251227958041961119
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & wise(X0))) [input p0]
4. (~brave(susan) <~> ~wise(susan)) => (humble(john) & ~humble(john)) [input p3]
11. ? [X0] : ~calm(X0) <=> (~patient(susan) & ~brave(susan)) [input p10]
20. ~humble(john) | ~wise(john) [input p19]
24. ~calm(mary) [input hypothesis]
26. (humble(john) & ~humble(john)) | (~brave(susan) <=> ~wise(susan)) [ennf transformation 4]
38. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [flattening 38]
45. (humble(john) & ~humble(john)) | ((~brave(susan) | wise(susan)) & (~wise(susan) | brave(susan))) [nnf transformation 26]
62. (? [X0] : ~calm(X0) | (patient(susan) | brave(susan))) & ((~patient(susan) & ~brave(susan)) | ! [X0] : calm(X0)) [nnf transformation 11]
63. (? [X0] : ~calm(X0) | patient(susan) | brave(susan)) & ((~patient(susan) & ~brave(susan)) | ! [X0] : calm(X0)) [flattening 62]
64. (? [X0] : ~calm(X0) | patient(susan) | brave(susan)) & ((~patient(susan) & ~brave(susan)) | ! [X1] : calm(X1)) [rectify 63]
65. ? [X0] : ~calm(X0) => ~calm(sK5) [choice axiom]
66. (~calm(sK5) | patient(susan) | brave(susan)) & ((~patient(susan) & ~brave(susan)) | ! [X1] : calm(X1)) [skolemisation 64,65]
82. wise(X0) | strong(X0) [cnf transformation 39]
83. wise(X0) | ~strong(X0) [cnf transformation 39]
105. humble(john) | ~wise(susan) | brave(susan) [cnf transformation 45]
128. ~brave(susan) | calm(X1) [cnf transformation 66]
145. ~humble(john) | ~wise(john) [cnf transformation 20]
150. ~calm(mary) [cnf transformation 24]
157. wise(X0) [subsumption resolution 82,83]
172. humble(john) | brave(susan) [subsumption resolution 105,157]
174. 4 <=> brave(susan) [avatar definition]
178. 5 <=> humble(john) [avatar definition]
181. 4 | 5 [avatar split clause 172,178,174]
231. 16 <=> calm(mary) [avatar definition]
233. ~calm(mary) <- (~16) [avatar component clause 231]
279. 26 <=> ! [X1] : calm(X1) [avatar definition]
280. calm(X1) <- (26) [avatar component clause 279]
282. 26 | ~4 [avatar split clause 128,174,279]
305. ~humble(john) [subsumption resolution 145,157]
306. ~5 [avatar split clause 305,178]
316. ~16 [avatar split clause 150,231]
317. $false <- (~16, 26) [subsumption resolution 233,280]
318. 16 | ~26 [avatar contradiction clause 317]
323. $false [avatar sat refutation 181,282,306,316,318]
% SZS output end Proof for 6315196251227958041961119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is generous or not quiet and vice versa. If someone is both not happy and not old then someone is both humble and old and vice versa. If john is both not tall and not funny then lucy is tall. Everyone who is either funny or not wise is both patient and not creative and vice versa. Everyone who is either not humble or not brave is either not rich or curious. Everyone who is funny or not strong is either funny or happy. Everyone who is happy or not curious is not happy or not patient. If john is tall then someone is funny and vice versa. If mary is either not happy or curious then mary is either generous or wise and vice versa. If lucy is both creative and wise then mary is strong and vice versa. If someone is either quiet or not rich then someone is brave or not happy and vice versa. Everyone who is not patient or tall is both not funny and not wise. If susan is either not kind or old then mary is either not tall or patient and vice versa. Everyone who is not wise is patient or not curious. If someone is kind then someone is both curious and happy. If someone is either not curious or not wise then fred is not creative and vice versa. Alice is either tall or generous. John is funny or not quiet. Someone is either not generous or brave. Someone is humble. Alice is not humble. Lucy is both not calm and not funny. Someone is strong. Alice is brave or not old. | John is kind. | contradiction | ((?[X]:(~happy(X)))<=>(?[X]:((generous(X)|~quiet(X)))))&
((?[X]:((~happy(X)&~old(X))))<=>(?[X]:((humble(X)&old(X)))))&
(((~tall(john)&~funny(john)))=>(tall(lucy)))&
(![X]:((funny(X)<~>~wise(X))<=>(patient(X)&~creative(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(~rich(X)<~>curious(X))))&
(![X]:((funny(X)|~strong(X))=>(funny(X)<~>happy(X))))&
(![X]:((happy(X)|~curious(X))=>(~happy(X)|~patient(X))))&
((tall(john))<=>(?[X]:(funny(X))))&
(((~happy(mary)<~>curious(mary)))<=>((generous(mary)<~>wise(mary))))&
(((creative(lucy)&wise(lucy)))<=>(strong(mary)))&
((?[X]:((quiet(X)<~>~rich(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((~patient(X)|tall(X))=>(~funny(X)&~wise(X))))&
(((~kind(susan)<~>old(susan)))<=>((~tall(mary)<~>patient(mary))))&
(![X]:(~wise(X)=>(patient(X)|~curious(X))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&happy(X)))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>(~creative(fred)))&
((tall(alice)<~>generous(alice)))&
((funny(john)|~quiet(john)))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:(humble(X)))&
(~humble(alice))&
((~calm(lucy)&~funny(lucy)))&
(?[X]:(strong(X)))&
((brave(alice)|~old(alice))) | kind(john) | [
"p6",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1177050274906910286461016
% SZS output start Proof for 1177050274906910286461016
7. ! [X0] : ((~curious(X0) | happy(X0)) => (~patient(X0) | ~happy(X0))) [input p6]
12. ! [X0] : ((tall(X0) | ~patient(X0)) => (~wise(X0) & ~funny(X0))) [input p11]
14. ! [X0] : (~wise(X0) => (~curious(X0) | patient(X0))) [input p13]
15. ? [X0] : kind(X0) => ? [X0] : (happy(X0) & curious(X0)) [input p14]
25. kind(john) [input hypothesis]
29. ? [X0] : kind(X0) => ? [X1] : (happy(X1) & curious(X1)) [rectify 15]
35. ! [X0] : ((~patient(X0) | ~happy(X0)) | (curious(X0) & ~happy(X0))) [ennf transformation 7]
36. ! [X0] : (~patient(X0) | ~happy(X0) | (curious(X0) & ~happy(X0))) [flattening 35]
37. ! [X0] : ((~wise(X0) & ~funny(X0)) | (~tall(X0) & patient(X0))) [ennf transformation 12]
38. ! [X0] : ((~curious(X0) | patient(X0)) | wise(X0)) [ennf transformation 14]
39. ! [X0] : (~curious(X0) | patient(X0) | wise(X0)) [flattening 38]
40. ? [X1] : (happy(X1) & curious(X1)) | ! [X0] : ~kind(X0) [ennf transformation 29]
68. ? [X0] : (happy(X0) & curious(X0)) | ! [X1] : ~kind(X1) [rectify 40]
69. ? [X0] : (happy(X0) & curious(X0)) => (happy(sK7) & curious(sK7)) [choice axiom]
70. (happy(sK7) & curious(sK7)) | ! [X1] : ~kind(X1) [skolemisation 68,69]
105. ~patient(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 36]
128. ~wise(X0) | patient(X0) [cnf transformation 37]
138. ~curious(X0) | patient(X0) | wise(X0) [cnf transformation 39]
139. curious(sK7) | ~kind(X1) [cnf transformation 70]
140. happy(sK7) | ~kind(X1) [cnf transformation 70]
155. kind(john) [cnf transformation 25]
156. ~patient(X0) | ~happy(X0) [duplicate literal removal 105]
324. ~curious(X0) | patient(X0) [subsumption resolution 138,128]
326. 36 <=> ! [X1] : ~kind(X1) [avatar definition]
327. ~kind(X1) <- (36) [avatar component clause 326]
329. 37 <=> happy(sK7) [avatar definition]
331. happy(sK7) <- (37) [avatar component clause 329]
332. 36 | 37 [avatar split clause 140,329,326]
334. 38 <=> curious(sK7) [avatar definition]
336. curious(sK7) <- (38) [avatar component clause 334]
337. 36 | 38 [avatar split clause 139,334,326]
396. $false <- (36) [resolution 327,155]
397. ~36 [avatar contradiction clause 396]
407. patient(sK7) <- (38) [resolution 324,336]
421. ~happy(sK7) <- (38) [resolution 407,156]
422. $false <- (37, 38) [subsumption resolution 421,331]
423. ~37 | ~38 [avatar contradiction clause 422]
424. $false [avatar sat refutation 332,337,397,423]
% SZS output end Proof for 1177050274906910286461016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both not calm and wise.
If someone is either funny or quiet then mary is not kind or not creative and vice versa.
Everyone who is humble is kind or brave and vice versa.
Everyone who is either not generous or not calm is not brave or not funny and vice versa.
Everyone who is happy or not curious is not happy and vice versa.
If paul is not tall then john is tall and vice versa.
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Everyone who is either not tall or not funny is not tall and vice versa.
If someone is kind then someone is quiet.
If susan is either old or not creative then someone is humble or not kind.
Everyone who is both not tall and not quiet is either humble or not happy and vice versa.
Everyone who is not humble or kind is not patient.
If someone is both not creative and not generous then lucy is not humble.
Everyone who is not calm is both funny and old.
Someone is both not strong and not curious.
Lucy is either patient or creative.
Paul is not generous or strong.
Someone is both old and strong.
Someone is either not humble or patient.
Susan is wise or happy. | Fred is old. | entailment | (![X]:(generous(X)=>(~calm(X)&wise(X))))&
((?[X]:((funny(X)<~>quiet(X))))<=>((~kind(mary)|~creative(mary))))&
(![X]:(humble(X)<=>(kind(X)|brave(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~brave(X)|~funny(X))))&
(![X]:((happy(X)|~curious(X))<=>~happy(X)))&
((~tall(paul))<=>(tall(john)))&
(((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
(((old(susan)<~>~creative(susan)))=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((~humble(X)|kind(X))=>~patient(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(~humble(lucy)))&
(![X]:(~calm(X)=>(funny(X)&old(X))))&
(?[X]:((~strong(X)&~curious(X))))&
((patient(lucy)<~>creative(lucy)))&
((~generous(paul)|strong(paul)))&
(?[X]:((old(X)&strong(X))))&
(?[X]:((~humble(X)<~>patient(X))))&
((wise(susan)|happy(susan))) | old(fred) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3788801210409759758748959
% SZS output start Proof for 3788801210409759758748959
5. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~happy(X0)) [input p4]
8. ! [X0] : (happy(X0) <=> (~brave(X0) | ~old(X0))) [input p7]
22. ~old(fred) [input hypothesis]
39. ! [X0] : (((~curious(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 5]
40. ! [X0] : ((~curious(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [flattening 39]
47. ! [X0] : ((happy(X0) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | ~happy(X0))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | ~happy(X0))) [flattening 47]
83. ~happy(X0) | ~happy(X0) [cnf transformation 40]
93. happy(X0) | old(X0) [cnf transformation 48]
123. ~old(fred) [cnf transformation 22]
126. ~happy(X0) [duplicate literal removal 83]
195. old(X0) [subsumption resolution 93,126]
246. $false [subsumption resolution 123,195]
% SZS output end Proof for 3788801210409759758748959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall then someone is strong or tall.
Everyone who is not kind or not curious is both generous and wise and vice versa.
If someone is both old and calm then someone is both wise and generous and vice versa.
Everyone who is not kind or creative is funny or patient.
Everyone who is both generous and not tall is either generous or not funny and vice versa.
If fred is old then fred is both calm and old and vice versa.
Everyone who is not quiet is both not humble and not happy.
Everyone who is either not humble or curious is both not humble and not brave and vice versa.
If someone is either creative or not curious then john is funny or generous and vice versa.
Everyone who is rich is either tall or not patient.
Everyone who is not creative or quiet is either not humble or creative and vice versa.
Everyone who is either not brave or not kind is not wise and vice versa.
If someone is both kind and not humble then someone is not curious.
Everyone who is not quiet is either not generous or not strong and vice versa.
Everyone who is funny is kind and vice versa.
Someone is strong or not brave.
Someone is not generous or not brave.
Mary is not brave.
Lucy is either wise or happy.
Someone is either not happy or curious.
Paul is either generous or not old.
Fred is both calm and brave. | Lucy is happy. | contradiction | ((?[X]:((creative(X)<~>tall(X))))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(generous(X)&wise(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((~kind(X)|creative(X))=>(funny(X)|patient(X))))&
(![X]:((generous(X)&~tall(X))<=>(generous(X)<~>~funny(X))))&
((old(fred))<=>((calm(fred)&old(fred))))&
(![X]:(~quiet(X)=>(~humble(X)&~happy(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(~humble(X)&~brave(X))))&
((?[X]:((creative(X)<~>~curious(X))))<=>((funny(john)|generous(john))))&
(![X]:(rich(X)=>(tall(X)<~>~patient(X))))&
(![X]:((~creative(X)|quiet(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~brave(X)<~>~kind(X))<=>~wise(X)))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:(~curious(X))))&
(![X]:(~quiet(X)<=>(~generous(X)<~>~strong(X))))&
(![X]:(funny(X)<=>kind(X)))&
(?[X]:((strong(X)|~brave(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(~brave(mary))&
((wise(lucy)<~>happy(lucy)))&
(?[X]:((~happy(X)<~>curious(X))))&
((generous(paul)<~>~old(paul)))&
((calm(fred)&brave(fred))) | happy(lucy) | [
"p1",
"p7",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 958558266414777390504968
% SZS output start Proof for 958558266414777390504968
2. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (wise(X0) & generous(X0))) [input p1]
8. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (~brave(X0) & ~humble(X0))) [input p7]
12. ! [X0] : ((~brave(X0) <~> ~kind(X0)) <=> ~wise(X0)) [input p11]
19. wise(lucy) <~> happy(lucy) [input p18]
23. happy(lucy) [input hypothesis]
36. ! [X0] : (((~curious(X0) | ~kind(X0)) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 2]
37. ! [X0] : ((~curious(X0) | ~kind(X0) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | (curious(X0) & kind(X0)))) [flattening 36]
47. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (brave(X0) | humble(X0))) & ((~brave(X0) & ~humble(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 8]
48. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | brave(X0) | humble(X0)) & ((~brave(X0) & ~humble(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [flattening 47]
56. ! [X0] : ((((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | wise(X0)) & (~wise(X0) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0))))) [nnf transformation 12]
66. (~happy(lucy) | ~wise(lucy)) & (happy(lucy) | wise(lucy)) [nnf transformation 19]
75. wise(X0) | kind(X0) [cnf transformation 37]
76. wise(X0) | curious(X0) [cnf transformation 37]
94. ~humble(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 48]
98. ~curious(X0) | humble(X0) | brave(X0) | humble(X0) [cnf transformation 48]
113. ~kind(X0) | ~brave(X0) | wise(X0) [cnf transformation 56]
126. ~happy(lucy) | ~wise(lucy) [cnf transformation 66]
133. happy(lucy) [cnf transformation 23]
136. ~humble(X0) | ~curious(X0) [duplicate literal removal 94]
137. ~curious(X0) | humble(X0) | brave(X0) [duplicate literal removal 98]
213. ~brave(X0) | wise(X0) [subsumption resolution 113,75]
242. 23 <=> wise(lucy) [avatar definition]
244. ~wise(lucy) <- (~23) [avatar component clause 242]
246. 24 <=> happy(lucy) [avatar definition]
249. ~23 | ~24 [avatar split clause 126,246,242]
272. 24 [avatar split clause 133,246]
278. curious(lucy) <- (~23) [resolution 76,244]
357. 36 <=> humble(lucy) [avatar definition]
359. humble(lucy) <- (36) [avatar component clause 357]
408. humble(lucy) | brave(lucy) <- (~23) [resolution 137,278]
411. 43 <=> brave(lucy) [avatar definition]
413. brave(lucy) <- (43) [avatar component clause 411]
414. 43 | 36 | 23 [avatar split clause 408,242,357,411]
439. ~curious(lucy) <- (36) [resolution 359,136]
443. $false <- (~23, 36) [subsumption resolution 439,278]
444. 23 | ~36 [avatar contradiction clause 443]
463. wise(lucy) <- (43) [resolution 413,213]
464. $false <- (~23, 43) [subsumption resolution 463,244]
465. 23 | ~43 [avatar contradiction clause 464]
466. $false [avatar sat refutation 249,272,414,444,465]
% SZS output end Proof for 958558266414777390504968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not curious is humble and vice versa.
If paul is both not calm and not strong then someone is either not patient or old and vice versa.
Everyone who is not calm is not old and vice versa.
Everyone who is not humble is either calm or old.
Everyone who is not generous or not quiet is both not humble and not funny and vice versa.
Everyone who is creative or not creative is both wise and old.
If someone is curious or tall then someone is both not happy and humble and vice versa.
If someone is both calm and patient then someone is rich or not old.
If someone is both kind and not happy then someone is either strong or not calm and vice versa.
Everyone who is either wise or not funny is not humble.
If lucy is not generous or wise then susan is wise or not quiet.
Everyone who is not funny is rich or strong.
Everyone who is not strong is both not brave and not wise.
John is not generous or brave.
Someone is either not rich or not happy.
Someone is not curious.
Someone is either not rich or generous. | Paul is patient. | contradiction | (![X]:((~creative(X)&~curious(X))<=>humble(X)))&
(((~calm(paul)&~strong(paul)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:(~humble(X)=>(calm(X)<~>old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~humble(X)&~funny(X))))&
(![X]:((creative(X)|~creative(X))=>(wise(X)&old(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~happy(X)&humble(X)))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:((rich(X)|~old(X)))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((wise(X)<~>~funny(X))=>~humble(X)))&
(((~generous(lucy)|wise(lucy)))=>((wise(susan)|~quiet(susan))))&
(![X]:(~funny(X)=>(rich(X)|strong(X))))&
(![X]:(~strong(X)=>(~brave(X)&~wise(X))))&
((~generous(john)|brave(john)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>generous(X)))) | patient(paul) | [
"p1",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4096690798302469745755154
% SZS output start Proof for 4096690798302469745755154
2. (~strong(paul) & ~calm(paul)) <=> ? [X0] : (~patient(X0) <~> old(X0)) [input p1]
6. ! [X0] : ((~creative(X0) | creative(X0)) => (old(X0) & wise(X0))) [input p5]
13. ! [X0] : (~strong(X0) => (~wise(X0) & ~brave(X0))) [input p12]
18. patient(paul) [input hypothesis]
23. ! [X0] : ((old(X0) & wise(X0)) | (creative(X0) & ~creative(X0))) [ennf transformation 6]
30. ! [X0] : ((~wise(X0) & ~brave(X0)) | strong(X0)) [ennf transformation 13]
33. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (strong(paul) | calm(paul))) [nnf transformation 2]
34. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | strong(paul) | calm(paul)) [flattening 33]
35. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X1] : ((~old(X1) | patient(X1)) & (old(X1) | ~patient(X1))) | strong(paul) | calm(paul)) [rectify 34]
36. ? [X1] : ((~old(X1) | patient(X1)) & (old(X1) | ~patient(X1))) => ((~old(sK0) | patient(sK0)) & (old(sK0) | ~patient(sK0))) [choice axiom]
37. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(sK0) | patient(sK0)) & (old(sK0) | ~patient(sK0))) | strong(paul) | calm(paul)) [skolemisation 35,36]
72. ~strong(paul) | ~patient(X0) | ~old(X0) [cnf transformation 37]
82. wise(X0) | ~creative(X0) [cnf transformation 23]
83. wise(X0) | creative(X0) [cnf transformation 23]
84. old(X0) | ~creative(X0) [cnf transformation 23]
85. old(X0) | creative(X0) [cnf transformation 23]
104. ~wise(X0) | strong(X0) [cnf transformation 30]
111. patient(paul) [cnf transformation 18]
113. 1 <=> ! [X0] : (~patient(X0) | ~old(X0)) [avatar definition]
114. ~patient(X0) | ~old(X0) <- (1) [avatar component clause 113]
116. 2 <=> strong(paul) [avatar definition]
118. ~strong(paul) <- (~2) [avatar component clause 116]
119. 1 | ~2 [avatar split clause 72,116,113]
145. old(X0) [subsumption resolution 84,85]
146. wise(X0) [subsumption resolution 82,83]
215. strong(X0) [subsumption resolution 104,146]
233. $false <- (~2) [subsumption resolution 118,215]
234. 2 [avatar contradiction clause 233]
235. ~patient(X0) <- (1) [subsumption resolution 114,145]
238. $false <- (1) [resolution 235,111]
239. ~1 [avatar contradiction clause 238]
240. $false [avatar sat refutation 119,234,239]
% SZS output end Proof for 4096690798302469745755154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not wise or calm and vice versa.
If someone is funny or not tall then susan is not wise.
Everyone who is not patient or calm is either wise or humble and vice versa.
If lucy is not wise then susan is brave or creative.
Everyone who is both not wise and not brave is quiet or not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind.
Paul is either wise or funny.
Lucy is both not creative and not generous.
Alice is not funny.
Someone is not humble. | Paul is not rich. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((funny(X)|~tall(X))))=>(~wise(susan)))&
(![X]:((~patient(X)|calm(X))<=>(wise(X)<~>humble(X))))&
((~wise(lucy))=>((brave(susan)|creative(susan))))&
(![X]:((~wise(X)&~brave(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | ~rich(paul) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 468674724807238528566453
% SZS output start Proof for 468674724807238528566453
5. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> (~rich(X0) | quiet(X0))) [input p4]
9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8]
25. ~rich(paul) [input hypothesis]
44. ! [X0] : (((~brave(X0) & ~wise(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (brave(X0) | wise(X0)))) [nnf transformation 5]
45. ! [X0] : (((~brave(X0) & ~wise(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | brave(X0) | wise(X0))) [flattening 44]
60. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9]
97. ~brave(X0) | rich(X0) [cnf transformation 45]
106. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 60]
109. patient(X0) | brave(X0) | patient(X0) [cnf transformation 60]
138. ~rich(paul) [cnf transformation 25]
141. ~patient(X0) | brave(X0) [duplicate literal removal 106]
142. patient(X0) | brave(X0) [duplicate literal removal 109]
210. 17 <=> ! [X1] : rich(X1) [avatar definition]
211. rich(X1) <- (17) [avatar component clause 210]
225. brave(X0) [subsumption resolution 141,142]
300. rich(X0) [resolution 97,225]
301. 17 [avatar split clause 300,210]
302. $false <- (17) [resolution 211,138]
307. ~17 [avatar contradiction clause 302]
308. $false [avatar sat refutation 301,307]
% SZS output end Proof for 468674724807238528566453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is quiet or not strong and vice versa.
If mary is both not rich and not funny then mary is either calm or strong.
Everyone who is either not humble or brave is brave.
If someone is wise or not happy then someone is tall and vice versa.
Everyone who is not funny or not quiet is quiet and vice versa.
Everyone who is both curious and creative is not happy or not tall and vice versa.
Everyone who is both old and not old is either not strong or not funny and vice versa.
Everyone who is not generous is happy or not happy.
Everyone who is both not creative and not generous is not creative and vice versa.
Everyone who is either wise or rich is either quiet or kind and vice versa.
If alice is either kind or not rich then fred is not generous or calm.
Everyone who is either not kind or not quiet is both quiet and not creative and vice versa.
Everyone who is both not strong and not rich is either creative or not brave.
Everyone who is happy or patient is either not strong or old.
If someone is not creative then someone is both generous and tall and vice versa.
Everyone who is patient or not generous is either funny or humble and vice versa.
Someone is generous.
Someone is not generous.
Someone is either not funny or not wise.
Someone is either happy or calm.
Someone is quiet or not creative.
Someone is both calm and not brave. | Alice is not rich. | neutral | (![X]:(old(X)<=>(quiet(X)|~strong(X))))&
(((~rich(mary)&~funny(mary)))=>((calm(mary)<~>strong(mary))))&
(![X]:((~humble(X)<~>brave(X))=>brave(X)))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)|~quiet(X))<=>quiet(X)))&
(![X]:((curious(X)&creative(X))<=>(~happy(X)|~tall(X))))&
(![X]:((old(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(![X]:(~generous(X)=>(happy(X)|~happy(X))))&
(![X]:((~creative(X)&~generous(X))<=>~creative(X)))&
(![X]:((wise(X)<~>rich(X))<=>(quiet(X)<~>kind(X))))&
(((kind(alice)<~>~rich(alice)))=>((~generous(fred)|calm(fred))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(quiet(X)&~creative(X))))&
(![X]:((~strong(X)&~rich(X))=>(creative(X)<~>~brave(X))))&
(![X]:((happy(X)|patient(X))=>(~strong(X)<~>old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((patient(X)|~generous(X))<=>(funny(X)<~>humble(X))))&
(?[X]:(generous(X)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((calm(X)&~brave(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is funny or calm is either happy or old.
If susan is either not brave or not calm then someone is quiet.
Everyone who is not tall is generous or not kind.
Everyone who is either wise or tall is either calm or kind and vice versa.
If someone is both not quiet and funny then someone is kind or humble and vice versa.
Everyone who is both patient and not old is either not humble or not generous and vice versa.
If susan is either not kind or generous then john is not funny or not wise and vice versa.
If mary is both not rich and calm then someone is not funny and vice versa.
Everyone who is calm or creative is not humble or kind and vice versa.
If someone is not funny then alice is both not quiet and quiet and vice versa.
Everyone who is not wise is not strong or wise and vice versa.
Everyone who is both old and not strong is happy.
If paul is not curious or old then someone is wise and vice versa.
Everyone who is both generous and not happy is either not calm or patient.
Everyone who is not humble is not happy and vice versa.
Everyone who is brave is not patient or not calm and vice versa.
John is not kind or kind.
Someone is both not patient and calm.
Someone is old or creative.
Someone is either not old or tall.
Lucy is both not old and not strong.
Someone is both quiet and funny.
Someone is not rich.
Someone is brave or not strong. | Lucy is strong. | contradiction | (![X]:((funny(X)|calm(X))=>(happy(X)<~>old(X))))&
(((~brave(susan)<~>~calm(susan)))=>(?[X]:(quiet(X))))&
(![X]:(~tall(X)=>(generous(X)|~kind(X))))&
(![X]:((wise(X)<~>tall(X))<=>(calm(X)<~>kind(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:((patient(X)&~old(X))<=>(~humble(X)<~>~generous(X))))&
(((~kind(susan)<~>generous(susan)))<=>((~funny(john)|~wise(john))))&
(((~rich(mary)&calm(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)|creative(X))<=>(~humble(X)|kind(X))))&
((?[X]:(~funny(X)))<=>((~quiet(alice)&quiet(alice))))&
(![X]:(~wise(X)<=>(~strong(X)|wise(X))))&
(![X]:((old(X)&~strong(X))=>happy(X)))&
(((~curious(paul)|old(paul)))<=>(?[X]:(wise(X))))&
(![X]:((generous(X)&~happy(X))=>(~calm(X)<~>patient(X))))&
(![X]:(~humble(X)<=>~happy(X)))&
(![X]:(brave(X)<=>(~patient(X)|~calm(X))))&
((~kind(john)|kind(john)))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:((old(X)|creative(X))))&
(?[X]:((~old(X)<~>tall(X))))&
((~old(lucy)&~strong(lucy)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(~rich(X)))&
(?[X]:((brave(X)|~strong(X)))) | strong(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6892649788404995387838399
% SZS output start Proof for 6892649788404995387838399
11. ! [X0] : (~wise(X0) <=> (wise(X0) | ~strong(X0))) [input p10]
25. strong(lucy) [input hypothesis]
61. ! [X0] : ((~wise(X0) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | wise(X0))) [nnf transformation 11]
62. ! [X0] : ((~wise(X0) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | wise(X0))) [flattening 61]
127. wise(X0) | ~strong(X0) | wise(X0) [cnf transformation 62]
129. ~wise(X0) | ~wise(X0) [cnf transformation 62]
153. strong(lucy) [cnf transformation 25]
154. wise(X0) | ~strong(X0) [duplicate literal removal 127]
155. ~wise(X0) [duplicate literal removal 129]
246. ~strong(X0) [subsumption resolution 154,155]
269. $false [subsumption resolution 153,246]
% SZS output end Proof for 6892649788404995387838399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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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